BCA - RC Spreadsheet User Guide Version 3

CCIP-008

A cement and concrete industry publication

CI/Sfb

UDC 624.04

User Guide to RC Spreadsheets: v3


This user guide provides guidance on the use of RC Spreadsheets v3 for the design of reinforced concrete elements.

For more information on the spreadsheets visit www.concretecentre.com/rcspreadsheets

User guide to Excel spreadsheets for design to BS 8110: Part 1, 1997 (Amd. 3) and BS EN 1992: 2004 Part 1-1 and its UK National Annex

C H Goodchild BSc CEng MCIOB MIStructE R M Webster CEng FIStructE

Charles Goodchild is Principal Structural Engineer for The Concrete Centre where he promotes efficient concrete design and construction. He was responsible for the concept, content and management of this publication and of the RC Spreadsheets. Rod Webster of Concrete Innovation & Design is principal author of the spreadsheets. He has been writing spreadsheets since 1984 and is expert in the design of tall concrete buildings and in advanced analytical methods.


The release of Version 3 of the spreadsheets and user guide follows the publication of BS EN 1992-1-1 (Eurocode 2) and its UK National Annex and the publication of Amendment 3 to BS 8110 Part 1: 1987.


CCIP-008 Published July 2006 ISBN 1-904818-38-2 Price Group O © The Concrete Centre Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey, GU17 9AB Tel: +44 (0)1276 606800 Fax: +44 (0)1276 606801 www.concretecentre.com

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Foreword This publication was originally produced by the Reinforced Concrete Council (RCC) as part of its project ‘Spreadsheets for concrete design to BS 8110 and EC2’. Since their release in 2000 the spreadsheets have proved enormously popular and have been maintained by the RCC and its successor The Concrete Centre. The release of Version 3 of the spreadsheets follows the publication of BS EN 1992-1-1 (Eurocode 2) plus its UK National Annex and the publication of Amendment 3 to BS 8110 Part 1: 1987. The requirements within these standards have necessitated the revision of all the published spreadsheets. This user guide gives guidance on the use of all design spreadsheets to BS 8110 and Eurocode 2 contained on the CD ROM RC Spreadsheets: v3, published by The Concrete Centre (order ref. CCIP-008CD).

Acknowledgements The ideas and illustrations come from many sources. The help and guidance received from many individuals are gratefully acknowledged. Thanks are due to members of the original project’s Advisory Group for their time and effort in helping to make the project feasible and in bringing it to fruition. The members of the Advisory Group are listed on the inside back cover. Special appreciation is extended to: Richard Cheng, BSc, CEng, Eur Ing, FIStructE, author of the retaining wall and basement wall spreadsheets, Peter Noble for conversions and checking, and to Andy Pullen for initial studies into compatibility of spreadsheet software. Also the late Sami Khan for help with post-tensioning spreadsheets.

The Advisory Group Members S Alexander S Alhayderi Dr H Al-Quarra I Baldwin C Barker M Beamish A Beasley T Bedford G Belton R Bhatt R Bickerton P Blackmore D Blackwood M Brady C Buczkowski A Campbell Dr P Chana G Charlesworth L Cheng Mr Chichger R Collison A Craddock M Morton J Curry J Dale

H Dikme C P Edmondson J Elliott I Feltham G Fernando M Fernando I Francis A Fung P Gardner J Gay P Green A Hall N Harris G Hill D W Hobbs R Hulse M Hutcheson A Idrus N Imms P Jennings D Kennedy G Kennedy R Jothiraj Dr S Khan A King

G King S King K Kus I Lockhart M Lord B Lorimer M Lovell Dr Luker J Lupton M Lytrides Prof I Macleod F Malekpour A McAtear A McFarlane F Mohammad A Mole M Morton R Moss B Munton C O’Boyle Dr A Okorie T O’Neill B Osafa-Kwaako D Patel D Penman

M Perera B Quick Y Rafiq A Rathbone M Rawlinson P Reynolds H Riley N Russell U P Sarki T Schollar A Stalker A Starr M Stevenson B Stoker B Treadwell A Truby R Turner T Viney Dr P Walker B Watson J Whitworth C Wilby S Wilde A Wong E Yarimer

Published by The Concrete Centre Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey GU17 9AB Tel: +44 (0)1276 606800 Fax: +44 (0)1276 606801 CCIP-008 Published July 2006 ISBN 1-904818-38-2 Price Group O © The Concrete Centre User Guide v1 published by the British Cement Association on behalf of the Reinforced Concrete Council. User Guide v2 published electronically by The Concrete Centre. CCIP publications are produced by The Concrete Society on behalf of the Cement and Concrete Industry Publications Forum – an industry initiative to publish technical guidance in support of concrete design and construction. CCIP publications are available from the Concrete Bookshop at www.concretebookshop.com Tel: +44 (0)7004 607777 All advice or information from The Concrete Centre is intended for those who will evaluate the significance and limitations of its contents and take responsibility for its use and application. No liability (including that for negligence) for any loss resulting from such advice or information is accepted by the Concrete Centre or their subcontractors, suppliers or advisors. Readers should note that The Concrete Centre publications are subject to revision from time to time and should therefore ensure that they are in possession of the latest version. Cover artwork: D J Killoran - The Concrete Society. Printed by Cromwell Press, Trowbridge, UK.

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User Guide to RC Spreadsheets: v3 Contents INTRODUCTION

1

GENERAL NOTES

3

SPREADSHEETS TO BS 8110

17

Elements

19

Analysis

35

Slabs

38

Beams

72

Columns

113

Walls

125

Stairs

139

Foundations

146

Tabular versions

158

SPREADSHEETS TO EUROCODE 2

179

Elements

185

Analysis

205

Slabs

208

Beams

243

Columns

270

Stairs

284

Foundations

287

ADMIN FOLDER

298

REFERENCES AND FURTHER READING

299

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User Guide to RC Spreadsheets: v3 Contents in full INTRODUCTION

1

GENERAL NOTES

3

Using the spreadsheets

10

Menu.xls

16

SPREADSHEETS TO BS 8110

17

Elements

19

RCC11 Element Design.xls RCC12 Bending and Axial Force.xls

26

RCC13 Punching Shear.xls

28

RCC14 Crack Width.xls

33

Analysis

RCC21 Subframe Analysis.xls

35

Slabs

RCC31 One-way Solid Slabs (A & D).xls

38

RCC31R Rigorous One-way Slabs.xls

43

RCC32 Ribbed Slabs (A & D).xls

50

RCC32R Rigorous Ribbed Slabs.xls

56

RCC33 Flat Slabs (A & D).xls

64

RCC41 Continuous Beams (A & D).xls

72

Beams

Columns

Walls

RCC41R Rigorous Continuous Beams (A & D).xls

78

RCC42 Post-tensioned Slabs & Beams (A & D).xls

85

RCC43 Wide Beams (A & D).xls

107

RCC51 Column Load Take-down & Design.xls

113

RCC52 Column Chart generation.xls

118

RCC53 Column Design.xls

120

RCC54 Circular column charting .xls

123

RCC61 Basement Wall.xls

125

RCC62 Retaining Wall.xls

132

Stairs

RCC71 Stair Flight & Landing - Single.xls

139

RCC72 Stairs & Landings - Multiple.xls

142

Foundations

RCC81 Foundation Pads.xls

146

RCC82 Pilecap Design.xls

149

Tabular versions

RCC91 One-way Solid Slabs (Tables).xls

158

RCC92 Ribbed Slabs (Tables).xls

161

RCC93 Flat Slabs (Tables).xls

166

RCC94 Two-way Slabs (Tables).xls

173

RCC95 Continuous Beams (Tables).xls

175

ii

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SPREADSHEETS TO EUROCODE 2

179

General notes to Eurocode 2 versions

181

Elements

TCC11 Element Design.xls

185

TCC12 Bending and Axial Force.xls

194

TCC13 Slab Punching.xls

196

TCC14 Crack Width.xls

201

Analysis

TCC21 Subframe Analysis.xls

205

Slabs

TCC31 One-way Slabs.xls

208

TCC31R Rigorous One-way Slabs.xls

214

TCC32 Ribbed Slabs (A&D).xls

221

TCC33 Flat Slabs (A&D).xls

228

TCC33X Flat Slabs (A&D).xls

237

Beams

Columns

Stairs Foundations

TCC41 Continuous Beams.xls

243

TCC41R Rigorous Continuous Beams.xls

249

TCC42 Post-tensioned Analysis & Design.xls (Beta)

256

TCC43 Wide Beams (A & D).xls

264

TCC51 Column Load Take-down Design.xls

270

TCC52 Column Chart generation.xls

276

TCC53 Column Design.xls

278

TCC54 Circular Column Design.xls

280

TCC55 Axial Column Shortening.xls

282

TCC71 Stair Flight & Landing - Single.xls

284

TCC81 Foundation Pads.xls

287

TCC82 Pilecap Design.xls

291

ADMIN FOLDER

298

REFERENCES AND FURTHER READING

299

iii

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Introduction

Introduction The RC spreadsheets were originally produced under the Reinforced Concrete Council’s project, ‘Spreadsheets for concrete design to BS 8110 and EC2’. They were released in January 2000 and have been maintained and extended by the RCC and its successor The Concrete Centre. They continue to be supported by The Concrete Centre.

Eurocode 2 parts 1-1 and 1-2 together with their UK National Annexes have now been published. Students and both inexperienced and experienced engineers will all need to grasp an understanding of design to this code. There are differences between EC2 and BS 8110. The spreadsheets should help with the transition.

In recognition of the new and updated spreadsheets made available as part of the version 2.x issue, it was decided to revise (but not publish) the second edition of the User Guide.

Whilst the spreadsheets to BS 8110 provide a consensus of current commercial reinforced concrete design practice, the spreadsheets to Eurocode 2, provide a consensus of design proceedures to this new design code. The introduction of Eurocode 2 will provide commercial opportunities for those who are prepared to use it.

The introduction of Eurocode 2[3], its National Annex and Amd of BS 8110:1997[2] has necessitated the revision of all the spreadsheets and publication of version 3 of the User Guide. This third edition of the User Guide provides guidance on the use of all spreadsheets produced to date (July 2006). For the experienced engineer, the spreadsheets allow the rapid production of clear and accurate design calculations. The spreadsheets allow younger users to understand concrete design and help them to gain experience by studying their own ‘what if’ scenarios. The individual user should be able to answer his/ her own questions by chasing through the cells to understand the logic used. Cells within each spreadsheet can be interrogated and can have their formulae checked and values traced. The original spreadsheets reflected a consensus of opinion on several design issues. The version 3 Eurocode 2 spreadsheets reflect a consensus of opinion of a limited number of engineers. Students and young engineers may follow the ‘model’ calculations presented in the spreadsheets to form an understanding of current reinforced concrete design. The spreadsheets are intended to follow normal design practice and cater for the design of low- to medium-rise multi-storey concrete framed buildings. They are offered as shareware. However, users are required to register when using them in any commercial capacity. Registration is through The Concrete Bookshop (07004 607777 and www.concretebookshop.com). The original project was jointly funded by the RCC and the Department of the Environment Transport and the Regions (DETR) under its Partners in Technology scheme. It was made possible by the support and contributions of time given by individual members of industry. The project was managed by the RCC and guided by an 80-strong Advisory Group of interested parties, including consulting engineers and software houses. In producing the original spreadsheets several issues had to be addressed. Firstly, which spreadsheet package should be used? Excel (© Microsoft Corporation) appeared to hold about 70% of the market amongst structural engineers and was thus adopted. More specifically, Excel ’97© was originally adopted as being de facto the most widely available spreadsheet in the field. To avoid complications, it was decided not to produce corresponding versions using other spreadsheet packages. The spreadsheets are compatible with later versions of Excel.

It is believed that both novices and experienced users of spreadsheets will be convinced that spreadsheets have a great potential for teaching BS 8110 and Eurocode 2, improving concrete design and, above all, improving the concrete design and construction process. The spreadsheets to Eurocode 2 should help all engineers to familiarise themselves with the details of this new design code.

Version 2.x The version 2.x released in 2003[3] introduced new spreadsheets to BS 8110, to the more finalised EN 1992-1-1 (Eurocode 2) and an overarching menu spreadsheet. Previously issued spreadsheets to BS 8110 were updated. The new spreadsheets introduced were: ■ Menu

BS 8110 ■ RCC31R Rigorous One-way Slabs ■ RCC32R Rigorous Ribbed Slabs ■ RCC41R Rigorous Continuous Beams ■ RCC43 Wide Beams (A&D) ■ RCC54 Circular Column Design ■ RCC82 Pilecap Design

Eurocode 2 ■ RCCen11 Element Design ■ RCCen12 Bending and Axial Force ■ RCCen13 Punching Shear ■ RCCen14 Crack Width ■ RCCen21 Subframe analysis ■ RCCen31 One-way Solid Slabs (A & D) ■ RCCen31R Rigorous* One-way Solid Slabs ■ RCCen32 Ribbed Slabs (A & D)

1

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■ RCCen33 Flat Slabs (A & D) ■ RCCen41 Continuous beams (A & D) ■ RCCen41R Rigorous* Continuous Beams ■ RCCen43 Wide Beams (A&D) ■ RCCen52 Column Chart generation ■ RCCen53 Column Design ■ RCCen55 Axial Column Shortening ■ RCCen81 Foundation Pads ■ RCCen82 Pilecap Design

Using and improving the spreadsheets Since their release in 2000 the spreadsheets have proved to be enormously popular. They may now be regarded as having now been thoroughly tested by engineers in practice but this does not mean that they are infallible! The user is referred to Managing the spreadsheets and other General Notes that follow. The older spreadsheets’ usefulness and robustness have been enhanced by users reporting problems or suggesting improvements. Comments or suggestions for improvement are welcomed. Contact The Concrete Centre’s Helpdesk at [email protected] or on 0700 4 500 500.

Version 3 The release of version 3 of the spreadsheets follows the publication of BS EN 1992-1-1 (Eurocode 2)[3] and the UK National Annex and the publication of Amendment 3 to BS 8110 Part 1: 1987[2]. The requirements within these documents necessitated the revision of all previously published spreadsheets. The opportunity has been taken to introduce new spreadsheets as follows:

BS 8110 ■ RCC82 Pilecap Design

Eurocode 2 ■ TCC33X Flat Slabs (Whole floor) ■ TCC41R Rigorous Continuous Beams ■ TCC42 Post-tensioned Slabs and Beams (A&D) (β version) ■ TCC43 Wide Beams (A&D) ■ TCC54 Circular Column Charting ■ TCC71 Stair Flight and Landing - single ■ TCC81 Foundation Pads ■ TCC82 Pilecap Design

Spreadsheets numbered RCCen11, RCCen12 etc released as Beta versions have been released for use as TCC11, TCC12 etc.

2


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General notes

General notes Managing the spreadsheets Use Spreadsheets can be a very powerful tool. Their use has become increasingly common in the preparation of design calculations. They save time, money and effort. They provide the facility to optimise designs and they can help instill experience. However, these benefits have to be weighed against the risks associated with any endeavour. These risks must be recognised and managed. In other words appropriate levels of supervision and checking, including self-checking, must, as always, be exercised when using these spreadsheets.

Advantages

■ The limitations of the program may not be sufficiently

apparent to the user. ■ For unusual structures, even experienced engineers may not

have the ability to spot weaknesses in programs for analysis and detailing The committee’s report continued: “Spreadsheets are, in principle, no different from other software…” With regard to these spreadsheets and this publication, The Concrete Centre hopes to have addressed more specific concerns by demonstrating “clear evidence of adequate verification” by documenting the principles, theory and algorithms used in the spreadsheets. The spreadsheets have also had the benefit of the Advisory Group’s overview and inputs. Many, especially the spreadsheets to BS 8110, have had several years use and maintenance. Inevitably, some unconscious assumptions, inconsistencies, etc.[9] will remain.

For the experienced engineer, the spreadsheets help in the rapid production of clear and accurate design calculations for reinforced concrete elements. The contents are intended to be sufficient to allow the design of low to medium-rise multi-storey concrete framed buildings.

Liability

Spreadsheets allow users to gain experience by studying their own ‘what if’ scenarios. Should they have queries, individual users should be able to answer their own questions by chasing through the cells to understand the logic used. Cells within each spreadsheet can be interrogated, formulae checked and values traced. Macleod[7] suggested that, in understanding structural behaviour, doing calculations is probably not a great advantage; being close to the results probably is.

As with all software, users must be satisfied with the answers these spreadsheets give and be confident in their use. These spreadsheets can never be fully validated but have been through Beta testing, both formally and informally. The BS 8110 versions have been used for several years and as a result of feedback they have been updated to address known errors. However, users must satisfy themselves that the uses to which the spreadsheets are put are appropriate.

Other benefits include quicker and more accurate reinforcement estimates, and the possibilities for electronic data interchange (EDI) Already, bending schedules derived from spreadsheets are the basis of some EDI and the control of bar-bending machines. Standardised, or at least rationalised, designs make the checking process easier and quicker.

This is especially true with the spreadsheets to Eurocode 2. While the Eurocode 2 versions have been through Beta testing, they have not yet been used in anger. Also, Eurocode 2 is a completely new code to most designers and so there is little experience of design to this standard.

Appropriate use In its deliberations{8} the Standing Committee on Structural Safety (SCOSS) noted the increasingly wide-spread availability of computer programs and circumstances in which their misuse could lead to unsafe structures. These circumstances include: ■ People without adequate structural engineering knowledge or

training may carry out the structural analysis. ■ There may be communication gaps between the design

initiator, the computer program developer and the user. ■ A program may be used out of context. ■ The checking process may not be sufficiently fundamental.

A fundamental condition of use Is that the user accepts responsibility for the input and output of the computer and how it is used.

Control Users and managers should be aware that spreadsheets can be changed and must address change control and versions for use. The flexibility and ease of use of spreadsheets, which account for their widespread popularity, also facilitate ad hoc and unstructured approaches to their subsequent development. Quality Assurance procedures may dictate that spreadsheets are treated as controlled documents and subject to comparison and checks with previous methods prior to adoption. Users’ Quality Assurance schemes should address the issue of changes. The possibilities of introducing a company’s own password to the spreadsheets and/ or extending the revision history contained within the sheet entitled Notes! might be considered.

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Application The spreadsheets have been developed with the goal of producing calculations to show compliance with codes. Whilst this is the primary goal, there is a school of thought[10] that designers are primarily paid for producing specifications and drawings that work on site and are approved by clients and/ or checking authorities. Producing calculations happens to be a secondary exercise, regarded by many experienced engineers as a hurdle on the way to getting the project approved and completed. From a business process point of view, the emphasis of the spreadsheets might, in future, change to establishing compliance once members, loads and details are known. Certainly this may be the preferred method of use by experienced engineers. The spreadsheets have been developed with the ability for users to input and use their own preferred material properties, bar sizes and spacings, etc. However, user preferences should recognise moves for efficiency through standardisation. Another long-term objective is automation. To this end, spreadsheet contents might in future be arranged so that input and output can be copied and pasted easily by macros and/ or linked by the end-user. There are counter arguments about users needing to be closer to the calculations and results in order to ensure they are properly considered – see Appropriate use above. We emphasise that it is up to the user how he/ she uses the output. The spreadsheets have been produced to cater for both first-time users and the very experienced without putting the first-time user off. Nonetheless, their potential applications are innumerable.

Summary With spreadsheets, long-term advantages and savings come from repeated use but there are risks that need to be managed. Spreadsheets demand an initial investment in time and effort, but the rewards are there for those who make the investment. Good design requires sound judgement based on competence derived from adequate training and experience, not just computer programs.

Familiarisation There are many different ways to present structural concrete calculations. ‘Calcs’ should demonstrate compliance with relevant design codes of practice, but different designers want to investigate different criteria and want to set out calculations in different ways. Spreadsheets cannot satisfy everyone. The spreadsheets presented here have been set out to cover the criteria that may be deemed ‘usual’. It is incumbent on the user to judge whether these criteria are pertinent and sufficient for the actual case in hand. It is also incumbent on the user to ensure that inputs are correct and that outputs are of the correct order of magnitude.

The spreadsheets are intended to follow normal design practice and cater for the design of low- to medium-rise multi-storey concrete framed buildings. Each type of element may be designed in several different ways, e.g. horizontal frame elements may be designed using: ■ Element design: design of simple elements to BS 8110: Part

1[2] or BS EN 1992[3] ■ Tabular design: design of elements based on moments and

shears derived from BS 8110: Part 1 Tables 3.12 and 3.5 ■ Analysis and design: design of elements based on moments

and shears from analysis, e.g. sub-frame analysis, embodied within the spreadsheets

Element design The element design spreadsheets illustrate the basic principles of reinforced concrete design from input material properties, dimensions, moments, shears and axial loads, etc. They form the basis of element design used in succeeding spreadsheets. The moments, shears and axial loads used should be derived from separate analysis (e.g. hand calculations, sub-frame analysis spreadsheet or other analysis package). For further explanation the user is referred to BS 8110, BS EN 1992-1-1 or a number of standard reference works[11, 12 , 13] .

Tabular design The tabular design spreadsheets use Tables 3.12 and 3.5 from BS 8110: Part 1 to automate the derivation of design moments and shears. However, the use of these tables is restricted for slabs. BS 8110: Part 1, Clause 3.5.2.4, restricts the use of Table 3.12 to where: ■ In a one-way slab, the area of a bay (one span x full width)

exceeds 30m2 ■ The ratio of characteristic imposed loads, Qk , to

characteristic dead loads, Gk does not exceed 1.25 ■ The characteristic imposed load, Qk, does not exceed 5

kN/m2 , excluding partitions

■ Additionally, for flat slabs, there are at least three rows of

panels of approximately equal span in the direction being considered. For beams, Clause 3.4.3, Table 3.5 is valid only where: ■ Characteristic imposed loads, Qk, do not exceed characteristic

dead loads, Gk ■ Loads are substantially uniformly distributed over three or

more spans ■ Variations in span length do not exceed 15% of the longest

span If design parameters stray outside these limits, the tabular design spreadsheets should be used with caution.

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General Notes Analysis and design

Column design

To provide for more general application, these versions combine sub-frame analysis with design. Spreadsheets for one-way slabs, ribbed slabs, flat slabs and beams provide powerful design tools. Sub-frame analysis is also used in the post-tensioned concrete design spreadsheets.

Column design is presented in, essentially, two different ways; either an amount of reinforcement is determined or the capacity of a section is checked – two valid design approaches.

The sub-frame analysis spreadsheet RCC21.xls may of course be used alone (and the elements designed by other means such as RCC11.xls). The flat slab spreadsheet RCC33 is intended to be used onedirection at a time. TCC33x designs flat slabs to BS EN1992-1-1 in two directions at one time. The post-tensioned concrete design spreadsheet follows the 1994 ‘BS’ version of Concrete Society TR43[14] and involves sub-frame analysis at various limit states. The principles used are applicable to both beams and slabs with either bonded or unbonded tendons being designed to BS 8110. A Beta version of the post-tensioned concrete design spreadsheet to Eurocode 2 and the 2005 version of Concrete Society TR43 is included. The examples of the retaining wall and basement wall spreadsheets are based on common UK practice.

Under RCC11 Element Design.xls (or RCC11.xls for short) or TCC11, the amount of reinforcement is calculated by iterating to find the neutral axis depth in order to solve two simultaneous equations. Under RCC52.xls for single axis bending and RCC53.xls for two axis bending, N-M interaction charts are derived from presumed reinforcement arrangements. Individual load cases are checked against the capacity of the column with the various reinforcement arrangements. TCC52 and TCC53 similarly. RCC51.xls is set out so that the user may undertake a traditional column load take down, assess design moments and critical axis before calculating the amount of reinforcement required. TCC51.xls similarly. RCC12.xls determines the capacity of an unsymmetrical reinforced column (or beam). TCC12.xls similarly.

Deflections In most spreadsheets deflection checks are based on span:depth criteria in the codes. Estimates of actual deflections are available within the ‘rigorous’ spreadsheets.

Rigorous spreadsheets Deflection can be the governing criterion of many designs. These spreadsheets allow the estimation of deflection to BS 8110 Parts 1 and 2 or Eurocode 2 Part 1-1. Rather than just check span-toeffective depth ratios, the spreadsheets calculate deflections at 1 /20 the spans using vigorous methods. The Eurocode 2 spreadsheets follows methods described in TR58[30].

Others Other spreadsheets provide for the design of pad foundations catering for one or two columns, punching shear, stairs (either as single flights and single landings or flights and landings as in a stair core), small retaining walls and basement walls. More detail and further references are given within the spreadsheets themselves.

Terminology As with all software, spreadsheets have their own jargon. The basic terminology for layout is shown on the screen dump below:

Spreadsheet terminology Excel file name

Cell reference Cell

Drop down menu bar

Toolbars (use View/Toolbars to switch on and off) Formula bar Scroll bar

Worksheet area

Sheet tabs

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Sheet Architecture

The Concrete Centre

Project

Spreadsheets to BS 8110

Client

Advisory Group

Location

Level 2, Beam on line 6, from B to E

Made by

SUBFRAME ANALYSIS to BS8110:2005

Each spreadsheet may contain several linked sheets (i.e. layers or pages) that deal with different aspects of design. The sheet’s name on the sheet tab gives an indication of the content. For the more involved spreadsheets, individual sheets are devoted to a full explanation of the design (with references for educational and validation purposes) or analysis, etc. and other sheets give an abridged version more in keeping with the requirements of experienced practicing engineers. Further sheets may contain analysis calculations, data for graphs and calculation of reinforcement weight. All spreadsheets have a Notes! sheet where disclaimers, status and revision histories relating to each spreadsheet are incorporated (sheet names are differentiated by the use of an appended exclamation mark). Those sheets with names in capitals are intended for printing out as design calculations. Other sheets are available to view in the spreadsheets. These may need to be printed for checking purposes and parts of them, such as simple design routines, may be pasted into word-processed calculations.

Originated from RCC21.xls v3.0 on CD

Date

RMW Checked

Page

36

11-Apr-06 Revision

chg

© 2006 TCC

Job No

-

R68

BENDING MOMENT DIAGRAMS (kNm) 1000

1000 800

800

600

600 400

400

200

200

0

0

-200

-200

-400

-400

-600

-600

-800

-800

-1000 0

10

B

20

30

SUPPORT No

0

40

E

Elastic Moments

10

B

20

1

2

3

4

5

Elastic M Redistributed M ßb

95.3 90.5 0.950

743.3 557.5 0.750

868.6 694.9 0.800

427.6 406.2 0.950

34.3 32.6 0.950

Redistribution

5.0%

25.0%

20.0%

5.0%

5.0%

SPAN No

Elastic M Redistributed M ßb SHEAR FORCE DIAGRAMS (kN)

30

40

E

Redistributed Envelope

1

2

3

4

185.0 152.1 0.822

633.1 746.8 1.180

400.1 373.5 0.934

121.4 118.8 0.979

~ ~ ~

~ ~ ~

kNm kNm ~

~ ~ ~

Based on support moments of min(ßbM, Malt/ßb)

500

500 400 300 200 100 0 -100 -200 -300 -400 -500

400 300 200 100 0 -100 -200 -300 -400 -500

0

10

20

30

Elastic Shears

B

SPAN No

Elastic V Redistributed V

40

0

E 1

191.0 177.7

10

20

2

312.6 302.0

435.6 422.8

30

40

Redistributed Shears

B

E

3

432.2 433.2

356.9 345.1

282.0 273.7

ACTIONS! sheet Main graphical output of Bending Moment Diagrams, Shear Force Diagrams. Also input for redistribution percentages.

Sheet tabs (from RCC 41.xls) Sheet tabs

Typical spreadsheet screens

Project


Client

Advisory Group

Location

D&D: Main Beam, from grid C to H

The spreadsheets are intended to be as consistent as possible. Generally, upper sheets consist of calculations, notes and workings as illustrated in the examples below, which gives an indication of the contents of a typical spreadsheet. The first sheet consists of input, followed by results of analysis, design, weight of reinforcement, analysis, detailed design with references, graph data and finally a revision history.

Advisory Group Level 2, Beam on line 6

Made by

from B to E

RMW

SUBFRAME ANALYSIS to BS8110:2005 Originated from RCC21.xls

LOCATION

Revision

chg

© 2006 TCC

59 Job No

-

SPAN 3

LEFT CENTRE M kNm 208.9 192.7 ßb 1.00 0.99 d mm 327.5 322.5 1860 1447 As mm² 286 0 As' mm² TOP STEEL Layer 1 4 H 25 2 H 16 0 0 Layer 2 As prov mm² 1963 As' prov 402 BTM STEEL Layer 1 3 H 16 3 H 25 0 0 Layer 2 As' prov mm² 603 As prov 1473 DEFLECTION Permanent = 13.00 < 24.00 Imposed = 5.77 < 12.00 mm Affecting partitions = 15.56 < 17.14 ok SHEAR V kN 222.2 Link Ø 2.262 10 v N/mm² 0.743 Nominal vc N/mm² LINKS H10 @ 125 for 1875 H10 @ 225 No 2 2 legs

Page

Apr-2006

Checked

ACTIONS

DESIGN

4

R68

RIGHT 206.6 0.86 327.5 1799 357 H

25

1963 H

16

0

As prov 3 0

As' prov 603 Precamber (mm) = 0 Increase btm As by 0% V 215.8 v 2.197 vc 0.743 H10 @ 150 for 1800 2

The Concrete Centre


Client Location

Date

rmw

RIGOROUS CONTINUOUS BEAMS to BS 8110:2005 Originated from RCC41R.xls v3.0 on CD

Project

The Concrete Centre Made by

v3.0 on CD

Supports from grid

Checked

to grid

% As Cover min S Links Main bars max V Crack width

35 Job No

-

ok ok ok ok ok ok ok

CHECKS

Page

11-Apr-2006 Revision

chg

© 2006 TCC

B

Date

R68

E

ok ok ok ok ok ok

0.233


0.300

0.266

SPANS SPAN 1 SPAN 2 SPAN 3 SPAN 4 SPAN 5 SPAN 6

L (m)

H (mm)

bw (mm)

hf (mm)

Type

7.000 12.000 12.000 6.000

600 600 600 600

375 375 375 375

150 150 150 150

T T T T

LOADING PATTERN

bf (mm)

1355 2055 2055 1215 0 0

DEAD IMPOSED

min

max

1 0

1.4 1.6

SUPPORTS ABOVE (m)

Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Support 7 LOADING Span 1 UDL PL 1 PL 2 Part UDL Span 2 UDL PL 1 PL 2 Part UDL Span 3 UDL

H (mm)

B (mm)

End Cond

H (mm)

B (mm)

End Cond

2.95 3.00 0.00 K 4.00

400 400

300 300

F P

BELOW (m)

3.10 3.10 3.10

400 300 400

300 300 300

P P P

400

300

P

3.10

300

300

P

UDLs (kN/m)

PLs (kN)

Dead Load

Imposed Load

Position from left

Loaded Length

17.50 24 5

5.60 6 18

~~~~~ 2.000 4.500

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~

Imposed Load

Position from left

Loaded Length

12.50

~~~~~

~~~~~ ~~~~~ ~~~~~

32.20

12.50

~~~~~

25

25

5.000

~~~~~ ~~~~~ ~~~~~

24.42

8.65

~~~~~

~~~~~

Span 4 UDL PL 1 PL 2 Part UDL Span 5 UDL PL 1 PL 2 Part UDL Span 6 UDL

ACTIONS

M ßb d As As' TOP STEEL Layer 1 L 2 DESIGN

kNm mm mm² mm²

4 0

LEFT 209.9 0.85 327.5 1819 403 H

25

3

0

0

CENTRE 169.7 0.98 325.0 1264 0 H

16

3

RIGHT 57.3 1.00 332.0 421 0 H

16

0

SPANS! sheet This sheet shows the design of the left, centre and right hand side of each span. Input is needed for the diameter of bars and number of legs of links required. Extraneous spans are blanked out.

Position (m)

Dead Load

32.20

SPAN 4

MAIN! sheet

6


17/07/2006 17:01:59

General notes Project Location


REINFORCEMENT DESIGN

ANALYSIS I

Level 2, Beam on line 6

SPAN 1

Span =

7.500

m

BS8110

Top Steel

SUBFRAME ANALYSIS to BS8110:2005 Originated from RCC21.xls v3.0 on CD

© 2006 TCC

LEFT 92.8 1.000 625 176.6

ANALYSIS Min load

1.0 0.4

Live load

x dead load x dead load +

1.6

x imposed load

(Table 2.1)

Distribution Factors SUPT 1

SUPT 2

Up col

Aw Af X bar I Stiffness Sum Factor

R

Lo col

1.6E+09 542372881

1.6E+09 387096774

0.2105

0.1503

L 225000 147000 211.08871 1.1527E+10 1646679868 2576149523

Up col

225000 147000 211.08871 1.1527E+10 1646679868 3.E+09

0.6392

1.6E+09 400000000

675000000 163306452

0.1207

0.0493

0.4970

SUPT 4 L Aw Af X bar I Stiffness Sum Factor

0.3741

L 225000 252000 181.132075 1.324E+10 1103349057

Up col

225000 252000 181.132075 1.324E+10 1103349057 3.E+09

0.3330

Lo col

R

L

0 0

0 0

225000 126000 219.230769 1.1075E+10 1845865385

0.0000

0.0000

0.6259

Up col

225000 126000 219.230769 1.1075E+10 1845865385 2.E+09

0.7994

R

Lo col

0 0

0.4254

1.6E+09 387096774

0.0000

SUPT 5

Up col

225000 252000 181.132075 1.324E+10 1103349057 3.E+09

SUPT 3 R

Lo col

0.1492

225000 252000 181.13 1E+10 1E+09

0.4254

SUPT 6 R

Lo col

L

1.6E+09 300000000

675000000 163306452

0 0 #DIV/0! #DIV/0! 0

0.1299

0.0707

0.0000

0 0 #DIV/0! #DIV/0! 0 0.E+00

1.0000

R

Up col

Lo col

0 0

0 0

0 0 #DIV/0! #DIV/0! 0

0.0000

0.0000

0.0000

SUPT 7 L

Up col

Aw Af

Lo col

Partial UDL factors

0 0

X bar

a

#DIV/0!

I

#DIV/0!

Stiffness Sum Factor

0

b

0

0 0.E+00

0

0

0.0000

0.0000

0.0000

1

2

3

4

5

6

0 0

0 0

0.2 0.225

0 0

#DIV/0! #DIV/0!

#DIV/0! #DIV/0!

Fixed End Moments Min load Cant

SPAN 1 R

L

UDL PL 1 PL 2 part UDL FEM

SPAN 2 R

L

SPAN 3 R

L

SPAN 4 R

L

SPAN 5 R

L

SPAN 6 R

L

131.48 0.00 0.00 0.00 131.48

788.90 131.48 0.00 0.00 0.00 131.48

2443.40 386.40 0.00 42.53 0.00 428.93

386.40 0.00 30.38 0.00 416.78

1806.84 293.04 0.00 0.00 28.24 321.28

293.04 0.00 0.00 8.71 301.75

385.50 52.50 21.33 1.41 0.00 75.24

52.50 10.67 4.22 0.00 67.39

0.00 0.00 #DIV/0! #DIV/0! #DIV/0! 0.00

0.00 #DIV/0! #DIV/0! #DIV/0! 0.00

0.00 0.00 #DIV/0! #DIV/0! #DIV/0! 0.00

0.00 #DIV/0! #DIV/0! #DIV/0! 0.00

134.26 0.00 0.00 0.00 134.26

805.56 134.26 0.00 0.00 0.00 134.26

2617.36 394.56 0.00 85.07 0.00 479.63

394.56 0.00 60.76 0.00 455.32

1765.87 283.30 0.00 0.00 38.40 321.70

283.30 0.00 0.00 11.84 295.14

464.28 47.88 17.07 8.66 0.00 73.61

47.88 8.53 25.99 0.00 82.40

0.00 0.00 #DIV/0! #DIV/0! #DIV/0! 0.00

0.00 #DIV/0! #DIV/0! #DIV/0! 0.00

0.00 0.00 #DIV/0! #DIV/0! #DIV/0! 0.00

0.00 #DIV/0! #DIV/0! #DIV/0! 0.00

Live load Cant UDL PL 1 PL 2 part UDL FEM

Moment Distribution HiCol Min load

27.68 -15.56 1.14 -1.32 0.03 -0.10

Sum

-0.01 11.87

SUPT 1

-131.48 84.04 73.91 -47.25 -5.39 3.45 6.25 -3.99 -0.15 0.10 0.45 -0.29 0.05 -0.03 -20.34

LoCol

HiCol

19.76

35.91

-11.11

-2.62

0.81

3.04

-0.94

-0.07

0.02

0.22

-0.07

0.03

-0.01 8.47

0.01 36.50

SUPT 2

131.48 147.83 42.02 -10.79 -23.62 12.50 1.72 -0.30 -2.00 0.90 0.05 0.10 -0.14 0.03 299.79

-428.93 99.05 -20.31 -7.23 -1.52 8.37 -1.11 -0.20 0.18 0.61 -0.26 0.07 0.08 0.02 -351.20

LoCol

HiCol

14.66

0.00

SUPT 3

416.78 -40.63 49.53 -3.04 -3.61 -2.22 4.19 0.35 -0.10 -0.52 0.30 0.15 0.03 -0.11 421.11

-1.07 1.24 -0.03 0.09 0.01 0.00 14.90

-321.28 -40.63 -42.37 -3.04 8.84 -2.22 -5.01 0.35 1.31 -0.52 -0.66 0.15 0.21 -0.11 -404.97

LoCol

HiCol

-14.25

0.00

-1.07 -0.78 0.12 -0.18 0.05 -0.04 -16.14

Deflection

ANALYSIS! sheet This sheet shows calculations carried out using moment distribution.

Project


Client

Advisory Group

Location

3rd Floor slab, from 1 to 5a

rmw

RIBBED SLABS to BS 8110:2005 (Analysis & Design) Originated from RCC32.xls v3.0 on CD

Checked

chg

© 2006 TCC

Date

Project Location

Revision

Support 1 Span 1 Support 2 Span 2 Support 3 Span 3 Support 4

R68

BEAM

No

Type

Dia

Length

Unit Wt

Weight

D UDL

2 5 1 2 4 4 2 4 3 2 4

H H H H H H H H H H H

12 8 16 20 8 12 20 8 12 20 8

1025 1025 2225 2250 2250 4425 3625 3625 4675 2400 2400

0.888 0.395 1.578 2.466 0.395 0.888 2.466 0.395 0.888 2.466 0.395

1.8 2.0 3.5 11.1 3.6 15.7 17.9 5.7 12.5 11.8 3.8

L UDL D PUDL L PUDL PL 1

PL 2

X

M(r) all M(r) odd M(r) even 70% max 70% min Lower bound Upper bound

1150 400 3475 4750 3475 5900 1725

k tens 1.485

k comp 1.050

Allowed

3.4.4.4 3.4.4.4 3.4.4.4 3.4.4.4 3.12.5.3 3.12.11.2.7

ok

3.12.11.2.7

Eqn 8 >

2175 38.2 12 219.0 0.156 0.0092 208.1 194 325 325 No 657 348 0.159 186.0

ok

Allowed

34.88 Fig 3.12 Table 3.18

3.4.4.4 3.4.4.4 3.4.4.4 3.4.4.4 3.12.5.3 3.12.11.2.7

ok

3.12.11.2.7

Eqn 8

36.489

>

34.88

GRAPH DATA I

© 2006 TCC

1.578 2.466 1.578 3.853 1.578 3.853 1.578

1.8 1.0 5.5 36.6 11.0 45.5 8.2

26

0 0 0 -80.7 0 0 32.2 0 44.7 44.7 0 44.7 44.7 0 44.7 44.7

37 0 0 76.8 0 32.2 44.7 0 44.7 44.7 0 44.7 44.7 0 44.7 44.7

7 32.2 44.7 0 44.7 44.7

7 -80.7 7 0 32.2 0 44.7 44.7 7 44.7 44.7 12 44.7 69.7

7 78.1 7 32.2 44.7

19 32.2 44.7 7 44.7 44.7

7 44.7 44.7 12 69.7 94.7

19 -80.7 19 0 32.2 7 44.7 44.7 19 33.1 33.1 19 33.1 33.1

19 0 19 24.4 33.1 7 44.7 44.7 19 33.1 33.1 19 33.1 33.1

31 24.4 33.1 7 44.7 44.7

31 -26 31 0 24.4

33 23.1 47.1 35.5 23.1 28.1

31 0 31 17.5 23.1 20.5 33.1 33.1 33 47.1 53.1 35.5 28.1 46.1

37 17.5 23.1 20.5 40.6 37.6

37 -80.7 37 0 17.5 22.9 40.6 37.6 37 0 0 37 0 0

37 104 37 0 0 22.9 33.1 33.1 37 0 0 37 0 0

37 0 0

37 -26 37 0 0 31 23.1 23.1 37 0 0 37 0 0

37 26 37 0 0 31 23.1 23.1 37 0 0 37 0 0

3

3 2 2

SPAN 1

Beam

16 20 16 25 16 25 16

ok

ok

325 325 No 657 348 0.159 116.2 36.335

Fig 3.12 Table 3.18

MOMENT DIAGRAMS

M(e) all

H H H H H H H

ok

Spreadsheets to BS 8110 Level 2, Beam on line 6

LOADING DIAGRAM SUPPORTS

1 1 1 2 2 2 3

2175 246.4 16 217.0 0.132 0.0601 201.4 1294 0.00% 1294 100 Yes 189 1508 0.695 357.5

3.7.4.2

1875 20.6 12 219.0 0.156 0.0057 208.1 121

Job No

-

M(e) odd


2175 176.0 20 215.0 0.156 0.0438 204.0 912 54.36% 1408 200 Yes 358 1571 0.731 179.7

Base ratio 26


M(e) even

BOTTOM STEEL

1875 82.1 16 217.0 0.132 0.0233 206.2 489 0.00% 489 400 No ok 651 503 0.232 405.1 k comp 1.050

3.4.4.3 Fig 3.13

/47

APPROXIMATE WEIGHT of REINFORCEMENT TOP STEEL

1875 144.0 20 215.0 0.156 0.0415 204.3 865 47.52% 1276 225 Yes ok 378 1396 0.649 191.7 k tens 1.478

Ref

0.25L 58.8 1.000


Page

Apr-2006

RIGHT 328.5 0.800 2175 614.5

BAR! sheet This sheet shows the design of the distribution concrete section in detail and gives references to the appropriate clause numbers in BS 8110. The designs for Spans 2,3 etc follow on.


kNm Total Design M ßb Be mm Mt max kNm MIDDLE STRIP b mm 3425 M kNm 1.8 Bar dia mm 12 d mm 219.0 K' 0.156 K 0.0003 z mm 208.1 As mm²/m 6 As enhancement deflection control As final mm²/m 325 S mm 325 Clause b ? No S max mm 657 As prov mm²/m 348 =% % 0.159 fs N/mm² 5.7 Deflection Base ratio 26 COLUMN STRIP b mm 625 M kNm 92.8 Bar dia mm 16 d mm 217.0 K' 0.156 K 0.0789 z mm 195.9 As mm²/m 1743 As enhancement deflection control As final mm²/m 1743 S mm 100 Clause b ? Yes S max mm 175 As prov mm²/m 2011 =% % 0.927 N/mm² 289.0 fs

SPAN 319.9 1.077

Beam

0 0 0 0 0 0 0 0 0 0 0 0 0

0 36 95.3 -39 0 37.8 90.5 -40.9 66.7 -27.3 -40.9 90.5 0

0.35 -10 32.4 -45.7 0 -11.9 32.3 -48.5 22.7 -32 -48.5 32.3 0

0.7 -48.1 -22.5 -48.4 0 -53.7 -17.9 -52.1 -15.7 -33.9 -53.7 0 0

1.05 -78.2 -69.4 -47.2 0 -87.5 -60.2 -51.7 -33 -54.8 -87.5 0 0

1.4 -100 -108 -42 0 -113 -94.5 -47.5 -29.4 -75.8 -113 0 0

1.75 -115 -139 -32.9 0 -131 -121 -39.2 -23.1 -97.5 -131 0 0

2.1 -121 -162 -19.9 0 -141 -139 -27.1 -13.9 -114 -141 0 0

2.45 -119 -177 -2.93 0 -143 -150 -10.9 -2.05 -124 -150 0 0

2.8 -109 -184 18 0 -137 -152 9.11 12.6 -129 -152 12.6 0

3.15 -91.5 -183 42.9 0 -123 -146 33.1 30 -128 -146 33.1 0

3.5 -65.8 -175 71.7 0 -101 -133 61.1 50.2 -122 -133 61.1 0

3.85 -32.1 -158 104 0 -71 -111 93 73.1 -110 -111 93 0

4.2 9.57 -133 141 0 -33.1 -81.9 129 98.8 -93 -93 129 0

4.55 59.2 -100 182 0 12.9 -44.5 169 127 -70.1 -70.1 169 0

4.9 117 -59.3 226 0 66.7 0.96 212 158 -41.5 -41.5 212 0

5.25 182 -10.6 275 0 129 54.4 260 192 -7.41 -7.41 260 0

0 7 743 354 741 0 557 442 557 520 248 0 557 0

0.6 7.6 501 245 491 0 316 335 316 351 172 0 351 0

1.2 8.2 282 149 265 0 97 240 97 197 104 0 240 0

1.8 8.8 85.9 63.5 62.2 0 -98.1 156 -98.1 60.1 43.6 -98.1 156 0

2.4 9.4 -86.4 -10 -117 0 -270 83.3 -270 -7.01 -82 -270 83.3 0

3 10 -235 -71.9 -273 0 -418 22.6 -418 -50.4 -191 -418 22.6 0

3.6 10.6 -361 -122 -406 0 -543 -26.5 -543 -85.6 -284 -543 0 0

4.2 11.2 -463 -161 -515 0 -644 -64 -644 -113 -360 -644 0 0

4.8 11.8 -541 -188 -600 0 -722 -89.9 -722 -132 -420 -722 0 0

5.4 12.4 -566 -194 -632 0 -747 -94.3 -747 -136 -443 -747 0 0

6 13 -553 -183 -626 0 -733 -82 -733 -128 -438 -733 0 0

6.6 13.6 -516 -160 -597 0 -695 -58.2 -695 -112 -418 -695 0 0

7.2 14.2 -456 -126 -543 0 -635 -22.7 -635 -88.1 -380 -635 0 0

7.8 14.8 -373 -80.1 -467 0 -550 24.3 -550 -56.1 -327 -550 24.3 0

8.4 15.4 -266 -22.7 -367 0 -443 82.9 -443 -15.9 -257 -443 82.9 0

9 16 -135 46.3 -244 0 -312 153 -312 32.4 -171 -312 153 0

5 25 4 3 19 11 3 2 32 3

SPAN 2 Local X X M(e) all M(e) odd M(e) even Beam M(r) all M(r) odd M(r) even 70% max 70% min Lower bound Upper bound Beam

9 16 18 12 -9 -1 2 -1 88 -6 -1 2

SPAN 3

WEIGHT! sheet Calculates the theoretical weight of reinforcement required. 12.92

GRAF! sheet Data for graphs used in charts.

202.3

7


17/07/2006 17:02:10

contain variously checks, print boxes and combo-boxes, (see Help in Excel). Print buttons (buttons with macros assigned to them) automatically print out the calculation sheets providing macros that have not been switched off. Combo-boxes allow choices between specified options.

Disclaimer All advice or information from the British Cement Association and/or Reinforced Concrete Council is intended for those who will evaluate the significance and limitations of its contents and take responsibility for its use and application. No liability (including that for negligence) for any loss resulting from such advice or information is accepted by the BCA, TCC or their subcontractors, suppliers or advisors. Users should note that all TCC software and publications are subject to revision from time to time and should therefore ensure that they are in possession of the latest version. This spreadsheet should be used in compliance with the accompanying publication 'Spreadsheets for concrete design to BS 8110 and EC2' available from The Concrete Centre, Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey GU17 9AB.

Status of spreadsheet Public release version. Revision history

Date

This spreadsheet is shareware. It may be distributed freely, but may not be used for commercial purposes until the user has registered with the RCC

RCC11 Element Design.xls

Action

RCC11 v3.1

Differentiation between flat slabs and other slabs on SLAB page.

RCC11 v3.0

Updated to 2005 versions of BS8110 & BS8666

317

03-Feb-04

RCC11 v2.2

Minor correction to cell N12 on "SLAB" (> changed to < ).

289

21-Jan-03

RCC11 v2.1

11-Oct-02

DETR logo replaced by DTI.

To the right hand side of many spreadsheets are intermediate calculations, data for graphs, etc. These ‘workings’ are not considered vital to understanding the calculation; they may nonetheless be viewed and investigated. ‘Workings’ may also be contained on supplementary sheets.

Size (kB)

Version

15-Feb-06 20-Oct-05

331

289

RCC11 v2.0

Version 2 enhancements

304

01-Oct-02

RCC11 v1.7

COLUMN: Minor mods to N37:U37; Chart at U2 reactivated.

284

22-Jun-01

RCC11 v1.6

Addition of input controls.

284

26-Jan-01

RCC11 v1.5


283

05-Dec-00

RCC11 v1.4

SHEAR:K22 lateral link spacing corrected.

189 185 183

24-Nov-00

RCC11 v1.3

SHEAR:C19 & C20 reformatted, and lateral link spacing check added (C Braidwood).

30-May-00

RCC11 v1.2

R Lawson comments incorporated ( γc refs etc).

08-May-00

RCC11 v1.1

Revisions to TEE~BEAM. Option of required compression rebar added. Neutral axis, x allowed below flange soffite - IStructE 'Green book' method followed where flanges outside bw have z = d-hf/2, and bw acts as beam.

182

03-Aug-99

RCC11 v1.0

First public release. Includes β version comments & chg mods to COLUMN

190

Other sheets

NOTES! sheet Disclaimers, status and revision history of the spreadsheet.

Upper sheets The calculations are intended to mimic hand-written calculations as far as possible with a little more explanation by way of references to codes and derivation of numbers than would usually be the case in normal submissions. Sheets intended for printing out are divided into three sections: calculations, operating instructions and workings. The output is intended to be sufficient to allow detailing, although the designer should always consider and allow for rationalising reinforcement both within and between elements. Input cells are in blue and are underlined (so they can be recognised in black and white printouts). The cells under Operating Instructions to the right hand side contain help and error messages that are intended to help the user with the correct operation of the spreadsheet. They also

These sheets are not necessarily intended for printing out and may not be understandable without reference to the printed calculations. For instance, in the case of RCC52.xls Calcs!, the NM relationship in a particular column is calculated for increments of neutral axis depth. Many iterations are required in order to construct the N-M graph. Therefore there are many calculations and these are set out in tables. The volume of calculations makes it difficult to produce legible print-outs on a limited number of sheets.

Notes! The Notes! sheet shows the disclaimer, status and revision history of each spreadsheet. The disclaimer and status should be read and understood. The revision history provides a record of the spreadsheet being used and may provide a basis for users’ Quality Assurance procedures. The revision/ version and name of the spreadsheet should appear on all print-outs. This example is taken from RCC52.xls Notes!

Typical Upper sheet

Concurrent software being used

Combo-box (Used for automated choices)

8


17/07/2006 17:02:24

General notes Example of an ‘other’ sheet Spreadsheets to BS 8110 Columns at A1, A2 etc

Project Location

CALCULATIONS I

COLUMN CHART FOR SYMMETRICALLY REINFORCED RECTANGULAR COLUMNS BENT ABOUT THE X-X AXIS TO BS 8110:2005 Originated from 'RCC52.xls' v3.0 on CD

© 2006 TCC

CALCULATIONS .67fcu/m = fy/m = net fy/m =

32

13.40 434.78 421.38

N/mm² N/mm²

0.00 480.00

ALL CALCULATIONS DERIVED FROM FIGURE 3.3 AND CLAUSE 3.4.4.1

408.42 480.00

N/mm²

Bar diameter

d' = N=0 quadratic n max =

54

mm

a = 4824.000 913.2

n Fc c strain t strain fsc fst Fsc Fst z

Steel comp stress

N

Fc + Fsc - Fst

Neutral axis Conc comp force Steel comp strain Steel tens strain Steel tens stress Steel comp force Steel tens force Conc lever arm

M

MOR

Labels

for chart

N diff M diff

25

N=0 88.26 425764 0.00136 0.01022 258.32 434.8 623255 1049019 306.28 0.00 312.39 87.10 11.98

d= 346 mm Asc = 4825.5 mm² b = ######## c = -9.E+07 Interval = 5.497 (24 intervals between N=0 and Nbal) (solve for zero N) 93.76 99.25 104.75 110.25 115.74 121.24 452281 478797 505313 531830 558346 584862 0.00148 0.00160 0.00170 0.00179 0.00187 0.00194 0.00942 0.00870 0.00806 0.00748 0.00696 0.00649 283.43 305.76 325.74 343.73 360.02 374.82 434.8 434.8 434.8 434.8 434.8 434.8 683837 737709 785928 829338 868625 904349 1049019 1049019 1049019 1049019 1049019 1049019 303.81 301.34 298.86 296.39 293.92 291.44 87.10 167.49 242.22 312.15 377.95 440.19 324.37 335.24 345.15 354.22 362.56 370.26 80.39 10.87

74.73 9.91

69.93 9.08

65.80 8.34

62.24 7.69

59.14 7.11

126.74 611379 0.00201 0.00606 388.34 434.8 936975 1049019 288.97 499.34 377.36

132.23 637895 0.00207 0.00566 400.74 434.8 966888 1049019 286.49 555.76 383.94

137.73 664412 0.00213 0.00529 412.15 434.8 994414 1049019 284.02 609.81 390.04

143.23 690928 0.00218 0.00496 421.38 434.8 1016688 1049019 281.55 658.60 395.25

148.72 717444 0.00223 0.00464 421.38 434.8 1016688 1049019 279.07 685.11 397.07

56.43 6.58

54.04 6.10

48.79 5.20

26.52 1.82

26.52 1.69

Bar diameter

d' = N=0 quadratic n max =

50.5

mm

a = 4824.000 922.5

d= 349.5 mm Asc = 2945.2 mm² b = 370831.72 c = -5.E+07 Interval = 6.253 (24 intervals between N=0 and Nbal)

Notes! sheet Disclaimer All advice or information from the British Cement Association and/or Reinforced Concrete Council is intended for those who will evaluate the significance and limitations of its contents and take responsibility for its use and application. No liability (including that for negligence) for any loss resulting from such advice or information is accepted by the BCA, TCC or their subcontractors, suppliers or advisors. Users should note that all TCC software and publications are subject to revision from time to time and should therefore ensure that they are in possession of the latest version. This spreadsheet should be used in compliance with the accompanying publication 'Spreadsheets for concrete design to BS 8110 and EC2' available from The Concrete Centre, Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey GU17 9AB.

Status of spreadsheet Public release version. Revision history

This spreadsheet is shareware. It may be distributed freely, but may not be used for commercial purposes until the user has registered with the RCC RCC11 Element Design.xls

Date

Version

Action

Size (kB)

15-Feb-06

RCC11 v3.1

Differentiation between flat slabs and other slabs on SLAB page.

331

20-Oct-05

RCC11 v3.0

Updated to 2005 versions of BS8110 & BS8666

317

03-Feb-04

RCC11 v2.2

Minor correction to cell N12 on "SLAB" (> changed to < ).

289

21-Jan-03

RCC11 v2.1

DETR logo replaced by DTI.

289

11-Oct-02

RCC11 v2.0

Version 2 enhancements

304

01-Oct-02

RCC11 v1.7

COLUMN: Minor mods to N37:U37; Chart at U2 reactivated.

284

22-Jun-01

RCC11 v1.6


284

26-Jan-01

RCC11 v1.5


283 189

05-Dec-00

RCC11 v1.4

SHEAR:K22 lateral link spacing corrected.

24-Nov-00

RCC11 v1.3

SHEAR:C19 & C20 reformatted, and lateral link spacing check added (C Braidwood).

185

30-May-00

RCC11 v1.2

R Lawson comments incorporated ( γc refs etc).

183

08-May-00

RCC11 v1.1

Revisions to TEE~BEAM. Option of required compression rebar added. Neutral axis, x allowed below flange soffite - IStructE 'Green book' method followed where flanges outside bw have z = d-hf/2, and bw acts as beam.

182

03-Aug-99

RCC11 v1.0

First public release. Includes β version comments & chg mods to COLUMN

190

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Using the spreadsheets Frequently Asked Questions Macros When loading the individual spreadsheets, Excel may warn about the presence of macros. All the macros provided in the files are either to allow automated printing of the ‘calculations’ or to provide choices by way of combo-boxes. The printing macros have been assigned to buttons. Turning the macros off may affect the actual function of the spreadsheets but will certainly make printing of the sheets as configured more difficult and make the choice of options very much more difficult.

Fonts Unless the appropriate fonts Tekton and Marker (supplied in the CD-ROM) have been installed by the user, the appearance on screen will be different from that intended. These upright fonts have been used to emulate a designer’s handwriting and to allow adequate information to be shown across the page and in each cell. If problems are experienced it is most likely that the fonts on your computer screen will have defaulted to the closest approximation of the fonts intended (e.g. the toolbar may say Tekton but a default font such as Arial will have been used). The spreadsheets will work but not as intended – ends of words may be missing, numbers may not fit cells resulting in a series of hashes, #####. Column width and cell overlap problems only occur when the correct fonts are not loaded. It is strongly recommended that the Tekton and Marker fonts are copied into your computer’s font library. The Freewave fonts may be found in the Fonts folder on the CD-ROM.

■ to the right hand side of the spreadsheets, cells under

Operating Instructions contain help and error messages. ■ Queries may be e-mailed to [email protected].

Preference will be given to those who have registered.

Support E-mailed questions, comments, developments and suggestions are welcomed. Send them to [email protected]. Preference will be given to those who are registered, as detailed above.

Shareware These spreadsheets are offered as shareware. This can be considered a ‘try before you buy’ system where you are expected to pay the program owners a registration fee if you find the program useful or if the programs are used for commercial use. In general you may pass on copies of shareware programs to colleagues within the UK, although commercial (for a fee) distribution requires special written permission from the publisher.

Availability/registration The RC Spreadsheets are made available as shareware from The Concrete Centre see www.concretecentre.com/rcspreadsheets. However, the spreadsheets may not be used for commercial purposes until the user has purchased and validated a licence.

They may be copied in the following manner, either:

Licences may be purchased from The Concrete Bookshop (www.concretebookshop.com, Tel +44 (0)7004-607777) or via The Concrete Centre website. Licences may be validated via www.concretecentre.com/rcspreadsheets. The purchase price includes

■ Start/Settings/Control Panel/Fonts/ File/ Add Fonts and when

■ Permission to use the spreadsheets for commercial purposes

asked ‘copy fonts to system directory?’ answer ‘yes’. or ■ Through Microsoft Explorer and copying (or dragging)

the font files into your font library, usually contained in Windows/ Set-up/ Fonts

Help A printed copy of this User Guide is available from The Concrete Bookshop (07004 607777 or www.concretebookshop.com). The User Guide is also available as an Adobe Acrobat file UserGuid pdf, (on the CD-ROM). A copy of Adobe Acrobat Reader will be required to read this file. Help is also available at the following places: ■ Within Excel under Help

for at least one year ■ A hard copy of this publication, User Guide to RC

Spreadsheets: v3 ■ CD-ROM containing RC Spreadsheets: v3, together with

Admin files, which themselves contain fonts, issue sheets, user guide files etc. ■ Occasional e-mails to inform them of any revisions

orchanges to the spreadsheets or other relevant information ■ Details of how to download updates of the spreadsheets ■ Preferential treatment with regard to support

Further information, updates, FAQs, free trial download versions of some spreadsheets, latest news and other information on the RC-Spreadsheet suite is available on www.concretecentre. com/rcspreadsheets

10


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General notes Overseas use The spreadsheets have been developed and maintained for use within the UK. The Concrete Centre reserves the right to pass details of non-UK registrants to any future owner of the non-UK copyright or overseas distributor of the spreadsheets.

Updates It is intended that The Concrete Centre’s website will include updated versions of the spreadsheets. Registrants will be provided with information on how to download updates.

Using the spreadsheets for the first time Base versions Initially, always start from the base versions on the CD-ROM. If in doubt, go back to the version on the CD-ROM. These safeguards are to avoid using corrupted or bespoke files. Eventually, familiarity with the spreadsheets and Quality Assurance procedures may overtake this basic precaution.

software and networks only recognise eight characters for a file name. In use, users may be requested by the system to allow abbreviated names, e.g. RCC11.xls . As shorthand, the spreadsheets are generally referred to by their number rather than their name in full, i.e. RCC11.xls is used as shorthand for RCC11 Element Design.xls.

Loading a spreadsheet for the first time Under Windows ’98, NT, 2000, 2002 or XP insert the spreadsheet CD-ROM into the CD drive (drive D: assumed). A spreadsheet can be loaded using one of the following methods: ■ Your computer may automatically present a view of the files

available on the CD-ROM in which case double click the mouse pointer on the spreadsheet of your choice, e.g.MENU. xls//. If not already loaded and presuming it is available, Excel will boot up and load up with MENU.xls ready for operation. Excel will most probably warn about macros before loading the spreadsheet fully. In order to proceed, enable macros (see below). Otherwise ■ From ‘My Computer’, double click(//) on My Computer, double

Please note that whilst all spreadsheet cells, apart from input cells, are covered by nominal protection, it is possible to change the contents of cells. Original versions are available on CD-ROM or from The Concrete Centre’s website www.concretecentre.com. Also, please note conditions of use and disclaimers associated with the use of the spreadsheets contained within the sheet titled Notes! and elsewhere in this User guide.

Excel The spreadsheets are normal Excel files. Excel (© Microsoft Corporation) is a standalone package or may be included as part of the Microsoft Office package on PCs or Macs. The files are compatible with Excel 2002, part of Office 2002, and are likely to be compatible with future versions of Excel. Those not familiar with Excel are directed to the Help functions within Excel and relevant literature available at book and computer shops. Please note that the spreadsheets will not necessarily work with previous versions of Excel (e.g. ’95, 5.x etc.) or other spreadsheet programs. This is due to incompatibility between software and backward incompatibility between versions. (To check which version of Excel you are running see sign-on screen, or Help/ About Microsoft Excel). Those running Excel 2000 are advised to use the Save As/ .xls function to avoid inordinately large file sizes.

click on D (assumed CD drive) //double click on spreadsheet of ones choice //. ■ Successively click Start/ Programs/ Microsoft Explorer/ double

click mouse on CD Drive (D)//. Double click the mouse pointer on the spreadsheet of your choice, e.g.Menu.xls//. If not already loaded and available, Excel will boot up and load up with Menu.xls. ■ Successively click Start/ Programs/ Microsoft Excel. Once

Excel has booted up, click mouse pointer on File in top menu bar/ click mouse on Open/ click mouse on the ‘Look in’ box and scroll through to the CD Drive ■ Click mouse on the CD Drive (D)//. Double click mouse on the

spreadsheet of your choice, e.g. Menu.xls//. The design spreadsheets may, if the user wishes, be loaded direct. In the above instructions replace MENU.xls with the name of the spreadsheet required. The advantages of using MENU.xls are explained later. No installation program per se is included. Under file managers such as Microsoft Explorer, the CD-ROM versions of the spreadsheets can be dragged and dropped into an appropriate folder specified by the user. Alternatively, from within Excel, the spreadsheets can be loaded directly from the CD-ROM – but should users wish to save the modified spreadsheet, it has to be saved to an alternative drive.

Long file names The base versions of the spreadsheets are saved with long file names to aid familiarity with each spreadsheet’s purpose. Some 11


17/07/2006 17:02:39

Default font size Even with the correct fonts installed, the appearance of the sheets might be different from those intended. This may be due to the default font size on the user’s computer being different from the font size 12 used in the development of the spreadsheets. For instance if the user’s default font size is 10, pages will appear and print narrower than intended (as unformatted cells will revert to a narrower cell width than intended). Please ensure that the default font size is set at 12. (In Excel check Tools/ Options/ General/ Standard font and size). If standard font or size is changed it will become effective only after rebooting Excel. While the spreadsheets were developed using Tekton 12, many True Type font size 12 (e.g. Arial or preferably Times New Roman 12) may give adequate presentation. If a series of hashes (#####) still appears, it may be necessary to resize the column width.

Screen view The spreadsheets have been developed assuming that part, if not the whole, of the Operating Instructions column is in view. This column contains comments, instructions, checks, explanations, etc. and is important for the correct operation of the spreadsheets. Generally, a screen zoom of 75% has been used as a default size on the sheets. Occasionally, other zoom sizes have been used in order to aid comprehension.

or cleared by using a blank or hyphen; clearing the cell completely would produce ‘0’ on subsequent sheets.

Values in red or red backgrounds During operation, values in red or cells with red backgrounds flag either incorrect data to be changed or excess data to be cleared (manually). Even a space as an entry might generate red backgrounds. If you make a mess of it, start again from the base version of the spreadsheet on the CD-ROM.

#DIV/0! (Divide by zero) errors In some spreadsheets, #DIV/0! results may arise and be displayed. In sheets intended for printing out, #DIV/0! indicates an error in or invalid input. In sheets of workings, they have no relevance to the validity of the sheet or the spreadsheet as a whole. Please note that in many cases, but not all, a very small value has been used rather than zero in order to avoid #DIV/0! (divide by zero) problems in Excel, e.g. [RCC53.xls] Cases!B3:B8 where =IF(ERROR(G3),0.000001,G3) has been used.

Printing The sheets may be printed out in several ways:

Screen resolution The spreadsheets have been developed in 1024 x 768 resolution, so that their appearance will be acceptable between SVGA (800 x 600) and 1280 x 1024.

■ Through the automated print buttons in the spreadsheets

(using these print macros will over-write print areas defined elsewhere) ■ Using the Print icon on Excel’s standard toolbar ■ Using File/ Print within Excel

They will obviously work in VGA (600 x 480), but higher resolutions are recommended.

■ Copying and pasting (special) parts of the spreadsheets to

Input

■ Pasting as other formats will probably require some

In the spreadsheets, input data is blue and underlined. New data may be input by overwriting default values or by entering values in ‘greyed-out’ cells. Entering data in far-left greyed-out cells may also remove the grey conditional background to other cells, which will then require data entry. Some input cells refer back to data on previous sheets within a workbook. These are coloured magenta, but change back to blue if other data is entered. Do not copy and paste input from one cell to another as this may cause formatting and other errors. Do not use Space, Enter (the space equals text). If similar input is required in other cells then use ‘= cell reference’ with caution, e.g. ‘= B16’ in the appropriate input cell. All non-input cells should have nominal protection and the contents of these cells can only be overwritten if the user has taken positive steps to overwrite original contents. In the page headers the ‘Made by’ and ‘Checked’ boxes should be completed

a word processor or other package. Pasting (special) into a word processor file as a bitmap produces a wysiwyg image. pre-copying formatting of the spreadsheet and/ or postformatting of receiving cells. Print areas may be defined by: ■ Highlighting area then clicking File/ Print Area/ Set Print Area ■ Clicking View/Page Break Preview and adjusting boundaries

to suit Print previewing can be achieved using the Print Preview icon on the standard toolbar.

Print formatting Different hardware and software are configured in many different ways. This situation leads to many variations on the actual print from individual printers. Best results are likely to be obtained from Windows printers but even these may not produce printing that is identical to that intended. Some manipulation for printing with your configuration may be inevitable.

12


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General notes AutoComplete Excel’s facility for AutoCompleting cells (e.g. entering ‘T’ might autoComplete to ‘Type’) can be a mixed blessing. In most spreadsheets it should be turned off via Tools/ Options / Edit and clearing the Enable AutoComplete for cell values box.

Continued use Conditions of use: disclaimers A fundamental condition of use that the user accepts responsibility for the input and output of the computer and how it is used. Whilst the spreadsheets have been checked with all reasonable care and diligence, they cannot be guaranteed for every eventuality. Users must satisfy themselves that the uses to which the spreadsheets are put are appropriate. Users must have read, understood and accepted the disclaimer contained on the inside front cover of this publication (and repeated in the sheet named Notes! in each spreadsheet).

Nominal protection Users and managers should be aware that the spreadsheets can be changed. Beyond nominal cell and sheet protection, the files are open and can be changed. There are several reasons for this: ■ The files can be customised by users to their own preferred

methods of presentation and design (e.g. deflections might be calculated to part 2 of BS 8110; individual firms’ or project logos might replace the The Concrete Centre logo).

be used as record copies to help identify changes. Users’ Quality Assurance procedures may dictate the use of more sophisticated protection measures.

Development The nominal protection within the spreadsheets may be overridden to allow customisation and individual development. Any development of the spreadsheets should be undertaken by experienced staff who have a good understanding of the problems and pitfalls of both design and spreadsheets. It may take an experienced engineer four or five times longer to prepare a spreadsheet than it would to produce the equivalent manual calculation. Robust, commercially acceptable spreadsheets may take 50 times as long. They can take even longer to test, check and correct. Only repetition of use makes the investment of time worthwhile. With relatively open files, designers are at liberty to alter the spreadsheets as they wish. However, they must satisfy themselves that any alterations are correct and do not interfere with any other aspect of the spreadsheet in question and conform to any Quality Assurance procedures. Notwithstanding the above, copyright of the spreadsheet contents remains with The Concrete Centre. Altered or amended versions of the spreadsheets may not be sold or hired without the written permission of the Centre. Please inform The Concrete Centre of any major discrepancies found or improvements made.

Saving files/ file management Many users save spreadsheets to a directory and/ or folder of their choice. This is particularly true where spreadsheets pertaining to a particular project are saved to a folder given the project’s name.

■ The protection should stop inadvertent changes and

corruption of cells.

Linking spreadsheets

■ Developments and improvements can be made and fed back

to The Concrete Centre. Such feedback is encouraged and allows a wider consensus to be gained. ■ Protection can always be overcome by determined users. ■ Fully protected files can hide cell contents . ■ Spreadsheet emulators are at present unsuitable for this

application. ■ Different designers want different facilities available to them

and should not be restricted. The spreadsheets are all protected but with no password, in other words users have to do something positive if they are to change any formulae, and must therefore take responsibility for any deliberate or accidental changes. The project’s Advisory Group held this to be a sensible position.

To avoid complications, links between different design spreadsheets have not been used. Nonetheless, for the experienced user, linking provides a powerful tool. The results of one spreadsheet can be linked through to become the input for another, or project data can be auto-loaded. This minimises the amount of input required and at the same time reduces the scope for error in data transfers. For example, the results of a beam analysis can be carried through to beam design. Any links created by the user are at his or her discretion.

Assumptions made During the course of development of these spreadsheets, a number of structural and computing assumptions have been made. These are discussed below.

Users and managers must address change control and versions for use. The Concrete Centre can only control the base versions issued on CD-ROM (and web page). The published examples can 13


17/07/2006 17:02:43

As enhancement

Reinforcement densities

Several of the BS8110 spreadsheets contain automatic routines that increase As in order to reduce service stress fs and therefore increase modification factors in order to satisfy deflection checks. The ‘As enhancement’ values are the percentages by which As required for bending are increased in order to satisfy deflection criteria.

Some spreadsheets give an indication of weight of reinforcement in the margin under ‘Operating Instructions’. These densities should be used with great caution. Many factors can affect actual reinforcement quantities on specific projects. These include different methods of analysis, non-rectangular layouts, large holes, actual covers used, detailing preferences (curtailment, laps and wastage), and the unforeseen complications that inevitably occur. As may be examined in the sheets entitled ‘Weight’, the densities given relate to simple rectangular layouts and the author’s interpretation of BS 8110. They make no specific allowance for wastage.

Redistribution Those spreadsheets with analysis allow redistribution in accordance with BS 8110: Part 1, Clause 3.2.2.1 or Eurocode 2 Clause 5.5. The user may choose between three options. These options do not affect redistribution at supports but do determine how span moments are calculated, as shown in Table 1.

The densities assume that the areas or volumes of slabs are measured gross, e.g. slabs are measured through beams. Beam reinforcement densities relate to web width multiplied by overall depth.

Table 1 Redistribution options in spreadsheets with analysis Spreadsheet option number

Design support moment

Design span moments Support moment from which span moment is calculated

Comments

0

ßbM

ßbM

Design span moments will probably be less than elastic moment (minimum of 70% of elastic moment). This option may lead to a kinked bending moment diagram as the 70% kicks-in in the spans. In the case of thin sections such as slabs, consideration of span deflection and service stress often leads to reinstatement of any reinforcement theoretically saved.

1

ßbM

Minimum of ßbM and Malt/ßb

Design span moments might be less than elastic moment but less likely than with option 0. Increasing the minimum support moment for the calculation of span moment from Malt to Malt/ßb is seen as a sensible compromise between options 0 and 2.

2

ßbM

Minimum of ßbM and Malt

Design span moments cannot be less than elastic moment. Most often used but, if, typically, 20% redistribution is specified at supports, design span moments will increase by about 10% over elastic span moments. Again, in thin sections, consideration of deflection and service stress can limit additional amounts of reinforcement due to increased span moment.

Where ßb = (moment after redistribution)/(moment before redistribution) = 100% - % redistribution requested M = elastic moment at support, all spans loaded Malt = maximum elastic Moment at support, alternate spans loaded

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General notes Rationalisation of reinforcement Although it may appear that many of the spreadsheets give least weight solutions (hence more bars, more work), the amounts of reinforcement derived are actually accurate (and not necessarily rationalised). It is intended, therefore, that the amounts of reinforcement derived from the spreadsheet should be considered as minimal. The user should specify more rationalised reinforcement layouts to the detailer. Rationalisation should be done manually – there would seem to be too many variables and personal preferences to enable automatic rationalisation. A detailer can always close up spacing and/ or reduce bar diameters if desired.

Analysis: cantilever deflections and support rotation Support rotations are ignored. Support rotation cannot be determined except as part of a rigorous deflection analysis. Rotations cannot be easily derived from moment distribution, and in any case, gross section slopes are of little or no value. It is assumed that BS 8110’s or Eurocode 2’s deemed-to-satisfy l/d checks are adequate. If support rotations are expected to be critical additional checks should be undertaken.

Most often the spreadsheets require bar size as input, rather than bar spacing. This can lead to unusual, but correct, spacings. Where bar diameter input is available, it may be worth investigating larger bars (at larger centres). For instance, in the design of a flat slab it would probably be preferable to use 4828 larger bars at greater centres rather than 6840 smaller bars at small centres (weight is marginally different, 82.5 kg/m3 c.f. 80.8 kg/m3). This results in 30% fewer bars compared with 2% extra steel. Rationalised arrangements with least number of bars (without breaking the spacing rules) and least number of bar marks are always preferable. Eventually, it may be possible to automate this process, but for the time being it is between the program user (i.e. the designer) and the detailer to decide how to rationalise bar arrangements. Any estimates of reinforcement must take this process into account. Other spreadsheets tend to size bars in such a way that minimum centres (or clear spacings) are not exceeded. It is assumed that issues of detail will be considered by the engineer and detailer. Issues such as radius of bottom bars and beam bearings, space between bars in narrow beams, spliced bars at supports of beams, connection details, etc. need to be considered.

Definitions of imposed and live loads For the BS8110 spreadsheets, imposed load is taken to be the characteristic imposed load input by the user. For floors this might be the minimum imposed floor loads described in BS 6399[19] Part 1 Table 1. Live load is taken to be that part of the ultimate load that is not characteristic dead load (i.e. in BS8110 spreadsheets, live load = n - gk ). (For the Eurocode 2 spreadsheets no such distinction is needed. Variable actions should be as described in BS EN 1991-1[35]. For permanent actions, γG is intended to be constant across all spans and therefore not ‘live’.)

15


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Menu.xls This spreadsheet acts as both menu program, allowing the user to load the spreadsheet they want to use, and as a version checker. It is intended to help the user designing a number of elements at one session and to help ensure that the most up to date versions of the spreadsheets are in use. To work properly it must reside in the same folder as the design spreadsheets themselves.

Welcome!

Depending upon the level of security you have set up on your version of Excel, you may be asked whether you wish macros to run; please answer ‘Enable macros’. Once Menu.xls is loaded, you may also be asked whether you want to update links. If you wish the current version numbers in your folder to be displayed answer ‘Update’.

Welcome!

BS8110!

Welcome gives a quick introduction to the spreadsheets by covering in outline: Limitations & Assumptions System requirements ■ Disclaimer ■ Licence conditions ■ Instructions for Use ■ Basic Instructions ■ Macros

BS8110!

Eurocode 2!

This sheet shows the spreadsheets available for the design of elements to BS 8110. Adjacent to the title of each spreadsheet is a button which may be clicked in order to load that spreadsheet.

Eurocode 2! Similarly, this sheet highlights the spreadsheets available for the design of elements to Eurocode 2. Adjacent to the title of each spreadsheet is a button that may be clicked in order to load that spreadsheet.

Versions!

In due course further spreadsheets will be released and made available.

Versions! This sheet shows the version number of each spreadsheet in your folder.

16


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17


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18


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RCC11 Element Design.xls

RCC11 Element Design.xls RCC11.xls includes sheets for designing: ■ Solid slabs, ■ Rectangular beams ■ T beams (and ribbed slabs) for bending ■ Beam shear an ■ Columns with axial load and bending about one axis

RCC11.xls designs elements to BS 8110: Part 1, 1997 including Amd 3[2]. It is assumed that loads, moments, shears, etc. are available for input from hand calculations or analysis from elsewhere. A governing criterion can be deflection; span-todepth ratios are used as per BS 8110: Part 1, Clause 3.4.6.

SLAB! This sheet allows for the design of a section of solid slab in a single simply-supported span, in a continuous span, at supports or in a cantilever. These choices have a bearing on deflection limitations and the user should choose the appropriate location from the combo-box to the right hand side. The user may also choose to allow for no or nominal compression steel; this again affects deflection factors. To an extent the spreadsheet will automatically increase reinforcement in order to lower service stresses and enhance allowable span to depth ratios. The spreadsheet allows a certain amount of theoretical over-stress as defined by the user in cell M7. Engineering judgement is required to ensure that any over-stress is acceptable and that specified reinforcement is sensibly rationalised. Slight variances in reinforcement requirements may be found. These are due to the spreadsheet allowing marginal over-stress and allowing centres in increments of 25 mm.

RECT~BEAM! This sheet designs rectangular beams. The location of the beam may be either in a single simply-supported span, in a continuous span, at supports or in a cantilever. These choices have a bearing on deflection limitations and the user should choose the appropriate location from the combo-box to the right hand side. When considering span reinforcement, the spreadsheet will, where necessary, automatically increase reinforcement in order to lower service stresses and enhance allowable span-to-depth ratios. In checking deflection, the sheet entitled RECT~BEAM! includes two bars of the specified reinforcement diameter to derive a modification factor for compression reinforcement. The facility to specify additional compression reinforcement to enhance span-to-depth ratios is contained within TEE~BEAM!

TEE~BEAM! TEE~BEAM! designs T beams and L beams in single simplysupported span, end span, internal span or cantilever locations. Again, these choices have a bearing on deflection limitations and the user should choose the appropriate location from the combo-box to the right hand side. With respect to the effective width of the flange, the user may also choose that the section is considered as a tee- or inverted L beam. A default value for the width of the flange bf is calculated and displayed as input. This cell may be overwritten if, for instance, say the user wishes to allow for openings, etc. The default is calculated as being: web width + 0.14 span for T beams, internal span web width + 0.16 span for T beams, end span web width + 0.07 span for L beams, internal span web width + 0.08 span for L beams, end span In the determination of compression steel, where the neutral axis lies below flange, the concrete in web, bw, below flange has been ignored. This is seen as a valid alternative to the approach in Clause 3.4.4.5. In order to calculate the appropriate deflection factor for compression reinforcement, there is a facility to specify compression reinforcement. When considering deflection, the spreadsheet will, where necessary, automatically increase span reinforcement in order to lower service stresses and enhance allowable span-to-depth ratios.

SHEAR! This sheet checks beams or slabs for shear and calculates any shear reinforcement required. It is hoped that the input is selfexplanatory. Providing the applied load is fundamentally a UDL, or where the principal load is located further than 2d from the face of the support, BS 8110: Clause 3.4.5.10 allows shear to be checked at d from the face of support. Checks for maximum shear (either 5.0 N/mm2 or 0.8fc u 0.5 ) are carried out automatically. In beams, the designed links will be necessary for a distance from the support before reverting to nominal link arrangements. A maximum link spacing of 600 mm is used; this is seen as a sensible maximum. Apart from punching shear, shear in slabs is rarely critical (see RCC13.xls).

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COLUMN! This sheet designs symmetrical rectangular columns where both axial load, N, and maximum design moment, Mx are known (see BS 8110: Part 1, Clauses 3.8.2, 3 and 4). It iterates x/h to determine where the neutral axis lies. The sheet includes stress and strain diagrams to aid comprehension of the final design. For simplicity, where three or more bars are required in the top and bottom of the section, it is assumed that a (rotationally) symmetrical arrangement will be required for the side faces. This appears to be common practice, for small to medium sized columns. For more detailed consideration see RCC52.xls. In particular, see RCC53.xls regarding the issue of side bars. COLUMN! assumes that the moment entered has already been adjusted, if necessary, for bi-axial bending. For many side and all corner columns, there is no other choice than to design for bi-axial bending, and the method given in Clause 3.8.4.5 must be adhered to, i.e., RCC53.xls or sheets 2 and 3 of RCC51.xls should be used. In theory, negative amounts of reinforcement required can be obtained but these are superseded by requirements for minimum amounts of reinforcement in columns. No adjustment is made in the area of concrete occupied by reinforcement. Theoretical overstressing by up to 2% is considered to be acceptable. Maximum link centres are given. The routine in the area L61:U81 investigates shear when, in accordance with Clause 3.8.4.6, M/N > 0.6h. In such cases either a maximum allowable shear is shown where shear is critical, or input of shear and number of legs in links allows the links to be designed for the applied shear. Even in unbraced structures shear is rarely likely to be critical.

Notes! This sheet gives disclaimers and revision history

20


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RCC11 Element Design.xls RCC11 Element/ SLABS!

ELEMENT DESIGN to BS 8110:2005

SOLID SLABS Originated from RCC11.xls v3.1

© 2006 TCC

INPUT Location D&D: interior span solid slab γc = 1.50 Design moment, M 216.0 kNm/m fcu 40 N/mm² γ s = 1.15 ßb 1.00 fy 500 N/mm² span 6500 mm steel class A mm Section location CONTINUOUS SPAN Height, h 1000 mm Compression steel NONE Bar Ø 20 mm to these bars (deflection control only) cover 50 ONE or TWO WAY SLAB OUTPUT D&D: interior span solid slab Compression steel = NONE d = 1000 - 50 - 20/2 = 940.0 mm . (3.4.4.4) K' = 0.156 > K = 0.006 ok . (3.4.4.4) z = 940.0 [0.5 + (0.25 - 0.006 /0.893)]^½ = 933.6 > 0.95d = 893.0 mm (3.4.4.1) As = 216.00E6 /500 /893.0 x 1.15 = 556 < min As = 1300 mm²/m PROVIDE H20 @ 225 = 1396 mm²/m . (Eqn 8) fs = 2/3 x 500 x 556 /1396 /1.00 = 132.8 N/mm² (Eqn 7) Tens mod factor = 0.55 + (477 - 132.8) /120 /(0.9 + 0.244) = 2.000 (3.4.6.3) Permissible L/d = 26.0 x 2.000 = 52.000 . Actual L/d = 6500 /940.0 = 6.915 ok . . .

21


17/07/2006 17:03:12

RCC11 Element Design/ RECT~BEAMS!


RECTANGULAR BEAMS Originated from RCC11.xls v3.1

© 2006 TCC

INPUT Location D&D: Main beam 1st Floor @internal support Design moment, M 282.0 kNm fcu 35 ßb 0.70 fy 500 steel class A Span 8000 mm Height, h 500 mm Comp cover 40 Breadth, b 300 mm Tens cover 48 Tens Ø mm Side cover 35 25 Comp Ø mm Section location 12 OUTPUT (3.4.4.4) (3.4.4.4) (3.4.4.4)

(Fig 3.3) (Fig 3.3)

(Fig 3.3)

(Eqn 8) (Table 3.11) (Table 3.10) (3.4.6.3) (3.4.6.1)

N/mm² N/mm²

c 1.50 s 1.15

mm to main reinforcement mm to main reinforcement mm to main reinforcement CONTINUOUS SPAN

D&D: Main beam 1st Floor @internal support d = 500 - 48 - 25/2 = 439.5 mm K' = 0.104 < K = 0.139 compression steel required z = 439.5(0.5 + (0.25 - 0.104/0.893)^½ ) = 380.7 < 417.5 mm x = (439.5 - 380.2) /0.45 = 131.9 mm d' = 40 + 12/2 = 46.0 mm . Gross fsc = 434.8 N/mm² from strain diagram net fsc = 434.8 - 0.67 x 35 /1.5 = 419.1 > 0 N/mm² Excess M = M - Mu = 282.0(0.139 - 0.104) /0.139 = 70.4 kNm As' = 70.4E6 /419.1 /(439.5 - 46.0) = 427 mm² PROVIDE 4H12 compression steel = 452 mm² . fst = 434.8 N/mm² . As = (70.4E6 /393.5 + 211.6E6 /380.2) /434.8 = 1692 mm² .

.

.

As enhanced by 14% for deflection PROVIDE 4H25 tension steel = 1963 mm² fs = 2/3 x 500 x 1,692 /1,963 /0.70 = 410.3 N/mm² Comp mod factor = 1 + 0.343 /(3 + 0.343) = 1.103 < 1.5 Tens mod factor = 0.55 + (477 - 410.3) /120 /(0.9 + 4.866) = 0.646 < 2 Permissible L/d = 26.0 x 1.103 x 0.646 = 18.533 Actual L/d = 8000 /439.5 = 18.203 ok .

22


17/07/2006 17:03:17

RCC11 Element Design.xls RCC11 Element Design/ TEE~BEAMS!


SIMPLE TEE & L BEAMS Originated from RCC11.xls v3.1

© 2006 TCC

INPUT

Location D&D: Main beam, 1st Floor 8m span c 1.50 M 280.0 kNm fcu 40 N/mm² s 1.15 ßb 1.00 fy 500 N/mm² steel class A span 8000 mm Comp cover 48 mm to main reinforcement h 500 mm bw 300 mm Tens cover 40 mm to main reinforcement bf 400 mm Side cover 35 mm to main reinforcement INTERIOR SPAN hf 100 mm Section location mm Section shape T BEAM Tens Ø 32 Top steel 2 no & Ø 12 .

OUTPUT

D&D: Main beam, 1st Floor 8m span d = 500 - 40 - 32/2 = 444.0 mm K' = 0.156 > K = 0.089 x = 444 /0.45(0.5 - (0.25 - 0.089 /0.893)^½) = 110.4 mm z = 444 - 0.45 x 110.4 = 394.3 < 421.8 mm As' = 0 < 226 mm² As = 280.0E6 / 394.3 /500 x 1.15 = 1633 mm² . . PROVIDE 3H32 bottom = 2413 mm² fs = 2/3 x 500 x 1,633 /2,413 = 225.6 N/mm² Comp mod factor = 1 + 0.170 /(3 + 0.170) = 1.054 < 1.5 Tens mod factor = 0.55 + (477 - 225.6) /120 /(0.9 + 3.551) = 1.021 < 2 Permissible L/d = 24.1 x 1.054 x 1.021 = 25.961 Actual L/d = 8000 /444.0 = 18.018 ok

(3.4.4.4) (3.4.4.4) (3.4.4.4)

(3.4.4.4)

(Eqn 8) (Table 3.11) (Table 3.10) (3.4.6.3) (3.4.6.1)

.

(within flange)

23


17/07/2006 17:03:19

RCC11 Element Design/ SHEAR!


BEAM SHEAR Originated from RCC11.xls v3.1

© 2006 TCC

INPUT Location D&D: Main beam, 1st Floor 8m span, RH end c 1.50 fcu = 35 N/mm² d b s 1.15 540 400 fyl = 500 N/mm² steel class A Main Steel

Link

Legs

Side cover

Shear V

UDL

4

25

10

2

35

264.0

97.9

No

mm Ø

mm Ø

No

mm

kN

kN/m

OUTPUT (Eqn 3) (Table 3.8)

D&D: Main beam, 1st Floor 8m span, RH end

As = 1963 N/mm² = 0.909% v = 264.0 x 10³ /400 /540 = 1.222 N/mm² vc = 0.685 N/mm², from table 3.8 (v - vc)bv = 214.9 N/mm PROVIDE 2 legs H10 @ 300 = 227.7 N/mm Provide for distance of 300 mm then nominal links = 2 legs H10 @ 400

24


17/07/2006 17:03:22

RCC11 Element Design.xls RCC11 Element Design/ COLUMN!

ELEMENT DESIGN to BS 8110:2005 SYMMETRICAL RECT-ANGULAR COLUMN DESIGN

COLUMN DESIGN Originated from RCC11.xls v3.1

INPUT

© 2006 TCC

Location D&D: external column Axial load, N 1654 kN Moment, M 125.0 kNm height, h 300 mm breadth, b 300 mm Max bar Ø mm 32 cover (to link) 30 mm

fcu 40 fy 500 fyv 500 γm 1.15 γm 1.50 steel class A

D&D: external column Link Ø CALCULATIONS from M As = {M - 0.67fcu.b.dc(h/2 - dc/2)}/[(h/2-d').(fsc+fst).gm] from N As = (N - 0.67fcu.b.dc/gm) / (fsc - fst)

8

N/mm² N/mm² N/mm² steel concrete

mm (3.4.4.1) (Figs 2.1, 2.2 & 3.3)

where As = Ast = Asc: dc=min(h,0.9x)

.67fcu/gm = fy/gm = from iteration, n.a. depth, x, = 0.67.fcu.b.dc/gm = Steel comp strain = Steel tens strain = Steel stress in comp. face, fsc = Steel stress in tensile face, fst = from M, As =

17.9 N/mm² 434.8 N/mm² 225.9 1089.7 0.00266 0.00031 435 62 1515

mm

d' = d=

54.0 mm 246.0 mm

dc =

203.3 mm

kN

N/mm² N/mm² mm²

(Comp. stress in reinf.) (Tensile stress in reinf.) from N, As = 1516 mm²

OK

OUTPUT D&D: external column As req'd = 1515mm² T&B:- PROVIDE 4H32 (ie 2H32T&B - 1609mm² T&B - 3.6% o/a - @ 192cc.) Links : - PROVIDE H8 @ 300 . Strain diagram

Stress diagram 0

0.00350

17.9 N/mm²

0.00266 435

Notes 2

-0.00031

Stresses in N/mm

-62 -0.00115

Compression +ve 0

- - - Neutral axis

25


17/07/2006 17:03:26

RCC12 Bending and Axial Force.xls This spreadsheet gives an interaction chart for moment against axial load for rectangular sections with asymmetrical reinforcement arrangements. Initially intended for beams with axial load it is also applicable to asymmetrically or symetrically reinforced columns.

MAIN! Moments are considered to be about the x-x axis. All applied loads and moments should be ultimate and positive, as positive moments induce tension in the bottom reinforcement. With asymmetrical arrangements of reinforcement the diagram indicates that negative moments are theoretically possible. After much consideration, the diagram is considered to be correct but strictly is valid only for load cases where the member is operating above 0.1fcu and with at least minimum eccentricity. These limits are shown on the graph. A reciprocal diagram is generated automatically when top and bottom steels are reversed in the input.

Calcs! Calcs! Shows the derivation of the chart where moment capacity is calculated at intervals of neutral axis depth from n.a. depth for N = 0 to n.a. depth for N = Nbal , then in intervals from n.a. depth for N = Nbal to n.a. depth for N = Nuz. This sheet shows workings and is not necessarily intended for printing out other than for checking purposes.

Notes! This sheet gives disclaimers and revision history.

26


17/07/2006 17:03:30

RCC12 Bending and Axial Force.xls RCC12 Bending and Axial Force/ MAIN!

Project


Client Location

Advisory Group Beam C1-2, Level 3

Made by

BENDING AND AXIAL FORCE to BS 8110:2005

Checked

Revision

chg

-

The Concrete Centre Date

RMW

Originated from RCC12.xls v 3.0 on CD

© 2006 TCC

Page

11-Apr-06

27 25 Job No

R68

MATERIALS fcu fy

γs γc

35 N/mm² 500 N/mm²

SECTION h b

1.15 1.50

COVERS (to main steel) TOP 30 mm BOTTOM 30 mm SIDES 30 mm

450 mm 300 mm

REINFORCEMENT TOP BOTTOM

Bar Ø

No

Area

%

Space

25 32

2 3

982 2413

0.727 1.787

190.0 72.0

. .

M:N interaction chart for 450 x 300 section, C35 concrete.

4000

AXIAL COMPRESSION, N kN

3000

2400 2000 M min

1000

1000 0.1Acfcu

0

-1000

-2000 -200

-100

0

100

200

300

400

500

MOMENT, Mxx kNm LOADCASES

(ULS)

CASE

N

Mxx

CASE

N

Mxx

1

2400

100

2

1000

300

27


17/07/2006 17:03:31

RCC13 Punching Shear.xls This spreadsheet designs punching shear links. Essentially it is intended to be used with simple rectangular flat slabs to BS 8110 i.e. with RCC33.xls. Equally it can be used in conjunction with RCC81.xls or to check wide beams in, say, troughed slabs. The spreadsheet is presented as four pairs of sheets dealing with internal, edge, (external) corner and re-entrant corners. It should be remembered that in slabs these traditional links are time-consuming to fix on site – proprietary systems are generally much quicker to fix on site and this can far outweigh material costs.

INTERNAL! (Similarly EDGE!, CORNER! and REENTRANT!) These sheets constitute the input and main output. Input is fairly self-evident but, as ever, care must be exercised in ensuring correct values are used. The top diagram acts as a legend and the chart at the bottom of the sheet shows the column, any holes and link perimeters, and should act both as a check for input and help explain output. The x-x axis is across the page. To the right is a combo-box that allows either: ■ Input of both Vt (design shear transferred to column) and

Veff (design effective shear including allowance for moment transfer) is required. These figures should be available from sub-frame analysis e.g. output from RCC33.xls/ACTIONS! B55:J62 under Reactions. A value of Veff, computed from Vt and the factor according to location of the column (see BS 8110: Part 1, Clause 3.7.6) is suggested under Operating Instructions: in general this figure may be regarded as a maximum: calculating effective shear from moment transfer generally results in lower figures.

Reinforcement can be increased both ways to increase vc to overcome problems with rules regarding v > 2vc (see Clause 3.7.7.5). In the case of edge columns, a factor of 1.25 can be used if bending is about an axis parallel to edge and 1.4 if perpendicular (Clause 3.7.6.3). A worse case should be taken.

Int Dets! (Edge Dets!, Corner Dets! and Re-ent Dets! similar) These sheets show design calculations, determination of critical perimeters, enclosed areas and link requirements complete with references to BS 8110. They are not necessarily intended for printing out other than for checking purposes. The area load is deducted from Vt , before Vt is enhanced. These sheets use the relationship Veff /Vt to calculate shear at successive perimeters. Deductions for holes in the calculation of shear perimeters are calculated by finding the angle defined by the extremities of the hole. The projection of this angle is deducted from the appropriate perimeter.


or ■ Input of Vt alone. Veff defaults to the values given in BS 8110:

Part 1, Clause 3.7.6 The areas of steel in the two directions should be averages in each direction, i.e., ensure that it reflects the actual reinforcement in the sides of the perimeter, an average of column strips and middle strips as appropriate. Except when checking column face shear, holes under half the slab depth or 1/4 column side are ignored as in the second paragraph of BS 8110: Part 1, Clause 3.7.7.7. Multiple holes should be aggregated pro-rata as if they were one hole at one position. The shear at 1.5 d from the face of the column and at the first perimeter requiring no reinforcement is shown under Results. 28


17/07/2006 17:03:35

RCC13 Punching Shear.xls RCC13 Punching Shear/ INTERNAL!

Project


Client

Advisory Group

Location

ECBP Typical Floor Column B3


rmw INTERNAL Checked

PUNCHING SHEAR to BS8110:2005 Originated from RCC13.xls v3.0 on CD

© 2006 TCC

COLUMN

2 fcu N/mm 2 fyv N/mm link Ø mm steel class A DIMENSIONS A mm B mm G mm

40 500 10

STATUS VALID DESIGN

300 500 125

E F H

mm

LOADING

2954 16.10

0

0

3397.1

mm

484 455.5 469.75

MATERIALS

Vt ult UDL

SLAB

h

kN kN/m2 mm

525

dx dy ave d

RESULTS Veff = 3397.1 kN 2 At col. face, v max = 4.899 N/mm

PROVIDE LINKS (single leg) Perimeter 1 Perimeter 2 Perimeter 3 0 0 0 0 0 0

15 H10 @ 240 21 H10 @ 295 29 H10 @ 300 0 0 0 0 0 0

mm mm

mm mm

Date

Page


chg

29 31 Job No

-

R68

Legend

150 -50 100

vc = At 1.5d perimeter, v = At 3d perimeter, v =

2 Asx mm /m 5362 2 Asy mm /m 3908 ave As % 0.983

2 0.7349 N/mm 2 1.0886 N/mm 2 0.5896 N/mm

(Table 3.8)

. 234 from col face 587 from col face 940 from col face 0 0 0 0 0 0

Plan

29


17/07/2006 17:03:36

RCC13 Punching Shear/ EDGE!

Project


Client

Advisory Group

Location

Column B2


rmw EDGE Checked


2 fcu N/mm 2 fyv N/mm mm link Ø steel class A mm DIMENSIONS A mm B mm D

MATERIALS

LOADING

Vt ult UDL

kN/m

h

mm

SLAB

kN 2

40 500 8

STATUS VALID DESIGN

200 200 50

E F G H

mm

mm

-62.5 -275 150 125

0

0

1399

mm

207 187 197

223 14.40 250

dx dy ave d

PROVIDE LINKS (single leg) 6 H8 @ 220 7 H8 @ 265 0 0 0 0 0 0 0

mm mm

mm mm

Page


chg

30 32 Job No

-

R68

Legend


2


Perimeter 1 Perimeter 2 0 0 0 0 0 0 0

COLUMN

© 2006 TCC

Date

vc = 0.8032 N/mm 2 At 1.5d perimeter, v = 1.0364 N/mm 2 At 2.25d perimeter, v = 0.7813 N/mm

(Table 3.8)

. 98 from col face 246 from col face 0 0 0 0 0 0 0

Plan

30


17/07/2006 17:03:40

RCC13 Punching Shear.xls RCC13 Punching Shear/ CORNER!

Project


Client

Advisory Group

Location

Columns A1, D1, A5 & D5


rmw CORNER Checked COLUMN chg


© 2006 TCC

2 fcu N/mm fyv N/mm2 link Ø mm steel class A DIMENSIONS A mm B mm C mm D mm

40 500 8

STATUS VALID DESIGN

400 250 0 0

E F G H

mm

mm

-50 -250 100 100

LOADING

272.0 16.10

0

0

350

mm

215 195 205

MATERIALS

Vt ult UDL

SLAB

h

kN kN/m2 mm

250

dx dy ave d

Perimeter 1 Perimeter 2 Perimeter 3 Perimeter 4 Perimeter 5 0 0 0 0

6 H8 @ 140 8 H8 @ 125 5 H8 @ 275 6 H8 @ 265 7 H8 @ 265 0 0 0 0

mm

mm mm

Page


31 33 Job No

-

R68

Legend

Asx mm2/m 2010 2 Asy mm /m 2010 ave As % 0.983

vc = 0.8686 N/mm2 2 At 1.5d perimeter, v = 1.6585 N/mm 2 N/mm At 4.5d perimeter, v = 0.7741

RESULTS Veff = 340.0 kN 2 At hole face, vmax = 2.745 N/mm

PROVIDE LINKS (single leg)

mm

Date

(Table 3.8)

. 102 from col face 256 from col face 410 from col face 564 from col face 717.5 from col face 0 0 0 0

Plan

31


17/07/2006 17:03:44

RCC13 Punching Shear/ REENTRANT!

Project


Client

Advisory Group

Location

An example


rmw RE-ENTRANT Checked


CORNER

© 2006 TCC

2 fcu N/mm 2 fyv N/mm link Ø mm steel class A DIMENSIONS A mm B mm C mm D mm

40 500 10

STATUS VALID DESIGN

350 350 0 0

E F G H

mm

mm

-125 -425 250 250

LOADING

447.0 14.40

0

0

591.6

MATERIALS

Vt ult UDL

SLAB

h

kN 2 kN/m mm

250

dx dy ave d


PROVIDE LINKS (single leg) Perimeter 1 Perimeter 2 0 0 0 0 0 0 0

6 H10 @ 220 8 H10 @ 255 0 0 0 0 0 0 0

mm mm

mm mm mm

Date

Page


chg

32 34 Job No

-

R68

Legend


202 180 191

vc = At 1.5d perimeter, v = At 2.25d perimeter, v =

2 0.9841 N/mm 2 1.1738 N/mm 2 0.9209 N/mm

(Table 3.8)

. 95 from col face 239 from col face 0 0 0 0 0 0 0

Plan

32


17/07/2006 17:03:48

RCC14 Crack Widths.xls

RCC14 Crack Width.xls Crack Width! In the design of reinforced concrete structures, it is assumed that the tensile capacity of concrete does not contribute to the strength of the structure, and steel reinforcement is provided to resist the internal tensile forces that develop. Because steel reinforcement can develop the resisting tensile force only by extension (i.e. steel needs to extend to develop stress), and hence causes cracks to form in the surrounding concrete, cracks in reinforced concrete structures cannot be avoided. In day-today practical design, crack widths are controlled by limiting the maximum spacings of the tension reinforcement. However there are times when the engineer will need to carry out more rigorous analysis and calculations, e.g. in the design of water-retaining structures, and design for severe exposure where estimation/ prediction of crack width is important.

acr is the distance from the point considered to the surface of the nearest longitudinal bar. The input value is defaulted to the distance at the point on the tension face midway between two bars. However other values can be entered to suit other locations, e.g. corner bars. The default value can be reset by pressing the blue button on the right hand margin.


This spreadsheet calculates crack widths in accordance with BS 8110 and BS 8007. Crack width limits are set as: ■ BS 8110: Part 1, Clause 3.12.11.2.1 0.3 mm – In ‘normal’

reinforced concrete structures ■ BS 8007 0.2 mm – In water-retaining structures under severe

or very severe exposure ■ BS 8007 0.1 mm – In water-retaining structures with critical

aesthetic appearance In calculation of crack width, elastic theory with ‘cracked section’ is adopted. Both BS 8110: Part 2 and BS 8007 appendix B gives the crack width formula. w = 3acrεm/{1+2(acr-c)/(h-x)} In calculating crack width, w, the average strain, εm , at the level where cracking is being considered allows a stiffening effect, ε2 , of concrete between cracks where ε1 is the theoretical strain at the level considered, calculated on the assumption of a cracked section using half the concrete modulus Ec to allow for creep effects. ε2 = b(h-x)2/3EsAs(d-x) BS 8007 allows an additional enhancement factor of 1.5 in calculating e2 for structures designed with a crack width limit of 0.1 mm. The spreadsheet provides an option to adopt this enhanced factor if design crack width is limit to 0.1 mm. To choose this option, select the blue ‘check box’ on the right hand margin.

33


17/07/2006 17:03:52

RCC14 Crack Widths/ CRACK WIDTHS! Project

Client Location

Spreadsheets to BS 8110etc

The Concrete Centre

Advisory Group Grid line 1

Made by

Crack Width Calculations to BS8110: 2005/ BS8007:1987

Checked

RC

Originated from RCC14.xls v 3.0on CD

CRACK WIDTH CALCULATIONS - FLEXURE

Date

Revision

chg

© 2006 TCC

Page

11-Apr-2006

34 33 Job No

R68

-

-

INPUT 35 fcu= fy= 500 Area of reinforcement " As " = 2093 b= 1000 h= 250 d= 200 Minimum cover to tension reinforcement " CO " = 40 Maxmum bar spacing " S " = 150 Bar dia " DIA " = 20 " acr " =(((S/2)^2+(CO+DIA/2)^2)^(1/2)-DIA/2) as default or enter other value = 80.14 "acr " is distance from the point considered to the surface of the nearest longitudinal bar Applied service moment " Ms "= 69.0

N/mm2 N/mm2 mm2 mm mm mm mm mm mm mm KNm

CALCULATIONS moduli of elasticity of concrete " Ec" = (1/2)*(20+0.2*fcu) = moduli of elasticity of steel " Es " = Modular ratio " α " = (Es/Ec) = " ρ " = As/bd = 2 0.5 depth to neutral axis, "xx" = (-α.ρ +((α.ρ) + 2.α.ρ) .d =

13.5 200.0 14.81 0.010 85

KN/mm2 KN/mm2

mm

" Z " = d-(x/3) = 172 Reinforcement stress " fs " = Ms/(As*Z) = N/mm2 192 Concrete stress " fc " = (fs*As)/(0.5*b*x) = N/mm2 9.50 Strain at soffit of concrete beam/slab " ε1 " = (fs/Es)*(h-x)/(d-x) = 0.001375 Strain due to stiffening effect of concrete between cracks " ε2 " = Used ε2 = b.(h-x)2/(3.Es.As.(d-x)) for crack widths of 0.2 mm n/a ε2 = 1.5.b.(h-x)2/(3.Es.As.(d-x)) for crack widths of 0.1 mm ε2 = 0.000189 Average strain for calculation of crack width " εm "= ε1-ε2 = 0.001186 Calculated crack width, " w " = 3.acr.εm/(1+2.(acr-c)/(h-x)) CALCULATED CRACK WIDTH, 'w' =

0.19

mm

34


17/07/2006 17:03:54

RCC21 Subframe Analysis.xls

RCC21 Subframe Analysis.xls RCC21 Subframe Analysis.xls analyses sub-frames in accordance with BS 8110 using moment distribution. Inputs are required on two sheets.

MAIN! This single sheet consists of the main inputs, most of which should be self-explanatory. As in other spreadsheets, avoid pasting input from one cell to another as this may cause formatting and other errors. The dimension of the flange width, bf, is automated to be either bw + 0.07 x span for L beams or bw + 0.14 x span for T beams. Unwanted data cells are ‘greyed-out’. Supports may be specified by giving dimentions and end conditions in cells C21:J27. The use of C, K, or E in column C can alter the characteristics of a support from cantilever to knife-edge to encastre. Where supports are dimentions the remote ends of supports may be F for fixed in columns F and J; otherwise they default to pinned. Extraneous data is highlighted in red or by messages in red. Under Operating Instructions a number of checks, mainly for missing entries, are carried out and any problems are highlighted. At the bottom of the sheet a simplistic but to-scale arrangement and loading diagram is shown. This is given to aid data checking. It may prove prudent to write down expected values for bending moments at each support down before progressing to ACTIONS!

The user is required to input desired amounts of redistribution to the initial moments in line 26. Cell L14 allows three types of distribution according to the user’s preference for calculating span moments (see Redistribution). Redistribution input is included close to the bending moment diagrams in order to give the user control rather than relying on blanket redistribution. The sheet also tabulates elastic and redistributed ultimate shears and column moments according to the various load cases.

Analysis! This sheet details the moment distribution analysis carried out but is not necessarily intended for printing out other than for checking purposes

Graf! This sheet comprises data for graphs used on other sheets, particularly in ACTIONS! It is not necessarily intended for printing out other than for checking purposes


Also, under Operating instructions, the user should input the type of redistribution required as explained more fully under Redistribution. ■ 0 means full redistribution. ■ 1 limits alternate span upward redistribution to the

percentage specified. ■ 2 means no span moment redistribution.

UDLs are input as line loads e.g. 4kN/m2 for a 5.0 m wide bay would be input as 20 kN/m. Point loads should be at least 0.001m from supports. Ultimate and characteristic support reactions are given at the bottom of the sheet

ACTIONS! This sheet includes charts showing the elastic bending moment diagram, redistributed moment envelope, elastic shear forces and envelope of redistributed shear forces. These diagrams are based on data from the analysis undertaken in Analysis! at 1/20 span points. Maximum span and support moments are given. 35


17/07/2006 17:04:04

RCC21 Subframe Analysis/ MAIN!

Project


Client

Advisory Group

Location

Level 2, Beam on line 6


from B to E

RMW


LOCATION

Checked

Originated from RCC21.xls

v3.0 on CD

Supports from grid

B

to grid

Date

Page

Revision

Job No

-

chg

© 2006 TCC

36 35

11-Apr-2006

R68

E


L (m)

H (mm)

bw (mm)

hf (mm)

Type

7.000 12.000 12.000 6.000

600 600 600 600

375 375 375 375

150 150 150 150

T T T T

LOADING PATTERN

bf (mm)

1355 2055 2055 1215 0 0

DEAD IMPOSED

min

max

1 0

1.4 1.6

SUPPORTS ABOVE (m)

H (mm)

B (mm)

End Cond

H (mm)

B (mm)

End Cond

2.95 3.00 0.00 K 4.00

400 400

300 300

F P

3.10 3.10 3.10

400 300 400

300 300 300

P P P

400

300

P

3.10

300

300

P

UDLs (kN/m)

PLs (kN)

Dead Load

Imposed Load

Position from left

Loaded Length

17.50 24 5

5.60 6 18

~~~~~ 2.000 4.500

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Support 7 LOADING Span 1 UDL PL 1 PL 2 Part UDL Span 2 UDL PL 1 PL 2 Part UDL Span 3 UDL PL 1 PL 2 Part UDL

BELOW (m)

Position (m)

Dead Load

Imposed Load

Position from left

Loaded Length

32.20

12.50

~~~~~

~~~~~ ~~~~~ ~~~~~

32.20

12.50

~~~~~

25

25

5.000

~~~~~ ~~~~~ ~~~~~

24.42

8.65

~~~~~

7.5

4.5

1.500

~~~~~ ~~~~~ ~~~~~ 2.400

Span 4 UDL PL 1 PL 2 Part UDL Span 5 UDL PL 1 PL 2 Part UDL Span 6 UDL PL 1 PL 2 Part UDL

LOADING DIAGRAM

B

E

REACTIONS (kN) SUPPORT

ALL SPANS LOADED ODD SPANS LOADED EVEN SPANS LOADED Characteristic Dead Characteristic Imposed

1

2

3

4

5

153.5 177.7 27.2 72.8 47.4

724.8 465.9 621.0 354.6 142.7

778.3 568.4 636.4 386.7 148.1

478.4 415.9 271.0 237.2 91.4

75.0 -8.2 116.7 30.5 46.2

36


17/07/2006 17:04:06

RCC21 Subframe Analysis.xls RCC21 Subframe Analysis/ ACTIONS! The Concrete Centre

Project


Client

Advisory Group

Location

Level 2, Beam on line 6, from B to E

Made by

SUBFRAME ANALYSIS to BS8110:2005 Originated from RCC21.xls v3.0 on CD

Date

RMW Checked

Page

11-Apr-06 Revision

chg

© 2006 TCC

37 36 Job No

-

R68


1000

800

800

600

600 400

400

200

200

0

0

-200

-200

-400

-400

-600

-600

-800

-800

-1000 0

10

B

20

30

0

E

Elastic Moments SUPPORT No

40

10

B

20

1

2

3

4

5

95.3 90.5 0.950

743.3 557.5 0.750

868.6 694.9 0.800

427.6 406.2 0.950

34.3 32.6 0.950

Redistribution

5.0%

25.0%

20.0%

5.0%

5.0%

SPAN No

1

2

3

4

185.0 152.1 0.822

633.1 746.8 1.180

400.1 373.5 0.934

121.4 118.8 0.979

~ ~ ~

40

E



Elastic M Redistributed M ßb SHEAR FORCE DIAGRAMS (kN)

30

~ ~ ~

kNm kNm ~

~ ~ ~

Based on support moments of min(ßbM, Malt/ßb)

500

500 400 300 200 100 0 -100 -200 -300 -400 -500

400 300 200 100 0 -100 -200 -300 -400 -500

0

10

20

30

Elastic Shears

B

SPAN No


40

E

10

20


B

1

191.0 177.7

SPAN No

0

2

40

E

3

312.6 302.0

435.6 422.8

432.2 433.2

356.9 345.1

282.0 273.7

4

Elastic V

203.4

118.4

~

~

~

~

Redistributed V

204.7

116.7

~

~

~

~

1

2

3

4

21.0 15.0 55.6 39.7 -22.7 -16.2

80.7 32.9 0.7 0.3 116.5 47.6

COLUMN MOMENTS (kNm) ALL SPANS Above LOADED Below ODD SPANS Above LOADED Below EVEN SPANS Above LOADED Below

30

-40.2 51.6 -108.0

5

-4.1 -2.2 17.5 9.5 -22.2 -12.1

37


17/07/2006 17:04:10

RCC31 One-way Solid Slabs (A & D).xls This spreadsheet analyses and designs (A & D: Analysis and design) up to six spans of one-way solid slabs to BS 8110 using continuous beam analysis. There is user input on each of the first four sheets and choice of reinforcement for each span is implicit.

MAIN! This single sheet consists of the main inputs, most of which should be self-explanatory. The number of spans is altered by entering or deleting data in cells C16:C21 under L (m). Unwanted data cells are ‘greyedout’. The use of C, K or E can alter the characteristics of the end supports from cantilever to knife-edge to encastre. Extraneous data is highlighted in red or by messages in red. Under Operating Instructions a number of checks are carried out and problems are highlighted. For the purposes of defining load, the section is assumed to be 1.00 m wide. At the bottom of the sheet a simplistic loading diagram is given to aid data checking. Great care should be taken to ensure this sheet is completed correctly for the case in hand. It may prove prudent to write down expected values of bending moments at each support down before progressing to ACTIONS!

With regard to deflection, the area of steel required, As mm2 / m, shown under heading Design, may have been automatically increased in order to reduce service stress, fs, and increase modification factors to satisfy deflection criteria. The percentage increase, if any, is shown under Deflection. With respect to cantilevers, neither compression steel enhancement nor consideration of rotation at supports is included. Hogging moments at 1/4 span are checked and used in the determination of top steel in spans. Careful examination of the Bending Moment Diagram and Graf! should help to determine whether any curtailment of this reinforcement is warranted. To avoid undue sensitivity, especially with regard to deflection, reinforcement may be over-stressed by up to 2.5%.

WEIGHT! Weight! gives an estimate of the amount of reinforcement required in one direction of the slab per bay and per cubic metre. Bay and support widths are required as input.

Support reactions are given at the bottom of the sheet.

Simplified curtailment rules, as defined in BS 8110 Clause 3.12, are used to determine lengths of bars. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation, etc, etc. They do allow for distribution steel but not for reinforcement in supporting beams or for mesh.

ACTIONS!

Analysis!

This sheet shows bending moment and shear force diagrams from the analysis undertaken in Analysis! The user is required to input the desired amount of redistribution to the initial moments in line 25. Cell J14 allows three types of distribution according to the user’s preferences. Requesting redistribution at a cantilever produces a warning message in the remarks column.

This sheet details the moment distribution analysis carried out but is not necessarily intended for printing out other than for checking purposes.

SPANS! In SPANS! the user is required to choose top, bottom and link reinforcement for each span. The amounts of bending and shear reinforcement required and checks are derived from detailed calculations in Bar!Unwanted cells are ‘greyed-out’. Unless overwritten, reinforcement diameter specified for a support carries through both sides of the support, i.e. the diameter specified for the right hand support of a span carries over to the left hand support of the next span. It may be possible to obtain different numbers of bars each side of the support due to differences in moment either side of the support, differences in depth or to comply with minimum 50% span steel; practicality should dictate that the maximum number of bars at each support should be used.

Bar! This sheet shows design calculations, complete with references to BS 8110. It is not necessarily intended for printing out other than for checking purposes. In many instance service stress, fs, has been set to 1.0 or 0.0001 N/mm2 to avoid problems with division by zero.

Graf! This sheet comprises data for graphs used on other sheets, particularly in ACTIONS! It is not necessarily intended for printing out other than for checking purposes.


38


17/07/2006 17:04:12

RCC31 One-way Solid Slabs (A & D).xls RCC31 One-way Solid Slabs (A & D)/ MAIN!

Project


Client Location

Advisory Group 8th Floor slab


from A to G

rmw

ONE-WAY SOLID RC SLAB DESIGN to BS 8110:2005 c/w ANALYSIS Originated from RCC31.xls

LOCATION

Supports from grid

v3.0 on CD

A

© 2006 TCC

Date

Page

11-Apr-06

Checked

Revision

chg

-

39 38 Job No

R68

to grid G

MATERIALS

COVERS

fcu fy fyv steel class SPANS SPAN 1 SPAN 2 SPAN 3 SPAN 4

35 500 500 A

N/mm² N/mm² N/mm²

L (m)

H (mm)

8.000 7.200 7.200 4.500

350 250 250 250

h agg γs γc

steel

SPAN 6

IMPOSED

min

max

1

1.4 1.6

PL 1

mm mm

Dead Load

Imposed Load

Position from left

9.70 35.00

5.00

~~~~ 1.000

Support No

Type

1

K

5 K K(nife), C(antilever) or E(ncastre)

LOADING

UDLs (kN/m²) PLs (kN/m) Position (m)

UDL

25 25

concrete

LOADING PATTERN DEAD

Span 1

Top cover Btm cover

mm

SUPPORTS

SPAN 5

LOADING

20 1.15 1.50

Span 4 UDL

Dead Load

Imposed Load

Position from left

6.00

1.50

~~~~

PL 1

PL 2

PL 2

Span 2

Span 5

6.00

UDL

1.50

~~~~

~~~~

UDL

PL 1

PL 1

PL 2

PL 2

Span 3

Span 6

8.50

UDL

5.00

~~~~

UDL

PL 1

PL 1

PL 2

PL 2

LOADING DIAGRAM

A

G

REACTIONS (kN/m) SUPPORT Characteristic Dead Max Imposed Min Imposed MAX ULTIMATE

1

2

3

4

5

63.80 19.00 -0.72 120.17

72.78 27.17 6.45 141.99

49.39 22.79 5.46 108.37

51.45 25.77 3.07 110.70

6.59 3.28 -3.75 16.35 39


17/07/2006 17:04:13

RCC31 One-way Solid Slabs (A & D)/ ACTIONS!

Project


Client Location

Advisory Group 8th Floor slab, from A to G

Made by

ONE-WAY SOLID RC SLAB DESIGN to BS 8110:2005 c/w ANALYSIS

Checked



rmw

Revision

chg

© 2006 TCC

Page

39 40

11-Apr-06

Job No

-

R68

BENDING MOMENT DIAGRAMS (kNm/m) 100

100

50

50

0

0

-50

-50

-100

-100

-150

-150

-200

-200 0

5

A

10

15

20

25

G

Elastic Moments

SUPPORT No

1


1.000

Redistribution SPAN No Elastic M Redistributed M ßb

0

30

5

A

10

15

20

25

G


2

3

4

85.0 72.2 0.850 15.0%

60.4 60.4 1.000

71.2 64.1 0.900 10.0%

30

5

1

2

3

4

168.7 166.4 0.986

19.6 15.6 0.798

69.3 72.1 1.040

13.5 12.4 0.917

1.000

~ ~ ~

~ ~ ~

~ ~ ~

~ ~ ~

SHEAR FORCE DIAGRAMS (kN/m) 150

150

100

100

50

50

0

0

-50

-50

-100

-100

-150

-150 0

5

A SPAN No Elastic V Redistributed V SPAN No Elastic V Redistributed V

10

15

20

Elastic Shears

25

30

G

1

120.9 120.2

0

A

5

10

15

20


2

25

30

G

3

103.1 101.5

42.3 43.6

35.5 37.2

70.1 71.1

74.4 73.6

17.1 16.4

~ ~

~ ~

~ ~

~ ~

4

40.1 38.5

40


17/07/2006 17:04:16

RCC31 One-way Solid Slabs (A & D).xls RCC31 One-way Solid Slabs (A & D)/ SPANS! Project


Client

Advisory Group

Location

8th Floor slab, from A to G


ONE-WAY SOLID RC SLAB DESIGN to BS 8110:2005 c/w ANALYSIS Originated from RCC31.xls v3.0 on CD

Checked

LEFT

ACTIONS

DESIGN

kNm/m kN/m mm mm²/m mm²/m

H

TOP STEEL

As prov

mm²/m

As' prov SHEAR v vc

mm²/m

DEFLECTION & CHECKS

N/mm2 N/mm2

L/d % As d'/x

Av M ßb V d As As' As prov

As' prov SHEAR v vc DEFLECTION & CHECKS

L/d % As d'/x max S

H

As prov

20

H

As prov @ 175

1795

H

As' prov

Links not required Allowed 26.178 ok

R68

7000 72.2 0.85 101.47 317.0 552 0 16 16

(As increased by 32.8%) ok ok

ok

ok

ok

LEFT

CENTRE

RIGHT

16

335 0.201 0.613 32.877

7200 60.4 1.00 37.24 219.0 668 0

15.6 0.80

As top @ 225

H

As' prov @ 600

H

As prov

219.0 325 412 10

@ 175

449 12

@ 350

574 0.320 0.424

ok ok

16

@ 350

574

ok ok

894 H

BTM STEEL

@ 200

0 72.2 0.85 43.56 217.0 807 0 H

TOP STEEL

As' @0

0

25.397

SPAN 2

DESIGN

As'

565 0.377 0.420

max S

ACTIONS

12

-

RIGHT

315.0 1287 0

@ 225

41 40 Job No

166.4 0.99

503 H

BTM STEEL

12

Revision

CENTRE

1000 0.0 1.00 120.17 319.0 455 0

mm

Page

11-Apr-06

chg

© 2006 TCC

SPAN 1 Av M ßb V d As As'

Date

rmw

H

As prov @ 300

377

H

As' prov

12

@ 150

754 12

@ 300

377 0.170 0.576


ok

ok

ok

ok

ok

ok

ok

ok

ok

41


17/07/2006 17:04:19

RCC31 One-way Solid Slabs (A & D)/ SPANS! Project


Client

Advisory Group

Location



ONE-WAY SOLID RC SLAB DESIGN to BS 8110:2005 c/w ANALYSIS Originated from RCC31.xls v3.0 on CD

DESIGN

As prov As' prov SHEAR v vc

& CHECKS

L/d % As d'/x


As' prov SHEAR v vc DEFLECTION & CHECKS

L/d % As d'/x max S

As' @0

H

12

H

As prov @ 100

1131

H

As' prov


R68

7200 64.1 0.90 73.63 219.0 709 0 12 10


ok

ok

ok

LEFT

CENTRE

10

349 0.176 0.576 20.455

RIGHT

12.4 0.92

As top @ 150 @ 225

220.0 325 406

H

12

As' prov

411

H

As prov

10

@ 200

393 0.336 0.576

ok ok

12

@ 150

754

ok ok

754 H

BTM STEEL

219.0 797 0 10

As prov

0 64.1 0.90 38.55 219.0 709 0 H

TOP STEEL

@ 200

32.877

SPAN 4

DESIGN

12

-

RIGHT

0

565 0.325 0.576

max S

ACTIONS

As' @ 150

42 41 Job No

72.1 1.04

754 H

BTM STEEL

12

Revision

CENTRE

0 60.4 1.00 71.13 219.0 668 0 H

Page

Apr-2006

chg

LEFT

Av M ßb V d As As'

TOP STEEL

DEFLECTION

Checked

© 2006 TCC

SPAN 3 ACTIONS

Date

rmw

As' @ 275

H

As prov @ 225

349

H

As' prov

4500 0.0 1.00 16.35 219.0 325 0 12

@ 300

377 12

@ 300

377 0.075 0.457


ok ok

ok ok

ok ok

ok

ok

ok

42


17/07/2006 17:04:21

RCC31R Rigorous One-way Slabs.xls

RCC31R Rigorous One-way Slabs.xls This spreadsheet allows the estimation of deflections in one-way solid slabs according to BS 8110 Part 2. The spreadsheet is based on RCC31 but has an initial sheet JOBDATA! to allow input of all the variables and performance criteria required. The calculation of deflection is not carried out automatically. The user is required to press the ‘Calculate deflections’ button in column N of SPANS! (or elsewhere) when every other aspect of the design has been completed. Deflections are given as a range in a chart at the bottom of ACTIONS! They are shown as a range due to potential pattern loading. In SPANS! the worst case is compared with the specified serviceability criteria. It should be noted that the number of assumptions and uncertainties in the material and design criteria and construction process mean that deflection calculations carried out in this manner can be notoriously inaccurate (and usually over conservative) compared with actual measured deflections. For instance, a slab’s deflection is very dependent upon whether the slab has cracked in bending during construction or not. The calculated deflections might be regarded as being akin to a 95% confidence limit that they will not be exceeded in service. The spreadsheet analyses and designs up to six spans of one-way solid slabs to BS 8110 using continuous slab analysis. There is user input on each of the first four sheets and choice of reinforcement for each span is implicit. Input of spans and loads is in MAIN! User input is required for bar sizes used in SPANS!

JOBDATA! This sheet consists of the main inputs of material, loading, construction and serviceability criteria pertaining to the calculation of deflection to BS 8110 Part 2. Users are expected to use their knowledge of the project and judgement in completing this sheet. The default values given in this sheet are not unusual. For creep reference is made to Eurocode 2 Annex B.

MAIN! This single sheet consists of the main inputs of span and loads, most of which should be self-explanatory. The number of spans is altered by entering or deleting data under L (m). Unwanted data cells are ‘greyed-out’. The use of C, K or E can alter the characteristics of the end supports from cantilever to knife-edge to encastre. Extraneous data is highlighted in red or by messages in red. Under ‘Operating Instructions’ a number of checks are carried out and problems are highlighted. For the purposes of defining load, the section is assumed to be 1.00 m wide. At the bottom of the sheet a simplistic loading diagram is given to aid data checking. Great care should be taken to ensure this sheet is completed correctly for the case

in hand. It may prove prudent to write down expected values of bending moments at each support down before progressing to ACTIONS! Support reactions are given at the bottom of the sheet.

ACTIONS! This sheet shows bending moment and shear force diagrams from the analysis undertaken in Analysis! The user is required to input the desired amount of redistribution to the initial moments in line 25. Cell J14 allows three types of distribution according to the user’s preferences (see Table 1). Requesting redistribution at a cantilever produces a warning message in the remarks column. The chart at the bottom of the page shows calculated deflections at construction of partitions, and ranges for longer term deflections due to patterns of permanent and imposed loading. The worst case is taken in subsequent checks and this might be viewed as being unduly conservative.

SPANS! In SPANS! the user is required to choose top, bottom and link reinforcement for each span. The amounts of bending and shear reinforcement required and checks are derived from detailed calculations in Bar! Unwanted cells are ‘greyed-out’. Deflection calculations involve many iterative calculations, which may take some time on even the fastest of computers. Calculation of deflections is therefore controlled by clicking the ‘Calculate Deflections’ button in column N and should be undertaken once all the design is complete. Deflection results will only appear on this sheet after the ‘Calculate Deflections’ button has been used and the macro has been allowed to complete its iterations. They will disappear if relevant data (e.g. span, load) is changed. Should the span fail deflection criteria, the user has the option to increase bottom steel at cell M24 etc, and reuse the ‘Calculate Deflection’ button. Unless overwritten, reinforcement diameter specified for a support carries through both sides of the support, i.e. the diameter specified for the right hand support of a span carries over to the left hand support of the next span. It may be possible to obtain different numbers of bars each side of the support due to differences in moment at the edge of support,differences in depth or to comply with minimum 50% span steel; practicality should dictate that the greater number should be used. Hogging moments at 1/4 span are checked and used in the determination of top steel in spans. Careful examination of the 43


17/07/2006 17:04:24

Bending Moment Diagram and Graf! should help to determine whether any curtailment of this reinforcement is warranted.

WEIGHT! Weight! gives an estimate of the amount of reinforcement required in one direction of the slab per bay and per cubic metre. Bay and support widths and distribution steel diameters are required as input. Simplified curtailment rules, as defined in BS 8110 Part 1, Clause 3.12, are used to determine lengths of bars. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation, etc. They do not allow for reinforcement in supporting beams or for mesh.

Uls! This sheet details the moment distribution analysis carried out at the ultimate limit state but is not necessarily intended for printing out other than for checking purposes.

Def! This sheet calculates deflections at 1/20th points for each span and for each load condition. For each point and condition it considers moment - As, As’, d, d’, inertia - I, cracked neutral axis depth - x, cracked inertia – I, uncracked moment capacity – Mcr, z, final x, concrete stresses – fc, moment of resistance – MOR, curvature -1/r, load, slope and curvature to calculate deflection. The sheet is rather large and is not necessarily intended for printing out other than for checking purposes.



Sls! This sheet details the analysis carried out at the serviceability limit state at 1/20th points along each span. The results are used in Def!. This sheet is not necessarily intended for printing out other than for checking purposes.

Bar! This sheet shows design calculations, complete with references to BS 8110. It is not necessarily intended for printing out other than for checking purposes. In many instances, service stress, fs, has been set to 1.0 or 0.0001 N/mm2 to avoid problems with division by zero.

44


17/07/2006 17:04:25

RCC31R Rigorous One-way Slabs.xls RCC31R Rigorous One-way Slabs/ JOBDATA!

Project


Client

Advisory Group

Location

8th Floor slab


from A to G

rmw

RIGOROUS ONE-WAY SOLID RC SLAB DESIGN to BS 8110:2005 Originated from RCC31R.xls v3.0 on CD

LOCATION

Supports from grid

45 38

Revision

chg

-

Job No

R68

to grid G

MATERIALS

fcu fy fyv steel class

Page

11-Apr-06

Checked

© 2006 TCC

A

Date

COVERS

30 500 500 A


h agg γs γc

20 1.15 1.50

mm steel concrete

Maximum permanent ∆ = L / Maximum imposed ∆ = L / Max ∆ affecting partitions/walls = L / Maximum precamber = Permanent portion of imposed loading = Design crack width, Wk =

SERVICEABILITY CRITERIA

Top cover Btm cover Concrete density 250 500 350 50% 25% 0.3

25 25 24

mm mm kN/m³ 3.3.3 (Pt 2)

or 20 mm of permanent ∆ mm

2.2.3.4.2

CREEP COEFFICIENTS (to EN 1992-1)

RH Cement

50 N

% relative humidity Type (S, N, R or RS)

AMBIENT TEMPERATURES ºC

32 30.16

Loading

At age

kN/m²

Days

5.40 1.00 1.50 0.63 1.88 10.40

7 90 100 90 ∞

N/mm²

Table 3.1

kN/mm²

& Annex A

from 0 to 7 days

from 7 to 100 days

from 100 days on

20

20

20

At 70 years

LOADING SEQUENCE - Span 1

Self weight Partitions/walls Other dead loads Permanent imposed Variable load Composite

fcm = Ecm =

Ø0

Et

At 70 years Ø0

kN/mm²

3.44 2.11 2.07 2.11

6.80 9.68 9.82 9.68

2.94

7.65

Permanent

Et

At 90 days Ø (t,t0)

kN/mm²

3.44 2.11 2.07 2.11 0 2.41

6.80 9.68 9.82 9.68 30.16 8.84

Et kN/mm²

1.84 0 1.55

10.64 30.16 11.83

Total load

45


17/07/2006 17:04:26

RCC31R Rigorous One-way Slabs/ MAIN!

Project


Client

Advisory Group

Location

8th Floor slab


from A to G

rmw

RIGOROUS ONE-WAY SOLID RC SLAB DESIGN to BS 8110:2005 Originated from RCC31R.xls

SPANS SPAN 1 SPAN 2 SPAN 3

L (m)

H (mm)

6.000 6.000 6.000

225 225 225

v3.0 on CD

LOADING PATTERN

SPAN 5

DEAD

SPAN 6

IMPOSED

min

max

1

1.4 1.6

UDL

Checked

Revision

chg

-

Support No

Type

1

K K

46 38 Job No

R68

Dead Load

Imposed Load

Position from left

6.90

3.50

~~~~

4

K(nife), C(antilever) or E(ncastre)

LOADING


Span 1

Page

11-Apr-06

SUPPORTS

SPAN 4

LOADING

© 2006 TCC

Date

Span 4

Dead Load

Imposed Load

~~~~

UDL

PL 1

Position from left

PL 1

PL 2

PL 2

Span 2

Span 5

6.90

UDL

3.50

~~~~

~~~~

UDL

PL 1

PL 1

PL 2

PL 2

Span 3

Span 6

6.90

UDL

3.50

~~~~

UDL

PL 1

PL 1

PL 2

PL 2

LOADING DIAGRAM

A

G


1

2

3

4

16.56 9.45 -1.05 38.14

45.54 23.10 11.55 99.34

45.54 23.10 11.55 99.34

16.56 9.45 -1.05 38.14

46


17/07/2006 17:04:29

RCC31R Rigorous One-way Slabs.xls RCC31R Rigorous One-way Slabs/ ACTIONS!

Project


Client Location


Made by

RIGOROUS ONE-WAY SOLID RC SLAB DESIGN to BS 8110:2005

Checked

Originated from RCC31R.xls v3.0 on CD

BENDING MOMENT DIAGRAMS (kNm/m)


rmw

Revision

chg

© 2006 TCC

Page

47 39

11-Apr-06

Job No

-

Elastic

R68 Redistributed

80 60 40 20 0 -20 -40 -60

80 60 40 20 0 -20 -40 -60 0

2

4

6

8

10

12

14

16

A SUPPORT No

Elastic M Redistributed M ßb Redistribution SPAN No


18

1 0.0 0.0 1.000

2 54.9 46.7 0.850 15.0%

G 3 54.9 46.7 0.850 15.0%

1 50.2 47.7 0.950

2 28.8 22.8 0.792

3 50.2 47.7 0.950

SHEAR FORCE DIAGRAMS (kN/m)

0

20

2

4

6

8

10

12

A 4 0.0 0.0 1.000

~ ~ ~

~ ~ ~

~ ~ ~

~ ~ ~

~ ~ ~

14

16

18

20

G ~ ~ ~

Redistributed

Elastic 60

80 60 40 20 0 -20 -40 -60 -80

40 20 0 -20 -40 -60 0

2

4

6

8

10

12

14

16

18

20

0

G

A 1

SPAN No


2

4

6

8

10

12

14

16

A

18

20

G

2

3

39.1 38.1

54.9 53.6

45.8 45.8

45.8 45.8

54.9 53.6

39.1 38.1

~ ~

~ ~

~ ~

~ ~

~ ~

~ ~

#DIV/0!

#DIV/0!

#DIV/0!

SPAN No


DEFLECTIONS (mm) Precamber not included

.

10 0 -10 -20 -30 -40

SPAN No

Before partitions Permanent

1 8.8 22.4

2 0.1 2.8

3 8.8 22.4

mm mm

47


17/07/2006 17:04:32

RCC31R Rigorous One-way Slabs/ SPANS! Project


Client

Advisory Group

Location




Checked

LEFT

ACTIONS

DESIGN


H

TOP STEEL

As prov

mm²/m

As' prov SHEAR v vc

mm²/m

As top @ 250

10

As' prov @ 250

314 0.196 0.437

N/mm2 N/mm2

H H

As prov

As' @ 250

314 12

@ 175

646

LEFT

ACTIONS

DESIGN

As prov As' prov SHEAR v vc DEFLECTIONS mm CHECKS

As top @ 125

10

H

As' prov @ 250

314 0.235 0.551

H

As prov

ok

0.22

@ 250

H

As prov @ 350

323

ok

10

@ 250

314 0.275 0.551 5 0%

0.22

RIGHT

H

As' prov

Links not required Permanent = 2.77 < 24.00 Imposed = 7.93 < 12.00 Affecting partitions = 2.62 < 17.14 ok % As ok ok d'/x ok ok

Crack width

@ 125

6000 46.7 0.85 45.78 195.0 580 0

314 12

10

628

ok

194.0 293 293 10

6000 46.7 0.85 53.56 195.0 580 0

ok ok

22.8 0.79

628 H

BTM STEEL

10

R68

Precamber (mm) = Increase btm As by

CENTRE

0 46.7 0.85 45.78 195.0 580 0 H

TOP STEEL

H

As' prov

Links not required Permanent = 17.43 < 24.00 Imposed = 10.32 < 12.00 Affecting partitions = 13.67 < 17.14 ok CHECKS % As ok ok d'/x ok ok Crack width ok 0.00 ok 0.20

Av M ßb V d As As'

H

As prov

DEFLECTIONS mm

SPAN 2

-

RIGHT

194.0 595 293 10

48 40 Job No

47.7 0.95

314 H

BTM STEEL

10

Revision

CENTRE

0 0.0 1.00 38.14 195.0 293 0

mm

Page

11-Apr-06

chg

© 2006 TCC

SPAN 1 Av M ßb V d As As'

Date

rmw

0.15

10

@ 125

628 10

@ 250

314 0.235 0.551 0 0%

Precamber (mm) = Increase btm As by ok ok ok

0.22

48


17/07/2006 17:04:34

RCC31R Rigorous One-way Slabs.xls RCC31R Rigorous One-way Slabs/ SPANS! Project


Client

Advisory Group

Location




Checked

LEFT

DESIGN


As top @ 300

As' prov SHEAR v vc

10

H

As' prov @ 250

314 0.279 0.568

H

As prov

As' @ 250

314 12

@ 175

646

LEFT

ACTIONS

DESIGN

As prov As' prov SHEAR v vc DEFLECTIONS mm CHECKS

As top #DIV/0!

10

H

As' prov @ 450

175 #VALUE! #NUM! #VALUE!

H

As prov

#DIV/0!

@ 250

452

ok

H

@ 250

5 0%

0.00

H

10

@ 175

449 10

175 #VALUE! #NUM! #VALUE! #VALUE! Precamber (mm) = Increase btm As by

#DIV/0! > 4% ok #DIV/0!

10

314 0.196 0.437

@ 450

As' prov

#VALUE!

#DIV/0!

@ 250

ok ok

As prov

#VALUE!

Permanent = #DIV/0! Imposed = #DIV/0! Affecting partitions = #DIV/0! % As #DIV/0! d'/x ok

Crack width

@ 175

449 12

10

314

0 0.0 0.00 #VALUE! -30.0 413 As' -196

-31.0 427 413 10

6000 0.0 1.00 38.14 195.0 293 0

RIGHT

0.0 0.00

#DIV/0! H

BTM STEEL

10

R68


CENTRE

0 0.0 1.00 #VALUE! -30.0 0 0 H

TOP STEEL

H

As' prov

Links not required Permanent = 17.42 < 24.00 Imposed = 10.33 < 12.00 Affecting partitions = 13.66 < 17.14 ok CHECKS % As ok ok d'/x ok ok Crack width ok 0.28 ok 0.20

Av M ßb V d As As'

H

As prov

DEFLECTIONS mm

SPAN 4

-

RIGHT

194.0 595 293 10

49 41 Job No

47.7 0.95

670 H

BTM STEEL

16

Revision

CENTRE

0 46.7 0.85 53.56 192.0 589 0 H

TOP STEEL

Page

Apr-2006

chg

© 2006 TCC

SPAN 3 ACTIONS

Date

rmw

5 0%

> 4% FAILS

#DIV/0!

#DIV/0!

#DIV/0!

49


17/07/2006 17:04:37

RCC32 Ribbed Slabs (A & D).xls Using continuous beam analysis, this spreadsheet analyses and designs up to six spans of ribbed slab to BS 8110. There is user input on each of the first three sheets and choice of reinforcement for each span is implicit.

Practicality should dictate that the greater number of bars are used for detailing. Hogging moments at 1/4 span positions within a span are checked and are used in the determination of top steel in spans.

MAIN!

WEIGHT!

This single sheet consists of the main inputs which should be self-explanatory. The number of spans is altered by entering or deleting data under L(m). Unwanted data cells are ‘greyed-out’.

WEIGHT! Gives an estimate of the amount of reinforcement required in one direction of the slab per rib and per square metre. Simplified curtailment rules, as defined in BS 8110: Part 1, Clause 3.12, are used in the determination of lengths of bars. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation, etc, etc. They do not allow for reinforcement in supporting beams or for mesh.

The use of C, K or F can alter the characteristics of the end supports from cantilever to knife-edge to fixed. Extraneous data is highlighted in red or by messages in red. Under Operating Instructions a number of checks are carried out and any problems are highlighted. For the purposes of defining load the section under consideration is assumed to be 1.00m wide. It will be seen from Bar! that moments per metre are converted to moments per rib, and calculations of reinforcement areas required etc., are based on moments and shear per rib. Great care should be taken to ensure this sheet is completed correctly for the case in hand. It may prove prudent to write expected values of bending moments at each support down before progressing to ACTIONS! Support reactions are given the bottom of the sheet

ACTIONS! This sheet shows bending moment and shear force diagrams from the analysis undertaken in Analysis! The user is required to input desired amount of redistribution to the initial moments in line 26. Cell L14 allows three types of distribution according to the user’s preferences. See Redistribution (page XX).

SPANS! In SPANS! the user is required to choose top, bottom and link reinforcement for each span. The amounts of bending and shear reinforcement required and checks are derived from detailed calculations in Bar!Unwanted cells are ‘greyed-out’.

Analysis! This sheet details the moment distribution analysis carried out. It is not necessarily intended for printing out, other than for checking purposes.

Bar! This sheet shows design calculations, complete with references to BS 8110. It is not necessarily intended for printing out other than for checking purposes. In spans, service stress, fs, may be reduced to satisfy deflection criteria. In many instances, minima of 1.0 or 0.0001 have been used to avoid problems with division by zero.



The reinforcement diameter specified for a support carries through both sides of the support, i.e. the diameter specified for the right hand support of a span carries over to the left hand support of the next span. It should be noted that hogging moment is checked both at the centre of support (solid section) and the solid/ rib intersection (ribbed section). As the moments at the solid/ rib intersection each side of the support may differ, it may be possible to obtain a design giving different numbers of bars each side of the support. 50


17/07/2006 17:04:40

RCC32 Ribbed Slabs (A & D).xls RCC32 Ribbed Slabs (A & D)/ MAIN!

Project


The Concrete Centre

Client Advisory Group Location 3rd Floor slab from 1 to 5a RIBBED SLABS to BS 8110:2005 (Analysis & Design) Originated from RCC32.xls

LOCATION

v3.0 on CD

Supports from grid

MATERIALS fcu 35 fy 500 fyv 500 steel class Density 23.6

1

h agg γm γm


Checked

chg

© 2006 TCC

to grid

5a

20 1.15 1.50

mm steel concrete

(Normal weight concrete)

kN/m³

H (mm)

Left

Right

2.000 7.000 7.500

275 275 275

450 1100 1100

1100 1100 450

Date

Page

51 43

11-Apr-06 Revision

Job No

-

R68

COVERS (to links, or if no links, to reinf) Top cover 20 mm Btm cover 20 mm Side cover 20 mm RIBS slab depth, hf 100 mm

Solid (mm) L (m)

Rib width Centres 1 in

150 900 10

Support No

Type

1 4

C K

mm mm

taper

SUPPORTS

K(nife), C (antilever) or E (ncastre)

LOADING UDLs (kN/m²) Span 1 UDL PL 1 PL 2 Span 2 UDL PL 1 PL 2 Span 3 UDL PL 1 PL 2

rmw

A


Made by

PLs (kN/m)

Position (m)

Self Weight

Add Dead Load

Imposed Load

Position from left

5.73 ~~~~ ~~~~ ~ 4.19 ~~~~ ~~~~ ~ 3.82 ~~~~ ~~~~

2.50

4.00

~~~~

~

~ 2.50 8.50

~ 4.00 1.00

~~~~ 1.450

~ 2.50

~ 4.00

~~~~

~

Span 4 UDL PL 1 PL 2 Span 5 UDL PL 1 PL 2 Span 6 UDL PL 1 PL 2

LOADING PATTERN DEAD IMPOSED

Self Weight

Add Dead Load

Imposed Load

Position from left

~~~~ ~~~ ~~~ ~

~

~

~~~ ~~~ ~

~

~

~

~

~~~~ ~~~~ ~~~~ min

max

1 0

1.4 1.6

LOADING DIAGRAM

1

5a


1

2

3

4

43.0 20.4 7.3 94.9

58.0 34.9 17.3 133.0

18.2 13.3 -1.6 46.6

~ ~ ~ ~

~ ~ ~ ~

~ ~ ~ ~

51


17/07/2006 17:04:41

RCC32 Ribbed Slabs (A & D)/ ACTIONS!

Project


Client

Advisory Group

Location



rmw


Checked

© 2006 TCC

Date

Page

Apr-2006 Revision

52 44 Job No

chg

-

R68

10

15

20

BENDING MOMENT DIAGRAMS (kNm/m) 120 100 80 60 40 20 0 -20 -40 -60 -80 -100

120 100 80 60 40 20 0 -20 -40 -60 -80 -100 0

5

1

10

15

5a


Elastic M Redistributed M ßb Redistribution

5

1

1

2

3

4

35.9 35.9 1.000 0.0%

97.9 83.2 0.850 15.0%

0.0 0.0 1.000

~ ~ ~

~ ~ ~

~ ~ #VALUE!

~ ~ #VALUE!

~ ~ #VALUE!

5

10

1

2

3

0.00 0.00 1.000

66.48 62.29 0.937

75.34 71.04 0.943

5a


0.0 0.0 1.000

SPAN No


0

20

kNm/m kNm/m ~


80

60

60

40

40

20

20

0

0

-20

-20

-40

-40

-60

-60

-80

-80 0

5

1

10

15

20

5a

Elastic Shears SPAN No


0

1

1


2

15

20

5a

3

0.0 0.0

35.9 35.9

58.2 59.1

66.8 67.1

70.3 68.3

47.9 46.6

~ ~

~ ~

~ ~

~ ~

~ ~

~ ~

SPAN No


52


17/07/2006 17:04:44

RCC32 Ribbed Slabs (A & D).xls RCC32 Ribbed Slabs (A & D)/ SPANS!

Project


Client

Advisory Group

Location




SPAN 1 ACTIONS

M kNm/m ßb d mm As mm² As' mm²

DESIGN

TOP STEEL

As prov

mm²

As' prov V v vc

mm²

BTM STEEL SHEAR

kN/m N/mm² N/mm²

LINKS DEFLECTION & CHECKS

LEFT 0.0 1.00 243.0 16 0 2H 12 /rib + 5 H8 between 478 1H 16 /rib 201 0.00 0.000 0.658 . L/d 8.368

Revision

chg

CENTRE 0.0 1.00 239.0 (x=26.6
201 20 314

/rib

Link Ø 6 2 H6 @ 1,200 Allowed 14.000 ok

-

ok

ok

ok ok

ok ok

ok ok

Dist to link

ok

ok

ok

LEFT 35.9 1.00 239.0 327 0 2H 20 /rib + 4 H8 between 829 2H 16 /rib 402 59.09 0.945 0.935 2 H6 @ 175 for 175 L/d 29.598

CENTRE 62.3 0.94 236.5 (x=26.3

DESIGN

TOP STEEL

As prov

mm²

As' prov V v vc

mm²

BTM STEEL kN/m N/mm² N/mm²

As T prov 2H As prov

452 25 982

/rib

Link Ø 6 2 H6 @ 1,200 Allowed 36.887 ok

53 45 Job No

R68

RIGHT 35.9 1.00 239.0 327 As' 0 2H 20 /rib + 4 H8 between As prov 829 1H 16 /rib As' prov 201 V 35.85 v 0.423 vc 0.935 .

ok

ACTIONS


Checked

© 2006 TCC

Page

11-Apr-06

% As Bar Ø & cover Bar spacing

SPAN 2

SHEAR

Date

rmw

RIGHT 83.2 0.85 239.0 759 As' 12 2H 20 /rib + 4 H8 between As prov 829 2H 16 /rib As' prov 402 V 67.12 v 1.126 vc 0.935 2 H6 @ 175 for 525 (As increased by 23.8%)


ok ok ok

ok ok ok

ok ok ok

Dist to link

ok

ok

ok

53


17/07/2006 17:04:47

RCC32 Ribbed Slabs (A & D)/ SPANS!

Project


Client

Advisory Group

Location




SPAN 3 ACTIONS


DESIGN

TOP STEEL

As prov

mm²

BTM STEEL SHEAR


As' prov V v vc

mm² kN/m N/mm² N/mm²

Date

rmw Checked

Revision

chg

© 2006 TCC

Page

Apr-2006 -

54 /46 Job No

R68

LEFT CENTRE RIGHT 83.2 @col face 71.0 0.0 0.85 0.94 1.00 239.0 236.5 (x=26.3

ok ok ok

ok ok ok

ok ok ok

Dist to link

ok

ok

ok

54


17/07/2006 17:04:49

RCC32 Ribbed Slabs (A & D).xls RCC32 Ribbed Slabs (A & D)/ WEIGHT!

Project


Client

Advisory Group

Location



rmw


Checked

© 2006 TCC

Date

Page

Apr-2006 Revision

55 /47 Job No

chg

-

R68


No

Type

Dia

Length

Unit Wt

Weight

2 5 1 2 4 4 2 4 3 2 4

H H H H H H H H H H H

12 8 16 20 8 12 20 8 12 20 8

1025 1025 2225 2250 2250 4425 3625 3625 4675 2400 2400

0.888 0.395 1.578 2.466 0.395 0.888 2.466 0.395 0.888 2.466 0.395

1.8 2.0 3.5 11.1 3.6 15.7 17.9 5.7 12.5 11.8 3.8


1 1 1 2 2 2 3

H H H H H H H

16 20 16 25 16 25 16

1150 400 3475 4750 3475 5900 1725

1.578 2.466 1.578 3.853 1.578 3.853 1.578

1.8 1.0 5.5 36.6 11.0 45.5 8.2

Span 1 Span 2 Span 3

1 9 9

H H H

6 6 6

800 800 800

0.222 0.222 0.222

0.2 1.6 1.6


BOTTOM STEEL

LINKS

SUMMARY

All figures approximate - see User Guide.

Reinforcement density (kg/m²) 12.92

Total rebar per rib, excluding mesh (kg)

202.3

55


17/07/2006 17:04:51

RCC32R Rigorous Ribbed Slabs.xls This spreadsheet analyses, designs and estimates deflections in up to six spans of continuous ribbed slab. Design is to BS 8110 Parts 1 and 2 and is analysed using continuous beam analysis,. There is user input on each of the first four sheets and choice of reinforcement for each span is implicit. The spreadsheet is based on RCC32 and similarly to RCC31R has an initial sheet JOBDATA! to allow input of all the variables and performance criteria required. The calculation of deflection is not carried out automatically. The user is required to press the ‘Calculate deflections’ button in column N of SPANS! when every other aspect of the design is complete. Deflections are given as a range in a chart at the bottom of ACTIONS! They are shown as a range due to potential pattern loading. In SPANS! the worst case is compared with the specified serviceability criteria. It should be noted that the number of assumptions and uncertainties in the material and design criteria and construction process mean that deflection calculations carried out in this manner can be notoriously inaccurate (and usually over conservative) compared to actual measured deflections. For instance, a slab’s deflection is very dependent upon whether the slab has cracked in bending during construction or not. The calculated deflections might be regarded as being akin to 95% confidence limits.


MAIN! This single sheet consists of the main inputs which should be self-explanatory. The number of spans is altered by entering or deleting data under L (m). Unwanted data cells are ‘greyedout’. The use of C, K or F can alter the characteristics of the end supports from cantilever to knife-edge to fixed. Extraneous data is highlighted in red or by messages in red. Under ‘Operating Instructions’ a number of checks are carried out and any problems are highlighted. The data under ‘Solid’ define the distances from support centrelines to the start of the ribbed cross-section. For the purposes of defining load the section under consideration is assumed to be 1.00 m wide. It will be seen from Bar! that moments per metre are converted to moments per rib, and calculations of reinforcement areas required etc., are based on moments and shear per rib. Great care should be taken to

ensure this sheet is completed correctly for the case in hand. It may prove prudent to write down expected values of bending moments at each support before progressing to ACTIONS! Combo-boxes to the right under Operating Instructions define minimum bar sizes to be used (e.g. at supports between ribs) and whether the user wants to use links or not. If links are required these may be either designed or nominal links; the centres of nominal links can be changed. Towards the bottom of the sheet a simplistic loading diagram is given to aid data checking. At the bottom of the sheet, support reactions are given.

ACTIONS! This sheet shows bending moment and shear force diagrams from the analysis undertaken in Analysis! The user is required to input desired amount of redistribution to the initial moments in line 21. Cell L14 allows three types of distribution according to the user’s preferences. See ‘Redistribution’ under ‘Assumptions made’ in Table 1. The chart at the bottom of the page shows calculated deflections at construction of partitions, and ranges for longer term deflections due to patterns of permanent and imposed loading. Deflection calculations involve many iterative calculations, which take some time on even the fastest of computers. Calculation of deflections is therefore controlled by clicking the ‘Calculate Deflections’ button in column L and elsewhere and should be undertaken once all the design is complete. The worst case deflection is taken in subsequent checks and this might be viewed as being unduly conservative.

SPANS! In SPANS! the user is required to choose top, bottom and link reinforcement for each span. The amounts of bending and shear reinforcement required and checks are derived from detailed calculations in Bar! Unwanted cells are ‘greyed-out’. The reinforcement diameter specified for a support carries through both sides of the support, i.e. the diameter specified for the right hand support of a span carries over to the left hand support of the next span. It should be noted that hogging moment is checked both at the centre of support (solid section) and the solid/ rib intersection (ribbed section). As the moments at the solid/ rib intersection each side of the support may differ, it may be possible to obtain a design giving different numbers of bars each side of the support. Practicality should dictate that the greater number of bars is used for detailing. Hogging moments at 1/4 span positions within a

56


17/07/2006 17:04:54

RCC32R Rigorous Ribbed Slabs.xls span are checked and are used in the determination of top steel in spans. For top steel at supports, reinforcement requirements are checked at both the support centreline (solid) and at the start of the ribbed cross-section. Deflection calculations involve many iterative calculations, and these are controlled by clicking the ‘Calculate Deflections’ button in column N. Deflection results will only appear on the spreadsheet after the ‘Calculate Deflections’ button has been used and the macro been allowed to complete its iterations. They will disappear again if relevant data (e.g. span, load) is changed. Should the span fail deflection criteria, the user has the option to increase bottom steel at cell M24 etc, and reuse the ‘Calculate Deflection’ button.


Notes! This sheet gives disclaimers and revision history as in the Notes! sheet in other spreadsheets.

WEIGHT! WEIGHT! Gives an estimate of the amount of reinforcement required in one direction of the slab per rib and per square metre. Simplified curtailment rules, as defined in BS 8110 Part 1, Clause 3.12, are used in the determination of lengths of bars. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation, etc. They do not allow for reinforcement in supporting beams or for mesh.

Uls! This sheet details the moment distribution analysis carried out at the ultimate limit state but is not necessarily intended for printing out other than for checking purposes.


Bar! This sheet shows design calculations, complete with references to BS 8110. It is not necessarily intended for printing out other than for checking purposes. In spans, service stress, fs, may be reduced to satisfy deflection criteria. In many instances, minima of 1.0 or 0.0001 have been used to avoid problems with division by zero.

Def! This sheet calculates deflections at 1/20th points for each span and for each load condition. The sheet is large and is not necessarily intended for printing out other than for checking purposes.

57


17/07/2006 17:04:56

RCC32R Rigorous Ribbed Slabs/ JOBDATA!

Project


Client

Advisory Group

Location

3rd Floor slab


from 1 to 5a

rmw

RIGOROUS RIBBED SLAB DESIGN to BS 8110:2005 Originated from RCC32R.xls v3.0 on CD

LOCATION

Supports from grid

to grid

Page

58 43

11-Apr-06

Checked

Revision

chg

-

© 2005 TCC

1

Date

Job No

R68

5a COVERS (to all steel)

MATERIALS N/mm² fcu 35 fy 500 N/mm² fyv 500 N/mm² steel class A SERVICEABILITY CRITERIA

Top cover h agg γs γc

20 1.15 1.50

mm steel concrete

Btm cover Side cover Concrete density

Maximum permanent ∆ = L / 250 Maximum imposed ∆ = L / 500 Max ∆ affecting partitions = L / 350 Maximum precamber = 50% Permanent portion of imposed loading = 25% 0.3 Design Crack width, W k = CREEP COEFFICIENTS (to EN 1992-1) 36 N/mm² RH 50 % relative humidity fcm = 31.37 kN/mm² Cement N Type (S, N, R or RS) Ecm = AMBIENT TEMPERATURES ºC

LOADING SEQUENCE (loads rationalised to kN/m²) Span 1 Span 2 kN/m² kN/m² Self weight 3.93 4.19 Partitions 1.00 1.00 Other dead loads 3.81 3.71 Permanent imposed 0.79 0.79 Variable load 2.37 2.36 Total 11.89 12.04 COMPOSITE E and φ VALUES - Span 1 At 70 years Et Ø0 kN/mm² Self weight 3.60 6.82 Partitions 2.74 8.40 Other dead loads 2.32 9.43 Permanent imposed 2.74 8.40 Variable load Composite 2.93 7.98 Permanent

from 0 to 7 days 15

Span 3 kN/m² 4.11 1.00 2.50 0.75 2.25 10.61

Span 4 kN/m² 4.27 1.00 2.50 0.75 2.25 10.77

At 70 years Et Ø0 kN/mm² 3.60 6.82 2.74 8.40 2.32 9.43 2.74 8.40 0 31.37 2.35 9.37 Total load

mm

20 20 23.6

mm

mm kN/m³ 3.3.3 (Pt 2)

or 20 mm of permanent ∆ mm

2.2.3.4.2 Table 3.1 & Annex A

from 7 to 60 days 17

Span 5 kN/m² 0.00 1.00 #DIV/0! #DIV/0! #DIV/0! #DIV/0!

20


from 60 days on 20

At age Days 7 28 60 28 ∞

At 28 days Et Ø (t,t0) kN/mm² 1.27 13.83 0 31.37 1.01 15.60 At partition loading

58


17/07/2006 17:04:56

RCC32R Rigorous Ribbed Slabs.xls RCC32R Rigorous Ribbed Slabs/ MAIN!

Project


Client

Advisory Group


Location 3rd Floor slab,

RIGOROUS RIBBED SLAB DESIGN to BS 8110:2005 Originated from RCC32R.xls

v3.0 on CD

Date

rmw

from 1 to 5a

Page

Checked

Revision

chg

-

© 2005 TCC

59 44

Apr-2006

Job No

R68

RIBS slab depth, hf Rib width

100 150

Centres Side taper of 1 in

mm mm

Solid (mm)


900 10

mm

SUPPORTS

L (m)

H (mm)

Left

Right

Support No

Type

6.500 7.000 7.500 6.500

275 275 275 275

450 1100 1100 1100

1100 1100 1100 1100

1 5

K K K(nife), or C(antilever)

LOADING PATTERN min

max

DEAD

1

1.4

IMPOSED

0

1.6

LOADING UDLs (kN/m²) PLs (kN/m) Position (m) Span 1 UDL PL 1 PL 2 Span 2 UDL PL 1 PL 2 Span 3 UDL PL 1 PL 2

Self Weight

Add Dead Load

Imposed Load

Position from left

3.93 ~~~~ ~~~~

2.50 8.50

4.00 1.00

~~~~ 0.450

4.19 ~~~~ ~~~~

2.50 8.50

4.00 1.00

~~~~ 1.450

4.11 ~~~~ ~~~~

2.50

4.00

~~~~

Span 4 UDL PL 1 PL 2 Span 5 UDL PL 1 PL 2 Span 6 UDL PL 1 PL 2

Self Weight

Add Dead Load

Imposed Load

Position from left

4.27 ~~~ ~~~

2.50

4.00

~~~~

~~~ ~~~ ~~~~ ~~~~ ~~~~

LOADING DIAGRAM

1

5a


1

2

3

4

5

23.4 12.7 -1.7 53.6

57.9 31.1 14.0 128.5

48.6 28.4 13.6 116.2

52.5 31.6 14.3 120.7

16.8 11.8 -1.9 42.5

~ ~ ~ ~

~ ~ ~ ~

59


17/07/2006 17:05:00

RCC32R Rigorous Ribbed Slabs/ ACTIONS! Project


Client

Advisory Group

Location

3rd Floor slab, , from 1 to 5a


rmw


Checked

Page

Apr-2006

45 60

Revision

chg

© 2005 TCC


Date

Job No

-

Elastic

R68

Redistributed

100 80 60 40 20 0 -20 -40 -60 -80

100 80 60 40 20 0 -20 -40 -60 -80 0

5

10

15

20

25

1

30

0

5a SUPPORT No

Elastic M Redistributed M ßb Redistribution

10

15

1

2

3

4

5

80.2 72.2 0.900 10.0%

68.1 68.1 1.000 0.0%

79.6 67.7 0.850 15.0%

0.0 0.0 1.000

~ ~ ~

~ ~ #VALUE!

~ ~ #VALUE!

1

2

3

4

60.47 58.31 0.964

51.71 48.59 0.940

53.85 51.09 0.949

60.16 56.94 0.947


20

25

30

5a

0.0 0.0 1.000

SPAN No


5

1 kNm/m kNm/m ~

Elastic

Redistributed

80 60 40 20 0 -20 -40 -60 -80

80 60 40 20 0 -20 -40 -60 -80 0

5

10

15

20

25

1

30

0

5a SPAN No

54.4 53.6

SPAN No

10

15

20

1

1


5

25

30

5a

2

3

63.3 62.1

68.1 69.0

56.2 57.4

57.2 58.8

60.3 61.0

43.7 42.5

~ ~

~ ~

~ ~

~ ~

4


63.8 62.0

DEFLECTIONS (mm) Precamber not included

.

10 0 -10 -20 -30 -40

Before partitions Permanent

1 11.2 24.6

2 6.4 20.8

3 9.8 24.0

4 10.7 24.0

#DIV/0! #DIV/0!

#DIV/0! #DIV/0!

mm mm

Variable

10.0

9.6

11.9

9.7

#DIV/0!

#DIV/0!

mm

SPAN No

60


17/07/2006 17:05:02

RCC32R Rigorous Ribbed Slabs.xls RCC32R Rigorous Ribbed Slabs/ SPANS!

Project


Client

Advisory Group

Location




SPAN 1 ACTIONS DESIGN

TOP STEEL

BTM STEEL SHEAR

LINKS DEFLECTIONS mm CHECKS


TOP STEEL

BTM STEEL SHEAR


Date

rmw Checked

© 2005 TCC

Page

11-Apr-06 Revision

chg

-

61 46 Job No

R68

LEFT CENTRE 0.0 58.3 1.00 0.96 243.0 239.0 (x=26.6
RIGHT 72.2 0.90 241.0 653 As' 0 2H 16 /rib + 5 H8 between As prov 653 2H 16 /rib As' prov 402 V 62.10 v 1.005 vc 0.801 2 H6 @ 175 for 700 Precamber (mm) = 0 Increase btm As by 0%

LEFT CENTRE 72.2 48.6 0.90 0.94 239.0 (x=26.6



ok ok ok

0.22

ok

ok ok ok

0.16

ok

61


17/07/2006 17:05:05

RCC32R Rigorous Ribbed Slabs/ SPANS!

Project


Client

Advisory Group

Location





TOP STEEL

BTM STEEL SHEAR



TOP STEEL

BTM STEEL SHEAR


Date

rmw Checked

© 2005 TCC

Page

Apr-2006 Revision

chg

-

62 /47 Job No

R68

LEFT CENTRE 68.1 @col face 51.1 1.00 0.95 241.0 239.0 (x=26.6

LEFT CENTRE 67.7 56.9 0.85 0.95 241.0 239.0 (x=26.6
RIGHT 0.0 1.00 241.0 0 As' 0 2H 16 /rib + 4 H8 between As prov 603 2H 16 /rib As' prov 402 V 42.52 v 0.568 vc 0.801 . Precamber (mm) = 0 Increase btm As by 0%



ok ok ok

0.22

ok

ok ok ok

0.00

ok

62


17/07/2006 17:05:08

RCC32R Rigorous Ribbed Slabs.xls RCC32R Rigorous Ribbed Slabs/ WEIGHT!

Project


Client

Advisory Group

Location



rmw


Checked

© 2005 TCC

Date

Page

Apr-2006 Revision

63 /48 Job No

chg

-

R68


No

Type

Dia

Length

Unit Wt

Weight

2 5 2 2 5 2 2 4 2 2 5 3 2 4

H H H H H H H H H H H H H H

12 8 16 16 8 12 16 10 12 16 8 12 16 8

2150 2150 4475 3375 3375 4425 3625 3625 4675 3500 3500 4175 2800 2800

0.888 0.395 1.578 1.578 0.395 0.888 1.578 0.617 0.888 1.578 0.395 0.888 1.578 0.395

3.8 4.2 14.1 10.7 6.7 7.9 11.4 8.9 8.3 11.0 6.9 11.1 8.8 4.4

Support 1 Span 1 Support 2 Span 2 Support 3 Span 3 Support 4 Span 4 Support 5

2 2 2 2 2 2 2 2 2

H H H H H H H H H

16 20 16 20 16 20 16 20 16

1150 4900 3475 4750 3475 5250 3475 4250 2375

1.578 2.466 1.578 2.466 1.578 2.466 1.578 2.466 1.578

3.6 24.2 11.0 23.4 11.0 25.9 11.0 21.0 7.5

Span 1 Span 2 Span 3 Span 4

8 12 10 7

H H H H

6 6 6 6

800 800 800 800

0.222 0.222 0.222 0.222

1.4 2.1 1.8 1.2

Support 1 Span 1 Support 2 Span 2 Support 3 Span 3 Support 4 Span 4 Support 5

BOTTOM STEEL

LINKS

SUMMARY

All figures approximate - see User Guide.



263.4

63


17/07/2006 17:05:11

RCC33 Flat Slabs (A & D).xls RCC33.xls analyses and designs bays of simple rectangular flat slabs to BS 8110: Part 1. The spreadsheet uses sub-frame analysis with pattern loading to calculate a bending moment envelope. This envelope may be subjected to redistribution. For a complete rectangular flat slab the user is expected to use the spreadsheet at least four times (internal bay(s) x - x, internal bay(s) y - y, edge bay(s) x - x and edge bay(s) y - y). Punching shear should be checked using RCC13.xls. The spreadsheet does not currently allow for holes or drops. If holes are considered critical then the user is directed towards using RCC21.xls (sub-frame analysis) and allowing for holes in the breadths used. See also Clause 3.7.5. The single load case of all spans loaded (Clause 3.5.2.3) is not used. Beyond panel aspect ratios of 1.5 consideration might be given to the appropriateness of using other forms of analysis (e.g. grillage or finite element).

MAIN!

Load input should define the loads on the slab only. A combobox is used to switch between the internal and edge bays. If EDGE is chosen, cells H14:I14 and E16:G16 become operative and information about the perimeter load along the edge and the distance of the edge from the centreline is required as input. Perimeter loading is assumed to be dead load. The spreadsheet also allows lines loads to be input. This facility might be used with caution to deal with small point loads being distributed over suitable widths in the two orthogonal directions. Cell L51 gives an estimate of reinforcement requirements for the element considered in the direction considered (not both directions). It will be noted that the example assumes the reinforcement is in the second layer; therefore warnings concerning cover greater than 40 mm should not be of too much concern.

This sheet provides the main inputs to the spreadsheet (although other inputs occur in other sheets). Most inputs are (we hope) self-explanatory.

The spreadsheet takes automatic measures to ensure deflection criteria are met. It may be argued that in this instance, with equal spans in the two directions, these measures are unwarranted in that deflection criteria will have been met in the orthogonal T1/ B1 layer.

LEGEND! should help with definition of dimensions, e.g. edge distance C is actually from centreline of column to edge of slab. Cover is defined as being to the layer being designed. The layering is set at T1 - B1 (& T2 - B2) although T1 - B2 might be deemed more appropriate (e.g. with prefabricated mats).

To the right under Operating instructions a number of checks are carried out. Box markers indicate where checks have been carried out and proved satisfactory.

The number of spans is altered by entering data in the appropriate cells. Unwanted data cells are ‘greyed-out’. The use of C, K, F or P can alter the characteristics of a support from Cantilever to Knifeedge to Fixed to Pinned. Extraneous data is highlighted in red or by messages in red. Under Operating Instructions a number of checks are carried out and problems found are highlighted. At the bottom of the sheet a simplistic loading diagram is given to aid data checking. Great care should be taken to ensure that this sheet is completed correctly for the case in hand. It may prove prudent to estimate values for bay width bending moments at each support by hand before progressing to ACTIONS! Cantilevers less than 1.00m should be described as end distances (rather than cantilevers; otherwise certain logic regarding breadth of effective moment transfer strip, be (see BS 8110: Part 1, Figure 3.13), goes wrong). End distances equivalent to the half width of the column should be used to define slabs whose edge is flush with the outside of the column. On edge columns, be restricts Mt max which in itself restricts the amount of moment transferred into columns above and below.

ACTIONS! This sheet shows bending moment and shear force diagrams from the analysis undertaken in Analysis! The user is required to input the desired amount of redistribution to the initial moments in line 26. Cell L14 allows three types of distribution according to the user’s preference. The sheet also provides output reactions and column moments. Using the value of Veff for punching shear obviates the need to use the 1.15, 1.25 and 1.4 factors in Clause 3.7.6.2 to determine Veff from Vt .

SPANS! SPANS! details the amounts of reinforcement required derived from detailed calculations in Bar!.

LEGEND! LEGEND! gives an explanation of the dimensions used in MAIN! and for the analysis and design.

64


17/07/2006 17:05:14

RCC33 Flat Slabs (A & D).xls WEIGHT! WEIGHT! gives an estimate of the amount of reinforcement required in one direction of the slab for the internal or end bays considered. Simplified curtailment rules, as defined in Clause 3.12, are used to determine lengths of bars. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, ‘rationalisation’, the effects of holes etc, etc. They do not allow for punching shear links or link carrier bars.

Analysis! This sheet details the moment distribution analysis carried out but is not necessarily intended for printing out other than for checking purposes. It is derived from RCC21.xls.

Bar! This sheet shows design calculations, complete with references to BS 8110. It is not necessarily intended for printing out other than for checking purposes. Hogging moments at 1/4 span positions within a span are checked and are used in the determination of top steel in spans.

Graf! This sheet comprises data for graphs used on other sheets, particularly in ACTIONS!


65


17/07/2006 17:05:15

RCC33 Flat Slabs (A & D)/ MAIN!

Project


Client Location

Advisory Group ECBP Typical Floor


A

from grids

to

D

rmw

FLAT SLAB ANALYSIS & DESIGN to BS 8110:2005 Originated from RCC33.xls

MATERIALS

fcu fyl fyv steel class


L (m)

7.500 7.500 7.500

40 500 500 A

v3.1 on CD


Checked

© 2006 TCC

h agg γs γc

GEOMETRY Bay type EDGE Slab depth, h 250 Edge Panel width, b 3750 Edge distance 300 End distance 125 End distance 125

20 1.15 1.50

mm steel concrete

Date

Page

11-Apr-06 Revision

66 49 Job No

chg

-

R68

COVERS Top cover Btm cover

mm

TO LAYER

25 25

1 1

PERIMETER LOADS characteristic 8.85 kN/m outside supports 1 & 4 2.47 10.00 kN/m along bay edge LOADING PATTERN

mm mm mm to C/L

DEAD IMPOSED

from supt 1 from supt 4

min

max

1.0

1.4 1.6

. SUPPORTS Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Support 7 LOADING

ABOVE (m)

3.750 3.750 3.750 3.750

H (mm)

B (mm)

End Cond

BELOW (m)

H (mm)

B (mm)

End Cond

250 400 400 250

400 400 400 400

F F F F

3.75 3.75 3.75 3.75

250 400 400 250

400 400 400 400

F F F F

Dead Load

Imposed Load

Position from left

Loaded Length

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~



Dead Load

Imposed Load

Position from left

Loaded Length

7.50

3.50

~~~~~

~~~~~ ~~~~~ ~~~~~

7.50

3.50

~~~~~

~~~~~ ~~~~~ ~~~~~

7.50

3.50

~~~~~

~~~~~ ~~~~~ ~~~~~


LOADING DIAGRAM

A

D

66


17/07/2006 17:05:16

RCC33 Flat Slabs (A & D).xls RCC33 Flat Slabs (A & D)/ ACTIONS!

Project


Client Location

Advisory Group ECBP Typical Floor, from grids A to D

Made by

FLAT SLAB ANALYSIS & DESIGN to BS 8110:2005

Checked

The Concrete Centre


Date

rmw

Revision

chg

© 2006 TCC

Page

11-Apr-06

67 50

Job No

-

R68


500

500

400

400

300

300

200

200

100

100

0

0

-100

-100

-200

-200

-300

-300

-400

-400 0

5

10

15

20

0

25

5

Elastic M Redistributed M ßb Redistribution End support reinf. Ø mm SPAN No


15

20

25

20

25



10

1

2

3

4

123.7 123.7 1.000

465.4 372.3 0.800 20.0%

465.4 372.3 0.800 20.0%

123.7 123.7 1.000

16 *

~ ~ ~

~ ~ ~

~ ~ ~

~ ~ ~

~ ~ ~

16 *

1

2

3

297.1 319.9 1.077

205.5 184.6 0.898

297.1 319.9 1.077

~ ~ ~

SHEARS FORCE DIAGRAMS (kN) 400

400

300

300

200

200

100

100

0

0

-100

-100

-200

-200

-300

-300

-400

-400 0

5

10

15

20

25

0

5


15

Redistributed Shears 1


10

2

3

258.2 263.9

343.6 331.1

297.0 297.0

297.0 297.0

343.6 331.1

258.2 263.9

~ ~

~ ~

~ ~

~ ~

~ ~

~ ~

SPAN No

Elastic V Redistributed V REACTIONS (kN) SUPPORT

ALL SPANS LOADED ODD SPANS LOADED EVEN SPANS LOADED Veff for punching Characteristic Dead Characteristic Imposed COLUMN MOMENTS (kNm) ALL SPANS Above LOADED Below ODD SPANS Above LOADED Below EVEN SPANS Above LOADED Below

1

2

3

4

323.0 323.9 153.4 404.9 168.7 49.3

628.2 481.6 487.3 878.0 326.4 114.8

628.2 481.6 487.3 878.0 326.4 114.8

323.0 323.9 153.4 404.9 168.7 49.3

1

2

3

4

54.7 54.7 59.4 59.4 23.0 23.0

-35.9 -35.9 -86.2 -86.2 32.1 32.1

35.9 35.9 86.2 86.2 -32.1 -32.1

-54.7 -54.7 -59.4 -59.4 -23.0 -23.0

67


17/07/2006 17:05:18

RCC33 Flat Slabs (A & D)/ SPANS!

Project


Client

Advisory Group

Location

ECBP Typical Floor, from grids A to D


FLAT SLAB ANALYSIS & DESIGN to BS 8110:2005 Originated from RCC33.xls v3.1 on CD

SPAN 1 ACTIONS

ßb Be Total M Mt max

kNm kNm

MIDDLE STRIP

Width mm M kNm d mm As mm²/m As deflection mm²/m As prov mm²/m Top steel Deflection

Date

rmw Checked

Revision

chg

© 2006 TCC

Page

Apr-2006 -

LEFT

CENTRE

RIGHT

1.000 625 92.8 176.6

1.077

0.800 2175 328.5 614.5

319.9

68 51 Job No

R68

3425 1.8 219.0 6

1875 1875 144.0 82.1 215.0 217.0 865 489 1276 489 Provide H20 @ 225 B1 Provide H16 @ 400 T1 Provide H12 @ 325 T1 348 1396 503 Provide H12 @ 325 T1 OK L/d = 7,500 /215.0 = 34.884 < 26.0 x 1.478 x 1.050 x 0.9 = 36.335 (As increased by 47.5 % for deflection)

COLUMN STRIP


625 92.8 217.0 1743

2175 2175 176.0 246.4 215.0 217.0 912 1294 1408 1294 Provide H20 @ 200 B1 Provide H16 @ 100:200 T1 Provide H16 @ 100 T1 2011 1571 1508 Provide H12 @ 325 T1 L/d = 7,500 /215.0 = 34.884 < 26.0 x 1.485 x 1.050 x 0.9 = 36.489 OK (As increased by 54.4 % for deflection)

CHECKS

% As Singly reinforced max S

SPAN 2 ACTIONS


kNm kNm

MIDDLE STRIP


ok ok ok

ok ok ok

LEFT

CENTRE

RIGHT

0.800 2175 328.5 614.5

0.898

0.800 2175 328.5 614.5

184.6

ok ok ok

1875 82.1 217.0 489 489 Provide H16 @ 400 T1 503

1875 1875 83.1 82.1 215.0 217.0 499 489 654 Provide H20 @ 450 B1 Provide H16 @ 400 T1 698 503 Provide H12 @ 325 T1 OK L/d = 7,500 /215.0 = 34.884 < 26.0 x 1.500 x 1.050 x 0.9 = 36.863 (As increased by 31.0 % for deflection)

COLUMN STRIP


2175 246.4 217.0 1294 1294 Provide H16 @ 100:200 T1 1508

2175 2175 101.5 246.4 215.0 217.0 526 1294 702 Provide H20 @ 400 B1 Provide H16 @ 100:200 T1 785 1508 Provide H12 @ 325 T1 OK L/d = 7,500 /215.0 = 34.884 < 26.0 x 1.548 x 1.050 x 0.9 = 38.038

(As increased by 33.6 % for deflection)

CHECKS


ok ok ok

ok ok ok

ok ok ok

68


17/07/2006 17:05:21

RCC33 Flat Slabs (A & D).xls RCC33 Flat Slabs (A & D)/ SPANS!

Project


Client

Advisory Group

Location



FLAT SLAB ANALYSIS & DESIGN to BS 8110:2005 Originated from RCC33.xls v3.1 on CD

SPAN 3 ACTIONS


kNm kNm

MIDDLE STRIP


Date

rmw Checked

Revision

chg

© 2006 TCC

Page

Apr-2006 -

LEFT

CENTRE

RIGHT

0.800 2175 328.5 614.5

1.077

1.000 625 92.8 176.6

319.9

69 52 Job No

R68

1875 82.1 217.0 489 489 Provide H16 @ 400 T1 503

1875 3425 144.0 1.8 215.0 219.0 865 6 1276 Provide H20 @ 225 B1 Provide H12 @ 325 T1 1396 348 Provide H12 @ 325 T1 OK L/d = 7,500 /215.0 = 34.884 < 26.0 x 1.478 x 1.050 x 0.9 = 36.335 (As increased by 47.5 % for deflection)

COLUMN STRIP


2175 246.4 217.0 1294 1294 Provide H16 @ 100:200 T1 1508

2175 625 176.0 92.8 215.0 217.0 912 1743 1408 Provide H20 @ 200 B1 Provide H16 @ 100 T1 1571 2011 Provide H12 @ 325 T1 OK L/d = 7,500 /215.0 = 34.884 < 26.0 x 1.485 x 1.050 x 0.9 = 36.489

(As increased by 54.4 % for deflection)

CHECKS


ok ok ok

ok ok ok

ok ok ok

69


17/07/2006 17:05:24

RCC33 Flat Slabs (A & D)/ LEGEND!

Project


Client Location


Made by


Checked


The Concrete Centre

© 2006 TCC

rmw chg

Date

Page

70 53

11-Apr-06 Revision

Job No

-

R68

Legend for Input Data

70


17/07/2006 17:05:26

RCC33 Flat Slabs (A & D).xls RCC33 Flat Slabs (A & D)/ WEIGHT!

Project


Client Location


Made by


Checked


The Concrete Centre rmw chg

© 2006 TCC

Date

Page

71 54

11-Apr-06 Revision

Job No

-

R68

No

WEIGHT of REINFORCEMENT TOP STEEL

Support 1

Mid Strip Col Strip

11 8

Span 1

6

Support 2

5

Span 2

6

Support 3

5

Span 3

6

Support 4

11

7 17 7 17 7 8

BTM STEEL

Span 1

9 11

Span 2

5

Span 3

9

6 11

Type

Dia

Length

Unit wt

Weight

H H H H H H H H H H H H H H

12 16 12 12 16 16 12 12 16 16 12 12 12 16

2350 2550 4950 4950 3750 3750 4950 4950 3750 3750 4950 4950 2350 2550

0.888 1.578 0.888 0.888 1.578 1.578 0.888 0.888 1.578 1.578 0.888 0.888 0.888 1.578

22.9 32.2 26.4 30.8 29.6 100.6 26.4 30.8 29.6 100.6 26.4 30.8 22.9 32.2

H H H H H H

20 20 20 20 20 20

6875 7750 6825 7650 6875 7750

2.466 2.466 2.466 2.466 2.466 2.466

152.6 210.2 84.2 113.2 152.6 210.2

SUMMARY Rebar for single direction only. All figures approximate - see User Guide. TOTAL REINFORCEMENT IN BAY (kg) 1465

REINFORCEMENT DENSITY (kg/m3)

63.6

71


17/07/2006 17:05:28

RCC41 Continuous Beams (A & D).xls The spreadsheet designs multiple-span rectangular or flanged beams using sub-frame analysis to derive moments and shears. The intention is to provide the design and analysis of up to six spans of continuous beams with columns above and below. Spans may incorporate cantilevers, fixed ends or knife-edge supports. There are three main sheets: MAIN!, ACTIONS! and SPANS!

MAIN! This sheet contains user input of materials, frame geometry and load data. Input data is blue and underlined. New data may be input by overwriting default values or by entering values in ‘greyed-out’ cells. Guidance on input for the type of section and type of end condition of the support is given under Operating Instructions. The sheet has been set up with as many ‘carry throughs’ as possible, i.e. input cells are made equal to preceding input cells to make the inputting of regular beams easier. Inputting C18 as “= C17” will insert 8.00 in the remaining spans: it will also remove the grey conditional background to the remaining spans, supports and loads and allow data entry. Deleting C18, indeed C19, will blank out remaining spans, etc. Generally, values in red or red backgrounds indicate either incorrect or excess data. For instance, if knife-edge supports are required, entering ‘K’ in cell C25 will elicit red data to the right, which needs to be cleared manually. Point loads should be at least 0.001m from a support. Do not copy and paste input values as this can corrupt formatting (“copy” and “Paste Special values” is OK). ‘Rebar layering’ refers to whether there are beams and therefore reinforcement in the other direction. Answering yes drops by one bar diameter the steel at the supports. With respect to cantilevers, design for bending caters for moments at the face of support; design for deflection considers the cantilever from the centre line of support. N.B. root rotation is not considered. In beam-to-beam situations the width of support can be input as being very small to avoid under-design in bending.

ACTIONS! ACTIONS! Includes bending moment and shear force diagrams, summaries of moments and shears and user input for amounts of redistribution. Users should ensure that the amounts of redistribution are always considered as there are no default values.

SPANS! This sheet designs reinforcement for bending in spans and supports and for shear in the spans. User input is required for the diameters of bending and shear reinforcement and for the number of legs of links in each span. Some intuition may be required to obtain sensible and rational arrangements of reinforcement. In order to discourage the use of second layers of reinforcement, the input cells for diameters of reinforcement in second layers are nominally protected. Support moments (including cantilever moments) are considered at the face of the support. This may lead to unequal amounts of reinforcement being designed for each side of the support. See Bar! Usually, the detailer would be expected to detail the larger amounts of reinforcement; however where different sections occur either side of a support, the detailer should be briefed as to the designer’s detailed requirements. Non-existent spans are blanked out. Besides the limit of maximum modification factor for deflection = 2.0, an additional limit of maximum allowable area of steel to comply with deflection criteria, Asdef, = 2 x Asreqd has been imposed.

WEIGHT! This sheet estimates the weight of reinforcement in the beam when designed according to normal curtailment rules as defined in BS 8110. Workings are shown on the right hand side of the sheet. The estimate may be printed out using File/print or the print button on the normal toolbar. It should be recognised that different engineers’ and detailers’ interpretations of these clauses, and different project circumstances and requirements will all have a bearing on actual quantities used.

Analysis! This sheet shows the moment distributions used in the analysis of the beam: it is not intended for formal printing. It will be seen that the loads are considered initially as 1.0gk over all spans then as (γgk - 1.0) + γqk qk over alternate spans.

Bar! Intended mainly for first time users and young engineers, this sheet gives further details of the calculations summarised in SPAN! Support moments are considered at faces of supports; checks at 1/4 span relate to hogging and any top steel required is provided in the span.

72


17/07/2006 17:05:31

RCC41 Continuous Beams (A & D).xls

Graf! This sheet provides data for the charts in MAIN! and ACTIONS!: it is not intended for formal printing.


73


17/07/2006 17:05:32

RCC41 Continuous Beams (A & D)/ MAIN! Project


Client Location

Advisory Group D&D: Main beam Grids C to H


from grid 1 to 3

CONTINUOUS BEAM (Analysis & Design) to BS 8110:2005 Originated from RCC41.xls v3.0 on CD

LOCATION

Supports from grid

1

SPANS SPAN 1 SPAN 2 SPAN 3

40 500 500 A


h agg γs γc

Job No

-

R68

3

20 1.15 1.50

COVERS (to all steel) Top cover 25 mm Btm cover 40 mm Side cover 35 mm

mm

L (m)

H (mm)

bw (mm)

hf (mm)

Type

bf (mm)

1.50 8.00 1.50

500 500 500

300 300 300

175 175 175

R R R

300 300 300


min

max

1 0

1.4 1.6

REBAR LAYERING Support steel in alt layer ? Y

SPAN 4 SPAN 5 SPAN 6 SUPPORTS Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Support 7 LOADING

74 55

Revision

chg

MATERIALS fcu fyl fyv steel class

Sheet No

11-Apr-06

Checked

© 2006 TCC

to grid

Date

rmw

ABOVE (m)

H (mm)

B (mm)

End Cond

C 3.50 3.50 K

300 300

300 300

F F

UDLs (kN/m)

PLs (kN)


BELOW (m)

5.00 4.00

H (mm)

B (mm)

End Cond

300 300

300 300

P P

Dead Load

Imposed Load

Position from left

Position (m)

Dead Load

Imposed Load

Position from left

Loaded Length

25.8

20.0

~~~~~

~~~~~ ~~~~~ ~~~~~

25.8

20.0

~~~~~

~~~~~ ~~~~~ ~~~~~

25.8 25.0

20.0

~~~~~ 1.50

~~~~~ ~~~~~ ~~~~~


Loaded Length

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

LOADING DIAGRAM

1

3


ALL SPANS LOADED ODD SPANS LOADED EVEN SPANS LOADED Characteristic Dead Max characteristic Imposed Min characteristic Imposed

1

2

3

4

0.0 0.0 0.0 0.0 0.0 0.0

362.6 198.7 295.8 134.1 103.9 32.1

543.9 252.9 515.5 211.1 163.6 11.0

-122.2 -5.9 -163.9 -36.4 16.9 -64.5

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0

74


17/07/2006 17:05:32

RCC41 Continuous Beams (A & D).xls RCC41 Continuous Beams (A & D)/ ACTIONS! Project


Client

Advisory Group

Location

D&D: Main beam Grids C to H, from grid 1 to 3



Date

rmw Checked

Revision

chg

© 2006 TCC

Page

11-Apr-06

75 56 Job No

-

R68


400

400

300

300

200

200

100

100

0

0

-100

-100

0

2

4

6

8

10

12

-200

-300

-300

-400

1

3



Elastic M Redistributed M ßb SHEARS (kN)

0

2

4

6

1

1

2

3

4

215.7 215.7 1.000

390.5 312.4 0.800 20.0%

0.0 0.0 1.000

~ ~ ~

~ ~ ~

~ ~ ~

~ ~ ~

~ ~ ~

1

2

3

259.55 295.71 1.139

0.00 0.00 0.700

10

12

300

300

200

200

100

100

0

0

-100

-100

-200

-200

-300

-300

-400

3


0.0 0.0 1.000

0.00 0.00 1.000

8

-200

kNm/m kNm/m ~

-400 0

2

4

6

8

10

Elastic Shears

1 SPAN No

12

0

3

2

4

2

0.0 0.0

102.2 102.2

251.8 260.4

297.6 287.8

264.2 259.4

-172.8 -163.9


~ ~

~ ~

~ ~

~ ~

~ ~

~ ~

2

3

4

91.2 47.9 20.5 10.8 105.3 55.3

-36.9 -24.2 -11.8 -7.7 -39.1 -25.7

1

10

12

3

3



8


1

1

6

75


17/07/2006 17:05:36

RCC41 Continuous Beams (A & D)/ SPANS! Project


Client

Advisory Group

Location




M ßb DESIGN d As As' TOP STEEL Layer 1 Layer 2 As prov BTM STEEL Layer 1 Layer 2 As' prov

1.00 450.0

mm²

3

Y

10

3

2

236 Y

10

mm²

mm²

157 3.356 30.7 0.227 0.413 H10 @ 325 for 650 2

L/d V v vc

kN N/mm² N/mm²

LINKS

legs

No

% As Cover min S max S Links Main bars max V Deflection

mm mm²

CHECKS


339 Y

12

As prov Allowed

226 9.388

12

As prov 2

339 Y

20

As' prov

628

61.5 0.459 0.468 H10 @ 325 for 975 2

10 Nominal

H10 @ 325 2 ok ok ok ok ok ok


CENTRE 295.7 1.14 434.0 1903

3

Y

25

2

3

1473 Y

20

mm²

mm² kN N/mm² N/mm²

LINKS

legs

As' prov 2

Link Ø

Y

RIGHT 270.5 0.80 417.0 1807

mm²

942 18.433 221.1 1.724 0.614 H10 @ 200 for 1800 2 L/d

V v vc

3

LEFT 177.5 1.00 427.5 1061

kNm

DEFLECTION SHEAR

12

ok

SPAN 2 M ßb DESIGN d As As' TOP STEEL Layer 1 Layer 2 As prov BTM STEEL Layer 1 Layer 2 As' prov

RIGHT 62.1 1.00 447.0 336

Y


CHECKS

ACTIONS

R68

mm²

DEFLECTION SHEAR

76 57 Job No

-

CENTRE 0.0 1.00 444.0 0

kNm mm

Revision

chg

LEFT

ACTIONS

Page

11-Apr-06

Checked

© 2006 TCC

SPAN 1

Date

rmw

No


Y

16

3

As' prov 3

402 Y

32

As prov Allowed

2413 25.145 Link Ø

10 Nominal


Y

32

As prov 3

2413 Y

20

As' prov

942

249.2 1.992 0.920 H10 @ 200 for 1800 2 ok ok ok ok ok ok ok

ok

76


17/07/2006 17:05:38

RCC41 Continuous Beams (A & D).xls RCC41 Continuous Beams (A & D)/ SPANS!

Project


Client

Advisory Group

Location




ACTIONS

M ßb DESIGN d As As' TOP STEEL Layer 1 Layer 2 As prov BTM STEEL Layer 1 Layer 2 As' prov

mm mm²

V v vc

CHECKS


-

CENTRE 0.0 0.70 444.0 0

3

Y

32

3

2

2413 Y

10

mm²

mm² kN N/mm² N/mm²

LINKS

legs

77 58 Job No

R68

RIGHT 0.0 1.00 450.0 0

mm²

DEFLECTION SHEAR

Revision

chg

LEFT 278.6 0.96 417.0 1876

kNm

Page

Apr-2006

Checked

© 2006 TCC

SPAN 3

Date

rmw

No

157 3.378 220.8 1.765 0.730 H10 @ 200 for 1400 2 ok ok ok ok ok ok ok

Y

25

3

As' prov 2

1473 Y

12

As prov Allowed

226 66.003 Link Ø

10 Nominal


Y

10

As prov 2

236 Y

10

As' prov

157

V

194.6 1.441 vc 0.325 H10 @ 200 for 400 2 v


ok

77


17/07/2006 17:05:41

RCC41R Rigorous Continuous Beams (A & D).xls The spreadsheet designs multiple-span rectangular or flanged beams and estimates deflection to BS 8110 Parts 2. It uses subframe analysis to derive moments and shears. For each span and load case it calculates deflections at 1/20th spans. The intention is to provide the design and analysis of up to six spans of continuous beams with columns above and below. Spans may incorporate cantilevers, fixed ends or knife-edge supports. There are four main sheets: JOBDATA!, MAIN!, ACTIONS! and SPANS! where the user is required to input data.

Users may choose to equate cells in their saved version to speed input.

The spreadsheet is based on RCC41 but has an initial sheet JOBDATA! to allow input of all the variables and performance criteria required. The calculation of deflection is not carried out automatically. The user is required to press the ‘Calculate deflections’ button in column N of SPANS! (or elsewhere) when every other aspect of the design has been completed. Deflections are given as a range in a chart at the bottom of ACTIONS! They are shown as a range due to potential pattern loading. In SPANS! the worst case is compared with the specified serviceability criteria.

With respect to cantilevers, design for bending caters for moments at the face of support; design for deflection considers the cantilever from the centre line of support. N.B. root rotation is not considered.

It should be noted that the number of assumptions and uncertainties in the material and design criteria and construction process mean that deflection calculations carried out in this manner can be notoriously inaccurate (and usually over conservative) compared with actual measured deflections. The calculated deflections might be regarded as being akin to 95% confidence limits.


MAIN! This sheet contains user input of frame geometry and load data. Input data is blue and underlined. New data may be input by overwriting default values or by entering values in ‘greyed-out’ cells. Guidance on input for the type of section and type of end condition of the support is given under Operating Instructions. Generally, values in red or red backgrounds indicate either incorrect or excess data. For instance, if knife-edge supports are required, entering ‘K’ in cell C18 will elicit red data to the right, which needs to be cleared manually. The sheet has not been set up with many ‘carry throughs’ (making the value of one cell equal another).

Do not copy and paste input values as this can corrupt formatting (copy and ‘paste values only’ is OK). ‘Rebar layering’ refers to whether there are beams in the other direction. Answering ‘yes’ drops by one bar diameter the steel at the supports.

In beam-to-beam situations the width of support can be input as being very small to avoid under-design in bending.

ACTIONS! ACTIONS! Includes bending moment and shear force diagrams, summaries of moments and shears and user input for amounts of redistribution. Users should ensure that the amounts of redistribution in row 22 are always considered - there are no default or automated values. Cell L14 determines how the redistribution is carried out (see Table 1 of this document). The chart at the bottom of the page shows calculated deflections at construction of partitions, and ranges for longer term deflections due to patterns of permanent and imposed loading. The worst case is taken in subsequent checks and this might be viewed as being unduly conservative.

SPANS! This sheet designs reinforcement for bending in spans and supports, and for shear in the spans. User input is required for reinforcement sizes – some intuition may be required to obtain sensible arrangements of reinforcement. The amounts of bending and shear reinforcement required and checks are derived from detailed calculations in Bar! Support moments (including cantilever moments) are considered at the face of the support. This may lead to unequal amounts of reinforcement being designed for each side of the support, see Bar! Non-existent spans are blanked out. Deflection calculations are controlled by clicking the ‘Calculate Deflections’ button in column N and should be undertaken once all the other design is complete. Deflection results will only appear on this sheet after the ‘Calculate Deflections’ button has been used and the macro been allowed to complete its iterations. They will disappear if relevant data (e.g. span, load) is changed. Should the span fail deflection criteria, the user has the option to

78


17/07/2006 17:05:43

RCC41R Rigorous Continuous Beams (A & D).xls increase bottom steel at cell M21 etc, and reuse the ‘Calculate Deflection’ button Hogging moments at are checked 1/4 span positions within a span and are used to determine the top steel in spans.

WEIGHT! This sheet estimates the weight of reinforcement in the beam when designed according to normal curtailment rules as defined in BS 8110. Workings are shown on the right hand side of the sheet. The estimate may be printed out using File/print or the print button on the normal toolbar. It should be recognised that different engineers’ and detailers’ interpretations of these clauses, and different project circumstances and requirements will all have a bearing on actual quantities used.



Uls! This sheet details the moment distribution analysis carried out at the ultimate limit state but is not necessarily intended for printing out other than for checking purposes. It will be seen that the loads are considered initially as 1.0gk over all spans then as (γgk - 1.0)gk + γgk qk on alternately odd and even spans.



Def! This sheet calculates deflections at 1/20th points for each span and for each load condition. For each point and condition it considers moment, As, As’, d, d’, uncracked neutral axis depth x, uncracked inertia - I, cracked neutral axis depth - x, cracked inertia – I, uncracked moment capacity – Mcr, z, final x, concrete stresses – fc, moment of resistance – MoR, curvature -1/r, load, slope and curvature, etc. to calculate deflection. The sheet is rather large and is not necessarily intended for printing out other than for checking purposes.

79


17/07/2006 17:05:44

RCC41R Rigorous Continuous Beams (A & D)/ JOBDATA!

Project


Client Location

Advisory Group D&D: Main Beam


from grid C to H

rmw


LOCATION

Supports from grid

MATERIALS N/mm² fcu 35 fyl 500 N/mm² fyv 500 N/mm² steel class A SERVICEABILITY CRITERIA

© 2006 TCC

C

h agg γs γc

to grid

H

20 1.15 1.50

mm

Maximum permanent ∆ = L / Maximum imposed ∆ = L / Max ∆ affecting partitions/walls = L / Maximum precamber = Permanent portion of imposed loading = Design Crack width, W k =

CREEP COEFFICIENTS (to EN 1992-1) RH 50 % relative humidity Cement N Type (S, N, R or RS) AMBIENT TEMPERATURES ºC

fcm = Ecm =

Date

Page

80 55

11-Apr-06

Checked

Revision

chg

-

COVERS (to links) Top cover 25 Btm cover 30 Side cover 30 Concrete density 24 250 500 or 20 mm 350 of permanent ∆ 50% 25% 0.3 mm

36 N/mm² 32.937 kN/mm²

Job No

R68

mm mm mm

kN/m³ 3.3.3 (Pt 2)

2.2.3.4.2

Table 3.1 & Annex A

from 0 to 7 days 16


from 60 days on 18

At age Days 7 28 60 28 ∞

LOADING SEQUENCE (loads rationalised to kN/m)

Self weight Partitions/walls Other dead loads Permanent imposed Variable load

Span 1 kN/m 16.80 5.00 11.20 3.75 11.25

Span 2 kN/m 16.80 5.00 12.40 3.75 11.25

Span 3 kN/m 16.80 5.00 17.40 4.38 13.13

Span 4 kN/m 16.80 5.00 11.20 3.75 11.25

Span 5 kN/m 0.00 5.00 #DIV/0! #DIV/0! #DIV/0!

Total

48.00

49.20

56.70

48.00

#DIV/0!

COMPOSITE E and φ VALUES - Span 1 At 70 years Et Ø0 kN/mm² Self weight 3.52 7.28 Partitions/walls 2.68 8.96 Other dead loads 2.31 9.96 Permanent imposed 2.68 8.96 Variable load Composite 2.95 8.34 Permanent load

At 70 years Et Ø0 kN/mm² 3.52 7.28 2.68 8.96 2.31 9.96 2.68 8.96 0 32.94 2.26 10.11 Total load

Span 6 kN/m 0.00 5.00 #DIV/0! #DIV/0! #DIV/0! #DIV/0!

123.00

At 28 days Et Ø (t,t0) kN/mm² 1.37 13.91 0 32.94 1.05 16.04 At partition loading

80


17/07/2006 17:05:45

RCC41R Rigorous Continuous Beams (A & D).xls RCC41R Rigorous Continuous Beams (A & D)/ MAIN! Project


Client

Advisory Group

Location



rmw


Bay width SPANS SPAN 1 SPAN 2 SPAN 3 SPAN 4 SPAN 5 SPAN 6 SUPPORTS Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Support 7

5000

Checked

chg

© 2006 TCC

H (mm)

bw (mm)

hf (mm)

Type

bf (mm)

6.000 6.000 6.000 6.000

375 375 375 375

300 300 300 300

125 125 125 125

T T T T

1140 960 1020 1080

H (mm)

B (mm)

End Cond

250 250 250 250 250

250 250 250 250 250

F F F F F

3.750 3.750 3.750 3.750 3.750

Sheet No

81 56

11-Jul-06 Revision

Job No

-

R68

mm

L (m)

ABOVE (m)

Date

BELOW (m)

3.75 3.750 3.750 3.750 3.750

LOADING PATTERN min

max

DEAD 1 1.4 IMPOSED 0 1.6 REBAR LAYERING Support steel in alt layer ? N

H (mm)

B (mm)

End Cond

250 250 250 250 250

250 250 250 250 250

F F F F F

LOADING DIAGRAM

C LOADING

H UDLs (kN/m)


PLs (kN)

Position (m)

Dead Load

Imposed Load

Position from left

Loaded Length

33.0

15.0

~~~~~

~~~~~ ~~~~~ ~~~~~

34.2

15.0

~~~~~

~~~~~ ~~~~~ ~~~~~

34.2 30.0

15.0 15.0

~~~~~ 2.50

~~~~~ ~~~~~ ~~~~~


Dead Load

Imposed Load

33.0

15.0

Position from left

Loaded Length

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~


ALL SPANS LOADED ODD SPANS LOADED EVEN SPANS LOADED Characteristic Dead Characteristic Imposed

1

2

3

4

5

186.7 188.4 69.2 84.7 45.0

448.2 338.1 350.5 216.6 95.5

472.4 348.8 321.4 219.3 97.1

481.3 381.9 360.1 233.3 99.1

182.4 64.5 184.5 82.5 42.8

81


17/07/2006 17:05:48

RCC41R Rigorous Continuous Beams (A & D)/ ACTIONS!

Project


Client

Advisory Group

Location



rmw


Checked

Date

Revision

chg

© 2006 TCC

Page

11-Apr-06 -

82 57 Job No

R68


300

300

200

200

100

100

0

0

-100

-100 -200

-200

-300

-300

C

H



SPAN No

1

2

3

4

5

252.7 214.8 0.850

240.2 240.2 1.000

278.1 236.4 0.850

79.8 79.8 1.000

~ ~ ~

~ ~ ~

~ ~ ~

15.0% 1

2

3

4

179.26 176.94 0.987

135.23 127.14 0.940

194.44 192.72 0.991

173.40 169.71 0.979

400

200

200

0

0

-200

-200

-400

-400



H

SPAN No

2

H

3

240.8 234.5

219.0 221.7

214.1 217.6

249.6 254.8

249.0 248.4

4

Elastic V

245.7

188.5

~

~

~

~

Redistributed V

238.8

184.5

~

~

~

~

COLUMN MOMENTS ALL SPANS Above LOADED Below ODD SPANS Above LOADED Below EVEN SPANS Above LOADED Below

kNm/m kNm/m ~


C

1

191.4 188.4

H

15.0%

400

C


81.8 81.8 1.000

Redistribution


C

1

2

3

4

5

35.6 35.6 40.9 40.9 11.5 11.5

-8.3 -8.3 -23.5 -23.5 11.5 11.5

6.8 6.8 24.5 24.5 -14.7 -14.7

1.3 1.3 -17.7 -17.7 19.6 19.6

-33.6 -33.6 -9.6 -9.6 -39.9 -39.9

kNm kNm kNm kNm kNm kNm

82


17/07/2006 17:05:51

RCC41R Rigorous Continuous Beams (A & D).xls RCC41R Rigorous Continuous Beams (A & D)/ SPANS!

Project


Client

Advisory Group

Location





TOP STEEL

BTM STEEL

DEFLECTION mm SHEAR

LINKS


ACTIONS DESIGN

TOP STEEL

BTM STEEL

DEFLECTION mm SHEAR

LINKS


0.163

ok



4

0.235

ok

-0.134

R68

RIGHT 186.2 0.85 327.5 1623 201 H

25

1963 H

16

0

As prov 3 0

As' prov 603 Precamber (mm) = 0 Increase btm As by 20% 202.8 2.064 0.743 H10 @ 150 for 1650 2 ok ok ok ok ok ok ok

0.003

ok ok ok ok ok

83 58 Job No

-

ok ok ok ok ok

LEFT CENTRE M kNm 188.6 127.1 ßb 0.91 0.94 d mm 327.5 325.0 As mm² 1694 947 113 0 As' mm² Layer 1 4 H 25 2 H 16 Layer 2 0 0 As prov mm² 1963 As' prov 402 Layer 1 2 H 16 4 H 20 Layer 2 0 0 As' prov mm² 402 As prov 1257 Permanent = 18.83 < 24.00 Imposed = 0.00 < 12.00 Affecting partitions = 22.15 > 17.14 FAILS V kN 189.2 Link Ø v N/mm² 1.926 10 vc N/mm² 0.743 Nominal H10 @ 175 for 1400 H10 @ 225 legs No 2 2

CHECKS

Revision

chg

© 2006 TCC

Page

11-Apr-06

Checked

LEFT CENTRE M kNm 58.8 176.9 ßb 1.00 0.99 d mm 332.0 322.5 433 1328 As mm² As' mm² 0 0 Layer 1 3 H 16 2 H 16 Layer 2 0 0 As prov mm² 603 As' prov 402 Layer 1 3 H 16 4 H 25 Layer 2 0 0 As' prov mm² 603 As prov 1963 Permanent = 16.34 < 24.00 Imposed = 4.88 < 12.00 Affecting partitions = 15.07 < 17.14 ok V kN 156.3 Link Ø v N/mm² 1.570 10 0.497 Nominal vc N/mm² H10 @ 200 for 1400 H10 @ 225 legs No 2 2

CHECKS

SPAN 2

Date

rmw

4

0.228

RIGHT 200.0 1.00 327.5 1787 210 H

25

1963 H

16

0

As prov 2 0


0.218

83


17/07/2006 17:05:54

RCC41R Rigorous Continuous Beams (A & D)/ SPANS! Project


Client

Advisory Group

Location





TOP STEEL

BTM STEEL

DEFLECTION mm SHEAR

LINKS


ACTIONS DESIGN

TOP STEEL

BTM STEEL

DEFLECTION mm SHEAR

LINKS


0.233

ok



4

0.117

ok

0.288

R68

RIGHT 206.6 0.86 327.5 1799 357 H

25

1963 H

16

0

As prov 3 0

As' prov 603 Precamber (mm) = 0 Increase btm As by 0% V 215.8 v 2.197 vc 0.743 H10 @ 150 for 1800 2 ok ok ok ok ok ok ok

0.300

ok ok ok ok MORE THAN 2 LAYERS

84 59 Job No

-

ok ok ok ok ok

LEFT CENTRE M kNm 209.9 169.7 ßb 0.85 0.98 d mm 327.5 325.0 As mm² 1819 1264 403 0 As' mm² Layer 1 4 H 25 3 H 16 0 0 0 Layer 2 As prov mm² 1963 As' prov 603 Layer 1 3 H 16 4 H 20 0 0 99 H Layer 2 As' prov mm² 603 As prov 1257 Permanent = 18.39 < 24.00 Imposed = 5.62 < 12.00 Affecting partitions = 16.28 < 17.14 ok V kN 207.0 Link Ø 2.107 10 v N/mm² 0.743 Nominal vc N/mm² H10 @ 150 for 1800 H10 @ 225 No 2 2 legs

CHECKS

Revision

chg

© 2006 TCC

Page

Apr-2006

Checked

LEFT CENTRE M kNm 208.9 192.7 ßb 1.00 0.99 d mm 327.5 322.5 1860 1447 As mm² 286 0 As' mm² Layer 1 4 H 25 2 H 16 Layer 2 0 0 As prov mm² 1963 As' prov 402 Layer 1 3 H 16 3 H 25 0 0 Layer 2 As' prov mm² 603 As prov 1473 Permanent = 13.00 < 24.00 Imposed = 5.77 < 12.00 Affecting partitions = 15.56 < 17.14 ok V kN 222.2 Link Ø 2.262 10 v N/mm² vc N/mm² 0.743 Nominal H10 @ 125 for 1875 H10 @ 225 No 2 2 legs

CHECKS

SPAN 4

Date

rmw

3

0.266

RIGHT 57.3 1.00 332.0 421 0 H

16

603 H

16

0

As prov 2 0


0.301

84


17/07/2006 17:05:56


RCC42 Post-tensioned Slabs & Beams (A & D).xls This spreadsheet designs post-tensioned slab and beam elements in accordance with BS 8110: Part 1, 1997. In essence the spreadsheet checks a number of parameters: stresses at transfer, stresses in service, moments of resistance at ULS, shear, vibration, deflection, neutral axis depth, and reinforcement service stress. These checks are shown in SUMMARY! The spreadsheet is set out in several sheets. ■ MAT DATA! Defines load cases, various options and material

properties. ■ SUMMARY! Summarises the design, analysis, checks and

outputs from the rest of the spreadsheet.

■ Commonly 70% to 75% is taken for initial estimates for

jacking force/ final force. This quantity is calculated at Details N68:N69 and has to be re-specified in Details! line 68 to be within 5% of that calculated. ■ With respect to allowable flexural tensile stresses in prestressed

beams (and slabs), BS 8110: Part 1, defines three classes (see Clause 4.3.4.3). These classes determine the limits of tensile stress. For example see BS 8110: Part 1, Clause 4.1.3, which also allows 5.0 N/mm2 tensile strength for C40 concrete. For Class 3, which is generally used for internal environments, cracking is allowed either up to 0.1 mm or, more usually, to 0.2 mm.

■ DETAILS! Shows the workings for the moment distribution

for the various load cases, profiles, prestress losses and checks in some detail. ■ DEFLECT! Shows workings for deflection at 1/20 points

along each span. ■ Graf! Provides the data for the graphs, and values generated

are used for checking. Users are referred to CS TR43 Post-tensioned concrete floors – Design Handbook(14), and Post-tensioned concrete floors(16) for further details of methods and values used.

■ Slab or Beam varies shear requirements and determines

whether nominal top bonded reinforcement is included in the spans or not. Nominal top steel is included in mid-span of beams. If slabs are specified, the user may choose to use nominal top steel to overcome hogging moments in the spans. Invoking the nominal bonded reinforcement in midspan should overcome most problems with hogging in, say, dissimilar spans of slabs. Slabs requires a second input; type of slab alters parameters used in checking vibration. ■ Normal curtailment rules for conventional reinforcement

A maximum of three spans may be considered. Cantilevers are not available. Shortening is calculated in the losses section, but is not used to modify column moments. The effects of restraint to both columns and prestress in the member must be considered. The spreadsheet considers one direction at a time only. The nub of this spreadsheet is page two of SUMMARY! The source of any failures or missing information (e.g. no tendons or no tendon height specified) will become apparent in SUMMARY ii. It is suggested that users may wish to create a second window of this part of the spreadsheet (Window/ New Window/ Arrange).

MATDATA! The first sheet includes all the general and material input data used in the subsequent sheets. Load combinations and load factors are defined. The input under Options should be selfexplanatory. The choices have implications on the design as shown below. ■ Stressing ends determines where prestressing losses occur ■ Prestressing system – Specifying unbonded or bonded changes

prestress loss calculations. Prestress losses tend to be higher with bonded tendons as wobble factors and coefficients of friction are higher but using several strands in a single duct can lead to overall economy, especially in more heavily loaded beams. Bonded systems tend to require less conventional reinforcement.

are not necessarily satisfactory for post-tensioned slabs and beams. Nonetheless the spreadsheet assumes that curtailment occurs at 0.3 x span. With regard to concrete, the usual minimum strength used in prestressing is 40 N/mm2 . The minimum allowable strength at transfer (i.e. when the tendons are initially stressed), fci, is 25 N/ mm2 .. Ambient temperatures during curing may be taken as 15oC for a UK summer, but otherwise may be dependent upon curing/ insulation regimes. Typically, long-term Relative Humidity may be taken as 45% indoors, or 85% outdoors for the UK. Other data used in the determination of various concrete factors, e.g. determination of creep factors, is shown on the right hand side of the sheet. These factors are case specific and have been derived from the best available data for the various parameters shown. The formulae for calculating creep factors and free shrinkage strain are from C&CA paper TDH 2391(17 ), and use the following factors. ■ Kb is a factor depending on the composition of the concrete, ■ Kc is an environmental factor, ■ Kd is a maturity factor, ■ Ke is an effective member thickness factor, and ■ Kt covers the development of the deferred deformation with

time. Factors used in the derivation of material data are given to the right hand side of the sheet. 85


17/07/2006 17:05:59

Details of strand used in the UK are given at the bottom of the sheet. Users should ensure that their chosen strand is readily available. Post-tensioned concrete floors(16) gives typical values for µ (coefficient of friction), K (wobble factors), Rel% (relaxation) and draw-in (mm) in Tables 2.6 and 7.1.

should be assessed from the ψ 2 factor in EC2, which is usually 20% of imposed load for dwellings, 30% for offices and stores, and 60% for parking. (One never takes 100%, as y2 adjusts for the very different f (creep) values. Hence 30% is appropriate for a more or less permanently loaded structures: the high value for parking is to compensate for long-term dynamic effects.)

It is usually assumed that working loads are applied at a concrete age of 60 days (user input). The quasi-permanent imposed load Factors used in the derivation of material data Assume

Final prestress + dead +

BS 8110 Table 4.2 30

3.8

0

40

5

0

0

50

5.8

5.8 1.271 3

0 1.267 4

1.258 5

1.249 6

1.245 7

1.235 8

1.225 9

1.210 10

1.195 11

1.185 12

1.170 13

1.160 14

1.145 15

0.8

1

1.5

2

2.5

3

4

5

6

7

8

9

10

Maturity Curve 0

4.9736

1.110 16 13

0.8

0.2

0.5

0.5

0.5

0.5

1

1

1

1

1

1

1

3

3

30

0

2.6

4.5

7.9

10.3

12.2

13.7

16.2

18

19.5

20.6

21.7

22.6

23.2

25.2

40

0

5.2

7.8

12.2

15.5

18.1

20.1

23.2

25.5

27.3

29

30.4

31.3

32.2

34.5

33.7

35.8

37.8

39.2

50

0

11.4

12.7

18.1

22.2

25.1

27.3

31.1

40.3

41.3

43.9

60

0

13.7

15.2

21.7

26.6

30.1

32.8

37.3

40.4

43

45.4

47

48.4

49.6

52.7

60 60 60

0 0 0

13.7 13.7 13.7

15.2 15.2 15.2

21.7 21.7 21.7

26.6 26.6 26.6

30.1 30.1 30.1

32.8 32.8 32.8

37.3 37.3 37.3

40.4 40.4 40.4

43 43 43

45.4 45.4 45.4

47 47 47

48.4 48.4 48.4

49.6 49.6 49.6

52.7 52.7 52.7

Longterm

fcu inf 67.2

Et inf 34.30

85 1.7

90 1.5

95 1.25

100 1

95 58.5

100 0

EARLY STRENGTH

LATE STRENGTH

1

4

0.8

5.8

60

37.3

40.4

3.1

39.78

40

60

0

100

60

64.8

67.2

Kc = Relative Humidity factor 30 35 40 3.2 3.13 3.05 50 55 2.85

2.4

64.80

45 2.95 2.77

50 2.85 0.08

55 2.77 0

60 2.65 2.850

65 2.5

70 2.3

75 2.13

80 1.9

Kd = Ambient factor 30 90 60 120 1.8 1.6 120 120 1500 1860

420 420 1.2 1.4 0.75

840 1860 1 0.2 0.25

2700 2700 0.75 30 660

5400 5400 0.65 1.550 0.911

10800

Kb = Cement Content & W/C Ratio factor 0.4 0.5 0.6 200 0.5 0.8 300 0.7 0.9 1.17 400 0.83 1.17 1.63 500 0.97 1.45 2 300 0.7 0.9 1.17 400 0.83 1.17 1.63 0.739 0.981 1.308

0.7 1.02 1.48 2.1 2.55 1.48 2.1 1.666

0.8 1.28 1.82 2.55 3.1 1.82 2.55 2.039

0.5 0.981 1.308 0.327

1.145

Ke = Effective Thickness factor 406.5 0 50 100 150 10 1.2 1 0.94 Span 1 400 450 0.72 Span 2 400 450 0.72 Span 3 #DIV/0! #DIV/0! #DIV/0!

406.5 200 0.85 0.709 0.709 #DIV/0!

#DIV/0! 250 0.795 0.011 0.011 #DIV/0!

300 0.75 6.5 6.5 #DIV/0!

350 0.733 0.719 0.719 #DIV/0!

400 0.72

450 0.709

500 0.7

55 360 360

60 330 20

65 305 0

70 275 380

75 243

80 205

85 162

90 115

150 0.907 0.55 0.55 #DIV/0!

200 0.8 0.513 0.513 #DIV/0!

250 0.71 0.037 0.037 #DIV/0!

300 0.65 6.5 6.5 #DIV/0!

350 0.587 0.548 0.548 #DIV/0!

400 0.55

450 0.513

500 0.5

Ultimate Shrinkage Strain - Bending 0 0.1 0.2 0.3 % 0.26 0.26 0.26 0.26 Kp 0.9418 0.9418 0.9418 0.9418 εcs 208.9 208.9 208.9 208.9 m 20.3909 Ec 28 32

0.4 0.26 0.9418 208.9

210 210 1.4 1.6 1

εc = Free Shrinkage Strain 40 45 50 420 405 380 50 55 380 Ke factor for Shrinkage 0 50 100 10 1.3 1.05 Span 1 400 450 Span 2 400 450 Span 3 #DIV/0! #DIV/0!

0.5 0.26 0.9418 208.9 Ø 2.3462

0.5 1.000

0.6 0.7 0.26 0.26 0.9418 0.9418 208.9 208.9 Ec 9.56309

0.8 0.26 0.9418 208.9

0.9 1 0.26 0.26 0.9418 0.9418 208.9 208.9 Ks = 23.75

Kt 0.93143

microstrain

Ultimate Shrinkage Strain - Prestress Span 1 Span 2 Span 3 % 0.3 0.3 0.3 Kp 0.9335 0.9335 0.9335 εcs 207.1 207.1 #DIV/0!

86


17/07/2006 17:06:01

RCC42 Post-tensioned Slabs & Beams (A & D).xls Loads are characteristic and are for the whole bay width (not expressed as kN/m2 – unless a 1 m bay width is being analysed). The self-weight is a user input. The construction load is intended to be that required to be applied during transfer (usually 1.5 kN/m2 ). However, designers should consider the load history of the slab to ensure worst cases are checked, e.g. temporary loads while casting floors above. Bay widths in the normal direction do not affect the loading unless, of course, the user chooses to introduce a suitable relationship (in the loads input).

SUMMARY! The first page (top part of the sheet entitled SUMMARY!) shows input for the sub-frame analysis, i.e. dimensions and loads. Input should be fairly self explanatory. It should be noted that H is in the plane of the screen and b, bw etc. at right angles to the plane of the screen. Several warnings are given under Operating Instructions and with conditional formatting should data be incorrect.

The current configuration being designed is shown in a chart. This gives a scale representation of the spans, supports, loads and an idealised cross section of each member. Charts also show representations of the tendon profiles and equivalent loads used in the analysis. For the tendons, a reversed parabolic profile is used but minimum lengths of straight tendon are used at the supports as recommended by Khan(16) . Service equivalent loads are shown: those at transfer may be viewed at DETAILS!B361: N372.

Supports can be made to be knife-edge by inputting K in column D: remote ends of columns can be either F for fixed, or P for pinned. The line can be left blank. A support width (h below) can be used in conjunction with a ‘K’ support so that design moments are used at the support face. Data under ‘Normal Direction’ is used for the vibration checks. The number of bays affects possible modes of vibration, which is checked in accordance with CS TR43(14) . The vibration response factors calculated are accordance with Steel Construction Institute(18) and Concrete Society guidelines. Vibration should not be a problem in post-tensioned slabs and beams. Normally, vibration response factors of 12 are used for very busy offices, 8 for normal offices, or 4 for high specification offices or laboratories where vibration is critical.

The next page (SUMMARY! B67:M79) is the nub of the spreadsheet: it has a number of key inputs and out-puts. These include inputs of PI / Pj (initial force/ jacking force), Pf / Pj (final force/ jacking force), number and height of tendons, and amounts of conventional reinforcement (some of the inputs are necessary to avoid circular arguments). With regard to Tendons the spreadsheet automatically calculates the number of tendons for each span using an algorithm. The algorithm uses either the maximum of the median stress levels,

Designers should be aware that the 2005 version of CS TR43Appendix G gives revised recommendations on vibration. Extract from SUMMARY!

SUMMARY ii: Tendons & bonded reinforcement (a) TENDONS No of STRANDS Recommended Use Recommend'd height Height mm Length Straight mm x to max Sag mm Pi kN Balance Load kN Pf kN Balance Load kN

Pj = 130 kN Supt 1

Span 1

24 24 295 300 150

24 24 40 40

2769 278.4 2521 253.4

5311 2763 2515

Pf/Pi = 24 24

26 24 40 40

485 480 150

2760 371.8 2513 338.5

7006 2763

2760 354.7 2513 322.9

2515

'EFFICIENCY' OK OK OK OK OK OK OK OK OK

VALID DESIGN

Supt 3

26 24

0 0 295

300 0

300 0

2769 261.5 2521 238.1

a

0 0.0 0 0.0

kN

Span 3

Supt 4

0 0 0 0

0 0

0 0 0

0 0.0 0 0.0

0

52% 59%

b(T)

53%

c(C)

81%

c(T)

94%

d

36%

e f

80.0%

47%

b(C)

8% 28%

g

GLOBAL STATUS

Pf/Pj =

Span 2

26 24

480 150

CHECKS Tendons (a) Stresses at transfer (b) Stresses in service (c) ULS MOR (d) Shear (e) Vibration (f) Deflection (g) Neutral axis depth Rebar stress

90.0%

Supt 2

0%

42%

83%

125%

87


17/07/2006 17:06:03

or the maximum permitted. The spreadsheet calculates the minimum number of strands required so that permissible concrete tensions are not exceeded at either the initial or final stage. Thus the numbers of tendons are then shown as recommended values, and the user can override them if required. Once the number of tendons for each span has been fixed, the program attempts to find an optimum single level of initial prestress for all strands (this often appears to be the maximum permissible). If the minimum force required generates excessive compressive stresses, the section is deemed to have failed. Tendons are assumed to be level through supports and follow a parabolic profile between. The points of inflection are taken to be at 1/10 of the clear span points. Besides number of tendons, the main user control is to adjust the value of Pf / Pj. This adjusts the number of tendons. One would rarely need to adjust tendon heights. The checks carried out are listed below. ■ Tendons (a) ■ Stresses at transfer (b)

DETAILS! Over nine pages, DETAILS! shows detailed calculations regarding section properties, distribution factors, moment distribution used for the sub-frame analysis, profiling constants, pre-stressing losses, balanced loads, ULS moment and shear checks, and finally vibration.

DEFLECT! The deflection sheet gives details of calculations dealing with defections.

TYPICALC! This sheet is intended to illustrate typical calculations for a particular point in a span in order to show how all the criteria are satisfied. The sheet illustrates the transfer and service stress checks and the calculation of Moment of Resistance carried out in tabular form in Graf! The point chosen is at 1/4 span and is highlighted in Graf!

■ Stresses in service (c) ■ ULS MOR (d) ■ Shear (e) ■ Vibration (f) ■ Deflection (g) ■ Neutral axis depth ■ Rebar stress

In the spreadsheet, those that are unsatisfactory are highlighted and directions are given for further information. There are also two charts. The ‘efficiency’ chart gives the user an idea of how hard the section is working or how far it is out. The second chart, ultimate limit state moment envelope and moments of resistance (capacity), should be used in conjunction with choosing amounts of bonded reinforcement.

Graf! Graf! provides the data for the charts of the configuration and loads, tendon profile, equivalent loads, ULS moments and capacities, shear envelopes, deflections, stresses at transfer and stresses in service within SUMMARY! Each chart is plotted at 1/20 points along each span. Many values within Graf! are used and checked for being minima or maxima for the various criteria. For instance it may be here that problems with hogging moments are found.


The third page (SUMMARY! B125:M171) shows stresses at transfer and in service in both tabular and chart form. It should be noted that, in keeping with current practice, moments are considered at the face of columns. Thus peak moments are not necessarily at column centrelines and moments might be different each side of an internal column. The convention used in the stress charts is: ■ Red squares – tension, blue circles – compression ■ Solid markers – bottom, hollow markers – top ■ Dotted lines – permissible stresses

The fourth page (SUMMARY iv) gives details of shear envelopes, vibration and deflection together with support reactions and column moments. 88


17/07/2006 17:06:07

RCC42 Post-tensioned Slabs & Beams (A & D).xls RCC42 Post-tensioned Slabs & Beams (A & D)/ MATDATA!

Project


Client

Advisory Group

Location

Level 2 - Beam on Grid 7


POST-TENSIONED ANALYSIS & DESIGN to BS 8110:2005 Originated from RCC42.xls

Date

RMW

v3.0 on CD

Checked

Revision

chg

© 2006 TCC

Page

89 70

11-Apr-2006

Job No

-

R68

POST-TENSIONED ANALYSIS & DESIGN to BS 8110:2005 - GENERAL DATA LOAD COMBINATIONS

NOTES INPUT IS UNDERLINED. Initial prestress + OW + construction load on all spans Initial prestress + OW + construction load on odd spans FRAMES ARE ASSUMED TO Initial prestress + OW + construction load on even spans BE BRACED Final prestress + dead + imposed load on all spans Final prestress + dead + imposed load on odd spans Final prestress + dead + imposed load on even spans Final prestress + factored dead and imposed load on all spans Final prestress + factored dead + factored imposed load on odd spans Final prestress + factored dead + factored imposed load on even spans Final prestress + dead + 30% imposed load on odd spans

SLS 1 SLS 2 SLS 3

INITIAL

SLS 4 SLS 5 SLS 6 ULS 1

FINAL

ULTIMATE

ULS 2 ULS 3

DEFLECTION

SLS 7

LOAD FACTORS

min

max

1 0

1.4 1.6

DEAD IMPOSED OPTIONS

VIBRATION Limiting reponse factor = 8

Stressing Ends

B (L, R, B) Prestress system U (U, B) Assume 20% max redistribution 0.7 BS 8110 Class 3 (Clause 4.1.3) . Slab or beam B (B or S) Limiting crack width 0.2 mm . In slabs, nominal top bonded reinforcement in span? Y (Y or N; use Y for dissimilar spans) Damping, ζ (2% to 8%) 5% Slab type S (S)olid, (R)ibbed or (W)affle, supported by beam

Jacking F/strength

fcu = 60 MATERIALS CONCRETE At days 4.80 fci = 39.78 Cement content 330 Ave ambient during curing = 15ºC STRAND

fpu = 1860 Ep = 195

REBAR

fy = 500 γm = 1.15

LOADING SEQUENCE

σc = 19.80 σt = Ec28 = 32 σic = 15.91 σit = Eci = 25.53 W/C ratio 0.55 OPC or RHPC ? γm = Longterm R/H % 50 Ap, mm² = 100 Rel % = 2

µ = 0.140 Draw in= 6 COVERS

to links

Permanent loads for Ø assessment

unmodified unmodified .

K = 0.0010 Depth to strand centre = 40 Top 25

Bottom 25

Sides 25

60 5.1

80 7.5

30% of Imposed is permanent

Load

@ Age

fcut

Et

Ø

Ec

kN/m²

days

N/mm²

kN/mm²

Creep

kN/mm²

4.80 60 -=-

39.78 64.80

25.53 33.54

3.64 2.14

5.51 10.69

-

30.80

2.45

8.92

13.81 Own weight 42.00 Applied dead Quasi-Permanent Imposed 9.60 COMBINED 65.41

5.80 4.97 OPC 1.50

NOTES on MATERIALS BRITISH LOW RELAXATION STRAND Type

Dia

Area

Breaking

Weight

Standard

15.2 12.5 15.7 12.9 15.2 12.7

139 93 150 100 165 112

1670 1770 1770 1860 1820 1860

1.090 0.730 1.180 0.785 1.295 0.890

Super Compact

RELAXATION at 0.7fpu 20 Ambient ºC 1.8 Relaxation

40 3.5

100 10.7

89


17/07/2006 17:06:08

RCC42 Post-tensioned Slabs & Beams (A & D)/ SUMMARY! i

Project


Client

Advisory Group

Location



POST-TENSIONED ANALYSIS & DESIGN to BS 8110:2005 Originated from RCC42.xls v3.0 on CD

Date

RMW

Page

11-Apr-2006

Checked

chg

© 2006 TCC

71 90

Revision

Job No

-

R68

SUMMARY I : Dimensions and Loads NORMAL DIRECTION

SPANS SPAN 1 SPAN 2 SPAN 3 SUPPORTS SUPPORT 1 SUPPORT 2 SUPPORT 3 SUPPORT 4 CONFIGURATION

LOADING

Lm

H mm

bw mm

hf mm

Section

bf mm

No Bays

BAY WIDTH m

12.000 12.500

525 525

1800 1800

200 200

T T

3000 3000

5 5

6.000 6.000

ABOVE m

H mm

B mm

End Cond

BELOW m

H mm

B mm

End Cond

4.000 4.000

300 300

600 600

F F

K

BEAM supporting Solid Slab to BS8110 Class 3 (0.2 mm crack width), fcu = 60, Stressed from Both Ends

UDLs~kN/m (char), PLs~kN (char), Position~m

SPAN 1

UDL PL 1 PL 2 Part UDL Construction

Applied

Imposed

Position

Loaded

OW

Dead

Load

from left

Length

SPAN 3

13.81

42.00

32.00

~~~~~

~~~~~ ~~~~~ ~~~~~

UDL PL 1 PL 2 Part UDL

~~~~~

~~~~~

18.00

~~~~~

~~~~~ C'strction

13.81

42.00

32.00

~~~~~

~~~~~ ~~~~~ ~~~~~

Applied

Imposed

Position

Dead

Load

from left

Length

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~

OW

~~~~

~~~~

Loaded

SPAN 2

UDL PL 1 PL 2 Part UDL Construction

~~~~~

TENDON PROFILE

~~~~~

18.00

~~~~~

GLOBAL STATUS VALID DESIGN

~~~~~

(heights to strand centre: see heights specified under TENDONS below) 480

300

300 43

40

EQUIVALENT LOADS in service 322 kN/m

400 300

241 kN/m

294 kN/m 190 kN/m

200 100 0

-62 kN/m

-56 kN/m

0 kN/m

-100 -200

90


17/07/2006 17:06:11

RCC42 Post-tensioned Slabs & Beams (A & D).xls RCC42 Post-tensioned Slabs & Beams (A & D)/ SUMMARY! ii

Project


Client

Advisory Group

Location



Date

RMW


Page

11-Apr-2006

Checked

Revision

chg

© 2006 TCC

91 72 Job No

-

R68

SUMMARY ii: Tendons & bonded reinforcement (a) TENDONS No of STRANDS Recommended Use Recommend'd height Height mm Length Straight mm x to max Sag mm Pi kN Balance Load kN Pf kN Balance Load kN

Pj = 130 kN Supt 1

Span 1

24 24 295 300 150

24 24 40 40

2769 278.4 2521 253.4

5311 2763 2515

Pf/Pi = 24 24

480 150

7006 2763

2760 354.7 2513 322.9

2515

'EFFICIENCY' OK OK OK OK

Main bar Ø No % Link Ø = No of legs (d) ULS MOMENTS Mu MOR

0 0 295

300 0

300 0

2769 261.5 2521 238.1

0 0.0 0 0.0

a

Supt 4

0 0 0 0

0 0

0 0 0 0

59% 81% 94%

d

36%

e f

0 0.0 0 0.0

53%

c(T)

OK OK OK

kN

Span 3

52%

b(T)

OK OK

80.0%

47%

c(C)

VALID DESIGN

REINFORCEMENT

26 24

b(C)

8% 28%

g

GLOBAL STATUS

Supt 3

26 24 40 40

485

2760 371.8 2513 338.5

Pf/Pj =

Span 2

26 24

480 150

CHECKS Tendons (a) Stresses at transfer (b) Stresses in service (c) ULS MOR (d) Shear (e) Vibration (f) Deflection (g) Neutral axis depth Rebar stress

90.0%

Supt 2

0%

42%

83%

125%

Input bonded rebar arrangement (Support bars cutailed at 0.3L) Supt 1

Span 1

Supt 2

Span 2

Supt 3

16 20 0.426%

20 20 0.665%

20 20 0.665%

12 20 0.239%

20 20 0.665%

10 8

8

8

8

8

1500.1 2440.3

1766.0 1883.9

8

Span 3

Supt 4

20 16 20 20 0.000% 0.000% 8

8

8

Span 3

Supt 4

0.0 0.0

0.0 0.0

With bonded reinforcement Supt 1

Span 1

42.2 1477.2

1523.2 2611.6

Supt 2

1529.6 2440.3

Span 2

Supt 3

11.5 1843.1

0.0 0.0

ULS MOMENT ENVELOPE/MOR 3000 2000 1000 0 -1000 -2000 -3000

91


17/07/2006 17:06:14

RCC42 Post-tensioned Slabs & Beams (A & D)/ SUMMARY! iii

Project


Client

Advisory Group

Location



Date

RMW


Checked

92 73

Revision

chg

© 2006 TCC

Page

11-Apr-2006

Job No

-

R68

SUMMARY iii STRESSES (b) STRESSES at TRANSFER Supt 1

Tendon height 286.8 Pi 2768.6 Max Compression 3.14 Max Tension 0.00

Span 1

Supt 2

41.8 2762.8 7.50 -1.69

462.3 2760.3 6.28 -2.76

Span 2

462.4 2760.3 6.09 -2.51

41.9 2762.9 7.52 -1.70

Supt 3

285.2 2768.6 2.92 0.00

0.0 0.0 0.00 0.00

Span 3

Supt 4

0.0 0.0 0.00 0.00

0.0 0.0 0.00 0.00

STRESSES AT TRANSFER

25 20 15 10 5 0 Com-Top

Com-Btm

Ten-Btm x 4

Ten-Top x 4

Com Limit

Ten Limit x 4

Col centres

(c) STRESSES in SERVICE Supt 1

Tendon height 286.8 Pf 2520.6 Max Compression 3.55 Max Tension 0.00

Span 1

40.5 2515.5 5.54 -2.28

Supt 2

462.3 2512.8 10.44 -4.35

Span 2

462.4 2512.8 10.56 -4.44

40.7 2515.7 6.79 -3.88

Supt 3

285.2 2520.6 4.07 -0.38

0.0 0.0 0.00 0.00

Span 3

Supt 4

0.0 0.0 0.00 0.00

0.0 0.0 0.00 0.00

STRESSES IN SERVICE

30 25 20 15 10 5 0 Com-Top

Com-Btm

Ten-Btm x 4

Ten-Top x 4

Com Limit

Ten Limit x 4

Col centres

92


17/07/2006 17:06:17

RCC42 Post-tensioned Slabs & Beams (A & D).xls RCC42 Post-tensioned Slabs & Beams (A & D)/ SUMMARY! iv Project


Client

Advisory Group

Location




SUMMARY iv (e) SHEAR

Date

RMW

Page

11-Apr-2006

Checked

Revision

chg

© 2006 TCC

93 74 Job No

-

R68

Link Ø = 10 Span 1

Left V 636.2 N cracked? Vc 1629.0 No of legs 8 Link spacing 375

Span 2

Right 881.9 Y 733.0 8 375

Span 3

Left 919.1 Y 753.3 8 375

Right 678.1 N 1629.0 8 375

Left 0.0 N 0.0 8 0

Right 0.0 N 0.0 8 0

ULS SHEAR ENVELOPE

1500 1000

938.5 650.6

500 0

0.0

-500

-678.1

-901.3

-1000 -1500

(f) VIBRATION Response factor

Span 1

Span 2

Span 3

0.60 OK

0.61 OK

0.00 OK

(g) DEFLECTION MAX DEFLECTIONS

15 10 5

7.97

6.88

0

0.0 0.00

-5 -10

-8.4

-15

-13.7

-20

Transfer

Span 1 = 8.6mm < 48

Final

Col centres

OK

Zero axis

Span 2 = 14mm < 50

OK -

SUPPORT REACTIONS ULS 4 ULS 5 ULS 6 DEAD IMPOSED COLUMN MOMENTS ULS 4

Above Below

ULS 5

Above Below

ULS 6

Above Below

Supt 1

Supt 2

Supt 3

Supt 4

650.6 655.6 199.2 274.6 147.0

1839.8 1361.7 1409.0 803.5 484.4

678.1 232.2 678.1 289.2 152.6

0.0 0.0 0.0 0.0 0.0

Supt 1

Supt 2

Supt 3

Supt 4

0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00

-

kN kN kN kN kN


93


17/07/2006 17:06:19

RCC42 Post-tensioned Slabs & Beams (A & D)/ TYPICALC!

Project Spreadsheets to BS 8110 Client Location

The Concrete Centre

Advisory Group Level 2 - Beam on Grid 7

Made by

RMW


Checked

Date

11-Apr-06 Revision

chg

© 2006 TCC

h = 525 mm, bw = 1800 mm

Job No

-

TYPICAL CALCULATION for Span 1 at 3.60 m from C/L of LH support Class 3 Tee section,

Page 94 75

R68 BS 8110 Reference

hf = 200 mm, bf =3000 mm.

Ac = 1185000mm2, Z top = 120.0E6 mm³, and Z bottom = 93.3E6 mm³ Tendons are unbonded, Ap = 100mm2, fpu = 1,860 N/mm2 and 75.9 mm from soffite There are 24 tendons, jacked to 1,302 N/mm² or 70.0% fpu Prestress losses at this section are -2,504.4 kN at transfer and -2,256.6 kN longterm (b) Stresses at transfer M = 395.0 kNm hogging, and prestressing force = 2,764.8 kN

4.3.5

Max compression (bottom) = M/Z + P/A = 395.0E3 / 93.3 + 2,764.8 / 1185 = 6.57 N/mm² < 15.91 N/mm² allowed

Max tension (bottom) = M/Z - P/A = -159.0E3 / 93.3 - 2,764.8 / 1185 = 0.96 N/mm² < 4.66 N/mm² allowed

(c) Stresses in service

4.3.4

M = 397.1 kNm sagging, and prestressing force = 2,517.0 kN Max compression (top) = 397.12E6 / 120.0E6 + 2,517.0E3 / 1185E3 = 5.43 N/mm² < 20.00 N/mm² allowed

Max tension (bottom) = 397.12 / 93.3 - 2,517.0 / 1185 = 2.13 N/mm² < 5.49 N/mm² allowed

(d) MOR at ultimate limit state

4.3.7

M = 1,383.7 kNm sagging, and prestressing force = 2,517.0 kN fpe = 1000 x 2,517.0 / 24 / 100 = 1,048.8 N/mm² Reinforcement d = 480 mm Rp = 1860 x 100 x 24 / 60 / 3000 / (525 - 75.86) = 0.055 fpe/fpu = 1,048.8 / 1860 x 1.15 = 0.648 Lte = 12,250 mm fpb (unbonded) = 1,048.8 + 7000 x (525 - 75.86) / 12,250 (1 - 1.7 x 0.055) = 1,281.3 N/mm²

Eq 52

Tendon force = 1,281.3 x 24 x 100 / 1000 = 3,075.2 kN Rebar force = 500 / 1.15 x 6,283 / 1000 = 2,731.8 kN Total tensile force = 3,075.2 + 2,731.8 = 5,807.0 kN Compression block depth, dn = 1000 / 5,807.0 / 0.45 / 60 / 3000 = 71.69 mm MOR = (3,075.2 ( 525 - 75.9 - 71.69 / 2) + 2,731.8 x (480 - 71.69 / 2)) / 1000

Eq 51

= 2,484.3 kNm > 1,383.7 ok

94


17/07/2006 17:06:22

RCC42 Post-tensioned Slabs & Beams (A & D).xls RCC42 Post-tensioned Slabs & Beams (A & D)/ DETAILS!

Project


Client

Advisory Group


Location Level 2 - Beam on Grid 7

Date

RMW


Page

Checked

Revision

chg

© 2006 TCC

95 76

11-Apr-2006 Job No

-

R68

DETAILED CALCULATIONS SECTION PROPERTIES Supt 1

Flange area, Af Web area, Aw Total area, Ac Flange Yf Web Yw Σ = Ac.Yt Yt Yb If Iw Σ = Ixx Zt Zb em St Sb

4.59 1.045 0.942

Span 1 240000 945000 1E+06

Supt 2

Span 2 240000 945000 1E+06

Supt 3

0 0 0 0

100

100

0

262.5 3E+08 229.59 295.41 5E+09 2E+10 3E+10 1E+08 9E+07 255.41 -1.521 4.244

184.59 2.822 -1.345

184.59 2.822 -1.345

262.5 3E+08 229.59 295.41 5E+09 2E+10 3E+10 1E+08 9E+07 255.41 -1.521 4.244

0

4.59 1.045 0.942

300.00 0.000 0.000

0 0 0.00 0.00 0 0 0 0 0 0.00 0.000 0.000

#VALUE! 0.000 0.000

DISTRIBUTION FACTORS SUPT 1

I Stiffness Sum Factor

SUPT 2

SUPT 3

SUPT 4

Up col

Lo col

R

L

Up col

Lo col

R

L

Up col

Lo col

R

L

Up col

Lo col

0

1.4E+09

2.8E+10

2.8E+10

0

1.4E+09

2.8E+10

2.8E+10

0

0

0

0

0

0

0

3.4E+08

2.3E+09

2.3E+09

0

3.4E+08

2.2E+09

2.2E+09

0

0

0

0

0

0

2.6E+09

4.8E+09

0.8719

0.4746

0.0000

0.0000

0.0000

0.1281

2.2E+09

0.0000

0.0697

0.4556

1.0000

0

0.0000

0.0000

0.0000

1.0000

Partial UDL factors 1

2

3

a b

0 0

0 0

0 0

R

L

0.0 #DIV/0! #DIV/0! 0.0 0.0

FIXED END MOMENTS OWN WEIGHT

Cant UDL PL 1 PL 2 part UDL FEM

SPAN 1

SPAN 2

SPAN 3

L

R

L

165.7 0.0 0.0 0.0

994.0 165.7 0.0 0.0 0.0

1078.6 179.8 0.0 0.0 0.0

179.8 0.0 0.0 0.0

0.0 0.0 #DIV/0! #DIV/0! 0.0

165.7

165.7

179.8

179.8

0.0

APPLIED DEAD R

IMPOSED



SPAN 1

SPAN 3

SPAN 2

L

R

L

R

L

504.0 0.0 0.0 0.0

3024.0 504.0 0.0 0.0 0.0

R

3281.3 546.9 0.0 0.0 0.0

546.9 0.0 0.0 0.0

0.0 0.0 #DIV/0! #DIV/0! 0.0

0.0 #DIV/0! #DIV/0! 0.0

504.0

504.0

546.9

546.9

0.0

0.0

216.0

1296.0 216.0

1406.3 234.4

234.4

0.0 0.0

0.0

216.0

216.0

234.4

234.4

0.0

0.0

LoCol

HiCol

SUPT 4

LoCol

CONSTRUCTION

384.0 0.0 0.0 0.0

2304.0 384.0 0.0 0.0 0.0

2500.0 416.7 0.0 0.0 0.0

416.7 0.0 0.0 0.0

0.0 0.0 #DIV/0! #DIV/0! 0.0

0.0 #DIV/0! #DIV/0! 0.0

384.0

384.0

416.7

416.7

0.0

0.0

LoCol

HiCol

Cant UDL FEM

MOMENT DISTRIBUTION HiCol

OWN WEIGHT

0.0

ODD SPANS

0.0

0.0

-165.7 144.4 -39.3 34.3 -17.1 14.9 -8.5 7.5 -3.7 3.2 -1.9 1.6 -0.8 0.7

0.0

-30.4

0.0 0.0 0.0 0.0

Σ

SUPT 1

SUPT 2

1.1

0.0

0.5

0.0

0.2

0.0

0.1

0.0

165.7 -78.6 72.2 -34.3 17.1 -17.1 7.5 -7.5 3.7 -3.7 1.6 -1.6 0.8 -0.8

30.4

0.0

125.1

21.2

0.0

5.0

0.0

2.2

0.0

LoCol

SUPT 3

HiCol

-75.5 0.0 -32.9 18.9 -16.4 8.2 -7.2 4.1 -3.6 1.8 -1.6 0.9 -0.8

-11.6

0.0

-5.0

0.0

-1.1

0.0

-0.5

0.0

-0.2

0.0

-0.1

0.0

0.0 -37.7 37.7 -16.5 16.5 -8.2 8.2 -3.6 3.6 -1.8 1.8 -0.8 0.8

-2.5

0.0

-104.0

-21.1

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

95


17/07/2006 17:06:24

RCC42 Post-tensioned Slabs & Beams (A & D)/ DETAILS!

Project


The Concrete Centre

Client Advisory Group Location Level 2 - Beam on Grid 7

Made by


DETAILED CALCULATIONS ii HiCol SUPT 1 OWN WEIGHT

0.0

EVEN SPANS

0.0

0.0

0.0 42.7 -37.2 21.3 -18.6 9.3 -8.1 4.6 -4.0 2.0 -1.8 1.0 -0.9

0.0

10.4

0.0 0.0 0.0 0.0

Σ IMPOSED ODD SPANS

0.0

-384.0 334.8 -91.1 79.5 -39.7 34.6 -19.8 17.3 -8.6 7.5 -4.3 3.8 -1.9 1.6

0.0

-70.4

0.0 0.0 0.0 0.0 0.0 0.0

Σ

LoCol

HiCol

0.0

0.0

0.0 98.9 -86.2 49.4 -43.1 21.5 -18.7 10.7 -9.4 4.7 -4.1 2.3 -2.0

0.0

24.0

0.0 0.0 0.0 0.0 0.0

Σ

0.0

-504.0 439.4 -119.6 104.3 -52.1 45.5 -26.0 22.7 -11.3 9.9 -5.7 4.9 -2.5 2.1

0.0

-92.4

APPLID DEAD

0.0

ODD SPANS

0.0 0.0 0.0 0.0 0.0

Σ

Revision

chg SUPT 2

0.0

85.3 0.0 42.7 -18.6 18.5 -9.3 9.3 -4.0 4.0 -2.0 2.0 -0.9 0.9

-179.8 81.9 -89.9 41.0 -20.5 17.8 -10.2 8.9 -4.5 3.9 -2.2 1.9 -1.0 0.8

0.0

127.9

-151.8

0.0

0.0

-5.5

0.0

-2.7

0.0

-1.2

0.0

-0.6

0.0

-0.3

0.0

-0.1 -10.4

49.2

0.0

11.7

0.0

5.1

0.0

2.5

0.0

1.1

0.0

0.6

0.0

0.2

0.0

384.0 -182.3 167.4 -79.5 39.7 -39.6 17.3 -17.3 8.6 -8.6 3.8 -3.8 1.9 -1.9

70.4

0.0

289.9

-241.0

-416.7 189.8 -208.3 94.9 -47.5 41.3 -23.7 20.6 -10.3 9.0 -5.2 4.5 -2.2 1.9 -351.8

0.0

0.0

-12.7

0.0

-6.3

0.0

-2.8

0.0

-1.4

0.0

-0.6

0.0

-0.3

0.0

197.8 0.0 98.9 -43.1 43.0 -21.6 21.5 -9.4 9.3 -4.7 4.7 -2.0 2.0

-24.0

0.0

296.4

64.6

0.0

15.3

0.0

6.7

0.0

3.3

0.0

1.5

0.0

0.7

0.0

0.3

0.0

504.0 -239.2 219.7 -104.3 52.1 -52.0 22.7 -22.7 11.3 -11.3 4.9 -4.9 2.5 -2.5

92.4

0.0

380.5

LoCol

12.5

0.0

6.3

0.0

2.7

0.0

1.4

0.0

0.6

0.0

0.3

0.0

0.1

0.0

179.8 -179.8 41.0 -41.0 20.5 -20.5 8.9 -8.9 4.5 -4.5 1.9 -1.9 1.0 -1.0

23.9

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-175.0 0.0 -76.3 43.7 -38.0 19.1 -16.6 9.5 -8.3 4.1 -3.6 2.1 -1.8

-26.8

0.0

-11.7

0.0

-5.8

0.0

-2.5

0.0

-1.3

0.0

-0.6

0.0

-0.3

0.0

0.0 -87.5 87.5 -38.1 38.1 -19.0 19.0 -8.3 8.3 -4.1 4.1 -1.8 1.8

-48.9

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

29.1

0.0

14.5

0.0

6.3

0.0

3.2

0.0

1.4

0.0

0.7

0.0

0.3

0.0

416.7 -416.7 94.9 -94.9 47.5 -47.5 20.6 -20.6 10.3 -10.3 4.5 -4.5 2.2 -2.2

55.4

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-229.6 0.0 -100.1 57.4 -49.9 25.0 -21.8 12.5 -10.8 5.4 -4.7 2.7 -2.4

-35.2

0.0

-15.3

0.0

-7.6

0.0

-3.3

0.0

-1.7

0.0

-0.7

0.0

-0.4

0.0

0.0 -114.8 114.8 -50.1 50.1 -25.0 25.0 -10.9 10.9 -5.4 5.4 -2.4 2.4

-316.3

-64.2

0.0

0.0

96 77 Job No

-

SUPT 3

HiCol

Page

11-Apr-2006

Checked

© 2006 TCC

IMPOSED EVEN SPANS

Date

RMW

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

R68

LoCol

HiCol

SUPT 4

LoCol

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

96


17/07/2006 17:06:27

RCC42 Post-tensioned Slabs & Beams (A & D).xls RCC42 Post-tensioned Slabs & Beams (A & D)/ DETAILS! Project


Client

Advisory Group


Location Level 2 - Beam on Grid 7 POST-TENSIONED ANALYSIS & DESIGN to BS 8110:2005 Originated from RCC42.xls v3.0 on CD

DETAILED CALCULATIONS iii HiCol SUPT 1 APPLID DEAD

0.0

EVEN SPANS

0.0

0.0

0.0 129.8 -113.2 64.9 -56.6 28.2 -24.6 14.1 -12.3 6.1 -5.3 3.1 -2.7

0.0

31.5

0.0 0.0 0.0 0.0

CONSTRUCTION ODD SPANS

Σ

0.0

-216.0 188.3 -51.3 44.7 -22.3 19.5 -11.1 9.7 -4.9 4.2 -2.4 2.1 -1.1 0.9

0.0

-39.6

0.0 0.0 0.0 0.0 0.0 0.0

CONSTRUCTION: EVEN SPANS

Σ

0.0

0.0

0.0 55.6 -48.5 27.8 -24.2 12.1 -10.5 6.0 -5.3 2.6 -2.3 1.3 -1.1

0.0

13.5

0.0 0.0 0.0 0.0 0.0

Σ

LoCol

chg SUPT 2

0.0

0.0

-1.8

0.0

-0.8

0.0

-0.4

0.0

259.6 0.0 129.8 -56.6 56.4 -28.3 28.2 -12.3 12.3 -6.1 6.1 -2.7 2.7

-16.6

0.0

-8.3

0.0

-3.6

0.0

-31.5

0.0

389.0

LoCol

-546.9 249.2 -273.4 124.6 -62.3 54.2 -31.1 27.1 -13.5 11.8 -6.8 5.9 -2.9 2.6 -461.8

27.7

0.0

6.6

0.0

2.9

0.0

1.4

0.0

0.6

0.0

0.3

0.0

0.1

0.0

216.0 -102.5 94.2 -44.7 22.3 -22.3 9.7 -9.7 4.9 -4.8 2.1 -2.1 1.1 -1.1

39.6

0.0

163.1

-135.6

-234.4 106.8 -117.2 53.4 -26.7 23.2 -13.3 11.6 -5.8 5.0 -2.9 2.5 -1.3 1.1 -197.9

0.0

0.0

-7.1

0.0

-1.5

0.0

-0.8

0.0

-0.3

0.0

-0.2

0.0

111.2 0.0 55.6 -24.2 24.2 -12.1 12.1 -5.3 5.3 -2.6 2.6 -1.1 1.1

-3.6

0.0

-13.5

0.0

166.7

-98.4 0.0 -42.9 24.6 -21.4 10.7 -9.3 5.3 -4.6 2.3 -2.0 1.2 -1.0

SUPT 2

SUPT 3

LoCol

R68 HiCol

1.8

0.0

0.9

0.0

0.4

0.0

546.9 -546.9 124.6 -124.6 62.3 -62.3 27.1 -27.1 13.5 -13.5 5.9 -5.9 2.9 -2.9

72.7

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

0.0

0.0

38.1

0.0

19.1

0.0

8.3

0.0

4.1

0.0

SUPT 4

0.0

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

LoCol

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-0.7

0.0

-0.3

0.0

-0.2

0.0

0.0 -49.2 49.2 -21.5 21.5 -10.7 10.7 -4.7 4.7 -2.3 2.3 -1.0 1.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-27.5

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

102

1109

-15.1

0.0

-6.6

0.0

-3.3

0.0

-1.4

0.0

1.8

0.0

0.8

0.0

0.4

0.0

0.2

0.0

234.4 -234.4 53.4 -53.4 26.7 -26.7 11.6 -11.6 5.8 -5.8 2.5 -2.5 1.3 -1.3

31.2

0.0

0.0

0.0

Min load Max load

1.0 0.4

x dead x dead +

16.3

0.0

8.2

0.0

3.6

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0

0.0 0.0 0.0

(3.2.1.2.2)

RIGHT

LEFT

RIGHT

582.8 416.0 419.7 1608.8 1312.4 1318.9 1109.4 2369.6 1688.5 1703.5

589.2 391.3 453.7 1626.7 1274.8 1385.7 1139.4 2395.9 1587.5 1842.2

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

REDISTRIBUTION 20% (3.2.2.1) ßb - 80% ßb + 110% Max M 194.1 1916.7 0.0 ULS 1 194.1 1916.7 1916.7 0.0 0.0 ULS 2 194.1 1857.4 1746.3 0.0 0.0 ULS 3 28.2 1873.9 1916.7 0.0 0.0

0.0 0.0 0.0 0.0

46.1 59.6 6.5 127.2 151.3 56.8 102.0 187.4 242.6 25.7

-

SUPT 3

HiCol

97 78 Job No

SUPT 4

LEFT

SLS 1 SLS 2 SLS 3 SLS 4 SLS 5 SLS 6 SLS 7 ULS 1 ULS 2 ULS 3

Revision

© 2006 TCC

HiCol

Page

11-Apr-2006

Checked

ELASTIC SUPPORT MOMENTS BEFORE EQUIVALENT LOADING SUPT 1

Date

RMW

1.6

x imposed (Table 2.1)

97


17/07/2006 17:06:30


Project


Client

Advisory Group



Date

RMW


Checked

Revision

chg

© 2006 TCC

Page

98 79

11-Apr-2006 Job No

-

R68

DETAILED CALCULATIONS iv

TOTAL LOADS Span 1


Span 2

PL1

PL2

part UD

UDL

PL1

PL2

part UD

UDL

PL1

PL2

part UD

381.7 381.7 165.7 1053.7 1053.7 669.7 784.9 1551.9 1551.9 669.7

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

397.6 172.6 397.6 1097.6 697.6 1097.6 817.6 1616.6 697.6 1616.6

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

151.6 55.0 162.5 418.7 246.8 437.9 317.6 655.0 209.1 655.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 0.00 0.00

0 0.00 0.00

4.898 0 0.00 0.00

0 0.00 0.00

0 0.00 0.00

SUPPORT SHEARS

BEFORE EQUIVALENT LOADING Span 1


0

UDL

146.1 161.1 48.4 403.4 430.1 229.7 308.5 632.4 637.4 181.0

Span 2

235.6 220.5 117.3 650.3 623.6 440.0 476.4 919.5 914.6 488.6

245.9 117.6 235.1 678.9 450.8 659.6 499.9 961.6 488.5 961.6

SLS SPAN MOMENT BEFORE EQUIVALENT LOADING SPAN 1 Left < > PL1 < > Elastic V SLS 3 48.4 0 48.4 0 SLS 5 430.1 0 430.1 0 X bar SLS 3 0.000 0.000 0.000 SLS 5 0.000 0.000 0.000 Span M SLS 3 6.5 -6.5 -6.5 -6.5 SLS 5 151.3 -151.3 -151.3 -151.3 SPAN 2 Elastic V SLS 2 117.6 0 117.6 0 SLS 6 659.6 0 659.6 0 X bar SLS 2 0.000 0 0.000 SLS 6 0.000 0 0.000 Span M SLS 2 391.3 -391.3 -391.3 -391.3 SLS 6 1385.7 -1385.7 -1385.7 -1385.7 SPAN 3 Elastic V SLS 3 0.0 100 0.0 100 SLS 5 0.0 100 0.0 100 X bar SLS 3 0.000 0 0.000 SLS 5 0.000 0 0.000 Span M SLS 3 0.0 0.0 0.0 0.0 SLS 5 0.0 0.0 0.0 0.0 TENDONS (a) Breaking load = 186.0 Supt 1

Span 1

Assume Supt 2

Pfmin 0 1181.3 1980.2 Pfmax 16289.9 4209.4 7334.2 MIN 1980.2 MAX 4209.4 OK Recomm'ed Number 24 Actual Number 24 Recomm'ed heights 40

2217.7 7244.9

Span 3

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

PL2

< >

Right

48.4 430.1 0.000 0.000 -6.5 -151.3

100 100 3.506 4.898 78.4 902.0

117.3 623.6

117.6 659.6 0 0 -391.3 -1385.7

100 100 8.518 7.512 109.5 1092.1

55.0 437.9

0.0 0.0 0 0

100 100 0.000 0.000

0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

104.2

kN max per strand

Span 2

Supt 3

1750.2 -6164.2 4293.3 16234.7 2217.7 4293.3 OK 26 24 40

0.0 0.0

419.7 1312.4

0.0 0.0

Loadings

13.81 87.81 12 MAX 78.4 902.0

0.00 0.00

13.81 87.81 12.5 MAX 109.5 1092.1

0.00 0.00

0.00 0.00 0 MAX 0.0 0.0

0.00 0.00

7.512 0 0.00 0.00

at

0.000

0

0

0.0 0.0 0.0 0.0 1 0 0

0 0.0 OK

at

at

2217.7 min 4209.4 max 104.2

0

Pf per strand 0.225

Max(MIN):Min(MAX) = 0.517 Margin OK

98


17/07/2006 17:06:33


Project


Client

Advisory Group



1050 -0.692 -1.758 0.9103 5161 1050 11700 260 440 -5E-05 1E-05 -6E-05 207.1 369.4

PRESTRESS LOSSES Supt 1

FRICTION & WOBBLE Angle θ 0.101 x left 0

x right

Cum θ left

m θ right

from left

Sum from right

Sum Loss DRAW-IN x left

chg

Span 2

0

1100 0.4091 -1.846 0.8988 6856 1250 12350 440 260 -6E-05 1E-05 -4E-05 369.4 200.8

0 0 0 0 0 0 0 0 0 0 0 0 0.0 0.0

Pj = 130 kN Span 1

Supt 2

Ap = 100

Lt max = 24650

Span 2

Supt 3

0

0

0.000 24050 12350 0 0

24050 12350 0 0

0.000 24050 12350 0 0

0.917 0.446 0.000 0.000

0.917 0.446 0.000 0.000

0.917 0.446 0.000 0

0.135 11700

0.128 11700 0

18556 6856

0.095 24050 12350

24050 24050 11700 0

18889 18889 6539 0.202

12350 12350 0 0.471

12350 12350

5494 5494

0 0

0.471 0.000

0.727 0.257

0.917 0.446

0.917 0.917 0.471 0.0 0.0

0.715 0.715 0.269 102.6 0.0

0.446 0.446 0 233.3 0.0

0.446 0.446

0.189 0.189

0.000 0

441.7

0.0 233.3 225.2 0.0

0.0 0.0 441.7 0.0

0.0 0.0 441.7 0.0

0.0 0.0 441.7 0.0

0.0 441.7 220.8

0.0 350.6 226.6

0.0 225.2 229.2

441.7 0.0 0.0 0.0 441.7 0.0 0.0 0.0 0.0 0.0 220.8

441.7

0.0 102.6 350.6 0.0

354.4 0.0 0.0 0.0 354.4 98.4 0.0 0.0 0.0 98.4 226.4

441.7

0.0 0.0 441.7 0.0

233.3 0.0 0.0 0.0 233.3 225.2 0.0 0.0 0.0 225.2 229.2

0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0

300

5461

12000

12300 300

19156 7156

24650 12650

19189 19189 6839 2768.0 2676.3 113.9

12650 12650 300 2890.9 2676.3 113.9

12350 12350

5494 5494

0 0

24650 12650 0 0

24650 12650 0 0

24650 12650 0 0

2665.5 2897.5 113.9

2665.5 2774.7 113.9

2665.5 2676.3 113.9

2665.5 0.0 0.0

2665.5 0.0 0.0

2665.5 0.0 0.0

21.4 361.9

21.4 364.5

21.4 364.5

21.4 361.7

21.4 356.2

0.0 0.0

0.0 0.0

0.0 0.0

2763

2760

2760

2763

2769

0

0

0

55.3

55.2

55.2

55.3

55.4

0.0

0.0

0.0

24350 24350 12000 Px left (B) 2671.1 Px right (B) 2676.3 Loss 113.9 ELASTIC LOSS Loss 21.4 Σ losses 356.2 2769

RELAXATION Loss 55.4 SHRINKAGE Loss 96.9 CREEP Loss 95.7 Σ losses 248.0

96.9

96.9

96.9

96.9

96.9

0.0

0.0

0.0

95.5 247.7

95.4 247.5

95.4 247.5

95.5 247.7

95.7 248.0

0.0 0.0

0.0 0.0

0.0 0.0

Final Force

2515

2513

2513

2515

2521

0

0

0

2521

Page

99 80


5161

x right

Initial Force

Checked

© 2006 TCC

DETAILED CALCULATIONS v PROFILING Span 1

a X Y Z b c net L y1 y3 A1 A2 A3 ya yc

Date

RMW

Job No

-

R68

STRESSING LENGTHS Stressed from BOTH ends No Length SPAN AVGE 24 24650 0 24650 24650 1 0 12300 24 24650 24650 0 12650 2 0 12650 0 24650 0 3 0 12650 0 0

Deanna Troi's Table for Bonded Tendons ß Z Pi 0.0008 12227 111.1 0.0000 0 0.0 0.0000 0 0.0 0.0000 0 0.0 0.0007 12522 111.5 0.0000 0 0.0

1 Left 2 Left 3 Left 1 Right 2 Right 3 Right

99


17/07/2006 17:06:36

RCC42 Post-tensioned Slabs & Beams (A & D)/ DETAILS! Project


Client

Advisory Group



Date

RMW


Page

Checked

Revision

Job No

chg

© 2006 TCC

100 81

11-Apr-2006

R68

-

DETAILED CALCULATIONS vi

BALANCE LOADS Supt 1

Span 1

Left 260 1050 5161

y1 260 a 1050 b 5161 INITIAL PRESTRESS V1 = -We 278.41 UDL 265.1 -67.7 FINAL PRESTRESS V1 = -We 253.45 UDL 241.4 -61.7 BALANCE LOAD FEM CENTRE LEFT

CENTRE RIGHT

LEFT END

RIGHT END

TOTALS

a/L b/L factor FEM i FEM f a/L b/L factor FEM i FEM f a/L b/L factor FEM i FEM f a/L b/L factor FEM i FEM f

Supt 2

Right 440 1050 6539

Left 440 1050 6539

0.073 -324.7 -295.6 0.088 0.056 0.049 163.5 148.8

0.004 15.7 14.3

Left 440 1100 6856

Supt 3

Right 260 1250 5494

Left 260 1250 5494

371.80 -67.7 354.1

354.66 322.4 -61.6

261.52 61.6 209.2

338.47 -61.7 322.4

322.87 293.5 -56.1

238.07 56.1 190.5

Span 1

Left 0.343 0.271 0.132 -442.5 -402.9

Span 2

Right 440 1100 6856

Span 2

Right

Left 0.460 0.330 0.130 -577.7 -525.9

0.055 -185.2 -168.6 0.457 0.671 0.130 -582.0 -529.8

0.055 -179.7 -163.6 0.088 0.056 0.049 216.0 196.6

0.004 11.7 10.7 0.088 0.944 0.049 218.3 198.7

0.003 10.1 9.2

0

Right 0 0 0

0

Left 0 0 0

Right 0 0 0

0.0

0.0

0.00 0.0

0.00

0.00 0.0

0 0 0

0.0 0.00

0.0

0.0

0.0

LoCol

HiCol

0

Right

Left 0.000 0.100 0.081 0.0 0.0

0.073 -324.5 -295.5 0.340 0.730 0.132 -432.8 -394.0

0.098 0.0 0.0 #DIV/0! #DIV/0! #DIV/0! 0.0 0.0

0.003 15.5 14.1 0.100 0.950 0.044 142.5 129.7

#DIV/0! 0.0 0.0

Right

0.009 0.0 0.0 0.800 0.500 0.098 0.0 0.0

#DIV/0! 0.0 0.0 #DIV/0! #DIV/0! #DIV/0! 0.0 0.0

FEM i

-588.1

-537.2

-531.3

-599.4

0.0

0.0

FEM f

-535.4

-489.0

-483.7

-545.7

0.0

0.0

BALANCE LOAD MOMENT DISTRIBUTION HiCol

INITIAL

0.0 0.0 0.0 0.0 0.0 0.0 0.0 Σ 2nd'y M

588.1 -512.7 1.4 -1.2 -10.3 9.0 0.3 -0.3 -2.2 1.9 0.1 -0.1 -0.5 0.4

LoCol

HiCol

-75.3

0.0

-0.2

0.0

1.3

0.0

0.0

0.0

0.3

0.0

0.0

0.0

0.1

0.0

SUPT 2

-537.2 2.8 -256.4 -20.6 -0.6 0.6 4.5 -4.5 -0.1 0.1 1.0 -1.0 0.0 0.0

531.3 2.7 299.7 -19.7 -0.7 0.6 4.9 -4.3 -0.1 0.1 1.1 -0.9 0.0 0.0

LoCol

SUPT 3

HiCol

0.4

0.0

-3.0

0.0

0.1

0.0

-0.7

0.0

0.0

0.0

-0.1

0.0

0.0

0.0

-599.4 599.4 1.3 -1.3 -9.9 9.9 0.3 -0.3 -2.1 2.1 0.1 -0.1 -0.5 0.5

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

SUPT 4

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

LoCol

0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

73.9

-73.9

0.0

-811.3

814.6

-3.3

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

61.2

-61.2

0.0

-301.3

304.6

0.0

0.0

12.7

0.0

0.0

0.0

#VALUE!

0.0

-68.6

0.0

0.4

0.0

-2.8

0.0

0.0

0.0

1.2

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0

-545.7 545.7 1.2 -1.2 -9.0 9.0 0.3 -0.3 -2.0 2.0 0.1 -0.1 -0.4 0.4

0.0

-0.2

483.7 2.4 272.8 -18.0 -0.6 0.5 4.5 -3.9 -0.1 0.1 1.0 -0.8 0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

FINAL

0.0

-489.0 2.5 -233.4 -18.7 -0.6 0.6 4.1 -4.1 -0.1 0.1 0.9 -0.9 0.0 0.0

0.0

67.3

-67.3

0.0

-738.6

741.6

-3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

55.7

-55.7

0.0

-274.3

277.3

0.0

0.0

11.5

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 Σ 2nd'ry M

SUPT 1

535.4 -466.8 1.3 -1.1 -9.4 8.2 0.3 -0.2 -2.0 1.8 0.1 -0.1 -0.4 0.4

0.3

0.0

0.0

0.0

0.1

0.1

0.0

-0.6

0.0

0.0

0.0

-0.1

0.0

0.0

0.0

0.0

0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0

100


17/07/2006 17:06:40


Project


Client

Advisory Group



Date

RMW


Page

Checked

Revision

chg

© 2006 TCC

101 82

11-Apr-2006 Job No

-

R68

DETAILED CALCULATIONS vii

SUPPORT MOMENTS WITH EQUIVALENT LOADING SUPT 1

SLS 1 SLS 2 SLS 3 SLS 4 SLS 5 SLS 6 SLS 7 ULS 1 ULS 2 ULS 3 DEAD IMPOSED

-27.8 -14.3 -67.4 60.0 84.0 -10.4 34.7 126.8 126.8 -39.1 25.1 46.4

SUPPORT SHEARS

SUPT 2

SUPT 3

RIGHT

LEFT

RIGHT

-225.4 -423.3 -360.9 885.1 533.2 644.1 397.8 1175.1 1004.7 1175.1 756.6 592.8

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 11.5 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

WITH EQUIVALENT LOADING Span 1

SLS 1 SLS 2 SLS 3 SLS 4 SLS 5 SLS 6 SLS 7 ULS 1 ULS 2 ULS 3 DEAD IMPOSED ELASTIC ULS 1 ULS 2 ULS 3

SUPT 4

LEFT

-228.6 -395.3 -391.6 870.2 573.8 580.3 370.9 1178.1 1118.8 1135.3 748.2 586.3

166.1 181.1 68.4 421.6 448.3 247.9 326.7 650.6 655.6 199.2 274.6 147.0

-20.0

612.3 673.7 213.2

-18.2

-20.0 -20.0 -18.2 -18.2 -18.2 -18.2 -18.2 -18.2 -18.2

-18.2 -18.2

ADJUSTED SPAN MOMENTS Left Span 1 V SLS 1 166.1 SLS 2 181.1 SLS 3 68.4 SLS 4 421.6 SLS 5 448.3 SLS 6 247.9 SLS 7 ULS 1 650.6 ULS 2 655.6 ULS 3 199.2 Xbar SLS 1 SLS 2 SLS 3 SLS 4 SLS 5 SLS 6 ULS 1 ULS 2 ULS 3 M SLS 1 -15.1 SLS 2 -1.6 SLS 3 -54.7 SLS 4 71.5 SLS 5 95.5 SLS 6 1.1 ULS 1 138.4 ULS 2 138.4 ULS 3 -27.52

Span 2

215.6 200.5 97.3 632.1 605.4 421.8 458.2 901.3 896.4 470.4 395.1 237.0

220.5 92.2 209.7 655.8 427.7 636.5 476.8 938.5 465.4 938.5 408.4 247.4

25.4

939.6 878.2 456.4

976.9 452.7 932.6

23.1

< >

0.0

177.0 80.4 187.9 441.8 269.9 461.0 340.7 678.1 232.2 678.1 289.2 152.6

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0

0.0 0.0 0.0

0.0

23.1

639.7 244.9 684.0

PL1

< >

PL2

< >

Right

0 0 0 0 0 0

166.1 181.1 68.4 421.6 448.3 247.9

0 0 0 0 0 0

166.1 181.1 68.4 421.6 448.3 247.9

100 100 100 100 100 100

215.6 200.5 97.3 632.1 605.4 421.8

0 0 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 15.1 1.6 54.7 -71.5 -95.5 -1.1 -138.4 -138.4 27.52

650.6 655.6 199.2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 15.1 1.6 54.7 -71.5 -95.5 -1.1 -138.4 -138.4 27.52

0 0 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 15.1 1.6 54.7 -71.5 -95.5 -1.1 -138.4 -138.4 27.52

650.6 655.6 199.2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 15.1 1.6 54.7 -71.5 -95.5 -1.1 -138.4 -138.4 27.52

100 100 100 5.223 5.695 4.955 4.801 5.105 4.442 5.031 5.069 3.570 449.0 517.4 224.2 940.6 1048.8 549.4 1498.3 1523.2 383.21

901.3 896.4 470.4

25.4 25.4 23.1 23.1 23.1 23.1 23.1 23.1 23.1

23.1

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0

281.4 114.7 118.4 1334.5 1038.1 1044.6 1642.4 1583.1 1599.55

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Loadings UDL PL1

31.8 31.8 13.8 87.8 87.8 55.8 65.4 129.3 129.3 55.8

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M

517.4 224.2

0

0

PL2

pUDL

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

X bar

12

T height

max min

@ 5.695 @ 4.955

41.8 41.5

1048.8 max 549.4 min

@ 5.105 @ 4.442

40.5 49.3

1523.2 max 383.2 min

@ 5.069 @ 3.570

40.7 77.1

101


17/07/2006 17:06:43


Project


Client

Advisory Group



V

Xbar

M

SLS 1 SLS 2 SLS 3 SLS 4 SLS 5 SLS 6 SLS 7 ULS 1 ULS 2 ULS 3 SLS 1 SLS 2 SLS 3 SLS 4 SLS 5 SLS 6 ULS 1 ULS 2 ULS 3 SLS 1 SLS 2 SLS 3 SLS 4 SLS 5 SLS 6 ULS 1 ULS 2 ULS 3

Revision

chg

© 2006 TCC

V

Xbar

M

SLS 1 SLS 2 SLS 3 SLS 4 SLS 5 SLS 6 SLS 7 ULS 1 ULS 2 ULS 3 SLS 1 SLS 2 SLS 3 SLS 4 SLS 5 SLS 6 ULS 1 ULS 2 ULS 3 SLS 1 SLS 2 SLS 3 SLS 4 SLS 5 SLS 6 ULS 1 ULS 2 ULS 3

R68

0

0

Left

< >

PL1

< >

PL2

< >

Right

UDL

PL1

PL2

pUDL

220.5 92.2 209.7 655.8 427.7 636.5

0 0 0 0 0 0

220.5 92.2 209.7 655.8 427.7 636.5

0 0 0 0 0 0

220.5 92.2 209.7 655.8 427.7 636.5

100 100 100 100 100 100

177.0 80.4 187.9 441.8 269.9 461.0

938.5 465.4 938.5

938.5 465.4 938.5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -285 -87 -149 -1349 -998 -1108 -1639 -1469 -1639

0 0 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -285 -87 -149 -1349 -998 -1108 -1639 -1469 -1639

938.5 465.4 938.5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -285 -87 -149 -1349 -998 -1108 -1639 -1469 -1639

100 100 100 6.934 6.679 6.593 7.469 7.663 7.249 7.257 8.339 7.257 480 221 542 1100 641 1199 1766 471 1766

678.1 232.2 678.1

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

285 87 149 1349 998 1108 1639 1469 1639

0 0 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -285 -87 -149 -1349 -998 -1108 -1639 -1469 -1639

31.8 13.8 31.8 87.8 55.8 87.8 65.4 129.3 55.8 129.3

Left

< >

PL1

< >

PL2

< >

Right

UDL

PL1

PL2

pUDL

0.0 0.0 0.0 0.0 0.0 0.0

100 100 100 100 100 100

0.0 0.0 0.0 0.0 0.0 0.0

100 100 100 100 100 100

0.0 0.0 0.0 0.0 0.0 0.0

100 100 100 100 100 100

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0

100 100 100 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 0 0 0 0 0 0 0 0

0.0 0.0 0.0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 0 0 0 0 0 0 0 0

100 100 100 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 0 0 0 0 0 0 0 0

0.0 0.0 0.0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 0 0 0 0 0 0 0 0

100 100 100 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 0 0 0 0 0 0 0 0

0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

13 13 13 12 12 12 12 12 12

M

X bar

542.2 221.2

0 0 0 0 0 0 0 0 0

#VALUE! #VALUE! #VALUE! 0 0 0 0 0 0

102 83 Job No

-

Loadings

@ 6.593 @ 6.679

41.9 41.2

1198.8 max 641.2 min

@ 7.249 @ 7.663

40.7 44.8

1766.0 max 471.5 min

@ 7.257 @ 8.339 0

40.7 59.8 0

M

X bar

12.5

T height

max min

Loadings

0

Page

11-Apr-2006

Checked

DETAILED CALCULATIONS viii

Span 2

Date

RMW

0

T height

0.0 0.0

max min

@ 0.000 @ 0.000

0.0 0.0

0.0 0.0

max min

@ 0.000 @ 0.000

0.0 0.0

0.0 0.0

max min

@ 0.000 @ 0.000

0.0 0.0

102


17/07/2006 17:06:45


Project


Client

Advisory Group


Location Level 2 - Beam on Grid 7 POST-TENSIONED ANALYSIS & DESIGN TO BS 8110 Originated from RCC42.xls v3.0 on CD

DETAILED CALCULATIONS ix (d) ULS MOMENT C Supt 1

DESIGN MOMENT TENDON HEIGHT fpe Hinges Lt Lte dt dr Rp fpe/fpu TABLE 4.4 1a 1b 2a 2b fpb bonded fpb unbonded TENDON FORCE As REBAR FORCE TOTAL TENSION dn Steel stress Zt Zr MOR

1523.2 40.7 1048 2 24.50 12250 484.3 480.0 0.051 0.648 1.00 1.00 1.00 1.00 1617 1301 3122 6283 2731.8 5854 72.3 435 448.2 443.9 2611.6

300.0 482.0 0.138 0.649 1.00 1 0.99 0.99 1605 1182 2836 4021 1748.4 4584 94.3 435 252.8 434.8 1477.2

(e) SHEAR

Span 1

V Mu M0 Cracked ? UNCRACKED

fcp Vco CRACKED Aps As d As% fpe/fpu vc Vcr Vc Asv/Sv Sv

f) VIBRATION ny : ly Ix : Iy λx : λy kx : ky ω δx : δy f'x : f'y fbx : fby fx : fy Nx : Ny Cx : Cy Rx : Ry R

Checked

chg

Left 636.2 42.2 213.5 N 2.127 1629.0 2400 6421 414.0 0.862 0.448 0.558 3531.2 1629.0 1.656 375

Right 881.9 1529.6 574.7 Y 2.120 1627.8 2400 8683 480.0 1.005 0.380 0.588 733.0 733.0 1.656 375

Supt 2

Left 1529.6 480.0 1047

Span 2

Right 1500.1 480.0 1047

1766.0 40.7 1048 2 24.50 12250 484.3 484.0 0.051 0.648 1.00 1.00 1.00 1.00 1617 1301 3122 2262 983.5 4105 50.7 435 459.0 458.7 1883.9

480.0 480.0 480.0 480.0 0.086 0.086 0.647 0.647 1.00 1.00 1 1 1 1 1 1 1617 1617 1281 1281 3075 3075 6283 2731.8 2731.8 5807 5807 119.5 119.5 435 435 420.3 420.3 420.3 420.3 2440.3 2440.3

Right 678.1 11.5 213.5 N 2.127 1629.0 2600 8883 210.0 2.350 0.394 0.916 12815.2 1629.0 1.656 375

Right 0.0 0.0 0

300.0 0.0 480.0 0.0 0.138 0.000 0.649 0.000 1.00 0.00 1 0 0.99 0 0.99 0 1605 0 1182 0 2836 0 6283 2731.8 2731.8 5568 2732 114.6 0.0 435 0 242.7 0.0 422.7 0.0 1843.1 0.0 0

Left 0.0 0.0 0.0 N 0.000 0.0 0 0 0.0 0.000 0.000 0.000 0.0 0.0 0.000 0

103 84 Job No

R68

Date

Supt 3

Left 11.5 300.0 1050

Span 2

Left 919.1 1500.1 574.7 Y 2.120 1627.8 2600 8883 480.0 1.028 0.392 0.592 753.3 753.3 1.656 375

Page


© 2006 TCC

Span 1

Right 42.2 300.0 1050

Date

RMW

0

0

0.0 0.0 0 0 0.00 0 0.0 0.0 0.000 0.000 0.00 0.00 0.00 0.00 0 0 0 0 0.0 0 0.0 0 0.0 0.0 0.0

Left 0.0 0.0 0

0.0 0.0 0.000 0.000 0.00 0 0 0 0 0 0 0 0.0 0 0.0 0 0.0 0.0 0.0 ft = 1.859

Right 0.0 0.0 0.0 N 0.000 0.0 0 0 0.0 0.000 0.000 0.000 0.0 0.0 0.000 0

Links required

nx = 2 Span 1

Span 2

0

5 6.000 3E+10 2E+09 1.934 5.170 1.267 1.037 65.41 54.51 8.56 13.69 6.11 6.32 6.11 6.32 6.11 6.32 1.388 2.036 246.7 243.4 0.36 0.25 0.60

5 6.000 3E+10 2E+09 2.015 4.963 1.246 1.041 65.41 54.51 13.99 13.69 6.01 4.96 6.01 4.96 6.01 4.96 1.404 1.995 248.3 275.3 0.35 0.26 0.61

0 0.000 0 0 0.000 0.000 0.000 0.000 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.000 1.000 0.0 0.0 0.00 0.00 0.00

Khan/Williams Ref (Concrete Society Method) (9.8) (9.9, 9.10)

(9.11) (9.12, 9.13) (9.14) (9.17, 9.18) (9.19) (9.20) (9.21)

103


17/07/2006 17:06:48


Location

As(b) = 6283 525 1050 525 563 43 43 4021 4021


© 2006 TCC

EC2 USERGUIDEv2.indd Sec1:104 0

δ

0

δ

M(SLS 5-7) -31.29 1/R -3E-08 Load -8E-06 Load x dist -0.001 End slope 0.001 Span δ 0 Cant δ 0 0 δ

DEFLECTIONS - IMPOSED

13.6 4E-08 1E-05 0.001 0.002 0 0

M (SLS 7) 1/R Load Load x dist End slope Span δ Cant δ

DEFLECTIONS - LONGTERM

77.5 1E-07 3E-05 0.003 -0.002 0 0


DEFLECTIONS at TRANSFER

1.05 8.67 1.05

0.53

80.51 8E-08 4E-05 0.047

0.53 8.53

27.69 3E-08 1E-05 0.008

2.03

2.03 7.31

1.07

1.07 6.61

-1.89

-0.93

177.2 5E-07 3E-04 0.303

-1.89 -11.13

-0.93 -10.62

137.6 4E-07 2E-04 0.11

-6.6 -8E-09 -5E-06 -0.005

73.9 9E-08 5E-05 0.026

1.62

1.62 8.81

133.30 1E-07 8E-05 0.13

2.96

2.96 7.94

173.4 5E-07 3E-04 0.496

-2.99

-2.99 -11.70

-132.8 -2E-07 -1E-04 -0.165

2.15

2.15 8.91

178.04 2E-07 1E-04 0.237

3.70

3.70 8.39

168.2 5E-07 3E-04 0.657

-4.02

-4.02 -12.22

-239.6 -3E-07 -2E-04 -0.406

d = 480 0 1650 2250 263 600 600 43 43 43 4021 4021 4021 TRANFORMED SECTION PROPERTIES at TRANSFER E= A 1E+06 1E+06 1E+06 1E+06 1E+06 Σ A.Yt 3E+08 3E+08 3E+08 3E+08 3E+08 Yt 234.1 234.1 234.1 234.1 234.1 Yb 290.9 290.9 290.9 290.9 290.9 Ixx 3E+10 3E+10 3E+10 3E+10 3E+10 TRANFORMED SECTION PROPERTIES - LONGTERM E= A 1E+06 1E+06 1E+06 1E+06 1E+06 Σ A.Yt 3E+08 3E+08 3E+08 3E+08 3E+08 Yt 242.1 242.1 242.1 242.1 242.1 Yb 282.9 282.9 282.9 282.9 282.9 Ixx 4E+10 4E+10 4E+10 4E+10 4E+10 TRANFORMED SECTION PROPERTIES - IMPOSED E= A 1E+06 1E+06 1E+06 1E+06 1E+06 Σ A.Yt 3E+08 3E+08 3E+08 3E+08 3E+08 Yt 232.9 232.9 232.9 232.9 232.9 Yb 292.1 292.1 292.1 292.1 292.1 Ixx 3E+10 3E+10 3E+10 3E+10 3E+10

SPAN 1 Distance Element b d' As(t)

Advisory Group

Client

2.61

2.61 8.94

214.71 2E-07 1E-04 0.363

4.27

4.27 8.66

161.7 5E-07 3E-04 0.799

-4.95

-4.95 -12.62

-327.0 -4E-07 -2E-04 -0.702

h= 2850 600 43 4021 25.53 1E+06 3E+08 234.1 290.9 3E+10 8.92 1E+06 3E+08 242.1 282.9 4E+10 33.54 1E+06 3E+08 232.9 292.1 3E+10

POST-TENSIONED ANALYSIS & DESIGN to BS 8110:2005


Project

2.99

2.99 8.89

243.31 2E-07 1E-04 0.497

4.68

4.68 8.76

153.8 4E-07 3E-04 0.921

-5.73

-5.73 -12.88

-395.0 -5E-07 -3E-04 -1.027

525 3450 600 43 4021 m= 1E+06 3E+08 234.1 290.9 3E+10 m= 1E+06 3E+08 242.1 282.9 4E+10 m= 1E+06 3E+08 232.9 292.1 3E+10

3.29

3.29 8.76

263.85 3E-07 2E-04 0.633

4.92

4.92 8.71

144.6 4E-07 3E-04 1.016

-6.33

-6.33 -12.96

-443.6 -6E-07 -3E-04 -1.354

bw = 4050 600 43 4021 7.83 1E+06 3E+08 234.1 290.9 3E+10 22.43 1E+06 3E+08 242.1 282.9 4E+10 5.96 1E+06 3E+08 232.9 292.1 3E+10

3.49

3.49 8.53

276.33 3E-07 2E-04 0.761

5.01

5.01 8.50

134.0 4E-07 2E-04 1.081

-6.73

-6.73 -12.84

-472.8 -6E-07 -4E-04 -1.657

1800 4650 600 43 4021 m-1= 1E+06 3E+08 234.1 290.9 3E+10 m-1= 1E+06 3E+08 242.1 282.9 4E+10 m-1= 1E+06 3E+08 232.9 292.1 3E+10

3.60

3.60 8.21

280.75 3E-07 2E-04 0.873

4.96

4.96 8.16

122.1 4E-07 2E-04 1.112

-6.91

-6.91 -12.51

-482.5 -6E-07 -4E-04 -1.909

bf = 5250 600 43 4021 6.83 1E+06 3E+08 234.1 290.9 3E+10 21.43 1E+06 3E+08 242.1 282.9 4E+10 4.96 1E+06 3E+08 232.9 292.1 3E+10 1E+06 3E+08 232.9 292.1 3E+10

1E+06 3E+08 232.9 292.1 3E+10

3.60

3.60 7.79

277.10 3E-07 2E-04 0.96

4.78

4.78 7.68

108.8 3E-07 2E-04 1.105

-6.88

-6.88 -11.95

4.11

4.11 6.41

78.3 2E-07 1E-04 0.957

-6.19

-6.19 -10.22

-395.3 -5E-07 -3E-04 -2.101

1E+06 3E+08 232.9 292.1 3E+10

1E+06 3E+08 242.1 282.9 4E+10

3.51

3.51 7.26

3.32

3.32 6.65

265.38 245.60 3E-07 2E-07 2E-04 1E-04 1.014 1.026

4.50

4.50 7.10

94.2 3E-07 2E-04 1.055

-6.63

-6.63 -11.19

-443.8 -6E-07 -3E-04 -2.157

1E+06 3E+08 242.1 282.9 4E+10

1E+06 3E+08 242.1 282.9 4E+10

-472.9 -6E-07 -4E-04 -2.085

1E+06 3E+08 234.1 290.9 3E+10

1E+06 3E+08 234.1 290.9 3E+10

1E+06 3E+08 234.1 290.9 3E+10

hf = 200 6450 7050 600 600 43 43 4021 4021

3000 5850 600 43 4021

DEFLECTION CALCULATIONS

3.05

3.05 5.94

217.76 2E-07 1E-04 0.987

3.64

3.64 5.65

61.0 2E-07 1E-04 0.809

-5.56

-5.56 -9.07

-327.4 -4E-07 -2E-04 -1.888

1E+06 3E+08 232.9 292.1 3E+10

1E+06 3E+08 242.1 282.9 4E+10

1E+06 3E+08 234.1 290.9 3E+10

7650 600 43 4021

bd3/12 =

2.69

2.69 5.16

181.86 2E-07 1E-04 0.889

3.11

3.11 4.82

42.3 1E-07 7E-05 0.606

-4.79

-4.79 -7.78

-240.1 -3E-07 -2E-04 -1.493

1E+06 3E+08 232.9 292.1 3E+10

1E+06 3E+08 242.1 282.9 4E+10

1E+06 3E+08 234.1 290.9 3E+10

2E+10 8250 600 43 4021

2.28

2.28 4.32

137.89 1E-07 8E-05 0.714

2.53

2.53 3.94

22.3 6E-08 4E-05 0.327

-3.91

-3.91 -6.38

-133.4 -2E-07 -1E-04 -0.875

1E+06 3E+08 231.2 293.8 3E+10

1E+06 3E+08 235.7 289.3 4E+10

9450 600 45 6283

1.81

1.81 3.42

85.85 8E-08 5E-05 0.475

1.93

1.93 3.05

0.9 3E-09 2E-06 0.015

-2.96

-2.96 -4.92

-7.3 -9E-09 -5E-06 -0.051

1E+06 3E+08 231.2 293.8 3E+10

1E+06 3E+08 235.7 289.3 4E+10

1.32

1.32 2.50

25.75 3E-08 2E-05 0.151

1.33

1.33 2.15

-21.8 -6E-08 -4E-05 -0.363

-2.02

-2.02 -3.45

138.3 2E-07 1E-04 1.03

1E+06 3E+08 231.2 293.8 3E+10

1E+06 3E+08 235.7 289.3 4E+10

1E+06 3E+08 231.8 293.2 3E+10

10050 600 45 6283

Revision

-

0.29

0.29 0.55

-120.9 -3E-07 -2E-04 -1.963

-0.47

-0.47 -0.93

405.3 5E-07 3E-04 2.938

1E+06 3E+08 231.2 293.8 3E+10

1E+06 3E+08 235.7 289.3 4E+10

1E+06 3E+08 231.8 293.2 3E+10

0

-302.9 -8E-07 -2E-04 -2.487 5E-04 0 0

0

406.1 5E-07 1E-04 1.489 -9E-04 0 0

1E+06 3E+08 231.2 293.8 3E+10

1E+06 3E+08 235.7 289.3 4E+10

1E+06 3E+08 231.8 293.2 3E+10

11700 263 45 6283

R68

104 85

11175 525 45 6283

Job No

Page

0.81

0.38

0

-42.41 -108.67 -181.10 -4E-08 -1E-07 -2E-07 -2E-05 -6E-05 -5E-05 -0.248 -0.622 -0.524 7E-04 0.81 0.38 0 1.56 0.76 0

0.76

0.76 1.28

-45.8 -1E-07 -7E-05 -0.76

-1.14

-1.14 -2.05

303.2 4E-07 2E-04 2.244

1E+06 3E+08 231.2 293.8 3E+10

1E+06 3E+08 235.7 289.3 4E+10

1E+06 3E+08 231.8 293.2 3E+10

10650 563 45 6283

11-Apr-2006

Date

The Concrete Centre

1E+06 3E+08 231.8 293.2 3E+10

chg

1E+06 3E+08 231.8 293.2 3E+10

8850 600 45 6283

Checked

RMW

Made by

RCC42 Post-tensioned Slabs & Beams (A & D)/ DEFLECTS!

104

17/07/2006 17:06:51


Location

As(b) = 2262 550 1100 550 588 45 45 6283 6283


© 2006 TCC

EC2 USERGUIDEv2.indd Sec1:105 0.0

δ -460.7 -5E-07 -1E-04 -0.018 -1E-04 0 0 0

M(SLS 4-7) 1/R Load Load x dist End slope Span δ Cant δ

δ


-327.0 -1E-06 -3E-04 -0.039 0.002 0 0



M (SLS 2) 437.0 1/R 6E-07 Load 2E-04 Load x dist 0.022 End slope -8E-04 Span δ 0 Cant δ 0 0 δ


0.08

0.08 9.29

-0.03 9.64 -0.03

-281.0 -3E-07 -2E-04 -0.185

-367.5 -4E-07 -2E-04 -0.113

2.4

2.37 45.23

1.1

1.10 46.06

-1.25

-0.53

-30.4 -1E-07 -6E-05 -0.063

-1.25 -24.66

-0.53 -25.08

-124.4 -4E-07 -2E-04 -0.12

332.7 4E-07 3E-04 0.281

435.7 6E-07 3E-04 0.172

0.30

0.30 9.00

-191.1 -2E-07 -1E-04 -0.209

3.8

3.84 44.32

12.9 4E-08 3E-05 0.044

-2.23

-2.23 -24.34

167.2 2E-07 1E-04 0.235

0.60

0.60 8.79

-109.8 -1E-07 -7E-05 -0.164

5.3

5.29 43.39

52.5 2E-07 1E-04 0.246

-3.30

-3.30 -24.10

20.4 3E-08 2E-05 0.039

d = 484 0 1725 2350 275 625 625 45 45 45 6283 6283 6283 TRANFORMED SECTION PROPERTIES at TRANSFER E= A 1E+06 1E+06 1E+06 1E+06 1E+06 Σ A.Yt 3E+08 3E+08 3E+08 3E+08 3E+08 Yt 226.4 226.4 226.4 226.4 226.4 Yb 298.6 298.6 298.6 298.6 298.6 Ixx 3E+10 3E+10 3E+10 3E+10 3E+10 TRANFORMED SECTION PROPERTIES - LONGTERM E= A 1E+06 1E+06 1E+06 1E+06 1E+06 Σ A.Yt 3E+08 3E+08 3E+08 3E+08 3E+08 Yt 220.4 220.4 220.4 220.4 220.4 Yb 304.6 304.6 304.6 304.6 304.6 Ixx 4E+10 4E+10 4E+10 4E+10 4E+10 TRANFORMED SECTION PROPERTIES - IMPOSED E= A 1E+06 1E+06 1E+06 1E+06 1E+06 Σ A.Yt 3E+08 3E+08 3E+08 3E+08 3E+08 Yt 227.2 227.2 227.2 227.2 227.2 Yb 297.8 297.8 297.8 297.8 297.8 Ixx 3E+10 3E+10 3E+10 3E+10 3E+10


Advisory Group

Client

0.94

0.94 8.62

-37.3 -4E-08 -2E-05 -0.071

6.7

6.68 42.40

88.6 3E-07 2E-04 0.525

-4.38

-4.38 -23.88

-107.7 -1E-07 -9E-05 -0.261

h= 2975 625 45 6283 25.53 1E+06 3E+08 226.4 298.6 3E+10 8.92 1E+06 3E+08 220.4 304.6 4E+10 33.54 1E+06 3E+08 227.2 297.8 3E+10



Project

1.30

1.30 8.46

26.4 3E-08 2E-05 0.06

8.0

7.96 41.30

121.0 4E-07 2E-04 0.868

-5.40

-5.40 -23.60

-217.1 -3E-07 -2E-04 -0.638

525 3600 625 45 6283 m= 1E+06 3E+08 226.4 298.6 3E+10 m= 1E+06 3E+08 220.4 304.6 4E+10 m= 1E+06 3E+08 227.2 297.8 3E+10

1.64

1.64 8.30

81.4 8E-08 5E-05 0.218

9.1

9.09 40.05

149.7 5E-07 3E-04 1.261

-6.31

-6.31 -23.21

-307.9 -4E-07 -3E-04 -1.061

bw = 4225 625 45 6283 7.83 1E+06 3E+08 226.4 298.6 3E+10 22.43 1E+06 3E+08 220.4 304.6 4E+10 5.96 1E+06 3E+08 227.2 297.8 3E+10

1.96

1.96 8.10

127.6 1E-07 8E-05 0.393

10.0

10.04 38.61

174.9 6E-07 3E-04 1.69

-7.07

-7.07 -22.67

-380.0 -5E-07 -3E-04 -1.504

1800 4850 625 45 6283 m-1= 1E+06 3E+08 226.4 298.6 3E+10 m-1= 1E+06 3E+08 220.4 304.6 4E+10 m-1= 1E+06 3E+08 227.2 297.8 3E+10

2.22

2.22 7.85

165.1 2E-07 1E-04 0.574

10.8

10.76 36.95

196.3 6E-07 4E-04 2.143

-7.63

-7.63 -21.93

-433.4 -6E-07 -4E-04 -1.936

bf = 5475 625 45 6283 6.83 1E+06 3E+08 226.4 298.6 3E+10 21.43 1E+06 3E+08 220.4 304.6 4E+10 4.96 1E+06 3E+08 227.2 297.8 3E+10 1E+06 3E+08 227.2 297.8 3E+10

1E+06 3E+08 227.2 297.8 3E+10

2.42

2.42 7.54

193.9 2E-07 1E-04 0.751

11.2

11.24 35.05

214.2 7E-07 4E-04 2.604

-7.97

-7.97 -20.97

2.54

2.54 7.15

213.9 2E-07 1E-04 0.913

11.5

11.45 32.88

228.4 7E-07 5E-04 3.061

-8.07

-8.07 -19.77

-484.3 -6E-07 -4E-04 -2.657

1E+06 3E+08 220.4 304.6 4E+10

1E+06 3E+08 220.4 304.6 4E+10

-468.2 -6E-07 -4E-04 -2.33

1E+06 3E+08 226.4 298.6 3E+10

1E+06 3E+08 226.4 298.6 3E+10

2.57

2.57 6.67

225.1 2E-07 1E-04 1.051

11.4

11.38 30.43

239.0 8E-07 5E-04 3.501

-7.92

-7.92 -18.32

-481.6 -6E-07 -4E-04 -2.888

1E+06 3E+08 227.2 297.8 3E+10

1E+06 3E+08 220.4 304.6 4E+10

1E+06 3E+08 226.4 298.6 3E+10

hf = 200 6725 7350 625 625 45 45 6283 6283

3000 6100 625 45 6283

DEFLECTION CALCULATIONS (ii)

2.52

2.52 6.11

227.6 2E-07 1E-04 1.153

11.0

11.01 27.68

245.9 8E-07 5E-04 3.909

-7.53

-7.53 -16.63

-460.4 -6E-07 -4E-04 -2.995

1E+06 3E+08 227.2 297.8 3E+10

1E+06 3E+08 220.4 304.6 4E+10

1E+06 3E+08 226.4 298.6 3E+10

7975 625 45 6283

bd3/12 =

2.38

2.38 5.45

221.3 2E-07 1E-04 1.209

10.3

10.34 24.62

249.2 8E-07 5E-04 4.272

-6.91

-6.91 -14.71

-420.4 -5E-07 -3E-04 -2.949

1E+06 3E+08 227.2 297.8 3E+10

1E+06 3E+08 220.4 304.6 4E+10

1E+06 3E+08 226.4 298.6 3E+10

2E+10 8600 625 45 6283

2.15

2.15 4.71

206.3 2E-07 1E-04 1.209

9.4

9.35 21.26

248.9 8E-07 5E-04 4.576

-6.06

-6.06 -12.57

-361.8 -5E-07 -3E-04 -2.722

1E+06 3E+08 227.2 297.8 3E+10

1E+06 3E+08 220.4 304.6 4E+10

9850 625 45 6283

1.83

1.83 3.88

182.5 2E-07 1E-04 1.142

8.1

8.06 17.58

244.9 8E-07 5E-04 4.808

-5.04

-5.04 -10.24

-284.4 -4E-07 -2E-04 -2.286

1E+06 3E+08 227.2 297.8 3E+10

1E+06 3E+08 220.4 304.6 4E+10

1.45

1.45 2.98

150.0 2E-07 1E-04 0.998

6.5

6.46 13.60

237.3 8E-07 5E-04 4.954

-3.87

-3.87 -7.77

-188.4 -2E-07 -2E-04 -1.61

1E+06 3E+08 227.2 297.8 3E+10

1E+06 3E+08 220.4 304.6 4E+10

1E+06 3E+08 226.4 298.6 3E+10

10475 625 45 6283

Revision

-

1.00

1.00 2.02

108.8 1E-07 7E-05 0.767

4.6

4.56 9.32

226.0 7E-07 5E-04 5.001

-2.60

-2.60 -5.20

-73.8 -1E-07 -6E-05 -0.668

1E+06 3E+08 227.2 297.8 3E+10

1E+06 3E+08 220.4 304.6 4E+10

1E+06 3E+08 226.4 298.6 3E+10

11100 625 45 6283

11-Apr-2006

Date

105 86

0.51

0.51 1.02

58.8 6E-08 4E-05 0.438

2.4

2.38 4.76

163.0 5E-07 3E-04 3.809

-1.30

-1.30 -2.60

6.7 9E-09 5E-06 0.064

1E+06 3E+08 227.2 297.8 3E+10

1E+06 3E+08 220.4 304.6 4E+10

1E+06 3E+08 226.4 298.6 3E+10

0

0.0 0 0 0 8E-04 0 0

0.0

0.0 1E-20 4E-18 5E-14 0.004 0 0

0

0.0 6E-21 2E-18 2E-14 -0.002 0 0

1E+06 3E+08 227.2 297.8 3E+10

1E+06 3E+08 220.4 304.6 4E+10

1E+06 3E+08 226.4 298.6 3E+10

12350 313 45 6283

R68 11725 625 45 6283

Job No

Page

The Concrete Centre

1E+06 3E+08 226.4 298.6 3E+10

chg

1E+06 3E+08 226.4 298.6 3E+10

9225 625 45 6283

Checked

RMW

Made by



105

17/07/2006 17:06:54

Location

EC2 USERGUIDEv2.indd Sec1:106 0 0 45 6283

As(b) = 0 0 0 0 0 45 45 6283 6283


42940 2E+06 45 -45 0.554

42940 2E+06 45 -45 0.554

42940 2E+06 45 -45 0.554

1E+05 6E+06 45 -45 1.736

1E+05 6E+06 45 -45 1.736

1E+05 6E+06 45 -45 1.736

31188 1E+06 45 -45 0.402

0

δ

0

δ 0.0 0 0 0 0 0 0 0

M(SLS 5-7) 1/R Load Load x dist End slope Span δ Cant δ

δ


0.0 0 0 0 0 0 0



0.0 0 0 0 0 0 0



Yt Yb Ixx

A Σ A.Yt

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.00

0.00 0.00

0.00

0.00

0.0 0 0 0

0.00 0.00

0.00 0.00

0.0 0 0 0

0.0 0 0 0

31188 1E+06 45 -45 0.402

0.0 0 0 0

31188 1E+06 45 -45 0.402

TRANFORMED SECTION PROPERTIES - IMPOSED

Yt Yb Ixx

A Σ A.Yt

TRANFORMED SECTION PROPERTIES - LONGTERM

Yt Yb Ixx

A Σ A.Yt

TRANFORMED SECTION PROPERTIES at TRANSFER



Client

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

31188 1E+06 45 -45 0.402

1E+05 6E+06 45 -45 1.736

42940 2E+06 45 -45 0.554

0 0 45 6283

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0 0 45 6283 E= 42940 2E+06 45 -45 0.554 E= 1E+05 6E+06 45 -45 1.736 E= 31188 1E+06 45 -45 0.402

d = -45

© 2006 TCC

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0 0 43 6283 m= 42940 2E+06 43 -43 0.529 m= 1E+05 6E+06 43 -43 1.66 m= 31188 1E+06 43 -43 0.384

h= 0 0 0 45 6283 25.53 42940 2E+06 45 -45 0.554 8.92 1E+05 6E+06 45 -45 1.736 33.54 31188 1E+06 45 -45 0.402



Advisory Group

Project

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

bw = 0 0 43 6283 7.83 42940 2E+06 43 -43 0.529 22.43 1E+05 6E+06 43 -43 1.66 5.96 31188 1E+06 43 -43 0.384

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0 0 43 6283 m-1= 42940 2E+06 43 -43 0.529 m-1= 1E+05 6E+06 43 -43 1.66 m-1= 31188 1E+06 43 -43 0.384

0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

bf = 0 0 43 6283 6.83 42940 2E+06 43 -43 0.529 21.43 1E+05 6E+06 43 -43 1.66 4.96 31188 1E+06 43 -43 0.384 0 0 43 6283

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

31188 1E+06 43 -43 0.384

1E+05 6E+06 43 -43 1.66

42940 2E+06 43 -43 0.529

0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

31188 1E+06 43 -43 0.384

1E+05 6E+06 43 -43 1.66

42940 2E+06 43 -43 0.529

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

31188 1E+06 43 -43 0.384

1E+05 6E+06 43 -43 1.66

42940 2E+06 43 -43 0.529

hf = 0 0 0 0 0 43 43 6283 6283

DEFLECTION CALCULATIONS (iii)

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

31188 1E+06 43 -43 0.384

1E+05 6E+06 43 -43 1.66

42940 2E+06 43 -43 0.529

0 0 43 6283

bd3/12 =

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

31188 1E+06 43 -43 0.384

1E+05 6E+06 43 -43 1.66

42940 2E+06 43 -43 0.529

0 0 0 43 6283

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

1E-04 -1E-04 -1 1 0.192

4E-04 -4E-04 -1 1 0.83

0 0 43 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

1E-04 -1E-04 -1 1 0.192

4E-04 -4E-04 -1 1 0.83

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

1E-04 -1E-04 -1 1 0.192

4E-04 -4E-04 -1 1 0.83

1E-04 -1E-04 -1 1 0.265

0 0 43 0

Revision

-

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

1E-04 -1E-04 -1 1 0.192

4E-04 -4E-04 -1 1 0.83

1E-04 -1E-04 -1 1 0.265

0 0 43 0

11-Apr-2006

Date

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

0.00

0.00 0.00

0.0 0 0 0

1E-04 -1E-04 -1 1 0.192

4E-04 -4E-04 -1 1 0.83

0.00 0 43 0

0

0.0 0 0 0 0 0 0

0

0.0 0 0 0 0 0 0

0

0.0 0 0 0 0 0 0

1E-04 -1E-04 -1 1 0.192

4E-04 -4E-04 -1 1 0.83

1E-04 -1E-04 -1 1 0.265

R68

106 86

1E-04 -1E-04 -1 1 0.265

0 0 43 0

Job No

Page

The Concrete Centre

1E-04 -1E-04 -1 1 0.265

chg

1E-04 -1E-04 -1 1 0.265

0 0 43 0

Checked

RMW

Made by


106

17/07/2006 17:06:57

RCC43 Wide Beams (A & D).xls

RCC43 Wide Beams (A & D).xls This spreadsheet designs multiple-span rectangular or flanged beams using sub-frame analysis to derive moments and shears. The intention is to provide the design and analysis of up to six spans of continuous wide beams with columns above and below. Spans may incorporate cantilevers, fixed ends or knife-edge supports. There are three main sheets: MAIN!, ACTIONS! and SPANS! This spreadsheet is very similar to RCC41.xls except that it caters for wide beams (beams wider than they are deep) by allowing two sizes of bar in one layer and by allowing top steel in the span to be augmented to help satisfy span:depth criteria. The selection of size and number of top and bottom bars is automated. The number of bars determined by either: ■ Area of steel required/ area of maximum sized bar (e.g.

32mm diameter) ■ Spacing rules ■ Number of legs of links required in shear.

Where the latter two may govern, two diameters of bending steel are allowed in the same layer to avoid excessive overspecification of reinforcement. Input to the right of SPANS! allows top steel to be increased to satisfy span:depth criteria. The designer and detailer are expected to rationalise this output (but always remembering that bar spacings should not be increased). The size of link to be used remains as manual input.

MAIN! This sheet contains user input of materials, frame geometry and load data, as explained earlier. ‘Rebar layering’ refers to whether there are beams in the other direction. Answering ‘yes’ drops by one bar diameter the steel at the supports. For instance when using splice bars at the support bars in the other direction has to be avoided - and allowed for in the design. With respect to cantilevers, design for bending caters for moments at the face of support; design for deflection considers the cantilever from the centre line of support. In beam-to-beam situations (where the beam soffits are the same depth), the width of support can be input as being very small to avoid under-design in bending.

ACTIONS! ACTIONS! includes bending moment and shear force diagrams, summaries of moments and shears and user input for amounts of redistribution. Users should ensure that the amounts of redistribution in row 26 are always considered - there are no default or automated values. Cell L14 determines how the redistribution is carried out (see also Table 1 of this document).

SPANS! This sheet designs reinforcement for bending in spans and supports and for shear in the spans. User input is required for link sizes (e.g. at cell I22) and the amount by which span top steel should be increased (e.g. at cell N21) in order to help meet deflection criteria. Non-existent spans are blanked out. Support moments (including cantilever moments) are considered at the face of the support. This may lead to unequal amounts of reinforcement being designed for each side of the support. See Bar! Besides the limit of maximum modification factor for deflection = 2.0, an additional limit of maximum allowable area of steel has been imposed to comply with deflection criteria, Asdef, = 2 x Asreq’d , i.e. an allowable increase of 100% bottom span steel.

WEIGHT! This sheet estimates the weight of reinforcement in the beam when designed according to normal curtailment rules as defined in BS 8110. Workings are shown on the right hand side of the sheet. The estimate may be printed out using ‘File/print’ or the print button on the normal toolbar. It should be recognised that different engineers’ and detailers’ interpretations of these clauses, and different project circumstances and requirements will all have a bearing on actual quantities used.

Analysis! This sheet shows the moment distributions used in the analysis of the beam: it is not intended for formal printing. It will be seen that the loads are considered initially as 1.0gk over all spans then as (gfg - 1.0)gk + gfqqk over alternate spans.

Bar! Intended mainly for first time users and young engineers, this sheet gives further details of the calculations summarised in SPAN! Support moments are considered at faces of supports;

107


17/07/2006 17:07:00

checks at 1/4 span relate to hogging and any top steel required at either of these points is provided throughout the span.



108


17/07/2006 17:07:01

RCC43 Wide Beams (A & D).xls RCC43 Wide Beams (A & D)/ MAIN! Project


Client Location

Advisory Group D&D: Main beam Grids C to H


from grid 1 to 3

WIDE BEAM (Analysis & Design) to BS 8110:2005 Originated from RCC43 v3.0 on CD

LOCATION

Supports from grid

1

to grid

SPANS SPAN 1 SPAN 2 SPAN 3 SPAN 4 SPAN 5 SPAN 6 SUPPORTS Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Support 7 LOADING

h agg γs γc


20 1.15 1.50

H (mm)

bw (mm)

hf (mm)

Type

bf (mm)

375 375 375

1200 1200 1200

125 125 125

T T T

1900 2100 2200

4.00

375

1200

125

T

1650

H (mm)

B (mm)

End Cond

300 300 300 300 300

300 300 300 300 300

F F F F F

UDLs (kN/m)

PLs (kN)

-

R68

COVERS (to all steel) Top cover 25 mm Btm cover 40 mm Side cover 35 mm

mm

5.50 8.00 8.50

3.75 3.75 3.75 3.75 3.75

Job No

3

L (m)

ABOVE (m)


40 500 250 A

109 55

Revision

chg

© 2006 TCC

Sheet No

11-Apr-06

Checked

MATERIALS fcu fyl fyv steel class

Date

rmw

BELOW (m)

3.75 3.75 3.75 3.75 3.75


min

max

1 0

1.4 1.6

REBAR LAYERING Support steel in alt layer ? N

H (mm)

B (mm)

End Cond

300 300 300 300 300

300 300 300 300 300

F F F F F

Dead Load

Imposed Load

Position from left

62.2

30.0

Position (m)

Dead Load

Imposed Load

Position from left

Loaded Length

62.2

30.0

~~~~~

~~~~~ ~~~~~ ~~~~~

62.2 25.0

30.0 25.0

~~~~~ 4.00

~~~~~ ~~~~~ ~~~~~

62.2

30.0

~~~~~

~~~~~ ~~~~~ ~~~~~


Loaded Length

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

LOADING DIAGRAM

1

3


ALL SPANS LOADED ODD SPANS LOADED EVEN SPANS LOADED Characteristic Dead Max Service Imposed Min Service Imposed

1

2

3

4

5

271.5 323.2 74.4 126.1 71.1 -16.3

1037.5 637.7 831.0 464.7 236.7 0.0

1178.6 889.8 907.4 551.6 273.4 0.0

965.4 830.3 539.8 438.4 210.0 0.0

134.2 -19 214.1 61.4 63.0 -32.9

0.0 0.0 0.0

0.0 0.0 0.0

109


17/07/2006 17:07:02

RCC43 Wide Beams (A & D)/ ACTIONS!

Project


Client

Advisory Group

Location




Date

rmw Checked

Revision

chg

© 2006 TCC

Page

11-Apr-06

110 56 Job No

-

R68


1000

1000

800

800

600

600

400

400

200

200 0

0

-200 0

5

10

15

20

25

30

-200

0

5

10

15

20

25

30

-400

-400

-600

-600

-800

1

3



1

1

2

3

4

5

95.0 95.0 1.000

661.2 661.2 1.000

888.9 755.6 0.850

661.3 661.3 1.000

33.6 33.6 1.000

~ ~ ~

~ ~ ~

~ ~ ~

Redistribution

3


kNm/m kNm/m ~

15.0%

SPAN No


1

2

3

4

291.64 291.64 1.000

561.87 533.32 0.949

542.57 528.36 0.974

136.11 136.11 1.000

800

800

600

600

400

400

200

200

0

0

-200

-200

-400

-400

-600

-600

-800

-800 0

5

10

15

20

25

Elastic Shears

1 SPAN No


30

0

3

SPAN No

10

15

2

25

30

3

3

471.5 471.5

570.4 566.0

605.1 592.4

604.6 589.0

570.3 563.0

4

Elastic V

406.1

214.1

~

~

~

~

Redistributed V

406.1

214.1

~

~

~

~


20


1

1

323.2 323.2

5

1

2

3

4

5

29.7 29.7 47.5 47.5 -3.8 -3.8

25.9 25.9 -20.6 -20.6 57.5 57.5

4.7 4.7 57.2 57.2 -49.2 -49.2

-42.8 -42.8 -61.9 -61.9 -0.8 -0.8

0.2 0.2 17.1 17.1 -16.8 -16.8

110


17/07/2006 17:07:05

RCC43 Wide Beams (A & D).xls RCC43 Wide Beams (A & D)/ SPANS!

Project


Client

Advisory Group

Location




SPAN 1 ACTIONS

M ßb DESIGN d As As' TOP STEEL Layer 1

BTM STEEL

kNm mm mm² mm²

As prov Layer 1

mm²

As' prov

mm²

DEFLECTION SHEAR

V v vc

kN N/mm² N/mm²

LINKS

legs

No


CHECKS



BTM STEEL

kNm mm mm² mm²

As prov Layer 1

mm²

As' prov

mm²

DEFLECTION SHEAR

V v vc

kN N/mm² N/mm²

LINKS

legs CHECKS


Revision

chg CENTRE 291.6 1.00 315.0 2241 0 2H20 + 5H16 . As' prov 1634 4H20 + 5H16 .

As prov Allowed

2262 27.490 Link Ø

10 Nominal

R10 @ 225 7 ok ok ok ok ok ok

Page

11-Apr-06 -

111 57 Job No

R68

RIGHT 540.1 1.00 324.0 4449 0 1H32 + 8H25 . As prov 4731 4H12 + 3H10 . As' prov 688 407.5 1.048 0.832 R10 @ 225 for 675 7 ok ok ok ok ok ok ok

ok

SPAN 2 ACTIONS

Checked

© 2006 TCC

LEFT 48.0 1.00 332.0 350 0 2H16 + 7H12 . 1194 4H12 + 3H10 . 688 L/d 17.460 258.1 0.648 0.518 R10 @ 225 for 675 7

Date

rmw

No

LEFT 577.9 1.00 324.0 4825 0 2H32 + 7H25 . 5045 1H20 + 6H16 . 1521 L/d 25.890 502.0 1.291 0.675 R10 @ 150 for 1050 7 ok ok ok ok ok ok ok

CENTRE RIGHT 533.3 668.6 0.95 0.86 309.0 324.0 4179 5787 0 0 1H20 + 6H16 3H32 + 7H25 . . As' prov 1521 As prov 5849 3H32 + 6H25 1H20 + 6H16 . . As prov 5358 As' prov 1521 Allowed 26.212 As auto-increased by 28.2 % Link Ø 528.4 10 1.359 Nominal 0.893 R10 @ 225 R10 @ 200 for 800 7 7 ok ok ok ok ok ok


ok

111


17/07/2006 17:07:08

RCC43 Wide Beams (A & D)/ SPANS!

Project


Client

Advisory Group

Location




SPAN 3 ACTIONS


BTM STEEL

kNm mm mm² mm²

As prov Layer 1

mm²

As' prov

mm²

. DEFLECTION SHEAR

V v vc

kN N/mm² N/mm²

LINKS

legs

No


kNm mm mm² mm²

4064 7H8

As' prov

mm²

352 12.618 341.6 0.869 0.624 R10 @ 225 for 450 7

DEFLECTION kN N/mm² N/mm²

LINKS

CHECKS


As' prov 1521 As auto-increased by 38.3 % Link Ø V 499.0 10 v 1.283 Nominal vc 0.850 R10 @ 225 R10 @ 225 for 900 7 7 ok ok ok ok ok ok ok

No


RIGHT 3.0 1.00 332.0 22 0 2H16 + 7H12

.

As' prov

2376 1H16 + 8H12

As prov Allowed

1106 37.733

.

legs

.

5985 28.312

CENTRE 136.1 1.00 317.0 1039 0 1H25 + 6H20

. mm²

V v vc

R68

RIGHT 578.4 1.00 324.0 4831 0 2H32 + 7H25 . As prov 5045 1H20 + 6H16

ok ok ok ok ok ok

LEFT 498.1 1.00 327.5 3986 0 7H25 + 2H20

As prov BTM STEEL Layer 1

SHEAR

112 58 Job No

ok

SPAN 4 M ßb DESIGN d As As' TOP STEEL Layer 1

-

.

As prov Allowed


CHECKS

ACTIONS

1521 27.508 524.9 1.350 0.709 R10 @ 150 for 1050 7

Revision

chg CENTRE 528.4 0.97 309.0 4140 0 4H16 + 4H12 . As' prov 1257 5H32 + 4H25

Page

Apr-2006

Checked

© 2006 TCC

LEFT 669.3 0.85 324.0 5794 0 3H32 + 7H25 . 5849 1H20 + 6H16

Date

rmw

.

As prov

1194 7H8

As' prov

352

.

Link Ø

10 Nominal

R10 @ 225 7 ok ok ok ok ok ok

.

149.0 0.374 0.518 R10 @ 225 for 450 7 ok ok ok ok ok ok ok

ok

112


17/07/2006 17:07:10

RCC51 Column Load Take-down & Design.xls

RCC51 Column Load Take-down & Design.xls Conventional column load take downs by hand can be timeconsuming. This spreadsheet emulates conventional column design to BS 8110(2) by providing on separate sheets: load take down from inputs of location, dimensions, levels and loads to give design axial loads and moments per floor. RCC51.xls is intended as a stand-alone column design spreadsheet for use when a subframe analysis is not available or is unwarranted. As in COLUMN! within RCC11.xls, this spreadsheet determines the area of steel required (As).

Please note when inputting a location for numbered gridlines to start with an apostrophe, i.e. use ’2 - 3 (otherwise 2 - 3 will give the result of -1!). Cantilevers may be dealt with by inputting no beam on the appropriate axis but inputting additional loads and moments (under ‘At column position, other applied loads (e.g. loads from cantilevers)’). Note that, so far as the column is concerned, cantilever moments will relieve (or even exceed fixed end) beam moments and should be specified as negative moments.

The spreadsheet is set up in such a way that one column size (input in CDES!) is used throughout the height of the column location and that the critical section for design occurs where axial load is at its maximum.

As explained under Operator Instructions deleting a level will ‘grey-out’ subsequent columns and set spans to 0.0 m. Enter data (and delete any subsequent hatches, #####) or equate cells to previous cells (avoid copying cells across) to get up to 10 levels of load take down. Deleting or setting a value of 0 in columns G to P will ‘grey-out’ values to the right, which will be set at 0.0. Generally, input values are carried through to the right. Red figures or red backgrounds mean inconsistent or incorrect data entries. Overwrite if incorrect.

The example is based on Designed and detailed (15) but differs in several respects: ■ Seven storeys used in the example rather than three (in order

to demonstrate automatic input adequately) ■ No special account taken of roof loadings (in order to

demonstrate automatic input adequately) ■ All columns are taken as 4.00 m long (again, in order to

Slab spans may be parallel to x or y, or two-way spanning. Troughed slabs may be modelled by using the topping thickness for the slab and adding widths of ribs within a bay to the width of the beam.

demonstrate automatic input adequately) ■ Load distribution according to BS 8110: Part 1, Clause 3.8.2.3,

i.e. reaction factors of 0.5 are used for loads from adjacent spans rather than results of analysis or using shear force factors from BS 8110: Part 1 Tables 3.5 and/or 3.12. ■ No double counting of floor slabs due to allowances for floor

slabs in design of, therefore reactions from, edge beams spanning parallel to floor slab span. As a default the level with maximum axial load with concurrent maximum moment, i.e. the bottom level, is chosen for consideration in DESMMNTS! (derivation of design moments) and CDES! (design). The user may investigate other levels by choosing the appropriate level in the combo-box on the right hand side of CDES!. Unbraced columns may be designed, but the spreadsheet demands some input of applied moment in LOADTD! in the appropriate axis. If the column is unbraced then it must be part of a stability frame – if only nominally – with moments that should be input as applied moments in LOADTD!

Some input (highlighted in magenta) defaults to values from other sheets. For instance column dimensions are input in CDES! The user may immediately see whether the design is viable or not and change dimensions accordingly. These cells are not protected so can be overwritten: beware. For troughed slabs use topping thickness and aggregate width of ribs with width of beam. Reduction factors for live load to according to BS 6399: Part 1(19) Clause 5.2 are automatically applied to axial load unless specified otherwise.

DESMMNTS! The basic design procedure is covered in BS 8110: Part 1 Clause 3.8. In order to determine design moments several inputs are required: ■ Values of ß for braced and unbraced columns are required

at G15:H15, see Clause 3.8.1.6 and Tables 3.19 and 3.20 as shown overleaf. ■ Whether the column is braced or un-braced – see BS 8110:

LOADTD! Input is self explanatory but, in order to facilitate use of this spreadsheet, some degree of automation has been introduced. It is vital that input data is hand checked to ensure the loads are described properly. It is also advised that a clean version of the spreadsheet should be used for each column analysed and designed (i.e. reload the base spreadsheet each time).

Part 1, Clause 3.8.1.5. ■ In order to evaluate Nuz and thus K accurately, an initial

assessment of the area of reinforcement, As, is required at cell N22. An indication of the probable percentage of reinforcement is given at Q23 (automation of this figure would cause a circular reference error in the spreadsheet). If As is set at 0% then effectively K = 1, which is conservative (see BS 8110: Part 1, equation 33 and definitions under Clause 3.8.1.1). 113


17/07/2006 17:07:13

Table 2 Values of ß for braced and unbraced columns

End condition at top

Values of ß for braced columns

Values of ß for unbraced columns

End condition at bottom

End condition at bottom

1

2

3

1

2

3

1

0.75

0.80

0.90

1.20

1.30

1.50

2

0.80

0.85

0.95

1.30

1.50

1.80

3

0.90

0.95

1.00

1.60

1.80

-

4

-

-

-

2.20

-

-

Condition 1 - column monolithically connected to beam at least as deep as the column in the plane considered (or foundation specifically designed for moment) Condition 2 - column monolithically connected to beams or slabs shallower than the column in the plane considered Condition 3- column connected to members which will provide some nominal restraint Condition 4- column unrestrained NOTE: Taken from BS 8110 Tables 3.19 and 3.20

CDES!

Ltdcalcs!

As in COLUMN! within RCC11.xls, this sheet designs symmetrical rectangular columns where both axial load, N, and design moment, Mx or My (see BS 8110: Part 1, Clause 3.8.2, 3 and 4) have been calculated from previous sheets. CDES! iterates x/h to determine where the neutral axis lies. The sheet includes stress and strain diagrams to aid comprehension of the final design (please refer to notes regarding COLUMN! in RCC11.xls).

This sheet shows workings for the load take-down and is not necessarily intended for printing out other than for checking purposes. Load distribution works according to BS 8110: Part 1, Clause 3.8.2.3 – “…axial force in a column may be calculated on the assumption that beams and slabs transmitting force into it are simply supported”.

Stiffs!

The spreadsheet is set up in such a way that one column size (input in CDES!) is used throughout the height of the column location and that the critical section for design occurs where axial load is at its maximum.

This sheet shows workings for beam and column stiffnesses and is not necessarily intended for printing out other than for checking purposes.

Other levels can be investigated by choosing the appropriate level from the combo-box located under Operating Instructions. Always ensure that the size of column designed is correct for the level under consideration.

In the determination of section properties, beams are considered full height – beam widths are deducted from slab widths. Moment distribution works according to BS 8110: Part 1, Clause 3.2.1.2.5 – “… beams possess half their actual stiffness”.

For simplicity, where three or more bars are required in the top and bottom of the section, a (rotationally) symmetrical arrangement of reinforcement is proffered, i.e. top and bottom reinforcement with additional side bars. The argument goes that using the critical axis method of BS 8110 to determine areas of steel in bi-axially bent columns implies that the bars are in the corners of the element. Therefore ‘additional’ side bars help ensure this is so. Counter-arguments suggest these additional bars are unnecessary. Bresaler’s load contour check [(Mx / Mux )a + (My / Muy )a < 1.0, where a = 2/3 + 5N/3Nuz], used in CP 110(20) is not adopted in this spreadsheet but may be investigated using RCC53.xls.


Some input (highlighted in magenta) defaults to values from other sheets. These cells are not protected so can be overwritten: beware. 114


17/07/2006 17:07:15

RCC51 Column Load Take-down & Design.xls RCC51 Column Load Take-down & Design/ LOADTD!

Project


Client

Advisory Group Edge Column B1

Location


(akin to D&D)

COLUMN LOAD TAKE DOWN & DESIGN FOR SYMMETRICALLY REINFORCED RECT. COLUMNS BENT ABOUT TWO AXES TO BS 8110:2005

Originated from RCC51.xls v3.0

Date

rmw

© 2006 TCC

INPUT

Page

11-Apr-06

Checked

Revision

chg

-

115 85 Job No

R68

1-2

Location Edge Column B1

(akin to D&D) Orientation

y A-B

x

x

H

B-C

3

24.0 1.40 1.60

0

0

0

included

included

included

concrete density, kN/m fgk fqk

y n/a Level

7

6

5

4

3

2

1

5.00 5.00 7.50 0.00

5.00 5.00 7.50

5.00 5.00 7.50

5.00 5.00 7.50

5.00 5.00 7.50

5.00 5.00 7.50

5.00 5.00 7.50

175 x

175 x

175 x

175 x

175 x

175 x

175 x

300 350 300 350 300 500 0 0

300 350 300 350 300 500

300 350 300 350 300 500

300 350 300 350 300 500

300 350 300 350 300 500

300 350 300 350 300 500

300 350 300 350 300 500

300 300 4.00

300 300 4.00

300 300 4.00

300 300 4.00

300 300 4.00

300 300 4.00

300 300 4.00

7

6

5

4

3

2

1

5.00 4.00

5.00 4.00

5.00 4.00

5.00 4.00

5.00 4.00

5.00 4.00

5.00 4.00

(swt.) gk kN/m included included included line loads (-extra over slab loads and beam self weight) A-B gk kN/m 5.0 5.0 5.0 qk kN/m 0.0 B-C gk kN/m 5.0 5.0 5.0 qk kN/m 0.0 1-2 gk kN/m 0.0 qk kN/m 0.0 n/a gk kN/m 0.0 qk kN/m 0.0

included

included

included

included

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

Dimensions Spans Cl to Cl

Slab

A-B B-C 1-2 n/a

thickness (solid) mm span direction,(II to) x, y or b width depth o/a width depth o/a width depth o/a width depth o/a

A-B A-B B-C B-C 1-2 1-2 n/a n/a

Column below H (ll to yy) B (ll to xx) Height (fl. to floor.)

mm mm m

Beams

Loads Slab

Beams

m m m m

mm mm mm mm mm mm mm mm (col above)

Level (characteristic uno) (inc swt.) gk kN/m2 qk kN/m2

At column position, other applied loads (eg loads from cantilevers) Gk kN (char) 0.0 Qk kN (char) 0.0 Mxx kNm (ult) 0.0 Myy kNm (ult) 0.0 Loads per floor Floor Floor Column below

OUTPUT

Gk Qk Gk

kN kN kN

133.8 75.0 8.6

133.8 75.0 8.6

133.8 75.0 8.6

133.8 75.0 8.6

133.8 75.0 8.6

133.8 75.0 8.6

133.8 75.0 8.6

7 to 6

6 to 5

5 to 4

4 to 3

3 to 2

2 to 1

Below 1

kN kN factor kN kN

142.5 75.0 1.0 75.0 319

284.9 150.0 0.9 135.0 615

427.4 225.0 0.8 180.0 886

569.9 300.0 0.7 210.0 1134

712.3 375.0 0.6 225.0 1357

854.8 450.0 0.6 270.0 1629

997.3 525.0 0.6 315.0 1900

kNm kNm kNm kNm

112.6 1.6 91.7 1.3

91.7 1.3 91.7 1.3

91.7 1.3 91.7 1.3

91.7 1.3 91.7 1.3

91.7 1.3 91.7 1.3

91.7 1.3 91.7 1.3

91.7 1.3

Column level

Cumulative loads in column. Gk Qk Redn Qk redn factors OK*? Qk red* Y N Moments in column about x-x Mxx top about y-y Myy top Mxx bottom Myy bottom

115


17/07/2006 17:07:16

RCC51 Column Load Take-down & Design/ DESMMNTS!

Project


Client

Advisory Group Edge Column B1

Location


(akin to D&D)

COLUMN LOAD TAKE DOWN & DESIGN FOR SYMMETRICALLY REINFORCED RECT. COLUMNS BENT ABOUT TWO AXES TO BS 8110:2005 Originated from RCC51.xls v3.0

INPUT

Orientation

about x-x about y-y 300 300

mm mm

lo, clear height ß

mm value

3500 0.90

3650 0.90

Braced or Unbraced?

B or U

B

B

kN kNm kNm

1900 91.7 0.0

1.3 0.0

kNm kN

1900 92.1 X-X

N top bottom

R68

-

(akin to D&D)

h (ll to yy) b (ll to xx)

Loads Axial Moments

116 86 Job No

Revision

chg

Location Edge Column B1 Level considered: Bottom (Max N)

Page

11-Apr-06

Checked

© 2006 TCC

Dimensions

Date

rmw

A-B

1-2 y x

x

B-C

H

y n/a Height (fl. to floor.) 4.00 m Column properties fcu fy cover to link Max sized main bar Probable percentage As link diameter

35 500 30 32 2.00% 8

mm mm % mm

OUTPUT Design criteria N M

about PROOF Slenderness le Slenderness Limit for short column Design column as Column is

mm

3150 3285 10.50 10.95 15.0 15.0 Short Short Short about x-x about y-y

Design moments (cont) about x-x about y-y Design moments for unbraced columns M2+100% Madd kNm n/a n/a eminN kNm n/a n/a Maximum kNm n/a n/a Design moments 1.3 91.7 about x-x about y-y Short Braced Braced

kNm Design moments Min eccentricity, 0.05 h Madd d Nuz Nbal K b' or, if slender, h? - b' ßa au Madd Eqns 32-35 ok to use? Braced columns M1 Mi Mi, (Mi=0 if Le/h>20) Mi, (Mi=0 if b/h>3)

kNm

28.5

n/a - short column 246 246 2200.1 2200.1 645.8 645.8 0.193 0.193 mm 246 246 0.082 0.089 mm 4.7 5.2 kNm 0.0 0.0 ok kNm 0.0 0.0 kNm 55.0 0.8 kNm 55.0 0.8 55.0 0.8 mm kN kN

Biaxial bending Mx/h' My/b Critical direction N/bhfcu ß

91.7 55.0 0.0 28.5 91.7

0.005 X-X 0.60 0.30

Maximum design moment = 91.7+0.30*246/246*1.3 =

Design moments for braced columns M2 kNm Mi+Madd kNm M1+Madd/2 kNm eminN kNm Maximum kNm

0.373

kNm

92.1

-

1.3 0.8 0.0 n/a 1.3

116


17/07/2006 17:07:19

RCC51 Column Load Take-down & Design.xls RCC51 Column Load Take-down & Design/ CDES!


Project

Client Advisory Group Location Edge Column B1


(akin to D&D)

rmw

COLUMN LOAD TAKE DOWN & DESIGN FOR SYMMETRICALLY REINFORCED RECT. COLUMNS BENT ABOUT TWO AXES TO BS 8110:2005 Originated from RCC51.xls v3.0

INPUT

Checked

chg

© 2006 TCC

Level designed: Bottom (Max N) kN Axial load, N 1900 Moment, M 92.1 kNm about X-X axis Height, h (ll to yy, L'r to xx) 300 mm Breadth, b (ll to xx) 300 mm Max bar diameter 32 mm cover (to link) 30 mm

fcu fy fyv γm γm Link Ø steel class

Date

Page

117 87

11-Apr-06 Revision

Job No

R68

-

35 500 500 1.15 1.5 8 A

N/mm² N/mm² N/mm² steel concrete mm

CALCULATIONS from M from N

As = {M - 0.67fcu.b.dc(h/2 - dc/2)}/[(h/2-d').(fsc+fst).m] As = (N - 0.67fcu.b.dc/m) / (fsc - fst) As = Ast = Asc: dc=min(h,0.9x) d' = 54 mm .67fcu/m = 15.6 N/mm² d= 246 mm fy/m = 434.8 N/mm² critical about X-X axis:…... h= 300 mm b= 300 mm

from iteration, neutral axis depth, x, = dc 0.67.fcu.b.dc/m Steel comp strain Steel tens strain Steel stress in comp. face, fsc Steel stress in tensile face, fst from M, As = from N, As =

266.3 239.7 1124.0 0.00279 -0.00027 435 -53 1590 1590

mm mm kN

N/mm2 N/mm2 mm2 mm2

(Comp. stress in reinf.) (Tensile stress in reinf.) OK

As req'd = 1590mm² T&B:- PROVIDE 4H32 (ie 2H32 T&B - 1609mm²T&B) - 3.57% o/a - @192 cc.) Links : - PROVIDE H8 @ 300 . OK Stress diagram

Strain diagram

15.6 N/mm² 0.00350

435

0.00279

about X-X axis

0.00027

53 -0.00044

Notes 2

Stresses in N/mm

Compression +ve

117


17/07/2006 17:07:22

RCC52 Column Chart generation.xls This spreadsheet generates axial load:design moment interaction charts for symmetrically reinforced rectangular columns. It checks the capacity of the columns with various arrangements of reinforcement against input load cases of axial load and uniaxial bending. Within RCC11.xls, COLUMN! allows the user to determine the area of steel required from inputs of axial load and moment about the x - x axis. Another approach, adopted in BS 5400(21) and CP 110(20) and more suited to the grouping of columns on particular projects and adopted here by RCC52.xls, is to give an interaction chart. This shows axial load against moment for symmetrical sections of specified size, strength and reinforcement. It works on the premise of calculating the moment and axial load capacities of a section with assumed amounts of reinforcement and assumed neutral axis depth. Iterations of neutral axis depth give data for the Axial load:Moment interaction chart for the specified section. The spreadsheet also checks the reinforcement required for input load cases. The user may try different arrangements of reinforcement. RCC52.xls assumes that the moments input in the load cases have already been adjusted, if necessary, for bi-axial bending. For many side and all corner columns, there is no choice but to design for bi-axial bending, and the method given in Clause 3.8.4.5 must be adhered to, i.e. RCC53.xls should be used.

The chart shows lines for 0.1fcuAc and Mmin. The user should be aware that all load cases should be within the boundaries of these lines.

Calcs! Calcs! Shows the derivation of the charts where moment capacity is calculated at intervals of neutral axis depth from n.a. depth for N = 0 to n.a. depth for N = Nbal, then at intervals from n.a. depth for N = Nbal to n.a. depth for N = Nuz.

Cases! Cases! identifies the smallest bar diameter that satisfies each of the load cases.


MAIN! Main! contains all input and output data, Bending is assumed to be about the x - x, i.e. horizontal axis, and the input moment is assumed to be the maximum design moment as defined in BS 8110 i.e. including Madd etc and in the correct orientation. Where more than two bars are required per face, the user may choose to specify a similar arrangement of bars on the side faces in order to avoid confusion in detailing and fixing. In this respect, there is also a question regarding design. To an extent all columns are bi-axially bent and BS 8110 directs that bi-axially bent columns are effectively designed about one axis only (by adding moment in the critical direction to account for moment in the non-critical direction). By implication the second axis is not designed specifically. One reason for adding side bars (when three, four or more bars are required T & B) in square(ish) sections, is to ensure that the second axis is catered for. Ideally with BS 8110, the resultant axis should be found and calculations done accordingly. But this presumes that the arrangement of bars is known to start with. With BS 5400 and CP 110 checks are carried out on a chosen section about both axes. Bi-axially bent columns are dealt with in RCC53.xls

118


17/07/2006 17:07:26

RCC52 Column Chart generation.xls RCC52 Column Chart generation/ MAIN!

Project


Client

Advisory Group

Location

Columns at A1, A2 etc


RMW

COLUMN CHART FOR SYMMETRICALLY REINFORCED RECTANGULAR COLUMNS Checked BENT ABOUT THE X-X AXIS TO BS 8110:2005 Originated from 'RCC52.xls ' v3.0 on CD

Date

Revision

chg

© 2006 TCC

Page

119 94

11-Apr-06

Job No

R68

-

MATERIALS fcu fy steel class SECTION h b with All bars in

30 500 A

N/mm²

400 400 3 400

mm

γm γm

N/mm²

1.15 1.5

steel concrete

Cover h agg

X

mm

30 20

X

bars per face wide faces

mm mm

SINGLE AXIS BENDING

BAR ARRANGEMENTS Type

Bar Ø

Asc %

Link Ø

Bar c/c

Nbal (kN)

Nuz (kN)

H H H H H H

32 25 20 16 12 10

3.02 1.84 1.18 0.75 0.42 0.00

8 8 6 6 6 6

146.0 149.5 154.0 156.0 158.0 159.0

1113.7 1104.4 1106.9 1105.8 1106.2 0.0

4177.4 3385.1 2938.3 2652.3 2429.9 0.0

Checks ok ok ok ok ok < 0.4% - ignored

N:M INTERACTION CHART for 400 x 400 column, grade C30, 30 mm cover and 3 bars on 400 mm faces 4500 KEY

M min

AXIAL COMPRESSION, N, kN

4000 6H32

3500

6H25

3000

3000

6H20

2500

6H16

2000

1850 6H12

1500

1500 1000

1000

1000

500

500

0.1fcuAc

0 0

LOADCASES

100

200 300 MOMENT Mx kNm

Load case

N (kN)

Mx' (kNm)

A1 top A1 bot A2 bot

500 1850 3000

200 100 50

6 H20 6 H16 6 H25

400

500

Load case

N (kN)

Mx' (kNm)

4 5 6

1500 1000 1000

150 150 50

6 H16 6 H12 6 H12

119


17/07/2006 17:07:27

RCC53 Column Design.xls RCC53.xls generates column design charts for symmetrically reinforced rectangular columns bent about two axes and checks input load cases. For circular columns RCC54.xls may be used. RCC53.xls also gives interaction charts, showing axial load against moment for the critical axis for symmetrical rectangular sections of specified size, strength and reinforcement arrangement. The user may try different arrangements of reinforcement. It also provides designs for input load cases, which are plotted on the relevant x- or y- axis chart. RCC53.xls takes account of any side-bars.

Philosophy of design for bi-axially bent columns When preparing this spreadsheet, there was some discussion about the interpretation of BS 8110 with respect to bi-axially bent columns and the provision of side bars. For simplicity, where three or more bars are required in the top and bottom of the section, it appears to be common practice, in small- to medium-sized columns at least, to provide a (rotationally) symmetrical arrangement of reinforcement, i.e. to provide additional side bars. The argument goes that using the critical axis method of BS 8110 to determine areas of steel in bi-axially bent columns implies that the bars are in the corners of the element. Therefore ‘additional’ side bars help ensure that this is so. There is a counter argument to suggest that the design procedure for bi-axially bent columns in BS 8110 makes the precaution of adding additional side bars unnecessary.

‘K’ in C40:C49 refers to the reduction factor as per equation 33 in BS8110.

CHARTS! CHARTS! shows two charts, one chart for when Mxx is critical and one for when Myy is critical. These Axial load:Moment interaction charts for the specified section also show relevant input load cases. The charts show lines for 0.1 fcuAc and Mmin (i.e. emin N). The user should be aware that all load cases should be within the boundaries of these lines. Due to a quirk in Excel, load cases can only be identified by axial load, N, on the charts.

Xcal! and Ycal! These sheets show the derivation of the charts where moment and axial load capacity is calculated at intervals of neutral axis depth (in intervals from n.a. depth for N = 0 to n.a. depth for N = Nbal, then in intervals from n.a. depth for N = Nbal to n.a. depth for N = Nuz. .).

Cases! Cases! identifies the smallest bar diameter that satisfies each of the load cases. Clause 3.8.3.2 is included for both directions (columns K & L) and the spreadsheet decides which axis is dominant.


(22)

Rafiq argues that the Bresaler’s load contour check, as used in CP 110( 20) should be adopted to ensure a safe design for bi-axially bent columns otherwise designed to BS 8110, as shown below. (Mx /Mux)a + (My /Muy)a < 1.0, where a = 2/3 + 5N/3Nuz

MAIN! MAIN! contains all input data and gives designs for the input load cases. Guidance for the input is given within the spreadsheet but users should be familiar with BS 8110: Part 1, Clause 3.8 which deals with column design. The input moments under LOADCASES are the initial end moments due to ultimate design loads is defined in BS 8110 about the appropriate axes for slender columns. The spreadsheet calculates the additional design ultimate moment induced by deflection of column (Madd), the critical direction for bi-axial bending and the design moment. 120


17/07/2006 17:07:31

RCC53 Column Design.xls RCC53 Column Design/ MAIN!

Project


Client Location

Advisory Group Ground floor columns at B1, B2 etc


Date

RMW

SYMMETRICALLY REINFORCED RECTANGULAR COLUMN DESIGN, BENT ABOUT TWO AXES TO BS 8110:2005 Checked Originated from RCC53.xls

MATERIALS fcu fy steel class SECTION h b with and

35 500 A

N/mm²

400 300 3 3

mm

N/mm²

v3.0 on CD

γm, steel γm, conc

Revision

chg

© 2006 TCC

1.15 1.5

Cover to link h agg

Page

121 96

11-Apr-06

Job No

-

30 20

R68

mm mm

mm

X

#N/A

X

#N/A

#N/A RESTRAINTS Lo (mm)

Top Condition

Btm Condition

Braced ?

ß

Le (mm)

3600 3600

2 2

2 2

Y Y

0.85 0.85

3060 3060

X-AXIS Y-AXIS LOADCASES

TOP MOMENTS (kNm)

AXIAL N (kN)

B1 B2 Loadcase 3 Loadcase 4 Loadcase 5 Loadcase 6

3500 3000 1000 1200 500 2500

BAR ARRANGEMENTS Bar Ø

H H H H H H

40 32 25 20 16 12

DESIGN MOMENTS (kNm) K

B1 B2 Loadcase 3 Loadcase 4 Loadcase 5 Loadcase 6

0.000 0.000 0.000 0.000 0.000 0.000

Asc %

Link Ø

8.38 5.36 3.27 2.09 1.34 0.75

10 8 8 6 6 6

X AXIS M add Mx

0.0 0.0 0.0 0.0 0.0 0.0

90.0 80.0 100.0 50.0 220.0 35.0

Slenderness

Lex/h = 7.65 Ley/b = 10.20 BTM MOMENTS (kNm)

M ix

M iy

M ix

M iy

90.0 80.0 100.0 50.0 220.0 35.0

25.0 60.0 35.0 150.0 90.0 25.0

90.0 80.0 100.0 50.0 220.0 35.0

25.0 60.0 35.0 150.0 90.0 25.0

BAR CENTRES (mm) 300 Face 400 Face

90 96 100 104 106 108

140 146 150 154 156 158

Y AXIS M add My

0.0 0.0 0.0 0.0 0.0 0.0

25.0 60.0 35.0 150.0 90.0 37.5

Status Column is SHORT

Nuz (kN)

Checks Asc > 6 % (3.12.6.2) ok ok ok ok ok

0 4573 3522 2929 2550 2255 COMBINED Axis M'

X Y X Y X Y

100.5 77.1 135.1 173.8 329.0 45.1

REBAR

max V *

8 H32 8 H32 8 H12 8 H25 No Fit 8 H25

99.6 102.3 52.0 86.5 97.3 88.1

SEE CHARTS ON NEXT SHEET

121


17/07/2006 17:07:32

RCC53 Column Design/ CHARTS!

Project


Client Location

Advisory Group Ground floor columns at B1, B2 etc


RMW

Date

Page

11-Apr-06

SYMMETRICALLY REINFORCED RECTANGULAR COLUMN DESIGN, BENT ABOUT Checked TWO AXES TO BS 8110:2005

Revision

chg

-


© 2006 TCC

122 97 Job No

R68

N:M interaction chart: Mx' critical 400 x 300 column (h x b), grade C35, 30 mm cover 5000 Mx min

4500

KEY

4000

AXIAL LOAD, kN

3500

3500

8H32 3000 8H25

2500

8H20

2000 1500

8H16

1000

1000

8H12 500

500

0

0.1fcuAc

0

0

100

200

300

400

500

Mx' kNm

N:M interaction chart: My' critical 400 x 300 column (h x b), moment about yy axis), Grade C35, 30 Cover 5000 My min

4500

KEY

4000

AXIAL LOAD kN

3500

8H32

3000

3000

8H25 2500

2500

2000

8H20

1500

8H16 1200

1000

8H12

500

0.1fcuAc

0

0

0

50

100

150

200

250

300

My' kNm 122


17/07/2006 17:07:36

RCC54 Circular column charting .xls

RCC54 Circular column charting .xls This spreadsheet generates design charts for circular reinforced concrete columns. It shows the interaction between axial load and applied moment. Designs for input design load cases are given.

MAIN! MAIN! contains all input data. It charts the relevant interaction diagram and gives designs for the input load cases. Some guidance for the input is given within the spreadsheet but users should be familiar with BS 8110 Part 1, Clause 3.8 Columns. The input moments should be the maximum design moments as defined in BS 8110.

Calcs! For each bar diameter size Calcs! works out the co-ordinates for the N-M interaction diagram. Calcs! first works out the geometry for columns with up to 16 bars, specifically the neutral axis depth associated with no axial load, i.e. for N=0. Then for increments of neutral axis depth, moment and axial load capacities are calculated. The size of the increment is increased when neutral axis depth exceeds 2/3d, i.e. as axial load predominates and less accuracy is necessary.

Circle! Circle! provides geometrical data for truncated circular sections as look-up data for other sheets, notably for Calcs!

Cases! For each load case, Cases! determines the smallest bar diameter that satisfies the axial load and moment requirements. The input load is used to look up the appropriate capacities from Calcs!. These capacities are then used to determine the maximum moment allowable with the specified axial load.


123


17/07/2006 17:07:38

RCC53 Column Design/ MAIN!

Project


Client

Advisory Group

Location



RMW

COLUMN CHART FOR CIRCULAR COLUMNS TO BS 8110:2005 Originated from 'RCC54.xls ' v3.0 on CD

Checked

Date

Revision

chg

© 2006 TCC

Page

124 94

12-Apr-06

Job No

R68

-

MATERIALS fcu fy steel class SECTION h

35 500 A 475

γm γm

N/mm² N/mm²

mm

with

1.15 1.5

steel

8

bars

Cover h agg

concrete

30 20

mm mm

BAR ARRANGEMENTS Type

Bar Ø

Asc %

Link Ø

Bar c/c

Nbal (kN)

Nuz (kN)

H H H H H H

40 32 25 20 16 12

5.67 3.63 2.22 1.42 0.91 0.51

10 8 8 6 6 6

139.4 144.1 146.9 150.4 152.0 153.5

719 948 1028 1142 1152 1293

6984 5467 4416 3824 3445 3150

Checks ok ok ok ok ok ok

N:M INTERACTION CHART for 475 diameter column, grade C35, 30 mm cover and 8 bars 8000 KEY

AXIAL COMPRESSION, N, kN

7000

M min

6000

8H40

5000

8H32 4100

4000

8H25

3600 8H20

3000

3000

2500 8H16

2000 1500

8H12

1000 650

0.1fcuAc

0 0

100

200

300

400

500

600

MOMENT M, kNm LOADCASES

Load case

N (kN)

M (kNm)

1 2 3

650 4100 3000

210 320 60

8 H20 8 H40 8 H16

Load case

N (kN)

M (kNm)

4 5 6

1500 2500 3600

160 210 175

8 H12 8 H25 8 H32

124


17/07/2006 17:07:39

RCC61 Basement Wall.xls

RCC61 Basement Wall.xls This spreadsheet designs simple retaining basement walls and is intended for walls up to 3.5 m high. It is based on complying with BS 8002: 1994(4) and BS 8004: 1986(23) . It may also be used to design walls to comply with CECP 2(6) and BS 8007(5). The spreadsheet has been developed with both the BS 8002 and the conventional (CECP 2) methods in mind. On balance, the spreadsheet provides reasonable flexibility and in doing so, encourages the designer to employ his/ her own engineering judgement and interpretation of the codes. The spreadsheet is intended to cover only short walls and to help ‘general’ engineers who, from time to time, design retaining walls as part of a wider interest in structures, rather than the specialists. The 3.5 m wall height is an arbitrary limit set for a short wall which is intended to cover over 90% of the cases encountered in ‘general’ structural designs. Although many of the design principles still apply to higher walls, criteria such as wall movements and the validity of the assumptions made (e.g. no wall friction) require further consideration and investigation. The effects of compaction pressures can be generated using idealised imposed/ surcharged loads. Residual lateral pressure calculations were considered to be too complicated to be covered in the spreadsheet. Many cells are referred to in formulae by names; for example, DATA!C24 is given the name H which is used in formulae at M50: N50, Diagrams!D146:D150, etc. A list of names and where they are defined can be seen by referring to Insert\ Name\ Define in Excel, having unprotected the current sheet. Input is required on three sheets. The spreadsheet is laid out in a very similar manner to RCC62. xls. Correct display of the diagrams requires that the Tekton and Marker fonts have been installed. See FAQ.

DATA! This single sheet consists of the main inputs. Most inputs, which are in blue and underlined, should be self-explanatory. The top diagram defines most input parameters. Please note that unless the Marker and Tekton fonts are loaded into the Windows font folder the diagram will not display correctly. A simplistic chart shows the geometry of a section of the wall and base. The spreadsheet is based on a number of assumptions, which should be assessed as being true or erring on the safe side in each case. These assumptions are: ■ Wall friction is zero ■ Minimum active earth pressure = 0.25qH ■ Granular backfill is used

■ The spreadsheet is not intended for walls over 3.5 m high

STABILITY! details other assumptions, i.e: ■ The wall idealised as a propped cantilever (i.e. pinned at top

and fixed at base) ■ The wall is braced ■ Maximum slenderness of wall is limited to 15, i.e. [ 0.9 x (He

- Tb/2)/Tw < 15 ] ■ Maximum ultimate axial load on wall is limited to 0.1fcu

times the wall cross-sectional area ■ Design span = Effective wall height = He - (Tb/2) ■ -ve moment is hogging (i.e. tension at external face of wall) ■ +ve moment is sagging (i.e. tension at internal face of wall) ■ ‘ Wall MT ‘ is maximum +ve moment on the wall ■ Estimated lateral deflections are used for checking the P∆

effects. Factors for γf can be set at 1.4 or 1.6 in accordance with BS 8110 or may be set to 1. The designer has, and should have, the final decision and responsibility to select the load factors he or she feels are suitable to the design conditions. Under Operating Instructions a number of checks are carried out and problems highlighted. An estimate of reinforcement per metre length of wall and base is given. Further details about DATA! can be seen under the description for RCC62.xls.

STABILITY! STABILITY! calculates the overturning and restoring moments, sliding and resisting forces on a section together with ground bearing pressures and factors of safety. Failures are highlighted. Factors of safety against overturning and sliding are required as input. As noted in the sheet, wall and/ or surcharge loads may have stabilising effects. By using the buttons at L37:L40, the user should toggle between maximum and minimum values to ascertain worst case(s) (perhaps this will be automated some time). In the case of sliding, where sliding resistance of the base alone is insufficient, the user may choose, outside of the spreadsheet, to rely on a propping force through the basement slab.

DESIGN! The first page of this sheet tabulates moments and shears. Input of eccentricity of vertical load, reinforcement diameters and centres is required for main bending steel on both internal and external faces and for transverse reinforcement. The spreadsheet works on the principle of checking a proposed 125


17/07/2006 17:07:42

section and reinforcement arrangement rather than proposing an arrangement of reinforcement. The second page details the design of both outer and inner parts of the base. Again, the spreadsheet works on the principle of checking a proposed section, and input of both reinforcement diameter and centres is required for both main bending and transverse reinforcement.

WEIGHT! This sheet shows the build up to the estimate of reinforcement weight given. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation, etc.

Diagrams! Diagrams! shows data for the charts used in other sheets but is not necessarily intended for printing out other than for checking purposes.

Crack width! This sheet shows calculations to determine crack widths in the wall. It is not necessarily intended for printing out, other than for checking purposes.


126


17/07/2006 17:07:44

RCC61 Basement Wall.xls RCC61 Basement Wall/ DATA!

Project

Spreadsheets to BS 8110 etc

Client Location


Made by

Basement wall design to BS8110:2005

Checked


rc

Originated from 'RCC61 Basement Wall..xls ' v3.0

Revision

chg

© 2006 TCC

B= BI =

DESIGN STATUS :

3500 150

Tw = Tb =

MATERIAL PROPERTIES steel class fcu = 35 γm = N/mm2 fy = 500 γm = N/mm2 Cover to tension reinforcement (co) = Max. allowable design surface crack width (W) = Concrete density = SOIL PROPERTIES Design angle of int'l friction of retained mat'l (Ø) = Design cohesion of retained mat'l (C ) = Density of retained mat'l (q ) = Submerged Density of retained mat'l (qs ) = Design angle of int'l friction of base mat'l (Øb) = Design cohesion of base mat'l (Cb ) = Density of base mat'l (qb ) = Allowable gross ground bearing pressure (GBP) = LOADINGS (unfactored) Surcharge load -- live (SQK) = Surcharge load -- dead (SGK) = Line load -- live (LQK) = Line load -- dead (LGK) = Distance of line load from wall (X) = Wall load -- live (WQK) = Wall load -- Dead (WGK) = LATERAL FORCES

Ko Kac Force (kN)

PE = PS(GK) = PS(QK) = PL(GK) = PL(QK) = PW =

31.25 12.50 12.50 10.00 7.50 0.00

Total

73.75

= =

LE = LS = LS = LL = LL = LW =

concrete steel mm mm kN/m3

30 0 20 13.33 20 0 10 150

degree kN/m2 kN/m3 kN/m3 degree kN/m2 kN/m3 kN/m2

10 10 15 20 250 50 50

kN/m2 kN/m2 kN/m kN/m mm kN/m kN/m

0.50 1.41

default Ko = (1-SIN Ø) = = 2Ko0.5

0.833 1.25 1.25 2.29 2.29 0.00

R68 VALID

225 350

A 1.50 1.15 40 0.3 24.0

Lever arm (m)

127 95 Job No

-

IDEALISED STRUCTURE and FORCE DIAGRAMS

DIMENSIONS(mm) H= 3000 Hw = 0 He = 2500

Page

12-Apr-2006

(0.2 or 0.3 mm only)

Wall Geometry

(Only granular backfill considered, ie "C" = 0) (default=2/3 of q), only apply when Hw >0 = 20.00 ASSUMPTIONS a) Wall friction is zero b) Minimum active earth pressure = 0.25qH c) Granular backfill h) Design not intended for walls over 3.5 m high i)Does not include check for temp or shrinkage eff

0.50

γf

Ultimate Force (kN)

1.40 1.40 1.60 1.40 1.60 1.40

43.75 17.50 20.00 14.00 12.00 0.00 107.25

127


17/07/2006 17:07:45

RCC61 Basement Wall/ STABILITY!

Project


Client Location


Made by


Checked


rc

Originated from 'RCC61 Basement Wall.xls' v3.0

Page


chg

© 2006 TCC

-

EXTERNAL STABILITY

96 128 Job No

R68

STABILITY CHECK :

OK

ANALYSIS - Assumptions & Notes 1) Wall idealised as a propped cantilever ( i.e. pinned at top and fixed at base ) 2) Wall is braced. 3) Maximum slenderness of wall is limited to 15, i.e [ 0.9*(He-Tb/2)/Tw < 15 ] 4) Maximum Ultimate axial load on wall is limited to 0.1fcu times the wall cross-sectional area 5) Design Span (Effective wall height) = He - (Tb/2) 6) -ve moment is hogging ( i.e. tension at external face of wall ) +ve moment is sagging ( i.e. tension at internal face of wall ) 7) " Wall MT. " is maximum +ve moment on the wall. 8) Estimated lateral deflections are used for checking the P ∆ effect . UNFACTORED LOADS AND FORCES Force (kN)

Lever arm to base (m)

Base MT. (kNm)

= = = = = =

26.98 11.62 11.62 10.00 7.50 0.00

0.78 1.16 1.16 2.12 2.12 0.00

-10.11 -4.68 -4.68 -3.32 -2.49 0.00

4.14 2.54 2.54 4.48 3.36 0.00

23.15 8.50 8.50 3.69 2.77 0.00

3.82 3.13 3.13 6.31 4.73 0.00

0.2 0.2 0.1 0.1 0.0 0.0

Total

67.73

-25.28

17.06

46.61

21.12

0.6

Lateral Force

PE PS(GK) PS(QK) PL(GK) PL(QK) PW

Wall MT. Reaction at Reaction at (kNm) Base (kN) Top (kN)

Estimated Elastic Deflection ∆ (mm)

GROUND BEARING FAILURE LOAD CASE: Wall Load Surcharge Taking moments about centre of base (anticlockwise "+") Vertical FORCES (kN) Lever arm (m)

Wall load = Wall (sw) = Base = Earth = Water = Surcharge = Line load = ¦V=

100 14.31 29.40 6.45 0.00 1.50 20.00 171.66

1.49 1.49 0.00 1.68 1.68 1.68 0.00

Moment (kNm)

148.75 21.29 0.00 10.80 0.00 2.51 0.00 ¦ Mv = 183.35

MOMENT due to LATERAL FORCES, Mo =

0.00

100

150

RESULTANT MOMENT, M = Mv + Mo =

165.24

kNm

ECCENTRICITY FROM BASE CENTRE, M / V = MAXIMUM GROSS BEARING PRESSURE =

145.34

200

m kN/m2

(using overall factor of safety instead of partial safety fa

SUM of LATERAL FORCES, P = BASE FRICTION, Fb = - ( V TANØb + B.Cb ) =

46.61 -62.48

3.50

50

kNm

SLIDING AT BASE

BEARING PRESSURE (kN/m²)

1 0

0

-18.11

0.96

MAX MIN

< 150 F.O.S =

OK

1.50

kN kN

Factor of Safety, Fb / P =

1.34

< 1.50

FAIL .. but

therefore, LATERAL RESISTANCE to be provided by BASEMENT SLAB = 7.43 kN

128


17/07/2006 17:07:49

RCC61 Basement Wall.xls RCC61 Basement Wall/ DESIGN!

Project


Client Location


Made by


Checked


rc


Page


chg

© 2006 TCC

-

STRUCTURAL DESIGNS (ultimate)

129 97 Job No

R68

DESIGN CHECKS :

OK BS8110

WALL ( per metre length ) AXIAL LOAD CAPACITY ( Limited to 0.1fcu ) = Force (kN)

γf

Lateral Force

PE PS(GK) PS(QK) PL(GK) PL(QK) PW

26.98 11.62 11.62 10.00 7.50 0.00

1.40 1.40 1.60 1.40 1.60 1.40

= = = = = =

Total

reference

787.50

> 150

kN

OK

3.4.4.1

Ultimate Ult. Moment Ult. Shear Ult. Shear Force (kN)at base (kNmat base (kN) at top (kN)

67.73

37.77 16.27 18.60 14.00 12.00 0.00

-14.15 -6.55 -7.49 -4.65 -3.99 0.00

32.41 11.90 13.60 5.17 4.43 0.00

5.35 4.38 5.00 8.83 7.57 0.00

98.64

-36.83

67.50

31.14

EXT MOMENT (kNm) INT

Design Bending Moments -50

31.3 -46.2

kNm kNm

Total Mmt on INTERNAL face (Mint+0.5Mecc+Mp) = Total Mmt on EXTERNAL face (Mext+0.5Mecc) =

0

50 0.00

top >

kNm kNm mm mm kNm kNm

0.57

WALL (m)

21.83 -36.83 125 0.6 18.8 0.08

1.13

1.70

< base

On INTERNAL face due to lateral forces, M int = On EXTERNAL face due to lateral forces, M ext = Eccentricity of Axial Loads = LATERAL DEFLECTION " ∆ " = Due to eccentricity of axial loads, M ecc = Due to P∆ effect, Mp =

2.26

2.83

EXTERNAL FACE WALL REINFORCEMENT :

MOMENT of RESISTANCE :

Min. As = φ= centres = As = d= z= As' = Mres =

293 16 200 1005 177 163 0 71.3

INTERNAL FACE

< 399 > 293

> 46.21

BASE of WALL SHEAR RESISTANCE:

RACK WIDTH to BS8100/8007 Temp & shrinkage effects not included

As = 100As/bd = vc = Vres =

1005 0.57% 0.72 127.1

X= Acr =

59.61 102.92

mm 2 mm < 549 mm > 293 mm 2 mm mm mm 2 > 31.29 kNm

293 12 200 565 179 170 0 41.8

Table 3.25

OK OK

3.12.11.2.7(b)

3.4.4.4 3.4.4.4

OK

TOP of WALL

φ= = > 67.50 mm mm

10 0.22% 0.52 93.3

@200 mm 393

> 31.14

mm2/m

N/mm2 kN

OK

< 0.30 mm

OK

Table 3.8

εm = 0.00055 W=

0.10

3.5.5.2

BS8007 App. B.2

REINFORCEMENT SUMMARY for WALL

INTERNAL FACE EXTERNAL FACE TRANSVERSE

Type

φ

centres

As

Min. As

H H H

mm 12 16 10

mm 200 200 225

mm 2 565 1005 349

mm 2 293 293 293

OK OK OK

129


17/07/2006 17:07:52

RCC61 Basement Wall/ DESIGN! Project


Client Location


Made by


Checked

The Concrete Centre rc


OUTER BASE ( per metre length ) γf = 1.50 Ult. Shear = 10.35 Ult. MT. = 1.67

130 98 Job No

-

R68 BS8110

SHEAR RESISTANCE:

455 12 225 503

mm2 mm mm mm2

d= Z= As' = Mres =

304 289 0 63.12

mm mm mm2 kNm

100As/bd = vc = Vres =

0.28% 0.42 126.35

εm = -0.0017

60.69 115.54

mm mm

INNER BASE ( per metre length ) Ult. Shear = -67.05 Ult. MT. = 39.60

kN kNm

reference

Min. As = φ= centres = As =

CHECK CRACK WIDTH IN ACCORDANCE WITH BS8100/8007 :

W=

Table 3.25

< 762 > 455

OK OK

3.4.4.4

> 1.67

OK

> 10.35

OK

2

N/mm kN

Table 3.8 3.5.5.2

Temp & shrinkage effects not included BS8007

-0.38 mm NO CRACKING

< 0.30

OK

App. B.2

(AT d from FACE of WALL) TENSION - BOTTOM FACE

BOTTOM REINFORCEMENT :


SHEAR RESISTANCE:

Min. As = φ= centres = As =

455 12 225 503

mm2 mm mm mm2

< 762 > 455

OK OK

d= Z= As' = Mres =

304 289 0 63.12

mm mm mm2 kNm

> 39.60

OK

100As/bd = vc = Vres =

0.17% 0.42

N/mm2 kN

> 67.05

OK

126.35

CHECK CRACK WIDTH IN ACCORDANCE WITH BS8100/8007 :

60.69 115.54

Revision

(ASSUMED) kN (AT d from FACE of WALL) kNm TENSION - BOTTOM FACE


X= Acr =

Page

12-Apr-2006

chg

© 2006 TCC


X= Acr =

Date

εm = -0.0006

mm mm

W=

Table 3.25

3.4.4.4

Table 3.8 3.5.5.2

Temp & shrinkage effects not included BS8007

-0.14 mm NO CRACKING

< 0.30

OK

App. B.2

REINFORCEMENT SUMMARY for BASE

TOP BOTTOM TRANSVERSE

Type

φ

centres

As

H T T

mm 12 12 12

mm 225 225 225

mm 503 503 503

Min. As 2

mm2 455 455 455

OK OK OK

130


17/07/2006 17:07:55

RCC61 Basement Wall.xls RCC61 Basement Wall/ WEIGHT!

The Concrete Centre

Project


Client Location


Made by


Checked

rc


Date

Revision

chg

© 2006 TCC

Page

12-Apr-2006

131 99 Job No

-

R68

APPROXIMATE WEIGHT OF REINFORCEMENT per metre length of wall No.

Type

Dia

Length

Unit Wt

Weight

WALL VERTICAL - Internal face VERTICAL - External face TRANSVERSE (Ext.+ Int.)

6 6 24

H H H

12 16 10

2746 2778 1000

0.888 1.578 0.617

14.63 26.31 14.80

BASE TOP (MAIN) BOTTOM (MAIN) TRANSVERSE ( T & B ) WALL STARTERS (Int.) WALL STARTERS (Ext.)

5 5 32 6 6

H H H H H

12 12 12 12 16

3596 3596 1000 1001 1193

0.888 0.888 0.888 0.888 1.578

15.96 15.96 28.41 5.33 11.30

SUMMARY

Total reinforcement per metre length of wall (kg)

133

131


17/07/2006 17:07:59

RCC62 Retaining Wall.xls RCC62.xls designs simple retaining walls with stems up to 3.0 m high. The spreadsheet has been developed with both the BS 8002 and the conventional (CECP 2) methods in mind. On balance, the spreadsheet provides reasonable flexibility and, in doing so, encourages the designer to employ their own engineering judgement and interpretation of the codes. It is based on complying with BS 8002: 1994(4) and BS 8004: 1986(23). It may also be used to design retaining walls to comply with CECP 2(6) and BS 8007(5). The spreadsheet is intended to cover only short walls and to help ‘general’ engineers who, from time to time, design retaining walls as part of a wider interests in structures rather than the specialists. The 3.0 m wall height is an arbitrary limit set for short wall which is intended to cover over 90% of the cases encountered in general structural designs. Although many of the design principles still apply to higher walls, criteria such as wall movements and the validity of the assumptions made (e.g. no wall friction) require further consideration and investigation. For instance, with reference to pressures, the engineer is expected to judge between using the default of ka (active coefficient) or inputting a larger figure relating to ko (at rest coefficient). The effects of compaction pressures can be generated using idealised imposed/ surcharged loads. Residual lateral pressure calculations were considered to be too complicated to be covered in the spreadsheet. Stability analysis is done about the toe of the base. (Stability analysis taken about toe of nib is ignored; the nib is a section sticking down from general level of the base, and stability analysis about its toe gives strange answers). Global slope stability checks are not undertaken in the spreadsheet and should be addressed using other means. Input is required on three sheets. Many cells are referred to in formulae by names; for instance DATA!C23 is given the name H which is used in formulae at C56: D60, Diagrams!D88:D137, etc. A list of names and where they are defined can be seen by referring to Insert\Name\Define in Excel having unprotected the current sheet. The spreadsheet is laid out in a very similar manner to RCC61.xls. Correct display of the diagrams requires that the Tekton and Marker fonts have been installed. See FAQ.

DATA! This single sheet consists of the main inputs. Most inputs, which are in blue and underlined, should be self-explanatory. The top diagram defines most input parameters. Please note that unless the Marker and Tekton fonts are loaded into the Windows font folder the diagram will not display correctly. The designer should determine the ‘Design Soil Parameters’ based on the combinations in BS 8002 which will give the worst credible loads i.e. the design values should be the lower of (a) the

peak strength reduced by a mobilisation factor or (b) the critical state strength. As default values, the earth pressure coefficients are calculated using the simplified Rankine’s formula for smooth vertical walls based on values of the design soil parameters. Alternatively, the engineer can enter his or her own coefficients to suit the conditions of the design by overwriting the default values. Maximum earth pressure occurs during service and not at ultimate limit state, as at ultimate limit state the actual earth pressure will be less. BS 8002(4) also uses a mobilisation factor on soil parameters, increasing load on the active side of the wall and reducing soil resistance on the passive side. In so doing, the code recommends that no further partial load factors are necessary in design of the structure. The above are not entirely compatible with BS 8110: Part 1, Table 2.1, nor to our knowledge have they been fully accepted by the general practising engineer. Many designers do seem to use the BS 8002 mobilisation factor as well as the traditional safety factors. Therefore the built-in partial load factors may be changed. Factors can be set at 1.4 or 1.6 in accordance with BS 8110 or may be set to 1.0. The designer has, and should have the final decision and responsibility to select the load factors he or she feels are suitable to the design conditions. BS 8002 suggests that no additional factors of safety are required in checking of external stability (i.e. over-turning and sliding) provided that the structure is in equilibrium and the ‘worst credible loads’ are used in the design. For the calculation of bearing pressures, all partial load factors are switched to unity and the design checks are based on allowable ground bearing pressure, i.e. the permissible stress approach. The bearing pressure is then factored up with the partial load factors adopted from above for the design of concrete base. Bearing pressure is calculated using the concept of ‘no tension’ equilibrium, i.e. triangular stress blocks are used when eccentricity is outside the middle third. BS 8002 has minimum surcharge and minimum unplanned excavation depth requirements. However in the spreadsheet, the surcharge loads are set as input data. The minimum 10 kN/m2 limit in BS 8002 has not been used with the understanding that the BS 8002 committee is considering reducing the 10 kN/m2 to 6 kN/m2 for 3 m high walls. The spreadsheet is based on a number of assumptions which should be assessed as being true or erring on the safe side in each case. These are: ■ Wall friction is zero ■ Minimum active earth pressure = 0.25qH. A minimum active

pressure of 0.25H (made to be a function of soil property rather than an arbitrary value equivalent to approx. 5 kN/m3 per m

132


17/07/2006 17:08:01

RCC62 Retaining Wall.xls height to cover conditions regarding tension cracks. However, this does not comply with BS 8002, which recommends that full hydrostatic pressure is used. As the majority of small retaining walls have granular backfills, the cohesion value of retaining soil has been ‘locked’ to zero. ● Granular backfill is used. Even a small value of effective

cohesion, c´, can significantly reduce active pressures. However, to acknowledge the fact that many retaining walls are built with granular backfill for drainage and to err on the side of caution, the spreadsheet assumes only cohesionless materials. ■ The spreadsheet does not include checks on rotational slide/

slope failure. ■ The spreadsheet does not include checks on the effects of

seepage of ground water beneath the wall. ■ The spreadsheet does not include checks on deflection of the

wall due to lateral earth pressures. ■ The spreadsheet is not intended for walls over 3.0 m high. ■ The spreadsheet includes for concrete self-weight.

Many engineers have reservations about including the effect of passive pressure in front of the wall and a warning message has been used to help ensure that passive pressure is considered only if it can be guaranteed that there will be no future excavation in front of the wall. Under Operating Instructions a number of checks are carried out and problems are highlighted. Kp is calculated using base material properties. Lever arm of passive reaction is measured from bottom base level downward. In the calculation of passive force, cohesion of the base material is also taken into consideration.

133


17/07/2006 17:08:03

RCC62 Retaining Wall/ DATA! Project


Client


Made by

RETAINING WALL design to BS 8110:2005

Checked

Location


rc

Originated from 'R RCC62.xls ' v3.0

Page


chg

© 2006 TCC

IDEALISED STRUCTURE and FORCE DIAGRAMS

134 101 Job No

-

R68

DESIGN STATUS:

VALID

WARNING : Passive pressure should only be considered if it can be guaranteed that there will be no future excavation in front of the wall.

DIMENSIONS (mm) B= 4000 H= 3250 Hw = 1500 BI = 1200 Hp = 300 BN = 0 Hn = 0 MATERIAL PROPERTIES steel class N/mm² γm = fcu = 35 N/mm² γm = fy = 500 cover to tension steel = Max allowable design surface crack width (W) = Concrete density = SOIL PROPERTIES Design angle of int'l friction of retained mat'l (Ø) = Design cohesion of retained mat'l (C ) = Density of retained mat'l (q ) = Submerged Density of retained mat'l (qs ) = Design angle of int'l friction of base mat'l (Øb) = Design cohesion of base material (Cb ) = Density of base material (qb ) = Allowable gross ground bearing pressure (GBP) = LOADINGS

Surcharge load -- live (SQK) = Surcharge load -- dead (SGK) = Line load -- live (LQK) = Line load -- dead (LGK) = Distance of line load from wall (X) =

LATERAL FORCES (unfactored)

PE = PS(GK) = PS(QK) = PL(GK) = PL(QK) =

Ka = Kp = Kpc = Kac =

Tw = Tb = TN = A 1.5 1.15 50 0.3 24

300 300 0

concrete steel mm mm kN/m³

(0.2 or 0.3 mm only)

Wall Geometry 30 0 20 5.00 20 10 10 200 10 10 10.3 43 0 0.33 2.04 2.86 1.15

degree kN/m² kN/m³ kN/m³ degree kN/m² kN/m³ kN/m²

(Only granular backfil considered, "C" = zero) [default=2/3*q (only apply when Hw13.33 ASSUMPTIONS

a) Wall friction is zero b) Minimum active earth pressure = 0.25qH c) Granular backfill d)Does not include check of rotational slide/slope f kN/m² e)Does not include effect of seepage of ground water beneath the wall. kN/m f)Does not include deflection check of wall due to kN/m lateral earth pressures mm h) Design not intended for walls over 3.0 m high i) Does not include check for temp. or shrinkage eff [ default ka = (1-SIN Ø)/(1+SIN Ø) ] 0.33 [ default kp = (1+SIN Øb)/(1-SIN Øb 2.04 [ default kpc = 2kp0.5 ] = 2.86 [ 2ka0.5 ]

Force

Lever arm

Moment about TOE

γf

Fult

Mult

(kN) 29.58 10.83 10.83 0.00 0.00

(m) LE = 1.194 LS = 1.63 LS = 1.63 LL = 3.25 LL = 3.25

(kNm) 35.33 17.60 17.60 0.00 0.00

1.40 1.40 1.60 1.40 1.60

(kN) 41.42 15.17 17.33 0.00 0.00

(kNm) 49.46 24.65 28.17 0.00 0.00

11.25

LW = 0.50

5.63

1.40

PW = Total PP =

62.50

-9.49

76.16

(LP-HN) = 0.15

-1.38

1.00

15.75

7.88

89.67

110.15

-9.49

-1.38

134


17/07/2006 17:08:04

RCC62 Retaining Wall.xls RCC62 Retaining Wall/ STABILITY!

The Concrete Centre


Project Client Location


Made by


Checked

Originated from 'RCC62.xls' v3.0

Date

rc

Revision

chg

© 2006 TCC

PE = PS(GK) = PS(QK) = PL(GK) = PL(QK) = PW = ¦P= Pp =

29.58 10.83 10.83 0.00 0.00 11.25

Lever arm (m)

LE = LS = LS = LL = LL = LW =

Moment (kNm)

1.08 1.63 1.63 3.25 3.25 0.50

32.05 17.60 17.60 0.00 0.00 5.63

-9.49

Vertical FORCE (kN)

Wall = Base = Nib = Earth = Water = Surcharge = Line load = ¦V=

F.O.S = 1.50 LOADING OPTION (select critical load combination) 9EARTH Warning: PS(GK) PS(QK) PL(GK) PL(QK) PW

(LP-HN) = 0.15

17.64 16.80 0.00 102.50 30.00 50.00 53.30

-1.38 = 71.50

Lever arm (m)

Moment (kNm)

1.35 2.00 0.00 2.75 2.75 2.75 1.50

23.81 33.60 0.00 281.88 82.50 137.50 79.95 ¦ Mr = 639.24

270.24

Warning: ALLOW BUOYANCY OF BASE

Factor of Safety, Mr / Mo = SLIDING

OK

62.50 ¦ Mo

Restoring Moments

R68

STABILITY CHECKS :

OVERTURNING about TOE (using overall factor of safety instead of partial safety factor) Lateral FORCE (kN)

135 102 Job No

-

EXTERNAL STABILITY

Overturning Moments

Page

12-Apr-2006

(using overall factor of safety instead of partial safety factor) Sum of LATERAL FORCES, P =

62.50

8.94 F.O.S =

> 1.50

OK

1.50

kN Red'n factor for passive force = 1.00

PASSIVE FORCE, Pp x Reduction factor (1) = -9.49 kN BASE FRICTION ( ¦ V TANØb + B Cb ) = -138.36 kN Sum of FORCES RESISTING SLIDING, Pr = -147.85 kN

Factor of Safety, Pr / P =

2.37

> 1.50

OK

GROUND BEARING FAIL Taking moments about centre of base (anticlockwise "+") : Vertical FORCES (kN) Lever arm (m)

Wall = Base = Nib = Earth = Water = Surcharge= Line load = ¦V=

21.24 28.80 0.00 102.50 30.00 50.00 53.30 285.84

0.65 0.00 2.00 -0.75 -0.75 -0.75 0.50

BEARING PRESSURE (KN/m²)

Moment (kNm)

4.00 0

13.81 0.00 0.00 -76.88 -22.50 -37.50 26.65 ¦ Mv = -96.42

0.00

50

Moment due to LATERAL FORCES, Mo =

71.50

kNm

Resultant Moment, M = Mv + Mo =

-24.91

kNm

Eccentricity from base centre, M / V = Therefore, MAXIMUM Gross Bearing Pressure ( GRP) =

-0.09 77

m kN/m²

100

< 200

OK

135


17/07/2006 17:08:08

RCC62 Retaining Wall/ DESIGN!

The Concrete Centre




Made by


Checked

rc


Date

Page


chg

© 2006 TCC

STRUCTURAL DESIGNS (ultimate)

136 103 Job No

-

R68

DESIGN CHECKS :

OK

WALL ( per metre length )

EARTH SURCHARGE(GK) SURCHARGE(QK) LINE LOAD(GK) LINE LOAD(QK) WATER Total

Force

Lever arm

Moment

(kN) 25.41 9.83 9.83 0.00 0.00 7.20

(m) 1.07 1.48 1.48 2.95 2.95 0.40

(kNm) 27.08 14.50 14.50 0.00 0.00 2.88

52.27

γf

V ult

M ult

1.4 1.4 1.6 1.4 1.6 1.4

(kN) 35.57 13.77 15.73 0.00 0.00 10.08

(kNm) 37.92 20.31 23.21 0.00 0.00 4.03

75.15

85.46

58.97

BS8110 reference MOMENT (KNm) 0

50

MAIN REINFORCEMENT : 100

Min. As =

φ=

top >

0.00

centres = Asprov =

0.59

390 20 150 2094

mm2 mm mm 2 mm

Table 3.25

< 364 > 390

OK OK

3.12.11.2.7(b)

WALL (m)

MOMENT of RESISTANCE : 1.18

d= z= As' = Mres =

< base

1.77

2.36

240 210.88 0 192.03

mm mm 2 mm kNm

3.4.4.4

> 85.46

OK

> 75.15

OK

< 0.30

OK

SHEAR RESISTANCE:

100 As/bd = vc = Vres =

2.95

0.87% 2 N/mm 0.77 184.24 kN

Table 3.8 3.5.5.2

Ultimate Bending Moment Diagram

CHECK CRACK WIDTH TO BS8110/BS8007 : Temperature and shrinkage effects not included)

X= Acr =

95.47 mm 86.05 mm εm = 0.0006 W= 0.12 mm

BS8007 App. B.2

REINFORCEMENT SUMMARY for WALL

VERTICAL EXT. FACE VERTICAL INT. FACE TRANSVERSE

Type

φ

Centres

As

H H H

mm 12 20 12

mm 150 150 150

mm 754 2094 754

Min. As 2

mm2 390 390 390

OK OK OK

136


17/07/2006 17:08:12

RCC62 Retaining Wall.xls RCC62 Retaining Wall/ DESIGN!


The Concrete Centre

Spreadsheets to BS 8110etc Advisory Group Grid line 1

Made by


Checked

Date

rc


Page


chg

© 2006 TCC

-

R68

BASE - unloaded side ( per metre length ) γf = V ult = M ult =

1.45 85.74 67.33

BS8110

(default = ult mt / non-factored mt 1.45 kN kNm ( '+' TENSION AT BOTTOM FACE)


mm2 mm mm 2 mm

d= z= As' = Mres =

242 223.36 0 130.17

mm mm mm2 kNm

> 67.33

OK


0.55% 0.66 159.32

N/mm2 kN

> 85.74

OK

φ=

centres = Asprov = MOMENT of RESISTANCE :

CHECK CRACK WIDTH TO BS8110/BS8007 :

X= Acr =

80.69 86.81

reference

390 16 150 1340

Min. As =

SHEAR RESISTANCE:

137 104 Job No

mm mm

Table 3.25

< 558 > 390

OK OK

3.12.11.2.7(b)

3.4.4.4

Table 3.8 3.5.5.2

(Temperature and shrinkage effects not included)

εm = 0.00054 W=

0.11

BS8007

< 0.30

mm

OK

App. B.2

BASE - loaded side ( per metre length ) V ult = M ult =

81.52 18.13

kN kNm

(TENSION - TOP FACE)

TOP REINFORCEMENT :

390 16 150 1340

mm2 mm mm mm2

d= z= As' = Mres =

242 223.36 0 130.17

mm mm mm2 kNm

> 18.13

OK


0.55% 0.66 159.32

N/mm2 kN

> 81.52

OK

Min. As = φ= centres = Asprov =

MOMENT RESISTANCE :

SHEAR RESISTANCE:

CHECK CRACK WIDTH to BS8100/ BS8007 :

X= Acr =

80.69 86.81

mm mm

Table 3.25

< 558 > 390

OK OK

3.12.11.2.7(b)

3.4.4.4

Table 3.8 3.5.5.2

(Temperature and shrinkage effects not included)

εm = -0.0003 W=

-0.05

BS8007

< 0.30

mm

OK

App. B.2

REINFORCEMENT SUMMARY for BASE

TOP (DESIGN) BOTTOM (DESIGN) TRANSVERSE

Type

φ

Centers

As

H H H

mm 16 16 12

mm 150 150 200

mm 1340 1340 565

Min. As 2

2

mm 390 390 390

OK OK OK

137


17/07/2006 17:08:15

RCC62 Retaining Wall/ WEIGHT!


The Concrete Centre

Spreadsheets to BS 8110etc Advisory Group Grid line 1

Made by


Checked


rc

Date

Page


chg

© 2006 TCC

138 105 Job No

-

R68

APPROXIMATE WEIGHT OF REINFORCEMENT No.

Type

Dia

Length

Unit Wt

Weight

WALL

VERTICAL - External face VERTICAL - Internal face TRANSVERSE (Ext.& Int.)

7 7 40

H H H

12 20 12

3046 3110 1000

0.888 2.466 0.888

18.93 53.69 35.51

BASE

TOP (MAIN) BOTTOM (MAIN) TRANSVERSE ( T & B ) WALL STARTERS (Ext.) WALL STARTERS (Int.)

7 7 42 7 7

H H H H H

16 16 12 12 20

4128 4128 1000 1155 1475

1.578 1.578 0.888 0.888 2.466

45.61 45.61 37.29 7.18 25.46

NIB

(assume same reinforcement as wall) INTERNAL FACE (MAIN) 7 EXTERNAL FACE (MAIN) 7 TRANSVERSE (EXT.+ INT.) 2

H H H

12 20 12

96 160 1000

0.888 2.466 0.888

0.60 2.76 1.78

SUMMARY

Approx total reinforcement per metre length of wall (kg)

274.4

138


17/07/2006 17:08:18

RCC71 Stair Flight & Landing - Single.xls

RCC71 Stair Flight & Landing - Single.xls RCC71.xls designs simply supported flights and landings to BS 8110. Input is required on two sheets.


FLIGHT! This single sheet consists of the input and main output. Inputs are in blue and underlined and most should be self-explanatory. Only simply supported spans are catered for. If flights are continuous with floors, the user should specify continuity steel over supports as appropriate. Calculations are done per metre width of flight. Input loads are assumed to be characteristic and acting vertically. They should account for any undercuts. Selfweight, moments and reactions are calculated automatically. The area of steel required, Asreq , may be automatically increased to increase modification factors and satisfy deflection criteria. Where the stair flight occupies more than 60% of the span an increase in allowable span to depth ratios of 15% is included in accordance with Clause 3.10.2.2. Nominal top reinforcement may be specified in order to help overcome deflection problems. Dimensions are not checked for compliance with Building Regulations. Ultimate, characteristic dead and characteristic imposed reactions are given below the indicative diagram.

LANDING! Again, this single sheet consists of the input and main output. Input defaults in magenta have been derived from FLIGHT! but may be overwritten. Calculations are done per metre width of landing. Inputs are underlined and most should be self-explanatory. As defaults, which can be overwritten, the material data and characteristic flight reactions carry over from FLIGHT! Selfweight, moments and reactions are calculated automatically. The maximum width of landing over which flight loads can be dispersed has been restricted to 1.8 m in the spirit of Clause 3.10.1.3. Reactions are ultimate, both total and per metre run. The area of steel required, As, can be automatically increased to satisfy deflection criteria.

Dias! Dias! calculates the reinforcement sizes and reinforcement percentages for deflection modification factors used in FLIGHT! and LANDING!

139


17/07/2006 17:08:20

RCC71 Stair Flight & Landing - Single/ FLIGHT!

Project


Client

Advisory Group

Location

South Staircase


FLIGHT

STAIR FLIGHTS AND LANDINGS to BS 8110:2005 Originated from RCC71.xls ' v3.0 on CD

MATERIALS fcu fy h agg Cover

35 500 20 25

N/mm² N/mm² mm mm

Checked

γm 1.5 concrete γm 1.15 steel steel class A Density 23.6 kN/m³ (Normal weight concrete)

Page

12-Apr-06 Revision

chg

© 2006 TCC

DIMENSIONS

a= b= c= d= e= Going = Rise = Rise =

Date

rmw

140 106 Job No

-

R68

Min bar Ø = 10 Max bar Ø = 16 Nominal top steel ? Y Sectional Elevation

600 2500 1200 -600 -100 250 1900 173

mm mm mm

landing A h = flight waist = landing B h =

175 200 200

mm mm mm mm total mm each step

L = 4300 10 treads Rake = 34.64 º

LOADING

Imposed 4.00 kN/m² Flight finishes 1.60 kN/m² Landing finishes 1.30 kN/m²

47.08 kN/m ult (20.87 + 11.16)

37.81 kN/m ult (16.91 + 8.84)

DESIGN

LANDING A, gk = 4.13 + 1.30 = 5.43 kN/m²

n = 1.4 x 5.43 + 1.6 x 4.0 = 14.00 kN/m²

FLIGHT, gk = 7.78 + 1.60 = 9.38 kN/m²

n = 1.4 x 9.38 + 1.6 x 4.0 = 19.53 kN/m²

LANDING C, gk = 4.72 + 1.30 = 6.02 kN/m²

n = 1.4 x 6.02 + 1.6 x 4.0 = 14.83 kN/m²

Zero shear is at 0.6 + (47.08 - 16.80) /19.53 = 2.151 m from left M = 47.08 x 2.151 - 16.80 x 2.151 - 19.53 x 1.551²/2 = 41.64 kNm/m d = 200 - 25 - 8 = 167 mm K = 0.0427 As = 604 mm²/m PROVIDE H16 @ 280 B = 718 mm²/m Enhanced by 17.9 % for deflection L/d = 4,300 /167 = 25.749 < 20.0 x 1.235 x 1.050 = 25.930 allowed

H10 @ 300 T in span OK

140


17/07/2006 17:08:21

RCC71 Stair Flight & Landing - Single.xls RCC71 Stair Flight & Landing - Single/ LANDING!

Project


Client

Advisory Group

Location

South Staircase


LANDING

STAIR FLIGHTS AND LANDINGS to BS 8110:2005 Originated from RCC71.xls' v3.0 on CD

MATERIALS fcu fy h agg Cover

35 500 20 25

Checked

γm 1.5 concrete γm 1.15 steel Density 23.6 kN/m³ (Normal weight concrete)

N/mm² mm mm

Page

141 107

12-Apr-06 Revision

Job No

chg

© 2006 TCC

N/mm²

Date

rmw

R68

Min bar Ø = 10 Max bar Ø = 16 Nominal top steel ? Y

DIMENSIONS

a = 1200 mm b = 1200 mm c = 250 mm d = 175 mm

depth, h = 175 mm width, w = 1200 mm L = 3000 mm

LOADING

LANDING

Imposed Finishes Slab

4.00 1.50 4.13

gk

qk

Flight a reaction 20.87 Flight b reaction 16.91

11.16 8.84

kN/m² kN/m² kN/m² kN/m kN/m

79.3 kN ult 74.0 kN ult 66.1 kN/m ult 61.6 kN/m ult n = 1.4 x 5.63 + 1.6 x 4.0 = 14.28 kN/m² n1 = (1.4 x 20.87 + 1.6 x 11.16)/1.20 = 39.23 kN/m² n2 = (1.4 x 16.91 + 1.6 x 8.84)/1.20 = 31.51 kN/m²

DESIGN

Zero shear is at (66.11 - 2.50) /(14.28 + 39.23) + 0.175 = 1.364 m from left M = 66.11 x 1.364 - 14.28 x 1.364²/2 - 39.23 x 1.189²/2 = 49.15 kNm/m d = 175 - 25 - 8 = 142 mm K = 0.0696 As = 870 mm²/m PROVIDE H16 @ 200 B = 1005 mm²/m Enhanced by 12.7 % for deflection H10 @ 325 T in span L/d = 3,000 /142 = 21.127 < 20.0 x 1.021 = 21.516 allowed OK

141


17/07/2006 17:08:25

RCC72 Stairs & Landings - Multiple.xls This spreadsheet designs the flights and landings of a staircase in a stair core to BS 8110. It is assumed that flights are supported on the landings and that the landings are simply supported on bearings at each end.

STAIRCORE! This single sheet consists of the input and main output. Inputs are in blue and underlined and most should be self-explanatory. Dimensions are not checked for compliance with Building Regulations. Simple supports are assumed. Calculations are done per metre width of flight and landing. Input loads are assumed to be characteristic and acting vertically. They should account for any undercuts. All stairs are assumed to start from flight 1. Superfluous flights and landings are blanked out. Self-weight, moments and reactions are calculated automatically. Where the stair flight occupies more than 60% of the span an increase in allowable span to depth ratios of 15% is included in accordance with Clause 3.10.2.2 and, as with other spreadsheets, the area of steel required may be automatically increased to satisfy deflection criteria. Ultimate reactions per metre are given.

Dias! Dias! calculates the reinforcement sizes and reinforcement percentages for deflection modification factors used in STAIRCORE!


142


17/07/2006 17:08:29

RCC72 Stairs & Landings - Multiple.xls RCC72 Stairs & Landings - Multiple/ STAIRCORE!

Project


Client

Advisory Group

Location

North Staircase


REINFORCED CONCRETE STAIRCASES to BS 8110:2005 Originated from RCC72.xls

MATERIALS fcu 35 fy 500 h agg 20 Cover 20 DIMENSIONS A = 1200 C = 250 L1 = L2 = L3 = L4 = L5 = L6 = STOREY Lower Typical Upper

LOADING

FLIGHT 1 Waist =

1200 1200 1200 1200 1200 750

v3.0 on CD

Checked

mm mm mm mm mm mm

HEIGHT

Imposed Flight finishes Landing finishes

mm

F1 = F2 = F3 = F4 = F5 = F6 =

2500 2500 2500 2500 2500 2500

mm

10 treads

mm

10 treads

mm

10 treads

mm

10 treads

mm

10 treads

mm

10 treads

RISERS

RISE

RAKE

22 22 22

159.1 mm 159.1 mm 159.1 mm

32.5 º 32.5 º 32.5 º

4.00 0.50 1.30

As = 363 mm²

Waist Steps Finishes

4.20 1.88 0.50 6.57

R68

kN/m² kN/m² kN/m²

a = 2.350 m b = 0.600 m L = 2.950 m

4.20 1.88 0.50 6.57 kN/m² n1 = 1.4x6.57+1.6x4.00 14.60 kN/m = 15.60 kN/m² M = 22.06 x 1.414 / 2 = 15.60 kNm/m

150

-

143 109 Job No

Plans

γm 1.5 concrete γm 1.15 N/mm² steel mm steel class A mm Density 23.6 kN/m³ (Normal weight concrete) No of Flights = 6 mm B= 150 mm bearing mm Going = 250 mm


FLIGHT 2 Waist =

Revision

chg

© 2006 TCC

Page

12-Apr-06

N/mm²

3500 mm 3500 mm 3500 mm

150

Date

RMW

mm

kN/m²

d = 125 mm

PROVIDE 5 H10 @ 270 B = 393 mm²

a = 2.500 m L = 3.700 m

n2 =

15.60

kN/m²

M = 19.50 x ( 1.850 - 0.625 ) = 23.89 kNm/m As = 561 mm²

22.06 kN/m K = 0.0285

L/d = 23.600 < 25.863 allowed

b = 0.600 m

19.50 kN/m d = 124 mm

OK

c = 0.600 m

19.50 kN/m K = 0.0444

PROVIDE 9 H12 @ 130 B = 1018 mm² L/d = 29.839 < 30.921 allowed As increased by 67.0 % for deflection

OK

143


17/07/2006 17:08:29

RCC72 Stairs & Landings - Multiple/ STAIRCORE!

Project


Client

Advisory Group

Location

North Staircase


REINFORCED CONCRETE STAIRCASES to BS 8110:2005 Originated from RCC72.xls v3.0 on CD

LANDING 1 +1.750 m h = 150 mm Self wt Finishes

3.54 1.30 4.84

kN/m²

FLIGHT 3 Waist = Waist Steps Finishes

150 4.20 1.88 0.50 6.57

mm

kN/m²

kN/m²

n1 = 14.60/1.20 = n2 = 19.50/1.20 = na = 1.4x4.84+1.6x4.0 =


150 4.20 1.88 0.50 6.57

a = 2.500 m L = 3.700 m

n3 =

15.60 kN/m²

mm

kN/m²

n3 = n2 = nb =

16.25 16.25 13.18

d = 124 mm

36.77 kN/m K = 0.0455

b = 0.600 m

19.50 d = 124 mm

kN/m²

OK

c = 0.600 m

19.50 K = 0.0444 OK


a = 2.500 m L = 3.700 m

n4 =

15.60 kN/m²

37.95 d = 124 mm

37.95 K = 0.0485

b = 0.600 m

19.50 d = 124 mm

OK

c = 0.600 m

19.50 K = 0.0444 OK

L = 2.800 m n3 = n4 = nc =

16.25 16.25 13.18


M = 37.95 x 1.400 - 12.91 - 14.14 = 26.08 kNm/m As = 616 mm²

34.23 kN/m


LANDING 3 +5.250 m h = 150 mm

R68

L = 2.800 m

M = 19.50 x ( 1.850 - 0.625 ) = 23.89 kNm/m

3.54 1.30 4.84

12.17 kN/m² 16.25 kN/m² 13.18 kN/m²


As = 561 mm²

Self wt Finishes

-


M = 37.95 x 1.400 - 12.91 - 14.14 = 26.08 kNm/m As = 616 mm² FLIGHT 4 Waist =

chg

144 110 Job No


LANDING 2 +3.500 m h = 150 mm 3.54 1.30 4.84

Revision

L = 2.800 m

M = 19.50 x ( 1.850 - 0.625 ) = 23.89 kNm/m As = 561 mm²

Self wt Finishes

Page

12-Apr-06

Checked

© 2006 TCC

M = 36.77 x 1.310 - 11.31 - 12.39 = 24.48 kNm/m As = 576 mm²

Date

RMW

37.95 d = 124 mm

37.95 K = 0.0485


OK

144


17/07/2006 17:08:33

RCC72 Stairs & Landings - Multiple.xls RCC72 Stairs & Landings - Multiple/ STAIRCORE!

The Concrete Centre


Project Client

Advisory Group

Location

North Staircase

Made by

REINFORCED CONCRETE STAIRCASES to BS 8110:2005 Originated from RCC72.xls v3.0 on CD

FLIGHT 5 Waist = Waist Steps Finishes

150 4.20 1.88 0.50 6.57

mm

kN/m²

a = 2.500 m L = 3.700 m

n5 =

15.60 kN/m²

kN/m²


150 4.20 1.88 0.50 6.57

kN/m²

n5 = n4 = nd =

16.25 16.25 13.18

LANDING 5 +8.750 m h = 150 mm Self wt Finishes

3.54 1.30 4.84

kN/m²

LANDING 6 +10.500 m h = 150 mm 3.54 1.30 4.84

19.50

d = 124 mm

K = 0.0444

kN/m²

a = 2.500 m L = 3.475 m

n6 =

37.95

37.95

d = 124 mm

K = 0.0485

15.60 kN/m²

18.24 d = 124 mm

c=

OK

0.375 m

20.77 K = 0.0401 OK

L = 2.800 m n5 = n6 = ne =

16.25 15.20 13.18


37.65 d = 124 mm

36.99 K = 0.0477


OK

L = 2.800 m

nf =

27.69 kN/m² 13.18

kN/m²

M = 43.66 x 1.119 - 8.25 - 15.10 = 25.52 kNm/m As = 596 mm²

b = 0.600 m


n6 = kN/m²

OK

kN/m²

M = 37.65 x 1.377 - 12.49 - 13.69 = 25.65 kNm/m As = 605 mm²

Self wt Finishes

19.50

kN/m²

M = 18.24 x ( 1.769 - 0.585 ) = 21.61 kNm/m As = 506 mm²

R68

c = 0.600 m

PROVIDE 7 H12 @ 180 B = 792 mm² L/d = 22.581 < 24.984 allowed As increased by 12.4 % for deflection mm

145 111 Job No

L = 2.800 m

M = 37.95 x 1.400 - 12.91 - 14.14 = 26.08 kNm/m As = 616 mm² FLIGHT 6 Waist =

-


LANDING 4 +7.000 m h = 150 mm 3.54 1.30 4.84

Revision

chg

b = 0.600 m

Page

12-Apr-06

Checked

© 2006 TCC

M = 19.50 x ( 1.850 - 0.625 ) = 23.89 kNm/m As = 561 mm²

Self wt Finishes

Date

RMW

26.46 d = 125 mm

43.66 K = 0.0467


OK

145


17/07/2006 17:08:36

RCC81 Foundation Pads.xls This spreadsheet designs simple pad foundations from input of material properties, dimensions and characteristic loads and moments. Single column bases and combined, double bases are catered for on separate sheets. A diagram is provided to illustrate the dimensions: a chart showing scale plan views is provided to help ensure gross errors are avoided. The ‘efficiency’ diagrams are provided so that the user may gauge how hard the base is working in respect to allowable increase in ground bearing pressure, bending and shear in the two axes together with a measure on punching shear capacity. If the design is invalid, this chart should help identify the problem. The spreadsheet does not allow for punching shear links – bending reinforcement is increased to ensure allowable shear, vc, is adequate. The user should note that punching shear perimeters can jump from being rectangular to being two- or three-sided, leading to unexpectedly large increases in reinforcement for increases in base thickness. Information from BS 8110: Part 1, Clause 3.7.7.8 and Figure 3.19 has yet to be fully incorporated in this spreadsheet.

the base a warning message is given; the general status message is updated as well. Factors of safety against overturning are checked (minimum 1.5). Warnings are also given at the onset of an uplift situation.

DOUBLE! In addition to graphs showing plan layout and ‘efficiency’, this sheet gives moment diagrams for the two principal axes. Design moments are taken at the edge of both column sections. Suggestions are made, under the Operating Instructions column at L31:L35, for the optimum plan size of the base and eccentricities given the column offsets from one another.

SINGLE!

The user’s attention is drawn to the fact that the analysis is done in two orthogonal directions. When column eccentricities are large in both directions the analysis may not account adequately for local effects (e.g. bottom cantilever moments on two sides of each column – loads in opposite corners gives bottom moments of 0 kNm). In such cases, it may be better to change the orientation of the base in such a way that eccentricity in one direction is minimal. Warnings about double eccentricities are given when the distances between column centrelines exceed 15% of the relevant base dimension in each orthogonal direction.

Suggestions are made, under the Operating Instructions column at L12, for the optimum plan size of the base.

Comparison with FE analysis suggests this is reasonable so long as the base is thick and rigid.

Where two centres are given, e.g. 14 T16 @ 200 & 325 B2, the reinforcement is subject to BS 8110: Part 1, Clause 3.11.3.2 and different centres are required, bars need to be grouped closer in the central part of the base.

Det2!

Det1!

The notes for Det! above also apply.

This sheet shows workings and is not necessarily intended for printing out other than for checking purposes.

Legends!

Warnings are given if columns encroach within 100 mm of an edge.

Allowable bearing pressure is taken as an allowable increase in bearing pressure and density of concrete –density of excavated material (i.e. soil) is used in the calculations. The program assumes that pads are embedded to depth H in the soil. A 25% over-stress is allowed where load cases include wind loads. Design moments are generally those at the face of the column. Both sides of the column are checked for moment in each direction to ensure maxima are identified. Shear enhancement is allowed for both beam and punching shear.

This sheet shows workings and is not necessarily intended for printing out other than for checking purposes.

This sheet shows dimensions, axes, corners and notation used.

Graf! This sheet comprises data for graphs for both SINGLE! and DOUBLE!


Neither crack widths, factors of safety against sliding, nor water tables are catered for. Where resultant eccentricities are outside 146


17/07/2006 17:08:39

RCC81 Foundation Pads.xls RCC81 Foundation Pads/ SINGLE!

Project


Client Location

Advisory Group Level -1 Base B1


Single column base

PAD FOUNDATION DESIGN to BS 8110:2005 Originated from RCC81.xls

MATERIALS

fcu fy Densities - Concrete Bearing pressure

N/mm² N/mm² kN/m³

1.5 1.15

steel class

concrete steel

A

Key

STATUS VALID DESIGN

128.0

100%

Grnd Brg Pressure fsx

55%

(As/Asprov) fsy

52%

Bending

Shear

3

4

184.6 184.6

175.7 175.7

184.6 184.6

175.7 175.7

REINFORCEMENT Detail to 3.11.3.2 Mxx = 603.4 kNm b = 3000 mm d = 437.5 mm As = 3339 mm² PROVIDE 13 H25 @ 200 & 250 B1 As prov = 6381 mm²

kN at d from col face N/mm² kN at 2d from col face

% N/mm²

45% 98% 25%

50%

75%

100%

125%

Detail to 3.11.3.2

Myy = 592.9 kNm b = 3000 mm d = 412.5 mm As = 3480 mm² PROVIDE 13 H25 @ 200 & 275 B2 As prov = 6381 mm² Asy increased 70% for shear .

Vyy = 629.9 kN at d from col face v = 0.509 N/mm² or Vyy = 311.2 kN at 2d from col face v = 0.251 N/mm² vc = 0.563 N/mm²

. mm

v yy

Efficiency

.

N/mm²

44%

0%

Asx increased 80% for shear

N/mm²

v xx

punching

characteristic

2

PUNCHING SHEAR d ave = 425 As prov = 0.501 v = 0.541

γs

R68

WIND

1

625.8 0.477 286.9 0.219 0.544

γc

mm

Plot (to scale)

characteristic

IMPOSED

BEARING PRESSURES kN/m²

BEAM SHEAR Vxx = v= or Vxx = v= vc =

-

mm kN/m³

147 113 Job No

kN/m² (net allowable increase)

Overturning FOS = Large Uplift FOS = infinite

no wind with wind

Revision

ey = 0

Axial (kN) 1480.0 Mx (kNm) -20.0 My (kNm) Hx (kN) Hy (kN)

CORNER

20 50 21

Checked

chg

© 2006 TCC

h agg cover Soil

Page

12-Apr-06

COLUMN h = 500 b = 500

COLUMN REACTIONS kN, kNm DEAD

v3.2 on CD

35 500 24 185

DIMENSIONS mm BASE L = 3000 B = 3000 depth H = 500 ex = 0

Date

RMW

.

u crit = v max = vc =

7100 mm 2.782 N/mm² at col face 0.553 N/mm²

147


17/07/2006 17:08:41

RCC81 Foundation Pads/ DOUBLE!

Project


Client

Advisory Group

Location

Base B3/B4


Combined base

PAD FOUNDATION DESIGN to BS 8110:2005 Originated from RCC81.xls v3.2 on CD

MATERIALS

fcu fy Densities - Concrete Bearing pressure

35 500 24 185

COLUMN REACTIONS kN, kNm Column 1 (rhs)

DEAD

Axial 1369.5 Mx My Hx Hy

Date

RMW Checked

h agg cover Soil

N/mm² kN/m³

kN/m² (net allowable)

Revision

chg

© 2006 TCC

N/mm²

Page

12-Apr-06

20 50 21

-

mm

γc

mm

γs

148 114 Job No

R68

1.5 1.15

concrete steel

kN/m³

STATUS VALID DESIGN

characteristic

IMPOSED

Column 2 (lhs)

WIND

1369.5

Axial Mx My Hx Hy

DEAD

IMPOSED

1369.5

1369.5

WIND

DIMENSIONS mm BASE

L= B= depth H = Σex = Σey =

COLUMN 1 (rhs)

6000 5000 800 3000 0

COLUMN 2 (lhs)

h1 = 450 b1 = 450

h2 = 450 b2 = 450

ex1 = 1500 ey1 = 0

ex2 = 1500 ey2 = 0

Overturning FOS = Large

Uplift FOS = infinite PLOT (to scale)

BEARING PRESSURES kN/m² CORNER

no wind with wind

characteristic

1

2

3

4

185.0 185.0

185.0 185.0

185.0 185.0

185.0 185.0

REINFORCEMENT Btm Mxx - 1113.1 b = 5000 d= 740 As = 3642

Bending

mm mm mm²

83%

v xx

31%

v yy

75%

punching

91% 0%

50%

100%

150%

Efficiency'

& 30 H25 @ 225 B2 As prov = 14726

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

Myy + 0.0 d= 720 As = 0 & 20 H20 @ 325 T2 As prov = 6283 .

200 0 -200 -400 -600 -800 -1000 -1200

Moment

Vyy = 2559.6 v = 0.595 or Vyy = 1380.5 v = 0.321 vc = 0.427

Zero axis

0.0 0.5 1.0

16545 mm

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

0 -1000 -2000 -3000 -4000

.

u crit =

Columns

Mx Diagram (1.4Gk + 1.6Qk)

.

. BEAM SHEAR Vxx = 732.7 kN at d v = 0.198 N/mm² kN at 2d or Vxx = 0.0 v = 0.000 N/mm² vc = 0.318 N/mm²

mm

98%

(As/Asprov) fsy

Myy - 4252.8 b = 6000 d = 717.5 As = 14350

kNm

100%

fsx

Shear

PROVIDE 17 H20 @ 275 & 325 B1 As prov = 5341 mm² Detail to clause 3.11.3.2 Top Mxx + kNm 0.0 d= 740 mm As = 0 mm² PROVIDE 17 H20 @ 275 & 325 T1 As prov = 5341 mm² .

PUNCHING SHEAR d ave = 729

Grnd Brg Pressure

.

-5000

148


17/07/2006 17:08:44


RCC82 Pilecap Design.xls This spreadsheet designs pilecaps with between two and six piles, and then prepares a sketch drawing of each type of cap together with a bar schedule. Bending theory is employed throughout to design the caps. Depending upon the pilecap’s dimensions, the alternative truss method of design may be possible, but is not covered by this spreadsheet. There are seven main sheets: DOUBLE!, 3CAP!, 4CAP!, 5CAP!, 6CAP!, SCHEDULE! and DRAWING! Each of the first five sheets contains two pages that may be printed out. The first (or upper) page contains input data and a summary of results, while the second (or lower) page shows more detailed calculations. The selection of size and number of top and bottom bars is automated. The number of bars determined by either: ■ Area of steel required/ area of maximum sized bar (40mm

diameter) ■ Spacing rules or ■ Number of legs of links required in shear.

The size of link to be used has also been automated. The designer and detailer may wish to rationalise the output given on the DRAWING! sheet. But doing so will obviously affect the bar data on SCHEDULE!

Page numbers for printing do not follow on from previous sheets, so must be entered by the user. This allows for intermediate calculation pages (perhaps for loading) to be inserted.

SCHEDULE! This sheet is a bar schedule complying with BS 8666, for the pilecap drawing on the DRAWING! sheet. Beneath the operating instructions, the number of each type of cap must be entered. These numbers are then used on the schedule and the drawing.

DRAWING! This sheet draws approximately to scale plans and elevations with reinforcement and bar marks for each of the cap types. It is intended for printout to an A3 sheet. If the user wishes to add additional notes, these may be added in cell U27.

Graf! This sheet provides data for the charts in all sheets. It is not intended for formal printing.

DOUBLE!

Notes!

The DOUBLE! sheet is where all material properties are entered, together with covers, pile diameter and pile tolerance. All subsequent sheets use these same properties. Pile tolerance is the amount by which a pile may deviate from its intended position. This value is used in calculation to increase bending moments to allow for this possible deviation. Pile reactions are not similarly increased.

This sheet gives disclaimers and revision history.

Dimensional data for a double pile cap and the supported column are then entered, followed by characteristic column axial loads, moments and horizontal shears for dead load, imposed load and wind load. The results of calculations for all BS 8110 loading combinations are then displayed below (on page X), together with the required arrangement of reinforcement. More detailed calculations may be found by scrolling down to page X.

3CAP!, 4CAP!, 5CAP! and 6CAP! These sheets are identical in function to DOUBLE!, but deal with caps having 3, 4, 5 and 6 piles respectively. However, material properties, pile diameter and tolerance are picked up from DOUBLE! 149


17/07/2006 17:08:48

RCC82 Pilecap Design/ DOUBLE!

Project


Client

BigBucks PLC Pilecap G14

Location


Double Pilecap

PILECAP DESIGN to BS 8110:2005 Originated from RCC82.xls

MATERIALS

fcu fy Pile capacity DIMENSIONS mm

35 500 200

N/mm² kN

h agg T&S cover Btm cover Conc density

COLUMN

20 50 75 23.6

Revision

-

© 2006 TCC

Page

12-Apr-06

Checked

v 3.1 on CD

N/mm²

Date

Rod

-

mm

γc

mm

γs

mm

steel class

101 150 Job No

1.5 1.15

P2000 concrete steel

A

kN/m³

PILECAP

→ = 350 ↑ = 350 Pile Ø = 375 Tolerance = 150

A= B= C= E= depth H =

400 1500 400 750 400

COLUMN ACTIONS kN, kNm characteristic

Axial (kN) M (kNm) H (kN)

DEAD

IMPOSED

WIND

218 23.2 0

104.2 10.4 0

27.5 2.7 0

PLOT (to scale)

KEY

STATUS VALID DESIGN PILE REACTIONS kN

REINFORCEMENT BOTTOM M = 196.9 kNm

d = 309.0 mm,

As = 1,611 mm² 9 H16 B = 1,810 mm²

Gk + Qk Gk + Qk +Wk

PILE 1

PILE 2

147.4 159.3

192.2 207.7

TOP M = 0.0 kNm

d = 337.0 mm,

As min = 416 mm²

6 H10 T = 471 mm²

6 H10 02 T

LINKS

V = 279.7 kN, v = 1.131 N/mm² vc = 0.68 N/mm² (v - vc)b = 361.4 N/mm 4 Legs H8 @ 225 LINKS = 388.5 N/mm

9 H16 01 B Links 10 H8 03.225 + 2x10 H8 04.225 ELEVATION

150


17/07/2006 17:08:49

RCC82 Pilecap Design.xls RCC82 Pilecap Design/ DESIGN!

The Concrete Centre

Project


Client

BigBucks PLC Pilecap G14 - Detailed Calculations

Location

Made by

Double Pilecap

PILECAP DESIGN to BS 8110:2005

Checked


Cap load (kN) = 17.4 or (kN/m) = 7.55

OVERTURNING MOMENTS - kNm characteristic DEAD IMPOSED 23.2 10.4

WIND 2.7

BENDING MOMENTS - kNm 1.4Gk + 1.6Qk M of col 149.5 M of col 196.9 BOTTOM STEEL Bottom M = d= K= z= As = Provide No = As prov = fs = Max clear S = Min clear S = Clear S = SHEAR PILE 1

196.9 309.0 0.0737 281.2 1611 1611 9 1810 297 158.4 25.0 67.5

PILE REACTIONS kN PILE 1 Gk + Qk 147.4 Gk + Qk +Wk 159.3 1.4Gk + 1.6Qk 215.4 Gk + 1.4Wk 118.9 1.2(Gk+Qk+Wk) 191.2

Gk + 1.4Wk 81.5 107.5

1.2(Gk+Qk+Wk) 132.9 175.0

TOP STEEL Top M = d= K= z= As = Provide No = As prov = fs = Max clear S = Min clear S = Clear S =

Ø16

9 H16 B

0.0 337.0 0.0000 320.2 0 416 6 471 0 252.8 25.0 124.8

Ø10

PILE 2 192.2 207.7 280.9 154.9 249.3

Page

12-Apr-06 Revision

-

© 2006 TCC

Piles @ (m) 1.500

Date

Rod

151 102 Job No

-

P2000

. . .

arm (m) 0.725 arm (m) 0.725 (including tolerance) K' = 0.1558 min As = 0.13%

6 H10 T

Crit section is 112.5 from pile centres 0.732 % 1.4Gk + 1.6Qk Gk + 1.4Wk 1.2(Gk+Qk+Wk) V 214.2 118.1 190.2 Av = 637.5 v = 0.8664 vc = 0.6797

PILE 2 V Av = 637.5 Max (v - vc)b = 361.4 No of legs = 4

279.7

154.1 v = 1.1314 Ø8 links Link spacing = 225

248.3 vc = 0.6797

4 Legs H8 @ 225 LINKS

151


17/07/2006 17:08:53

RCC82 Pilecap Design/ 3CAP!

Project


Client

BigBucks PLC Pilecap F13

Location


Rod

Triple Pilecap

PILECAP DESIGN to BS 8110:2005 Originated from RCC82.xls v 3.1 on CD

DIMENSIONS mm COLUMN

→ = 300 ↑ = 300 Pile Ø = 375 Min spacing = 1300 Tolerance = 150

Checked

Page

12-Apr-06 Revision

-

© 2006 TCC

152 14 Job No

-

P2000

PILECAP


350 1300 1126 375.33 400

PLOT (to scale)


Axial (kN) Mx (kNm) My (kNm) Hx (kN) Hy (kN)

Date

DEAD

IMPOSED

WIND

355.5 10.0 20.0

118.2 5.0 10.0

10.0 2.0 5.0

KEY

STATUS VALID DESIGN PILE REACTIONS kN characteristic

Gk + Qk Gk + Qk +Wk

PILE 1

PILE 2

PILE 3

140.4 139.3

168.9 172.9

191.9 199.0

REINFORCEMENT

EW (2-3)

M = 222.6 kNm, b = 1,050 mm d = 307.0 mm, As = 1,808 mm² 6 H20 B = 1,885 mm² V = 278.3 kN, bv = 1,050 mm v = 0.863 N/mm², (v-vc)b = 420 N/mm 4 Legs H8 @ 200 LINKS = 437 N/mm

NS (1-2/3)

M = 196.2 kNm, b = 1,798 mm d = 284.5 mm, As = 1,669 mm² 4 H25 B = 1,963 mm² V = 202.7 kN, bv = 1,234 mm v = 0.577 N/mm², (v-vc)b = 494 N/mm 4 Legs H8 @ 175 LINKS = 500 N/mm

4 H12 06 T1

6 H20 05 B1 Links 8 H8 07 200 + 2x8 H8 08 200

↑ ELEVATION

4 H12 10 T2

4 H25 09 B2 Links 7 H8 11 175 + 2x7 H8 12 175

← ELEVATION

152


17/07/2006 17:08:56

RCC82 Pilecap Design.xls RCC82 Pilecap Design/ 3CAP!

Project


Client

BigBucks PLC Pilecap F13

Location


Triple Pilecap


Cap load =

27.6

Checked

Group centre @

751

Page

12-Apr-06 Revision

-

© 2006 TCC

kN

Date

Rod

153 15 Job No

-

P2000

m from pile 1

PILE REACTIONS kN Gk + Qk Gk + Qk +Wk 1.4Gk + 1.6Qk Gk + 1.4Wk 1.2(Gk+Qk+Wk)

PILE 1 140.4 139.3 202.7 108.4 167.2

PILE 2 168.9 172.9 244.4 134.5 207.5

BENDING MOMENTS - kNm 1.4Gk + 1.6Qk My v of col 152.2 My ^ of col 196.2 222.6 Mx

PILE 3 191.9 199.0 278.3 154.2 238.8

222.6 1050 307.0 0.0643 283.2 1808 1808 6 1885 320 251.4 25.0 92.8

N-S STEEL M= b= d= K= z= As = Provide No = As prov = fs = Max clear S = Min clear S = Clear S =

Ø20

6 H20 B

SHEAR

Crit section is Ø8 links V = 278.3 b= av = 537.5 v= (v - vc)b = 420.0 No of legs = PILE 1 Ø8 links b= V = 202.7 av = 638.2 v= (v - vc)b = 493.6 No of legs =

.

Gk + 1.4Wk 81.4 108.4 123.4

E-W STEEL M= b= d= K= z= As = Provide No = As prov = fs = Max clear S = Min clear S = Clear S =

OVERTURNING MOMENTS - kNm characteristic DEAD IMPOSED WIND Mx 10.0 5.0 2.0 My 20.0 10.0 5.0

. .

112.5

1.2(Gk+Qk+Wk) 125.5 167.5 191.1

196.2 1798 284.5 0.0385 270.3 1669 1669 4 1963 283 275.0 25.0 161.3

Ø25

(including tolerance)

K' = 0.1558 min As = 0.13%

4 H25 B

from pile centres

PILES 2 & 3

PUNCHING

Column Face V = 686.8 v = 1.935 v max = 4.733 ok

1050 0.8632 4

As% = 0.585 vc = 0.7216 Spacing = 200

.

1234 0.5775 4

As% = 0.559 vc = 0.6224 Spacing = 175

.



At Fig 3.23 critical section µ = 4163 d ave = 295.75 v = 0.558 av = 494.0 ok vc 2d/av = 0.717

153


17/07/2006 17:08:59

RCC82 Pilecap Design/ 4CAP!

Project


Client

BigBucks PLC Pilecap E12

Location


Rod

4 Pile Cap

PILECAP DESIGN to BS 8110:2005

Checked


DIMENSIONS mm

Revision

-

© 2006 TCC

Page

12-Apr-06

154 28 Job No

-

P2000

PILECAP

COLUMN

→ = 300 ↑ = 400 Pile Ø = 375 Tolerance = 150

A= B= C= D= E= depth H =

350 1300 1300 650 650 450 PLOT (to scale)



Date

DEAD

IMPOSED

WIND

475.0 10.0 20.0 1.0 2.0

157.0 5.0 10.0 0.5 1.0

13.6 2.0 5.0 0.2 0.5

KEY

STATUS VALID DESIGN PILE REACTIONS kN

Gk + Qk Gk + Qk +Wk

PILE 1

PILE 2

PILE 3

PILE 4

150.5 151.1

162.6 164.8

174.6 179.3

186.7 192.9

REINFORCEMENT EW(1/3-2/4) M = 328.6 kNm,

b = 2,000 mm As = 2,168 mm² 11 H16 B1 = 2,212 mm²

d = 367.0 mm,

11 H10 14 T1

V = 505.5 kN, bv = 2,000 mm v = 0.689 N/mm², (v-vc)b = 800 N/mm 11 Legs H8 @ 300 LINKS = 801 N/mm

11 H16 13 B1 11 Link Legs ↑ ELEVATION

NS(1/2-3/4) M = 313.9 kNm,

b = 2,000 mm As = 2,165 mm² 11 H16 B2 = 2,212 mm²

d = 351.0 mm,

V = 523.2 kN, bv = 2,000 mm v = 0.745 N/mm², (v-vc)b = 800 N/mm 11 Legs H8 @ 300 LINKS = 801 N/mm

11 H10 16 T2

11 H16 15 B2 Links 11x7 H8 17 300 ← ELEVATION

Note: 5CAP! AND 6CAP! similar

154


17/07/2006 17:09:04

RCC82 Pilecap Design.xls RCC82 Pilecap Design/ 4CAP!

Project


Client

BigBucks PLC Pilecap E12

Location


4 Pile Cap


Cap load =

42.5

PILE REACTIONS kN PILE 2 162.6 164.8 235.1

PILE 3 174.6 179.3 252.8

PILE 4 186.7 192.9 270.4

Gk + 1.4Wk 1.2(Gk+Qk+Wk)

118.1 181.3

128.4 197.7

139.8 215.1

150.1 231.5

BENDING MOMENTS - kNm 1.4Gk + 1.6Qk My v of col 271.5 My ^ of col 313.9 My < of col 305.6 My > of col 328.6 E-W STEEL M= b= d= K= z= As = Provide No = As prov = fs = Max clear S = Min clear S = Clear S =

BOTTOM Ø16 328.6 2000 367.0 0.0349 348.7 2168 2168 11 2212 327 284.0 25.0 170.8

Gk + 1.4Wk 147.9 174.0 167.7 181.1 N-S STEEL

TOP Ø10 0.0 2000 395.0 0.0000 375.3 0 0 11 864

M= b= d= K= z= As = Provide No = As prov = fs = Max clear S = Min clear S = Clear S =

11 H10 T1

11 H16 B1 BEAM SHEAR EW (NS plane)

V = 505.5 av = 537.5

Revision

155 29 Job No

-

P2000

OVERTURNING MOMENTS - kNm characteristic DEAD IMPOSED WIND Mx 10.5 5.2 2.1 My 20.9 10.5 5.2

kN

PILE 1 150.5 151.1 217.4

Checked

Page

12-Apr-06

-

© 2006 TCC

Gk + Qk Gk + Qk +Wk 1.4Gk + 1.6Qk

Date

Rod

. . .

1.2(Gk+Qk+Wk) 227.5 268.0 257.7 279.0 BOTTOM Ø16 313.9 2000 351.0 0.0364 333.5 2165 2165 11 2212 326 284.0 25.0 170.8


TOP Ø10 0.0 2000 385.0 0.0000 365.8 0 0 11 864

K' = 0.1558 min As = 0.13%

11 H10 T2

11 H16 B2 Critical section is 112.5 mm from pile centres Ø8 links v = 0.6887 As% = 0.301 vc 2d/av = 0.6614 (v - vc)b = 800.0 No of legs = 11 Spacing = 300

.


NS (EW plane)

V = 523.2 av = 537.5

PUNCHING

v = 0.7453 vc 2d/av = 0.6420 No of legs = 11

Column Face V = 916.2 v = 1.823 v max = 4.733 ok

As% = 0.315 (v - vc)b = 800.0 Spacing = 300

.


At Fig 3.23 critical section µ = 4300 d ave = 359 v = 0.594 av = 537.5 vc 2d/av = 0.655 ok

Note: 5CAP! AND 6CAP! similar

155


17/07/2006 17:09:08

RCC82 Pilecap Design.xls RCC82 Pilecap Design/ SCHEDULE!

The Concrete Centre

Bar schedule ref :

Site ref :


Job no :

P2000

Member

Bar mark

Double Pilecaps

01

3-Pile Caps

4-Pile Caps

5-Pile Caps

6-Pile Caps

H 16

4

01

Rev:

-

Checked by :

-

Date prepared : 12-Apr-06 Prepared by :

Type and No. size of mbrs

202

No. of bars in each

9

Length of Total No. each bar † mm

36

Shape code

2675

21 00

A*

Rod B*

C*

D*

E/R *

mm

mm

mm

mm

mm

270

2175

02

H 10

4

6

24

2175

03

H8

4

10

40

2075

51

270

695

115

04

H8

4

20

80

500

31

115

50

270

05

H 20

3

6

18

2300

21

255

1890

06

H 12

3

4

12

1875

00

07

H8

3

8

24

1975

51

270

650

115

08

H8

3

16

48

500

31

115

50

270

270

1715

115

115

09

H 25

3

4

12

2125

21

10

H 12

3

4

12

1700

00

11

H8

3

7

21

1800

51

235

600

115

12

H8

3

14

42

475

31

115

50

235

115

13

H 16

5

11

55

2100

21

130

1890

14

H 10

5

11

55

1875

00 130

1890 290

115

440

115

490

120

15

H 16

5

11

55

2100

21

16

H 10

5

11

55

1875

00

17

H8

5

77

385

525

31

115

50

18

H 16

2

12

24

2625

21

130

2410

19

H 12

2

12

24

2400

00

21

H 16

2

12

24

2650

21

150

2410

22

H 10

2

12

24

2400

00

20

H8

2

120

240

675

31

115

50

23

H 16

1

14

14

2100

21

130

1890

00 145

3175

120

60

24

H 12

1

14

14

1875

26

H 16

1

12

12

3425

21

27

H 10

1

12

12

3175

00

28

H 10

1

84

84

750

31

This schedule complies with BS 8666.

1,641 kg on this schedule

* Specified in multiples of 5mm.

† Specified in multiples of 25mm.

PILECAP DESIGN to BS 8110:2005 © 2003-2005 Reinforced Concrete Council

156


17/07/2006 17:09:13

12 H16 18 B2

12 H10 22 T1

12 Link Legs ↑ ELEVATION

12 H16 21 B1

Links 12x10 H8 20 250 ← ELEVATION

12 H12 19 T2

PLAN (Pilecap D11)

↑ ELEVATION

Links 10 H8 03.225 + 2x10 H8 04.225 ← ELEVATION

9 H16 01 B

4 H25 09 B2

14 H12 24 T2

12 H10 27 T1

12 H16 26 B1

14 H16 23 B2

Links 14x6 H10 25 350 ← ELEVATION

14 Link Legs ↑ ELEVATION

PLAN (Pilecap C10)

Links 7 H8 11 175 + 2x7 H8 12 175 ↑ ELEVATION

4 H12 10 T2

Links 8 H8 07 200 + 2x8 H8 08 200 ← ELEVATION

6 H20 05 B1

11 Link Legs ← ELEVATION

11 H16 13 B1

11 H16 15 B2

PLAN (Pilecap E12)

Links 11x7 H8 17 300 ↑ ELEVATION

11 H10 16 T2

11 H10 14 T1

The Concrete Centre

PLAN (Pilecap F13) 4 H12 06 T1

This drawing is diagramatic. Connecting slabs & beams not shown.


PLAN (Pilecap G14)

6 H10 02 T

2 Pile Cap - 4 No 5 Pile Cap - 2 No

Refer to GA drawings for orientation and dimensions.

Project Job No Date Made by

Client Dwg No Revision Checked

P2000 12-Apr-06 Rod

BigBucks PLC 202 -

EC2 USERGUIDEv2.indd Sec1:157 3 Pile Cap - 3 No 6 Pile Cap - 1 No

NOTES Concrete grade C35. Cover 75 mm bottom. Cover 50 mm top & sides.


RCC82 Pilecap Design/ DRAWING!

157

17/07/2006 17:09:19

4 Pile Cap - 5 No

RCC91 One-way Solid Slabs (Tables).xls Design is often undertaken using the moment and shear factors taken from BS 8110: Part 1, Tables 3.5 and/ or 3.12. This series of spreadsheets uses factors for moment and shear based on these tables.

moments. The factors from Table 3.12 give rise to a single load case that has been subject to 20% redistribution: a bending moment envelope is inappropriate and the diagram is therefore indicative only. The factors used are given in the table below.

RCC91.xls designs simple one-way solid slabs to BS 8110. For three or more spans they use moment and shear factors from Table 3.12. The use of these factors is governed by Clause 3.7.2.7 (single load case and the conditions of Clause 3.5.2.3 are met {bays > 30 m2 , qk >/ 1.25 gk, qk >/ 5.0 kN/m2 } and at least three bays of approximately equal span (the corresponding factors for beams also restrict use of the factors to where spans differ by no more than 15% of the maximum span)). Where the relevant conditions are not met, users are directed towards RCC31. xls where continuous beam analysis overcomes many of these caveats.

The factors used are based on continuous end supports. The two-span factors were derived by modelling the appropriate number of spans with a single loadcase of 4 kN/m dead and 5 kN/m imposed and allowing any one span to be 15% less than the input length (strictly according to BS 8110 this is applicable to beams only).

The design of single- and two-span slabs is also possible. The factors used for two-span slabs should be considered subject to the same conditions as for using the factors from Table 3.12 of BS 8110.

As most contractors prefer prefabricated reinforcement mats might be considered. To the right of the sheet are calculations. An approximate reinforcement density is given.

MAIN! This single sheet consists of the input and main output. In itself it should prove adequate for the design of the simplest one-way solid slab designs. A nominal 1 m wide strip of slab is considered. Inputs are underlined and most should be self-explanatory. End support condition determines the factors applied for bending. Simple charts show the spans, loads and indicative bending

Table 3 Bending moment and shear force coefficients

The area of steel required, As, may be automatically increased to reduce service stress, fs, and to increase modification factors to satisfy deflection criteria. The option in line 42 to have top steel in spans influences modification factors used in deflection calculations.

Coefficient

Weight! Weight! gives an estimate of the amount of reinforcement required in a slab. Simplified curtailment rules, as defined in Clause 3.12 are used to determine lengths of bars. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers’ preferences,

End supports

End spans

First int supports

Interior spans

Interior supports

1 Span 2 Span 3 Span etc

0.00 0.00 0.00

0.125 0.086 0.075

~ 0.100 0.086

~ ~ 0.063

~ ~ (0.063)


0.040 0.040 0.040

0.105 0.066 0.075

~ 0.100 0.086

~ ~ 0.063

~ ~ (0.063)


0.50 0.46 0.46

Bending Simple support

Shear ~ 0.60 0.60

~ ~ 0.50

158


17/07/2006 17:09:23

RCC91 One-way Solid Slabs (Tables).xls rationalisation, the effects of holes etc, etc. It excludes supporting beams, trimming to holes etc. To the right of the sheet are calculations of length, etc.

Graf! This sheet comprises data for graphs used in MAIN! It is not necessarily intended for printing out other than for checking purposes.


159


17/07/2006 17:09:26

RCC91 One-way Solid Slabs (Tables)/ MAIN!

Project

Spreadsheets to BS 8110 & EC2

Client Location

Advisory Group 8rd Floor slab 1-WAY SOLID CONCRETE SLAB DESIGN to BS 8110:2005 Table 3.12 Originated from RCC91.xls

LOCATION

v3.0 on CD

Supports from grid End support condition is

DIMENSIONS Nº of spans Max Span Thickness, h cover

Nº m mm mm

A C


rmw Checked

Page

160 116


chg

© 2006 TCC

Job No

-

R68

STATUS

to grid F (C C)ontinuous or (S S)imple

VALID DESIGN

MATERIALS fy N/mm² 500 fcu N/mm² 35 Density kN/m³ 23.6 (Normal weight concrete)

3 7.200 200 20

Made by

γs = 1.15 γc = 1.50

steel class

A

100 50

LOADING Self Weight Additional Dead Total Dead, gk Imposed Load, qk Design load, n =

0

kN/m² kN/m² kN/m² kN/m² kN/m²

4.72 1.00 5.72 2.50 12.01

MAIN STEEL

-50 -100

A

F

END

kNm/m mm

mm²/m mm mm c/c mm²/m %

F Indicative Bending Moment Diagram

END

FIRST INT

INTERIOR

INTERNAL

BS 8110

SPANS

SUPPORTS

SPANS

SUPPORTS

Reference

0.040 24.9 175 0.023 166.3 344 H 10 225 349 0.199 535 (a)

0.075 46.7 172 0.045 162.9 659 H 16 150 1340 0.779 532 (a)

0.086 53.5 174 0.051 163.6 753 H 12 150 754 0.433 534 (a)

0.063 39.2 172 0.038 163.4 552 H 16 200 1005 0.584 532 (a)

0.000 0.0

Table 3.12

329

164 0 1.000 1.603 41.7 41.8

333

183 0 1.000 1.651 43 41.8

SUPPORTS

Factor M d K z As Rebar Ø @ As prov = Max S subclause

A

Geometry and Loading

(A & F)

M/bd²fcu Clause 3.4.4.4

12

Clause 3.12.11.2.7

DEFLECTION fs N/mm² Top steel provided % bd Comp Mod factor Tens Mod factor Perm L/d Actual L/d DISTRIBUTION STEEL

As =

SHEAR

0.13% Provide H

As auto-increased by 100 % = 10

260 at 300

END SUPPORT

FIRST INT SUPT

39.8 0.390 0.231 0.638

51.9 0.433 0.298 0.659

V kN/m As prov % v N/mm² vc N/mm²

Eqn 8 Table 3.11 Eqn 7

As auto-increased by 70 %

mm²/m

Table 3.9

Table 3.25

= 262 mm²/m INTERNAL SUPTS Table 3.12

equation 3 Table 3.8

OUTPUT/SUMMARY

PROVIDE CHECKS

END SUPPORTS H10 @ 225 T1

END SPANS H16 @ 150 B1

FIRST INT SUPPORTS H12 @ 150 T1

INTERIOR SPANS H16 @ 200 B1

INTERNAL SUPPORTS

BAR Ø < COVER

SINGLY REINFORCED

BAR SPACING

DEFLECTION

NO SHEAR LINKS

OK

OK

OK

OK

OK

DISTRIBUTION H10 @ 300


160


17/07/2006 17:09:27

RCC92 Ribbed Slabs (Tables).xls

RCC92 Ribbed Slabs (Tables).xls This spreadsheet designs simple single-, two-span and multiplespan ribbed slabs to BS 8110: Part 1 using the moment and shear factors in, or in the case of single and two spans, consistent with Table 3.12 of BS 8110.

or no links is a matter of choice for the designer. Most contractors prefer to prefabricate reinforcement for ribbed slabs on the ground or off-site: this means at least nominal links and nominal top steel are usually required.

The use of factors from Table 3.12 is governed by Clause 3.7.2.7 as follows

■ Designed links are taken to be those provided where (vc + 0.4)

< v < 0.8 fcu 0.5; ■ Minimal links are taken to be those that are required to

■ A single load case is assumed

provide shear resistance for vc < v < (vc+ 0.4)

■ Conditions of 3.5.2.3 are met

■ Nominal links are those used if required for temporary

● bays > 30 m2 ,

support only in areas where v < vc

● k >/ 1.25gk, ● k >/ 5.0 kN/m2 and at least three bays are of

approximately equal span ■ The corresponding factors for beams also restrict use of the

factors to where spans differ by no more than 15% of the maximum span. The factors used for two-span slabs should be considered subject to these same conditions. They were derived by modelling the appropriate number of spans with a single load case of 4 kN/ m2 dead and 5 kN/m2 imposed, and allowing any one span to be 15% less than the input length (strictly according to BS 8110 this is applicable to beams only). The factors used are based on continuous end supports. Where the relevant conditions are not met, users are directed towards RCC32.xls where continuous beam type analysis overcomes many of these caveats.

MAIN! This single sheet consists of the input and main output. In itself it should prove adequate for the simplest ribbed slab designs. Inputs are underlined and most should be self-explanatory. The option to have top steel in spans or not has bearings on whether shear links can be accommodated and on deflection calculations. The option to have links, minimal (or nominal) links

Table 4 Bending moment and shear force coefficients used in RCC 92

Coefficient

Under Bending, the Width of solid from CL in line 28 refers to the distance between centre line of support and the rib/ solid intersection. It determines where shear and, at internal supports, hogging moment in ribs are checked. The user inputs preferred diameters of reinforcement in the rib. At supports, these bars usually need to be supplemented by intermediate bars to comply with either spacing rules or with hogging moments in the solid section of slab. In spans, the area of steel required, As, may be automatically increased to reduce service stress, fs, and to increase modification factors to satisfy deflection criteria. An approximate reinforcement density is given. It excludes mesh, supporting beams, trimming to holes etc. Please note that the bending moment diagrams are indicative only. The factors from Table 3.12 give rise to a single load case that has been subject to 20% redistribution: a bending moment envelope is inappropriate. The factors used are given in the table below. The factors used are based on continuous end supports. The twospan factors were derived by modelling the appropriate number of spans with a single load case of 4 kN/m dead and 5 kN/m imposed and allowing any one span to be 15% less than the input length (strictly according to BS 8110 this is applicable to beams only).

End supports

End spans

First int supports

Interior spans

Interior supports

0.105 0.066 0.075

~ 0.100 0.086

~ ~ 0.063

~ ~ (0.063)

Bending


0.040 0.040 0.040

Shear


0.50 0.46 0.46

~ 0.60 0.60

~ ~ 0.50

161


17/07/2006 17:09:37

DETAILS! DETAILS! gives two pages of detailed calculations and references to BS 8110 justifying the output in MAIN! This sheet is intended as an explanation for the less experienced engineers and may prove useful for checking purposes. Maximum spacing, smax , at supports is based on rib centres: usually two large bars are required in the top of the rib for moment at the rib/ solid intersection and one, two or even three smaller bars (minimum T10) are required between to overcome spacing rules. Concentrating reinforcement with larger bars in the top of the rib raises the percentage steel in the rib at the rib/ solid interface, thereby maximising vc and reducing shear requirements. In terms of curtailment, 50% of reinforcement for maximum sagging is taken as being As req’d for bending, i.e. excluding any extra for deflection, etc. (Figure 3.25 refers to ‘reinforcement for max. moment’.) Ribbed slabs are taken as being “slabs” so the 40% rule is applied and 40% of As req’d is assumed at end supports. It is usually assumed that ‘ribs’ become ‘beams’ when they are at centres > 1.5 m Tapered links are assumed. Where required for shear resistance, links should be at maximum 0.75d centres.

WEIGHT! Weight! gives an estimate of the amount of reinforcement required in a slab. Simplified curtailment rules, as defined in Clause 3.12 are used to determine lengths of bars. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation, the effects of holes etc, etc. To the right of the sheet are calculations of length etc.

Graf! This sheet comprises data for graphs used in MAIN!


162


17/07/2006 17:09:39

RCC92 Ribbed Slabs (Tables).xls RCC92 Ribbed Slabs (Tables)/ MAIN!

Project


Client Location

Advisory Group 2nd Floor slab RIBBED SLAB DESIGN to BS 8110:2005 using table 3.12 coefficients Originated from RCC92.xls

LOCATION

The Concrete Centre

v3.0 on CD

rts from grid Support

A

Made by

Date

rmw Checked

to grid

Revision

chg

© 2006 TCC

Page

163 119

12-Apr-2006

Job No

prelim

R68

STATUS

F

VALID DESIGN DIMENSIONS Nº of spans Nº Max Span m depth o/a, h mm topping depth, hf mm Top steel in spans ? Min No of bars per rib Use Links? Y

5 rib width 7.200 rib centres 300 Side slope 100 Y Top cover (to links) 2 B/S cover (to links) (Y Y)es, (N N )o or (M)inimal

mm mm 1 in mm mm

MATERIALS fcu N/mm² fy N/mm² fyv N/mm² h agg mm

150 750 10

35 500 500 20

steel class A γc = 1.50 γs = 1.15 Density kN/m³ 24.0 (Normal weight concrete)

35 25

LOADING Self Wt + Dead Total Dead, gk Imposed qk Design load, n =

kN/m² kN/m² kN/m² kN/m² kN/m²

BENDING

4.00 1.50 5.50 5.00 15.70

A

END SUPPORTS (A & F)

Width solid from CL M kNm/m d mm As mm² As' mm²

150 32.6 254 233 0

F

A

F

Geometry and Loading

Indicative Bending Moment Diagram

END SPANS

FIRST INT SUPPORTS

INTERIOR SPANS

INTERNAL SUPPORTS

--61.1 259 428 0

500 70.0 249 511 0

--51.3 259 360 0

500 51.3 249 374 0

BS8110 Reference

Table 3.12

Fig 3.3 Fig 3.3

DEFLECTION

L/d Max

37.869

Actual L/d

27.799

44.162 OK

27.799

As auto increased by 28.1%

3.4.6.3

OK

3.4.5.1

As auto increased by 23.4%

TENSION REINFORCEMENT

Ø No As prov =

mm mm² %

10 3 Top+3H10 471 0.247

20 2 Btm 628 1.427

20 2 Top+2H10 785 0.421

20 2 Btm 628 1.427

20 2 Top+2H10 785 0.421

20 2 Btm 628 1.455

8 2 Top 101 0.228

12 2 Btm 226 0.534

8 2 Top 101 0.228

10 2 Btm 157 0.371

OUTER SUPT

FIRST INT SUPT

INT SUPT

37.2 0.863 0.897 6 175

45.0 1.063 0.908 6 175

36.5 0.863 0.908 6 175

18.23 16.56 52.01

43.59 39.60 124.38

39.63 36.00 113.08

END

END SPANS 2H8 T

FIRST INT SUPPORTS 2H20 /rib + 2H10 T Nominal B 2H6 @ 175

COMPRESSION ZONE REINFORCEMENT

Ø No As' prov =

mm² %

RIB SHEAR V v vc Link Ø @ REACTIONS Dead Imposed Ultimate

kN/rib N/mm² N/mm² mm kN/m kN/m kN/m

mm

Table 3.12 Eqn 3

NOMINAL

Table 3.8

6 175 solid weight included Table 3.12

OUTPUT/SUMMARY PROVIDE SUPPORTS MAIN STEEL 3H10 /rib + 3H10 T Nominal B LINKS 2H6 @ 175

2H20 B 2H6 @ 175

2H20 B 2H6 @ 175

for 875

from edge of solid CHECKS

INTERIOR SPANS 2H8 T

BAR Ø & COVER

SINGLE LAYERS

BAR SPACING

INTERNAL SUPPORTS 2H20 /rib + 2H10 T Nominal B 2H6 @ 175 for 175

DEFLECTION

SHEAR LINKS

GLOBAL STATUS

163


17/07/2006 17:09:41

RCC92 Ribbed Slabs (Tables)/ DETAILS!

Project


Client

Advisory Group

Location

2nd Floor slab


from grids A to F

RIBBED SLAB DESIGN to BS 8110:2005 using table 3.12 coefficients Originated from RCC92.xls v3.0 on CD

Date

rmw Checked

Revision

chg

© 2006 TCC

Page

12-Apr-2006

164 120 Job No

prelim

R68

DETAILED CALCULATIONS ave bw rib area

170.0 0.1090

mm m²

Gk = 39.63 MAIN STEEL Factor M/m M/rib d bf K' Web MOR Flange MOR K z x d' net fsc Excess M As' req max fst fst deflection As req bw/b Min % Min As

kNm/m kNm mm mm kNm kNm mm mm mm N/mm² kNm mm² N/mm² N/mm² mm²

mm²

self wt E/O solid Total SW Qk = 36.00

3.49 0.52 kN/m² 4.00 kN/m² kN/m²

F = 113.08

N = 15.705

kN/m width

END SUPPORTS

END SPANS

FIRST INT SUPPORTS

INTERIOR SPANS

INTERNAL SUPPORTS

BS 8110 Reference

0.04 32.6 24.42 254 750 0.1320 50.7 223.5 0.0144 241.3 28.2 41.0 0.0 0.0 0 434.8 --233 --0.13% 293

0.075 61.1 45.80 259 750 0.1558 62.2 245.1 0.0260 246.1 28.8 45.0 0.0 0.0 0 434.8 308.8 428 0.2267 0.18% 92

0.086 70.0 52.51 249 750 0.1320 48.7 214.8 0.0323 236.6 27.7 37.0 0.0 0.0 0 434.8 --511 --0.13% 293

0.063 51.3 38.47 259 750 0.1558 62.2 245.1 0.0218 246.1 28.8 45.0 0.0 0.0 0 434.8 341.5 360 0.2267 0.18% 92

0.063 51.3 38.47 249 750 0.1320 48.7 214.8 0.0236 236.6 27.7 36.0 0.0 0.0 0 434.8 --374 --0.13% 293

Table 3.12 -=-=-

3.4.4.4 Fig 3.3 -=3.4.4.4 -=-=-

Fig 3.3

Fig 3.3

Table 3.25

At EDGE of SOLID

M/m kNm/m M/rib kNm bf mm K z mm x mm net fsc N/mm² Excess M kNm As' req mm² fst N/mm² As req mm²

24.9 18.7 150 0.0552 237.3 37.1 0.0 0.0 0 434.8 181

residual steel 0.26% 57 10 3 236

38.1 28.5 150 0.0877 221.8 60.5 256.5 0.0 0 434.8 296

0.26% 0 10 2 157

residual steel min % 0.26% As resid 0 Ø extra 10 No 2 As prov 157

25.0 18.7 150 0.0576 231.9 38.0 36.9 0.0 0 434.8 186

Table 3.13 -=-

Fig 3.3

TENSION STEEL

Required Ø in rib No As prov Clear dist Min S Max S

mm²

ok mm² mm

ok ok

181 10 3 236 54.4 25.0 183.3

ok

ok ok

428 20 2 628 54.2 25.0 207.0

ok

ok ok

296 20 2 628 97.8 25.0 299.3

ok

ok ok

360 20 2 628 54.2 25.0 246.4

ok

ok ok

186 20 2 628 97.8 25.0 300.0

between bars 3.12.11.1 3.12.11.2.4

COMPRESSION STEEL

Required Ø No As' prov =% Clear dist Min S

ok mm²

ok mm

ok

171 20 2 628 1.455 55.6 25.0

ok

ok ok

0 8 2 101 0.228 123.0 25.0

ok

ok ok

128 12 2 226 0.534 70.8 25.0

ok

ok ok

0 8 2 101 0.228 123.0 25.0

ok

ok ok

108 10 2 157 0.371 74.6 25.0

Table 3.25

between bars 3.12.11.1

164


17/07/2006 17:09:49

RCC92 Ribbed Slabs (Tables).xls RCC92 Ribbed Slabs (Tables)/ DETAILS!

Project


Client

Advisory Group

Location

2nd Floor slab


from grids A to F

RIBBED SLAB DESIGN to BS 8110:2005 using table 3.12 coefficients Originated from RCC92.xls v3.0 on CD

DEFLECTION fs N/mm² Base ratio Tens Mod Comp Mod Perm L/d Actual L/d As req increased by

Date

rmw Checked

Revision

chg

© 2006 TCC

Page

12-Apr-2006 prelim

END SUPPORTS

END SPANS

FIRST INT SUPPORTS

INTERIOR SPANS

INTERNAL SUPPORTS

256.5

227.1 20.80 1.700 1.071 37.869 27.799 28.1%

157.1

190.8 20.80 1.983 1.071 44.162 27.799 23.4%

98.6

ok

165 121 Job No

R68 BS 8110 Reference Eqn 8 3.4.6.3/4 Table 3.10 Table 3.11 3.4.6.3

ok

3.4.5.1

RIB SHEAR

Factor V max V rib v vc (v-vc)bv Link Ø @ adjust to for adjust to

kN/m kN/m N/mm² N/mm² N/mm

ok mm mm mm mm

END SUPPORTS

FIRST INT SUPPORTS

INTERNAL SUPPORTS

0.46 52.01 37.24 0.8625 0.8975 68.0 6 191 175 0 0

0.6 67.85 44.99 1.0630 0.9080 68.0 6 187 175 795 875

0.5 56.54 36.51 0.8626 0.9080 68.0 6 187 175 75 175

ok

ok

Table 3.12 -=-

Eqn 3

ok

NOMINAL

Table 3.8

68.0 6 194 175 -----

Table 3.7 3.12.7.1 Spacing Spacing from solid from solid

As Dist

ok

64.4

ok

0

ok

0

ok

0

OK

3.4.5.5

As' Dist

ok

0

ok

0

ok

0

ok

0

OK

3.12.7.2

165


17/07/2006 17:09:54

RCC93 Flat Slabs (Tables).xls This spreadsheet designs simple rectangular flat slabs to BS 8110: Part 1 using moment and shear factors from Table 3.12. The use of these factors is also governed by Clause 3.7.2.7 as shown below. ■ A single load case is assumed ■ The conditions of 3.5.2.3 are met ● bays > 30m2 , ● qk >/ 1.25gk, ● qk >/ 5.0 kN/m2 and at least three bays of approximately

equal span ■ The corresponding factors for beams also restrict use of the

factors to where spans differ by no more than 15% of the maximum span. Where the relevant conditions are not met, users are directed towards RCC33.xls where sub-frame analysis overcomes many of the caveats made in the code restricting the use of bending moment and shear factors from Table 3.12. The spreadsheet does not currently allow for holes or drops. If holes are considered critical then the user is directed towards using RCC21.xls (sub-frame analysis) and allowing for holes in breadths used. Note should also be made of Clause 3.7.5., Openings in panels. Punching shear can be checked using RCC13. xls. It does not cater for single or two-span cases.

DETAILS! DETAILS! gives detailed calculations and references to BS 8110 justifying the output in MAIN! This sheet is intended as explanation for the less experienced engineers and may prove useful for checking purposes. Column transfer moments are limited to Mt max see Clause 3.7.4.2 and equation 24 A basic deflection ratio of 26 x 0.9 (see Clauses 3.4.6.1 and 3.7.8) is used in line 189 etc. Some engineers like to use a lower basic deflection ratio (rather than 26 in the code) to offset any potential problems with deflection of partitions and especially of cladding. Traditional shear links can be very time consuming on site, so in order to minimise the number of links the centres are maximised at 0.75d (see line 226 et seq). Additional bars may be necessary to act as carriers to these links if top and bottom bars cannot be arranged at the preferred spacings. Consideration should also be given to using proprietary systems.

WEIGHT! Weight! gives an estimate of the amount of reinforcement required in a slab. Simplified curtailment rules, as defined in Clause 3.12 are used to determine lengths of bars. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers preferences’, rationalisation, the effects of holes etc, etc. Additional link carrier bars are not included.

MAIN! This single sheet consists of the input and main output. In itself it should prove adequate for the simplest flat slab designs. Most inputs should be self-explanatory. A location plan helps with definition of dimensions. The number of spans is altered by changing the number of grid line inputs: deleting the end grid line name will decrease the number of spans. A combo-box is used to switch between the continuous and simply supported end support/ slab connection factors. Note the effect on column transfer moments. Edge distance, C, is actually from centreline of column to edge of slab. ‘Double penult’ means penultimate in both directions, i.e. internal column of corner bay. Please note that the bending moment diagrams are indicative only. The factors from Table 3.12 give rise to a single load case that has been subject to 20% redistribution: a bending moment envelope is therefore inappropriate.

Xdia! And Ydia! In these sheets each bending moment is designed using a different size bar (with different effective depths, d). The largest bar (i.e. minimum number of bars) consistent with maximum specified diameter and maximum spacing rules is identified and used in DETAILS! Thus a least bars solution is given. The Xdia! and Ydia! pages find the maximum diameter that can be used while complying with spacing rules. The sheet finds which of Clause 3.12.11.2.7 (a) or (b) applies. This has quite a dramatic effect on rationality of the bars and spacings. A detailer can always reduce bar diameters and/ or close-up spacing if he or she wishes provided that overall areas of steel are at least maintained.


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Client

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Location

ECBP Typical floor to BS8110


SIMPLIFIED FLAT SLAB DESIGN to BS 8110:2005 Cl 3.7.2.7 (Table 3.12) Originated from RCC93.xls

Date

rmw

v3.0 on CD

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STATUS VALID DESIGN NS Grids on lines

1

2

3

4

EW Grids on lines

A

B

C

D

5 COLUMNS

Nº m mm

X

Y

4 7.500 125

3 7.500 125

slab depth, h Top cover Btm cover

from C/L column

mm mm mm

250 25 25

H

mm

B

mm

1

Internal

Edge

Corner

400 400

400 250

400 250

MATERIALS fy

N/mm²

500

max bar Ø fyv

mm N/mm²

20

mm

1.15

steel

γm

1.5

concrete

20 500

Density

steel class A

23.6

Legend H

kN/m³


C

LOADING Self Wt

kN/m²

5.90

Perim Load

8.85

D

B

H

H

h agg γm

B

37

Ly

N/mm²

Ly

fcu

5

<-- X direction -->

Edge supports are CONTINUOUS

<-- Y direction -->

DIMENSIONS Nº of spans Span, L Edge dist, C

B

LOCATION

Lx

Lx

Lx

kN/m

kN/m²

1.50

kN/m²

7.40

DEFLECTION CONTROL

Imposed qk

kN/m²

2.50

Min % top steel in col strips

0.13

Design load, n

kN/m²

14.36

Same in top of middle strips?

N

Ly

+ Dead Total Dead, gk

3 or more approximately equal spans

A

C

%

Indicative Bending Moments - X Direction (kNm per bay)

Indicative Bending Moments - Y Direction (kNm per bay)

600

600 400

400 200

200

0

0 -200

-200 -400

-400

-600

-600

1

5

MAIN STEEL

A

INTERNAL COLUMN STRIPS

X DIRECTION

b

END SUPPORTS

0.575 END SPANS 3.750 PENULTIMATE SUPPORTS 3.750 INTERIOR SPANS 3.750 INTERIOR SUPPORTS 3.750

D

MIDDLE STRIPS

PERIMETER COLUMN STRIPS

REBAR

b

REBAR

b

REBAR

7H20 @ 75 T1

6.925 3.750 3.750 3.750 3.750

12H16 @ 575 T1

0.413 2.000 2.000 2.000 2.000

4H20 @ 100 T1

13H20 @ 275 B1 13H20 @ 200 : 400 T1 10H20 @ 375 B1 9H20 @ 300 : 600 T1

11H20 @ 325 B1 7H16 @ 525 T1 8H20 @ 450 B1 7H16 @ 525 T1

14H20 @ 125 B1 10H20 @ 150 : 300 T1 10H20 @ 200 B1 7H20 @ 200 : 400 T1

Y DIRECTION END SUPPORTS END SPANS PENULTIMATE SUPPORTS INTERIOR SPANS

0.575 3.750 3.750 3.750

SHEAR (ultimate) INTERNAL PENULTIMATE PENULTIMATE DOUBLE PENULTIMATE SIDE INTERNAL SIDE INTERNAL PENULTIMATE SIDE PENULTIMATE SIDE CORNER

6H20 @ 75 T2 21H20 @ 175 B2 15H20 @ 175 : 350 T2 15H20 @ 250 B2

6.925 3.750 3.750 3.750

Grid

Vt

LINKS

Ref

kN

Arrangement

12H16 @ 575 T2 17H20 @ 200 B2 8H16 @ 450 T2 12H20 @ 300 B2

0.450 2.000 2.000 2.000

4H20 @ 100 T2 15H20 @ 125 B2 10H20 @ 200 : 400 T2 11H20 @ 175 B2

Link Zone Width H x Breadth B

CHECKS

None None 3B etc B2 etc A3 etc

888.5 969.3 478.0

H8 @ 150 EW H10 @ 150 EW H8 @ 150 EW

1788 1826 1670

1788 1826 885

1782 1704 997

941 902 922

None A2 etc B1 etc A1 etc

525.7 525.7 341.1

H10 @ 150 EW H8 @ 150 EW H8 @ 150 EW

BAR Ø > COVER SINGLY REINFORCED BAR SPACING DEFLECTION SHEAR LINKS

OK OK OK OK OK


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RCC93 Flat Slabs (Tables)/ DETAIL! Project


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SIMPLIFIED FLAT SLAB DESIGN to BS 8110:2005 Cl 3.7.2.7 (Table 3.12) Originated from RCC93.xls v3.0 on CD

Date

rmw Checked

Revision

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© 2006 TCC

Page

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DETAILED CALCULATIONS

BS 8110 Reference

GENERAL

internal hc

0.451

m

edge hc

0.357

m

corner hc

Lx

7.500

m

Ly

7.500

m

Min As

0.357 325

m

3.7.1.4

mm²/m

3.7.1.1

MAIN STEEL - X DIRECTION END

END

PENULTIMATE

INTERIOR

INTERIOR

SUPPORTS

SPANS

SUPPORTS

SPANS

SUPPORTS

F

807.8

807.8

807.8

0.15Fhc

43.23

54.69

54.69

Total Mu

kNm

147.5

454.4

466.3

381.7

327.0

3.7.2.7

INTERNAL COLUMN STRIPS m

0.575

3.750

3.750

3.750

3.750

figs 3.12&3.13

Mu

b

kNm

147.5

249.9

349.7

209.9

245.2

3.7.2.10

d

mm

215

215

215

215

215

K'

0.156

0.156

0.156

0.156

0.156

3.4.4.4

K

0.150

0.039

0.055

0.033

0.038

3.4.4.4

z

mm

169.6

204.3

201.1

204.3

204.3

3.4.4.4

As

mm²

2001

2814

4001

2364

2761

3.4.4.4

As shear

mm²

365

Def enhancement

1767 1.405

0 1.282

As min

mm²

2001

3954

4001

3031

2761

Ø

mm

20

20

20

20

20

No bars

No

7

13

13

10

9

@

mm

75

275

200

375

300

&@

mm

~

~

400

~

600

As prov

mm²

2199

4084

4084

3142

2827

table 3.25

3.7.3.1

= mm²/m

3825

1089

1089

838

754

=

1.779

0.507

0.507

0.390

0.351

303.3

229.7

408.1

250.8

406.9

140

401

226

645

327

3.12.11.2.7

(b)

(b)

(b)

(a)

(b)

3.12.11.2.7

%

fs N/mm² Max S

mm

subclause

Eqn 8

MIDDLE STRIPS m

6.925

3.750

3.750

3.750

3.750

Mu

b

kNm

36.9

204.5

116.6

171.7

81.7

d

mm

217

215

217

215

217

figs 3.12&3.13 3.7.2.10

K'

0.156

0.156

0.156

0.156

0.156

3.4.4.4

K

0.003

0.032

0.018

0.027

0.013

3.4.4.4

z

mm

206.2

204.3

206.2

204.3

206.2

3.4.4.4

As

mm²

411

2302

1301

1934

912

3.4.4.4

table 3.25

Def enhancement

1.405

1.282

As min

mm²

2251

3235

1301

2480

1219

Ø

mm

16

20

16

20

16

No bars

No

12

11

7

8

7

@

mm

575

325

525

450

525

As prov

mm²

1407

2413

3456

1407

2513

= mm²/m

348

922

375

670

375

=

0.161

0.429

0.173

0.312

0.173

56.8

222.1

385.1

256.5

270.0

651

645

651

645

651

3.12.11.2.7

(a)

(a)

(a)

(a)

(a)

3.12.11.2.7

%

fs N/mm² Max S

mm

subclause

Eqn 8

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RCC93 Flat Slabs (Tables).xls RCC93 Flat Slabs (Tables)/ DETAIL! Project


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Page

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MAIN STEEL - X DIRECTION, continued END

END

PENULTIMATE

INTERIOR

INTERIOR

BS 8110

SUPPORTS

SPANS

SUPPORTS

SPANS

SUPPORTS

Reference


F 0.15Fhc Mu kNm b m d mm K' K z mm As mm² As shear mm² Def enhancement As min mm² Ø mm No bars No @ mm & @ mm As prov mm² = mm²/m % = fs N/mm² Max S mm subclause

510.3 27.31 93.2 0.413 215 0.156 0.132 176.6 1214 336 1214 20 4 100 ~ 1257 3046 1.417 322.0 140 (b)

184.8 2.000 215 0.156 0.054 201.2 2112

510.3 27.31 243.5 2.000 215 0.156 0.071 196.4 2852 2290

155.2 2.000 215 0.156 0.045 203.5 1754

1.956 4132 20 14 125 ~ 4398 2199 1.023 160.1 285 (b)

2852 20 10 150 300 3142 1571 0.731 378.3 169 (b)

1.662 2914 20 10 200 ~ 3142 1571 0.731 186.1 343 (b)

510.3 27.31 172.9 2.000 215 0.156 0.051 202.2 1967 1448 1967 20 7 200 400 2199 1100 0.511 372.7 245 (b)

3.7.2.10 figs 3.12&3.13

3.4.4.4 3.4.4.4 3.4.4.4 3.4.4.4

table 3.25

3.7.3.1

Eqn 8 3.12.11.2.7 3.12.11.2.7

MAIN STEEL - Y DIRECTION

Total Mu

kNm

END

END

PENULTIMATE

INTERIOR

INTERIOR

SUPPORTS

SPANS

SUPPORTS

SPANS

SUPPORTS

121.3

454.4

466.3

381.7

327.0

0.575 121.3 195 0.156 0.150 153.8 1815 380

3.750 249.9 195 0.156 0.047 184.1 3121

3.750 349.7 195 0.156 0.066 179.4 4484 1797

3.750 209.9 195 0.156 0.040 185.3 2606

3.750 245.2 195 0.156 0.046 184.3 3060 1130

figs 3.12&3.13

INTERNAL COLUMN STRIPS

b m Mu kNm d mm K' K z mm As mm² As shear mm² Def enhancement As min mm² Ø mm No bars No @ mm & @ mm As prov mm² = mm²/m % = fs N/mm² Max S mm subclause

3.7.2.10

3.4.4.4 3.4.4.4 3.4.4.4 3.4.4.4

1815 20 6 75 ~ 1885 3278 1.681 320.9 140

2.044 6379 20 21 175 ~ 6597 1759 0.902 157.7 328

4484 20 15 175 350 4712 1257 0.644 396.5 183

1.708 4450 20 15 250 ~ 4712 1257 0.644 184.4 393

3060 20 10 275 550 3142 838 0.430 405.8 268

table 3.25

(b)

(b)

(b)

(b)

(b)

3.12.11.2.7

3.7.3.1

Eqn 8 3.12.11.2.7

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Page

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MAIN STEEL - Y DIRECTION, continued END

END

PENULTIMATE

INTERIOR

INTERIOR

BS 8110

SUPPORTS

SPANS

SUPPORTS

SPANS

SUPPORTS

Reference

6.925 30.3 197 0.156 0.003 187.2 373

3.750 204.5 195 0.156 0.039 185.3 2539 2.044 5188 20 17 200 5341 1424 0.730 158.4 403 (b)

3.750 116.6 197 0.156 0.022 187.2 1433

3.750 171.7 195 0.156 0.033 185.3 2132 1.708 3641 20 12 300 3770 1005 0.516 188.5 585 (a)

3.750 81.7 197 0.156 0.015 187.2 1005

figs 3.12&3.13

1219 16 7 525 1407 375 0.191 297.4 591 (a)

table 3.25

MIDDLE STRIPS

b m Mu kNm d mm K' K z mm As mm² Def enhancement As min mm² Ø mm No bars No @ mm As prov mm² = mm²/m % = fs N/mm² Max S mm subclause

2251 16 12 575 2413 348 0.177 51.5 591 (a)

1433 16 8 450 1608 429 0.218 371.1 591 (a)

3.7.2.10

3.4.4.4 3.4.4.4 3.4.4.4 3.4.4.4

Eqn 8 3.12.11.2.7 3.12.11.2.7


F 0.15Fhc Mu kNm b m d mm K' K z mm As mm² As shear mm² Def enhancement As min mm² Ø mm No bars No @ mm & @ mm As prov mm² = mm²/m = % fs N/mm² Max S mm subclause

510.3 27.31 93.2 0.450 215 0.156 0.121 180.6 1187 359

184.8 2.000 215 0.156 0.054 201.2 2112

510.3 27.31 243.5 2.000 215 0.156 0.071 196.4 2852 1811

155.2 2.000 215 0.156 0.045 203.5 1754

510.3 27.31 172.9 2.000 215 0.156 0.051 202.2 1967 0

3.7.2.10 figs 3.12&3.13

3.4.4.4 3.4.4.4 3.4.4.4 3.4.4.4

1187 20 4 100 ~ 1257 2793 1.299 314.9 140

2.170 4584 20 15 125 ~ 4712 2356 1.096 149.4 285

2852 20 10 200 400 3142 1571 0.731 378.3 169

1.801 3159 20 11 175 ~ 3456 1728 0.804 169.2 343

1967 20 7 275 550 2199 1100 0.511 372.7 245

table 3.25

(b)

(b)

(b)

(b)

(b)

3.12.11.2.7

3.7.3.1

Eqn 8 3.12.11.2.7

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DEFLECTION - X DIRECTION

As req mm² As prov mm² fs N/mm² K ave As' prov mm² % 100As'/bd Comp Mod Tens Mod Perm L/d Actual L/d As enhanced

PERIMETER END SPANS

INTERNAL END SPANS

PERIMETER INTERIOR SPANS

INTERNAL INTERIOR SPANS

3264 6126 177.6 0.043 670 0.080 1.026 1.547 37.15 34.88 95.6%

5116 7540 226.2 0.035 1257 0.078 1.025 1.495 35.88 34.88 40.5%

2721 4398 206.2 0.036 670 0.080 1.026 1.555 37.33 34.88 66.2%

4298 5655 253.3 0.030 1257 0.078 1.025 1.482 35.55 34.88 28.2%

PERIMETER END SPANS

INTERNAL END SPANS

PERIMETER INTERIOR SPANS

INTERNAL INTERIOR SPANS

3382 7383 152.7 0.047 670 0.080 1.026 1.579 37.92 34.88 117.0%

5660 11938 158.0 0.043 1257 0.086 1.028 1.616 38.87 38.46 104.4%

2820 5341 176.0 0.039 670 0.080 1.026 1.618 38.84 34.88 80.1%

4739 8482 186.2 0.036 1257 0.086 1.028 1.633 39.27 38.46 70.8%

BS 8110 Reference

Eqn 8

Eqn 9 Eqn 7 3.4.6.1+3.7.8

DEFLECTION - Y DIRECTION

As req mm² As prov mm² fs N/mm² K ave As' prov mm² % 100As'/bd Comp Mod Tens Mod Perm L/d Actual L/d As enhanced PUNCHING SHEAR

Vt Veff/Vt ave d ave As

kN kN mm %

Eqn 8

Eqn 9 Eqn 7 3.4.6.1+3.7.8

INTERNAL None

PENULT None3B etc

DOUBLE PENULT B2 etc

SIDE INTERNAL A3 etc

SIDE INTERNAL None

0.0 1.15 205.0 0.390

888.5 1.15 205.0 0.468

969.3 1.15 205.0 0.575

478.0 1.40 205.0 1.096

0.0 1.40 215.0 1.145

1015 1015 1600 0.000 0.0 4060 0.000 0.622 No

1015 1015 1600 3.107 1004.8 4060 1.207 0.661 Yes

1015 1015 1600 3.390 1097.7 4060 1.319 0.708 Yes

633 865 900 3.616 643.1 2130 1.473 0.878 Yes

648 895 900 0.000 0.0 2190 0.000 0.880 No

0 0 0 0 0 0

150 1762 6070 8 41 2061

150 2059 6070 10 41 3220

150 770 3235 8 22 1106

0 0 0 0 0 0

0 0 0

1788 1788 2

1825 1825 2

1670 885 1

0 0 0

table 3.13 3.7.6.3

at 1.5d from column face

H mm B mm u 0 mm v max N/mm² V kN u mm v N/mm² vc N/mm² Links ?

3.7.7.6 3.7.7.6 Eqn 27

3.7.7.6

Eqn 28 table 3.9

Links at 0.5d & 1.25d

Sv mm EW Asv req mm² Total u mm Ø mm Number Asv prov mm² solve for H&B crit ( v = vc )

H crit mm B crit mm Additional 0.75d perimeters

3.7.7.6 3.7.7.5

3.7.7.6

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kN kN mm %

Checked

Page

CORNER A1 etc

SIDE PENULT A2 etc

SIDE PENULT B1 etc

341.1 1.25 215.0 1.358

525.7 1.40 205.0 1.206

525.7 1.40 215.0 1.255

648 573 575 3.435 400.8 1220 1.528 0.931 Yes

633 865 900 3.979 710.0 2130 1.626 0.906 Yes

648 895 900 3.793 708.9 2190 1.506 0.907 Yes

150 417 1902.5 8 13 653

150 1166 3235 10 22 1728

150 794 3305 8 23 1156

996 921 2

1782 941 2

1704 902 1

172 128


chg

© 2006 TCC

PUNCHING SHEAR, continued

Vt Veff/Vt ave d ave As

Date

rmw

Job No

-

R68 BS 8110 Reference

table 3.13 3.7.6.3

at 1.5d from column

H mm B mm u 0 mm v max N/mm² V kN u mm v N/mm² vc N/mm² Links ?

3.7.7.6 3.7.7.6

3.7.7.6

Eqn 28 table 3.9

Links at 0.5d & 1.25d

Sv mm EW Asv req mm² Total u mm Ø mm Number Asv prov mm² solve for H&B crit ( v = vc )

H crit mm B crit mm Additional 0.75d perimeters

3.7.7.6 3.7.7.5

3.7.7.6

172


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RCC94 Two-way Slabs (Tables).xls

RCC94 Two-way Slabs (Tables).xls This spreadsheet designs restrained two-way solid slabs in accordance with BS 8110: Part 1 using moment and shear factors from equations 14 to 20 (i.e. Tables 3.14 and 3.15). Input is required on the first two sheets.


MAIN! This single sheet consists of the input and main output. In itself it should prove adequate for the design of restrained two-way slabs. Inputs are underlined and most should be self-explanatory. Self-weight, moment and shear factors are calculated automatically. The use of the factors is also governed by Clause 3.5.3.5 (similar loads on adjacent spans, similar spans adjacent). Where the relevant conditions are not met, users are directed towards Clause 3.5.3.6 or alternative methods of analysis (e.g. sub-frame analysis). Whilst ultimate reactions to beams are given, shear per se is not checked as it is very rarely critical. The dimension ly must be greater than lx : bays where lx> ly are invalid. It is recognised that B1 can be parallel to ly and the user should specify in which layers the top and bottom reinforcement are located (see D33 and H33). In line 32 the user is asked to specify the diameter of reinforcement to be used. This reinforcement should be provided at the required centres in accordance with Clause 3.5.3.5 (1) to (7) (middle strips and column strips, torsion reinforcement at corners where an edge or edges is/ are discontinuous). The spreadsheet highlights whether additional reinforcement for torsion is required or not. As noted under Deflection, the area of steel required, Asreq , may be automatically increased in order to reduce service stress, fs , and increase modification factors to satisfy deflection criteria. An approximate reinforcement density is given. This is approximate only and excludes supporting beams, trimming to holes, etc.

WEIGHT! Weight! gives an estimate of the amount of reinforcement required in a slab. Simplified curtailment rules, as defined in Clause 3.12, are used to determine lengths of bars. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation, the effects of holes, etc, etc. To the right of the sheet are calculations of length, etc. Support widths are required as input as they affect curtailments and lengths.

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174

174


17/07/2006 17:10:27

RCC95 Continuous Beams (Tables).xls

RCC95 Continuous Beams (Tables).xls The spreadsheet designs multiple-span rectangular or flanged beams. It uses design ultimate bending moment and shear force factors from Table 3.5 of BS 8110: Part 1. As such its use should be limited, as defined by Clause 3.4.3, to where:

Graf!

■ Qk >⎜ Gk

Notes!

■ Substantially uniform loads over three or more spans ■ Variations in span < 15% lmax.

This sheet provides data for the charts in MAIN! and is not intended for formal printing.


The intention is to provide the design of a simple continuous beam on one sheet of A4.

MAIN! The input requirements are self-explanatory. Answering “Y” to Support in alt layer will incur additional cover to top bars at supports (of the same size as those being designed at that location) to allow for beams in the other direction. Users should ensure effective depths, d, are correct (see DETAIL!D15, etc.). The choice between rectangular, L or T beam is made via a combobox to the right hand side. When considering span reinforcement, the spreadsheet will, where necessary, automatically increase reinforcement in order to lower service stresses and enhance allowable span to depth ratios. The diagrams for loading and for bending moment are indicative only (the moment factors in Table 3.5 do not give rise to a moment envelope).

DETAIL! For first time users and young engineers, further detail of the calculations undertaken is given on the sheet named DETAIL!, pages 2 and 3 of the print-out.

Weight! This sheet estimates the weight of reinforcement in the beam when designed according to normal curtailment rules as defined in BS 8110. The estimate is repeated at the bottom of MAIN! at O62. Workings are shown on the right hand side of the sheet. The estimate may be printed out using File/print or the print button on the normal toolbar. It should be recognised that different engineers’ and detailers’ interpretations of these clauses, different project circumstances and requirements will all have a bearing on actual quantities of reinforcement used.

175


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RCC95 Continuous Beams (Tables)/ MAIN! Project


Client Location

Advisory Group D&D: Edge beam Grid 1 from A to J CONTINUOUS CONCRETE BEAM DESIGN to BS 8110:2005 Table 3.5 Originated from RCC95.xls

LOCATION

Supports: from grid

v3.0 on CD

A


Date

rmw Checked

Revision

176 132 Job No

-

chg

© 2006 TCC

to grid

Page

12-Apr-2006

R68

STATUS

J

VALID DESIGN DIMENSIONS Nº of spans Max Span depth, h bw hf bf

Nº m mm mm mm mm

5 5.00 350 300 175 650

MATERIALS fcu N/mm² fyl N/mm² fyv N/mm² h agg mm

Shape L BEAM Top cover mm 40 Bottom cover mm 40 Side cover mm 40 Support steel in alt layer ? Y

40 500 500 20

γm = 1.50 γm = 1.15 steel class A Density kN/m³ 23.6 (Normal weight concrete)

100 50

LOADING

0

Self Wt + Dead Total Dead, gk Imposed qk Design load, n =

kN/m kN/m kN/m kN/m kN/m

1.2 10.9 12.1 5.0 25.0

BENDING

-50 -100

A

END SUPPORTS

M d bf As As'

kNm mm mm mm² mm²

J Geometry and Loading

0.0 276 300 0 0

(A & J)

A

J Indicative Bending Moment Diagram

END SPANS

FIRST INT SUPPORTS

INTERIOR SPANS

INTERNAL SUPPORTS

BS8110 Reference

56.2 290 650 470 0

68.7 270 300 648 0

43.7 294 650 360 0

50.0 270 300 457 0

Table 3.5 3.4.1.5 3.4.4.4 3.4.4.4

Deflection

L/d Max Actual L/d

36.46 17.24

37.98 17.01

OK

3.4.6.3

OK

3.4.6.1

Tension reinforcement

Ø No As prov =

mm² %

16 2 Top 402 0.49

20 2 Btm 628 0.72

20 3 Top 942 1.16

12 4 Btm 452 0.51

20 2 Top 628 0.78

16 2 Btm 402 0.49

12 2 Top 226 0.26

12 2 Btm 226 0.28

12 2 Top 226 0.26

12 2 Btm 226 0.28

OUTER SUPT

FIRST INT SUPT

INT SUPT

NOMINAL

56.2 0.646 0.570 10 2 200

75.0 0.926 0.858 10 2 200

68.7 0.849 0.749 10 2 200

~ ~ ~ 10 2 200

END SUPPORTS 2 H16 T Nominal B

END SPANS 2 H12 T 2 H20 B

FIRST INT SUPPORTS 3 H20 T Nominal B

INTERNAL SPANS 2 H12 T 4 H12 B

INTERNAL SUPPORTS 2 H20 T Nominal B

2 H10 @ 200

2 H10 @ 200 for 600

2 H10 @ 200

2 H10 @ 200 for 600

BAR Ø < COVER

SINGLE LAYERS

BAR SPACING

DEFLECTION

SHEAR LINKS

GLOBAL STATUS

OK

OK

OK

OK

OK

VALID DESIGN

Compression reinforcement

Ø No As' prov =

mm² %

SHEAR V kN/m v N/mm² vc N/mm² Link Ø mm Legs No @ mm

Table 3.5 Eqn 3 Table 3.8

OUTPUT/SUMMARY

PROVIDE Main reinforcement

Links 2 H10 @ 200 for 800

from CL of support

CHECKS

176


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RCC95 Continuous Beams (Tables).xls RCC95 Continuous Beams (Tables)/ DETAILS!

The Concrete Centre

Project


Client

Advisory Group

Location

D&D: Edge beam Grid 1 from A to J

Made by

CONTINUOUS CONCRETE BEAM DESIGN to BS 8110:2005 Table 3.5 Originated from RCC95.xls v3.0 on CD

Revision

chg

Gk = 60.70

Page

12-Apr-2006

Checked

© 2006 TCC

DETAILED CALCULATIONS

Date

rmw

-

Qk = 25.00

177 133 Job No

F = 124.98

R68 kN

MAIN STEEL

Factor M kNm d mm bf mm K' Web Mres kNm Flange Mres kNm K z mm x mm d' mm net fsc N/mm² Excess M kNm As' req mm² fst N/mm² As req mm² bw/b Min % Min As

END SUPPORTS

END SPANS

FIRST INT SUPPORTS

INTERIOR SPANS

INTERNAL SUPPORTS

BS 8110 Reference

0.00 0.0 276 300 0.1558 142.4 --0.0000 262.2 30.7 78 0.0 0.0 0 434.8 0 --0.20% 210

0.09 56.2 290 650 0.1558 157.2 411.5 0.0257 275.5 32.2 56 0.0 0.0 0 434.8 470 0.4615 0.13% 137

0.11 68.7 270 300 0.1558 136.3 --0.0786 243.9 58.0 76 0.0 0.0 0 434.8 648 --0.20% 210

0.07 43.7 294 650 0.1558 161.6 419.7 0.0195 279.3 32.7 56 0.0 0.0 0 434.8 360 0.4615 0.13% 137

0.08 50.0 270 300 0.1558 136.3 --0.0571 251.6 40.9 68 0.0 0.0 0 434.8 457 --0.20% 210

Table 3.5

0.0

249.1 22.00 1.535 1.080 36.455 17.241

229.3

265.4 22.00 1.600 1.079 37.982 17.007

242.4

-=-

3.4.1.5 Fig 3.3 -=-=3.4.4.4 -=-=-

Fig 3.3

Fig 3.3

Table 3.25

DEFLECTION fs N/mm² Base ratio Tens Mod Comp Mod Perm L/d Actual L/d TENSION STEEL As Ø No As prov Clear dist Min S Max S

mm² mm mm² mm

ok ok

210 16 2 402 168.0 25.0 300.0

ok

ok ok

470 20 2 628 160.0 25.0 188.7

ok

ok

ok ok

648 20 3 942 70.0 25.0 205.0

ok

ok ok

360 12 4 452 50.7 25.0 177.1

Eqn 8 3.4.6.3/4 Table 3.10 Table 3.11 3.4.6.3

ok

3.4.6.1

ok

ok ok

457 20 2 628 160.0 25.0 193.9

between bars 3.12.11.1 Table 3.28 3.12.11.2.4

COMPRESSION STEEL Required mm² Ø ok No As' prov mm² ok =%

314 16 2 402 0.486

ok

ok

188 12 2 226 0.260

ok

ok

188 12 2 226 0.279

ok

ok

188 12 2 226 0.256

ok

ok

136 12 2 226 0.279

Table 3.25

177


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RCC95 Continuous Beams (Tables)/ DETAILS!

Project


Client

Advisory Group

Location

D&D: Edge beam Grid 1 from A to J


CONTINUOUS CONCRETE BEAM DESIGN to BS 8110:2005 Table 3.5 Originated from RCC95.xls v3.0 on CD

Date

rmw Checked

Revision

chg

© 2006 TCC

Page

12-Apr-2006

178 134 Job No

-

R68

SHEAR OUTER SUPPORT

FIRST INT SUPPORT

INTERNAL SUPPORT

NOMINAL

0.45 56.2

0.60 75.0

0.55 68.7

~ ~

Table 3.5

v N/mm²

0.646

0.926

0.849

~

Eqn 3

vc N/mm²

0.570

0.858

0.749

~

Table 3.8

120.0 10 2 218 200 0 800 0.0 0.0

120.0 10 2 203 200 0 600 90.0 0.0

120.0 10 2 203 200 0 600 0.0 0.0

120.0 10 2 218 200 ----0.0 0.0

Table 3.7

Factor V

kN

(v-vc)bv N/mm Link Ø ok Legs ok @ mm Adjust to mm for mm Adjust to mm As Dist ok As' Dist ok

ok ok

ok ok

ok ok

ok ok

ok ok

ok ok

-=-

3.12.7.1

3.12.7.1

from cl of supt 3.4.5.5 3.12.7.2

178


17/07/2006 17:10:39

Spreadsheets to Eurocode 2


179


17/07/2006 17:10:42

180


17/07/2006 17:10:43

General notes to Eurocode 2 versions

General notes to Eurocode 2 versions The Spreadsheets and Eurocode 2 The layout and workings of the spreadsheets to Eurocode 2 are in line with those to BS 8110 outlined in the previous section, Spreadsheets to BS 8110. The Introduction and General notes are common to the use of all spreadsheets in this publication. Descriptions of the spreadsheets to Eurocode 2 are given in the following pages.

should be available in 2006. It should be noted that EN 1992 – 1 –1 was calibrated using the contemporary BS standards for loading, which might therefore be used satisfactorily in conjunction with EN 1992 –1 –1 pending the final publication of BS EN 1991 series of standards. ■ BS EN197, cement and EN 206, concrete and its BS derivative

BS8500. These standards have been in use for some time in the UK. ■ BS EN10080 (steel for the reinforcement of concrete), BS

The spreadsheets are in accordance with Parts 1-1 and 1-2 of Eurocode 2 and their respective UK National Annexes (NAs). Parts 1-1 and 1-2 of Eurocode 2 (Eurocode 2: Design of concrete structures, Part 1-1 General rules and rules for buildings, BS EN 1992-1-1 and Eurocode 2: Design of concrete structures, Part 1-2 General rules – Structural fire design BS EN 1992-1-2) were published in December 2004. Each Eurocode has a National Annex. These specifiy the values of Nationally Determined Parameters (NDPs : factors relating to safety and UK conditions, requirements for durability, etc. e.g. values of cover, γm, αcc, k etc.) to be used within the Eurocodes in each country. The values of the NPDs used are documented on a separate sheet within each spreadsheet and allow for different values to be used, for instance when the project is outside the UK. The equivalents of these values are hidden away in BS 8110 and indeed in the BS 8110 spreadsheets. The UK National Annexes (NAs) that confirm or change Nationally Determined Parameters within Eurocode 2 were published in December 2005 Eurocode 2 will ultimately supersede all UK codes dealing with the design of concrete structures. All conflicting British Standards are due to be withdrawn in 2010. The spreadsheets have called for some interpretation of both Eurocodes and their NAs.

Implementation of Eurocode 2 BS EN 1992-1-1 and BS EN 1992-1-2 were published by BSI in December 2004. Their National Annexes were published in December 2005. BS EN 1992 is expected to be used generally in conjunction with other Eurocodes (and their UK National Annexes) for loading etc and other European Standards (ENs) for materials and execution. During the early stages of the implementation of BS EN 1992, all the related codes, standards and their UK National Annexes may not be available in their final form. Nonetheless, as PD6687[31] points out, EN 1992 –1 – 1 can still be used to design structures using: ■ BS EN 1990 Basis of structural design &. UK National Annex ■ BS EN 1991 series, Actions. Almost all UK National Annexes

4449 (BS 4449: 2005, reinforcement), BS4482 (BS 4482: 2005, fabric), BS 4483 (BS 4483: 2005, fabric), and BS 8666 (BS 8666: 2005, scheduling). These standards were published in late 2005 and came into effect on 1 January 2006. One of the fundamental assumptions in EC2 is that the requirements of ENV 13670 for execution and workmanship are complied with. This raises a difficulty in the UK, as EN 13670 (Execution of concrete structures) is some way off. However for the UK, the provisions of the National Structural Concrete Specification (NSCS) [ref 32] are considered equivalent to those in ENV 13670 for tolerance class 1. Other standards are in various states of readiness and in areas not specifically mentioned above, the designers might consider using current UK practice or current British Standards but they should satisfy themselves that they are compatible with BS EN 1992 and that the resulting reliability would be acceptable. For instance the spreadsheets for pad foundations, TCC 81 uses current UK practice for sizing (allowable under EN 1997) rather than the full limit state approach. In the UK, the process of converting from BS8110 to Eurocode might be perceived as being a large barrier. As with any change, there will be opportunities and threats. Eurocode 2 will be adopted only where there is commercial advantage in doing so but from calibration studies it would appear that there are significant gains to be made by adopting it in the design of building structures. The authors are confident that in the long run Eurocode 2 will be seen as being a very good standard allowing consistent safety across materials and opportunity for greater economy and even greater flair in concrete design and construction.

Notes regarding Eurocode2 In his comparison of design requirements in Eurocode 2 and BS 8110, Narayanan(24) gave the following outline description of Eurocode 2.

General layout BS EN 1992-1-1(1) and BS EN 1992-1-2 are broadly comparable to BS 8110: Parts 1 and 2. Eurocode 2 comprises principles and rules of application. Principles are general statements, 181


17/07/2006 17:10:44

definitions, other requirements, and analytical models for which no alternative is permitted. The rules of application are generally recognised rules that follow the principles and satisfy their requirements. Eurocode 2 is generally laid out to give advice on the basis of phenomena (e.g. bending, shear etc) rather than by member types as in BS 8110 (e.g. beams, slabs, columns etc). The Code does not provide derived formulae (e.g. for bending), only the details of the stress block are expressed). This is the traditional European approach.

Reinforcement Eurocode 2 is applicable for ribbed reinforcement with characteristic yield strengths of 400 to 600 MPa. Plain bar and mild steel reinforcement are, strictly, outside the Code. The characteristic yield strength of reinforcing steel to BS 4449:2005 will be 500 MPa. According to the UK National Annex, the partial factor for steel reinforcement is 1.15

Cover

The UK Nationally Determined Parameters (NDPs) that are used in the spreadsheets are taken from the relevant National Annex (NA) and are shown in a separate sheet within the spreadsheets.

Minimum concrete cover, cmin, is related to bond strength, durability and fire resistance. In addition to the minimum cover an allowance for deviations due to variations in execution (construction) should be allowed for in design. Eurocode 2 recommends that, for concrete cast against formwork, this allowance,- ∆cdev, is taken as 10 mm, unless the construction is subject to a quality assurance system in which case it could be reduced to 5 mm or even 0 mm where non-conforming members are rejected (e.g. in a precast yard). cmin + ∆cdev = nominal cover

Units for stress are mega Pascals, MPa (1 MPa = 1 N/mm2 ) Terminology employed will be generally familiar to UK engineers, although there are some new words. Thus ‘loads’ are referred to as ‘actions’; ‘bending moments’ and ‘shear forces’ are called ‘internal forces and moments’; ‘superimposed loads’ are ‘variable actions’; and ‘self-weight’ and ‘dead loads’ are referred to as ‘permanent actions’.

It is recommended that the nominal cover is clearly stated on the drawings.

Concrete strength

Cover for durability is governed by BS 8500. Guidance on the use of BS8500 is given in How to use BS8500 with BS 8110 - copy available from www.concretecentre.com.

Concrete strength in Eurocode 2 refers to the cylinder strength (fck) and cube strength (fcu). This fck/fcu notation is used throughout Eurocode 2. However, design is based on characteristic cylinder strengths not cube strengths and the spreadsheets refer to fck only. The relationship between cylinder and cube strengths is shown below in Table 5 along with approximate moduli of elasticity from Eurocode 2.

Fire resistance Eurocode 2, Part 1–2: Structural fire design[13], gives guidance on design for fire resistance of concrete structures. Although much of the Code is devoted to fire engineering methods, the design for fire resistance may still be carried out by referring to tables for minimum axis distances and dimensions for various elements. The axis distance is measured from the surface to the centre of the bar and is treated as a mean to be obtained during execution.

Eurocode 2 and the spreadsheets permit much higher strengths of concrete to be used than currently. The maximum characteristic cylinder strength fck permitted is 90N/mm2. Because the characteristics of higher strength concrete are different, some expressions in the Code are adjusted for classes above C50/60. Supplies of these high strength concretes should be assured before using them in design.

Axis distances and dimensions are given in section 5 of Part 1–2. Further advice on using the tabular methods is given in How to design concrete structures using Eurocode 2: Getting started [34].

The spreadsheets are unsuitable for the design of lightweight concrete.

Table 5 Relationship between cylinder and cube stregths

Property

Strength class C20/25

C25/30

C30/37

C35/40

C40/50

C45/50

C50/60

fck (cylinder)

20

25

30

35

40

45

50

fck (cube)

25

30

37

40

50

50

60

Ecm

29

30.5

32

33.5

35

36

37

‡ Based on the outline description of Eurocode 2 in Comparison of design requirements in Eurocode 2 and BS 8110, Narayanan( 24)

182


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General notes to Eurocode 2 versions Load combinations

Actions

BS EN1990 allows the designer (of UK structures) to use either Expression (6.10) or the less favourable of Exp (6.10a) or Exp (6.10b). For members supporting one variable action the combination 1.25Gk + 1.5Qk may be used. This combination is derived from Exp (6.10b) and can be used provided that the permanent actions (Gk) are not greater than 4.5 times the variable actions (Qk) and the structure is not used for storage.

The most notable difference between UK Standards and Eurocode 1 is the bulk density of reinforced concrete, which has been increased to 25 kN/m3.

Less economically designers may choose to use 1.35 Gk + 1.5 Qk (derived from Exp (6.10)). EN 1990 requires that actions should be checked using both γG.sup (=1.25 or 1.35) and γG.inf (= 1.0). γG.sup (i.e. 1.25 or 1.35) will always be the more onerous when designing for peak moments, but greater hogging moments in spans often occur when γG.inf is used. For this reason, a macro is employed in a number of spreadsheets to change γG to its lower value (1.0), record the results, then set it back to the higher value again. The larger value of the tensile force in the reinforcement, Ftd, from both sets of results is then used for the design of top steel in spans. For the serviceability limit states of deflection and cracking, the quasi-permanent load case is used. Generally a quasi-permanent load of Gk + Ψ2Qk is used where Ψ2 is a factor dependant on the use of the structure (see BS EN 1990 A1.2.2 and UK National Annex).

Load cases For building structures, the UK NA to Eurocode 2, Part 1–1 allows either of the following sets of load arrangements to be used: 1. Alternate or adjacent spans loaded 2. All or alternate spans loaded The spreadsheets use the all-or-alternate-spans-loaded case by default. Users may switch to 1, the alternate-or-adjacent-spansloaded by changing the setting in Notes!

Simplified arrangements for slabs According to the UK NA, the load arrangements can be simplified for slabs where only the all spans loaded needs to be checked (see Figure 3), provided the following conditions are met: a) In a one-way spanning slab the area of each bay exceeds 30

m2 (a bay means a strip across the full width of a structure bounded on the other sides by lines of support) b) The ratio of the variable action (Qk) to the permanent action

(Gk) does not exceed 1.25 c) The magnitude of the variable action excluding partitions

does not exceed 5 kN/m2.

Analysis Eurocode 2 dictates that the type of analysis should be appropriate to the problem being considered. The following are commonly used: linear elastic analysis, linear elastic analysis with limited redistribution and plastic analysis. Linear analysis may be carried out assuming cross sections are uncracked and remain plane (i.e. may be based on concrete gross sections) and linear stress-strain relationships and the use of mean values of elastic modulus. Linear analysis is the basis of the analyses used in the spreadsheets. In the rigorous spreadsheets the spans are checked at 1/20th points to see whether the section theoretically cracks under load; if so that section remains cracked and cracked section properties are applied and used in the serviceability calculations. (Cracked section properties are used only for the deflection calculations and not for the analysis as the process would become iterative, non-linear and would take a long time to run.) For ULS, the moments derived from elastic analysis may be redistributed to a maximum of 30% where Class B or C reinforcement is used or 20% if Class A reinforcement is used. According to BS8666:2000 reinforcement called up as may be 500 grade Class A, B or C.

Section analysis – Design assumptions The simplified rectangular concrete stress block as shown in Figure 3.5 of BS EN 1992-1-1 has been used throughout the spreadsheets, in conjunction with option B (the horizontal line) on the reinforcement stress/ strain curve (Figure 3.8 of BS EN 1992-1-1). In the case of columns and other members with axial force, these strain distributions have been modified by the imposition of the “hinge point” as shown in Figure 6.1. (of BS EN 1991-1-1). The rectangular stress block option has been chosen because of its’ relative simplicity, thereby making it more straightforward for users to follow the logic used in calculations. The choice of stress block normally makes little difference in the design of slabs and beams, but in column design, slightly higher axial loads may be resisted by employing the recto-parabolic stress block as shown in Figure 3.3 and option (A) in Figure 3.8. These options may be adopted for future versions of TCC12 and TCC51 to TCC54. Lever arm, z is restricted to a maximum of 0.95 x effective depth. This limit is derived from BS 8110 and avoids dangers associated with theoretically over-shallow neutral axis depths. 183


17/07/2006 17:10:48

Analysis & design spreadsheets – Top steel checks in spans Within the spreadsheets for continuous elements, it has been assumed that at least 50% of support reinforcement in beams and slabs will normally extend to a point 0.3L from the centrelines of support. The other 50% is assumed to be curtailed at a point 0.2L from the centrelines of support. However, the element is checked at 0.25L and 0.75L to determine the whether any top steel is required to resist hogging moment. If so the larger amount of top steel required is assumed to be necessary in the span between these two points. The adoption of a shear truss model in Eurocode 2 causes the force in tension reinforcement to be increased above MEd/z. This can be accommodated by using the shift rule to curtail bars at a distance al from where they are no longer required to resist bending moment. The spreadsheets take a slightly different approach by actually `calculating tensile force to be resisted, Ftd, at 0.25L and 0.75L, where Ftd = MEd/Z + ∆Ftd where ∆Ftd = 0.5VEd( cot θ – cot α) where θ = the angle of the compression strut cot α = 0 for vertical reinforcement The spreadsheets determine the values of MED and VEd at 1/20th points for all load combinations, then select those producing the highest value of Ftd. If either MEd or VEd is reversed for a particular combination, the additional tensile force is taken by bottom reinforcement, so the value of ∆Ftd is set to zero.

Shear The ‘variable strut inclination’ method is used in Eurocode 2 for the assessment of the shear capacity of a section. The assumed angle of the concrete compression strut can be altered to give the most economic design. In most cases the angle of the strut may be assumed to be 21.8º (ie where cot θ = 2.5). Angles above 21.8º may prove to be economic where shear loads are high. Further advice can be found in the guide ‘How to design concrete structures using Eurocode 2: Beams [12] in the ‘How to’ series.

rounded at the corners. The formulae are slightly different than those for beam shear. For instance where shear reinforcement is required, the contribution of the concrete resistance in punching shear is recognised (compared to beam shear where it is not).

αcc and shear αcc is a coefficient applied to the compression block that takes into account long-term effects on the compressive strength and unfavourable effects resulting from the way in which load is applied. According to EN 1992-1-1, αcc = 1.0. However, the UK National Annex to BS EN 1992-1-1 makes αcc = 0.85 for flexure and axial load and 1.0 for other phenomena. Generally, the spreadsheets adopt αcc = 1.0 for shear.

Deformation Generally, serviceability checks for deformation may be carried out using ‘deemed to satisfy’ span to effective depth rules that are similar to those in BS 8110. However, if a more detailed check is required, Eurocode 2 gives guidance which varies from the rules in BS 8110 Part 2. More rigorous approaches may be used if required and are covered in the ‘R’ (for Rigorous) series of spreadsheets. The methods employed are described in more detail in Deflections in concrete slabs and beam [30].

Detailing The rules for determining the anchorage and lap lengths are more complex than the simple tables in BS 8110. Eurocode 2 considers the effects of, amongst other things, the position of bars during concreting, the shape of the bar and cover. Designers and detailers are directed to more specialised references for further guidance eg IStructE/Con Soc Detailing Manual [28 ].

Applied shear force (VEd) is compared with three values for the resistance (VRd):VRdc = shear capacity of the concrete alone; VRd.max = shear resistance determined by the capacity of the notional concrete struts VRds = capacity of a section with shear reinforcement. The formula for VRds can be rewritten to give the area of shear reinforcement required per unit length. Asw/s With respect to punching shear, checks are carried at 2d from the face of the column and for a rectangular column, the perimeter is 184


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TCC11 Element Design.xls

TCC11 Element Design.xls TCC11.xls includes sheets for designing ■ Solid slabs ■ Rectangular beams and ■ T beams (and ribbed slabs) for bending ■ Beam shear ■ Columns with axial load and bending about one axis.

TCC11.xls designs elements to Eurocode 2: Part 1: 1992(3). It is assumed that loads, moments, shears, etc, are available for input from hand calculations or from analysis from elsewhere. Spanto-depth ratios and other ‘NDP’ values are taken from the UK National Annex (part of reference 3).

SLAB! This sheet designs a section of solid slab in a single simply supported span, in a continuous end or internal span, at supports or as a cantilever. Workings and references to clause numbers are given to the right hand side of the sheet. Input should be self-explanatory. Terminology may differ from the BS 8110 version: for instance the term δ is the redistribution factor (i.e. 1 – redistribution percentage/100). Concrete cylinder strength, fck, is changed using the combo-box to the right hand side. In spans, the location of the section being designed has a bearing on deflection limitations, and the appropriate location should be chosen from the combo-box to the right hand side. Similarly, the user should choose from the list of usage (dwelling, office/ store, parking etc.), which governs the proportion of imposed load affecting long-term deflection. Eurocode 2 requires the input of the relationship between dead and imposed loading. This is done at cells G9 and G10. When appropriate the sheet will automatically increase amounts of reinforcement in order to lower service stresses and enhance allowable span-to-depth ratios. The ‘cover’ specified at D12 should be the normal cover including the allowance in design for deviation ∆cdev. This allowance is spccified in cell D13 and is used in the checking of allowable maximum bar size.

RECT~BEAM! This sheet designs a rectangular beam in a single simply supported span, in a continuous end or internal span, at supports or as a cantilever. These choices have a bearing on deflection limitations and the user should choose the appropriate location from the combo-box to the right hand side. The user should similarly choose from the list of usage (dwelling, office/ store, parking, etc.), which governs the proportion of imposed load

affecting long-term deflection. This sheet will, where necessary, automatically increase reinforcement in order to lower service stresses and enhance allowable span to depth ratios. Again, input of the relationship between dead and imposed loading is required in cells D12 and D13. ψ2 is the quasi-permanent load factor applied to imposed loads in calculations of deflection. The factors are 0.2 for dwellings, 0.3 for offices, 0.6 for parking areas and 0.0 for snow and wind.

TEE~BEAM! TEE~BEAM! designs T beams and L beams in single simplysupported span, end span, internal span or cantilever locations. Again, these choices have a bearing on deflection limitations and the user should choose the appropriate location from the combo-box to the right hand side. With respect to the effective width of the flange, the user may also choose that the section is considered as a tee- or an inverted L beam. Again usage and whether brittle partitions are present must also be selected. A default value for the width of the flange bf must be input. Tips for values of bf ,max are given in cells J18 and:J19. In the determination of compression steel, where the neutral axis lies below flange, the concrete in web, bw, below the flange has been ignored. In order to calculate the appropriate deflection factor for compression reinforcement, there is a facility to specify the diameter of compression reinforcement. When considering deflection, the spreadsheet will, where necessary, automatically increase span reinforcement in order to lower service stresses and enhance allowable span-to-depth ratios.

SHEAR! This sheet designs beams for shear. Input is (we hope) selfexplanatory. Providing the applied load is fundamentally a UDL, or where the principal load is located further than 2d from the face of the support, Eurocode 2 allows shear to be checked at d from the face of support (as does BS 8110).The value of shear force, VEd, input at G11 can, provided there is diagonal compression and continuity of tension reinforcement for at least 2.5 d from the face of support, be evaluated at d from the face of support (see Clause 6.2.2(6)). Cell H11, requires the relevant ultimate uniformly distributed load to be specified. The sheet designs the links required at the section considered. If the beam loading is considered to be uniformly distributed, the ultimate UDL, n, can be entered to give the distance for which this arrangement is required before reverting to nominal link arrangement. 185


17/07/2006 17:10:52

COLUMN! This spreadsheet designs symmetrically reinforced rectangular columns bent about one axis where both axial load, NEd , and maximum design moment, MEd , are known. It is based on Eurocode 2 Figure 6.1 and 3.5. The spreadsheet iterates x/h to determine where the neutral axis lies. Assuming a value of x allows strains and therefore stresses to be determined using the principles shown in Figure 6.1. From these stresses the area of steel required for the design moment MEd and design axial load can be determined seperately. The neutral axis depth x is adjusted until the areas of steel considering MEd and NEd match. The sheet includes stress and strain diagrams to aid comprehension of the final design. Workings and references are shown to the right hand side of the sheet.

Kϕ = 1 + βϕef where β = 0.35 + (fck/200) – (λ/150) where λ = slenderness ratio l0/i where i = radius of gyration of the uncracked concrete section = h/3.46 for rectangular sections, where h is the depth in the direction under consideration and i = d/4 for circular sections where d is the diameter. ϕef = effective creep coefficient as defined in 5.6.1. lo = effective length of column In columns in an unbraced structures MEd = M02 + M2

Please note that for ‘stocky’ columns i.e. when λ ≤λ lim MEd = M02 = M + eiNEd where M = numerically higher moment from first order analysis ei = lo/400 ≤ (h/30) ≤ 20mm for columns in braced systems NEd = design axial action at ULS.

M02 M

M0e + M2

When λ >λllim, i.e when ‘slender’, the design bending moment in a column in a braced structure is: MEd= Maximum of {M0Ed + M2 ; M02 ; M01 + 0.5 M2} (see figure) where M0Ed = equivalent first order moment including the effect of imperfections (at about mid height) and may be taken as = M0e where M0e = (0.6M02 + 0.4M01) ≥ 0.4 M02 Note: M01 and M02 should have the same sign if they give tension on the same side. Attention should be paid to the sign of the bending moments. M2 = nominal second order moment in slender columns = NEd e2 where NEd = design axial action at ULS e2 = deflection = (1/r)l02/10 where 1/r = curvature = KrKϕ (fyd /(Es0.45d)) where Kr = (nu – n)/(nu – nbal) ≤ 1.0 where nu = 1 + ω where ω = mechanical reinforcement ratio = (As/Ac)(fyd/fcd) as in 5.6.1 above n = NEd/Acfcd as defined in 5.6.1 above; nbal = value of n corresponding to the maximum moment of resistance and may be taken as 0.4 Note: Kr may be derived fom column charts.

e iNE d

M02

M2 = NEd e 2

M01 moments for ‘stocky ’ columns

M02

=

+

First order

M0e + M2

0.5 M2 Additional second order moments for ‘slender columns ’

M01 + 0.5 M2 Total moment diagram for ‘slender columns ’

Moments in slender columns

For simplicity, where three or more bars are required in the top and bottom of the section, it is assumed that a symmetrical arrangement will be required for the side faces (see the argument included within the commentary for the BS 8110 version). COLUMN! assumes that the moment entered has already been adjusted, if necessary, for bi-axial bending. For many side and all corner columns, there is no other choice than to design for bi-axial bending, and the method given in Clause 5.8.9 must be adhered to, i.e.,TCC53.xls or sheets 2 and 3 of TCC51.xls should be used.

Theoretical shortfalls in area of up to 2% are considerer to be acceptable. In theory, negative amounts of reinforcement required can be obtained but these are superseded by requirements for minimum amounts of reinforcement in columns. No adjustment

186


17/07/2006 17:10:54

TCC11 Element Design.xls is made in the area of concrete occupied by reinforcement. Maximum link centres are given in Clause 9.5.2[4]. Column shear should be checked separately, in the event that this is likely to be critical.

INDIRECT! This spreadsheet considers indirect supports, e.g. where one beam is supported by another, to calculate additional legs of links required in the supporting beam.

Refs! This sheet comprises the values for Nationally Determined Parameters that have been used in the spreadsheet. These data reflect the values given in draft UK National Annexes for BS EN 1990, BS EN 1992 -1-1 and BS EN 1992-1-2 Designers should ensure that these data are current when the spreadsheet is used. When using TCC11 for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations.


187


17/07/2006 17:10:57

TCC11 Element Design/ SLAB!

188


17/07/2006 17:10:58

TCC11 Element Design.xls TCC11 Element Design/ RECT~BEAM

Section design to Eurocode 2 (BS EN 1992-1)

RECTANGULAR BEAMS Originated from TCC11.xls, v 1.3 on CD

INPUT

© 2003-2005 TCC

Beam type END SPAN

Location 1st Floor, Span 1

M span h b gk qk 2 =

kNm mm mm mm kN/m kN/m

0.6

370.0 0.85 8000 500 300 25.80 20.00 Shopping

fck fyk Steel class

30 500 A

REBAR

Ø

c = 1.50 s = 1.15 c,dev 10

N/mm² N/mm² COVER

to main bars

Tension 32 42 Comp'n 20 35 Side -42 brittle partitions? YES

OUTPUT 1st Floor, Span 1 . Effective depth, d = 500 - 42 - 32/2 = 442.0 mm Neutral axis, x = [442-(442² -2E6x370x1.5/0.85/300/30)]/0.8 = 272.2 mm (x/d) limit = 0.450 x/d actual = 0.616 > 0.450, x = 198.9 mm Lever arm, z = 442 - 0.4 x 198.9 = 362.4 mm d2 = 35 + 20/2 = 45 mm Gross fsc = 434.8 N/mm² from strain diagram Net fsc = 434.8 - 0.85 x 30 /1.5 = 417.8 N/mm² Excess M = 370 - 294.1 = 75.9 kNm Compession steel, As2 = 75.9E6 /417.8 /(442 - 45) = 457 mm² PROVIDE 2H20 COMPRESSION STEEL = 628 mm² Steel stress, fyd = 434.8 N/mm² from strain diagram ρ = 280 N/mm² Tension steel, As = 294.1E6/362.4/434.8 + 457.5 x 417.8/434.8 = 2306 mm² 9.2.1.1 (1) As min = 1.3 x 300 x 500 = 200 mm² 7.3.2 (1) As crack = 400 x 0.86 x 2.896 x 68.1/500 = 136 mm² . 7.4.2 As def = 2341 mm² PROVIDE 3H32 TENSION STEEL = 2413 mm² DEFLECTION QP M =370 x 37.8 /64.8 = 253.8 kNm s = 280 N/mm² 7.4.2 (2) Modification factor = 310 /280.0 = 1.107 Permissible L/d = 1.107 x 0.875 x 18.967 = 18.37 Actual L/d = 8000 /442 = 18.10 ok

.

189


17/07/2006 17:11:04

TCC11 Element Design/ TEE~BEAM!


SIMPLE TEE & L BEAMS Originated from TCC11.xls, v 1.3 on CD

INPUT

© 2003-2005 TCC

Location 1st Floor, Span 3 to 4

M span h bw bf hf gk qk

kNm

mm mm mm mm mm kN/m kN/m

Beam type END SPAN

275.0 1.00 9000 500 300 840 150 25.80 20.00

fck fyk teel class

30 500 A

N/mm²

REBAR

Ø

COVER

Tension Comp'n Side

25 12 -0.6

35 30 35 Shopping

2 =

c = 1.50 s = 1.15 ǻc,dev 10

N/mm²

brittle partitions? YES OUTPUT 1st Floor, Span 3 to 4 Effective depth, d = 500 - 35 - 25/2 = 452.5 mm Neutral axis, x = [452.5-¥(452.5² -2E6x275x1.5/0.85/300/30)]/0.8 = 56.0 mm (x/d) limit = 0.414 x/d actual = 0.124 ok Lever arm, z = 452.5 - 0.4 x 56.0 = 430.1 > 0.95d = 429.9 mm Tension steel, As = 275.0E6 /429.9 /434.8 = 1471 mm² 9.1.1.1 (1) As min = 1.3 x 300 x 452.5 = 204 mm² 7.3.2 (1) As crack = 400.0 x 0.86 x 2.896 x 87.6 /500 = 175 mm² for deflection, As def = 1893 mm² PROVIDE 4H25 TENSION STEEL = 1963 mm² . Service stress, QP M =275 x 45.8 /64.83 = 160.3 kNm ıs = 202 N/mm² 7.4.2 (2) Modification factor = 310 /201.7 = 1.537 Permissible L/d = 1.537 x 0.638 x 21.005 = 20.59 Actual L/d = 9000 /452.5 = 19.89 ok . . . . ıs = 202 N/mm² . . .

.

190


17/07/2006 17:11:10

TCC11 Element Design.xls TCC11 Element Design/ SHEAR!


BEAM SHEAR Originated from TCC11.xls, v 1.3 on CD

INPUT

Location

fck

N/mm²

fywk

N/mm²

Main Steel

Ø 25 No 2

OUTPUT 6.2.2 (1) equation (6.6) equation (6.9) 6.2.1 (8) 6.2.2 (1) equation (6.2) 9.2.2 (5) equation (6.9) equation (6.7) 9.2.2 (6)

© 2003-2005 TCC

1st Floor, Span 2 at 2E

30 500

c = 1.50

d

bw

s = 1.15

440

300

Link Ø

Legs

Side cover

VEd

n

10

2

30

258.0

64.8

mm

No

mm

kN at face

kN/m

1st Floor, Span 2 at 2E AsL = 982 mm² = 0.744% ν = 0.6(1 - 30/250) = 0.528 . VRd,max = VEd @ d = k= VRd,c = Asw/s (min)= Asw/s (max) = Asw/s = smax,L =

fcd = 20.0 N/mm² cot = 2.50 1 x 300 x 396.0 x 0.528 x 20.0 /2.90 /1000 = 432.6 kN 258 - 64.8 x 0.44 = 229.5 kN 1 + (200 /440) = 1.674 . 0.12 x 1.674 cube root(0.744 x 30) = 74.7 kN 0.08 x 300 /500 x 30 = 0.263 mm 0.5 x 300 /500 x 1.15 x 0.528 x 20.0 = 3.643 mm 229.5E3 /(396.0 x 434.8 x 2.50) = 0.533 > 0.263 330 mm smax,T = 330 mm 9.2.2 (8)

ok

.

ok ok

PROVIDE 2 legs T10 @ 275 Provide for distance of 825 mm from support face then nominal links = 2 legs T10 @ 325

191


17/07/2006 17:11:14

TCC11 Element Design/ COLUMN!

Section design to Eurocode 2 (BS EN 1992-1) SYMMETRICAL RECTANGULAR COLUMN DESIGN MOMENTS ABOUT X AXIS ONLY

COLUMN DESIGN Originated from TCC11.xls, v 1.3 on CD

© 2003-2005 TCC

INPUT

Location Column 2E

fck

35

N/mm²

fyk

500

N/mm²

Axial load, NEd

2507

kN

Moment, MEd

27.0

kNm

Main bar Ø

20

mm

height, h

300 325

mm

Link Ø c =

8 1.50

mm

mm

25

mm

s =

1.15

steel

breadth, b cover (to link )

concrete

CALCULATIONS from MED As = [M - αηfck.b.dc(h/2 - dc/2)] / [(h/2-d2).(σsc+σst).γc] Asc = Ast = As d c = min(h, λx) from NEd As = (N - αηfck.b.dc) / [(σsc - σst).γc] d2 = 43 mm αηfck /γc = 19.8 N/mm² d= 257 mm fyk /γs = 434.8 N/mm² from iteration, neutral axis depth, x = αηfcu.b.dc/γc = Steel comp strain = Steel tens strain = σsc = σst = from M, As =

374.7 1932.1 0.00258 -0.00092 434.8 -183.3 994

dc =

mm

299.7

mm

kN

N/mm² N/mm² mm²

(Comp. stress in reinf.) (Tensile stress in reinf.) from N, As = 994

415 net -163 net mm²

OK

OUTPUT Column 2E Requires 994mm² T&B:Links : -

PROVIDE 12T20 (ie 4T20 T&B - 1257mm² T&B - 3.87% o/a, @80 c/c.) PROVIDE T8 @ 300

Strain diagram

see clause 9.5.2 (4)

Stress diagram 19.8 N/mm²

0.00292

435

0.00258

Notes

0.00092

183 0.00058

Stresses in N/mm2 Compression +ve - - - Neutral axis

192


17/07/2006 17:11:20

TCC11 Element Design.xls TCC11 Element Design/ COLUMN!


Indirect Supports Originated from TCC11.xls, v 1.3 on CD

INPUT

Location

fywk h1 h2 bw1 bw2 VEd

OUTPUT

500 300 450 225 300 127.0

© 2003-2005 TCC

1st Floor, Beam 7D-E s = 1.15 N/mm² mm mm mm

Link Ø = 10

mm kN from secondary

1st Floor, Beam 7D-E a = Min(300/2 + 300/3, 300/2) = 150 mm d = Min(450/3 + 225/2, 450/2) = 225 mm fyd = 500 /1.15 = 434.78 N/mm² Extra Asw = 1000 x 127 /434.78 = 292 mm² PROVIDE 4 additional T10 legs within 2a

(and within d,if needed)

Asw,prov = 314 mm²

193


17/07/2006 17:11:26

TCC12 Bending and Axial Force.xls This spreadsheet gives an interaction chart for moment against axial load for rectangular sections with asymmetrical reinforcement arrangements. Primarily intended for beams with axial load, it is also applicable to asymmetrically reinforced columns.

MAIN! Moments are considered to be about the x-x axis. All applied loads and moments should be ultimate, with compressive axial loads positive and with positive moments inducing tension in the bottom reinforcement. With asymmetrical arrangements of reinforcement the diagram indicates that negative moments are theoretically possible. After much consideration, the diagram is considered to be correct but strictly is valid only for load cases where M is greater than Mmin as shown on the graph. A reciprocal diagram is generated automatically when top and bottom steels are reversed in the input.

Calcs! Calcs! shows the derivation of the chart where moment capacity is calculated at intervals of neutral axis depth from n.a. depth for N = 0 to n.a. depth for N = Nbal, then in intervals from n.a. depth for N = Nbal to n.a. depth for N = Nuz. This sheet shows workings and is not necessarily intended for printing out other than for checking purposes.

REFS! This sheet comprises the values for Nationally Determined Parameters that have been used in the spreadsheet. These data reflect the values given in draft UK National Annexes for BS EN 1992-1-1. Designers should ensure that these data are current when the spreadsheet is used. When using TCC12 for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations.


194


17/07/2006 17:11:31

TCC12 Bending and Axial Force.xls TCC12 Bending and Axial Force/ MAIN!

Project


Client

Advisory Group

Location


Beam C1-2, Level 3

Date

RMW Checked

BENDING AND AXIAL FORCE to EN 1992-1 : 2003 Originated from TCC12.xls v 3.0 on CD

Revision

chg

© 2002-2005 TCC

Page

30-Jun-06

-

195 205 Job No

FB625

MATERIALS fck fyk

35 500

N/mm²

h b

450 300

mm

γs γc

N/mm²

SECTION

1.15 1.50

COVERS (to main steel) TOP 35 mm BOTTOM 35 mm SIDES 35 mm

mm

REINFORCEMENT Bar Ø 25 32

TOP BOTTOM

No 2 3

Area 982 2413

% 0.727 1.787

Space 180.0 67.0

. .

M:N interaction chart for 450 x 300 section, Grade 35 concrete 5000

4000

AXIAL COMPRESSION, NEd kN

Mmin

3100

3000

2000 1600 1200

1000

0.1Acfck

0 -600 -1000

-2000 -500

-400

-300

-200

-100

0

100

200

300

400

500

MOMENT, MEdxx kNm LOADCASES

(ULS)

NEd

MEd

CASE

NEd

1

3100

-210

2

-600

180

3

1600

280

4

1200

-240

CASE

MEd

195


17/07/2006 17:11:32

TCC13 Slab Punching.xls This spreadsheet designs punching shear links. Essentially it is intended to be used with simple rectangular flat slabs to BS EN 1992-1-1, i.e. with TCC33.xls. Equally it can be used to check wide beams in, say, troughed slabs. The spreadsheet is presented as four pairs of sheets dealing with internal, edge, (external) corner and re-entrant corners. It should be remembered that in slabs, traditional links are timeconsuming to fix on site – proprietary systems are generally much quicker to fix on site and this far outweighs first cost. This spreadsheet may be used for some proprietary systems as well as for traditional links.

INTERNAL! (Similarly EDGE!, CORNER and REENTRANT!) These sheets constitute the input and main output. Input is fairly self-evident but, as ever, care must be exercised in ensuring correct values are used. The top diagram acts as a legend and the chart at the bottom of the sheet shows the column, any holes and link perimeters, and should act both as a check for input and help explain output. The x-x axis is across the page. To the right is a combo-box that allows either: ■ Input of both VEd (design shear transferred to column) and

ß VEd (design effective shear including allowance for moment transfer) is required. These figures should be available from subframe analysis e.g. output from TCC33.xls under Reactions. A value of ß VEd, computed from VEd and the factor according to location of the column (BS EN 1992-1-1, Clause 6.4.3) is suggested under Operating Instructions: in general this figure may be regarded as a maximum: calculating effective shear from moment transfer generally results in lower figures. or

The shear at 2.0d and at the column face are shown under ‘Results’, together with the perimeter (uout) at which shear reinforcement is no longer required. The given solution then indicates the number of link spurs required, with the number, spacing and diameter of the links in each spur. Detailed design calculations are shown to the right of each sheet (off screen). These sheets derive three alternative radial link configurations then check the validity of each before selecting the optimum solution. The amounts of reinforcement per perimeter may be converted to a traditional arrangement of links. Deductions for holes in the calculation of shear perimeters are calculated by finding the angle defined by the extremities of the hole. The projection of this angle is deducted from the appropriate perimeter.

GEOMETRY! This sheet shows the geometrical arrangements of link spurs assumed in the design calculations, which should also be used for detailing purposes.

Gra! This sheet contains charting data

Refs! This sheet contains values for nationally determined parameters used in the spreadsheets.

Notes!

■ Input of Vt alone. Veff defaults to the values given in BS EN

1992-1-1, Clause 6.4.3


or ■ Input of VEd alone. ß VEd defaults to the values given in BS EN

1992-1-1, Clause 6.4.3 The spreadsheet asks for the areas of steel in the two directions. These should be averages in each direction, i.e., ensure that it reflects the actual reinforcement in the sides of the perimeter; an average of column strips and middle strips may be appropriate. Holes more than 6d from the column face are ignored as in BS EN 1992-1-1, Clause 6.4.2 (3). Multiple holes should be aggregated pro-rata as if they were one hole at one location. 196


17/07/2006 17:11:38

TCC13 Slab Punching.xls TCC13 Slab Punching/ INTERNAL!

Project

Spreadsheets to EC2

Client

Advisory Group

Location


ECBP Typical Floor Column B3

rmw INTERNAL Checked

PUNCHING SHEAR to BS EN 1992-1: 2004

Originated from TCC13.xls Version 3.0 on CD © 2003-2006 TCC

2

MATERIALS

fck N/mm 35 2 fyk N/mm 500 Steel class A

DIMENSIONS

LOADING

A B G

VEd ult UDL

SLAB

h

mm mm mm

kN kN/m2

mm

400 400 150

965.5 16.10 250

VEd = 1060.7 kN RESULTS 2 At hole face, vEd = 3.612 N/mm

Date

COLUMN

STATUS VALID DESIGN . mm mm

200 50 150

ß VEd =

kN

1060.7

dx dy d

mm

215 195 205

mm mm

30-Jun-2006 Revision

chg

197 207

Job No

-

FB625

LEGEND

E F H

mm

Page

vRd,c = At 2d perimeter, vED,red = Uout required =

2 Asx mm /m 2 Asy mm /m 100ρL %

0.7199 1.3793 6542

N/mm2

1608 1608 0.786

in B + 6d in A + 6d

Equation (6.47)

N/mm2 mm

Equation (6.54)

SOLUTION Fig 6.22 (A) 12 link spurs of 5H10 @ 135 84 links plus 12 spurs of 2H10 @ 135 Sr = 135 mm St = 175.7 mm (6.52) & (9.11) Asw/Sr req = 6.949 Asw/Sr prov = 6.981 mm First link perimeter 100 mm from column face Uout = 7389 mm > 6,542 mm SPUR See GEOMETRY page for link locations. PLAN Some links shown may need to be re-located to avoid holes.

197


17/07/2006 17:11:40

TCC13 Slab Punching/ EDGE!

Project

Spreadsheets to EC2

Client

Advisory Group

Location


Column B2

rmw EDGE Checked

PUNCHING SHEAR to BS EN 1992-1: 2004 Originated from TCC13.xls Version 3.0 on CD © 2003-2006 TCC

MATERIALS

2 fck N/mm 35

STATUS

2 fyk N/mm 500

VALID DESIGN

mm

400

E

mm

-75

B

mm

250

F

mm

-275

G

mm

150

H

mm

150

ß VEd =

kN

627.7

dx dy d

mm

215 195 205

VEd ult UDL

SLAB

mm

0

kN

500.9 16.10

kN/m2

h

mm

250

mm mm

VEd = 627.7 kN

RESULTS


chg

198 208 Job No

-

FB625

LEGEND

A

D LOADING

COLUMN

Page

.

Steel class A DIMENSIONS

Date

2

At col. face, vEd = 4.069 N/mm


2

vRd,c =

0.7248

N/mm

At 2d perimeter, vED,red =

1.9656

N/mm2

Uout required =

3371

mm

2010 1340 0.802

in B + 3d+D in A + 6d

Equation (6.47)

Equation (6.54)

SOLUTION Fig 6.22 (A) 7 link spurs of 5H10 @ 110

35 links

. Sr = 110 St = 157.6 mm (6.52) & (9.11) Asw/Sr req = 4.886 Asw/Sr prov = 4.998 mm First link perimeter 100 mm from column face Uout = 3528 mm > 3,371 mm

mm

SPUR See GEOMETRY page for link locations. Some links shown may need to be re-located to avoid holes.

PLAN

198


17/07/2006 17:11:47

TCC13 Slab Punching.xls TCC13 Slab Punching/ CORNER!


The Concrete Centre

Spreadsheets to EC2 Advisory Group

Made by

Columns A1, D1, A5 & D5

rmw


CORNER Checked

Originated from TCC13.xls Version 3.0 on CD © 2003-2006 TCC

COLUMN

2 fck N/mm 35

MATERIALS

fyk

N/mm2

500


LOADING

400

E

mm

50

mm

250 0 0

F G H

mm

mm

-275 150 150

0

350

mm

215 195 205

VEd

kN 2

kN/m

h

mm

272.0 16.10 250

VEd = 408.0 kN RESULTS 2 At hole face, vEd = 4.185 N/mm

Job No

-

FB625

VALID DESIGN

mm

mm

Revision

chg

199 209

.

B C D

mm

Page

30-Jun-2006

LEGEND

A

ult UDL SLAB

STATUS

Date

dx dy d

mm

mm mm

vRd,c = At 2d perimeter, v = Uout required =


2 0.7754 N/mm 2 2.5486 N/mm 1711 mm

2010 2010 0.982

in B + 3d+D in A + 3d+C

Equation (6.47)

Equation (6.54)

SOLUTION Fig 6.22 (A) 4 link spurs of 4H12 @ 130

16 links

. St = 157.6 mm Sr = 130 (6.52) & (9.11) Asw/Sr req = 3.379 Asw/Sr prov = 3.480 mm First link perimeter 100 mm from column face Uout = 1886 mm > 1,711 mm

mm


PLAN

199


17/07/2006 17:11:55

TCC13 Slab Punching/ REENTRANTS!

Project

Spreadsheets to EC2

Client

Advisory Group

Location


An example

rmw RE-ENTRANT


Originated from TCC13.xls Version 3.0 on CD © 2003-2006 TCCCOLUMN

MATERIALS

2 fck N/mm 35

STATUS

2 fyk N/mm 500

VALID DESIGN


LOADING

mm

400

E

mm

200

mm

400 -100 -100

F G H

mm mm

-50 100 100

ß VEd =

kN

1065

dx dy d

mm

215 195 205

VEd ult UDL

SLAB

kN kN/m2

h

mm

478.0 16.10


chg

200 210 Job No

-

FB625

.

B C D

mm

Page

LEGEND

A

mm

Date

250

VEd = 1064.9 kN RESULTS 2 At col. face, vEd = 3.974 N/mm

mm

mm mm

vRd,c = At 2d perimeter, v = Uout required =


0.6774 1.7068 3442

N/mm2

1340 1340 0.654

in B + 6d in A + 6d

Equation (6.47)

N/mm2 mm

Equation (6.54)

SOLUTION Fig 6.22 (B) 12 link spurs of 3H10 @ 115

36 links

. Sr = 115 St = 130 mm (6.52) & (9.11) Asw/Sr req = 8.030 Asw/Sr prov = 8.195 mm First link perimeter 100 mm from column face Uout = 4212 mm > 3,442 mm

mm


PLAN

200


17/07/2006 17:12:03

TCC14 Crack Width.xls

TCC14 Crack Width.xls Crack Width! In the design of reinforced concrete structures, it is assumed that the tensile capacity of concrete does not contribute to the strength of the structure, and steel reinforcement is provided to resist the internal tensile forces that develop. Because steel reinforcement can develop the resisting tensile force only by extension (i.e. steel needs to extend to develop stress), and hence cracks are formed in the surrounding concrete: cracks in reinforced concrete structures cannot be avoided. In day-today practical design, crack widths are controlled by limiting the maximum spacing of the tension reinforcement. However there are times when the engineer will need to carry out more rigorous analysis and calculations, e.g. in the design of water-retaining structures, and design for severe exposure where estimation/ prediction of crack width is important. This spreadsheet calculates crack widths in accordance with BS EN 1992-1-1, Section 7.3. Recommended maximum crack widths for the various exposure classes are given in Table 7.1N (BS) of the National Annex to BS EN 1992-1-1. Essentially crack widths for reinforced concrete members under quasi-permanent loading is restricted to 0.3mm. For exposure conditions XO and XCI this limit may be relaxed [to 0.4mm]. The calculations shown are in accordance with Section 7.3.4 of BS EN 1992-1-1 and should be self-explanatory. For bridges reference should be made to BS EN 1992-2 Section 7.3 and the appropriate National Annex. For liquid retaining structures refer to BS EN 1992-3 Section 7

Notes! This sheet contains disclaimers and revision history.

201


17/07/2006 17:12:10

TCC14 Crack widths/ RECTANGULAR!

Project

The Concrete Centre

Spreadsheets to EC2

Client Advisory Group Location Grid line 1

Made by

rmw Checked

FLEXURAL CRACK WIDTH CALCULATION to BS EN 1992-1 : 2004 Originated from TCC14.xls v3.0 on CD

© 2002-2005 BCA for RCC

RECTANGULAR

Date 30-Jun-06

Page

202 212

Revision Job No

chg

-

565 129 314 31 200 12 L 25

mm2 mm mm2

FB625

LEGEND

INPUT fck = fyk = b= h= QP moment, M = Age at cracking = Cement type = Creep factor, =

30 500 1000 160 24.9 14 N 2.0

N/mm2 N/mm2 mm mm KNm days (S, N, R or RS)

Area of tension steel, As = d= Area of compression steel, As2 = d2 = Maxmum tension bar spacing, S = Max tension bar dia, Øeq = Short term or long term ? Cover to As, c =

mm mm mm (S or L) mm

CALCULATIONS modulus of elasticity of concrete = 22[(f ck+8)/10]0.3

Ecm =

32.8

Gpa

moduli of elasticity of steel

Es =

200.0

Gpa

Modular ratio

e =

18.27

' = 0.0024 mean concrete strength at cracking mean concrete tensile strength uncracked neutral axis depth [bh²/2+(e-1)(Asd+As2d2)]/[bh+(e-1)(As+As2)]

= fcm,t = fct,eff =

0.0044 34.26 2.61

Mpa Mpa

xu =

81.21

mm

bh³/12+bh(h/2-x)²+(e-1)[As(d-x)²+As2(x-d2)²]

Iu =

378

mm4 106

cracking moment = f ctI/(h-x)

Mcr =

12.51

kNm

uncracked 2 nd moment of area

< 24.9 kNm section is CRACKED fully cracked x = d[-e( - ') + {e²( - ')²+2e( + 'd2/d)}½]

xc =

41.19

mm

concrete stress = M/[bx(d-x/3)/2+(e-1)As2(x-d2)/x(d-d2)] stress in tension steel = ce(d-x)/x

c = s =

9.939 387.2

Mpa Mpa

effective tension area = min[2.5(h-d), (h-x)/3, h/2]b As /Ac,eff max final crack spacing = min[1.3/(h-x),3.4c+0.17Ø/ p,eff)]

Ac,eff = p,eff =

39605 0.0143

mm2

sr,max =

154.5

mm

sm-cm = Wk =

1474.6

µstrain

0.228

mm

average strain for crack width calculation CALCULATED CRACK WIDTH

202


17/07/2006 17:12:11

TCC14 Crack Width.xls TCC14 Crack widths/ SPANTEE!

Project

The Concrete Centre

Spreadsheets to EC2


Made by

rmw


© 2002-2005 BCA for RCC

TEE IN COMPRESSION

Checked

Date 30-Jun-06

Page

33 203

Revision Job No

chg

-

FB625

LEGEND

INPUT fck = fyk = bw = h= bf = hf = QP moment, M = Age at cracking = Cement type = Creep factor, =

2

Area of tension steel, As = 35 N/mm2 N/mm2 d= 500 Area of compression steel, As2 = 300 mm d2 = 450 mm Maxmum tension bar spacing, S = 2170 mm Max tension bar dia, Øeq = 125 mm 114.2 KNm Short term or long term ? 14 days Cover to As, c = N (S, N, R or RS) 2.0 modulus of elasticity of concrete = 22[(fck+8)/10]0.3 Ecm =

1473 399.5 236 33 87 25 L 38

mm mm 2 mm

34.1

Gpa


Es =

200.0

Gpa

Modular ratio

e =

17.61

mean concrete strength at cracking mean concrete tensile strength uncracked neutral axis depth [bwh²/2+(bf-bw)hf²/2+(e-1)(Asd+As2d2)]/[bwh+(bf-bw)hf+(e-1)(As+As2)]

fcm,t = fct,eff =

38.77 2.89

Mpa Mpa

xu =

138.21

mm

bwh³/12+bwh(h/2-x)²+(bf-bw)hf³/12+(bf-bw)hf(x-hf/2)²+(e-1)[As(d-x)²+As2(x-d2)²]

Iu =

6653

mm4 106

cracking moment = fctI/(h-x)

Mcr =

61.75

kNm

CALCULATIONS


uncracked 2nd moment of area

< 114.2 kNm section is CRACKED xc = 85.53 fully cracked x (within flange) c = concrete stress (x within flange) 3.234 stress in tension steel = ce(d-x)/x s = 209.0 effective tension area = min[2.5(h-d), (h-x)/3, h/2]bw As /Ac,eff max final crack spacing = min[1.3/(h-x),3.4c+0.17Ø/ p,eff)] average strain for crack width calculation CALCULATED CRACK WIDTH

mm Mpa Mpa mm2

Ac,eff = p,eff =

36447 0.0404

sr,max =

234.4

mm

sm-cm = Wk =

800.1

µstrain

0.188

mm

203


17/07/2006 17:12:19

TCC14 Crack widths/ SUPPORTTEE!

Project

The Concrete Centre

Spreadsheets to EC2


Made by

rmw TEE IN TENSION


© 2002-2005 BCA for RCC

Checked

Date 30-Jun-06

Page

204 33

Revision Job No

chg

-

FB625

LEGEND

INPUT fck = fyk = bw = h= bf = hf = QP moment, M = Age at cracking = Cement type = Creep factor, = CALCULATIONS

2 Area of tension steel, As = 35 N/mm N/mm2 d= 500 Area of compression steel, As2 = 300 mm d2 = 450 mm Maxmum tension bar spacing, S = 1222 mm Max tension bar dia, Øeq = 125 mm 147 KNm Short term or long term ? 14 days Cover to As, c = N (S, N, R or RS) 2.0 modulus of elasticity of concrete = 22[(fck+8)/10]0.3 Ecm =

2

mm mm 2 mm

1000 417 236 34 87.4 10 L 28


34.1

Gpa


Es =

200.0

Gpa

Modular ratio

e = =

17.61

' = 0.0019 mean concrete strength at cracking mean concrete tensile strength uncracked neutral axis depth [bwh²/2+(bf-bw)hf(h-hf/2)+(e-1)(Asd+As2d2)]/[bwh+(bf-bw)hf+(e-1)(As+As2)]

fcm,t = fct,eff =

0.0080 38.77 2.89

Mpa Mpa

xu =

303.18

mm

bwh³/12+bwh(h/2-x)²+(bf-bw)hf³/12+(bf-bw)hf(h-x-hf/2)²+(e-1)[As(d-x)²+As2(x-d2)²]

Iu =

4572

mm4 106

cracking moment = fctI/(h-x)

Mcr =

90.12

kNm

nd

uncracked 2 moment of area

< 147 kNm section is CRACKED fully cracked x = d[-e( - ') + {e²( - ')²+2e( + 'd2/d)}½]

xc =

162.30

mm

concrete stress = M/[bx(d-x/3)/2+(e-1)As2(x-d2)/x(d-d2)] stress in tension steel = ce(d-x)/x

c = s = hc,eff =

14.668 405.3 82.50

Mpa Mpa mm

Ac,eff = p,eff =

100815 0.0099

mm2

sr,max =

266.6

mm

sm-cm = Wk =

1341.0

µstrain

0.357

mm

height of tension zone = min[2.5(h-d), (h-x)/3, h/2] effective tension area As /Ac,eff max final crack spacing = min[1.3/(h-x),3.4c+0.17Ø/ p,eff)] average strain for crack width calculation CALCULATED CRACK WIDTH

204


17/07/2006 17:12:26

TCC21 Subframe Analysis.xls

TCC21 Subframe Analysis.xls TCC21 Subframe Analysis.xls analyses sub-frames one bay wide in accordance with BS EN 1992-1-1 using moment distribution. Inputs are required on two sheets.

MAIN! This single sheet consists of the main inputs, most of which should be self-explanatory. As in other spreadsheets, avoid pasting input from one cell to another as this may cause formatting and other errors. The dimensions of the flange widths, beff, are entered manually, but maximum permitted values can be seen in cells M12:M17. It is important that the correct usage of the members under consideration is selected from the combo-box to the right of the screen, as this affects the magnitude of quasi-permanent SLS moments.

The user is required to input desired amounts of redistribution to the initial moments in line 26. Cell L14 allows three types of distribution according to the user’s preference for calculating span moments (see Table 1). Redistribution input is included close to the bending moment diagrams in order to give the user control rather than relying on blanket redistribution. The sheet also tabulates elastic and redistributed ultimate shears and column moments according to the various load cases.

Uls! and Sls! These sheets detail the moment distribution analyses carried out for the ultimate and serviceability limit states respectively, but are not necessarily intended for printing out other than for checking purposes. All load cases to BS EN 1992-1-1 are calculated (but see Refs!)

Unwanted data cells are ‘greyed-out’. Supports may be specified by giving dimensions, etc. in C20: J26. The use of C, K or E in column C can alter the characteristics of a support from cantilever to knife-edge to encastre. Where supports are dimensioned, their remote ends (i.e the top of a column above or the bottom of a supporting column below) may be specified as being ‘F’ for fixed or ‘P’ for pinned in spreadsheet columns F and J. Extraneous data is highlighted in red or by messages in red. Under ‘Operating Instructions’ a number of checks, mainly for missing entries, are carried out and any problems are highlighted.

At the bottom of the sheet a simplistic but to-scale arrangement and loading diagram is shown. This is given to aid data checking. It may prove prudent to write down expected values for bending moments at each support down before progressing to ACTIONS!. UDLs are input as line loads per unit area e.g. 4kN/m2. Ultimate and characteristic support reactions are given at the bottom of the sheet.

ACTIONS!


Refs! This sheet comprises the values for nationally determined parameters that have been used in the spreadsheet. These data reflect the values given in draft UK National Annexes for EN 1990 and EN 1992. Designers should ensure that these data are current when the spreadsheet is used. When using TCC21 for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations. It should be noted that it is possible to switch on the adjacent spans loaded combination by changing ‘b’ to ‘a’ in cell D4. BS EN 1992-1-1 recommends using the adjacent and alternate load arrangements. However to the UK National Annex only the all spans and alternate load arrangements need to be considered.

Notes! This sheet contains disclaimers and revision history.

This sheet includes charts showing the elastic bending moment diagram, redistributed moment envelope, elastic shear forces and envelope of redistributed shear forces. These diagrams are based on data from the analysis undertaken in Analysis! at 1/20 span points. Maximum span and support moments are given. 205


17/07/2006 17:12:34

TCC21 Subframe Analysis MAIN!

The Concrete Centre

Project

Spreadsheets to EC2

Client

Advisory Group Worked Examples: Main beam Grids C to J

Location

SUBFRAME ANALYSIS Originated from TCC21.xls

LOCATION

SPAN 1 SPAN 2 SPAN 3 SPAN 4 SPAN 5 SPAN 6 SUPPORTS Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Support 7

5000

Checked

v3.0 on CD

B

to grid

Page

03-Jul-06 Revision

chg

© 2002-2005 TCC

-

206 216 Job No

FB625

Usage: Office

E

LOADING PATTERN

mm

L (m)

h (mm)

bw (mm)

hf (mm)

Type

beff (mm)

6.000 6.000 6.000 6.000

450 450 450 450

300 300 300 300

125 125 125 125

T T T T

2140 1680 1680 2140

SPANS

Date

rmw

to EN 1992-1 : 2004

Supports from grid Bay width

Made by

BS EN 1990: (6.10b)

DEAD IMPOSED

min

max

1.25

1.25 1.50

STATUS OK ABOVE (m)

H (mm)

B (mm)

End Cond

BELOW (m)

H (mm)

B (mm)

End Cond

250 300 300 300 250

250 300 300 300 250

F F F F F

3.750 3.750 3.750 3.750 3.750

250 300 300 300 250

250 300 300 300 250

F F F F F

UDLs (kN/m²)

PLs (kN)

Position (m)

Dead Load

Imposed Load

Position from left

Loaded Length

Dead Load

Imposed Load

Position from left

Loaded Length

37.8

15.0

~~~~~

~~~~~ ~~~~~ ~~~~~

37.8

15.0

~~~~~

~~~~~ ~~~~~ ~~~~~

37.8

15.0

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

37.8

15.0

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

3.750 3.750 3.750 3.750 3.750

LOADING DIAGRAM

LOADING Span 1 UDL PL 1 PL 2 Part UDL Span 2 UDL PL 1 PL 2 Part UDL Span 3 UDL PL 1 PL 2 Part UDL



ALL SPANS LOADED MAX ULTIMATE Characteristic Dead Maximum Imposed Minimum Imposed

1

2

3

4

5

178.7 179.3 93.3 41.1 -4.1

454.7 454.7 252.2 100.0 49.8

407.4 407.4 217.0 86.0 43.0

454.7 454.7 252.2 100.0 49.8

178.7 179.3 93.3 41.1 -4.1

206


17/07/2006 17:12:36

TCC21 Subframe Analysis.xls TCC21 Subframe Analysis ACTIONS!

Project

Spreadsheets to EC2

Client

Advisory Group

Location


Worked Examples: Main beam Grids C to J

rmw Checked

SUBFRAME ANALYSIS to EN 1992-1 : 2004

Originated from TCC21.xls v3.0 on CD

5

10

Page

207 217

03-Jul-06 Revision

chg

© 2002-2005 TCC

Job No

-

FB625

.

BENDING MOMENTS (kNm) 0

Date

15

20

25

30

0

400

5

10

15

20

25

30

300 250

300

200 150

200

100 100

50 0

0

-50 -100

-100 -150

-200

-200 -250

-300

B

E

Elastic Moments

SUPPORT No

Full SLS M Quasi-permanent M Elastic ULS M Redistributed ULS M δ

B

ULS

1

2

3

4

5

33.2 25.4 44.3 44.3 1.000

203.2 161.2 263.9 224.3 0.850

158.2 119.9 190.8 190.8 1.000

203.2 161.2 263.9 224.3 0.850

33.2 25.4 44.3 44.3 1.000

~ ~ ~ ~ ~

~ ~ ~ ~ ~

~ ~ ~ ~ ~

Redistribution 1

2

3

4

Full SLS M Quasi-permanent M Elastic ULS M Redistributed ULS M δ ULS SHEARS (kN)

137.1 106.2 183.2 188.1 1.027

88.2 62.7 119.8 116.9 0.976

88.2 62.7 119.8 116.9 0.976

137.1 106.2 183.2 188.1 1.027

300

300

200

200

100

100

0

0

-100

-100

-200

-200

-300

-300 5

B

10

15

20

25

SPAN No

30

0

E

Elastic Shears

178.2 179.3

SPAN No

5

10

B

1


kNm/m kNm/m kNm/m kNm/m ~

15.0%

15.0%

SPAN No

0

E


15

20


2

25

30

E

3

246.5 239.9

218.5 218.2

201.4 203.7

201.4 203.7

218.5 218.2

4

Elastic V

246.5

178.2

~

~

~

~

Redistributed V

239.9

179.3

~

~

~

~

1

2

3

4

5

20.3 20.3 22.2 22.2

-8.8 -8.8 18.1 18.1

10.8 10.8

8.8 8.8 18.1 18.1

-20.3 -20.3 22.2 22.2

COLUMN MOMENTS (kNm) Above ALL SPANS LOADED Below MAXIMUM Above MOMENT Below

ultimate

207


17/07/2006 17:12:41

TCC31 One-way Slabs.xls This spreadsheet analyses and designs up to six spans of one-way solid slabs to BS EN 1992-1-1 using continuous beam analysis. There is user input on each of the first four sheets and the choice of reinforcement for each span is implicit.

MAIN! This single sheet consists of the main inputs, most of which should be self-explanatory. The number of spans is altered by entering or deleting data under L (m) in cells C16:C21. Unwanted data cells are ‘greyed-out’. The use of C, K or E in J17:J18 can alter the characteristics of the end supports from cantilever to knife-edge or encastre. Erroneous data is highlighted in red or by messages in red. Under Operating Instructions a number of checks are carried out and problems are highlighted. For the purposes of defining load, the section is assumed to be 1.00 m wide. At the bottom of the sheet a simplistic loading diagram is given to aid data checking. It may prove prudent to write down expected values of bending moments at each support down before progressing to ACTIONS!

Current interpretation of EC2 requires that all spans should be loaded with both γGk,sup and γGk,inf , Gk,sup is used initially, and for γGk,inf the “Run γGk,inf Loadcase” button must be activated. A red warning message will appear if this has not been done, or if any relevant input data are subsequently changed. Using γGk,inf (=1.0) leads to higher hogging moments in spans. Maximum moments at supports are taken at centre of supports rather than side of supports as in the beam spreadsheets. Unless overwritten, reinforcement diameter specified for a support carries through both sides of the support, i.e. the diameter specified for the right hand support of a span carries over to the left hand support of the next span. It may be possible to obtain different numbers of bars each side of the support due to differences in depth or to comply with minimum percentage of span steel; issues of practicality and buildability should dictate that the largest number of bars is used throughout for each support. With regard to deflection, the area of steel required, As mm2/m, shown under ‘Design for the Centre’ part of the span, may have been automatically increased in order to reduce service stress, σs, and increase modification factors to satisfy deflection criteria. The percentage increase, if any, is shown under ‘Deflection’.

Support reactions are given at the bottom of the sheet. The top and bottom covers specified at J10:J11 should be nominal covers including ∆cdev. ∆ cdev is required in the checking of maximum bar size allowed.

ACTIONS! This sheet shows bending moment and shear force diagrams from the analysis undertaken in Analysis! The user is required to input the desired amount of redistribution to the initial moments in line 25. Cell J14 allows three types of distribution according to the user’s preferences. Requesting redistribution at a cantilever produces a warning message in the remarks column.

SPANS! SPANS! designs sections taken at the left, centre and right of each span. The user is required to choose the diameters for top, bottom and if necessary, link reinforcement for each span. The amounts of bending and shear reinforcement required and checks are derived from detailed calculations in Bar! The designer and detailer should agree as to how these minimum reinforcement arrangements are to be rationalised in the final detailed drawings. Unwanted cells are ‘greyed-out’.

With respect to cantilevers, neither compression steel enhancement nor consideration of rotation at supports is included. Hogging moments at 1/4 span are checked and used in the determination of top steel in the centre of spans. Careful examination of the Bending Moment Diagram and Graf! should help to determine whether any curtailment of this reinforcement is warranted (but see shift rule in Eurocode 2 Clause 9.2.1.3). To avoid undue sensitivity, especially with regard to deflection, reinforcement may be theoretically over-stressed by up to 2.5% The top steel in the centre of spans is determined by adding together the steel required for hogging at 1/4 span and the appropriate additional tensile force due to shear ∆Ftd (see CI 9.2.1.3). It is assumed that 100% hogging steel at supports will be curtailed at 0.25 span or max 50% at 0,2 span and 50% at 0.3 span.

WEIGHT! Weight! gives an estimate of the amount of reinforcement for both design and distribution steel required in the slab per bay and per cubic metre. Bay and support widths are required as input.

208


17/07/2006 17:12:46

TCC31 One-way Slabs.xls Simplified curtailment rules, as explained above and similar to those used with BS 8110, are used to determine lengths of bars. The figures should be treated as estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation, etc, etc. They do not allow for reinforcement in supporting beams or for mesh.

Uls! This sheet details the moment distribution analysis carried out at the ultimate limit state. The following patterns for imposed loading are considered to find a worse case. ■ All spans loaded

Refs! This sheet comprises the values for Nationally Determined Parameters that have been used in the spreadsheet. These data reflect the values given in draft UK National Annexes for EN 1990 and EN 1992. Designers should ensure that these data are current when the spreadsheet is used. When using TCC31 for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations. It should be noted that it is possible to switch on the adjacent spans loaded combination by changing ‘b’ to ‘a’ in cell D6. BSEN 1992-1-1 recommends using the adjacent and alternate load cases. However to the UK NA only the cell spans and alternate load cases need to be considered.

■ Odd spans loaded ■ Even spans loaded ■ Adjacent spans loaded* ● Spans 1 & 2 and 5 & 6 loaded*


● Spans 2 & 3 loaded* ● Spans 3 & 4 loaded* ● Spans 4 & 5 loaded*

* According to the UK National Annex, it is not necessary to consider the adjacent-spans-loaded case and the option of using this case may be switched on or off at Refs!D6. Uls! is not necessarily intended for printing out other than for checking purposes.

Sls! This sheet details the analysis carried out at the serviceability limit states corresponding to full service load and to quasipermanent load. It uses the same load cases as Uls! and finds upper and lower bound limits at 1/20 th points along the spans. Again this sheet is not necessarily intended for printing out other than for checking purposes.

Bar! This sheet shows design calculations, complete with references to BS EN 1992-1-1. It is not necessarily intended for printing out other than for checking or educational purposes. In many instances, service stress, σs, has been set to 1.0 or 0.0001 N/mm2 to avoid problems with division by zero.


209


17/07/2006 17:12:47

TCC31 One-way Slabs/ MAIN!

Project


Client

Advisory Group

Location


8th Floor slab

from A to G

ONE-WAY SOLID RC SLAB DESIGN to EN 1992-1: 2004 Originated from TCC31.xls v3.0 on CD

LOCATION

Supports from grid

A

Date

rmw Checked

Revision

chg

© 2003- 2006 TCC

MATERIALS

220 210 Job No

-

Wk Wk

to grid G

Page

03-Jul-06

FB625

0.4 0.3

mm top

25 25 10

mm

mm btm

COVERS

fck fyk fywk Steel class

30 500 500 B

dg γs γc


20 1.15 1.50

Top cover Btm cover c,dev

mm steel concrete Usage: Shopping

L (m)

H (mm)

5.000 5.000 5.000 5.000

160 160 160 160

SPANS SPAN 1 SPAN 2 SPAN 3 SPAN 4

BS EN 1990: (6.10b)

SPAN 6

IMPOSED

min

max

1.25

1.25 1.50

Dead

Imposed

Position

Load

Load

from left

7.34

3.00

~~~~

Supt No

Type

1

K

5 K K(nife), C(antilever) or E(ncastre)

LOADING


UDL

With brittle partitions

LOADING PATTERN

DEAD

Span 1

mm

SUPPORTS

SPAN 5

LOADING

mm

Span 4 UDL

PL 1

Dead

Imposed

Position

Load

Load

from left

7.34

3.00

~~~~

PL 1

PL 2

PL 2

Span 2

Span 5

7.34

UDL

3.00

~~~~

~~~~

UDL

PL 1

PL 1

PL 2

PL 2

Span 3

Span 6

7.34

UDL

3.00

~~~~

UDL

PL 1

PL 1

PL 2

PL 2

LOADING DIAGRAM

A

G


1

2

3

4

5

14.42 6.70 -0.80 27.94

41.94 17.14 8.57 75.89

34.08 13.93 6.97 65.65

41.94 17.14 8.57 75.89

14.42 6.70 -0.80 27.94

210


17/07/2006 17:12:49

TCC31 One-way Slabs.xls TCC31 One-way Slabs/ ACTIONS!

The Concrete Centre


Project Client

Advisory Group

Location

Made by


Date

rmw Checked

ONE-WAY SOLID RC SLAB DESIGN to EN 1992-1: 2004


Revision

chg

© 2003- 2006 TCC

Page

211 221

03-Jul-06

Job No

-

FB625


40

30

30

20

20

10

10

0

0

-10

-10

-20

-20

-30

-30 -40

-40 0

2

4

6

8

A

10

12

14

16

18

1

Elastic M Redistributed M

1.000

ßb Redistribution SPAN No Elastic M Redistributed M ßb

0

22

G

Elastic Moments

SUPPORT No

20

2

A

2

3

4

36.6 31.1 0.850 15.0%

24.4 24.4 1.000

36.6 31.1 0.850 15.0%

1

2

3

4

28.8 28.6 0.992

17.4 17.1 0.986

17.4 17.1 0.986

28.8 28.6 0.992

4

6

8

10

12

14

16

18

20

22

G

Redistributed Envelope 5

1.000

~ ~ ~

~ ~ ~

~ ~ ~

~ ~ ~


50

40

40

30

30

20

20

10

10

0

0

-10

-10

-20

-20

-30

-30

-40

-40

-50

-50 0

2

4

A

6

8

Redistributed V

Redistributed V

14

16

18

20

22

0

G

1

28.1 27.9

SPAN No Elastic V

12

Elastic Shears

SPAN No Elastic V

10

A

2

4

6

8

10

12

14


2

16

18

20

22

G

3

41.5 40.4

36.6 36.3

32.1 32.8

32.1 32.8

36.6 36.3

28.1 27.9

~ ~

~ ~

~ ~

~ ~

4

41.5 40.4

211


17/07/2006 17:12:55

TCC31 One-way Slabs/ SPANS! Project


Client

Advisory Group

Location



Date

rmw Checked



Page

Revision

Job No

chg

© 2003- 2006 TCC

212 222

03-Jul-06 -

FB625 .

.

SPAN 1 ACTIONS

DESIGN

LEFT

Av M δ VEd d As As'

kN/m mm mm²/m mm²/m

B

As prov

mm²/m

As' prov SHEAR vEd vRdct

mm²/m

DESIGN

N/mm2 N/mm2

L/d % As d'/x σs max S

As prov

DEFLECTION & CHECKS


B

As prov

129.0 538 194 8

As' @ 250

201 12

B

As prov @ 175

646 .

B

As' prov


5000 31.1 0.85 40.38 129.0 589 0 12 10


ok

ok

ok

ok

ok

ok

LEFT

CENTRE

RIGHT

10

196 0.271 0.592 38.760

5000 24.4 1.00 32.83 129.0 458 0

17.1 0.99

As top @ 175 @ 400

129.0 321 194

Y

10

As' prov

196

Y

As prov

12

@ 350

224 0.299 0.592

ok ok

12

@ 175

646

ok ok

646 Y


@ 350

0 31.1 0.85 36.31 129.0 589 0 Y

BTM STEEL

10

B

As' prov

38.760


TOP STEEL

As top @ 250

224 0.203 0.542

SPAN 2 ACTIONS

8

RIGHT

28.6 0.99

201 B

BTM STEEL

DEFLECTION & CHECKS

0 4.3 1.00 27.94 131.0 187 0

mm kNm/m

TOP STEEL

CENTRE

@ 400

Y

As prov @ 350

323 .

Y

As' prov

12

@ 225

503 10

@ 400

196 0.241 0.545


ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

212


17/07/2006 17:12:59

TCC31 One-way Slabs.xls TCC31 One-way Slabs/ SPANS! Project


Client

Advisory Group

Location


8th Floor slab, from A to G Checked



SPAN 3 ACTIONS

DESIGN

As prov As' prov SHEAR vEd vRdct DEFLECTION & CHECKS

DESIGN


As prov

196

Y

12

Y

As prov @ 350

323 .

Y

As' prov

12 10

ok

ok

ok

ok

ok

ok

ok

ok

ok

LEFT

CENTRE

RIGHT

10


38.760

@ 400

196 0.268 0.592

ok

12

@ 175

646

ok

224 0.302 0.592

& CHECKS

As' prov

As' @ 400

5000 31.1 0.85 36.31 129.0 589 0

ok

As' prov SHEAR vEd vRdct DEFLECTION

10

FB625


28.6 0.99

As top @ 175

646 Y

RIGHT

129.0 321 194

Y

As prov

0 31.1 0.85 40.38 129.0 589 0 Y

BTM STEEL

@ 400

38.760


TOP STEEL

As top @ 225

196 0.244 0.545

SPAN 4 ACTIONS

10

Job No

17.1 0.99

503 Y

BTM STEEL

12

213 223

Revision

CENTRE

0 24.4 1.00 32.83 129.0 458 0 Y

TOP STEEL

Page

03-Jul-06

chg

© 2003- 2006 TCC

LEFT


Date

rmw

Y

As' prov @ 350

Y

As prov

129.0 538 194 8

As' @ 250

201 12

Y

As prov @ 175

646 .


Y

As' prov

5000 4.3 1.00 27.94 131.0 187 0 8

@ 250

201 10

@ 350

224 0.200 0.542

(As increased by 16.2%)

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

213


17/07/2006 17:13:03

TCC31R Rigorous One-way Slabs.xls This spreadsheet allows the estimation of deflections in one-way solid slabs according to BS EN 1992-1-1. Eurocode 2 recognises that members in bending exist in a state partway between uncracked and fully cracked. The spreadsheet considers both construction and design pattern loading in assessing whether a section is cracked or not (i.e. whether the flexural tensile strength of the concrete is exceeded during these stages of the slabs life). Once cracked, it is assumed that a section remains cracked. The spreadsheet is based on TCC31 but has an initial sheet JOBDATA! to allow input of all the variables and performance criteria required. Deflections are given as a range in a chart at the bottom of ACTIONS!

The number of spans is altered by entering or deleting data under L (m). Unwanted data cells are ‘greyed-out’. The use of C, K or E can alter the characteristics of the end supports from cantilever to knife-edge to encastre. Extraneous data is highlighted in red or by messages in red. Under ‘Operating Instructions’ a number of checks are carried out and problems are highlighted. For the purposes of defining load, the section is assumed to be 1.00 m wide. At the bottom of the sheet a simplistic loading diagram is given to aid data checking. Great care should be taken to ensure this sheet is completed correctly for the case in hand. It may prove prudent to write down expected values of bending moments at each support down before progressing to ACTIONS! Support reactions are given at the bottom of the sheet.

They are shown as a range due to potential pattern loading. In SPANS!, the worst case is compared with the specified serviceability criteria. It should be noted that the number of assumptions and uncertainties in the material and design criteria and construction process render deflection calculations carried out in this manner can be inaccurate (and usually conservative) compared to actual measured deflections. For instance, a slab’s deflection is very dependent upon whether the slab has cracked in bending during construction or not. The calculated deflections might be regarded as being akin to a 95% confidence limit that they will not be exceeded in service. The spreadsheet analyses and designs up to six spans of one-way solid slabs to BS EN 1992-1-1 using continuous slab analysis. There is user input on each of the first four sheets and choice of reinforcement for each span must be done/ assumed to have been done by the user. Input of spans and loads is in MAIN!, User input is required for bar sizes used in SPANS!

JOBDATA! This sheet consists of the main inputs of material, loading, construction and serviceability criteria pertaining to the calculation of deflection to BS EN 1992-1-1. Users are expected to use their knowledge of the project and judgement in completing this sheet. For creep reference is made to Eurocode 2. Reference may be made to the Concrete Centre publication How to design concrete structures to Eurocode 2: Deflection’(27) for guidance on values to be used. The default values given in this sheet are not unusual.

MAIN! This single sheet consists of the main inputs of span and loads, most of which should be self-explanatory.

ACTIONS! This sheet shows bending moment and shear force diagrams from the analysis undertaken in Analysis! The user is required to input the desired amount of redistribution to the initial moments in line 25. Cell J14 allows three types of distribution according to the user’s preferences (see Table 1). Requesting redistribution at a cantilever produces a warning message in the remarks column. The chart at the bottom of the page shows calculated deflections at construction of partitions, and ranges for longer term deflections due to patterns of permanent and imposed loading. The worst case is taken in subsequent checks and this might be viewed as being unduly conservative.

SPANS! In SPANS! the user is required to choose top, bottom and where necessary link reinforcement for each span. The amounts of bending and shear reinforcement required and checks are derived from detailed calculations in Bar! Unwanted cells are ‘greyed-out’. Eurocode 2 requires that all spans should be loaded with both γGk,sup and γGk,inf (=1.0) γGk,sup is used initially, and for γGk,inf the Run -γGk,inf (=1.35 or 1.25) Loadcase button must be activated. A red warning message will appear if this has not been done, or if any relevant input data are subsequently changed. Using γGk,inf (=1.0) leads to higher hogging moments in spans. Unless overwritten, reinforcement diameter specified for a support carries through both sides of the support, i.e. the diameter specified for the right hand support of a span carries over to the left hand support of the next span. It may be possible

214


17/07/2006 17:13:08

TCC31R Rigorous One-way Slabs.xls to obtain different numbers of bars each side of the support due to differences in depth or to comply with the minimum percentage of span steel; practicality may dictate that the maximum number of bars at each support should be used. Hogging moments at 1/4 span are checked and used in the determination of top steel in spans. Careful examination of the Bending Moment Diagram and Graf! should help to determine whether any curtailment of this reinforcement is warranted.

WEIGHT! Weight! gives an estimate of the amount of reinforcement required in one direction of the slab per bay and per cubic metre. Bay and support widths and distribution steel diameters are required as input.

- εc, z, final x, concrete stresses –σc, curvature -1/r, slope and curvature to calculate deflection. The sheet is rather large and is not necessarily intended for printing out other than for checking purposes.


Refs! This sheet comprises the values for nationally determined parameters that have been used in the spreadsheet.

Simplified curtailment rules, similar to those defined in BS 8110, are used to determine lengths of bars.

These data reflect the values given in draft UK National Annexes for EN 1990 and EN 1992.

The figures should be treated as estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation, etc. They do not allow for reinforcement in supporting beams or for mesh.

Designers should ensure that these data are current when the spreadsheet is used. When using TCC31R for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations. It should be noted that it is possible to switch on the adjacent spans loaded combination by changing ‘b’ to ‘a’ in cell D6. BSEN 1992-1-1 recommends using the adjacent and alternate load arrangements. However to the UK National Annex only the cell spans and alternate load arrangements need to be considered.

Uls! This sheet details the moment distribution analysis carried out at the ultimate limit state but is not necessarily intended for printing out other than for checking purposes. All load cases to BS EN 1992-1-1 are calculated.

Sls!


This sheet details the analysis carried out at the serviceability limit state at 1/20th points along each span. The results are used in Def!. This sheet is not necessarily intended for printing out other than for checking purposes.

Bar! This sheet shows design calculations, complete with references to prEN 1992-1-1. It is not necessarily intended for printing out other than for checking purposes. In many instances, service stress, σs, has been set to 1.0 or 0.0001 N/mm2 to avoid problems with division by zero.

Def! This sheet calculates deflections at 1/20th points for each span and for each load condition. For each point and loading stage it considers moment, As, As’, d, d2 , uncracked neutral axis depth - x, uncracked inertia - I, cracked neutral axis depth - x, cracked inertia – I, uncracked moment capacity – Mcr, distribution factor 215


17/07/2006 17:13:10

TCC31R Rigourous One-way Slabs/ JOBDATA!

Project


Client

Advisory Group

Location


8th Floor slab

from A to G

rmw Checked

RIGOROUS ONE-WAY SOLID RC SLAB DESIGN to EN 1992-1 : 2004 Originated from TCC31R.xls

LOCATION

Supports from grid

MATERIALS fck fyk fywk

35 500 500

Steel class

B


to grid

dg s c

20 1.15 1.50

03-Jul-06 Revision

COVERS Top cover Btm cover

25 25

mm mm

Concrete density Curing time

25 3

kN/m³ days

Maximum permanent ∆ = L /

SERVICEABILITY CRITERIA Degree of restraint 60% (50% = nominal, 100% = severe)

250 Maximum imposed ∆ = L / 500 Max ∆ affecting partitions = L / 350 Maximum precamber = 50% of permanent ∆ Design Crack width, W k = 0.4 mm top or 0.3 mm btm

CREEP COEFFICIENTS (to Annex A) RH 50 % relative humidity Cement N Type (S, N, or R) AMBIENT TEMPERATURES ºC

LOADING SEQUENCE (loads rationalised to kN/m²) Span 1 Span 2 kN/m² kN/m² Self weight 6.25 6.25 Partitions 1.00 1.00 Other dead loads 1.50 1.50 Permanent imposed 0.45 0.45 Variable load 1.05 1.05 Composite 10.25 10.25

fcm = Ecm =

43 35.781

216 226 Job No

-

G

mm steel concrete

Page

chg

v 3.0 on CD © 2002-2006 TCC

A

Date

N/mm² kN/mm²

FB625

7.4.1(5)

7.4.1(6) 7.4.1(5) Table 7.1

Table 3.1 & Annex B

from 0 to 7 days 20


from 90 days on 20

Span 3 kN/m² 6.25 1.00 1.50 0.45 1.05 10.25


At age Days 7 60 90 90 ∞

Span 4 kN/m² 6.25 1.00 1.50 0.45 1.05 10.25


COMPOSITE E and Ø VALUES - Span 1 (other spans omitted for clarity )

Self weight Partitions Other dead loads Permanent imposed Variable load Composite

To 70 years Et Ø0 kN/mm² 2.63 9.85 1.75 13.00 1.62 13.65 1.75 13.00 2.33

10.75

Quasi-permanent

To 70 years Et Ø0 kN/mm² 2.63 9.85 1.75 13.00 1.62 13.65 1.75 13.00 0 37.77 2.09 11.60

To 60 days Et Ø (t,t0) kN/mm² 1.07 17.33 SW + partitions Construction load from day 14 0.70 21.09

Total load

216


17/07/2006 17:13:12

TCC31R Rigourous One-way Slabs.xls TCC31R Rigourous One-way Slabs/ MAIN!

The Concrete Centre

Project


Client Location


Made by

RIGOROUS ONE-WAY SOLID RC SLAB DESIGN to EN 1992-1 : 2004

Checked

SPAN 1 SPAN 2 SPAN 3 SPAN 4

L (m)

H (mm)

7.600 7.600 7.600 7.600

250 250 250 250

SPAN 5

LOADING PATTERN DEAD

SPAN 6

min

max

1.25

1.25 1.50

FB625

Dead

Imposed

Position

Load

Load

from left

7.75

2.50

~~~~

Type

1

K K

K(nife), C(antilever) or E(ncastre)

Office Useage LOADING


UDL

217 227 Job No

-

Supt No 5

BS EN 1990: (6.10b)

Span 1

Revision

SUPPORTS

IMPOSED

LOADING

Page

03-Jul-06

chg

Originated from TCC31R.xls v 3.0 on CD © 2002-2006 TCC

SPANS

Date

rmw

Span 4 UDL

PL 1

Dead

Imposed

Position

Load

Load

from left

7.75

2.50

~~~~

4.90

~~~~

~~~~

PL 1

PL 2

PL 2

Construction

4.90

~~~~

~~~~

Construction

Span 2

Span 5

7.75

UDL

2.50

~~~~

~~~~

UDL

PL 1

PL 1

PL 2

PL 2

Construction

4.90

~~~~

~~~~

Construction

Span 3

~~~~

~~~~

Span 6

7.75

UDL

2.50

PL 1

PL 2

PL 2

Construction

4.90

~~~~

~~~~

UDL

PL 1

~~~~

Construction

~~~~

~~~~

LOADING DIAGRAM

A

G


1

2

3

4

5

23.14 8.48 -1.02 41.74

67.31 21.71 10.86 113.34

54.70 17.65 8.82 98.06

67.31 21.71 10.86 113.34

23.14 8.48 -1.02 41.74 217


17/07/2006 17:13:17

TCC31R Rigourous One-way Slabs/ ACTIONS!

Project


Client

Advisory Group

Location


8th Floor slab, from A to G,

Checked


Page

218 228

03-Jul-06 Revision

chg



Date

rmw

-

Job No

FB625

Redistributed

Elastic

100

100

50

50

0

0

-50

-50 -100

-100 0

2

4

6

8

10

12

14

16

A SUPPORT No



0

18 20 22 24 26 28 30 32

2

G

A

1 0.0 0.0 1.000

2 83.1 70.6 0.850 15.0%

3 55.4 55.4 1.000 0.0%

4 83.1 70.6 0.850 15.0%

1 64.5 64.9 1.005

2 37.7 38.1 1.011

3 37.7 38.1 1.011

4 64.5 64.9 1.005


4

6

8

10 12 14 16 18 20 22 24 26 28 30 32

G 5 0.0 0.0 1.000

~ ~ ~

~ ~ ~

~ ~ ~ Redistributed

Elastic

80 60 40 20 0 -20 -40 -60 -80

~ ~ ~

100 50 0 -50 -100 0

2

4

6

8

10

12

14

16

0

18 20 22 24 26 28 30 32

A

G 1

SPAN No


41.6 41.7

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32

A

G

2

3

62.0 60.3

54.7 54.0

47.9 49.0

47.9 49.0

54.7 54.0

41.6 41.7

~ ~

~ ~

~ ~

~ ~

4

SPAN No


2

62.0 60.3

DEFLECTIONS (mm) Precamber not included 10 0 -10 -20 -30 -40

SPAN No

SW + parts (inst) Quasi permanent Variable

1 15.8 25.5

2 1.8 4.6

3 1.8 4.6

4 15.8 25.5

#DIV/0!

#DIV/0!

mm mm

5.1

2.3

2.3

5.1

#DIV/0!

#DIV/0!

mm

218


17/07/2006 17:13:22

TCC31R Rigourous One-way Slabs.xls TCC31R Rigourous One-way Slabs/ SPANS!

Project


Client

Advisory Group

Location



Date

rmw Checked


Page

Revision

Job No

chg


219 229

03-Jul-06 -

FB625

.

SPAN 1

LEFT

ACTIONS

DESIGN



B

TOP STEEL

As prov

mm²/m


mm²/m

DEFLECTIONS mm CHECKS

10 10

As top @ 350

N/mm2

B

As' prov @ 250

314 0.184 0.565

N/mm2

B

As prov

ok

SPAN 2 Av M δ VEd d As As' As prov

223 12


12 10

@ 125

905

As top @ 125

T

As' prov @ 350

224 0.241 0.572

ok

B

As' prov

T

As prov

0.21

10

@ 250

314 0.262 0.572 0 10%

ok ok

0.21

7600 55.4 1.00 49.03 219.0 613 0 @ 225

T

As prov @ 250

452

ok

@ 125

RIGHT

223 12

12

905

ok ok

219.0 422 219 8

7600 70.6 0.85 60.32 219.0 781 0


0.15

T

As' prov

Links not required Permanent = 4.58 < 30.40 Imposed = 2.34 < 15.20 Affecting partitions = 2.81 < 21.71 ok % As ok ok d'/x ok ok σs ok ok

Crack width

B

As prov

38.1 1.01

905 T

BTM STEEL

CHECKS

As' @ 225

CENTRE

0 70.6 0.85 54.04 219.0 781 0 T

TOP STEEL

DEFLECTIONS mm

8

ok

0.00

LEFT

DESIGN

219.0 717 219


Crack width

ACTIONS

RIGHT

64.9 1.01

224 B

BTM STEEL

CENTRE

0 9.7 1.00 41.74 220.0 210 0

mm

0.17

12

@ 175

646 10

@ 350

224 0.210 0.566 0 0%

Precamber (mm) = Increase btm As by ok ok ok ok

0.21

219


17/07/2006 17:13:26

TCC31R Rigourous One-way Slabs/ SPANS!

Project


Client

Advisory Group

Location



Date

rmw Checked


LEFT

ACTIONS

DESIGN

Av M δ VEd d As As' As prov

As' prov SHEAR vEd vRdct DEFLECTIONS mm CHECKS

10

As top @ 175

T

As' prov @ 350

224 0.218 0.566

T

As prov

ok

SPAN 4

DESIGN

Av M δ VEd d As As' As prov

@ 250

452


12 10

As top @ 125

T

As' prov @ 250

314 0.269 0.572

T

As prov

ok

0.21

10

@ 350

224 0.233 0.572 0 0%

ok ok ok

T

As prov @ 125

905

ok

@ 125

ok

As' @ 225

223 12

12

905

0.21

RIGHT

219.0 717 219 8

7600 70.6 0.85 54.04 219.0 781 0


0.17

T

As' prov


Crack width

T

As' prov

64.9 1.01

905 T

BTM STEEL

CHECKS

12

T

As prov

CENTRE

0 70.6 0.85 60.32 219.0 781 0 T

TOP STEEL

DEFLECTIONS mm

As' @ 225

223

ok

0.21

LEFT

ACTIONS

219.0 422 219 8

FB625

RIGHT


Crack width

-

38.1 1.01

646 T

BTM STEEL

12

220 230 Job No

CENTRE

0 55.4 1.00 49.03 219.0 613 0 T

TOP STEEL

Revision

chg


SPAN 3

Page

03-Jul-06

0.15

7600 9.7 1.00 41.74 220.0 210 0 10

@ 350

224 10

@ 250

314 0.176 0.565


0 10%

ok ok ok ok

0.00

220


17/07/2006 17:13:31

TCC32 Ribbed Slabs (A&D).xls

TCC32 Ribbed Slabs (A&D).xls Using continuous beam analysis, this spreadsheet analyses and designs up to six spans of ribbed slab to EN 1992-1-1[3]. There is user input on each of the first three sheets and choice of reinforcement for each span is implicit.

It should be noted that hogging moment is checked both at the centre of support (solid section) and the solid/ rib intersection (ribbed section). As the moments at the solid/ rib intersection each side of the support may differ, it may be possible to obtain a design giving different numbers of bars each side of the support.

MAIN!

Practicality should dictate that the maximum number of bars at each support is used for detailing.

This single sheet consists of the main inputs, which should be self-explanatory. The number of spans is altered by entering or deleting data under L (m). Unwanted data cells are ‘greyedout’. The use of C, K or F can alter the characteristics of the end supports from cantilever to knife-edge to fixed. Extraneous data is highlighted in red or by messages in red. Under ‘Operating Instructions’ a number of checks are carried out and any problems are highlighted. For the purposes of defining load the section under consideration is assumed to be 1.00 m wide. It will be seen from Bar! that moments per metre are converted to moments per rib, and calculations of reinforcement areas required etc. are based on moments and shears per rib. Great care should be taken to ensure this sheet is completed correctly for the case in hand. Combo-boxes to the right under ‘Operating Instructions’ define minimum bar sizes to be used (e.g. at supports between ribs), the type of usage of the slab (this affects the magnitude of quasipermanent SLS moments) and whether the user wants to use links or not. If links are required these may be either designed or nominal links; the centres of nominal links can be changed. Towards the bottom of the sheet a simplistic loading diagram is given to aid data checking. At the bottom of the sheet, support reactions are given.

ACTIONS! This sheet shows bending moment and shear force diagrams from the analysis undertaken in Analysis! The user is required to input the desired amount of redistribution to the initial moments in line 26. Cell L14 allows three types of distribution according to the user’s preferences. See Table 1.

SPANS! In SPANS! the user is required to choose top, bottom and link reinforcement for each span. The amounts of bending and shear reinforcement required and checks are derived from detailed calculations in Bar!Unwanted cells are ‘greyed-out’.

The top steel in the centre of spans is determined by adding together the steel required for hogging at 0.25L (¼ span) and the appropriate additional tensile force due to shear = ∆ Ftd (see BS EN 1992-1-1 9.2.1.3). Similarly at 3/4 span. The higher figure is used to determine for top steel in the span. It is assumed that 100% hogging steel at supports is curtailed at 0.25L or a maximum of 50% is curtailed at 0.2L span and the remainder at 0.3L. With regard to deflection, the area of steel required, As mm2/m, shown under ‘Design for the Centre’ part of the span, may be automatically increased in order to reduce service stress, σs, and therefore increase modification factors to satisfy deflection criteria. The percentage increase, if any, is shown under ‘Deflection’. With respect to cantilevers, neither compression steel enhancement nor consideration of rotation at supports is included.

WEIGHT! WEIGHT! gives an estimate of the amount of reinforcement required in one direction of the slab per rib and per square metre. Simplified curtailment rules, similar to those defined in BS 8110, are used to determine lengths of bars. The figures should be treated as estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation, etc. They do not allow for reinforcement in supporting beams or for mesh.

Uls! This sheet details the moment distribution analysis carried out at the ultimate limit state. The following patterns for imposed loading are considered to find a worse case. ■ All spans loaded ■ Odd spans loaded ■ Even spans loaded ■ Adjacent spans loaded* ● Spans 1 & 2 and 5 & 6 loaded*

The reinforcement diameter specified for a support carries through both sides of the support, i.e. the diameter specified for the right hand support of a span carries over to the left hand support of the next span.

● Spans 2 & 3 loaded* ● Spans 3 & 4 loaded* ● Spans 4 & 5 loaded*

221


17/07/2006 17:13:36


Sls! This sheet details the analysis carried out at the serviceability limit states corresponding to full service load and to quasipermanent load. It uses the same load cases as Uls! and finds upper and lower bound limits at 1/20th points along the spans. Again this sheet is not necessarily intended for printing out other than for checking purposes.

Bar! This sheet shows design calculations, complete with references to prEN 1992-1-1. It is not necessarily intended for printing out other than for checking purposes. In many instances, service stress, ss, has been set to 1.0 or 0.0001 N/mm2 to avoid problems with division by zero.


Refs! This sheet comprises the values for nationally determined parameters that have been used in the spreadsheet. These data reflect the values given in draft UK National Annexes for EN 1990 and EN 1992. Designers should ensure that these data are current when the spreadsheet is used. When using TCC31R for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations. It should be noted that it is possible to switch on the adjacent spans loaded combination by changing ‘b’ to ‘a’ in cell D6. BSEN 1992-1-1 recommends using the adjacent and alternate load arrangements. However to the UK National Annex only the cell spans and alternate load arrangements need to be considered.


222


17/07/2006 17:13:38

TCC32 Ribbed Slabs (A&D).xls TCC32 Ribbed Slabs (A&D)/ MAIN!

Project


Client

Advisory Group


Location 3rd Floor slab

from 1 to 5a

RIBBED SLABS to EN 1992-1: 2004 Originated from TCC32.xls

LOCATION

Supports from grid

MATERIALS fck fyk fywk

35 500 500

Steel class Density

A 25

1

N/mm²

dg γs γc

N/mm²

Wk

N/mm²


SPAN 1 SPAN 2 SPAN 3 SPAN 4 SPAN 5 SPAN 6

v 3.0 on CD

Revision

5a

20 1.15 1.50 0.40

mm

0.30

mm btm

chg

-

Left

Right

8.000 9.000 8.000

275 275 275

300 450 450

450 450 300

25 30 30 10

mm

slab depth, hf

100

mm

Rib width Centres 1 in

150 900 10

mm

concrete mm top

mm mm mm

RIBS

mm

taper

SUPPORTS Support No

Type

1 K 4 K K(nife), C(anti(antilever) or E(ncastre) Usage: Vehicle<= 30kN

LOADING UDLs (kN/m²) Span 1 UDL PL 1 PL 2 Span 2 UDL PL 1 PL 2 Span 3 UDL PL 1 PL 2

FB625

Top cover Btm cover Side cover c,dev

steel

Solid (mm) H (mm)

223 233 Job No

COVERS (to links, or if no links, to reinf)

to grid

L (m)

Page

03-Jul-06

Checked © 2003-2006 TCC

kN/m³

SPANS

Date

rmw

PLs (kN/m)


Position (m)

Self

Add Dead

Imposed

Position

Weight

Load

Load

from left

3.65 ~~~~ ~~~~

2.50

4.00

~~~~

3.67 ~~~~ ~~~~

2.50 8.50

4.00 1.00

~~~~ 1.450

3.65 ~~~~ ~~~~

2.50

4.00

~~~~

Self

Span 4 Weight UDL PL 1 ~~~ PL 2 ~~~ Span 5 UDL ~~~ PL 1 PL 2 ~~~ Span 6 UDL PL 1 ~~~~ PL 2 ~~~~


min 1.25

Add Dead

Imposed

Position

Load

Load

from left

~~~~

~~~~

max 1.25 1.50

LOADING DIAGRAM

1

5a


1

2

3

4

18.5 14.5 -2.2 43.5

65.9 38.5 2.2 138.1

59.3 37.8 2.1 128.8

18.8 14.5 -2.1 43.9

~ ~ ~ ~

~ ~ ~ ~

~ ~ ~ ~

223


17/07/2006 17:13:39

TCC32 Ribbed Slabs (A&D)/ ACTIONS!

Project


Client

Advisory Group

Location



rmw Checked

RIBBED SLABS to EN 1992-1: 2004

Originated from TCC32.xls v 3.0 on CD

Date

Revision

chg

© 2003-2006 TCC

Page

03-Jul-06

234 224 Job No

-

FB625


120

100

100

80

80

60

60

40

40

20

20

0

0

-20

-20

-40

-40

-60

-60

-80

-80 -100

-100 0

5

1

10

15

20

25

5a

Elastic Moments

SUPPORT No


Redistribution

5

1

10

15

1

2

3

4

105.2 89.4 0.850 15.0%

101.6 86.4 0.850 15.0%

0.0 0.0 1.000

~ ~ ~

~ ~ ~

~ ~ #VALUE!

~ ~ #VALUE!

~ ~ #VALUE!

1

2

3

73.49 69.27 0.943

62.07 59.73 0.962

74.78 70.49 0.943

20

25

30

5a


0.0 0.0 1.000

SPAN No


0

30

kNm/m kNm/m ~


80

60

60

40

40

20

20

0

0

-20

-20

-40

-40

-60

-60

-80

-80 0

5

1

10

15

20

25


0

5a


30

5

10

1

1

15

20


2

25

30

5a

3

44.8 43.5

67.9 65.9

72.2 72.2

63.2 63.3

67.4 65.5

45.2 43.9

~ ~

~ ~

~ ~

~ ~

~ ~

~ ~

SPAN No


224


17/07/2006 17:13:46

TCC32 Ribbed Slabs (A&D).xls TCC32 Ribbed Slabs (A&D)/ SPANS!

Project


Client

Advisory Group

Location



Date

rmw Checked



Revision

chg

© 2003-2006 TCC

Page

03-Jul-06

-

235 225 Job No

FB625

.


M

d As As2

kNm/m mm mm² mm²

TOP STEEL

As prov

mm²

As2 prov SHEAR VEd VEd per rib VRd,c

mm²

BTM STEEL kN kN kN


DESIGN

As T prov 2H As prov

314 25 982

/rib

Link Ø 8 2H8 @ 1,200 Allowed 45.8 ok

RIGHT 89.4 0.85 232.0 840 As2 245 2H 20 /rib + 2H12 between As prov 855 2H 16 /rib As2 prov 402 VEd 65.89 VEd per rib 53.39 VRd,c 35.42 2H8 @ 150 for 300 (As increased by 12.4%)

ok

ok

ok

ok

ok

ok

ok

ok

Max Asw/s

ok

M

d As As2

kNm/m

mm mm² mm²

TOP STEEL

As prov

mm²


mm²

BTM STEEL kN kN kN


CENTRE 69.3 0.94 224.5 (x=28.1

SPAN 2 ACTIONS

LEFT 0.0 1.00 236.0 0 0 3H 12 /rib + 2H8 between 440 2H 16 /rib 402 43.53 35.24 29.96 2H8 @ 175 for 350 L/d 35.63

LEFT 89.4 0.85 232.0 840 233 2H 20 /rib + 2H12 between 855 2H 16 /rib 402 72.18 59.05 35.42 2H8 @ 150 for 300 L/d 40.09

ok ok

CENTRE 59.7 0.96 224.5 (x=28.1
314 25 982

/rib




ok

ok

ok

ok

ok

ok

ok

ok

Max Asw/s

ok

ok ok

225


17/07/2006 17:13:50

TCC32 Ribbed Slabs (A&D)/ SPANS!


The Concrete Centre

Spreadsheets to Eurocode 2 Advisory Group

Made by

3rd Floor slab, from 1 to 5a Checked



SPAN 3 ACTIONS

M

d As As2

DESIGN

kNm/m

mm mm² mm²

TOP STEEL

As prov

mm²


mm²

BTM STEEL kN kN kN


Date

rmw

LEFT 86.4 @col face 0.85 232.0 811 208 2H 20 /rib + 2H12 between 855 2H 16 /rib 402 65.51 53.05 35.42 2H8 @ 150 for 300 L/d 35.63

CENTRE 70.5 0.94 224.5 (x=28.1
Revision

chg

© 2003-2006 TCC

314 25 982

/rib


Page

03-Jul-06

-

/236 226 Job No

FB625



ok

ok

ok

ok

ok

ok

ok

ok

ok

Max Asw/s

ok

ok

226


17/07/2006 17:13:55

TCC32 Ribbed Slabs (A&D).xls TCC32 Ribbed Slabs (A&D)/ WEIGHT!

Project


Client

Advisory Group

Location



rmw Checked



© 2003-2006 TCC

Date

Page

03-Jul-06 Revision

227 237 Job No

chg

-

FB625


Location

No

Type

Dia

Length

Unit Wt

Weight

Support 1

3 2 4 2 2 4 2 2 4 3 2

T T T T T T T T T T T

12 8 10 20 12 10 20 12 10 12 8

2375 2375 4775 4250 4250 5275 4250 4250 4775 2375 2375

0.888 0.395 0.617 2.466 0.888 0.617 2.466 0.888 0.617 0.888 0.395

6.3 1.9 11.8 21.0 7.5 13.0 21.0 7.5 11.8 6.3 1.9


2 2 2 2 2 2 2

T T T T T T T

16 25 16 25 16 25 16

1000 7200 2175 8050 2175 7200 1575

1.578 3.853 1.578 3.853 1.578 3.853 1.578

3.2 55.5 6.9 62.0 6.9 55.5 5.0

Span 1 Span 2 Span 3

11 12 11

H H H

8 8 8

825 825 825

0.395 0.395 0.395

3.6 3.9 3.6

Span 1 Support 2 Span 2 Support 3 Span 3 Support 4

BOTTOM STEEL

LINKS

SUMMARY

All figures approximate - see User Guide



315.9

227


17/07/2006 17:14:00

TCC33 Flat Slabs (A&D).xls TCC33.xls analyses and automatically designs bays of simple rectangular flat slabs to BS EN 1992-1-1. The spreadsheet uses sub-frame analysis with pattern loading (as TCC21.xls) to calculate a bending moment envelope. This envelope may be subjected to redistribution. For a complete rectangular flat slab the user is expected to use the spreadsheet at least four times (internal bay(s) x - x, internal bay(s) y - y, edge bay(s) x - x and edge bay(s) y - y). Punching shear should be checked using TCC13.xls, or by hand. See also Eurocode 2 Clause 6.4., Punching. Beyond panel aspect ratios of 1.5 consideration might be given to the appropriateness of using other forms of analysis (e.g. grillage or finite element).

Cantilevers less than 1.00 m should be described as end distances rather than cantilevers; otherwise certain logic regarding breadth of effective moment transfer strip, be (see BSEN1992-1-1 Clause 9.4.2), goes wrong. On edge columns, be restricts the transfer moment, M, which in itself restricts the amount of moment transferred into columns above and below. End distances equivalent to the half width of the column should be used to define slabs whose edge is flush with the outside of the column. Load input should define the loads on the slab only. A combobox is used to switch between the internal or edge bays. If EDGE is chosen, cells F17 I15:J15 and E17:G17 become operative and information about the perimeter load along the edge and the distance of the edge from the centreline is required as input. Perimeter loading is assumed to be dead load.

MAIN!

Cell L52 gives an estimate of reinforcement requirements for the element considered in the direction considered (not both directions).

This sheet provides the main inputs to the spreadsheet (although other inputs occur in other sheets).

The spreadsheet takes automatic measures to ensure deflection criteria are met.

Most inputs are self-explanatory. LEGEND! should help with definition of dimensions, e.g. end distance in MAIN! F18: F19 is actually from centreline of column to the end/edge of the slab. Cover is defined as being to the layer under design.

To the right under Operating instructions a number of checks are carried out. Box markers indicate where checks have been carried out and proved satisfactory.

The layering is set at T1 - B1 (& T2 - B2) although T1 - B2 might be deemed more appropriate (e.g. with prefabricated mats)., Some cells have comments attached to them where terms might be unfamiliar to UK users. To the right hand side, by using the various combo boxes, the user should choose the type of usage, whether internal or edge bay, the preferred maximum size of bar, and whether brittle partitions need to be considered in the design. These all have effects on the detailed design. Covers requested at J9:J10 should be nominal covers (including ∆cdev). The number of spans is altered by entering data in the appropriate cells. Unwanted data cells are ‘greyed-out’. As with TCC 21, where support dimentions are not used the use of C, K, F or P can alter the characteristics of a support from Cantilever to Knife-edge to Fixed to Pinned. Extraneous data is highlighted in red or by messages in red. Under Operating Instructions in column L, a number of checks are carried out and problems found are highlighted. At the bottom of the sheet a simplistic loading diagram is given to aid data checking. Great care should be taken to ensure that this sheet is completed correctly for the case in hand. It may prove prudent to estimate values for bay width bending moments at each support by hand before progressing to ACTIONS!

ACTIONS! This sheet shows bending moment and shear force diagrams from the analysis undertaken in Analysis! The user is required to input the desired amount of redistribution to the initial moments in line 26. Cell L14 allows three types of distribution according to the user’s preference. The sheet also provides output reactions and column moments. For punching shear calculations, the values of ex/by and u1/u1* given in D60:I61 may be used for determination of the shear enhancement factor, ß

SPANS! SPANS! details the amounts of reinforcement required derived from detailed calculations in Bar! The warning message “Results Invalid - Run with Gk,inf may appear. This occurs when a check of the left hand side of support 2 reveals that the γGk,inf load case has not been calculated. The button to the right should be depressed to run the γGk,inf load case. EC2 requires that all spans should be loaded with both γGk,sup and γGk,inf. γGk,sup is used initially, and for γGk,inf the “Run-γGk,inf Loadcase” button must be activated. A red warning message will appear if this has not been done, or if any relevant input data are subsequently changed. Using γGk,inf (=1.0) leads to higher hogging moments in spans.

228


17/07/2006 17:14:04

TCC33 Flat Slabs (A&D).xls The top steel in the centre of spans is determined by adding together the steel required for the greater hogging at 1/4 span and the appropriate additional tensile force due to shear ∆Fed (see CI 9.2.1.3). It is assumed that 100% hogging steel at supports will be curtailed at 0.25 span or max 50%at 0,2 span and 50% at 0.3 span.

Bar!

LEGEND!

Hogging moments at 1/4 span positions within a span are checked and are used in the determination of top steel in spans.

LEGEND! gives an explanation of the dimensions used in MAIN! and for the analysis and design.

WEIGHT! WEIGHT! gives an estimate of the amount of reinforcement required in one direction of the slab for the internal or end bays considered. Simplified curtailment rules, similar to those used with BS 8110, are used to determine lengths of bars. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation, the effects of holes etc, etc. They do not allow for punching shear links or link carrier bars.

Uls! This sheet details the moment distribution analysis carried out at the ultimate limit state. The following patterns for imposed loading are considered to find a worse case. ■ All spans loaded ■ Odd spans loaded

This sheet shows design calculations, complete with references to BS EN 1992-1-1. It is not necessarily intended for printing out other than for checking purposes. The selection of bar sizes is automated.

Graf! This sheet comprises data for graphs used on other sheets, particularly in ACTIONS!

Refs! This sheet comprises Nationally Determined Parameters (NDP’s) contained within in the UK’s (draft) National Annexes to EN1990 (basis of design) and BS EN 1992-1-1. This page should be reviewed each time the spreadsheet is used to ensure the values remain valid for the UK or are valid for the country where the works are to be carried out or changed to suit. It is suggested that this page is printed out to accompany submissions of calculations that include this spreadsheet. It should be noted that it is possible to switch on the adjacent spans loaded by changing ‘b’ to ‘a’ in cell D6. BSEN 1992-1-1 recommends using the adjacent and alternate load arrangement. However to the UK National Annex only the cell spans and alternate load arrangements need to be considered.

■ Even spans loaded

Notes!

■ Adjacent spans loaded*


● Spans 1 & 2 and 5 & 6 loaded* ● Spans 2 & 3 loaded* ■ Spans 3 & 4 loaded* ■ Spans 4 & 5 loaded*



229


17/07/2006 17:14:05

TCC33 Flat Slabs (A&D)/ MAIN!

The Concrete Centre

Spreadsheets to EC2

Project Client

Advisory Group

Location

Made by

ECBP Typical Floor

FLAT SLAB ANALYSIS & DESIGN to Originated from TCC33.xls v3.0 on CD

MATERIALS

fck fyk fywk Steel class L (m)


7.500 7.500 7.500 7.500 7.500

35 500 500 A

A

from grids

to

D

rmw

EN 1992-1 : 2004 © 2003 - 2005 TCC

dg s c Wk


20 1.15 1.50 0.4 0.3

mm steel concrete mm top

325 325

H (mm)

B (mm)

End Cond

450 450 450 450 450 450

450 450 450 450 450 450

F F F F F F

Page

230 240

03-Jul-06

Checked

Revision

Job No

chg

-

FB625

COVERS Top cover Btm cover c,dev

mm

TO LAYER

25 25 10

1 1 mm

mm btm

PERIMETER LOADS characteristic 4.00 kN/m outside supports 1 & 6

GEOMETRY Bay type INTERNAL Slab depth, h 230 mm Int Panel width, b 7500 mm End distance End distance

Date


from supt 1 from supt 6

min

max

1.25

1.25 1.50

. SUPPORTS Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Support 7

ABOVE (m)

3.750 3.750 3.750 3.750 3.750 3.750

BELOW (m)

3.75 3.75 3.75 3.75 3.75 3.75 Usage: Office

LOADING

UDLs (kN/m²)


PLs (kN/m)

H (mm)

B (mm)

End Cond

450 450 450 450 450 450

450 450 450 450 450 450

F F F F F F


Position (m)

Dead

Imposed

Position

Loaded

Load

Load

from left

Length

6.75

5.00

~~~~~

~~~~~ ~~~~~ ~~~~~

6.75

5.00

~~~~~

~~~~~ ~~~~~ ~~~~~

6.75

5.00

~~~~~

~~~~~ ~~~~~ ~~~~~


Dead

Imposed

Position

Loaded

Load

Load

from left

Length

6.75

5.00

~~~~~

~~~~~ ~~~~~ ~~~~~

6.75

5.00

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

LOADING DIAGRAM

A

D

230


17/07/2006 17:14:07

TCC33 Flat Slabs (A&D).xls TCC33 Flat Slabs (A&D)/ ACTIONS!


The Concrete Centre

Spreadsheets to EC2 Advisory Group

Made by


rmw Checked

FLAT SLAB ANALYSIS & DESIGN to EN 1992-1 : 2004


Date

Revision

chg

© 2003 - 2005 TCC

Page

03-Jul-06

-

231 241 Job No

FB625


800

600

600

400

400

200

200

0

0

-200

-200

-400

-400

-600

-600

Elastic Moments SUPPORT No Elastic M Redistributed M δ Redistribution End support reinf. Ø mm

2

3

4

5

6

400.8 249.4 0.622

632.5 506.0 0.800 20.0%

558.0 530.1 0.950 5.0%

558.0 530.1 0.950 5.0%

632.5 506.0 0.800 20.0%

400.8 249.4 0.622

16 *

SPAN No Elastic M Redistributed M δ


1

~ ~ ~

16 *

1

2

3

4

5

363.0 468.8 1.291

320.2 322.2 1.006

328.4 309.9 0.944

320.2 322.2 1.006

363.0 468.8 1.291

~ ~ ~


600

400

400

200

200

0

0

-200

-200

-400

-400

-600

-600

0

10

20

30

40

0

10


1


427.2 413.8

SPAN No

2

482.3 482.6

452.5 444.9

452.5 444.9

482.3 482.6

4

Elastic V Redistributed V REACTIONS (kN/m) SUPPORT

443.9 451.2

20

40

3

443.9 451.2

448.0 448.0

448.0 448.0

427.2 413.8

~ ~

~ ~

5

1

2

3

4

5

6

ALL SPANS LOADED MAXIMUM Characteristic Dead Characteristic Imposed For punching ex /by

490.1 490.1 222.0 141.9

927.0 927.0 395.8 288.5 0.2225

899.2 899.2 377.8 285.0 0.2107

899.2 899.2 377.8 285.0 0.2107

927.0 927.0 395.8 288.5 0.2225

490.1 490.1 222.0 141.9

u1 /u1*

1.3114

COLUMN MOMENTS (kNm) ALL SPANS Above LOADED Below WITH MAX Above REACTION Below

30


(6.43) 1.3114

1

2

3

4

5

6

115.5 115.5 115.5 115.5

-23.9 -23.9 -23.9 -23.9

3.6 3.6 3.6 3.6

-3.6 -3.6 -3.6 -3.6

23.9 23.9 23.9 23.9

-115.5 -115.5 -115.5 -115.5

(6.44)

#DIV/0! #DIV/0! #DIV/0! #DIV/0!

231


17/07/2006 17:14:12

TCC33 Flat Slabs (A&D)/ SPANS!

Project

Spreadsheets to EC2

Client

Advisory Group

Location


Made by


rmw


Revision

Checked


chg

© 2003 - 2005 TCC

Page

232 242

03-Jul-06

-

Job No

FB625 .

.

SPAN 1 δ Be Total M Mt max

ACTIONS

kNm kNm

MIDDLE STRIP


COLUMN STRIP


CHECKS

% As Singly reinforced σs max S

SPAN 2 δ Be Total M Mt max

ACTIONS

kNm kNm

MIDDLE STRIP


COLUMN STRIP


CHECKS


LEFT

CENTRE

RIGHT

1.000 1000 165.0 230.9

1.291

0.800 3750 430.4 883.6

468.8

6500 16.0 199.0 30

3750 211.0 199.0 684 321 Provide H12 @ 375 T1 Provide H12 @ 150 B1 302 754 Provide H12 @ 375 T1 L/d = 7,500 /199 = 37.69 < 45.40 x 1.00 x 0.830 = 84.74 1000 165.0 197.0 2195

3750 257.8 199.0 837 542 Provide H16 @ 75 T1 Provide H12 @ 125 B1 2681 905 Provide H12 @ 325 T1 L/d = 7,500 /199 = 37.69 < 34.09 x 1.00 x 1.105 = 61.54

3750 107.6 201.0 346 Provide H8 @ 125 T1 402 OK

3750 322.8 199.0 1056 Provide H12 @ 75:150 T1 1131 OK

ok ok ok ok

ok ok ok ok

LEFT

CENTRE

RIGHT

0.800 3750 430.4 883.6

1.006

0.950 3750 432.3 883.6

322.2

3750 107.6 201.0 346


3750 177.2 199.0 575 246 Provide H12 @ 75:150 T1 Provide H12 @ 175 B1 1131 646 Provide H12 @ 325 T1 L/d = 7,500 /199 = 37.69 < 59.36 x 1.00 x 0.635 = 92.94 ok ok ok ok

ok ok ok ok

ok ok ok ok

3750 108.1 200.0 349 Provide H10 @ 225 T1 349 OK

3750 324.2 199.0 1061 Provide H12 @ 75:150 T1 1131 OK ok ok ok ok

232


17/07/2006 17:14:18

TCC33 Flat Slabs (A&D).xls TCC33 Flat Slabs (A&D)/ SPANS!

Spreadsheets to EC2

Project Client

The Concrete Centre

Advisory Group

Location


rmw


ACTIONS

δ Be Total M Mt max

kNm kNm

MIDDLE STRIP


COLUMN STRIP


CHECKS


SPAN 4 ACTIONS


kNm kNm

MIDDLE STRIP


COLUMN STRIP


CHECKS


chg

© 2003 - 2005 TCC

Page

03-Jul-06 Revision

Checked


SPAN 3

Date

Made by

-

LEFT

CENTRE

RIGHT

0.950 3750 432.3 883.6

0.944

0.950 3750 432.3 883.6

309.9

243 233 Job No

FB625

3750 108.1 200.0 349

3750 3750 139.5 108.1 200.0 200.0 450 349 128 Provide H10 @ 225 T1 Provide H10 @ 150 B1 Provide H10 @ 225 T1 349 524 349 Provide H12 @ 375 T1 L/d = 7,500 /200 = 37.50 < 88.38 x 1.00 x 0.424 = 135.85 OK 3750 324.2 199.0 1061

3750 3750 170.5 324.2 199.0 199.0 553 1061 238 Provide H12 @ 75:150 T1 Provide H12 @ 200 B1 Provide H12 @ 75:150 T1 1131 565 1131 Provide H12 @ 375 T1 L/d = 7,500 /199 = 37.69 < 63.12 x 1.00 x 0.597 = 84.96 OK ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

LEFT

CENTRE

RIGHT

0.950 3750 432.3 883.6

1.006

0.800 3750 430.4 883.6

322.2

3750 108.1 200.0 349

3750 145.0 200.0 468 133 Provide H10 @ 225 T1 Provide H10 @ 150 B1 349 524 Provide H12 @ 375 T1 L/d = 7,500 /200 = 37.50 < 83.02 x 1.00 x 0.452 = 131.56

3750 107.6 201.0 346 Provide H8 @ 125 T1 402 OK

3750 324.2 199.0 1061

3750 3750 177.2 322.8 199.0 199.0 575 1056 246 Provide H12 @ 75:150 T1 Provide H12 @ 175 B1 Provide H12 @ 75:150 T1 1131 646 1131 Provide H12 @ 325 T1 OK L/d = 7,500 /199 = 37.69 < 59.36 x 1.00 x 0.635 = 92.94 ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

233


17/07/2006 17:14:22

TCC33 Flat Slabs (A&D)/ SPANS!

Project

Spreadsheets to EC2

Client

Advisory Group

Location

The Concrete Centre

rmw


ACTIONS


kNm kNm

MIDDLE STRIP


COLUMN STRIP


CHECKS


chg

© 2003 - 2005 TCC

Page

-

LEFT

CENTRE

RIGHT

0.800 3750 430.4 883.6

1.291

1.000 1000 165.0 230.9

468.8

3750 107.6 201.0 346


3750 257.8 199.0 837 542 Provide H12 @ 75:150 T1 Provide H12 @ 125 B1 1131 905 Provide H12 @ 325 T1 L/d = 7,500 /199 = 37.69 < 34.09 x 1.00 x 1.105 = 61.54 ok ok ok ok

ok ok ok ok

234 244

03-Jul-06 Revision

Checked


SPAN 5

Date

Made by


Job No

FB625

6500 2.1 199.0 4 Provide H12 @ 375 T1 302 OK

1000 165.0 197.0 2195 Provide H16 @ 75 T1 2681 OK ok ok ok ok

234


17/07/2006 17:14:27

TCC33 Flat Slabs (A&D).xls TCC33 Flat Slabs (A&D)/ LEGEND!

Spreadsheets to EC2

Project Client

Advisory Group

Location



rmw



© 2003 - 2005 TCC

Date

Page

235 245

03-Jul-06

Checked

Revision

chg

-

Job No

FB625

Legend for input data on MAIN sheet

Diagram shows legend for frames centred on EW gridlines - rotate 90° for frames centred on NS gridlines.

235


17/07/2006 17:14:32

TCC33 Flat Slabs (A&D)/ WEIGHT!

The Concrete Centre

Project

Spreadsheets to EC2

Client Location


Made by


Checked


rmw © 2003 - 2005 TCC

Date

Page

246 236

03-Jul-06 Revision

Job No

chg

-

FB625

No WEIGHT of REINFORCEMENT Mid Strip Col Strip TOP STEEL Support 1 18 15 Span 1 10 12 Support 2 30 38 Span 2 10 12 Support 3 17 38 Span 3 10 10 Support 4 17 38 Span 4 10 12 Support 5 30 38 Span 5 10 12 Support 6 18 15

BTM STEEL

Span 1

25 30

Span 2

25

Span 3

25

Span 4

25

Span 5

25

22 19 22 30

Type

Dia

Length

Unit wt

Weight

T T T T T T T T T T T T T T T T T T T T T T

12 16 12 12 8 12 12 12 10 12 12 12 10 12 12 12 8 12 12 12 12 16

2725 2725 5050 5050 3750 3750 5050 5050 3750 3750 5050 5050 3750 3750 5050 5050 3750 3750 5050 5050 2725 2725

0.888 1.578 0.888 0.888 0.395 0.888 0.888 0.888 0.617 0.888 0.888 0.888 0.617 0.888 0.888 0.888 0.395 0.888 0.888 0.888 0.888 1.578

43.5 64.5 44.8 53.8 44.4 126.5 44.8 53.8 39.3 126.5 44.8 44.8 39.3 126.5 44.8 53.8 44.4 126.5 44.8 53.8 43.5 64.5

T T T T T T T T T T

12 12 10 12 10 12 10 12 12 12

6975 7950 6825 7650 6825 7650 6825 7650 6975 7950

0.888 0.888 0.617 0.888 0.617 0.888 0.617 0.888 0.888 0.888

154.8 211.7 105.2 149.4 105.2 129.0 105.2 149.4 154.8 211.7

SUMMARY Rebar for single direction only. All figures approximate - see User Guide. TOTAL REINFORCEMENT IN BAY (kg) 2850

3

REINFORCEMENT DENSITY (kg/m )

43.3

236


17/07/2006 17:14:39

TCC33X Flat Slabs (A&D).xls

TCC33X Flat Slabs (A&D).xls TCC33X designs flat slabs in both orthogonal directions by running TCC33 for each grid line and collecting the data generated. It uses macros heavily and takes some time to run, once the “Run Results” button is pressed. It is intended to be used for the design of flat slabs in braced structures only, where all columns are on grid and where there are no major openings.

indicates that the central half of the column strip has bars at 125 mm centres, with 250 mm centres being required over the remainder of the strip width.

This spreadsheet also checks basic punching shear stresses around each column and gives an indication of the degree of shear reinforcing required. As it is impractical within this spreadsheet to model a variety of holes adjacent to columns, the user should check the effects of holes separately by using TCC13.

Summary 6 gives both characteristic and maximum ultimate column reactions.

Sheets ACTIONS!, SPANS!, LEGEND!, Weight!, Uls!, Sls!, Bar!, Gra!, Refs! and Notes!, work in the same way as TCC33.

Summary 8 indicates the levels of punching shear stress by summarizing actual stress divided by allowable stress at both the basic control perimeter, u1 and at the column face. Where values are greater than unity, shear links or studs are required and may be designed using TCC13. Alternatively or additionally, greater punching resistance may be provided at a column by either a) increasing levels of top reinforcement, or b) adding shear heads at columns (see INPUT! cell K34).

INPUT! All relevant materials, geometric and loading data is input on this sheet.

Summary 5 gives principal design bending moments throughout each gridline.

Summary 7 similarly displays column design moments and values of ß VEd for punching shear.

As spans are entered into cells C13:E18, the key diagram below will change in order to serve as a visual check on the correct input of geometry. Although the plan is to scale, the columns on this key diagram are indicative only and do not reflect the column sizes entered.

MAIN! ACTIONS! SPANS! LEGEND! WEIGHT! Uls! Sls! Bar! Graf! Refs!

Correct gridlines must be entered at cells G13 to H19. These are used to name the various runs on individual grids, so it is important that there are no duplicates and that the correct number of grids are entered.

These sheets are identical to the sheet of the same name in TCC33, except that input values are controlled from INPUT! and may not be amended. In MAIN! if it is required to print out detailed calculations for a particular gridline, the gridline should be selected via the combo-boxes in L16. First select direction (either EW or NS), then the required gridline.

The edge distances (centre line of column to edge of slab) in cells O12 to O15 are equally important, as both analysis and punching shear calculations are very sensitive to these values.

In ACTIONS!, the redistribution is controlled by INPUT! L22.

When all input is complete, the “RUN RESULTS” button should be clicked. This then designs the frame on each gridline in turn, and summarizes data on the RESULTS sheet. If any data changes are subsequently made, the RESULTS VALID message at cell P17 will change to “PRESS RUN BUTTON”.

RESULTS! This sheet has eight printable pages: Summary 1 repeats the key and legend diagrams, displays validity checks for the sub-frames on all gridlines, gives a guide to the levels of shear stress and gives the reinforcement density as designed.

In SPANS! the γGk,inf case is run automatically when the Run Results Button is used.

Punch! This sheet gives details of the various values used in punching shear calculations at all columns. These being, dave, pl, vRdc, u1, u1*, u0, ß and vEd.


Summary 2 to Summary 4 display reinforcement call-ups for each of the four layers, T1, T2, B1 and B2. The top steel in some column strips will have a call-up such as 20 H16 @ 125:250. This 237


17/07/2006 17:14:43

TCC33X Flat Slabs (A&D)/ INPUT!

The Concrete Centre

Project

Spreadsheets to EC2

Client

Advisory Group Third floor slab

Made by


Checked

Location

Originated from TCC33X.xls v3.0 on CD

fck fyk Steel class

SPANS (m) Span A - B

N-S 7.500

Span B - C Span C - D Span D - E

7.500 7.500 7.500

1 A

35 500 A

N/mm² N/mm²

Span 1 - 2

E-W 7.500

Span 2 - 3 Span 3 - 4

7.500 7.500

dg c,dev Wk

GRIDLINES

MATERIALS

20 5 0.4 0.3 N/S 1

Revision

mm mm top

Top cover Btm cover

2 3 4

B C D E

238 248 SLAB DEPTH (mm)

25 25

h=

250

EDGE DISTANCES (mm)

mm btm

E/W A

FB625

Page

-

COVERS (mm)

mm

Job No

03-Jul-06

chg

© 2004-6 The Concrete Centre

COLUMN SIZES (mm) Internal North edge South edge East edge West edge Corners

400 250 250 400 400 250

400 400 400 250 250 250

Redistribution

15%

%

Preferred max bar Ø End support reinf. Ø

20 20

mm

Brittle partitions ? Usage

Yes

Columns heads ?

No

North South

125 125

East West

125 125

LOADING (kN/m²)

4

Columns below Yes Length 3.750 m End condition F F or P E

Date

Rod

Applied dead 0.50 Partitions 1.00 Imposed 2.50 Perimeter cladding kN/m 8.50

mm

st

AGE at 1 CRACKING 14 days (3 - 28)

Office Columns above ? Yes Length 3.750 m End condition F F or P Projection from column face

mm

238


17/07/2006 17:14:45

TCC33X Flat Slabs (A&D).xls TCC33X Flat Slabs (A&D)/ RESULTS! Summary 1 and Summary 2 Project

Spreadsheets to EC2

Client

Advisory Group

Location

Third floor slab


Date

Rod Checked



Summary 1 1 A


Page

249 239

03-Jul-06 Revision

chg

Job No

-

FB625

4

Rotate 90° for frames centred on NS gridlines.

Rebar Layering B1 & T1

B2 & T2

E Legend for frames on EW gridlines

TO SCALE PLAN VALIDITY Grid Grid Grid Grid

PUNCHING

Deflection

%age As

End bar Ø

1 2 3 4

Grid A Grid B Grid C Grid D Grid E

Deflection

%age As

End bar Ø

SHEAR VERY HIGH at SOME COLUMNS

Heads with a 400 projection should give few or no links at internal columns.

See page Summary 8

Alternatively, increases in top steel over columns will reduce link requirements.

REINFORCEMENT

Estimated quantities (excluding any shear links) Concrete volume, m³ 172.0

Quantities allow for laps, but not for wastage, rationalisation or steel increases for shear. Total weight, Tonnes 12.84 Rebar density, kg/m³ 74.7 Project

Spreadsheets to EC2

Client

Advisory Group

Location

Third floor slab

Rebar density, kg/m² 18.7


Rod Checked




chg

Date

Page

03-Jul-06 Revision

250 239 Job No

-

FB625

Summary 2

RESULTS - DESIGN TOP REINFORCEMENT Grid 1

Layer T2 Grid 2

Grid 3

Grid 4

Support A

Column strip

4 H20 @ 150

4 H20 @ 225

4 H20 @ 225

4 H20 @ 150

Middle strip

13 H10 @ 275

25 H10 @ 275

25 H10 @ 275

13 H10 @ 275

Span A - B

Column strip

8 H10 @ 275

14 H10 @ 275

14 H10 @ 275

8 H10 @ 275

Middle strip

7 H10 @ 275

14 H10 @ 275

14 H10 @ 275

7 H10 @ 275

Support B

Column strip

15 H16 @ 100:200

23 H16 @ 125:250

23 H16 @ 125:250

15 H16 @ 100:200

Middle strip

19 H8 @ 100

30 H8 @ 125

30 H8 @ 125

19 H8 @ 100

Span B - C

Column strip

10 H10 @ 200

10 H12 @ 375

10 H12 @ 375

10 H10 @ 200

Middle strip

7 H10 @ 275

14 H10 @ 275

14 H10 @ 275

7 H10 @ 275

Support C

Column strip

10 H16 @ 150:300

17 H16 @ 175:350

17 H16 @ 175:350

10 H16 @ 150:300

Middle strip

15 H8 @ 125

22 H8 @ 175

22 H8 @ 175

15 H8 @ 125

Span C - D

Column strip

10 H10 @ 200

10 H12 @ 375

10 H12 @ 375

10 H10 @ 200

Middle strip

7 H10 @ 275

14 H10 @ 275

14 H10 @ 275

7 H10 @ 275

Support D

Column strip

15 H16 @ 100:200

23 H16 @ 125:250

23 H16 @ 125:250

15 H16 @ 100:200

Middle strip

19 H8 @ 100

30 H8 @ 125

30 H8 @ 125

19 H8 @ 100

Column strip

8 H10 @ 275

14 H10 @ 275

14 H10 @ 275

8 H10 @ 275

Middle strip

7 H10 @ 275

14 H10 @ 275

14 H10 @ 275

7 H10 @ 275

Column strip

4 H20 @ 150

4 H20 @ 225

4 H20 @ 225

4 H20 @ 150

Middle strip

13 H10 @ 275

25 H10 @ 275

25 H10 @ 275

13 H10 @ 275

Span D - E Support E

Column strip Middle strip Column strip Middle strip Column strip Middle strip Column strip Middle strip

239


17/07/2006 17:14:51

TCC33X Flat Slabs (A&D)/ RESULTS! Summary 3 and Summary 4 Project

Spreadsheets to EC2

Client

Advisory Group

Location

Third floor slab


Date

Rod Checked



Summary 3 TOP REINFORCEMENT Grid A

Layer T1 Grid B


Page

Revision

chg

Grid C

Grid D

Grid E

Support 1

Column strip

4 H20 @ 175

4 H20 @ 250

4 H20 @ 250

4 H20 @ 250

4 H20 @ 175

Middle strip

9 H12 @ 400

18 H12 @ 400

18 H12 @ 400

18 H12 @ 400

9 H12 @ 400

Span 1 - 2

Column strip

5 H12 @ 400

11 H12 @ 350

11 H12 @ 350

11 H12 @ 350

5 H12 @ 400

Middle strip

5 H12 @ 400

10 H12 @ 400

10 H12 @ 400

10 H12 @ 400

5 H12 @ 400

Support 2

Column strip

12 H16 @ 125:250

19 H16 @ 150:300

19 H16 @ 150:300

19 H16 @ 150:300

12 H16 @ 125:250

Middle strip

19 H8 @ 100

25 H8 @ 150

25 H8 @ 150

25 H8 @ 150

19 H8 @ 100

Span 2 - 3

Column strip

9 H10 @ 225

11 H12 @ 350

11 H12 @ 350

11 H12 @ 350

9 H10 @ 225

Middle strip

8 H10 @ 250

10 H12 @ 400

10 H12 @ 400

10 H12 @ 400

8 H10 @ 250

Support 3

Column strip

12 H16 @ 125:250

19 H16 @ 150:300

19 H16 @ 150:300

19 H16 @ 150:300

12 H16 @ 125:250

Middle strip

19 H8 @ 100

25 H8 @ 150

25 H8 @ 150

25 H8 @ 150

19 H8 @ 100

Span 3 - 4

Column strip

5 H12 @ 400

11 H12 @ 350

11 H12 @ 350

11 H12 @ 350

5 H12 @ 400

Middle strip

5 H12 @ 400

10 H12 @ 400

10 H12 @ 400

10 H12 @ 400

5 H12 @ 400

Support 4

Column strip

4 H20 @ 175

4 H20 @ 250

4 H20 @ 250

4 H20 @ 250

4 H20 @ 175

Middle strip

9 H12 @ 400

18 H12 @ 400

18 H12 @ 400

18 H12 @ 400

9 H12 @ 400

251 240

03-Jul-06

Job No

-

FB625

Column strip Middle strip Column strip Middle strip Column strip Middle strip Column strip Middle strip Column strip Middle strip Column strip Middle strip

Project

Spreadsheets to EC2

Client

Advisory Group

Location

Third floor slab


Rod Checked



Summary 4 BOTTOM REINFORCEMENT Span A - B

Column strip

Span B - C

Column strip

Span C - D

Column strip

Span D - E

Column strip

Middle strip

Middle strip

Middle strip

Middle strip


Grid 1 H16 @ 225 H16 @ 250 H16 @ 325 H16 @ 375 H16 @ 325 H16 @ 375 H16 @ 225 H16 @ 250

Layer B2 Grid 2 H12 @ 125 H12 @ 175 H10 @ 150 H10 @ 175 H10 @ 150 H10 @ 175 H12 @ 125 H12 @ 175

Grid 3 H12 @ 125 H12 @ 175 H10 @ 150 H10 @ 175 H10 @ 150 H10 @ 175 H12 @ 125 H12 @ 175

Grid 4 H16 @ 225 H16 @ 250 H16 @ 325 H16 @ 375 H16 @ 325 H16 @ 375 H16 @ 225 H16 @ 250

Grid A H16 @ 225 H16 @ 275 H12 @ 250 H12 @ 300 H16 @ 225 H16 @ 275

Grid B H12 @ 150 H10 @ 125 H8 @ 150 H8 @ 150 H12 @ 150 H10 @ 125

Grid C H12 @ 150 H10 @ 125 H8 @ 150 H8 @ 150 H12 @ 150 H10 @ 125

Grid D H12 @ 150 H10 @ 125 H8 @ 150 H8 @ 150 H12 @ 150 H10 @ 125

chg

Date

Page

03-Jul-06 Revision

240 252 Job No

-

FB625

Column strip Middle strip Column strip Middle strip

Layer B1 Span 1 - 2

Column strip Middle strip

Span 2 - 3

Column strip

Span 3 - 4

Column strip

Middle strip

Middle strip

Grid E H16 @ 225 H16 @ 275 H12 @ 250 H12 @ 300 H16 @ 225 H16 @ 275

Column strip Middle strip Column strip Middle strip Column strip Middle strip

240


17/07/2006 17:14:58

TCC33X Flat Slabs (A&D).xls TCC33X Flat Slabs (A&D)/ RESULTS! Summary 5 and Summary 6 Project

Spreadsheets to EC2

Client

Advisory Group

Location

Third floor slab


Checked



Summary 5 RESULTS FROM ANALYSIS - BENDING MOMENTS Grid 1 Grid 2 Support A 76.86 107.26 Span A - B 261.97 424.88 Support B 316.53 524.40 Span B - C 174.50 272.06 Support C 231.18 377.92 Span C - D 174.50 272.06 Support D 316.53 524.40 Span D - E 261.97 424.88 Support E 76.86 107.26

Grid A 78.11 265.64 306.08 141.25 306.08 265.64 78.11

Support 1 Span 1 - 2 Support 2 Span 2 - 3 Support 3 Span 3 - 4 Support 4

Date

Rod

Grid B 108.45 428.91 513.05 208.30 513.05 428.91 108.45

Project

Spreadsheets to EC2

Client

Advisory Group

Location

Third floor slab

Revision

chg


Page

Job No

-

Grid 4 76.86 261.97 316.53 174.50 231.18 174.50 316.53 261.97 76.86

Grid C 108.45 428.91 513.05 208.30 513.05 428.91 108.45

Grid D 108.45 428.91 513.05 208.30 513.05 428.91 108.45

FB625 kNm

at support centrelines and maxima in spans

Grid 3 107.26 424.88 524.40 272.06 377.92 272.06 524.40 424.88 107.26

241 253

03-Jul-06

Grid E 78.11 265.64 306.08 141.25 306.08 265.64 78.11


Rod Checked




chg

Date

Page

03-Jul-06 Revision

241 254 Job No

-

FB625

Summary 6 COLUMN REACTIONS Characteristic dead load, kN Grid A Grid B Grid C Grid D Grid E

Grid 1 146.52 287.30 248.58 287.30 146.52

Grid 2 280.63 420.33 412.30 420.33 280.63

Grid 3 280.63 420.33 412.30 420.33 280.63

Grid 4 146.52 287.30 248.58 287.30 146.52

Grid 2 105.23 213.80 206.33 213.80 105.23

Grid 3 105.23 213.80 206.33 213.80 105.23

Grid 4 49.04 108.33 95.99 108.33 49.04

Grid 2 508.29 845.59 824.36 845.59 508.29

Grid 3 508.29 845.59 824.36 845.59 508.29

Grid 4 256.52 521.27 454.40 521.27 256.52

Characteristic imposed load, kN Grid A Grid B Grid C Grid D Grid E

Grid 1 49.04 108.33 95.99 108.33 49.04

Maximum ultimate load VEd, kN Grid A Grid B Grid C Grid D Grid E

Grid 1 256.52 521.27 454.40 521.27 256.52

without enhancement factor,

241


17/07/2006 17:15:03

TCC33X Flat Slabs (A&D)/ RESULTS! Summary 7 and Summary 8 Project

Spreadsheets to EC2

Client

Advisory Group

Location

Third floor slab


Date

Rod Checked



Revision

chg


Page

242 255

03-Jul-06

Job No

-

FB625

Summary 7 COLUMN MOMENTS Ultimate, kNm Grid 1

Grid 2

Grid 3

Grid 4

32.70 / 33.46

44.52 / -13.95

44.52 / 13.95

32.70 / -33.46

Grid A

Above Below

32.70 / 33.46

44.52 / -13.95

44.52 / 13.95

32.70 / -33.46

Grid B

Above

-10.84 / 45.24

-31.72 / -38.97

-31.72 / 38.97

-10.84 / -45.24

Below

-10.84 / 45.24

-31.72 / -38.97

-31.72 / 38.97

-10.84 / -45.24

Grid C

Above

0.00 / 45.24

0.00 / -38.97

0.00 / 38.97

0.00 / -45.24

Below

0.00 / 45.24

0.00 / -38.97

0.00 / 38.97

0.00 / -45.24

Grid D

Above

10.84 / 45.24

31.72 / -38.97

31.72 / 38.97

10.84 / -45.24

Below

10.84 / 45.24

31.72 / -38.97

31.72 / 38.97

10.84 / -45.24

Grid E

Above

-32.70 / 33.46

-44.52 / -13.95

-44.52 / 13.95

-32.70 / -33.46

Below

-32.70 / 33.46

-44.52 / -13.95

-44.52 / 13.95

-32.70 / -33.46

Grid 2 601.5 990.7 936.4 990.7 601.5

Grid 3 601.5 990.7 936.4 990.7 601.5

Grid 4 327.4 609.6 511.5 609.6 327.4

Above Below Above Below

Punching shear load VEd, kN Grid A Grid B Grid C Grid D Grid E

Grid 1 327.4 609.6 511.5 609.6 327.4

Project

Spreadsheets to EC2

Client

Advisory Group

Location

Third floor slab


Rod Checked



Summary 8 PUNCHING, v Ed / v Rdc Grid A Grid B Grid C Grid D Grid E


Adjacent holes will increase values

Grid 1

Grid 2

Grid 3

Grid 4

2.270 2.101 1.886 2.101 2.270

2.107 1.640 1.640 1.640 2.107

2.107 1.640 1.640 1.640 2.107

2.270 2.101 1.886 2.101 2.270

Date

Page

03-Jul-06 Revision

chg

256 Job No

-

FB625

Without column heads No links Some links Many links Very many

PUNCHING, v Ed / v Rd.max Grid A Grid B Grid C Grid D Grid E

Adjacent holes will increase values

Grid 1

Grid 2

Grid 3

Grid 4

0.531 0.546 0.458 0.546 0.531

0.539 0.497 0.470 0.497 0.539

0.539 0.497 0.470 0.497 0.539

0.531 0.546 0.458 0.546 0.531

v Rd.max (Mpa) = 6.020 < 50% 50 to 75% 75 to 100% FAILS

242


17/07/2006 17:15:09

TCC41 Continuous Beams.xls

TCC41 Continuous Beams.xls The spreadsheet designs multiple-span rectangular or flanged beams to BS EN 1991-1-1 using sub-frame analysis to derive moments and shears. The intention is to provide the design and analysis of up to six spans of continuous beams with columns above and below. Spans may incorporate cantilevers, fixed ends or knife-edge supports. There are three main sheets: MAIN!, ACTIONS! and SPANS!

MAIN! This sheet contains user input of materials, frame geometry and load data. Input data is blue and underlined. New data may be input by overwriting default values or by entering values in ‘greyed-out’ cells. Entering a value of 5.0 in cell C18 will clear a line of data in both the span and support data ready for input. Guidance on input for the type of section and type of end condition of the support is given under ‘Operating instructions’. The dimensions of the flange widths, beff, are entered manually, but maximum permitted values can be seen in cells M12:M17. It is important that the correct usage of the members under consideration is selected from the combo-box to the right of the screen, as this affects the magnitude of quasi-permanent SLS moments. The sheet has been set up with as many ‘carry throughs’ as possible, i.e. input cells are made equal to preceding input cells to make the inputting of regular beams easier. Inputting C18 as = C17 will insert 6.00 in the remaining spans: it will also remove the grey conditional background to the remaining spans, supports and loads and allow data entry. Deleting C18, indeed C19, will blank out remaining spans, etc. Generally, values in red or red backgrounds indicate either incorrect or excess data. For instance, if knife-edge supports are required, entering ‘K’ in cell C24 will elicit red data to the right, which needs to be cleared manually. Point loads should be at least 0.001m from a support. Do not copy and paste input values as this can corrupt formatting (copy and paste values only is OK). ‘Rebar layering’ refers to whether there are beams in the other direction. Answering yes drops by one bar diameter the steel at the supports. For instance when using splice bars at the support bars in the other direction have to be avoided - and allowed for in the design. With respect to cantilevers, design for bending caters for moments at the face of support; design for deflection considers the cantilever from the centre line of support. In beam-to-beam situations the width of support can be input as being very small to avoid under-design in bending.

The dimensions of the flange widths, beff, are entered manually, but maximum permitted values can be seen in cells M12:M17. It is important that the correct usage of the members under consideration is selected from the combo-box to the right of the screen, as this affects the magnitude of quasi-permanent SLS moments.

ACTIONS! ACTIONS! includes bending moment and shear force diagrams, summaries of moments and shears and user input for amounts of redistribution. Users should ensure that the amounts of redistribution are always considered and selected in line 26 as there are no default values.

SPANS! This sheet designs reinforcement for bending in spans and supports and for shear in the spans. User input is required for reinforcement sizes – some intuition may be required to obtain sensible arrangements of reinforcement. Non-existent spans are blanked out. Support moments (including cantilever moments) are considered at the face of the support. This may lead to unequal amounts of reinforcement being designed for each side of the support. See Bar! EC2 requires that all spans should be loaded with both γGk,sup and γGk,inf . γGk,sup is used initially, and for γGk,inf the “Run γGk,inf Loadcase” button must be activated. A red warning message will appear if this has not been done, or if any relevant input data are subsequently changed. Using γGk,inf (=1.0) leads to higher hogging moments in spans. With regard to deflection, the area of steel required, As mm2 /m, shown under ‘Design for the Centre’ part of the span, may have been automatically increased in order to reduce service stress, σs, and increase modification factors to satisfy deflection criteria. The percentage increase, if any, is shown under ‘Deflection’. An additional limit of maximum allowable area of steel to comply with deflection criteria, As def, = 1.5 x As reqd has been imposed in line with UK Nation Annex, Note 5 to Table 7.4.N (BS). With respect to cantilevers, neither compression steel enhancement nor consideration of rotation at supports is included. The top steel in the centre of spans is determined by adding together the steel required for hogging at 1/4 span and the appropriate additional tensile force due to shear ∆Fed (see CI 9.2.1.3). It is assumed that 100% hogging steel at supports will be curtailed at 0.25 span or max 50%at 0,2 span and 50% at 0.3 span.

243


17/07/2006 17:15:15

WEIGHT!

Refs!

This sheet estimates the weight of reinforcement in the beam when designed according to normal curtailment rules similar to those defined in BS 8110. Workings are shown on the right hand side of the sheet. The estimate may be printed out using File/print or the print button on the normal toolbar. It should be recognised that different engineers’ and detailers’ interpretations of these clauses, and different project circumstances and requirements will all have a bearing on actual quantities used.

This sheet comprises the values for nationally determined parameters that have been used in the spreadsheet. These data reflect the values given in draft UK National Annexes for EN 1990 and EN 1992.

Uls! This sheet details the moment distribution analysis carried out at the ultimate limit state. The following patterns for imposed loading are considered to find a worse case.

Designers should ensure that these data are current when the spreadsheet is used. When using TCC31 for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations. It should be noted that it is possible to switch on the adjacent spans loaded arrangement by changing ‘b’ to ‘a’ in cell D7. BS EN 1992-1-1 recommends using the adjacent and alternate load arrangements. However to the UK National Annex, only the alt spans and alternate spans load arrangements need to be considered.

■ All spans loaded ■ Odd spans loaded ■ Even spans loaded ■ Adjacent spans loaded*


● Spans 1 & 2 and 5 & 6 loaded* ● Spans 2 & 3 loaded* ■ Spans 3 & 4 loaded* ■ Spans 4 & 5 loaded*




Graf! This sheet provides data for the charts in MAIN! and ACTIONS!: it is not intended for formal printing. 244


17/07/2006 17:15:17

TCC41 Continuous Beams.xls TCC41 Continuous Beams/ MAIN! Project

Spreadsheets to EC2

Client

Advisory Group

Location


Worked Examples: Main beam Grids C to J CONTINUOUS BEAM ANALYSIS & DESIGN

to

rmw


chg

© 2000-2006 TCC

MATERIALS 30

N/mm²

fyk

500

N/mm²

dg (mm) γs

fywk Steel class

500 A

N/mm²

γc


Revision

-

FB625

20

Wk (mm)Top 0.4

Top cover

20

mm

Wk (mm)Btm 0.3

Btm cover

30

mm

Side cover

30

mm

1.50 5000

c,dev 10 mm

L (m)

h (mm)

bw (mm)

hf (mm)

Type

beff (mm)

450 450 450 450

300 300 300 300

125 125 125 125

T T T T

2170 1715 1715 2170

H (mm)

B (mm)

End Cond

BELOW (m)

H (mm)

B (mm)

End Cond

250 300 300 300 250

250 300 300 300 250

F F F F F

3.750 3.750 3.750 3.750 3.750

250 300 300 300 250

250 300 300 300 250

F F F F F

3.750 3.750 3.750 3.750 3.750

245 255 Job No

1.15

6.000 6.000 6.000 6.000

ABOVE (m)

Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Support 7

Bay width

Page

03-Jul-06

COVERS (to links)

STATUS OK

fck

SUPPORTS

Checked

EN 1992-1 : 2004

Date

Usage: Shopping

LOADING PATTERN (6.10b) min max DEAD 1.25 1.25 IMPOSED 1.50 REBAR LAYERING Support steel in alt layer ? N


LOADING DIAGRAM

LOADING

UDLs (kN/m²)

PLs (kN)

Position (m)

Dead

Imposed

Load

Load

Position from left

Loaded Length

37.8

12.0

~~~~~

~~~~~ ~~~~~ ~~~~~

37.8

12.0

~~~~~

~~~~~ ~~~~~ ~~~~~

37.8

12.0

~~~~~

~~~~~ ~~~~~ ~~~~~

1 169.2 169.7 93.3 32.8 -3.3

2 421.3 421.3 252.3 80.0 39.9

3 385.2 385.2 217.0 68.8 34.4


REACTIONS (kN) SUPPORT ALL SPANS LOADED MAX ULTIMATE Characteristic Dead Max Imposed Min Imposed

Dead

Imposed


Load

Load

Position from left

Loaded Length

37.8

12.0

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

4 421.3 421.3 252.3 80.0 39.9

5 169.2 169.7 93.3 32.8 -3.3

245


17/07/2006 17:15:18

TCC41 Continuous Beams/ ACTIONS! Project

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rmw Checked

CONTINUOUS BEAM ANALYSIS & DESIGN to EN 1992-1 : 2004


Date

Revision

chg

© 2000-2006 TCC

Page

03-Jul-06

-

256 246 Job No

FB625


250

250

200

200

150

150

100

100

50

50

0

0

-50

-50

-100

-100

-150

-150

-200

-200

-250

Elastic Moments SUPPORT No Elastic M Redistributed M δ


1

2

3

4

5

40.9 40.9 1.000

246.9 197.5 0.800

178.5 178.5 1.000

246.9 197.5 0.800

40.9 40.9 1.000

~ ~ ~

~ ~ ~

~ ~ ~

Redistribution SPAN No

20.0% 1

Elastic M 169.8 Redistributed M 181.3 δ 1.068 SHEARS FORCE DIAGRAMS (kN)

kNm/m kNm/m ~

20.0%

2

3

4

108.9 113.9 1.046

108.9 113.9 1.046

169.8 181.3 1.068

250

300

200 200

150 100

100

50 0

0

-50 -100

-100 -150

-200

-200 -300

-250

Elastic Shears SPAN No Elastic V Redistributed V

165.8 169.7

COLUMN MOMENTS (kNm) ALL SPANS Above LOADED Below ALT SPANS Above LOADED Below

2

3

230.6 222.4

204.4 201.6

188.2 192.6

188.2 192.6

204.4 201.6

165.8 169.7

~ ~

~ ~

~ ~

~ ~

1

2

3

4

5

19.0 19.0 20.4 20.4

-8.3 -8.3 -15.6 -15.6

8.6 8.6

8.3 8.3 15.6 15.6

-19.0 -19.0 -20.4 -20.4

SPAN No Elastic V Redistributed V


4

230.6 222.4

246


17/07/2006 17:15:25

TCC41 Continuous Beams.xls TCC41 Continuous Beams/ SPANS! Project

Spreadsheets to EC2

Client

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Location



Date

rmw Checked



Revision

chg

© 2000-2006 TCC

Page

247 257

03-Jul-06

-

Job No

FB625

.

SPAN 1 ACTIONS

TOP STEEL

M

d As As2 Layer 1 As prov Layer 1

mm²

BTM STEEL

As2 prov

mm²

DESIGN

mm mm²

3

H

12

3

5

339 H

10

393 15.02 161.5 52.7 409.0 305 H8 @ 300 for 600 2

L/d VEd VRd,ct VEd,max s req

mm

legs

No

kN kN kN

LINKS

CHECKS

ACTIONS

TOP STEEL

As prov Layer 1

mm²

BTM STEEL

As2 prov

mm²

mm mm²

As2 prov 3

339 H

25

As prov Allowed

1473 24.52

..

LINK Ø

H

10

As prov 3

1100 H

10

As2 prov

236

212.6 75.6 410.0 221 H8 @ 200 for 1200 2

8 NOMINAL

382 H8 @ 300 2 . ok ok ok ok ok ok


CENTRE 113.9 1.05 404.0 683

RIGHT 150.3 1.00 416.0 917

mm²

14

3

H

10

4

1100 H

10

236 14.85 191.8 75.6 410.0 249 H8 @ 225 for 900 2


mm

legs

No

kN kN kN

LINKS


14

LEFT 175.5 0.86 417.0 1089

kNm

DEFLECTION

CHECKS

12

ok

M

d As As2 Layer 1

DESIGN

RIGHT 172.4 0.80 417.0 1068

H



SPAN 2

SHEAR

CENTRE 181.3 1.07 399.5 1099

mm²

DEFLECTION SHEAR

LEFT 45.3 1.00 416.0 264

kNm


H

12

9

As2 prov 4

452 H

16

As prov Allowed

804 31.12

..

LINK Ø

8 NOMINAL

382 H8 @ 300 2 . ok ok ok ok ok ok

H

12

As prov 3

1018 H

10

As2 prov

236

182.8 73.6 409.0 263 H8 @ 250 for 750 2 ok ok ok ok ok ok ok

ok

247


17/07/2006 17:15:29

TCC41 Continuous Beams/ SPANS! Project

Spreadsheets to EC2

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Worked Examples: Main beam Grids C to J Originated from TCC41.xls v3.0 on CD

ACTIONS

TOP STEEL

M


mm²

BTM STEEL

As2 prov

mm²

DESIGN

mm mm²

VEd VRd,ct VEd,max s req

mm

legs

No

9

H

12

4

3

1018 H

10

236 14.85 182.8 73.6 409.0 263 H8 @ 250 for 750 2

kN kN kN

TOP STEEL

M


mm²

BTM STEEL

As2 prov

mm²

mm mm²

14

452 H

16

As prov Allowed

804 31.12

..

10

As prov 3

1100 H

10

As2 prov

236

191.8 75.6 vc 410.0 249 H8 @ 225 for 900 2 V

8

v

NOMINAL

382 H8 @ 300 2 . ok ok ok ok ok ok


CENTRE 181.3 1.07 402.0 1092

3

H

10

3

1100 H

10

236 14.93 212.6 75.6 410.0 221 H8 @ 200 for 1200 2


mm

legs

No


As2 prov 4

LINK Ø

H

RIGHT 45.3 1.00 417.0 263

mm²

kN kN kN

LINKS

CHECKS

14

LEFT 172.4 0.80 417.0 1068

kNm

DEFLECTION SHEAR

12

ok

SPAN 4

DESIGN

FB625

RIGHT 175.5 0.86 417.0 1089

H



ACTIONS

-

CENTRE 113.9 1.05 404.0 683

L/d

LINKS

CHECKS

258 248 Job No

mm²

DEFLECTION SHEAR

LEFT 150.3 1.00 416.0 917

kNm

Revision

chg

© 2000-2006 TCC

Page

03-Jul-06

Checked


SPAN 3

Date

rmw


H

12

4

As2 prov 4

339 H

20

As prov Allowed

1257 21.25

..

LINK Ø

8 NOMINAL

382 H8 @ 300 2 . ok ok ok ok ok ok

H

10

As prov 4

314 H

10

As2 prov

314

161.5 52.8 410.0 305 H8 @ 300 for 600 2 ok ok ok ok ok ok ok

ok

248


17/07/2006 17:15:34

TCC41R Rigorous Continuous Beams.xls

TCC41R Rigorous Continuous Beams.xls This spreadsheet allows the estimation of deflections in continuous beams according to BS EN 1992-1-1 and generally in accordance with Concrete Society TR58, Deflections in concrete beams and slabs [30]. Deflection is very dependant on whether and how much of an element cracks under service loads. Eurocode 2 recognises that members in bending exist in a state partway between uncracked and fully cracked. This spreadsheet considers construction and design pattern loading in assessing whether a section is cracked or not (i.e. whether the flexural tensile strength of the concrete is exceeded during these stages of the beam’s life). Once cracked, it is assumed that a section remains cracked. The spreadsheet is based on TCC41 but has an initial sheet JOBDATA! to allow input of all the variables and performance criteria required. Deflections are given as a range in a chart at the bottom of ACTIONS! They are shown as a range due to potential pattern loading. In SPANS!, the worst case is compared with the specified serviceability criteria. It should be noted that the number of assumptions and uncertainties in the material and design criteria and construction process mean that deflection calculations carried out in this manner can be inaccurate (and usually conservative) compared with actual measured deflections. For instance, a slab’s deflection is very dependent upon whether the slab has cracked in bending during construction or not. The calculated deflections might be regarded as being akin to a 95% confidence limit that they will not be exceeded in service. The spreadsheet analyses and designs up to six spans of continuous beams using sub-frame analysis. There is user input on each of the first four sheets and choice of reinforcement for each span is implicit. Input of spans and loads is in MAIN!. User input is required for bar sizes used in SPANS!

JOBDATA!

ACTIONS! This sheet shows bending moment and shear force diagrams from the analysis undertaken in Analysis! The user is required to input the desired amount of redistribution to the initial moments in line 21. Cell L14 allows three types of distribution according to the user’s preferences (see Table 1, page 14) in General Notes. Requesting redistribution at a cantilever produces a warning message in the remarks column. The chart at the bottom of the page shows calculated deflections at construction of partitions, and ranges for longer term deflections due to patterns of permanent and imposed loading. The worst case is taken in subsequent checks and this might be viewed as being unduly conservative.

SPANS! In SPANS! the user is required to choose top, bottom and link reinforcement for each span. The amounts of bending and shear reinforcement required and checks are derived from detailed calculations in Bar! Unwanted cells are ‘greyed-out’. EC2 requires that all spans should be loaded with both γGk,sup and γGk,inf , γGk,sup is used initially, and for γGk,inf the ‘Run -γGk,inf Loadcase’ button must be activated. A red warning message will appear if this has not been done, or if any relevant input data are subsequently changed. Using γGk,inf (=1.0) leads to higher hogging moments in spans. Unless overwritten, reinforcement diameter specified for a support carries through both sides of the support, i.e. the diameter specified for the right hand support of a span carries over to the left hand support of the next span. It may be possible to obtain different numbers of bars each side of the support due to differences in depth or to comply with the minimum percentage of span steel; practicality may dictate that the maximum number of bars at each support should be used. The top steel in the centre of spans is determined by adding together the steel required for hogging at 1/4 span and the appropriate additional tensile force due to shear ∆FEd (see CI 9.2.1.3). It is assumed that 100% hogging steel at supports will be curtailed at 0.25 span or max 50%at 0,2 span and 50% at 0.3 span.

This sheet consists of the main inputs of material, loading, construction and serviceability criteria pertaining to the calculation of deflection to EN 1992-1-1. Users are expected to use their knowledge of the project and judgement in completing this sheet. For creep reference is made to Eurocode 2. Reference may be made to the ‘How to Design’ leaflet (due to be published by the Concrete Centre during 2006) on calculating deflections for guidance on values to be used. The default values given in this sheet are not unusual.

WEIGHT!

MAIN!

Weight! gives an estimate of the total amount of reinforcement required in the beam and per cubic metre.

Input is identical to TCC41. 249


17/07/2006 17:15:39

Simplified curtailment rules, similar to those defined in BS 8110, are used to determine lengths of bars. The figures should be treated as approximate estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation etc.

It should be noted that it is possible to switch on the adjacent spans loaded arrangement by changing ‘b’ to ‘a’ in cell D6. BSEN 1992-1-1 recommends using the adjacent and alternate load arrangements. However to the UK National Annex only the all spans and alternate load arrangements need to be considered.

Uls!

Notes!

This sheet details the moment distribution analysis carried out at the ultimate limit state but is not necessarily intended for printing out other than for checking purposes.



Bar! This sheet shows design calculations, complete with references to EN 1992-1-1. It is not necessarily intended for printing out other than for checking purposes. In many instances, service stress, σs, has been set to 1.0 or 0.0001 N/mm2 to avoid problems with division by zero.

Def! This sheet calculates deflections at 1/20th points for each span and for each load condition. For each point and loading stage it considers moment, As, As’, d, d2 , uncracked neutral axis depth - x, uncracked inertia - I, cracked neutral axis depth - x, cracked inertia – I, uncracked moment capacity – Mcr, distribution factor - ε, z, final x, concrete stresses – σc, curvature -1/r, slope and curvature to calculate deflection. The sheet is rather large and is not necessarily intended for printing out other than for checking purposes.


Refs! This sheet comprises the values for nationally determined parameters that have been used in the spread-sheet. These data reflect the values given in draft UK National Annexes for EN 1990 and EN 1992. Designers should ensure that these data are current when the spreadsheet is used. When using TCC31R for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations.

250


17/07/2006 17:15:41

TCC41R Rigorous Continuous Beams.xls TCC41R Rigorous Continuous Beams/ JOBDATA!

The Concrete Centre

Spreadsheets to EC2

Project Client

Advisory Group

Location

Made by


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CONTINUOUS BEAM ANALYSIS & DESIGN to EN 1992-1 : 2004 Originated from TCC41R.xls v 3.0 on CD

Date

251 261

Revision

chg

© 2002-2006 BCA for RCC

Page

03-Jul-06

Job No

-

FB625

COVERS (to links)

MATERIALS

35 500 500 B

fck fyk fywk Steel class

dg γs γc


20 1.15 1.50

mm

Btm cover Side cover

SERVICEABILITY CRITERIA

Maximum permanent = L /

Degree of restraint 60%

Max affecting partitions = L /

Maximum imposed = L / Maximum precamber =

(50% = nominal, 100% = severe)

Design Crack width, Wk =

CREEP COEFFICIENTS (to Annex A)

80 N

RH Cement

Curing time

fcm = Ecm =

% relative humidity Type (S, N, R or RS)

AMBIENT TEMPERATURES ºC

25 25 25

Top cover

0.4

250 500 500 50%

mm mm mm

7.4.1(5)

*

7.4.1(6)

of permanent

mm top or

0.3

7.4.1(5)

mm btm

3 days 43 N/mm² 35.78 kN/mm²

Table 7.1

Table 3.1 & Annex A

from 0 to 7 days

from 7 to 60 days

from 60 days on

18

18

18

LOADING SEQUENCE (loads rationalised to kN/m)

Self weight Partitions/walls Other dead loads Permanent imposed Variable load Total

Span 1

Span 2

Span 3

Span 4

Span 5

Span 6

At age

kN/m

kN/m

kN/m

kN/m

kN/m

kN/m

Days

17.34 5.00 15.66 3.00 7.00 48.00

17.34 5.00 16.86 3.00 7.00 49.20

17.34 5.00 16.86 3.00 7.00 49.20

17.34 5.00 15.66 3.00 7.00 48.00

0.00 0.00 5.00 5.00 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

7 28 60 60 ∞

Construction loading

14

COMPOSITE E and Ø VALUES - Span 1 To 70 years

0 Self weight Partitions/walls Other dead loads Permanent imposed

2.11 1.63 1.41 1.63

Et kN/mm²

11.49 13.62 14.87 13.62

Variable load Composite

1.75

13.02

Quasi-permanent

To 70 years

0

Et kN/mm²

2.11 1.63 1.41 1.63 0

11.49 13.62 14.87 13.62 37.77

1.49

14.35

Total load

To 28 days

(t,t0) 0.61

Et kN/mm²

22.22

SW + partitions

from 14 to 28 days 0.53

23.42

Construction load

251


17/07/2006 17:15:42

TCC41R Rigorous Continuous Beams/ MAIN!

The Concrete Centre

Project

Spreadsheets to EC2

Client Location

Advisory Group Worked Examples: Main beam Grids C to J

Made by


Checked

Originated from TCC41R.xls v 3.0 on CD

Bay width

SPANS SPAN 1 SPAN 2 SPAN 3 SPAN 4 SPAN 5 SPAN 6 SUPPORTS Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Support 7

5000

rmw chg

© 2002-2006 BCA for RCC

h (mm)

bw (mm)

hf (mm)

Type

beff (mm)

6.000 6.000 6.000 6.000

450 450 450 450

300 300 300 300

125 125 125 125

T T T T

2150 1700 1700 2150

H (mm)

B (mm)

End Cond

250 250 250 250 250

250 250 250 250 250

F F F F F

PLs (kN)

Position (m)

ABOVE (m)

3.750 3.750 3.750 3.750 3.750

BELOW (m)

3.750 3.750 3.750 3.750 3.750

Page

03-Jul-06 Revision

-

252 262 Job No

FB625

Office Useage

STATUS OK

mm

L (m)

Date

LOADING PATTERN min max DEAD 1.25 1.25 IMPOSED 1.50 REBAR LAYERING Support steel in alt layer ? N

H (mm)

B (mm)

End Cond

250 250 250 250 250

250 250 250 250 250

F F F F F

Dead Load

Imposed Load

Position from left

Loaded Length

33.0

15.0

~~~~~

~~~~~ ~~~~~ ~~~~~

12.14

~~~~~

~~~~~

~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~

LOADING DIAGRAM

LOADING

UDLs (kN/m²)

Span 1 UDL PL 1 PL 2 Part UDL Construction Span 2 UDL PL 1 PL 2 Part UDL Construction Span 3 UDL PL 1 PL 2 Part UDL Construction

Dead Load

Imposed Load

Position from left

Loaded Length

33.0

15.0

~~~~~

~~~~~ ~~~~~ ~~~~~

12.14

~~~~~

~~~~~

~~~~~

34.2

15.0

~~~~~

~~~~~ ~~~~~ ~~~~~

12.14

~~~~~

~~~~~

~~~~~

34.2

15.0

~~~~~

~~~~~ ~~~~~ ~~~~~

12.14

~~~~~

~~~~~

~~~~~

1 165.4 166.1 95.0 166.1 81.5 42.9 -4.5

2 417.7 350.3 353.1 417.7 223.6 92.3 47.4

3 380.7 312.5 312.5 380.7 196.3 90.4 44.9

REACTIONS (kN) SUPPORT ALL SPANS LOADED ODD SPANS LOADED EVEN SPANS LOADED MAX ULTIMATE Characteristic Dead Max characteristic Imposed Min characteristic Imposed

Span 4 UDL PL 1 PL 2 Part UDL Constr'n Span 5 UDL PL 1 PL 2 Part UDL

~~~~~ Span 6 UDL PL 1 PL 2 Part UDL ~~~~~

4 417.7 353.1 350.3 417.7 223.6 92.3 47.4

5 165.4 95.0 166.1 166.1 81.5 42.9 -4.5

252


17/07/2006 17:15:50

TCC41R Rigorous Continuous Beams.xls TCC41R Rigorous Continuous Beams/ ACTIONS!

Project

Spreadsheets to EC2

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rmw Checked



BENDING MOMENT DIAGRAMS (kNm)

300 200

100

100

0

0

-100

-100

-200

-200

SPAN No Elastic M Redistributed M δ

1

2

3

4

5

41.5 41.5 1.000

239.4 191.5 0.800

177.8 160.0 0.900

239.4 191.5 0.800

41.5 41.5 1.000

~

20.0%

10.0%

20.0%

HOGS

HOGS

1

2

3

4

171.0 177.5 1.038

117.4 117.9 1.003

117.4 117.9 1.003

171.0 177.5 1.038

SHEARS FORCE DIAGRAMS (kN)

Revision

253 263 Job No

-

FB625

Redistributed

200

Redistribution

Page

03-Jul-06

chg

© 2002-2006 BCA for RCC

Elastic

300

SUPPORT No Elastic M Redistributed M δ

Date

Elastic

~

Redistributed

300

300

200

200 100

100 0

0

-100

-100

-200

-200

-300

-300

SPAN No


1

164.6 166.1

COLUMN MOMENTS (kNm) ALL SPANS

Above

204.5 200.9

3

188.0 190.4

188.0 190.4

204.5 200.9

4

SPAN No


2

224.8 216.8

224.8 216.8

164.6 166.1

1

2

18.6

-4.1

3

4

5

4.1

-18.6

LOADED

Below

18.6

-4.1

4.1

-18.6

ODD SPANS

Above

20.8

-9.3

6.2

-2.6

-9.9

LOADED

Below

20.8

-9.3

6.2

-2.6

-9.9

EVEN SPANS

Above

9.9

2.6

-6.2

9.3

-20.8

LOADED

Below

9.9

2.6

-6.2

9.3

-20.8

DEFLECTIONS (mm) Precamber not included 5.0 0.0 -5.0 -10.0 -15.0

SPAN No

At striking Quasi permanent Variable

1

2

3

4

3.1 8.0 2.2

0.7 3.4 1.4

0.7 3.4 1.4

3.1 8.0 2.2

#DIV/0! #DIV/0!

#DIV/0! #DIV/0!

mm mm mm

253


17/07/2006 17:15:54

TCC41R Rigorous Continuous Beams/ SPANS!

Project

Spreadsheets to EC2

Client

Advisory Group

Location


Worked Examples: Main beam Grids C to J © 2002-2006 BCA for RCC

Page

254 264

03-Jul-06

Checked



Date

rmw

Revision

chg

-

Job No

FB625

.

SPAN 1

LEFT CENTRE M kNm 44.4 177.5 d 1.00 1.04 DESIGN d mm 411.0 407.0 As mm² 261 1056 As2 mm² TOP STEEL Layer 1 3 B 12 3 B 12 Layer 2 mm² 339 As2 prov 339 As prov BTM STEEL Layer 1 3 B 10 4 B 20 Layer 2 mm² 236 As prov 1257 As2 prov DEFLECTION Permanent = 8.04 < 24.00 Imposed = 2.18 < 12.00 mm Affecting partitions/walls = 4.91 < 12.00 ok SHEAR VEd kN 158.2 LINK Ø VRd,ct kN 56.5 8 kN 460.7 NOMINAL VEd,max s req mm 306 354 LINKS B8 @ 300 for 600 B8 @ 300 No 2 2 legs . CHECKS % As ok ok Cover ok ok min S ok ok Links ok ok Main bars ok ok max V ok Crack width mm ok 0.09 ok 0.29

RIGHT 172.8 0.80 407.0 1082

ACTIONS

4 As prov 3

20

1257 B

10

As2 prov 236 Precamber (mm) = Increase btm As by 208.9 82.3 456.2 219 B8 @ 200 for 1200 2 ok ok ok ok ok ok ok

SPAN 2

LEFT CENTRE M kNm 175.1 117.9 d 0.83 1.00 DESIGN d mm 407.0 407.0 As mm² 1098 701 As2 mm² TOP STEEL Layer 1 4 B 20 4 B 12 Layer 2 mm² 1257 As2 prov 452 As prov BTM STEEL Layer 1 3 B 10 3 B 20 Layer 2 mm² 236 As prov 942 As2 prov DEFLECTION Permanent = 3.44 < 24.00 Imposed = 1.43 < 12.00 mm Affecting partitions/walls = 2.78 < 12.00 ok SHEAR VEd kN 192.7 LINK Ø kN 82.3 8 VRd,ct kN 456.2 NOMINAL VEd,max s req mm 241 354 LINKS B8 @ 225 for 900 B8 @ 300 No 2 2 legs . CHECKS % As ok ok Cover ok ok min S ok ok Links ok ok Main bars ok ok max V ok Crack width mm ok 0.29 ok 0.21

B

0.30

RIGHT 140.4 0.90 407.0 860

ACTIONS

3 As prov 3

B

20

942 B

10


0.31

254


17/07/2006 17:16:00

TCC41R Rigorous Continuous Beams.xls TCC41R Rigorous Continuous Beams/ SPANS!

Project

Spreadsheets to EC2

Client

Advisory Group

Location


Worked Examples: Main beam Grids C to J © 2002-2006 BCA for RCC

Revision

chg

-

SPAN 3

LEFT CENTRE M kNm 140.4 117.9 d 0.90 1.00 DESIGN d mm 407.0 407.0 860 701 As mm² As2 mm² TOP STEEL Layer 1 3 B 20 4 B 12 Layer 2 mm² 942 As2 prov 452 As prov BTM STEEL Layer 1 3 B 10 3 B 20 Layer 2 mm² 236 As prov 942 As2 prov DEFLECTION Permanent = 3.43 < 24.00 Imposed = 1.43 < 12.00 mm Affecting partitions/walls = 2.77 < 12.00 ok SHEAR VEd kN 182.2 LINK Ø VRd,ct kN 74.8 8 VEd,max kN 456.2 NOMINAL s req mm 257 354 LINKS B8 @ 250 for 750 B8 @ 300 No 2 2 legs . CHECKS % As ok ok Cover ok ok min S ok ok Links ok ok Main bars ok ok max V ok Crack width mm ok 0.31 ok 0.21

255 265 Job No

FB625

RIGHT 175.1 0.83 407.0 1098

ACTIONS

4 As prov 3

B

20

1257 B

10


SPAN 4

LEFT CENTRE M kNm 172.8 177.5 d 0.80 1.04 DESIGN d mm 407.0 407.0 1082 1056 As mm² As2 mm² TOP STEEL Layer 1 4 B 20 3 B 12 Layer 2 mm² 1257 As2 prov 339 As prov BTM STEEL Layer 1 3 B 10 4 B 20 Layer 2 mm² 236 As prov 1257 As2 prov DEFLECTION Permanent = 8.04 < 24.00 Imposed = 2.18 < 12.00 mm Affecting partitions/walls = 4.90 < 12.00 ok SHEAR VEd kN 208.9 LINK Ø VRd,ct kN 82.3 8 VEd,max kN 456.2 NOMINAL mm 219 354 s req LINKS B8 @ 200 for 1200 B8 @ 300 legs No 2 2 . CHECKS % As ok ok Cover ok ok min S ok ok Links ok ok ok ok Main bars ok max V Crack width mm ok 0.30 ok 0.29

Page

03-Jul-06

Checked



Date

rmw

0.29

RIGHT 44.4 1.00 411.0 261

ACTIONS

3 As prov 3

B

12

339 B

10


0.09

255


17/07/2006 17:16:05

TCC42 Post-tensioned Analysis & Design.xls (Beta) This spreadsheet designs post-tensioned beam and one-way spanning slab elements in accordance with BS EN 1992-1:2004. In essence the spreadsheet checks a number of parameters:■ stresses at transfer, ■ stresses in service, ■ moments of resistance at ULS, ■ shear, ■ vibration, ■ deflection, ■ neutral axis depth, and ■ reinforcement service stress

The spreadsheet is set out in several sheets. ■ JOBDATA! Defines load cases, various options and material

properties. ■ LOADS! Is where loadings, spans and section data are

entered. ■ CONTROL! Is where tendons and bonded reinforcement are

adjusted to find a solution. ■ RESULTS! Summarises the design, analysis, checks and

outputs from the rest of the spreadsheet. ■ TYPICALC! Shows a typical longhand calculation for the first

span. ■ DETAILS! Shows the workings for the moment distribution

for the various load cases, profiles, prestress losses and checks in some detail. ■ Def! Shows workings for deflection at 1/20 points along each

span. ■ Gra! Provides the data for the graphs, and values generated

are used for checking. ■ Refs! Is where nationally determined parameters are set.

Users are referred to Concrete Society TR43 Post-tensioned concrete floors – Design Handbook[33] for further details of methods and values used. A maximum of three spans may be considered. Cantilevers are not available. Shortening is calculated in the losses section, but is not used to modify column moments. The effects of restraint to both columns and prestress in the member must be considered. The spreadsheet considers one direction at a time only. The nub of this spreadsheet is CONTROL! page. The source of any failures or missing information (e.g. no tendons or no tendon height specified) will become apparent on CONTROL! Users may wish to create a split window in this part of the spreadsheet (Window/ Split) to obtain a more comprehensive view. CONTROL! Also shows the results of the parameter checks from RESULTS!

JOBDATA! The first sheet includes all the general and material input data used in the subsequent sheets. Load combinations and load factors are defined. The input under Options should be selfexplanatory. Some of the input is controlled via the combi-boxes in the right margin. The choices have implications on the design as shown below. ■ Stressing ends determines where prestressing losses occur. ■ Prestressing system – Specifying unbonded or bonded

changes the prestress loss calculations. Prestress losses tend to be higher with bonded tendons as wobble factors and coefficients of friction are higher but using several strands in a single duct can lead to overall economy, especially in more heavily loaded beams. Bonded systems may require less conventional reinforcement. ■ The exposure class to Eurocode 2 determines both the

permissible crack width and the allowable flexural tensile stresses in prestressed beams (and slabs). ■ The Slab or Beam pull-down varies shear requirements and

determines whether nominal top bonded reinforcement is included in the spans or not. Nominal top steel is included in mid-span of beams. If slabs are specified, the user may choose to use nominal top steel to overcome hogging moments or reduce deflection in the spans. Invoking the nominal bonded reinforcement in mid-span should overcome most problems with hogging in say, dissimilar spans of slabs. ■ Beams requires a second input; slab type (type of slab

supported by the beam) alters parameters used in checking vibration. ■ Normal curtailment rules for conventional reinforcement

are not necessarily satisfactory for post-tensioned slabs and beams. Nonetheless the spreadsheet assumes that curtailment occurs at 0.3 x span. With regard to concrete, the usual minimum cylinder strength used in prestressing is 32 MPa, although 40 MPa would be more usual. Ambient temperatures during curing may be taken as 15°C for a UK summer, but otherwise may be dependent upon curing/ insulation regimes. Typically, long-term Relative Humidity may be taken as 55% indoors, or 80% outdoors. Under loading sequence, the ages of transfer and additional loading are entered. These values are used to determine relevant creep and shrinkage factors. These factors are case specific and have been derived from Annex B of EC2. Details of strand used in the UK are given at the bottom of the sheet. Users should ensure that their chosen strand is readily available. TR43 Post-tensioned concrete floors – design handbook gives typical values for µ (coefficient of friction), K (wobble factors), Rel% (relaxation) and draw-in (mm).

256


17/07/2006 17:16:10

TCC42 Post-tensioned Analysis & Design.xls (Beta) LOADS!

■ Pi / Pj (initial force/ jacking force),

The top part of this page is for input of data for the sub-frame analysis, i.e. dimensions and loads.

■ number and height of tendons, and

Input should be fairly self explanatory. It should be noted that H is in the plane of the screen and b, bw etc. are at right angles to the plane of the screen. Several warnings are given under ‘Operating Instructions’ and with conditional formatting should data be incorrect. Supports may be specified as being knife-edge by inputting K in column D: remote ends of supporting columns may be either F for fixed, or P for pinned. The line can be left blank. A support width (h below) can be used in conjunction with a ‘K’ support so that design moments at the face of support are used. Data under ‘Normal Direction’ are used for the vibration checks. The number of bays affects possible modes of vibration, which is checked in accordance with the original Concrete Society TR43 [14] . The vibration response factors calculated are accordance with Concrete Society guidelines. Vibration should not be a problem in post-tensioned slabs and beams. Normally, vibration response factors of 12 are used for very busy offices, 8 for normal offices, or 4 for high specification offices or laboratories where vibration is critical. Designers should be aware that the 2005 version of Concrete Society TR43 Appendix G gives revised recommendations on vibration. (At the time of releasing the Beta 3 version, it was considered that these recommendations were unsuited to spreadsheet Further guidance is being prepared by The Concrete Centre). If vibration is considered to be critical more specialist software and experience should be sought and used. Loads specified should be characteristic and for the whole bay width (not expressed as kN/m2 – unless a 1 m bay width is being analysed). Under ‘dead at transfer’, the self-weight should be input together with any other loads present at transfer. However, designers should consider the load history of the slab to ensure worst cases are checked, e.g. temporary loads while casting floors above. Bay widths in the normal direction do not affect the loading unless, of course, the user chooses to introduce a suitable relationship (in the loads input). The current configuration being designed is shown in a chart. This gives a scale representation of the spans, supports, loads and an idealised cross section of each member.

■ Pf / Pj (final force/ jacking force), ■ amounts of conventional reinforcement.

There are also two charts. The ‘efficiency’ chart gives the user an idea of how hard the section is working or how far it is out or what is critical to the design. The second chart, ultimate limit state moment envelope and moments of resistance (capacity), should be used in conjunction with choosing amounts of bonded reinforcement. With regard to Tendons, the spreadsheet automatically calculates a recommended number of tendons for each span using an algorithm. The algorithm uses either the maximum of the median stress levels, or the maximum permitted. The spreadsheet calculates the minimum number of strands required so that permissible concrete tensions or compressions are not exceeded at either the initial or final stages. The numbers of tendons are then shown as recommended values, and the user should override them as required. Once the number of tendons for each span has been fixed, the program attempts to find an optimum single level of initial prestress for all strands (this often appears to be the maximum permissible). If the minimum force required generates excessive stresses, the section is deemed to have failed. Tendons are assumed to be level through supports and follow a parabolic profile between. The points of inflection are taken to be at 1/10 of the clear span points. Besides number of tendons, the main user control is to adjust the tendon heights. The recommended tendon heights given in row 16 should normally be used. Short and long-term prestress losses are initially assumed by the spreadsheet and then actual losses are calculated, based on the remaining data. This process results in calculated and assumed losses being different. To equalise (or balance) these, the ‘Balance Losses’ button needs to be clicked (in some cases more than once). Details of bonded rebar should then be entered under ‘REINFORCEMENT’ (this may then require the ‘Balance Losses’ button to be clicked again). If the message in cell N46 reads “no links required’, links may be omitted by entering zero in cell D46. The checks carried out are listed below.

At the bottom of the page, charts also show representations of the tendon profiles and equivalent loads used in the analysis. For the tendons, a reversed parabolic profile is used but minimum lengths of straight tendon are used at the supports as recommended by Khan(16). Service equivalent loads are shown: those at transfer may be viewed at Gra! C368: N369.

CONTROL! This page is the nub of the spreadsheet: it has a number of key inputs and outputs. These include inputs of

■ Tendons (a) ■ Stresses at transfer (b) ■ Stresses in service (c) ■ ULS MOR (d) ■ Shear (e) ■ Vibration (f) ■ Deflection (g) ■ Neutral axis depth ■ Rebar stress

257


17/07/2006 17:16:12

In the spreadsheet, those that are unsatisfactory are highlighted and directions are given for further information. These checks are visualised in the ‘efficiency’ chart.

■ equivalent loads,

A second chart shows the ultimate limit state moment envelope and the moments of resistance of the section (capacity). It is intended that it is used in conjunction with choosing amounts of bonded reinforcement.

■ deflections,

RESULTS! This page shows stresses at transfer and in service in both tabular and chart form. It should be noted that, in keeping with current practice, moments are considered at the face of columns. Thus peak moments are not necessarily at column centrelines and moments might be different each side of an internal column. The convention used in the stress charts is: ■ Red squares – tension, blue circles – compression ■ Solid markers – bottom, hollow markers – top ■ Dotted lines – permissible stresses

Below the stress diagrams, there are details of shear envelopes, vibration and deflection together with support reactions and column moments.

TYPICALC! This sheet is intended to illustrate typical calculations for a particular point in a span in order to show how all the criteria are satisfied. The sheet illustrates the transfer and service stress checks and the calculation of Moment of Resistance carried out in tabular form in Gra! The point chosen is at 0.3L in the first span and is highlighted in Gra!

■ ULS moments and capacities, ■ shear envelopes, ■ stresses at transfer and ■ stresses in service

Each chart is plotted at 1/20 points along each span. Many values within Gra! are used and checked for being minima or maxima for the various criteria. For instance it may be here that problems with hogging moments are found.

Refs! This sheet comprises Nationally Determined Parameters (NDP’s) contained within in the UK’s National Annexes to EN1990 (basis of design) and to BS EN 1992-1-1. This page should be reviewed each time the spreadsheet is used to ensure the values remain valid for the UK or are valid for the country where the works are to be carried out or changed to suit. It is suggested that this page is printed out to accompany submissions of calculations that include this spreadsheet. It should be noted that it is possible to switch on the adjacent spans loaded by changing ‘b’ to ‘a’ in cell D11. BS EN 1992-1-1 recommends using the adjacent and alternate load arrangement. However to the UK National Annex, only the all spans and alternate load arrangements need to be considered.


DETAILS! Over nine pages, DETAILS! shows detailed calculations regarding section properties, distribution factors, moment distribution used for the sub-frame analysis, profiling constants, pre-stressing losses, balanced loads, ULS moment and shear checks, and finally vibration.

Def! The deflection sheet gives details of calculations dealing with defections.

Gra! Graf! provides the data for the charts within CONTROL! and RESULTS! That show: ■ the configuration and loads, ■ tendon profile,

258


17/07/2006 17:16:14

TCC42 Post-tensioned Analysis & Design.xls (Beta) TCC42 Post-tensioned Analysis & Design/ JOBDATA!

Project

Spreadsheets to EC2

Client

Advisory Group

Location



Date

rmw

POST-TENSIONED ANALYSIS & DESIGN to BS EN 1992-1:2004 Originated from TCC42.xls v6 on CD

Page

Checked

Revision

chg

© 2005 TCC

259 269

03-Jul-2006

Job No

-

FB625

POST-TENSIONED ANALYSIS & DESIGN to BS EN 1992-1:2004 - GENERAL DATA LOAD COMBINATIONS SLS 1 TRANSFER SLS 3 SLS 4

Transfer prestress + dead load at transfer Final prestress + dead + full imposed load on all spans Final prestress + dead + full imposed load on odd spans Final prestress + dead + full imposed load on even spans

SLS 5

Final prestress + dead + frequent imposed load on all spans

SLS 6

Final prestress + dead + frequent imposed load on odd spans

SLS 7

SLS 2

RARE

FREQUENT

ULTIMATE

SLS 9 SLS 10

Final prestress + dead + QP imposed load on even spans

ULS 1 ULS 2

Final prestress + factored dead and imposed load on all spans Final prestress + factored dead + factored imposed load on odd spans

ULS 3

Final prestress + factored dead + factored imposed load on even spans

ULS LOADING PATTERN Dead Imposed OPTIONS

MATERIALS

USAGE

Final prestress + dead + frequent imposed load on even spans Final prestress + dead + QP imposed load on all spans Final prestress + dead + QP imposed load on odd spans

SLS 8

QUASIPERMANENT

NOTES INPUT IS UNDERLINED. FRAMES ARE ASSUMED TO BE BRACED

min 1.25 0

max 1.25 1.50

Office

VIBRATION Limiting reponse factor R=8

DEFLECTION Limit QP deflection to L/ 250 Limit after construction to L/ 500

BS EN 1990: (6.10b)

Exposure class is XC2, XC3, XC4 Prestress system is unbonded and stressed from left end Wmax, mm = 0.3 Beam supporting solid slab Jacking force /fpk = 0.8 Top bonded rebar in spans? Yes (Helps to reduce deflections - recommended) Damping, ζ (1% to 4½%) 1.5% Slab type S (S)olid, (R)ibbed or (W)affle, supported by beam CONCRETE At transfer, 4 days,

fck = 40 fck(i) = 26.54

Cement type R Ave ambient during curing = 18ºC fpk = 1860 Eps = 195

STRAND

REBAR

fyk = 500 m = 1.15

LOADING SEQUENCE

Ecm = 35.22 Ecm(i) = 31.91

c,max = 18.00 c,max(i) = 11.94

Curing time (days) = 3 Longterm R/H % 55 Aps, mm² = 100

Grade A

Loading sequence for assessment fctm fctm,fl Load @ Age

Design hypothetical tensile stresses to limit cracking .

µ = 0.060 , draw in = 6

Rel % = 2.5

t,max = 5.09 t,max (i) = 3.66 c = 1.50

K = 0.0050 Depth to strand centre = 41

COVERS

Top

Bottom

Sides

to links

25

25

25

2 = 0.3 Ecm(t)

Rare combination

Ecm(t)

Load

kN/m

days

MPa

MPa

Creep

GPa

kN/m²

Creep

GPa

Dead at transfer Applied dead Quasi-permanent imposed COMBINED

14.63 42.00 7.50 64.13

4 30 -=-

2.52 3.51

2.71 3.77

2.12 1.65

11.31 13.30

2.12 1.65

11.31 13.30

1.76

12.78

14.63 42.00 25.00 81.63

1.73

12.89

NOTES on MATERIALS BRITISH LOW RELAXATION STRAND Type Dia Area Standard 15.2 139 12.5 93 Super 15.7 150 12.9 100 Compact 15.2 165 12.7 112

fpk 1670 1770 1770 1860 1820 1860

Weight 1.090 0.730 1.180 0.785 1.295 0.890

60 5.1

80 7.5

100 10.7

RELAXATION at 0.7fpk Ambient ºC Relaxation

20 1.8

40 3.5

259


17/07/2006 17:16:16

TCC42 Post-tensioned Analysis & Design/ LOADS!

The Concrete Centre

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POST-TENSIONED ANALYSIS & DESIGN to BS EN 1992-1:2004

Checked

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Originated from TCC42.xls v6 on CD

Page

Revision

chg

© 2005 TCC

260 270

03-Jul-2006

Job No

-

FB625

Dimensions and Loads NORMAL DIRECTION

SPANS Span 1 Span 2 Span 3 SUPPORTS Support Support Support Support

1 2 3 4

CONFIGURATION

LOADING

Lm

H mm

bw mm

hf mm

Section

beff mm

No Bays

Bay width m

12.000 12.500

525 525

1800 1800

200 200

T T

3000 3000

5 5

6.000 6.000

Above m

H mm

b mm

End cond

Below m

H mm

b mm

End cond

4.000 4.000

300 300

600 600

F F

K

SLAB supporting Solid Slab, Exposure class XC2, XC3, XC4, Wk = 0.3 mm, fck = 40, Stressed from Both Ends

UDLs~kN/m (char), PLs~kN (char), Position~m Dead at

SPAN 1 transfer 14.63 UDL

Applied

Imposed

Position

Loaded

Dead at

Dead

Load

from left

Length

SPAN 3 transfer

42.00

25.00

~~~~~

~~~~~ ~~~~~ ~~~~~

PL 1 PL 2 Part UDL

Applied

Imposed

Position

Loaded

Dead

Load

from left

Length

~~~~~

~~~~~ ~~~~~ ~~~~~

UDL PL 1 PL 2 Part UDL

SPAN 2 UDL

14.63

42.00

25.00

PL 1 PL 2

~~~~~

~~~~~ ~~~~~ ~~~~~


Part UDL

TENDON PROFILE

(heights to strand centre: see heights specified under TENDONS below) 484

295

295 43

41

EQUIVALENT LOADS in service 400 300 200 100 0 -100 -200

301 kN/m 266 kN/m

222 kN/m

169 kN/m -57 kN/m

-50 kN/m

0 kN/m

260


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TCC42 Post-tensioned Analysis & Design.xls TCC42 Post-tensioned Analysis & Design/ CONTROL!

The Concrete Centre

Project

Spreadsheets to EC2

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Made by


Checked

Date

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Page

03-Jul-2006 Revision

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© 2005 TCC

261 271 Job No

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FB625

Tendons & bonded reinforcement (a) TENDONS

Pj = 149 kN Supt 1

Pi/A =

Span 1

Pi/Pj

93.3%

P30/Pj Pf/Pj No of strands Recommended Use Recommend'd height Height mm Length Straight mm x to max Sag mm

2.18

Supt 2

2581 252.5

Pf kN

2431

Balance Load kN

233.0

90.9%

89.1%

100.0%

87.7%

84.9%

100.0%

10 18 41 41

10 18

13 18

13 18 41 41

484 484 150

484 150

2545 2377

2498

2498

342.8

315.2

0 0

2349

2350

316.4

292.2

0 0

0 0

295 0

0 0

2282

2421

0

228.5

0.0

2274

#DIV/0!

211.9

0.0

a

0

0 0.0

#DIV/0!

#DIV/0! 0.0

44%

OK

51%

OK

81%

b(T)

OK

37%

OK

63%

c(T)

OK

61%

OK - see note OK

20%

e

OK

9%

OK

96%

g

GLOBAL STATUS

VALID DESIGN

REINFORCEMENT

Input bonded rebar arrangement (Support bars cutailed at 0.3L)

0%

20%

Span 1

Required at SLS Main bar Ø No As provided

Supt 4

0

295 295 0

2453

'EFFICIENCY'

Neutral axis depth Rebar stress

13 18

7047

CHECKS Tendons (a) Stresses at transfer (b) Stresses in service (c) ULS MOR (d) Shear (e) Vibration (f) Deflection (g)

Span 3

100.0%

5272

Pi kN

Supt 3

90.4%

10 18 295 295 150

Balance Load kN

MPa max

Span 2

40%

60%

80%

Span 2

100%

120%

0

Supt 1

btm

top

Supt 2

btm

top

Supt 3

btm

top

Supt 4

2638 20 9

1590 16 9

1898 20 9

2638 20 9

2723 25 8

1898 20 9

2638 20 9

0 16 8

0 16 10

0 12 15

2827

1810

2827

2827

3927

2827

2827

1608

2011

1696

%

0.299%

0.191%

0.299%

0.299%

0.416%

0.299%

0.299%

0.000%

0.000%

0.000%

Link Ø = No of legs

8 4

4

4

4

4

4

4

8

8

8

Span 3

Supt 4

0.0 0.0

0.0 0.0

(d) ULS MOMENTS Mu MOR

With bonded reinforcement Supt 1

Span 1

60.9 1128.8

633.8 1418.5

Supt 2

948.7 1543.6

945.9 1544.1

Span 2

872.9 1773.0

Supt 3

0.0 1099.3

0.0 0.0

ULS MOMENT ENVELOPE/MOR 2000 1500 1000 500 0 -500 -1000 -1500 -2000

261


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TCC42 Post-tensioned Analysis & Design/ RESULTS!

The Concrete Centre

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© 2005 TCC

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Revision

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Results (2) (e) SHEAR

VEd - Vtd cracked ? (VEd - Vtd)/VRdc

Link Ø = 8 Span 1 Left Right

Left

444.4

566.1

610.3

N 0.661

Y 0.854

4 0

4 0

No of legs Link spacing

Span 2 Right

0 Left

Right

512.4

#DIV/0!

#DIV/0!

Y 0.921

N 0.783

N #DIV/0!

N #DIV/0!

4 0

4 0

8 0

8 0

ULS SHEAR ENVELOPE (VEd) 1000 500

758.6

571.3

0

0.0

-500

-594.0

-727.3 -1000

(f) VIBRATION Response factor

Span 1 0.62 OK

Span 2 0.73 OK

Span 3 0.00 OK

(g) DEFLECTION MAX DEFLECTIONS (mm)

10 5 0 -5 -10 -15 -20 -25 -30

At transfer Quasi-permanent After construction

Span 1 = -4.2mm Span 1 = 12mm < 48 Span 1 = 11.7mm < 24

Span 2 = -4.2mm Span 2 = 26.3mm < 50 Span 2 = 23.9mm < 25

OK OK

. . .

OK OK

SUPPORT REACTIONS ULS 1 ULS 2 ULS 3 Dead Imposed

Supt 1 534.3 534.3 303.0 274.0 114.8

Supt 2 1557.3 1322.9 1338.6 823.7 378.5

Supt 3 559.6 325.2 559.6 289.6 119.2

Supt 4 0.0 0.0 0.0 0.0 0.0

COLUMN MOMENTS

Supt 1 0.00 54.82 0.00 105.14 0.00 -92.58

Supt 2 0.00 15.81 0.00 -100.24 0.00 118.22

Supt 3 0.00 0.00 0.00 0.00 0.00 0.00

Supt 4 0.00 0.00 0.00 0.00 0.00 0.00

ULS 1 ULS 2 ULS 3

Above Below Above Below Above Below

. .

kN kN kN kN kN


262


17/07/2006 17:16:34

TCC42 Post-tensioned Analysis & Design.xls (Beta) TCC42 Post-tensioned Analysis & Design/ TYPICALC!

Project

The Concrete Centre

Spreadsheets to EC2

Client Advisory Group Location Level 2 - Beam on Grid 7

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Date

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03-Jul-06 Revision

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263 274 Job No

-

FB625

TYPICAL CALCULATION EC2 Ref

for Span 1 at 3.60 m from C/L of LH support Class XC2, XC3, XC4 Tee section,

h = 525 mm, bw = 1800 mm

hf = 200 mm, bf =3000 mm.

Table 4.1

Ac = 1185000mm², Z top = 120.0E6 mm³, and Z bottom = 93.3E6 mm³ Tendons are unbonded, Ap = 100mm², fpk = 1,860 N/mm2 and 75.0 mm from soffite There are 18 tendons, jacked to 1,488 N/mm² or 80% fpk Prestress losses at this section are 121.4 kN at transfer and 283.3 kN longterm

5.10.5 & 6

(b) STRESSES at TRANSFER M = 311.4 kNm hogging, and prestressing force = 2,557.0 kN Max compression (bottom) = M/Z + P/A = -311.4E3 / 120.0 + 2,557.0 / 1185 = 5.50 N/mm² < 11.94 N/mm² allowed

5.10.2.2(5)

Max tension (bottom) = M/Z - P/A = 311.4E3 / 120.0 - 2,557.0 / 1185 = 0.44 N/mm² < 3.66 N/mm² allowed

TR43

(c) STRESSES in SERVICE Frequent M = 314.7 kNm sagging, and prestressing force = 2,395.1 kN Max compression (top) = 314.7E6 / 120.0E6 + 2,395.1E3 / 1185E3 = 4.19 N/mm² < 18.00 N/mm² allowed

5.10.2.2(5)

Quasi-permanent M = 260.4 kNm sagging Max tension (bottom) = 260.4 / 93.3 - 2,395.1 / 1185 = 1.35 N/mm² < 5.09 N/mm² allowed

TR43

(d) MOR at ultimate limit state M = 611.7 kNm sagging, and prestressing force = 2,395.1 kN pe = 1000 x 2,395.1 / 18 / 100 = 1,330.6 N/mm² Reinforcement d = 484 mm Tendon force = 0.9 (2,395.1 + 100 /1000 x 18 x 100) = 2,317.6 kN

5.10.8(2)

As = /4 x 16² x 9 = 1,810 mm² Rebar force = 500 / 1.15 x 1,810 / 1000 = 786.8 kN Total tensile force = 2,317.6 + 786.8 = 3,104.4 kN fcd = 1 x 0.85 x 40/1.5 = 22.67 N/mm²

3.1.7(3)

Compression block depth, x = 1000 x 3,104.4 / 22.67 / 3000 = 45.65 mm

Fig 3.5

MOR = (2,317.6 ( 525 - 75.0 - 45.65 / 2) + 786.8 x (484 - 45.65 / 2)) / 1000 = 1,352.8 kNm > 611.7 ok

263


17/07/2006 17:16:38

TCC43 Wide Beams (A & D).xls This spreadsheet designs multiple-span rectangular or flanged beams, to prEN 1992-1, using sub-frame analysis to derive moments and shears. The intention is to provide the design and analysis of up to six spans of continuous wide beams with columns above and below. Spans may incorporate cantilevers, fixed ends or knife-edge supports. There are three main sheets: MAIN!, ACTIONS! and SPANS! This spreadsheet is very similar to TCC41.xls, but caters for wide beams by allowing two sizes of bar in one layer and by allowing top steel in the span to be augmented to help satisfy span:depth criteria. The selection of size and number of top and bottom bars is automated. The number of bars determined by either: ■ area of steel required/ area of maximum sized bar, ■ spacing rules or ■ number of legs of links required in shear.

Where the latter two may govern, two diameters of bending steel are allowed in the same layer to avoid excessive over-specification of reinforcement. Input to the right of SPANS! allows top steel to be increased to satisfy span:depth criteria. The designer and detailer are expected to rationalise this output (but always remembering that bar spacings should not be increased).

The sheet has not been set up with many ‘carry-throughs’ (making the value of one cell equal another). Users may choose to emulate cell D17 in other cells in their saved version to speed input. Generally, values in red or red backgrounds indicate either incorrect or excess data. For instance, if knife-edge supports are required, entering ‘K’ in cell C25 will elicit red data to the right, which needs to be cleared manually. ‘Rebar layering’ refers to whether there are beams in the other direction. Answering yes drops by one bar diameter the steel at the supports. For instance when using splice bars at the support bars in the other direction have to be avoided - and allowed for in the design. With respect to cantilevers, design for bending caters for moments at the face of support; design for deflection considers the cantilever from the centre line of support. In beam-to-beam situations (where the beam soffits are the same depth), the width of support can be input as being very small to avoid under-design in bending.

ACTIONS! ACTIONS! includes bending moment and shear force diagrams, summaries of moments and shears and user input for amounts of redistribution. Users should ensure that the amounts of redistribution are always considered as at line 26 there are no default values.

The size of link to be used remains as manual input.

MAIN! This sheet contains user input of materials, frame geometry and load data. Input data is blue and underlined. New data may be input by overwriting default values or by entering values in ‘greyed-out’ cells. Entering a value of 5.0 in cell C20 will clear a line of data in both the span and support data ready for input. It will also initiate red data that will clear as the appropriate missing data is added. Guidance on input for the type of section and type of end condition of the support is given under ‘Operating instructions’. The dimensions of the flange widths, beff, are entered manually, but maximum permitted values can be seen in cells M14:M19. It is important that the correct usage of the members under consideration is selected from the combo-box to the right of the screen, as this affects the magnitude of quasi-permanent SLS moments. The ‘brittle partitions’ switch affects the span:depth modifier for spans greater than 7 m.

SPANS! This sheet designs reinforcement for bending in spans and supports and for shear in the spans. User input is required for link sizes (e.g. at cell I22) and the amount by which span top steel should be increased (e.g. at cell N21). Non-existent spans are blanked out. Support moments (including cantilever moments) are considered at the face of the support. This may lead to unequal amounts of reinforcement being designed for each side of the support. See Bar! Beneath ‘Operating instructions’, both maximum and minimum main bar diameters may be selected. Also, for each span, the percentage of span top steel may be increased in order to improve the permissible span:depth ratio. Besides the limit of maximum modification factor for deflection = 2.0, an additional limit of maximum allowable area of steel to comply with deflection criteria, As def, = 1.5 x As reqd, i.e. an allowable increase of 1.5 As req ie.50% bottom span steel, has been imposed in line with Note 5 to Table 7.4 N(BS) in the UK National Annex.

264


17/07/2006 17:16:44

TCC43 Wide Beams (A & D).xls EC2 requires that all spans should be loaded with both γGk,sup and γGk,inf. γGk,sup is used initially, and for γGk,inf the Run γGk,inf Loadcase button must be activated. A red warning message will appear if this has not been done, or if any relevant input data are subsequently changed. Using γGk,inf (=1.0) leads to higher hogging moments in spans. The top steel in the centre of spans is determined by adding together the steel required for hogging at 1/4 span and the appropriate additional tensile forces due to shear ∆ FEd (see CI 9.2.1.3). It is assumed that 100% hogging steel at supports will be curtailed at 0.25 span or max 50%at 0,2 span and 50% at 0.3 span.

Bar! Intended mainly for first time users and young engineers, this sheet gives further details of the calculations summarised in SPAN! Support moments are considered at faces of supports; checks at 1/4 span relate to hogging and any top steel required at either of these points is provided throughout the span.


WEIGHT! Weight! gives an estimate of the total amount of reinforcement required in the beam and per cubic metre. Simplified curtailment rules, similar to those defined in BS 8110, are used to determine lengths of bars. The figures should be treated as estimates only as they cannot deal with the effects of designers’ and detailers’ preferences, rationalisation etc.

Uls! This sheet details the moment distribution analysis carried out at the ultimate limit state. The following patterns for imposed loading are considered to find a worse case. ■ All spans loaded ■ Odd spans loaded

Refs! This sheet comprises the values for nationally determined parameters that have been used in the spreadsheet. These data reflect the values given in draft UK National Annexes for EN 1990 and EN 1992. Designers should ensure that these data are current when the spreadsheet is used. When using TCC31 for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations. It should be noted that it is possible to switch on the adjacent spans loaded arrangement by changing ‘b’ to ‘a’ in cell D6. BS EN 1992-1-1 recommends using the adjacent and alternate load arrangements. However to the UK National Annex only the cell spans and alternate load arrangements need to be considered.

■ Even spans loaded ■ Adjacent spans loaded* ● Spans 1 & 2 and 5 & 6 loaded* ● Spans 2 & 3 loaded*


● Spans 3 & 4 loaded* ● Spans 4 & 5 loaded*



265


17/07/2006 17:16:46

TCC43 Wide Beams (A & D)/ MAIN!

Project

Spreadsheets to EC2

Client

Advisory Group

Location


Worked Examples: Main beam Grids C to J WIDE BEAM ANALYSIS & DESIGN

to

rmw


MATERIALS 35

N/mm²

fyk

500

N/mm²

dg (mm) γs

fywk Steel class

500 A

N/mm²

γc

SPAN 1 SPAN 2 SPAN 3 SPAN 4 SPAN 5 SPAN 6

SUPPORTS Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Support 7

Revision

-

20

Wk (mm)Top 0.4

Top cover

27

mm

Wk (mm)Btm 0.3

Btm cover

27

mm

Side cover

27

mm

Bay width

1.50 5000

c,dev 10 mm

LOADING PATTERN min max DEAD 1.25 1.25 IMPOSED 1.50 REBAR LAYERING Support steel in alt layer ? N

L (m)

h (mm)

bw (mm)

hf (mm)

Type

beff (mm)

390 390 390 390

1200 1200 1200 1200

125 125 125 125

T T T T

2600 2900 3000 2700

H (mm)

B (mm)

End Cond

BELOW (m)

H (mm)

B (mm)

End Cond

300 300 300 300 300

300 300 300 300 300

F F F F F

3.750 3.750 3.750 3.750 3.750

300 300 300 300 300

300 300 300 300 300

F F F F F

3.750 3.750 3.750 3.750 3.750

FB625

1.15

5.500 8.000 8.500 4.000

ABOVE (m)

276 266 Job No

COVERS (to links)

STATUS OK

.

Page

03-Jul-06

chg

© 2003-2006 TCC

fck

SPANS

Checked

EN 1992-1 : 2004

Date

Usage: Office


LOADING DIAGRAM

LOADING Span 1 UDL PL 1 PL 2 Part UDL Span 2 UDL PL 1 PL 2 Part UDL Span 3 UDL PL 1 PL 2 Part UDL

Office usage

UDLs (kN/m²)

PLs (kN)

Position (m)

Dead Load

Imposed Load

Position from left

Loaded Length

63.0

30.0

~~~~~

~~~~~ ~~~~~ ~~~~~

63.0 25.0

30.0 25.0

~~~~~ 4.00

~~~~~ ~~~~~ ~~~~~

63.0

30.0

~~~~~

~~~~~ ~~~~~ ~~~~~

1 245.2 278.6 126.1 80.8 -22.3

2 952.5 952.5 471.4 232.9 75.8

3 1078.4 1078.4 558.1 273.5 131.2

REACTIONS (kN) SUPPORT ALL SPANS LOADED MAX ULTIMATE Characteristic Dead Max Imposed Min Imposed


4 889.1 889.1 446.7 211.3 44.4

Dead Load

Imposed Load

Position from left

Loaded Length

63.0

30.0

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

~~~~~

~~~~~ ~~~~~ ~~~~~

5 117.4 169.4 59.4 63.5 -34.7

266


17/07/2006 17:16:48

TCC43 Wide Beams (A & D).xls TCC43 Wide Beams (A & D)/ ACTIONS!

Project

Spreadsheets to EC2

Client

Advisory Group

Location



rmw

WIDE BEAM ANALYSIS & DESIGN to EN 1992-1 : 2004


Date

Page

03-Jul-06

Checked

Revision

chg

-

© 2003-2006 TCC

267 277 Job No

FB625

BENDING MOMENTS (kNm) 0

5

10

15

20

25

0

30

1000

800

800

600

600

400

400

5

10

15

20

25

30

200

200 0 0 -200

-200

-400

-400

-600

-600

Elastic Moments SUPPORT No Elastic M Redistributed M δ


1

2

3

4

5

63.7 63.7 1.000

602.9 602.9 1.000

812.5 690.6 0.850

601.2 601.2 1.000

15.4 15.4 1.000

~ ~ ~

~ ~ ~

~ ~ ~

Redistribution

kNm/m kNm/m ~

15.0%

SPAN No

1

Elastic M 250.3 Redistributed M 250.3 δ 1.000 SHEARS FORCE DIAGRAMS (kN)

2

3

4

488.5 487.7 0.998

475.2 482.8 1.016

100.7 100.7 1.000

800

600

600

400

400 200

200 0

0

-200

-200

-400 -400

-600 -800

-600 0

5

10

15

20

25

30

0

5

10

Elastic Shears SPAN No 278.6 278.6

SPAN No

25

30

2

3

434.6 434.6

516.0 517.8

554.2 541.8

552.9 538.6

515.8 514.8

169.4 169.4

~ ~

~ ~

~ ~

~ ~

4

Elastic V Redistributed V COLUMN MOMENTS (kNm) ALL SPANS LOADED ALT SPANS LOADED

20



15

Above Below Above Below

377.1 377.1 1

2

3

4

5

22.1 22.1 31.9 31.9

18.9 18.9 35.1 35.1

3.3 3.3 30.6 30.6

-30.3 -30.3 -39.9 -39.9

1.0 1.0 9.4 9.4

267


17/07/2006 17:16:54

TCC43 Wide Beams (A & D)/ SPANS

Project

Spreadsheets to EC2

Client

Advisory Group

Location



Revision

chg

© 2003-2006 TCC

Page

278 268

03-Jul-06

Checked



Date

rmw

Job No

-

FB625

.

SPAN 1 ACTIONS

M

DESIGN

d As As2

TOP STEEL

CENTRE

RIGHT

62.6 1.00

250.3 1.00

501.3 1.00

mm

348.0 435

345.0 1756

340.5 3767

mm² mm²

Layer 1 As prov

BTM STEEL

LEFT kNm

701

mm²

L/d

DESIGN

1747

As prov

8H16 + 2H12 0 . As prov 1835 Allowed

46.06

3888

4H12 + 2H10 0 . As2 prov 609

..

kN

260.1

LINK Ø

416.1

VRd,ct

kN

10

VEd,max s req

mm

201.6 1560.4 415 H10 @ 250 for 500

415 H10 @ 250

278.6 1526.8 415 H10 @ 250 for 500

legs

No

6

6

6

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

kN


M d d As As2

NOMINAL

ok

ok ok

SPAN 2 ACTIONS

15.94

As2 prov

VEd

LINKS

CHECKS

0 6H25 + 3H20 .

4H12 + 2H10 0 . 609

DEFLECTION SHEAR

0 7H16 + 3H12 .

mm²

Layer 1 As2 prov

0 7H10 + 3H8 .

LEFT 526.6 1.00 340.5 3982 0

CENTRE 487.7 1.00 343.0 3442 0

RIGHT 636.4 0.86 340.5 4958 0

7H25 + 2H20 .

6H16 + 2H12 .

9H25 + 2H20 .

kNm mm mm² mm²

TOP STEEL

Layer 1 As prov Layer 1

mm²

BTM STEEL

4064 4H12 + 2H10

As2 prov

mm²

609

As prov

23.32

Allowed


kN

499.3

LINK Ø

523.3

kN

10

mm

282.8 1526.8 343 H10 @ 250 for 500

415 H10 @ 250

304.0 1526.8 326 H10 @ 250 for 500

legs

No

6

6

6

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

As2 prov 1433 10H20 + 2H16

. DEFLECTION SHEAR

L/d

kN

LINKS

CHECKS


As prov 5046 4H12 + 2H10

.

.

3544 25.99

NOMINAL

ok

As2 prov

609

..

ok ok

268


17/07/2006 17:16:59

TCC43 Wide Beams (A & D).xls TCC43 Wide Beams (A & D)/ SPANS!

Project

Spreadsheets to EC2

Client

Advisory Group

Location



SPAN 3 ACTIONS

M d d As As2

DESIGN

TOP STEEL

BTM STEEL

RIGHT 525.3 1.00 340.5 3972 0

9H25 + 2H20

7H12 + 5H10

7H25 + 2H20

.

.

mm mm²

5046 4H12 + 2H10 .

As2 prov

mm²

609 24.78


kN

520.1

LINK Ø

kN

10

mm

304.0 1526.8 328 H10 @ 250 for 500

415 H10 @ 250

282.8 1526.8 346 H10 @ 250 for 500

legs

No

6

6

6

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

L/d

kN


ACTIONS

M d d As As2

DESIGN

As2 prov 1184 11H20 + 2H16 . As prov Allowed

.

As2 prov 609 As auto-increased by 6.9 % V

496.3

v

NOMINAL

vc

ok ok

LEFT 478.5 1.00 340.5 3575 0 8H25

kNm mm mm² mm²

Layer 1 mm²

BTM STEEL

As prov Layer 1

3927 4H12 + 2H10

As2 prov

mm²


kN

mm

legs

No

CENTRE 100.7 1.00 348.0 700 0 7H20 + 2H16

.

DEFLECTION

L/d kN kN

LINKS

RIGHT 25.2 1.00 348.0 175 0 7H10 + 3H8

. As2 prov

2601 8H10 + 2H8

609

As prov

729

11.49 358.5

Allowed

250.52

.


3858 26.19

As prov 4064 4H12 + 2H10

ok

TOP STEEL

CHECKS

.

mm²

SPAN 4

SHEAR

FB625

As prov Layer 1

LINKS

CHECKS

-

CENTRE 482.8 1.02 343.0 3408 0

mm²

DEFLECTION SHEAR

279 269 Job No

LEFT 635.3 0.85 340.5 4949 0

kNm

Layer 1

Revision

chg

© 2003-2006 TCC

Page

03-Jul-06

Checked



Date

rmw

. As prov 701 4H12 + 2H10

.

. As2 prov

609

..

LINK Ø

150.8

10

279.6 1526.8 415 H10 @ 250 for 500

415 H10 @ 250

201.6 1560.4 415 H10 @ 250 for 500

6

6

6

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

ok

NOMINAL

ok

ok ok

269


17/07/2006 17:17:03

TCC51 Column Load Take-down Design.xls Conventional column load take-downs by hand can be timeconsuming. This spreadsheet emulates conventional column design to Eurocode 2 by providing load take down from inputs of location, dimensions, levels and loads to give design axial loads and moments per floor, and to foundations. TCC51.xls is intended as a stand-alone column design spreadsheet for use when a subframe analysis is not available or is unwarranted. This spreadsheet also determines the area and arrangement of steel required (As) for all lifts in RESULTS! or individual lifts in CALC!. This spreadsheet is intended for use with braced columns only. Moments and vertical loads for unbraced structures should be derived from a frame analysis, and then should be designed via TCC53 or TCC54. Load distribution is according to shear force factors from Tables in the ISE/ ICE Manual for the design of reinforced concrete building structures to EC2(28). Column moments are assessed via a limited moment distribution routine making conservative assumptions regarding remote spans etc. There is no double counting of floor slabs due to allowances for floor slabs in design of, therefore reactions from, edge beams spanning parallel to floor slab span. As a default the level with maximum axial load with concurrent maximum moment, i.e. the bottom level, is chosen for consideration in CALC! (long-hand design). The user may investigate other levels by choosing the appropriate level via the arrows on the right hand side of CALC!.

INPUT!

in the remainder of rows 28 to 39. Slab spans may be parallel to x or y, or two-way spanning. If there are more than twelve storeys in a structure, upper storeys (>12) may be calculated first with “No” entered in the “column above” cell, D22. For the remaining lower storeys, cell D22 may then be set to “Yes”, with data related to the upper storeys being entered on row 22 and cells M27 to P27. The check box to the top right hand side of this page allows the user to select whether or not EN 1990 loading equations 6.10a and 610b should be used to determine ULS loads and moments. This may make a considerable difference to results, and it is recommended that this box should be un-checked unless the user is fully familiar with these equations. When all input on this page has been completed, go to the next page called:

RESULTS! This page displays the following results: ■ Characteristic dead and imposed loads applied to the column

at each level, including imposed load reduction factors to EN1991 and its’ UK National annex. ■ Cumulative loads at each level, both characteristic and

ultimate (NEd). ■ The summation of ultimate initial moments and additional

moments due to slenderness on each axis. ■ The reinforcement arrangement required at each level, based

on a user specified number of bars. All relevant materials, geometric and loading data is input on this sheet. After materials data, number of storeys, column location and base condition should be selected. If the number of storeys is reduced below 12, rows at the foot of this page will be “browned out” so that the correct number of storeys is displayed. The base condition refers to whether or not the column should be fixed or pinned at foundation level. Under column location, the selection from a list of five differing locations should be self-explanatory. “Double penultimate” means a column that is penultimate in both directions. As this selection is made, the key diagram changes to indicate relevant plan dimensions with the column to be designed highlighted in red. The X and Y spans should then be input together with edge distances. Next, level references should be entered in cells B28 to B39, and the general, geometric and loading data for each floor

The number of main bars is entered at each level or the “Set all lifts to” button may be used to insert the specified number of bars in each lift of the column. Initially and after changing the number of bars at any level, “CHECK” buttons to the right will be highlighted in red to indicate that the arrangement has yet to be determined. Then clicking either an individual CHECK button or the “Check all levels” button will calculate bar arrangements. The recommended procedure is to initially set all lifts to a standard number of bars, click the “Check all levels” button, then change and check any lifts that appear unsuitable or where “NO FIT” appears under the number of bars. It should also be remembered that the concrete grade for each lift may be amended in cells O27 to O39 of INPUT!

CALC! This sheet shows detailed calculations for a single lift of the column. As a default, the level with maximum axial load with

270


17/07/2006 17:17:08

TCC51 Column Load Take-down Design.xls concurrent maximum moment, i.e. the bottom level, is chosen for consideration here. The user may investigate other levels by choosing the appropriate level via the arrows on the right hand side of the page. After summarising the actions on the chosen lift of column, a check is made to determine whether or not the column is slender, then the section is analysed to find the moments of resistance about both axes for the given axial load. On the second page of CALC!, firstly moments due to imperfections are calculated and it is decided about which axis these will be critical. Design first order moments (M0Ed) are then derived by adding imperfection (Mi) moments to the basic first order design moment (m0E). Finally, single axis and biaxial checks are carried out to ensure that applied moments are less than the section’s moments of resistance.

Refs! Relevant National Annex values are tabulated here, both for BS EN 1990 and BS EN 1992. These values are editable for use in other countries.

Notes! This page contains details of spreadsheet status, revision history and program assumptions, as well as a standard disclaimer clause.

Select! On this page, checks for the chosen number of bars at each level are carried out for six different bar diameters. The smallest bar diameter that passes all checks is then selected for display on RESULTS!

Col~M On this page, flexural stiffnesses are calculated for all beams and columns and limited moment distributions are carried out to determine column moments.

Slen! Here the effective heights of columns and slenderness ratios are determined from relative rotational stiffnesses, as well as nominal moments due to imperfections.

M2! This is where second order moments are calculated, for each lift and for each possible bar diameter.

Secs! Here the section moments of resistance are determined for the given axial load at each level, for each possible bar diameter and on both axes.

Gra! This page contains data for generation of the diagrams.

271


17/07/2006 17:17:10

TCC51 Column Load Take-down Design/ INPUT! Project Client Location

The Concrete Centre

Spreadsheets to Eurocode 2 BigBucks PLC Column G14

BRACED FRAMES ONLY

Made by

03-Jul-06

Checked

COLUMN LOAD TAKE DOWN & DESIGN for RECTANGULAR COLUMNS to EN 1992: 2004

Originated from TCC51.xls version 3.0 on CD

Beam fck (N/mm²) 30 Concrete density (kN/m³ ) 25 fyk (N/mm² ) 500

© 2004 - 2005 TCC

10

No of storeys (this sheet)

Column Location

Revision

-

CHG

Page

282 272 Job No

FB625

EN 1990 Allow 610a & 6.10b ? (,t0) =

Double penultimate Span X1

Span X2

Yes 2.00

· No

Span Y1

Steel class A

Date

Rod

Base condition

Span Y2

Pinned

KEY PLAN

Span Y1 Span Y2

3.750 4.000

Column above? No

Storeys

Solid hf Direction || to

Roof 9 8 7 6 5 4 3 2 1

mm

125 125 125 125 125 125 125 125 125 125

X, Y or B

Y Y Y Y Y Y Y Y Y Y

West North

5.500 6.000 Gk

DIMENSIONS SLAB Span Level

Edge distances (mm )

Beam spans (m ) Span X1 Span X2

Qk

COLUMN SECTION Min column cover (mm ) 30 c,dev (mm ) 10

0 0

0

M0EX

M0EY LOADS

Span Y1 h

300 300 300 300 300 300 300 300 300 300

bw

250 250 250 250 250 250 250 250 250 250

BEAM SIZES (mm ) Span Y2 Span X1 h

300 300 300 300 300 300 300 300 300 300

bw

250 250 250 250 250 250 250 250 250 250

h

350 350 350 350 350 350 350 350 350 350

bw

300 300 300 300 300 300 300 300 300 300

Span X2

COLUMN BELOW

mm mm fck Height (m )

h

bw

H

B

N/mm²

350 350 350 350 350 350 350 350 350 350

. 300 300 300 300 300 300 300 300 300 300

250 250 250 250 300 300 300 300 300 300

300 300 300 300 450 450 450 450 450 450

30 30 30 30 30 30 30 35 35 35

gk

SLAB qk

Cat

floor to floor kN/m² kN/m² A to K

3.750 3.750 3.750 3.750 3.750 3.750 4.500 4.500 4.500 4.500

5.20 5.20 5.20 5.20 5.20 5.20 6.30 6.30 6.30 6.30

1.50 4.00 4.00 4.00 4.00 4.00 5.00 5.00 5.00 5.00

I B B B B B D D D D

BEAM LINE LOADS N-S E-W kN/m

kN/m

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

272


17/07/2006 17:17:11

TCC51 Column Load Take-down Design.xls TCC51 Column Load Take-down Design/ RESULTS!

Project


The Concrete Centre

Client

BigBucks PLC

Made by

Location Column G14

Rod Checked

COLUMN LOAD TAKE DOWN & DESIGN to EN 1992: 2004


© 2004 - 2005 TCC

CHG

Date

03-Jul-06 Revision

-

Page 273 283

Job No

FB625

Braced frames only Characteristic Gk Qk

Below Level

Roof Clear height

9 Clear height

8 Clear height

7 Clear height

6 Clear height

5 Clear height

4 Clear height

3 Clear height

2 Clear height

1 Clear height

0 Clear height

0 Clear height

from above Loaded area Category

0.0

0.0

164.8

41.3 0.0

Design Moments about NEd

X-X

Y-Y

M0Ed

5.15

2.54

M2

0.00

0.00

Reinforcement No Bar and Ø

4

27.536

I

reduction

3.400

Cumulative

164.8

41.3

5.15

2.54

H12

164.8

M0Ed

5.12 0.00

1.42 0.00

4

M0Ed

5.12 5.12

1.42 1.42

M2

0.00

0.00

M0Ed

5.12 5.11 0.00

1.42 0.88 0.00

H12

5.11 5.55 0.00

0.88 1.33 0.00

H16

5.55 5.52 0.00

1.33 2.16 0.00

H12

5.52 6.20 0.00

2.16 1.74 0.00

H12

6.20 6.17 0.00

1.74 1.45 0.00

H20

6.17 6.18 0.00

1.45 0.96 0.00

H20

6.18 7.80 45.29

0.96 0.20 30.20

H25

53.09 #N/A #N/A

30.41 #N/A #N/A

H32

#N/A #N/A #N/A #N/A

#N/A #N/A #N/A #N/A

#N/A

27.536

B

reduction

110.1 15.1

3.400

Cumulative

329.6 164.8

136.4 110.1

reduction

15.1

494.4 164.8

231.4 110.1 43.6

Loaded area Category

Loaded area Category

27.536

B

3.400 Cumulative Loaded area Category 27.536

B


B


B


D

reduction

659.2 169.9 reduction



4.150 Cumulative 1201.7 Loaded area Category 202.7 27.536

D

reduction


D

reduction


D

reduction


0.00

reduction

0.000 Cumulative 1809.8 Loaded area Category 0.0 27.536 0.000

0.00

reduction

Cumulative 1809.8

298.0 110.1 43.6 364.5 110.1 43.6 431.1 137.7 52.1 516.7 137.7 52.8 601.5 137.7 53.2 686.0 137.7 53.5 770.2 0.0 #N/A #N/A 0.0 #N/A #N/A

267.7

616.1

M2

964.5

1270.1

M2 M0Ed

1582.1

M2 M0Ed

1894.1

M2 M0Ed

2275.6

M2 M0Ed

2656.0

M2 M0Ed

3035.9

M2 M0Ed

3415.3

M2 M0Ed

#N/A

M2 M0Ed

#N/A

M2

Layout

H12

4

4 4 4 4 4 6 6 6 6 #N/A

273


17/07/2006 17:17:17

TCC51 Column Load Take-down Design/ CALC!

The Concrete Centre

Project


Client Location

BigBucks PLC Column G14

Made by


Checked

Date

Rod


© 2004 - 2005 TCC

Section calculation for column below level 2

Page

274 284

03-Jul-06 Revision

CHG

Job No

-

FB625

300 x 450 with 6 H25 bars

fcd = cc x fck /c = 0.85 x 35 /1.5 = 19.83 N/mm² fyd = fyk /s = 500 /1.15 = 434.78 N/mm² Valid design

STATUS ACTIONS

from load take-down, NEd = 3,035.9 kN

n = 1000 x 3,035.9 /19.83 /300 /450 = 1.134

from bending analysis, M0xx top = 0.10 kNm

5.8.8.3 (3) M 0 are applied moments

M0yy top = 1.42 kNm

M0xx btm = 0.12 kNm

M0yy btm = 0.27 kNm

combining top and bottom moments, m0Exx = 0.11 kNm

and m0Eyy = 0.96 kNm

(5.32)

SLENDERNESS from flexural stiffness analysis, L0x = 2.576 m

and L0y = 3.084 m

rxx = (300² /12) = 86.60 mm

(5.15)

ryy = (450² /12) = 129.90 mm

therefore, x = 2,576 /86.60 = 29.74

gross section

and y = 3,084 /129.90 = 23.74

efx = 2 x 0.741 = 1.481

efy = 2 x 0.611 = 1.222

limx = 22x2.538/(1+0.2 x 1.481)/1.134 = 40.46

limy = 22x1.893/(1+0.2 x 1.222)/1.134 = 31.42

29.74 40.46 therefore column is short

(5.19) (5.13N)

23.74 31.42 therefore column is short

SECTION ANALYSIS cu3 = 0.0035 and c3 = 0.00175 from Table 3.1

= 0.80

= 1.00

.fcd = 19.83 x 1.00 = 19.83 N/mm²

net fyd = 434.78 - 19.83 = 414.95 N/mm²

d2 = 30 + 8 + 25/2 = 50.5 mm

As = x 25² /4 x 6 = 2,945 mm²

About xx axis

About yy axis

d = 300 - 50.5 = 249.5 mm (1-c3/c3u)h = 300(1 - 175 /350) = 150 mm

3.19) to (3.22)

d = 450 - 50.5 = 399.5 mm (1-c3/c3u)h = 450(1 - 175 /350) = 225 mm

there are 2 bars in xx faces Neutral axis depth x = 305.33 mm Conc comp force, Fc = MIN(0.8 x 305.33 ; 300)450 x 19.83 /1000 = 2,180.1 kN Limiting strain, c max = c3 /[x-(1-c3/c3u)h]x 0.00344 Intermediate bars are at 150, 0, 0, 0, 0, 0, 0 & 0 µ-strain at main compression steel = 3,440(305.3- 50.5)/305.3 = 2,871

(total of 6 bars)

x = 476.29 mm

by iteration

Fc = MIN(0.8 x 476.29 ; 450)300 x 19.83 /1000 = 2,267.1 kN c max = c3 /[x-(1-c3/c3u)h]x 0.00332 and at No intermediate bars

Figure 6.1 from column face

sc = 3,317(476.3- 50.5)/476.3 = 2,965

µ-strains at intermediate bars = 1,750, 0, 0, 0, 0, 0, 0, 0

si = No intermediate bars

µ-strain at main tension steel = 3,440(305.3- 249.5)/305.3 = 629

st = 3,317(476.3- 399.5)/476.3 = 535

Net stress at main compression steel = Min(200000s, fyd) - .fcd = 414.95

hinge point

and 3 bars in yy faces

sc = Min(200000s, fyd) - .fcd = 414.95

N/mm²

si = No intermediate bars

N/mm²

Net stress at main tension steel = Min(200000s, fyd) = 125.80

st = Min(200000s, fyd) = 106.95

N/mm²

Force at main compression steel = 414.95 x 982 /1000 = 407.4 kN

Fsc = 414.95 x 1,473 /1000 = 611.1 kN

Net stresses at intermediate bars = 330.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0

Forces at intermediate bars = Ass = 324.1 kN

Fsi = Ass = 0.0 kN

Force at main tension steel = 125.80 x 982 /1000 = 123.5 kN

Fst = 106.95 x 1,473 /1000 = 157.5 kN

NRd = Fc + Fs = 2,180.1 + 407.4 + 324.1 + 123.5 = 3,035.1 kN NEd Conc lever arm, z = Max(d - x /2, d - h/2) = 127.37 mm MRd = fcz + Fsa - NRd(d - h/2) = 277.67 + 113.32 - 301.99 Moment of resistance, MRd = 89.00 kNm

NRd = 2,267.1 + 611.1 + 0.0 + 157.5 = 3,035.7 kN NEd z = 208.98 mm

value of x selected to match N Ed & N Rd

MRd = 473.80 + 213.26 - 529.73 MRd = 157.33 kNm

274


17/07/2006 17:17:22

TCC51 Column Load Take-down Design.xls TCC51 Column Load Take-down Design/ CALC! Project

The Concrete Centre


Client BigBucks PLC Location Column G14

Rod

03-Jul-06

275 285

CHG

-

FB625



Section calculation for column below level 2

© 2004 - 2005 TCC

continued

n = MIN(1, MAX(, 2 /4.5) = 0.943 IMPERFECTIONS M i x = 0.943 x 0.005 x 2.576 x 500 = 6.07 kNm M i y = 0.943 x 0.005 x 3.084 x 500 = 7.27 kNm Inperfections critical about xx axis, therefore set Miy = 0 SECOND ORDER MOMENTS x = 0.35 + 35 /200 - 29.74 /250 = 0.406 y = isx = 81.24 mm isy = dx = 231.2 mm dy = Kx = Max(1, 1 + 0.406 x 1.481) = 1.602 Ky = nu = Asfyd /(Acfcd) = 1.478 1/r0 = yd /(0.45d) = 2.08910E-5 1/r0 = 1/r = KrK1/ro = 1.068710E-5 1/r = M0Edx = m0E + M i = 6.18 Knm M 2 x = NEd(1/r)L0² /² = 21.81 kNm Column is short IGNORE

5.2 (5) (5.1) & (5.2) 5.8.9 (2)

0.35 + 35 /200 - 23.74 /250 = 0.430 5.8.8.3 (4) 174.50 mm radius of gyration of steel 399.5 mm 5.8.8.3 (2) Max(1, 1 + 0.430 x 1.222) = 1.526 5.8.8.3 (1) Kr = (nu - n) /(nu - nbal) = 0.319 5.8.8.3 (1) 5.8.8.3 (1) 1.20910E-5 0.589310E-5 (5.34)

M0Edy = 0.96 Knm M 2 y = 17.24 kNm Column is short IGNORE

5.8.2 (5)P (5.32) 5.8.2 (6)

SINGLE AXIS CHECKS M0Ed + M 2 = 6.18 kNm Minimum moment, M Ed,min x = 20 x 3,035.9 /1000 = 60.72 kNm Therefore design moment, M Ed x = 60.72 kNm < 89.00 OK

M0Ed + M 2 = 0.96 kNm MEd,min y = 20 x 3,035.9 /1000 = 60.72 kNm and M Edy = 60.72 kNm < 157.33 OK

(5.31) 6.1 (4)

BIAXIAL CHECK Max of x/y and y/x = 1.253 < 2 exb eyh = 0.103 BIAXIAL CHECK NOT REQUIRED . 3,958.0 kN . 3,035.9 /3,958.0 = 0.767 a = 1.612 from table . 0.7555 <1 OK

(5.38a & b) 5.8.9 (3) 5.8.9 (4)

275


17/07/2006 17:17:28

TCC52 Column Chart generation.xls This spreadsheet generates axial load:design moment interaction charts for symmetrically reinforced rectangular columns. It checks the capacity of the columns with various arrangements of reinforcement against input load cases of axial load and uniaxial bending. Within TCC11.xls, COLUMN! allows the user to determine the area of steel required from inputs of axial load and moment about the x - x axis. The approach of TCC52 is to give an interaction chart. This shows axial load against moment for symmetrical sections of specified size, strength and reinforcement. It works on the premise of calculating the moment and axial load capacities of a section with assumed amounts of reinforcement and assumed neutral axis depth. Iterations of neutral axis depth give data for the Axial load:Moment interaction chart for the specified section. The spreadsheet also checks the reinforcement required for input load cases. The user may try different arrangements of reinforcement.

Refs! This sheet comprises the values for nationally determined parameters that have been used in the spreadsheet. These data reflect the values given in draft UK National Annexes for BS EN 1990 and BS EN 1992. Designers should ensure that these data are current when the spreadsheet is used. When using TCC31R for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations.


RCC52.xls assumes that the moments input in the load cases have already been adjusted, if necessary, for bi-axial bending. For many side and all corner columns, there is no choice but to design for bi-axial bending, and TCC53.xls should then be used. Moments due to imperfections and second order moments in slender columns are added automatically.

MAIN! Main! contains all input and output data, including details of members connected to the top and bottom of the column. These are used to assess slenderness criteria and additional moments. Bending is assumed to be about the x - x, i.e. horizontal axis, and the input moment is assumed to be the maximum design moment as defined in EC2. Any additional moments due to slenderness are added by the program. The dotted line within the chart indicates minimum design moment.

Calcs! Calcs! shows the derivation of the charts where moment capacity is calculated at intervals of neutral axis depth from n.a. depth for N = 0 to n.a. depth for N = Nbal, then at intervals from n.a. depth for N = Nbal to n.a. depth for N = Nuz.

Cases! Cases! identifies the smallest bar diameter that satisfies each of the load cases.

276


17/07/2006 17:17:35

TCC52 Column Chart generation.xls TCC52 Column Chart generation/ MAIN!

Project

Spreadsheets to EC2

Client

Advisory Group

Location



Date

RMW

COLUMN CHART FOR SYMMETRICALLY REINFORCED RECTANGULAR COLUMNS BENT ABOUT THE X-X AXIS TO EN 1992-1 : 2004 Originated from TCC52.xls v3.0 on CD

Checked

Revision

chg

© 2003-05 TCC

Page

277 287

03-Jul-06

Job No

-

FB625

MATERIALS fck fyk Steel class DESIGN SECTION h b Bars per face All bars in

32 500 2 A

s c ef

N/mm² N/mm²

1.15 1.5 1.15

Cover dg c,dev

steel concrete

b (mm)

Clear height, L = 400 250 2 250

3600 mm RESTRAINTS Top F Fixed Btm F Fixed Braced Y .

mm mm No

wide faces

35 mm 20 mm 10 mm CONNECTING BEAMS/SLABS

Top left 350 Top right 350 Bottom left 350 Bottom right 350 Beam stiffnesses are Column above? Y

BAR ARRANGEMENTS

h (mm)

500 500 500 500 70%

Remote end L (m)

(F) or (P)

7.5 F 6 F 7.5 F 6 F of uncracked stiffness Col below? Y

Data on connecting beams only affects loadcases, not charting.

Type

Bar Ø

Asc %

Link Ø

Bar c/c

Nbal (kN)

Nuz (kN)

Checks

H H H H H H

40 32 25 20 16 12

5.03 3.22 1.96 1.26 0.80 0.45

10 8 8 8 8 8

120.0 132.0 139.0 144.0 148.0 152.0

0.0 733.7 752.9 764.9 773.5 781.1

0.0 2880.9 2465.0 2230.4 2080.2 1963.5

Asc > 4 % ok ok ok ok ok

N:M INTERACTION CHART for 400 x 250 column, grade C32, 35 mm cover and 2 bars on 250 mm faces 3500

3000

AXIAL COMPRESSION, NEd (kN)

Min M

2600

2500

2500 H32

2000

H25 H20

1750

H16 H12

1500

1350 1000

Nbal 610 500

500

0 0

50

100

150

200

250

300

MOMENT MEd (kNm) LOADCASES Double curvature ? Yes

Load case

NEd (kN)

1 2 3

500 1750 2600

m0e (kNm) MEd (kNm)

165 120 35

167.7 129.3 52.0

4 H25 4 H32 4 H32

Load case

NEd (kN)

m0e (kNm)

MEd (kNm)

4 5 6

610 1350 2500

80 185 150

83.2 192.2 163.3

4 H12 4 H32 No Fit

277


17/07/2006 17:17:36

TCC53 Column Design.xls TCC53.xls generates column design charts for symmetrically reinforced rectangular columns bent about two axes and checks input load cases. TCC53.xls also gives interaction charts, showing axial load against moment for the critical axis for symmetrical rectangular sections of specified size, strength and reinforcement arrangement. The user may try different arrangements of reinforcement. It also provides designs for input load cases, which are plotted on the relevant x- or y- axis chart. TCC53.xls takes account of any side-bars specified.

MAIN! MAIN! contains all input data and gives designs for the input load cases. Guidance for the input is given within the spreadsheet but users should be familiar with BS EN 1992-1-1 Section 5.8 The input moments are the initial end moments due to ultimate design loads as defined in BS EN 1990 about the appropriate axes. Madd, the critical direction for bi-axial bending and design moments are calculated.

considered and the critical axis identified. MEd is calculated by adding NEde1 for imperfections and where necessary M2(=NEde2) for second order moments in slender columns. MEd is used in the design and plot (in CHARTS!).

Refs! This sheet comprises the values for nationally determined parameters that have been used in the spreadsheet. These data reflect the values given in draft UK National Annexes for EN 1990 and EN 1992. Designers should ensure that these data are current when the spreadsheet is used. When using TCC31R for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations.


CHARTS! CHARTS! shows two charts, one chart for when MEdx is critical and one for when MEdy is critical. These Axial load:Moment interaction charts for the specified section also show relevant input load cases. The load cases are identified by axial load only (a quirk of Excel!).

Xcal! and Ycal! These sheets show the derivation of the charts where moment and axial load capacity is calculated at intervals of neutral axis depth (in intervals from n.a. depth for N = 0 to n.a. depth for N = Nbal, then in intervals from n.a. depth for N = Nbal to n.a. depth for N = Nuz).

Slen! The calculations on this sheet determine slenderness criteria and effective column lengths about both axes.

Cases! Cases! identifies the smallest bar diameter that satisfies each of the load cases. Calculations are made for both directions and the spreadsheet decides which axis is dominant. Bi-axial bending is 278


17/07/2006 17:17:43

TCC53 Column Design.xls TCC53 Column Design/ MAIN!

Project

EC2 Comparative Design

Client

BRE

Location


Column D2

Date

RMW

SYMMETRICALLY REINFORCED RECTANGULAR COLUMN DESIGN, BENT ABOUT TWO AXES TO EN 1992-1 : 2004 Originated from TCC53.xls v 3.0 on CD

Checked

Page

03-Jul-06 Revision

Job No

-

© 2002-2005 TCC

279 289

FB625

MATERIALS fck fyk

35 500

2.9

h b with and

325 275 2 2

s c

1.15 1.5

Cover to link dg

30 20

mm

ef Steel class .

1.6 A

c,dev

10

mm

N/mm² N/mm²

SECTION mm

mm

mm

X

bars per 275 face

X

bars per 325 face

ie. 325 x 275 columns with 4 bars Remote

RESTRAINTS

CONNECTING BEAMS/SLABS

Storey height (mm)

Top

Btm

Condition

Condition

Braced ?

5000 5000

F F

P P

Y Y

L (mm)

L0 (mm)

h0 (mm)

4500 4825

3459 3709

149

X-AXIS Y-AXIS

X-AXIS Y-AXIS

BAR ARRANGEMENTS Bar Ø H 32 H 25 H 20 H 16 H 12 H 10 LOADCASES 1 2 3 4 5 6 DESIGN MOMENTS 1 2 3 4 5 6

Asc %

Link Ø

3.60 2.20 1.41 0.90 0.51

8 8 8 8 8 8

h (mm)

Top West 300 500 Top East 300 500 Top North 7000 175 7000 175 Top South Bottom West Bottom East Bottom North Bottom South 70% Beam stiffnesses are Column above? Y BAR CENTRES (mm) Nuz (kN) 275 Face 325 Face 167 174 179 183 187 189

TOP MOMENTS (kNm)

AXIAL

b (mm)

217 224 229 233 237 239

(F) or (P)

8 6 5 5

F F F F

of uncracked stiffness Col below? Y Checks

ok ok ok ok ok As or Ø < minimum

2835 2421 2188 2038 1922

BTM MOMENTS (kNm)

N (kN)

m0x

m0y

2126.1 2030.5 1025 783 600 1570

19.5 29.9 50.0 80.0 120.0 130.0

2.5 2.5 2.5 2.5 2.5 2.5 Critical

Biaxial Check

MEd x

MRd x

MEd y

MRd y

axis

Equation (5.39)

42.5 48.4 58.8 80.0 120.0 130.0

57.6 69.3 87.3 92.7 126.3 157.7

38.4 41.0 40.3 6.3 5.2 11.2

100.1 107.2 98.2 96.2 117.5 164.7

X X X X X X

0.691 0.634 0.878 0.863 0.965 0.807

X AXIS

end

L (m)

m0x

m0y Moments m 0 at top and bottom of column (from analysis) are combined to find m 0e . The moment due to imperfections (e 1 N) and the second order moment (M 2 ) are then added to obtain M Ed In the table below.

Y AXIS

REBAR

4 4 4 4 4 4

H25 H25 H12 H12 H20 H32

SEE CHARTS ON NEXT SHEET

279


17/07/2006 17:17:44

TCC54 Circular Column Design.xls TCC54.xls generates a column design chart for symmetrically reinforced circular columns of an inputted size with an inputted number of bars. It checks input load cases of ultimate axial load and resolved moment.

MAIN! MAIN! contains all input data and gives designs for the input load cases. Guidance for the input is given within the spreadsheet but users should be familiar with BS EN 1992-1-1 especially Section 5.8. The input moments are the ultimate design moments from analysis resolved around an appropriate axis. Allowances for imperfections (NEde1) and where appropriate for second order effects (M2=NEde2) in slender columns are added automatically to the first order moment input at E57 to give MEd in cells F57etc. The input moment at E57 should have been resolved for bending in two directions by the user.

Refs! This sheet comprises the values for Nationally Determined Parameters that have been used in the spreadsheet. These data reflect the values given in draft UK National Annexes for BS EN 1990 and BS EN 1992. Designers should ensure that these data are current when the spreadsheet is used. When using TCC54 for permanent design, designers are strongly advised too include a copy of this sheet with any design calculations.


The axial load:moment interaction chart for the specified section also show relevant input load cases. The load cases are identified.

Calcs! These sheets show the derivation of the charts where moment and axial load capacity is calculated at intervals of neutral axis depth (in intervals from n.a. depth for N = 0 to n.a. depth for N = Nbal, then at intervals from n.a. depth for N = Nbal to n.a. depth for N = Nuz.

Circle! The calculations on this sheet determine slenderness criteria and effective column lengths about both axes.

Cases! Cases! identifies the smallest bar diameter that satisfies each of the load cases. Calculations are made for both directions and the spreadsheet decides which axis is dominant.

280


17/07/2006 17:17:50

TCC54 Circular Column Design.xls TCC54 Circular Column Design/ MAIN!

Project

Spreadsheets to EC2

Client

Advisory Group

Location



RMW

CIRCULAR COLUMN DESIGN TO EN 1992-1 : 2004

Checked


Date

Page

Revision

chg

© 2004-05 TCC

281 291

03-Jul-06

Job No

-

FB625

MATERIALS fck 30 fyk 500 2.41 Steel class A DESIGN SECTION h 475 with 8

s c

N/mm² N/mm²

1.15 1.5 1.45

ef

L= Top Btm Braced

mm

bars

Cover dg c,dev

steel concrete

RESTRAINTS 3600 mm F Fixed F Fixed Y .

Top left Top right Bottom left Bottom right

30 mm 20 mm 5 mm CONNECTING BEAMS/SLABS

end

b (mm)

h (mm)

L (m)

(F) or (P)

350 350 350 350

500 500 500 500

7.5 6 7.5 6

F F F F

Beam stiffnesses are Column above? Y BAR ARRANGEMENTS

Remote

70%

of uncracked stiffness

Col below? Y

Data on connecting beams only affects loadcases, not charting.

Type

Bar Ø

Asc %

Link Ø

Bar c/c

Nbal (kN)

Nuz (kN)

Checks

H H H H H H

40 32 25 20 16 12

5.67 3.63 2.22 1.42 0.91 0.51

10 8 8 8 8 8

163.0 165.3 166.7 167.7 168.5 169.3

0.0 899.0 963.0 1185.1 1355.4 1363.9

0.0 5264.4 4386.9 3892.1 3575.5 3329.2

Asc > max %

N:M interaction chart

ok ok ok ok ok

for 475 diameter column, grade C30/37 concrete and 30 mm cover

6000

Min M 5000

AXIAL LOAD NEd (kN)

8H32 4000

8H25 LC2 8H20 8H16

3000

LC1

LC3

LC5

8H12

2000

LC6 1000

LC4 0 0

50

100

150

200

250

300

350

400

MEd (kNm)

450

MOMENT MEd X (kNm) Loadcase

NEd (kN)

m0e (kNm)

MEd (kNm)

Loadcase

NEd (kN)

m0e (kNm)

Double

1

2600

40

57.6

8 H12

4

610

170

174.1

8 H16

curvature ?

2

3500

110

133.7

8 H25

5

2750

315

333.6

8 H32

Yes

3

2850

120

139.3

8 H20

6

1500

240

250.1

8 H20

LOADCASES

281


17/07/2006 17:17:51

TCC55 Axial Column Shortening.xls This spreadsheet works out column shortenings in accordance with BS EN 1992-1-1 Clauses 3.1.3(1), 3.1.3(3)and Annex B, creep and shrinkage strain. It works from the roof down and assumes that time 0 equates to construction of the lowest column. When ‘shortenings between floors’ need to be considered, this spreadsheet calculates the longterm floor displacements due to columns being loaded incrementally. A detailed construction history is input so that time-dependent creep and shrinkage factors may be computed. A maximum of 12 lifts of columns are currently catered for. It would not be practical to superimpose further storeys by running this spreadsheet more than once, but an extended version could be produced at a later date if demand exists. To investigate particular situations it is suggested that the spreadsheet is run more than once. For instance, to investigate column shortenings that affect partitions, it is suggested that the spreadsheet is run twice once at partition installation and secondly at say 30 years.

MAIN! MAIN is used to input materials, dimensional and load data. Enter general data first, before geometry and loading sequence.

Any differential shortening between connected vertical members will generate a transfer of vertical load. If connecting slabs or beams are stiff and/ or short, such load transfer can be substantial and, in tall buildings, may even be critical at ULS. If such effects are considered to be critical between a group of vertical members, the following procedure is recommended: ■ Run each column or wall and save it under an individual file

name. ■ Write a routine within one of these worksheets to assess the

amount of load transfer at each level, using long-term cracked section properties for connecting horizontal members. This will link the results between worksheets. Remember to adjust estimated displacements by any elastic shortening that may have been included in a global frame analysis. ■ Add a routine in each linked worksheet to modify the long-

term floor loads at each level, by adding transfer loads into cells MAIN!Q15:Q26, which are already set up for this purpose. NOTE: transfer of loads should be damped by a constant factor, to reduce the number of iterations required. ■ Write a VBA macro to iterate this transfer process until a

balance is reached (ie. residual transfer is close to zero). ■ Differential foundation displacements may also need to be

considered within this process.

Eurocode 2 permits RH (relative humidity) values between 10% and 100%. Values of 50% (internal exposure) and 80% (external exposure) are considered typical in the UK. Exposure will be external during the construction period, followed by a reduced RH in use, so when in doubt, a value of 65% could be appropriate. The formulae in BS EN 1992-1-1 are used for concrete strength gain (3.1.2(6)) with age and for Young’s modulus, E (Table 3.1). At present, specific values of gain of strength and E (determined from tests) cannot be accommodated by this spreadsheet, but may be accommodated at a later date.

Creep1!

`Shortenings between floors’ are the amounts by which individual column lifts may shorten in length following construction of the floor immediately above. This value will directly affect any cladding or brittle partitions between floors.

Again, in a series of cascading calculations, Creep2 similarly calculates elastic shortenings that occur before each floor is constructed.

‘Floor Displacements’ are the long-term net displacements of floors from the level at which they were constructed. The floor at an individual column may therefore be cast at say 50% of this value above the nominal floor level, in order to minimise racking effects. The particular shape of the curve is defined by effects of incremental loading and the effects of drying shrinkage. It is assumed that any ‘shortenings between floors’ have been compensated for and therefore dealt with prior to a floor’s construction. The difference between floor displacements of adjacent columns will create a racking effect on any attached cladding or brittle partitions.

Shrink!

In a series of cascading calculations, Creep1 calculates the total creep and elastic shortenings based on applied dead and permanent imposed loads. Concrete E values are based on the mean 28 day strength fcm, adjusted by creep factors ϕ that allow for both age at loading and load duration.

Creep2!

Shrink! calculates the amount of drying shrinkage; for both total long-term and before construction of each floor.


282


17/07/2006 17:17:57

TCC55 Axial Column Shortening.xls TCC55 Axial Column Shortening/ MAIN!

The Concrete Centre

Project Spreadsheets to EC2 Client

Advisory Group

Made by

Location Column K2 AXIAL COLUMN SHORTENING to EN 1992-1 : 2004 Originated from TCC55.xls v3.0 on CD

No of Storeys 12

chg

© 2002-2005 TCC

Cement type

Ambient temp, ºC 20

283 293

RR

Relative humidity % 50

Job No

-

FB625

Quartzite Quartzite 250 days from level 0

Aggregate Occupancy at Curing time 2 .

Geometry & Loading Sequence

Roof 11 10 9 8 7 6 5 4 3 2 1

Page

03-Jul-06

Checked Revision

General Data

LEVEL

Date

rmw

3

days

0.3 0.3

Permanent Load

Column below

Time gap days

fck

Length

H

B

14 14 14 14 14 14 14 14 14 14 14 14

40 40 40 40 40 60 60 60 60 80 80 80

3750 3750 3750 3750 3750 3750 3750 3750 3750 3750 3750 3750

300 300 400 450 450 450 450 500 500 500 500 500

300 300 400 450 450 450 450 500 500 500 500 500

Col

Floor

At age Balance Age

ASL

SW

SW

days

of Gk

452 1257 1257 1257 1963 1257 2592 3217 3217 3217 3217 4825

2.2 2.2 3.8 4.9 4.9 4.9 4.9 6.0 6.0 6.0 6.0 6.0

354.4 354.4 354.4 354.4 354.4 354.4 354.4 354.4 354.4 354.4 354.4 354.4

7 7 7 7 7 7 7 7 7 7 7 7

118.1 118.1 118.1 118.1 118.1 118.1 118.1 118.1 118.1 118.1 118.1 118.1

Perm

Age

days Imposed days 28 28 28 28 28 28 28 28 28 28 28 28

44.3 62.0 62.0 62.0 62.0 62.0 62.0 62.0 62.0 62.0 62.0 62.0

82 96 110 124 138 152 166 180 194 208 222 236

Shortenings Between Floors (mm)

11 - R 10 - 11 9 - 10 8-9 7-8 6-7 5-6 4-5 3-4 2-3 1-2 0-1

Creep & Elastic 1.87 3.16 2.59 2.90 3.40 3.18 3.45 3.15 3.51 3.26 3.56 3.69

Shrinkage 2.15 1.89 1.95 1.94 1.85 1.83 1.71 1.67 1.67 1.63 1.63 1.55

Total

32.7

20.0

12.7

45.00

4.02 5.05 4.54 4.84 5.25 5.01 5.16 4.82 5.18 4.88 5.19 5.24

0.11% 0.13%

33.7

22.0

11.6

41.25

0.12% 0.13%

32.7

22.0

10.8

37.50

0.14% 0.13%

31.7

21.9

9.7

33.75

0.14% 0.13%

29.8

21.2

8.6

0.14% 0.13% 0.14% 0.14%

30.00

Level (m)

Lift

27.1

19.5

7.6

26.25 24.3

17.7

6.6

22.50

Floor Displacements (mm) Floor

Level

Roof 11 10 9 8 7 6 5 4 3 2 1

45.00 41.25 37.50 33.75 30.00 26.25 22.50 18.75 15.00 11.25 7.50 3.75

Creep & Elastic 20.0 22.0 22.0 21.9 21.2 19.5 17.7 15.3 13.0 10.0 7.1 3.7

Shrinkage 12.7 11.6 10.8 9.7 8.6 7.6 6.6 5.6 4.6 3.5 2.5 1.3

15.3

5.6

20.9

Total 32.7 33.7 32.7 31.7 29.8 27.1 24.3 20.9 17.6 13.5 9.6 5.0

18.75 17.6

13.0

4.6

15.00 10.0 13.5

3.5

11.25 7.1 9.6

2.5

Floors

7.50

C and E 1.3 3.75.0

Shrinkage Total

3.75

0 0.0 0

5

10

15

20

25

30

35

40

Vertical Displacement (mm)

283


17/07/2006 17:17:59

TCC71 Stair Flight & Landing - Single.xls TCC71.xls designs simply supported flights and landings to BS EN 1992. Input is required on two sheets.

FLIGHT! This single sheet consists of the input and main output. Inputs are in blue and underlined and most should be self-explanatory. Only simply supported spans are catered for. If flights are continuous with floors, the user should specify continuity steel over supports as appropriate. Calculations are done per metre width of flight. Input loads are assumed to be characteristic and acting vertically. They should account for any undercuts. Selfweight, moments and reactions are calculated automatically. The area of steel required, Asreq, may be automatically increased to increase modification factors and satisfy deflection criteria. Nominal top reinforcement may be specified in order to help overcome deflection problems. Dimensions are not checked for compliance with Building Regulations. Ultimate, characteristic dead and characteristic imposed reactions are given below the indicative diagram.

LANDING! Again, this single sheet consists of the input and main output. Input defaults in magenta have been derived from FLIGHT! but may be overwritten. Calculations are done per metre width of landing. Inputs are underlined and most should be self-explanatory. As defaults, which can be overwritten, the material data and characteristic flight reactions carry over from FLIGHT! Selfweight, moments and reactions are calculated automatically. The maximum width of landing over which flight loads can be dispersed has been restricted to 1.8 m as with BS 8110. Reactions are ultimate, both total and per metre run. The area of steel required, As, can be automatically increased to satisfy deflection criteria.

Dias! Dias! calculates the reinforcement sizes and reinforcement percentages for deflection modification factors used in FLIGHT! and LANDING!


284


17/07/2006 17:18:05

TCC71 Stair Flight & Landing - Single.xls TCC71 Stair Flight & Landing -single/ LANDING!

Project

Spreadsheets to EC2

Client

Advisory Group

Location

South Staircase


Date

rmw

FLIGHT

STAIR FLIGHTS AND LANDINGS to EN 1992-1: 2004 Originated from TCC71.xls v3.0 on CD

Checked

Revision

chg

© 2005 TCC

Page

03-Jul-06

-

285 295 Job No

FB625

MATERIALS fck fyk dg Cover

30 500 20 25

Mpa Mpa mm mm

c 1.5 concrete s 1.15 steel Density 25 kN/m³ (Normal weight concrete)

Min bar Ø = Max bar Ø = Steel class = Nominal top steel ?

DIMENSIONS a= b= c= d= e= Going = Rise = Rise =

600 2500 1200 -600 -100 250 1900 173

10 16 A Y

SECTIONAL ELEVATION mm mm mm

landing A, h = flight waist = landing C, h =

200 175 200

mm mm mm mm total mm each step

L = 4300 10 treads Rake = 34.64 º

LOADING Imposed 4.00 kN/m² Flight finishes 1.60 kN/m² Landing finishes 1.30 kN/m²

43.64 kN/m ult (21.54 + 11.16)

34.37 kN/m ult (16.91 + 8.84)

DESIGN LANDING A, gk = 5.00 + 1.30 = 6.30 kN/m²

n = 1.25 x 6.30 + 1.50 x 4.0 = 13.87 kN/m²

FLIGHT, gk = 7.48 + 1.60 = 9.08 kN/m² LANDING C, gk = 5.00 + 1.30 = 6.30 kN/m²

n = 1.25 x 9.08 + 1.50 x 4.0 = 17.33 kN/m² n = 1.25 x 6.30 + 1.50 x 4.0 = 13.87 kN/m²

Zero shear is at 0.6 + (43.64 - 16.64) /17.33 = 2.157 m from left M = 43.64 x 2.157 - 16.64 x 2.157 - 17.33 x 1.557²/2 = 37.22 kNm/m d = 175 - 25 - 8 = 142 mm K = 0.0615 As = 640 mm²/m PROVIDE H16 @ 270 B = 745 mm²/m s = 232.8 Mpa

Enhanced by 16.0 % for deflection

L/d = 4,300 /142 = 30.28 > 22.7 x 1.331 x 1.000 = 30.28 allowed

H10 @ 350 T in span OK

285


17/07/2006 17:18:06

TCC71 Stair Flight & Landing - single/ LANDING!

Project

Spreadsheets to EC2

Client

Advisory Group

Location

South Staircase


Date

rmw

STAIR FLIGHTS AND LANDINGS to EN 1992-1: 2004


LANDING

Checked

Page

03-Jul-06 Revision

chg

© 2005 TCC

296 286 Job No

FB625

MATERIALS fck fyk dg Cover

30 500 20 25

DIMENSIONS a = 1200 b = 1200 c = 250 d = 175 LOADING LANDING

c 1.5 concrete s 1.15 steel Density 25 kN/m³ (Normal weight concrete)

N/mm² N/mm² mm mm

mm mm

Min bar Ø = 10 Max bar Ø = 16 Nominal top steel ? Y

depth, h = 175 mm width, w = 1200 mm

mm

L = 3000 mm

mm

Imposed Finishes Slab

4.00 1.50 4.38

gk

qk

kN/m² kN/m²

73.50 kN ult 61.25 kN/m ult

68.12 kN ult 56.77 kN/m ult

kN/m²

Flight a reaction 21.54

11.16

kN/m

Flight b reaction 16.91

8.84

kN/m

n = 1.25 x 5.88 + 1.5 x 4.0 = 13.34 kN/m² n1 = (1.25 x 21.54 + 1.5 x 11.16)/1.20 = 36.37 kN/m² n2 = (1.25 x 16.91 + 1.5 x 8.84)/1.20 = 28.64 kN/m²

DESIGN Zero shear is at (61.25 - 2.33) /(13.34 + 36.37) + 0.175 = 1.360 m from left M = 61.25 x 1.360 - 13.34 x 1.360²/2 - 36.37 x 1.185²/2 = 45.43 kNm/m d = 175 - 25 - 8 = 142 mm K = 0.0751 As = 792 mm²/m PROVIDE H16 @ 160 B = 1257 mm²/m s = 310.1 Mpa Enhanced by 50.0 % for deflection L/d = 3,000 /142 = 21.12 > 19.1 x 1.000 x 1.000 = 19.05 allowed

H10 @ 350 T in span FAILS

286


17/07/2006 17:18:12

TCC81 Foundation Pads.xls

TCC81 Foundation Pads.xls (Subject to further interpretation)

This spreadsheet designs simple pad foundations from input of material properties, dimensions and characteristic loads and moments. Single column bases and combined double bases are catered for on separate sheets. This version is “subject to interpretation” as the full implications of Eurocode 7 and its National Annex have yet to be incorporated. For example, ground bearing pressure distribution at ULS will in due course be changed from trapezoidal to rectangular. This spreadsheet was prepared in line with BS EN 1997 [29] but before UK National Annex to EN1997-1 was available. The spreadsheets therefore may not fully integrate with the NA but has been prepared on the basis of Prescriptive measure (i.e. comparable experience) and therefore in line with ‘traditional’ methods of design (including the 25% allowable overload for wind load and trapezoidal or triangular ground pressure distributions at ULS rather than rectangular). A diagram is provided to illustrate the dimensions: a chart showing scale plan views is provided to help ensure gross errors are avoided. The ‘efficiency’ diagrams are provided so that the user may gauge how hard the base is working in respect to allowable increase in ground bearing pressure, bending and shear in the two axes together with a measure on punching shear capacity. If the design is invalid, this chart should help identify the problem. The spreadsheet does not allow for punching shear links – bending reinforcement is increased to ensure allowable shear, vRd c, is adequate. The user should note that punching shear perimeters can jump from being four-sided to being two- or three-sided, leading to unexpectedly large increases in reinforcement for increases in base thickness. TCC81.xls allows the user to specify whether or not equations 6.10a and 6.10b of EN 1990 may be employed. Warnings are given if columns overlap base edges.

SINGLE! Suggestions are made, under the ‘Operating instructions’ column, for the optimum plan size of the base. It is important that the principal usage of the structure is selected from the combo-box in column L. This is used in the determination of partial load factors, if EN 1990 equations 6.10a and 6.10b are permitted. The usage selected here is also utilised on the DOUBLE! sheet. Where two centres are given, e.g. 14 T16 @ 200 & 325 B2, bars need to be grouped more closely in the central part of the base.

DOUBLE! In addition to graphs showing plan layout and ‘efficiency’, this sheet gives moment diagrams for the two principal axes. Design moments are taken at the edge of both column sections Suggestions are made, under the ‘Operating instructions’ column, for the optimum plan size of the base and eccentricities given the column offsets from one another. The user’s attention is drawn to the fact that the analysis is done in two orthogonal directions. When column eccentricities are large in both directions the analysis may not account adequately for local effects (e.g. bottom cantilever moments on two sides of each column – loads in opposite corners gives bottom moments of 0 kNm). In such cases, it may be better to change the orientation of the base in such a way that eccentricity in one direction is minimal. Warnings about double eccentricities are given when the distances between column centrelines exceed 15% of the relevant base dimension in each orthogonal direction. Comparison with FE analysis suggests this is reasonable so long as the base is thick and rigid.

Legends! This sheet shows dimensions, axes, corners and notation used.

SingleDet! This sheet shows workings and is not necessarily intended for printing out other than for checking purposes. Allowable bearing pressure is taken as an allowable increase in bearing pressure and density of concrete –density of excavated material (i.e. soil) is used in the calculations. The program assumes that pads are embedded to depth H in the soil. Design moments are generally those at the face of the column. Both sides of the column are checked for moment in each direction to ensure maxima are identified. Shear enhancement is allowed for both beam and punching shear. Neither crack widths, factors of safety against sliding, nor water tables are catered for. Where resultant eccentricities are outside the base a warning message is given; the general status message is updated as well. Factors of safety against overturning are checked (The equilibrium limit state EQU to EN 1990). Warnings are also given at the onset of an uplift situation.

287


17/07/2006 17:18:18

DoubleDet! This sheet shows workings and is not necessarily intended for printing out other than for checking purposes. The notes for SingleDet! above also apply.

Graf! This sheet comprises data for graphs for both SINGLE! and DOUBLE!

Refs! This sheet comprises the values for nationally determined parameters that have been used in the spreadsheet. These data reflect the values given in draft UK National Annexes for EN 1990 and EN 1992. Designers should ensure that these data are current when the spreadsheet is used. When using TCC81 for permanent design, designers are strongly advised to include a copy of this sheet with any design calculations.


288


17/07/2006 17:18:20

TCC81 Foundation Pads.xls TCC81 Foundation Pads/ SINGLE!

Project


Client

Advisory Group

Location

Level -1 Base B1


Single column base

PAD FOUNDATION DESIGN to EN 1992-1 : 2004 Originated from TCC81.xls v 3.0 on CD

MATERIALS

fck fyk

Densities - Concrete Bearing pressure Steel class DIMENSIONS mm

30 500 25 200 A

BASE

L= B= depth H = ex =

dg cover Soil

N/mm² kN/m³

20 50 18

DEAD

Axial (kN) 1500.0 Mx (kNm) -20.0 My (kNm) Hx (kN) Hy (kN) ψ0 =

mm kN/m³

FB625

concrete steel mm

h = 500 b = 500 ey = 0 Plot (to scale)

characteristic

IMPOSED

128.0

Grnd Brg Pressure As/Asprov

0.7

BEARING PRESSURES kN/m²

Key

WIND

0.5

Shear

STATUS VALID DESIGN

94%

sx

61%

sy

59%

vEd xx

49%

vEd yy

50%

Punching

characteristic

1

2

3

4

188.8 188.8

179.9 179.9

188.8 188.8

179.9 179.9

REINFORCEMENT of As within 1,820 mm Mxx = 572.5 kNm b = 3000 mm d= 440 mm As = 3150 mm² Provide 17H20 @ 160 & 205 B1 As prov = 5341 mm²

99% 0%

25%

kN at d from col face N/mm² kN at 2d from col face N/mm² N/mm²

PUNCHING SHEAR d ave = 430 mm As prov = 0.414 % vEd = 0.464 N/mm²

75%

100%

125%

of As within 1,760 mm

Myy = 562.3 kNm b = 3000 mm d= 420 mm As = 3242 mm² Provide 17H20 @ 155 & 215 B2 As prov = 5341 mm² Asy increased 60% for shear

.

593.7 0.450 272.2 0.206 0.462

50%

Efficiency

Asx increased 67% for shear BEAM SHEAR VEdxx = vEd = or VEd xx = vEd = vRd,c =

-

Usage: Office c 1.5 s 1.15 Wk 0.3

mm

299 289 Job No

kN/m² (net allowable increase)

see EN 1990 - Table A1.1

no wind with wind

Revision

chg

© 2003-2006 TCC

N/mm²

Checked

Page

03-Jul-06

COLUMN

3000 3000 500 0

COLUMN REACTIONS kN, kNm

CORNER

Date

RMW

.

VEDyy = vEd = or VEDyy = vEd = vRd,c =

597.4 0.474 295.1 0.234 0.473

kN at d from col face

u crit = vEd max = vRd,c =

7404 2.750 0.467

mm

N/mm² kN at 2d from col face N/mm² N/mm²

.

. N/mm² at col face N/mm²

289


17/07/2006 17:18:21

TCC81 Foundation Pads/ DOUBLE!


The Concrete Centre

Spreadsheets to Eurocode 2 Advisory Group

Made by

Base B3/B4

Date

RMW

Combined base

PAD FOUNDATION DESIGN to EN 1992-1 : 2004


Checked

290 300

Revision

chg

© 2003-2006 TCC

Page

03-Jul-06

Job No

-

FB625

Usage: Office MATERIALS

fck fyk Densities - Concrete Bearing pressure

30 500 25 125

COLUMN REACTIONS kN, kNm Column 1 (rhs)

Axial Mx My Hx Hy

dg cover Soil

N/mm² N/mm² kN/m³

20 50 18

mm

c

mm

s

1.5 1.15 A

Steel class

kN/m³

concrete steel

kN/m² (net allowable) characteristic

DEAD

IMPOSED

WIND

Column 2 (lhs)

225.0

225.0

112.5

Axial Mx My Hx Hy

DEAD

IMPOSED

WIND

225.0

225.0

112.5 50.0 25.0

DIMENSIONS mm COLUMN 1 (rhs)

BASE

L= B= depth H = ex = ey =

3000 3000 475 300 1000

COLUMN 2 (lhs)

h1 = 300 b1 = 300

h2 = 300 b2 = 300

ex1 = 150 ey1 = 500

ex2 = 150 ey2 = 500

STATUS VALID DESIGN PLOT (to scale)

BEARING PRESSURES kN/m² CORNER

no wind with wind

1

103.3 142.1

REINFORCEMENT Btm Mxx - 421.7 b = 3000 d= 419 As = 2437

characteristic

2

3

103.3 142.1

103.3 114.6

mm mm mm²

0.0 421 0

kNm mm mm²

PUNCHING SHEAR d ave = 413

sy

97% 45%

235.6 3000 407 1401

28%

vEd yy

84%

Punching 0%

kN at d N/mm² kN at 2d N/mm² N/mm²

133%

Efficiency 0.5

1.0

1.5

2.0

Moment

.

.

2.5

Columns

3.0

3.5

Zero axis

Mx Diagram (1.35G+1.05Q)

Vyy = v= or Vyy = v= vc =

219.3 0.180 18.0 0.015 0.326

u crit =

8990

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

50 0 -50 -100 -150

. mm

85%

vEd xx

& 17H12 @ 150 & 200 B2 As prov = 1923 0.0 Detail to clause 3.11.3.2 50 0 Myy + 0.0 -50 d= 413 -100 -150 As = 0 -200 & 19H8 @ 125 & 175 T2 -250 -300 As prov = 955 -350 .

PROVIDE 19H8 @ 175 T1 As prov = 955 mm² . BEAM SHEAR Vxx = 365.9 v = 0.291 or Vxx = 169.6 v = 0.135 vc = 0.324

sx

As/Asprov

103.3 114.6

Myy b= d= As =

kNm

91%

Grnd Brg Pressure

Shear

PROVIDE 23H12 @ 150 B1 As prov = 2601 mm² Top Mxx + d= As =

4

mm

.

-200

290


17/07/2006 17:18:29


TCC82 Pilecap Design.xls (Subject to further interpretation)

This spreadsheet designs pilecaps with between two and six piles, and then prepares a sketch drawing of each type of cap together with a bar schedule. Bending theory is employed throughout to design the caps. This version is “subject to interpretation” as the full implications of Eurocode 7 and its National Annex have yet to be incorporated. This spreadsheet was prepared in line with BS EN 1997 [29] but before UK National Annex to EN1997-1 was available. The spreadsheets therefore may not fully integrate with the NA but has been prepared on the basis of Prescriptive measure (i.e. comparable experience) and therefore in line with ‘traditional’ methods of design (including the 25% allowable overload for wind load). This spreadsheet was prepared in line with BS EN 1997 [29] but before UK National Annex to EN1997-1 was available. The spreadsheets therefore may not fully integrate with the NA but has been prepared on the basis of Prescriptive measure (i.e. comparable experience) and therefore in line with ‘traditional’ methods of design (including the 25% allowable overload for wind load). Depending upon the pilecap’s dimensions, the alternative strutand-tie method of design may be possible, but is not covered by this spreadsheet. There are seven main sheets: DOUBLE!, 3CAP!, 4CAP!, 5CAP!, 6CAP!, SCHEDULE! and DRAWING! Each of the first five sheets contains two pages that may be printed out. The first (or upper) page contains input data and a summary of results, while the second (or lower) page shows more detailed calculations. The selection of size and number of top and bottom bars is automated. The number of bars determined by either: ■ area of steel required/ area of maximum sized bar (taken to

be 32 mm diameter), ■ spacing rules or ■ number of legs of links required in shear.

allow for this possible deviation. Pile reactions are not similarly increased. Dimensional data for a double pile cap and the supported column are then entered, then column axial loads, moments and horizontal shears for dead load, imposed load and wind load. The results of calculations for all Eurocode 2 loading combinations are then displayed below (on page 1), together with the required arrangement of reinforcement. More detailed calculations may be found by scrolling down to page 2.

3CAP!, 4CAP!, 5CAP! and 6CAP! These sheets are identical in function to DOUBLE!, but deal with caps having 3, 4, 5 and 6 piles respectively. Material properties, pile diameter and tolerance are picked up from DOUBLE!. Page numbers for printing do not follow on from previous sheets, so must be entered by the user. This allows for intermediate calculation pages (perhaps for loading) to be inserted.

SCHEDULE! This sheet is a bar schedule complying with BS 8666, for the pilecap drawing on the DRAWING! sheet. Beneath the ‘Operating instructions’, the number of each type of cap must be entered. These numbers are then used on the schedule and the drawing.

DRAWING! This sheet draws approximately to scale plans and elevations with reinforcement and bar marks for each of the cap types. It is intended for printout to an A3 sheet. If the user wishes to add additional notes, these may be added in cell U27.

Graf!

The size of link to be used has also been automated. The designer and detailer may wish to rationalise the output given on the DRAWING! sheet. But doing so will obviously affect the bar data on SCHEDULE!

DOUBLE!

This sheet provides data for the charts in all sheets. It is not intended for formal printing


The DOUBLE! sheet is where all material properties are entered, together with covers, pile diameter and pile tolerance. All subsequent sheets use these same properties. Pile tolerance is the amount by which a pile may deviate from its intended position. This value is used in calculation to increase bending moments to 291


17/07/2006 17:18:34

TCC82 Pilecap Design/ DOUBLE!

Project


Client

BigBucks PLC

Location

Pilecap G14


Rod

Double Pilecap

PILECAP DESIGN to EN 1992-1: 2004

fck fyk Steel class Pile capacity

35 500 A 525

N/mm² N/mm²

-

© 2003-2006 TCC


MATERIALS

Checked

dg T&S cover Btm cover

20 50 75

Date

Page

03-Jul-06 Revision

-

302 292 Job No

FB625

mm

Usage: Traffic, 30 to 160kN γc 1.5 concrete γs 1.15 steel

mm

Conc density

mm

25

kN/m³

kN


→= ↑= Pile Ø = Tolerance =

350 350 450 0

PILECAP


400 1500 400 750 400

COLUMN ACTIONS kN, kNm characteristic DEAD

Axial (kN) M (kNm) H (kN)

218 23.2 0 0 =

IMPOSED

WIND

104.2 10.4 0 0.7

27.5 2.7 0 0.5

PLOT (to scale) STATUS VALID DESIGN

PILE REACTIONS kN

REINFORCEMENT BOTTOM M = 164.2 kNm

d = 309.0 mm, As = 1,296 mm² 7H16 B = 1,407 mm² TOP M = 0.0 kNm d = 338.0 mm, As = 0 mm² 4H8 T = 201 mm²

KEY

Gk + Qk Gk + Qk +Wk

PILE 1

PILE 2

147.9 159.9

192.7 208.3

4H8 02 T

LINKS

VEd = 293 kN, vEd = 1.185 N/mm² vRd 2d/av = 0.825 N/mm² Asw/S = 0.9691 mm 4 Legs H8 @ 200 LINKS = 1.0053 mm

7H16 01 B Links 11H8 03.200 + 2x11H8 04.200 ELEVATION

292


17/07/2006 17:18:37

TCC82 Pilecap Design.xls TCC82 Pilecap Design/ DOUBLE!

Project


Client

BigBucks PLC

Location


Pilecap G14 - Detailed Calculations

Double Pilecap



Cap load (kN) = 18.4 or (kN/m) = 8.00

Piles @ (m) 1.500

OVERTURNING MOMENTS - kNm characteristic DEAD 23.2

IMPOSED 10.4

WIND 2.7

Date

Rod Checked © 2003-2006 TCC

PILE REACTIONS kN PILE 1 Gk + Qk 147.9 Gk + Qk +Wk 159.9 1.35Gk + 1.5Qk 206.4 1.0Gk + 1.5Wk 120.7 1.35Gk + 1.5Qk + 0.75Wk 229.2

Revision

-

PILE 2 192.7 208.3 269.0 157.0 294.4

Page

03-Jul-06

-

303 293 Job No

FB625

BENDING MOMENTS - kNm M of col M of col BOTTOM STEEL Bottom M = d= K= z= As = Provide No = As prov = s = Max S = Min S = S= SHEAR PILE 1

1.35Gk + 1.5Qk 113.6 149.5

164.2 309.0 0.0614 291.2 1296 1296 7 1407 286 193.1 41.0 111.3

1.0Gk + 1.5Wk 65.6 86.5 TOP STEEL Top M = d= K= z= As = Provide No = As prov = s = Max S = Min S = S=

Ø16

7H16 B

1.35Gk + 1.5Qk + 0.75Wk

126.6 164.2

0.0 338.0 0.0000 321.1 0 0 4 201 0 300.0 33.0 225.3

Ø8

arm (m) 0.575 arm (m) 0.575 (including tolerance) K' = 0.2067 min As = 0.167%

4H8 T

Crit section is 135.0 from pile centres 0.569% 1.35Gk + 1.5Qk 1.0Gk + 1.5Wk 1.35Gk + 1.5Qk + 0.75Wk VEd 227.7 205.0 119.6 av = 440.0 vEd = 0.9211 cot = 2.50 vRd 2d/av = 0.8246

PILE 2 VEd av = 440.0

267.5

Asw/S required= 0.9691 No of legs = 4

155.9 vEd = 1.1851

mm

Ø8 links Link spacing = 200

cot = 2.50

293.0 vRd 2d/av = 0.8246 vRd,max = 4.152


293


17/07/2006 17:18:42

TCC82 Pilecap Design/ 3CAP!

Project


Client

BigBucks PLC

Location


Pilecap F13

Triple Pilecap



Checked

Page

03-Jul-06 Revision

-

© 2003-2006 TCC

-

294 14 Job No

FB625

Usage: Office


PILECAP

→ = 300 ↑ = 300


Pile Ø = 450 Min spacing = 1300 Tolerance = 0

350 1300 1126 375.33 400

PLOT (to scale)



Date

Rod

DEAD

IMPOSED

WIND

355.5 10.0 20.0

118.2 5.0 10.0

10.0 2.0 5.0

0 =

0.7

0.5

KEY

STATUS VALID DESIGN PILE REACTIONS kN characteristic

Gk + Qk Gk + Qk +Wk

PILE 1

PILE 2

PILE 3

141.0 139.9

169.4 173.4

192.5 199.6

REINFORCEMENT

EW (2-3)

M = 178.2 kNm, b = 1,050 mm d = 309.0 mm, As = 1,396 mm² 7H16 B = 1,407 mm² VEd = 274.1 kN, bw = 1,050 mm vEd = 0.845 N/mm², Asw/S = 0.994 mm 4 LegsH8 @ 200 LINKS = 1.005 mm

NS (1-2/3)

M = 117.1 kNm, b = 1,798 mm d = 293.0 mm, As = 967 mm² 5H16 B = 1,005 mm² VEd = 194.9 kN, bv = 1,260 mm vEd = 0.528 N/mm², Asw/S = 1.193 mm 4 LegsH8 @ 150 LINKS = 1.340 mm

4H8 06 T1

7H16 05 B1 Links 8H8 07 200 + 2x8H8 08 200

ELEVATION

4H8 10 T2

5H16 09 B2 Links 8H8 11 150 + 2x8H8 12 150

ELEVATION

294


17/07/2006 17:18:48

TCC82 Pilecap Design.xls TCC82 Pilecap Design/ 3CAP!

Project


Client

BigBucks PLC

Location


Pilecap F13

Triple Pilecap



Cap load =

29.2

Date

Rod

kN

Checked © 2003-2006 TCC

Group centre @

751

Page

03-Jul-06 Revision

-

-

15 295 Job No

FB625

m from pile 1

PILE REACTIONS kN Gk + Qk Gk + Qk +Wk 1.35Gk + 1.5Qk 1.0Gk + 1.5Wk 1.35Gk + 1.5Qk + 0.75Wk

PILE 1 141.0 139.9 194.9 108.8 193.8

PILE 2 169.4 173.4 234.7 135.4 238.7

PILE 3 192.5 199.6 267.0 155.4 274.1

OVERTURNING MOMENTS - kNm characteristic . Mx My

DEAD 10.0 20.0

IMPOSED 5.0 10.0

WIND 2.0 5.0

. .

BENDING MOMENTS - kNm My v of col My ^ of col Mx

1.35Gk + 1.5Qk 117.1 113.1 173.6

1.0Gk + 1.5Wk 65.4 65.5 101.0

E-W STEEL M= b= d= K= z= As = Provide No = As prov = s = Max S = Min S = S=

178.2 1050 309.0 0.0508 293.6 1396 1396 7 1407 307 165.6 41.0 94.7

N-S STEEL M= b= d= K= z= As = Provide No = As prov = s = Max S = Min S = S=

Ø16

7H16 B

SHEAR PILES 2 & 3 VEd = av = Asw/S = PILE 1 VEd = av = Asw/S =

Crit section is Ø8 links 274.1 b= 515.0 vEd = 0.9939 No of legs = Ø8 links 194.9 b= 615.7 vEd = 1.1926 No of legs =

PUNCHING VEd = vEd = vRd,max =

At column Face 664.7 1.840 4.152 ok

135.0

1.35Gk + 1.5Qk + 0.75Wk

116.4 115.6 178.2

117.1 1798 293.0 0.0217 278.4 967 967 5 1005 298 177.1 41.0 142.0

Ø16


K' = 0.2067 min As = 0.167%

5H16 B

from pile centres

1050 0.8448 4

l = 0.434% vRd 2d/av = 0.6434 Spacing = 200

cot = 2.50 vRd,max = 4.152 4 LegsH8 @ 200 LINKS

1260 0.5280 4

l = 0.272% vRd 2d/av = 0.5110 Spacing = 150

cot = 2.50 vRd,max = 4.152 4 LegsH8 @ 150 LINKS

At u1 = d ave = l =

465.7 from column face (1.55d perimeter) 4126 = 1.112 301.0 vEd = 0.5353 0.231% vRd 2d/av = 0.6546

ok

295


17/07/2006 17:18:54

TCC82 Pilecap Design/ SCHEDULE!

Bar schedule ref :

The Concrete Centre Site ref :


Job no :

FB625

Member

Double Pilecaps

3-Pile Caps

4-Pile Caps

5-Pile Caps

6-Pile Caps

Bar mark

No. of mbrs

No. of bars in each

01

Rev:

-

Checked by :

-

Date prepared : 03-Jul-06 Prepared by :

Type and size

202

Length of Total No. each bar † mm

Shape code

Rod

A*

B*

C*

D*

E/R *

mm

mm

mm

mm

mm

130

2175

01

H 16

4

7

28

2375

21

02

H8

4

4

16

2175

00

03

H8

4

11

44

2075

51

270

695

115

04

H8

4

22

88

500

31

115

50

270

05

H 16

3

7

21

2475

21

320

1890

06

H 12

3

4

12

1875

00

07

H8

3

8

24

1975

51

270

650

115

08

H8

3

16

48

500

31

115

50

270

09

H 16

3

5

15

1975

21

155

1715

10

H 12

3

4

12

1700

00

115

115

11

H8

3

8

24

1825

51

240

600

115

12

H8

3

16

48

475

31

115

50

240

115

13

H 16

5

18

90

2225

21

145

1975

14

H8

5

10

50

1975

00

15

H 16

5

18

90

2225

21

145

1975 345

120

450

120

495

120

16

H8

5

10

50

1975

00

17

H 10

5

100

500

600

31

120

60

18

H 12

2

19

38

2625

21

125

2410

19

H8

2

10

20

2400

00

21

H 12

2

20

40

2625

21

125

2410

22

H8

2

11

22

2400

00

20

H 10

2

80

160

700

31

120

60

125

1890

125

3175

120

60

23

H 12

1

28

28

2100

21

24

H 12

1

14

14

1875

00

26

H 12

1

17

17

3400

21

27

H 12

1

9

9

3175

00

28

H 10

1

84

84

750

31

This schedule complies with BS 8666.

1,770 kg on this schedule

* Specified in multiples of 5mm.

† Specified in multiples of 25mm.

PILECAP DESIGN to EN 1992-1: 2004 © 2003-2006 TCC

296


17/07/2006 17:18:59

19H12 18 B2

11H8 22 T1

10 Link Legs

ELEVATION

20H12 21 B1

Links 10x8H10 20 325 ELEVATION

10H8 19 T2

PLAN (Pilecap D11)

ELEVATION

Links 11H8 03.200 + 2x11H8 04.200 ELEVATION

7H16 01 B

5H16 09 B2

14 Link Legs

ELEVATION

17H12 26 B1

28H12 23 B2

Links 14x6H10 25 350 ELEVATION

14H12 24 T2

9H12 27 T1

PLAN (Pilecap C10)

Links 8H8 11 150 + 2x8H8 12 150

ELEVATION

4H8 10 T2

Links 8H8 07 200 + 2x8H8 08 200 ELEVATION

7H16 05 B1

18H16 15 B2

Links 10x10H10 17 200

ELEVATION

10H8 16 T2

10 Link Legs ELEVATION

18H16 13 B1

PLAN (Pilecap E12) 10H8 14 T1

The Concrete Centre

PLAN (Pilecap F13) 4H8 06 T1

This drawing is diagramatic. Connecting slabs & beams not shown.

Client

PLAN (Pilecap G14)

4H8 02 T

2 Pile Cap - 4 No 5 Pile Cap - 2 No

Refer to GA drawings for orientation and dimensions.

Project Job No Date Made by

Spreadsheets to Eurocode 2 FB625 03-Jul-06 Rod

BigBucks PLC 202 -

Dwg No Revision Checked

EC2 USERGUIDEv2.indd Sec1:297 3 Pile Cap - 3 No 6 Pile Cap - 1 No

NOTES Concrete grade C35. Cover 75 mm bottom. Cover 50 mm top & sides.


TCC82 Pilecap Design/ DRAWING!

297

17/07/2006 17:19:02

4 Pile Cap - 5 No

Admin folder Under the Admin folder will be found several files associated with the use of the spreadsheets.

Readme.doc

Column width and cell overlap problems may occur unless the correct fonts and default font size are installed. To the best of our knowledge these fonts are copyright-free.

Essential for first time users of the spreadsheets in Word format.

By Others

Spreadsheet Issue sheet.xls

The TCC disclaim any responsibility for programs by others. These programs and files are provided to help dissemination. They are subject to the authors’ conditions of use.

This file shows the version history of the spreadsheets.

Bar Schedule

UserGuid Version 3.doc: ‘Word’ file of User Guide This file formed the basis of the printed User Guide. It may be loaded, read and printed out by using Word 97 or subsequent releases. The file is included to provide help and to allow printing of parts of the document. It may also be used as a basis for comment.

User Guide Version 3.pdf: ‘Adobe Acrobat’ file of the User Guide This User Guide will be made available as an Acrobat file on future editions of the accompanying CD-ROM. It will present the full User Guide in colour. Adobe Acrobat Reader v 4.0 or later will be required to read and interrogate the .pdf file.

This folder contains Barshed8666.xlt, a spreadsheet template for the scheduling of steel for the reinforcement of concrete to BS 8666:2005. The aim of the spreadsheet is to reduce the time taken to produce a bar schedule, eliminate arithmetical errors, reduce scheduling errors, increase compliance with the BSI specified format for bar scheduling and to facilitate electronic data interchange. The spreadsheet has the additional ability to produces weight schedules without the need for additional input. The spreadsheet presents a familiar interface to the user who has produced schedules by hand and it is simple to use. It will guide the user through the scheduling process while checking the input is in accordance with British Standard requirements. This template is made available as shareware by its author, Chris Buczkowski. For further information, including registration details and support, etc. go to www.structural-engineering.fsnet.co.uk or email: [email protected]

The Fonts This folder contains the font files: ■ Tekton~i.ttf ■ Tekton~n.ttf ■ Marker.ttf

These fonts have been included in order to give users access to the fonts intended for the spreadsheets. These upright fonts were used in the spreadsheets in order to emulate a designer’s handwriting and to allow an adequate amount of information to be shown across the page and in each cell. As described under Loading a spreadsheet for the first time see (FAQ), unless the appropriate fonts and default font size have been installed, the appearance on screen will be different from the publication and from that intended.

298


17/07/2006 17:19:07

References and further reading

References and further reading References 1 Goodchild, C.H. Economic concrete frame elements. British Cement Association, Crowthorne, 1997. 128 pp. 2 BRITISH STANDARDS INSTITUTION. BS 8110: 1997. Structural use of concrete. Part 1. Code of practice for design and construction. British Standards Institution, London, 1997 up to and including Amendment 3. 3 BRITISH STANDARDS INSTITUTION. BS EN 1992-1-1: 2004. Eurocode 2: Design of concrete structure (part 1-1) General rules and rules for buildings, including UK National Annex to BS EN 1992-1-1: Design of Concrete Structures Part 1-1 BSI London 2005. 4 BRITISH STANDARDS INSTITUTION. BS 8002: 1994. Code of practice for earth retaining structures. British Standards Institution, London, 1994. 5 BRITISH STANDARDS INSTITUTION. BS 8007: 1987. Code of practice for design of concrete structures for retaining aqueous liquids. British Standards Institution, London, 1987. 6 INSTITUTION OF STRUCTURAL ENGINEERS ET AL. Earth retaining structures. (Civil Engineering Code of Practice No. 2.) Institution of Structural Engineers, London, 1975. 224 pp. 7 MACLEOD, I.A. ET AL. Information technology for the structural engineer. The Structural Engineer, Vol. 77, No. 3, 2 February 1999. pp. 23 - 25. 8 STANDING COMMITTEE ON STRUCTURAL SAFETY. Standing Committee on Structural Safety, 10th report, July 1992 – June 1994. SETO Ltd, London, 1994. 32 pp. 9 ANSLEY, M. Liability concerns require adaptable software. Concrete International, Vol. 19, No. 12, December 1997. pp. 37, 38. 10 KHAN, S. Techno Consultants Ltd, Manchester. Correspondence with authors, May 1999. 11 MOSLEY, W.H. & BUNGEY, J.H. Reinforced concrete design (4th edition). Macmillan, Basingstoke, 1990. 392 pp. 12 REYNOLDS, C.E. & STEEDMAN, J.C. Reinforced concrete designer’s handbook (10th edition). E&FN Spon, London, 1998. 448 pp.

19 BRITISH STANDARDS INSTITUTION. BS 6399: Part 1: 1996. Loading for buildings. Code of practice for dead and imposed loads. British Standards Institution, London, 1996. 20 BRITISH STANDARDS INSTITUTION. CP 110: 1972. Code of practice for the structural use of concrete. British Standards Institution, London, 1972. 21 BRITISH STANDARDS INSTITUTION. BS 5400: 1988. Steel, concrete and composite bridges. British Standards Institution, London, 1988. 22 RAFIQ, M.Y. AND SOUTHCOMBE, C. Genetic algorithms in optimal design and detailing of reinforced concrete biaxial columns supported by a declarative approach for capacity checking. International Journal of Computers and Structures, 69 (1998), pp 443 - 457. 23 BRITISH STANDARDS INSTITUTION. BS 8004: 1986. Code of practice for foundations. British Standards Institution, London, 1986. 24 NARAYANAN, R S. Comparison of design requirements in EC2 and BS 8110. The Structural Engineer, Vol. 67, No 11, 6 June 1989, pp. 218 227. 25 BEEBY, A.W. ET AL. Worked examples for the design of concrete buildings. British Cement Association, Crowthorne, 1994. 256 pp. 26 BEEBY, A.W. & NARAYANAN, R.S. Designers handbook to Eurocode 2 Part 1.1: Design of concrete structures. Thomas Telford Ltd, London, 1994. 242 pp. 27 WEBSTER, R. & Brooker, O. How to design concrete structures using Eurocode 2: Deflections. The Concrete Centre, Camberley, Draft in preparation 2005, 6pp. 28 INSTITUTION OF STRUCTURAL ENGINEERS. Manual for the design of reinforced concrete building structures to EC2. I Struct E, Draft in preparation 2005. 29 BRITISH STANDARDS INSTITUTION BS EN 1997-1: 2004, Eurocode 7: Geotechnical design. Part 1. General rules, BSI, London 30 CONCRETE SOCIETY. Deflections in concrete slabs and beams, Technical Report 58, The Concrete Society, Camberley. 2005

13 ALLEN, A.H. Reinforced concrete design to BS 8110 - simply explained. E&FN Spon, London, 1988. 256 pp.

31 BRITISH STANDARDS INSTITUTION, PD 6687, Background paper to the UK National Annex to BS EN 1992-1-1 and BS EN 1992-1-2, BSI, London. 2006

14 THE CONCRETE SOCIETY. Post-tensioned concrete floors – Design Handbook, Technical Report No 43. The Concrete Society, Slough (now Crowthorne), 1994. 162 pp.

32 CONSTRUCT, National Structural Concrete Specification for building construction (NSCS) Third Edition, 2004, Concrete Society, Camberley

15 HIGGINS, J.B. & ROGERS, B.R. Designed and detailed (BS 8110:1997). British Cement Association, Crowthorne, 1998. 28 pp.

33 CONCRETE SOCIETY, Technical Report 43 Post-tensioned concrete floors – Design Handbook, Second Edition, Concrete Society, Camberley 2005

16 KHAN, S. & WILLIAMS, M. Post -tensioned concrete floors. Butterworth Heinnemann, Oxford, 1995. 312 pp. 17 CEMENT AND CONCRETE ASSOCIATION. Basic data for the prediction of shrinkage and creep. Training note TDH 2391. Cement and Concrete Association (now British Cement Association), Slough (now Crowthorne), 11 pp. 18 WYATT, T A. Design guide on the vibration of floors. Pub. No. 076, Steel Construction Institute, Ascot, 1989. 43 pp.

34 Brooker, O. How to design concrete structures using Eurocode 2:Getting Started. The Concrete Centre, 2005 35 BRITISH STANDARDS INSTITUTION BS EN 1991-1: 2002 Eurocode1: Actions on structures - Part 1-1 General Actions - Densities, Self weight, imposed loads for Buildings, BSI, 2002, including UK national Annex to BS EN 1991-1: 2002 Actions on Structures Part 1-1, BSI, 2005

299


17/07/2006 17:19:08

Further reading 1 INSTITUTION OF STRUCTURAL ENGINEERS; INSTITUTION OF CIVIL ENGINEERS. Manual for the design of reinforced concrete building structures. London, ISE, London, 1985. 88 pp. 2 REYNOLDS, C.E. & STEEDMAN, J.C. Examples of the design of reinforced concrete buildings to BS 8110 (4th edition). E&FN Spon, London, 1992. 320 pp. 3 MOSLEY, W.H. Et Al. Reinforced concrete design to Eurocode 2 (EC2). Macmillan, London, 1996. 426 pp. 4 THE CONCRETE CENTRE - How to design concrete structures using Eurocode 2 . Guides including Introduction to Eurocodes, Getting started, Slabs, Beams, Columns, Foundation, Fleet Slabs and Deflection calculations. The Concrete Centre, Camberley, 2005-2006. See also www.eurocode2.info 5 THE CONCRETE CENTRE - Concise Eurocode 2 for the design of concrete structures to BS EN 1992-1-1:2004 and the UK National Annex:2005. The Concrete Centre Camberley, due 2006. 6 THE INSTITUTION OF STRUCTURAL ENGINEERS/CONCRETE SOCIETY Standard Method of Detailing Structural Concrete – a manual for best practice. IStructE London 2006.

300


17/07/2006 17:19:10

Foreword This publication was originally produced by the Reinforced Concrete Council (RCC) as part of its project ‘Spreadsheets for concrete design to BS 8110 and EC2’. Since their release in 2000 the spreadsheets have proved enormously popular and have been maintained by the RCC and its successor The Concrete Centre. The release of Version 3 of the spreadsheets follows the publication of BS EN 1992-1-1 (Eurocode 2) plus its UK National Annex and the publication of Amendment 3 to BS 8110 Part 1: 1987. The requirements within these standards have necessitated the revision of all the published spreadsheets. This user guide gives guidance on the use of all design spreadsheets to BS 8110 and Eurocode 2 contained on the CD ROM RC Spreadsheets: v3, published by The Concrete Centre (order ref. CCIP-008CD).

Acknowledgements The ideas and illustrations come from many sources. The help and guidance received from many individuals are gratefully acknowledged. Thanks are due to members of the original project’s Advisory Group for their time and effort in helping to make the project feasible and in bringing it to fruition. The members of the Advisory Group are listed on the inside back cover. Special appreciation is extended to: Richard Cheng, BSc, CEng, Eur Ing, FIStructE, author of the retaining wall and basement wall spreadsheets, Peter Noble for conversions and checking, and to Andy Pullen for initial studies into compatibility of spreadsheet software. Also the late Sami Khan for help with post-tensioning spreadsheets.

The Advisory Group Members S Alexander S Alhayderi Dr H Al-Quarra I Baldwin C Barker M Beamish A Beasley T Bedford G Belton R Bhatt R Bickerton P Blackmore D Blackwood M Brady C Buczkowski A Campbell Dr P Chana G Charlesworth L Cheng Mr Chichger R Collison A Craddock M Morton J Curry J Dale

H Dikme C P Edmondson J Elliott I Feltham G Fernando M Fernando I Francis A Fung P Gardner J Gay P Green A Hall N Harris G Hill D W Hobbs R Hulse M Hutcheson A Idrus N Imms P Jennings D Kennedy G Kennedy R Jothiraj Dr S Khan A King

G King S King K Kus I Lockhart M Lord B Lorimer M Lovell Dr Luker J Lupton M Lytrides Prof I Macleod F Malekpour A McAtear A McFarlane F Mohammad A Mole M Morton R Moss B Munton C O’Boyle Dr A Okorie T O’Neill B Osafa-Kwaako D Patel D Penman

M Perera B Quick Y Rafiq A Rathbone M Rawlinson P Reynolds H Riley N Russell U P Sarki T Schollar A Stalker A Starr M Stevenson B Stoker B Treadwell A Truby R Turner T Viney Dr P Walker B Watson J Whitworth C Wilby S Wilde A Wong E Yarimer

Published by The Concrete Centre Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey GU17 9AB Tel: +44 (0)1276 606800 Fax: +44 (0)1276 606801 CCIP-008 Published July 2006 ISBN 1-904818-38-2 Price Group O © The Concrete Centre User Guide v1 published by the British Cement Association on behalf of the Reinforced Concrete Council. User Guide v2 published electronically by The Concrete Centre. CCIP publications are produced by The Concrete Society on behalf of the Cement and Concrete Industry Publications Forum – an industry initiative to publish technical guidance in support of concrete design and construction. CCIP publications are available from the Concrete Bookshop at www.concretebookshop.com Tel: +44 (0)7004 607777 All advice or information from The Concrete Centre is intended for those who will evaluate the significance and limitations of its contents and take responsibility for its use and application. No liability (including that for negligence) for any loss resulting from such advice or information is accepted by the Concrete Centre or their subcontractors, suppliers or advisors. Readers should note that The Concrete Centre publications are subject to revision from time to time and should therefore ensure that they are in possession of the latest version. Cover artwork: D J Killoran - The Concrete Society. Printed by Cromwell Press, Trowbridge, UK.

Cover files.indd 2

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CCIP-008

A cement and concrete industry publication

CI/Sfb

UDC 624.04



This user guide provides guidance on the use of RC Spreadsheets v3 for the design of reinforced concrete elements.

For more information on the spreadsheets visit www.concretecentre.com/rcspreadsheets

User guide to Excel spreadsheets for design to BS 8110: Part 1, 1997 (Amd. 3) and BS EN 1992: 2004 Part 1-1 and its UK National Annex


Charles Goodchild is Principal Structural Engineer for The Concrete Centre where he promotes efficient concrete design and construction. He was responsible for the concept, content and management of this publication and of the RC Spreadsheets. Rod Webster of Concrete Innovation & Design is principal author of the spreadsheets. He has been writing spreadsheets since 1984 and is expert in the design of tall concrete buildings and in advanced analytical methods.


The release of Version 3 of the spreadsheets and user guide follows the publication of BS EN 1992-1-1 (Eurocode 2) and its UK National Annex and the publication of Amendment 3 to BS 8110 Part 1: 1987.


CCIP-008 Published July 2006 ISBN 1-904818-38-2 Price Group O © The Concrete Centre Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey, GU17 9AB Tel: +44 (0)1276 606800 Fax: +44 (0)1276 606801 www.concretecentre.com

Cover files.indd 1

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BCA - RC Spreadsheet User Guide Version 3

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