Manual on Seismic Evaluation & Retrofit of Multistory Rc Blds

Manual on

Seismic Evaluation and Retrofit of Multi-storeyed RC Buildings

March, 2005

SHEAR WALL

STEEL BRACING

CONCRETE JACKETING

Retrofit of soft-storeyed building

Sponsored by

Department of Science and Technology Government of India

Indian Institute of Technology Madras Chennai 600 036

Structural Engineering Research Centre Chennai 600 113

Prepared by Structural Engineering Laboratory Department of Civil Engineering Indian Institute of Technology Madras Chennai 600 036

In collaboration with Structural Engineering Research Centre Taramani, Chennai 600 113

Sponsored by Department of Science and Technology Government of India

PREFACE

The Manual of Seismic Evaluation and Retrofit of Multi-storeyed RC Buildings is the outcome of a research project, jointly undertaken by IIT Madras and SERC Chennai, with the sponsorship of the Department of Science and Technology, Government of India.

The purpose of this Manual is to provide a methodology to enable a structural engineer to assess the seismic vulnerability of existing multi-storeyed buildings in India and to select suitable methods of retrofit, wherever required and possible. Thus, the Manual has been organised into two major parts: the first part dealing with seismic evaluation (data collection, preliminary evaluation and detailed analysis) and the second dealing with seismic retrofit (global and local retrofit strategies). Various options of seismic retrofit are possible, and the designer is required to re-analyse the retrofitted structure to ensure that the desired performance is achieved. Some explanatory examples demonstrating the prescribed procedure are given in the chapter on case studies. Detailed references are also cited in this Manual for users interested in further research. Seismic retrofit is still in a nascent stage, and considerable research and experience with practical real-life applications is called for.

i

This Manual is intended primarily for use by the practising engineer, but is also useful for academic purposes. Some background information on the basic theoretical concepts are given, but for a full understanding, the user is expected to have a reasonable knowledge of structural dynamics, earthquake engineering, reinforced concrete design and IS code requirements. It is also assumed that the user has some exposure to the use of standard finite element software packages (such as SAP 2000, STAAD Pro, etc.). As part of the DST sponsored project, a software called SAVE (Seismic Analysis and Vulnerability Evaluation), has also been developed (as an alternative to existing commercial packages) and is now made freely available for users of this Manual. Details of SAVE (User Manual and CD) are given separately, and are not included in the scope of this Manual.

This Manual in its present form represents a consolidation of several studies (theoretical and experimental) and discussions undertaken by the coordinators of the DST-sponsored project, which commenced in 2002. As part of the project, as many as 40 sample buildings located in different parts of India (in Zones III, IV and V) were evaluated, including the difficult process of data collection and field survey. It is observed from these case studies that the majority of existing multi-storeyed buildings in India, particularly residential apartment complexes, fail to meet the current code compliance requirements and are in danger of damage (of varying degrees) in the event of a earthquake of expected intensity.

Occupants of multi-storeyed apartment complexes were a worried lot in the aftermath of the Gujarat earthquake in 2001, but this worry has gradually faded with time, and lessons have not been learnt. It should not take another disastrous earthquake to make us act proactively to avoid such disasters. Building owners have a responsibility of getting their buildings properly evaluated and strengthened, before it is too late.

ii

Unfortunately, there are at present few structural engineers who have the expertise to assess the seismic vulnerability and suggest appropriate retrofit measures. This Manual is expected to enhance that number manifold. Workshops and training programmes related to the use of this Manual are planned for this purpose.

Numerous persons have helped us in preparing this Manual. These include project associates, Ph.D. and M.S. research scholars, M.Tech. and B.Tech. students, laboratory technicians and secretarial staff. A list of all the major contributors is given in the Acknowlegement page.

We are also grateful to the Department of Science and

Technology for their funding and encouragement.

IITM –SERC Project Team March 12, 2005.

iii

IITM – SERC Project Team

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Dr. Devdas Menon Principal Investigator Dr. Amlan K Sengupta Dr. V Kalyanaraman Dr. A Meher Prasad Dr. S R Satish Kumar Dr. P Alagusundaramoorthy Mr. V T Badari Narayanan Mr. Gnanasekharan Mr. Pradip Sarkar Ms S Prathibha Mr. Rajib Chowdhury Mr. Robin Davis P Dr. S R Uma Mr. A. Asokan Mr. G Ravi Kumar Ms. K N S Susmitha Mr. Anand Gupta Mr. Biju Kumar Patir Mr. Lakki Reddy Ms. Praseetha Krishnan Mr. Rajesh Lal Mr. Ramaseshan Mr. Ramesh Pativada Mr. Ravi Chugh Mr. Santosh K Barnwal Mr. Sheshu Reddy Mr. Shiv Shanker Mr. Srinivas, B. Mr. Srinivasulu Reddy

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

iv

Mr. T S Krishnamoorthy Principal Investigator Dr. N Lakshmanan Mr. C V Vaidyanathan Dr. K Muthumani Mr. K Balasubramanian Dr. K Balaji Rao Mr. R Ravichandran Mr. N Gopalakrishnan Mr. M Manjuprasad Mr. K Satish Kumar Dr. B H Bharatkumar Ms. P. Kamatchi Ms. R Sreekala Mr. D Dhiman Basu Mr. S. Avinash Mr. S Gopalakrishnan


CONTENTS

Preface

i

1. INTRODUCTION

1

1.1 Background 1.2 Objective 1.3 Scope 1.4 Methodology

2. PRELIMINARY EVALUATION

7

2.1 Introduction 2.2 Data Collection and Condition Assessment of Building 2.3 Rapid Visual Screening 2.3.1 Scores for a building 2.3.2 Cut-off Score 2.3.3 Building Type Descriptions 2.3.4 Score Modifier 2.4 Quick Checks for Strength and Stiffness 2.4.1 Column Shear 2.4.2 Shear Stress in Shear Wall 2.4.3 Axial Stress in Column 2.4.4 Frame Drift 2.4.5 Strong Column – Weak Beam Check 2.5 Evaluation Statements 2.6 Decision for Detailed Evaluation

vii


3. EVALUATION BASED ON LINEAR ANALYSIS

35

3.1 Introduction 3.2 Computational Model 3.2.1 Material properties 3.2.2 Structural element model 3.2.2.1 3.2.2.2 3.2.2.3 3.2.2.4 3.2.2.5

Beams and columns Beam-column joints Slabs Appendages Walls (structural and non structural)

3.2.3 Modelling of Column Ends at Foundation 3.2.4 Load Combinations 3.3 Linear Analysis Methods 3.3.1 Equivalent static method 3.3.1.1 3.3.1.2 3.3.1.3 3.3.1.4 3.3.1.5 3.3.1.6

Centre of mass Centre of rigidity of storey Effect of torsion Seismic weight Lumped mass Calculation of lateral forces

3.3.2 Response spectrum analysis 3.4 Evaluation Results

4. EVALUATION BASED ON NONLINEAR PUSHOVER ANALYSIS

53

4.1 Introduction 4.2 Capacity Spectrum, Demand Spectrum & Performance Point 4.3 Pushover Analysis Procedure 4.3.1 Seismic Load Distribution 4.3.2 Load Deformation Behaviour of Elements 4.4 Performance Based Analysis 4.4.1 Performance Objective 4.4.2 Performance Levels of Structure and Elements 4.4.3 Seismic Hazard Levels 4.4.4 Selection of Performance Objective 4.5 Evaluation Results

5. SEISMIC RETROFIT

63

5.1 Introduction 5.2 Goals of Retrofit 5.3 Definitions

viii


5.4 Steps of Retrofit 5.5 Performance Objectives 5.6 Retrofit Strategies 5.6.1

Global Strategies

5.6.2

Local Strategies

5.6.3

Energy Dissipation and Base Isolation

5.6.4

Mitigating Geological Hazards

6. BUILDING DEFICIENCIES

70

6.1 Introduction 6.2 Global Deficiencies 6.2.1

Plan Irregularities

6.2.2

Vertical Irregularities

6.3 Local Deficiencies 6.3.1

Columns

6.3.2

Beams and Beam-Column Joints

6.3.3

Slabs

6.3.4

Unreinforced Masonry Walls

6.3.5

Precast Elements

6.3.6

Deficient Construction

6.4 Miscellaneous Deficiencies 6.4.1

Deficiencies in Analysis

6.4.2

Lack of Integral Action

6.4.3

Failure of Stair Slab

6.4.4

Pounding of Buildings

6.4.5

Geotechnical Aspects

6.4.6

Inadequate detailing and documentation

7. GLOBAL RETROFIT STRATEGIES 7.1 Introduction 7.2 Structural Stiffening 7.2.1

Addition of Infill Walls

7.2.2

Addition of Shear Walls

7.2.3

Addition of Steel Braces

7.3 Reduction of Irregularities 7.4 Reduction of Mass

ix

84


8. LOCAL RETROFIT STRATEGIES

90

8.1 Introduction 8.2 Column Strengthening 8.2.1

Concrete Jacketing

8.2.2

Steel Jacketing

8.2.3

Fibre Reinforced Polymer Wrapping

8.3 Beam Strengthening 8.3.1

Concrete Jacketing

8.3.2

Steel Plating

8.3.3

FRP Wrapping

8.3.4

Use of FRP Bars

8.3.5

External Prestressing

8.4 Beam-Column Joint Strengthening 8.4.1

Concrete Jacketing

8.4.2

Concrete Fillet

8.4.3

Steel Jacketing

8.4.4

Steel Plating

8.4.5

Fibre Reinforce Polymer (FRP) jacketing

8.5 Wall Strengthening 8.6 Footing Strengthening

9. CASE STUDY I

129

10. CASE STUDY II

173

11. CASE STUDY III

211

APPENDIX A: MAPPING OF SOIL TYPE

A1

APPENDIX B: MODELLING OF INFILL MASONRY WALL

B1

B.1 Modelling of Masonry Infill B.2 Effect of Openings

x


B.3 Strength of Equivalent Strut B.3.1 Local Crushing Failure B.3.2 Shear Failure

APPENDIX C: MODELLING OF PLASTIC HINGES

C1

C.1 Flexural Hinges for Beams and Columns C.1.1 Stress Strain Characteristics of Concrete C.1.2 Stress Strain Characteristics of Steel C.1.3 Moment-curvature Relationship C.1.4 Modelling of Moment-curvature in Confined RC Sections C.1.4.1 Assumptions C.1.4.2 Numerical Algorithm for Moment-curvature for Beam Sections C.1.4.3 Numerical Algorithm for Moment-curvature for Column Sections

C.1.5 Moment Rotation Parameters C.2 Shear Hinges for Beams and Columns C.3 Axial Hinges for Equivalent Struts

APPENDIX D: VULNERABILITY INDEX

D1

APPENDIX E: ADDITION OF STEEL BRACES

E1

E.1 Types of Bracing E.2 Connection of Braces to RC Frame E.3 Analysis and Design of Braces E.4 Non-Buckling Braces

xi


CHAPTER I INTRODUCTION

1.1

BACKGROUND

Existing multi-storey buildings in earthquake prone regions of India are vulnerable to severe damage under earthquakes, as revealed by the recent Gujarat earthquake. There is urgent need for seismic evaluation and retrofit of deficient buildings. There are experts in the country who can assist in the seismic evaluation and retrofit of individual buildings on a case-to-case basis. The magnitude of the work, however, is so large that it cannot be accomplished by limited number of experts, and needs involvement of many structural engineers, who are properly trained. Hence, there is a need to provide appropriate guidelines for seismic evaluation and retrofit of existing buildings to the vast majority of structural engineers in our country who lack the expertise. To address this problem, this manual has been prepared to facilitate seismic evaluation and recommend strategies for retrofitting, so that the risk of failure is minimised in the event of a future earthquake. This manual addresses the seismic evaluation of existing RC multi-storey building. The document is a part of a research project supported by Department of Science and Technology (DST), Government of India.

1


Indian codes of practice for earthquake resistant design (IS 1893: 2002) and detailing (IS 13920: 1993) give guidelines to construct new buildings which are expected to perform adequate in terms of load and deformation capacities. The existing buildings constructed as per older codes are likely to show inherent deficiencies and may not meet the demands as estimated by the current codes. Hence, the task of seismic evaluation involves correlation between the imposed demand level of earthquake and the expected performance level of building. The code refers to two levels of earthquakes such as Design Basis Earthquake (DBE) and Maximum Considered Earthquake (MCE). The concept of seismic design philosophy is to ensure life safety under DBE and prevent collapse of the building under MCE. These are two performance objectives which are to be ascertained with the existing buildings.

A systematic procedure is to be followed in assessing the vulnerability of existing buildings. undertaken.

Firstly, a detailed survey of the building of interest should be The basic information would include a review of the building

configuration, soil profile and the period of construction. An evaluation is to be performed based on the available documents, to ensure code compliance. This is done with the help of quick checks and evaluation statements. The above tasks form the essence of the preliminary evaluation procedure.

However, a detailed evaluation is necessary in order to identify the deficiencies associated with the structural components with regard to the expected behaviour of the building. The code compliance of the building can be ascertained only when the available member capacities are compared with the respective demands due to the earthquake. The demands in the structural members are determined for the seismic forces estimated as per IS 1893-2002 through linear static analysis. The member capacities are determined using the procedures prescribed in IS 456-2000. The deficient members are identified when the Demand to Capacity Ratios (DCR) exceed unity indicating the need for retrofitting in order to establish compliance with prevailing codes.

2

Chapter I - Introduction

In the case of deficient buildings, a more enhanced and sophisticated analysis procedure is recommended to determine the load versus deformation behaviour of the building taking into account of the non-linear behaviour of its components. Non-linear static pushover analysis provides a basis to determine whether the building can meet the imposed displacement demand at expected performance level. It also indicates the likely mode of failure and the spatial distribution of plastic hinges. If the performance is unsatisfactory various retrofit strategies can be tried to achieve satisfactory performance.

1.2

OBJECTIVES

The objective of the manual is to provide comprehensive guidelines for seismic evaluation and retrofit based on the Indian code of practice. The followings are the main objectives. 1. To give a well-defined procedure that enables a proper assessment of the seismic vulnerability of a given (existing) multi-storeyed RC building. 2. To propose various strategies for seismic retrofit that can be used for buildings found to be deficient. 3. To develop software that facilitates Seismic Analysis and Vulnerability Evaluation (“SAVE”) of RC buildings.

The work related to the first two objectives is covered in this manual. It may be noted that any of the commercially available software can be used to carry out the analysis. Details of the free software SAVE developed as part of this DST sponsored project are given separately (user manual and CD), and are not included in this manual.

3


1.3

SCOPE

This procedure aims at two seismic safety objectives, namely (i) life safety under design basis earthquake and (ii) collapse prevention objective under maximum considered earthquake. It does not address other performance objectives. The buildings treated in this section are mid-rise (3 to 10 storeys) reinforced concrete moment resisting framed buildings. The report deals only with structural aspects of the building. Non-structural and geotechnical aspects lie outside the scope of the report. Special attention should be taken for the evaluation of buildings located in liquefiable soils.

1.4

METHODOLOGY

The evaluation process essentially consists of two phases, viz., preliminary evaluation and detailed evaluation. Preliminary evaluation is a quick procedure to identify potential risks in buildings due to earthquakes. If the building satisfies the requirements of preliminary evaluation, detailed analysis may not be necessary.

The following are the methods recommended for detailed analysis: 1.

Linear static analysis – Equivalent static analysis as per IS 1893: 2002

2.

Linear dynamic analysis – Response spectrum analysis as per IS 1893: 2002

3.

Non-linear static analysis – Push-over analysis

It is recommended that all the above methods be performed sequentially for a proper assessment of the seismic vulnerability, as demonstrated in the case studies given in Chapter XI. It may be noted that more rigorous analysis (nonlinear dynamic time-history analysis) is possible, but this is not recommended as it is more involved and time consuming and not recommended for normal building. Figure 1.1 gives the flowchart explaining the evaluation and retrofit process.

4

Chapter I - Introduction

Preliminary evaluation

NO

Deficiencies?

YES Detailed evaluation

NO

Deficiencies?

Retrofit not necessary

YES Development of retrofit scheme

Post-retrofit analysis

NO

Deficiencies?

Report preparation

YES Development of different retrofit scheme Figure 1.1: Flowchart summarizing the evaluation and retrofit process

The steps to be undertaken in the seismic evaluation of existing building are as follows, 1.

Preliminary evaluation i)

Data collection and condition assessment of building.

5


2.

ii)

Rapid Visual Screening (optional).

iii)

Quick checks for strength and stiffness.

iv)

Evaluation statements (structural checklist).

Detailed evaluation i)

Computational modelling.

ii)

Perform linear static and dynamic analysis and check the code compliance at critical section.

iii)

Study DCR of structural components

iv)

Perform non-linear (static) push-over analysis and assess the performance.

v)

Compare with performance objectives i

Code compliance

i

Desired failure mechanism

i

Drift capacity

The first two among these three performance objectives are mandatory requirements to be satisfied whereas the third one is a desirable performance objective.

3.

Selection and design of retrofit strategies and subsequent verification of the retrofit scheme.

Remodelling the structure according to the trial retrofit scheme and analysing the building model. If the performance is not satisfactory different retrofit scheme is to be selected.

4.

Preparation of seismic evaluation and retrofit report.

6


CHAPTER II PRELIMINARY EVALUATION

2.1

INTRODUCTION

The purpose of the preliminary evaluation is to identify the areas of seismic deficiencies in a building under investigation.

It is a ‘non-detailed’ analysis

consisting of the following procedures i)

Data collection and condition assessment of building.

ii)

Rapid Visual Screening (optional).

iii)

Quick checks for strength and stiffness.

iv)

Evaluation statements (structural checklist).

The collection of all available data pertaining to the building structure, especially related to the construction, as well as an on-site inspection of the building form the first step in the preliminary evaluation procedure. The Rapid Visual Screening procedure, adapted from FEMA 154∗ gives some preliminary idea, based on a scoring system, of the seismic vulnerability of the building.

However, this

screening is optional and not mandatory, as FEMA guidelines are not directly applicable to Indian conditions. ∗

The RVS procedure was proposed by Applied Technology Council in the documents FEMA 154 and FEMA 155. In the present report, the data collection form shown in Table 2.1, is adapted from FEMA 154 published in 2002. The form was modified to include the seismic zones and soil types as per IS 1893: 2002 and to define the ‘pre-code’ and ‘post-benchmark’ criteria.

7


“Quick checks” are approximate checks for strength and stiffness of building components. The evaluation statements are in the form of a simple questionnaire that gives an overall idea of the building and identifies areas of potential weakness, in terms of seismic performance. It also checks the conformity with seismic design and detailing provisions.

2.2

DATA COLLECTION & CONDITION ASSESSMENT OF BUILDING

In order to facilitate a proper assessment, it is necessary to collect as much relevant data of the building as possible through drawings, enquiry, design calculations and soil report (if available), etc. It may be noted that physical evaluation (condition survey and walk through) of the building is essential. Condition survey and walk through of the building gives a general description of the building. It notes the available drawings and reports, identifies the basic architectural features, material properties and their deterioration and several helpful information. A suggested form of the building survey data sheet is given in Table 2.1 and 2.2 is modified from the proposed amendment in town and country planning legislations, Regulations for Land Use Zoning in Natural Hazards Zone of India (Draft version, 2005). Table 2.1: Building survey data sheet: General data S.No. Description 1

Address of the building

2

• Name of the building • Plot number • Locality/Town ship • District • State Name of owner

3

Name of builder

4

Name of Architect/Engineer

Information

8

Notes

Chapter II – Preliminary Evaluation

Table 2.1 (Contd.): Building survey data sheet: General data S.No. Description

Information

Notes

5

Name of Structural Engineer

6

Use of building

7

9

Number of storeys above ground level Number of basements below ground level Type of structure

10

• Load bearing wall • RC frame • RC frame and shear wall • Steel frame Soil data

IS 1904: 1986

11

• Type of soil • Design safe bearing capacity Dead loads (unit weight adopted)

IS 875: Part 1:

12

• Earth • Water • Brick masonry • Plain cement concrete • Floor finish • Other fill materials Imposed (live) loads

8

• •

IS 1893: 2002

1987

IS 875: Part 2:

Floor loads Roof loads

1987

13

Cyclone/Wind

IS 875: Part 3: 1987

14

• Speed • Design pressure intensity History of past earthquakes and tremors

15

Seismic zone

IS 1893: 2002

16

Importance factor, I

IS 1893: 2002

17

Seismic zone factor, Z

IS 1893: 2002

18

Response reduction factor, R

IS 1893: 2002

19

Fundamental natural period, T

IS 1893: 2002

9


Table 2.1 (Contd.): Building survey data sheet: General data S.No. Description 20

Information

Design Horizontal acceleration

Notes IS 1893: 2002

spectrum value (Ah) 21

Seismic design lateral force

22

Expansion/ Separation joints

Table 2.2: Building survey data sheet: Building Data (moment resisting frame) S.No. Description 1

Information

2

Type of building • Regular frames • Regular frames with shear wall • Irregular frames • Irregular frames with shear wall • Open ground storey Number of basements

3

Number of floors

4

Horizontal floor system • Beams and slabs • Waffle slab • Ribbed floor • Flat slab with drops • Flat plate without drops Soil data • Type of soil • Recommended foundation - Independent footings - Raft - Piles • Recommended bearing capacity • Recommended type, length, diameter and load capacity of piles • Depth of water table • Chemical analysis of ground water • Chemical analysis of soil

5

10

Notes IS 1893: 2002

IS 1498: 1970


Table 2.2 (Contd.): Building survey data sheet: Building Data (MRF) S.No. Description 6

7

8 9 10 11 12

13 14 15

Information

Foundations • Depth below ground level • Type − Independent − Interconnected − Raft − Piles System of interconnecting foundations • Plinth beams • Foundation beams Grades of concrete used in different parts of building Method of analysis Computer software used Torsion included Base shear a) Based on approximate fundamental period b) Based on dynamic analysis c) Ratio of a/b Distribution of seismic forces along the height of building The columns of soft ground storey specially designed Clear minimum cover provided in • Footing • Column • Beams • Slabs • Walls

11

Notes

IS 1893: 2002 Cl. 7.12.1

IS 1893: 2002 IS 1893: 2002

IS 1893: 2002 IS 1893: 2002



Information

Ductile detailing of RC frame • Type of reinforcement used • Minimum dimension of beams • Minimum dimension of columns • Minimum percentage of reinforcement of beams at any cross section • Spacing of transverse reinforcement at any section of beam • Spacing of transverse reinforcement in 2d length of beam near the ends • Ratio of capacity of beams in shear to capacity of beams in flexure • Maximum percentage of reinforcement in column • Confining stirrups near ends of columns and in beamcolumn joints − Diameter − Spacing • Ratio of shear capacity of columns to maximum seismic shear in the storey • Column bar splices location and spacing of hoops in the splice • Beam bar splices location and spacing of hoops in the splice

Notes IS 456, Cl. 5.6 IS 13920, Cl. 6.1 IS 13920, Cl. 7.1.2 IS 456: 2000 Cl. 26.5.1.1(a) IS 13920: 1993 Cl. 6.2.1 (a)

IS 13920: 1993 Cl. 6.3.5

IS 456: 2000 Cl. 26.5.3.1 IS 13920, Cl. 7.4

IS 13920, Cl. 7.2.1 IS 13920, Cl. 6.3.5

However, in many cases, such drawings may not be available (or at best, partially available). Tables 2.3 to 2.6∗ summarize the data collection process, relating to the availability of the drawings and level of evaluation.

The various data to be

collected when the original construction drawings are available are indicated in ∗

These items are from Table 5.1 to Table 5.4 of ATC-40 (Volume 1): “Seismic Evaluation and Retrofit of Concrete Buildings,” Applied Technology Council, California.1996.

12


Tables 2.3 and 2.4. Tables 2.5 and 2.6 should be followed when construction drawings are not available. It is suggested, as shown in tables that in addition to the visual inspection, it is recommended to carry out non-destructive testing to assess the strength of concrete. Table 2.3: Information required for Preliminary evaluation when original construction drawings are available. Item Structural calculations

Required Yes No ×

Site seismicity and

×

geotechnical report Foundation report Prior seismic assessment reports Condition survey of building Alteration and as built assessment

Helpful but not essential Helpful but updated report should be done.

×

Helpful but not essential

×


× ×

Walk through dimensioning Non-structural walk through

Comment

× ×

Unless required by undocumented alterations Identify falling hazards, weight

Core testing

×

Rebound hammer testing

×

Aggregate testing

×

Reinforcement testing

×

Reinforcement location

×

verification Non-structural exploration

×

13

Unless concrete appears substandard Unless concrete appears substandard

Unless insufficient info. on drawing


Table 2.4: Information required for detailed seismic evaluation when original construction drawings are available. Item Structural calculations

Required Yes No ×

Site seismicity and geotechnical report Foundation report Prior seismic assessment reports Condition survey of building Alteration and as built assessment

×


×


×


×

Spot checking is appropriate

×

Non-structural walk through

×

Core testing

×


×

Aggregate testing

×

Reinforcement testing verification

Could be helpful

×

Walk through dimensioning

Reinforcement location

Comment

Identify falling hazards, weight Minimum 2 per floor, 8 per building Minimum 8 per floor, 16 per building Each core ×

Optional Pachometer @ 10% of critical

×

location, Visual @ 2 locations. Verify anchorage and bracing

Non-structural exploration

×

conditions for components sensitive to building performance.

It is desirable to do core testing, when the condition of the concrete is suspect. Any evidence of deterioration, cracking and corrosion of reinforcement should be noted.

Testing of reinforcement for yield/ ultimate strength and ductility is

desirable. It is also desirable to ascertain the nature of reinforcement detailing, especially anchorage of bars and hooks, spacing of stirrups/ ties to the extent possible using device such as rebar locator.

14


Table 2.5: Information required for Preliminary evaluation when original construction drawings are not available. Item

Required Yes

Structural calculations

×

Site seismicity and geotechnical

×

report Foundation report

×

Prior seismic assessment reports

×

Condition survey of building

×

Alteration and as built assessment

×


×


×

Core testing (limited)

×

Comment

No

Could minimize scope of site work Could minimize scope of site work Could minimize scope of site work Could minimize scope of site work

Sufficient to define primary element Identify falling hazards, weight Minimum 2 per floor, 8 per building Could be helpful, especially


×

if concrete appears substandard

Aggregate testing

×

Several cores


×

Reinforcement location verification

×


×

Could be helpful

Unless there is sufficient evidence to suggest that the ductile detailing provision of IS 13920: 1993 have been followed, it is judicious to assume non-compliance with the code.

Based on an assessment of reliability of the data collected, an

15


approximate “knowledge factor” should be applied to the material properties for detailed analysis (Table 3.2). Table 2.6: Information required for detailed seismic evaluation when original construction drawings are not available. Item

Required Yes

Structural calculations

Comment

No ×

Could be helpful

×


Foundation report

×


Prior seismic assessment reports

×


Site seismicity and geotechnical report

Condition survey of building

×

Alteration and as built assessment

× Must be done very


×

thoroughly, particularly if structure will be retrofitted. Identify falling hazards,


×

Core testing (limited)

×


×

Aggregate testing

×

Each core


×

2 per type

Reinforcement location verification

×

weight Minimum 2 per floor, 8 per building Minimum 8 per floor, 16 per building

Pachometer for all critical location, Visual on 25%. Verify anchorage and


×

bracing conditions for components sensitive to building performance.

16


2.3

RAPID VISUAL SCREENING

The Rapid Visual Screening (RVS) was proposed by FEMA as a means of quickly assessing, using a scoring system, the seismic vulnerability of buildings in a locality, based only on visual inspection. Considerable research has gone into the formulation of the RVS scoring system, and although the specific scores may not be directly applicable to Indian conditions, the RVS does provide a rough guideline for reference. Since the RVS is based on visual inspection, the results may vary from that of a detailed analysis. In general, however, it is expected that the building that passes the RVS cut-off score criterion, will be found to perform adequately during an earthquake.

If a large number of buildings need to be

evaluated, performing the RVS helps to minimise the number of buildings that require a detailed analysis. Table 2.7: Rapid Visual Screening data collection form Region of Seismicity

High Seismicity Moderate Seismicity Low Seismicity (Zone V) (Zone IV) (Zone II and III) URM URM URM Building Type MRF SW MRF SW MRF SW INF INF INF Basic Score

2.5

2.8

1.6

3.0

3.6

3.2

4.4

4.8

4.4

Mid rise

+0.4

+0.4

+0.2

+0.2

+0.4

+0.2

+0.4

-0.2

-0.4

High rise

+0.6

+0.8

+0.3

+0.5

+0.8

+0.4

+1.0

0.0

-0.4

-1.5

-1.0

-1.0

-2.0

-2.0

-2.0

-1.5

-2.0

-2.0

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.8

-0.8

-0.8

Pre-code

-1.2

-1.0

-0.2

-1.0

-0.4

-1.0

N/A

N/A

N/A

Postbenchmark

+1.4

+2.4

N/A

+1.2

+1.6

N/A

+0.6

+0.4

N/A

Soil Type I

-0.4

-0.4

-0.4

-0.6

-0.8

-0.6

-0.6

-0.4

-0.4

Soil Type II

-0.6

-0.6

-0.4

-1.0

-1.2

-1.0

-1.4

-0.8

-0.8

Soil Type III

-1.2

-0.8

-0.8

-1.6

-1.6

-1.6

-2.0

-2.0

-2.0

Vertical irregularity Plan irregularity

Final Score Comments

17


In this procedure the building under consideration is compared with a benchmark building through visual inspection. Table 2.7 represents the data collection form, which quantifies the potential seismic hazard for any building based on the seismicity level of the locality. The form addresses reinforced concrete (RC) moment resisting frame buildings (MRF), concrete shear wall buildings (SW) and concrete frame buildings with un-reinforced masonry infill walls (URM INF).

2.3.1

Scores for a Building

In the data collection form, for a particular type of building, the structural scoring system consists of a basic structural hazard (BSH) score and a set of score modifiers. The BSH score can be defined as negative logarithm of probability of collapse of the benchmark building under maximum considered earthquake (MCE).

Thus a BSH score for moment resisting frame (MRF) in moderate

seismicity region of 3.0 implies that for every thousand (103) benchmark buildings one building is likely to collapse. Benchmark buildings are the representative building for which the structural hazard scores (BSH score) were developed∗ for different seismic regions.

A

Benchmark building is a low rise, ordinary building (not detailed as per seismic detailing code) located on an average rock strata (Soil Type B of UBC 1997) and it has no plan and vertical irregularity. The building is assumed to be designed as per the current seismic code.

2.3.2

Cut-off Score

FEMA 154 recommends that if the final score is less than the cut off score of 2, a detailed analysis of the building is required. In selected cases, in order to have a safer environment (at a correspondingly higher cost) a higher cut-off value can be used.

∗

The BSH scores are developed from fragility and capacity curves, generated by HAZUS (developed by National Institute of Building Sciences, USA) based on seismic hazard maps.

18


2.3.3

Building Type Descriptions

There are three different building types mentioned in Table 2.7. The definitions of these buildings are as follows. (a)

Concrete Moment Resisting Frame Buildings (MRF): The buildings with

reinforced concrete frame as the only lateral load resisting system. (b)

Concrete Shear Wall Buildings (SW): Buildings with shear walls are

considered in this type. It also includes buildings having shear walls and frames, but where the frames are either not designed to carry lateral load or do not fulfil the requirements of dual system. These buildings generally perform better than concrete frame buildings and this is reflected in the magnitude of BSH score. (c)

Concrete Frames with Un-reinforced Masonry Infill Walls (URM-INF): In

this type of buildings, un-reinforced masonry infill walls are also part of the lateral load resisting system.

2.3.4 Score Modifier BSH scores were calculated for a standard benchmark building. For a specific building, which may have different characteristics due to higher number of storeys or structural irregularities or different soil type, it is necessary to modify the BSH scores using score modifiers (SM)**. So a specific building will arrive at a final score (S) after modifying the BSH score. The final score S is an estimate of the probability that the building will collapse if a ground motion equal to or exceeding the MCE ground motion occurs. S = BSH ± SM. Definitions∗ for the score modifiers used in Table 2.7 are discussed below. High-rise and Mid-rise Buildings: 4 to 7 storey buildings are categorised as midrise building whereas buildings with 8 or more storeys are as high-rise building.

**

A positive modifier implies reduced probability of failure and vice versa. The following definitions of the score modifiers are from FEMA 154, changed suitably as per IS 1893: 2002 and IS 13920: 1993. ∗

19


Plan irregularity and Vertical irregularity: This are defined in detail in Tables 2.9 and 2.10 in the section 2.5 Pre-code: Buildings designed for gravity loads only and not for lateral loads are defined as pre-code buildings. In the absence of any mention of code in the construction documents, it is difficult to judge ‘pre-code’. Then, if at the beamends, the bottom steel is less than 50% of the top steel provided, the building can be considered to be designed for gravity loads only. As the benchmark building is assumed to be designed as per the current seismic code, pre-code buildings have a negative score modifier. Post-benchmark: Building designed and constructed as per the ductile detailing requirements of IS 13920: 1993 are considered as post-benchmark buildings. Values of the score modifier for post-benchmark buildings are positive as these buildings perform better than the benchmark building under seismic loading.

Soil Type Definition∗∗: Score modifiers for three soil types are mentioned in the data collection form. Soil Type I (Rock or hard soil): well graded gravel and sand gravel mixtures with or without clay binder, and clayey sands poorly graded or sand clay mixtures with standard penetration count, N > 30. Soil Type II (Medium soil): All soils with 10 ≤ N ≤ 30 poorly graded sands or gravely sands with little or no fines with N > 15. Soil Type III (Soft soil): All soils other than sands poorly graded with N < 10.

2.4

QUICK CHECKS FOR STRENGTH AND STIFFNESS

The ‘quick checks’ involve a set of initial calculations that checks the average shear stress in the columns, shear walls etc and average axial stresses in columns ∗∗

The values of the score modifier for soil type were obtained by mapping the soil types given in UBC-1997 to soil Types I, II and III as given in IS 1893: 2002. The details of the mapping is discussed in Appendix-A.

20


in each storey, due to the design lateral force determined from IS 1893-2002. This includes a drift check which is a measure of the stiffness of the building and also a strong column-week beam check recommended by IS 13920: 1993. The details of the checks are given below.

2.4.1 Column Shear The base shear (VB) is to be calculated as per Clause 7.5.3 of IS 1893: 2002. The calculation of the base shear is explained in Section 3.3.1.5. The shear at each storey (Vj) is calculated from the base shear as follows: n

Vi = ∑ Qi

(2.1)

i

where, Vi

Qi

≡ Storey shear at ith storey, ≡ Design lateral force at ith storey (Ref. Section 3.3.1.5),

n

≡ Total number of storeys above ground level,

i

≡ Number of storey level under consideration,

Wi

≡ Seismic weight of ith storey,

The average shear stress in the columns (assuming that nearly all the columns in the frame have similar stiffness) is given by,

⎛ nc ⎜ ⎝ nc − n f

τ avg = ⎜

⎞ ⎛ Vi ⎞ ⎟⎟ ⎜ ⎟ ⎠ ⎝ Ac ⎠

(2.2)

Where, nc ≡ Total number of columns in that particular storey,

nf ≡ Total number of frames in the direction of loading, Ac ≡ Summation of the cross sectional areas of columns in the storey under consideration,

Vi ≡ shear at storey, i.

21


⎛

n

⎞

The term ⎜⎜ c ⎟⎟ is based on the assumption that shear force carried by the ⎝ nc − n f ⎠ columns at the end of RC frames are typically half of those carried by interior columns. However, this leads to a very conservative estimate of shear for one-bay frame (twice of the correct value), but this discrepancy is not so serious for frames which are typically more redundant. If the average column shear stress (τavg) is greater than 0.4 MPa, a more detailed evaluation of the structure should be performed.

2.4.2

Shear Stress in Shear Wall

The average shear stress in the walls at a storey can be calculated as follows.

τ avg = Where, Vi

Aw

Vi Aw

(2.3)

≡ shear at the storey under consideration, ≡ summations of the horizontal cross sectional area of all shear walls in the direction of loading. The wall area should be reduced by the area of openings.

If the average shear stress in shear walls (τavg) is greater than 0.35 MPa or 0.074√fck MPa, a more detailed evaluation of the structure should be performed.

2.4.3

Axial Stress in Column

The base shear VB is assumed to be distributed in a parabolic pattern, in accordance with 1893: 2002. The overturning moment due to these forces develop axial forces in the columns. This may be computed as 5⎛V P= ⎜ B 8 ⎜⎝ n f

⎞⎛ h ⎞ ⎟⎟ ⎜ ⎟ ⎠⎝ L ⎠

22

(2.4)


Here, h is the total height of the building, L is the total length of a frame and nf is the number of frames in the direction of lateral forces. The factor 5 8 accounts for the height of the resultant lateral force above base level. The axial stress calculated from the force should be less than 0.24 fck for acceptance.

2.4.4

Frame Drift

The approximate storey drift ratio can be determined using the following equation. It considers that the storey displacement is equal to the flexural displacement of a representative column, including the effect of end rotation due to bending of a representative beam.

DR =

kb + kc h VcC d k b k c 12 E

(2.5)

where, DR ≡ Inter storey displacement divided by the storey height,

kb ≡ I/L for a representative beam, kc ≡ I/h for a representative column, L ≡ Effective length of the beam, h ≡ Storey height, I ≡ Moment of inertia, E ≡ Modulus of elasticity, Vc ≡ Shear in column, Cd ≡ Deflection amplification factor to include inelastic effect. For ordinary RC moment resisting frames, Cd = 2. For the value of I, an equivalent cracked section moment of inertia equal to half of the gross section can be used. The above equation can be applied to the ground storey if the columns are fixed against rotation at the bottom (for pile and raft foundations). If the columns are pinned at the bottom (for isolated footing), an equivalent storey height equal to twice the storey height shall be used in calculating the value of kc. If the drift ratio exceeds the limiting drift ratio of 0.015, the structure needs to be evaluated for full frame analysis using the design lateral forces.

23


2.4.5

Strong Column – Weak Beam Check

At a beam-column junction, according to good design principle, failure of the column should not precede that of the beam, in order to avoid catastrophe (Global failure). As shown in Figure 2.1, a strong column-weak beam combination is able to sustain higher lateral loads through development of large number of plastic hinges at the beam-ends prior to formation of collapse mechanism. In contrast under strong beam-weak column construction, plastic hinging at the top and bottom locations of the columns in a storey can bring down the entire building at low lateral loads.

∆

∆ θ θ

(a) Strong Column-Weak Beam

(b) Strong Beam-Weak Column

Figure 2.1: Failure mechanism in an RC frame

A quick check (in an overall sense) of ascertaining whether plastic hinges formed first in the beam sections rather than the adjoining column sections is by checking that the sum of the moment capacities of the columns shall be 20% greater than that of the beams at frame joints.

i.e., ∑ Moment capacities of the columns > 1.2 ∑ Moment capacities of the beams

24


2.5

EVALUATION STATEMENTS

The evaluation statements seek clarification on a variety of structural seismicresistant features, which if non-compliant, suggest that detailed evaluation is required. The evaluation statements depend on the type of lateral load resisting systems. Here, only the statements relevant for concrete moment resisting frame buildings, with or without shear walls, are listed. The evaluation statements∗ are listed in Tables 2.8 to 2.15.

Each of the statements should be marked as

“compliant” (C), “non-compliant” (NC) or “not applicable” (NA). “Compliant” statements identify issues that are acceptable as positive seismic resistant qualities, while “non-compliant” statements identify issues that need further investigation. Certain statements that may not apply to the building under consideration can be marked as “not applicable”. Table 2.8: Evaluation statements − Building system

Statements

C / NC / NA

Load path: The structure shall contain one complete load path for seismic force effects from any horizontal direction that serves to transfer the inertial forces from the mass to the foundation. Adjacent buildings: An adjacent building shall not be located next to the structure being evaluated closer than 4% of the height. Mezzanines: Interior mezzanine levels shall be braced independently from the main structure, or shall be anchored to the lateral-force-resisting elements of the main structure. (Clause 7.3.4 IS 13920: 1993). No deterioration of concrete: There shall be no visible deterioration of concrete or reinforcing steel in any of the verticalor lateral-force-resisting elements.

∗

The evaluation statements are based on FEMA 310 and are modified to match the clauses of IS 1893: 2002 and IS 13920: 1993. The definitions of structural irregularities are as per IS 1893: 2002 and the detailing provisions are as per IS13920: 1993. The statements for the life safety performance level are selected. The statements which are solely for immediate occupancy performance level are disregarded.

25


Table 2.9: Evaluation statements − Vertical irregularities

Statements (Figure 2.2 and Table 5 of IS 1893: 2002)

C / NC / NA

No weak storey: The lateral strength of a storey shall not be less than 80% of the strength in the storey above. No soft storey: The lateral stiffness of a storey shall not be less than 70% of that in the story above or less than 80% of the average lateral stiffness of the three storeys above. No mass irregularity: There shall be no storey with seismic weight more than 200% of that of its adjacent storeys. The irregularity need not be considered in case of roofs. No vertical geometric irregularity: There shall be no storey with the horizontal dimension of the lateral-force-resisting system more than 150% of that in its adjacent storey. No vertical discontinuities: All vertical elements in the lateral-loadresisting system shall be continuous to the foundation.

Table 2.10: Evaluation statements − Plan Irregularities

Statements (Figure 2.3 and Table 4 of IS 1893: 2002)

No Torsion irregularity: The distance between the storey centre of rigidity and the storey centre of mass shall be less than 20% of the width of the structure in either plan dimension. No diaphragm discontinuity: There shall be no diaphragm with abrupt discontinuity or variation in stiffness, including those having cut out or open areas greater than 50% of the gross enclosed diaphragm area. The diaphragms shall not be composed of splitlevel floors. No re-entrant corners: Both projections of structure beyond the reentrant corners shall not be greater than 15% of its plan dimension in the given direction. No out of plane offsets: There shall be no discontinuity in a lateralforce-resisting path, such as out of plane offsets of vertical elements. No non-parallel system: There shall be no vertical element resisting the lateral force, not parallel to or symmetric about major orthogonal axes of the lateral-force-resisting system.

26

C / NC / NA


Table 2.11: Evaluation statements − Moment resisting frames

Statements (Figure 2.4 and Figure 2.5)

Redundancy: The number of lines of moment frames in each principal direction shall be greater than or equal to 2. The number of bays of moment frames in each line shall be greater than or equal to 2. No interfering wall: All infill walls placed in moment frames shall be isolated from structural elements. Shearing stress check: The building satisfies the quick check of the shear stress in the frame columns. (Section 2.4.1) Axial stress check: The building satisfies the quick check of the axial stress in the frame columns. (Section 2.4.3) Drift check: The building satisfies the quick check of storey drift. (Section 2.4.4.) Short captive columns: There shall be no columns at a level with height/depth ratios less than 50% of the nominal height/depth ratio of the typical columns at that level. (Clause 7.4.5, IS 13920: 1993) No shear failures: The shear capacity (VuR) of a frame column shall be greater than the shear demand which occurs when the column attains the probable moment capacity (Mpr). i.e., VuR ≥ 2Mpr/L. Consider Mpr = 1.4 MuR, where MuR is the moment of resistance in absence of axial load. (Clause 7.3.4, IS 13920: 1993) Strong column-weak beam: The building satisfies the quick check of strong column weak beam. (Section 2.4.5). Column bar splices: All column bar splices shall be provided only in the central half of the member length and hoops provided at spacing not exceeding 150 mm centre to centre. (Clause 7.2.1, IS 13920: 1993) Column tie spacing: Frame columns shall have ties spaced at or less than b/2 throughout their length and at or less than b/4 or 100 mm at all potential plastic hinge locations. (Clause 7.4.6, IS 13920: 1993) Beam bars: At least two longitudinal top and two longitudinal bottom bars shall extend continuously throughout the length of each frame beam. At least 25% of the longitudinal bars provided at the joints for either positive or negative moment shall be continuous throughout the length of the members.

27

C / NC / NA


Kn

Fn Storey Strength (lateral)

Storey Stiffness Kn-1 (lateral) Kn-2

Fn-1 Fn-2 F3 F2

K3 K2

F1

K1

F < 0.8 F i i +1

⎧ 0.7 ki+1 ⎪ ⎪ ⎪ ki < ⎨⎪ ⎛ ki+1 + ki+2 + ki+3 ⎞⎟ ⎪⎪0.8⎜⎜ ⎟ ⎜ ⎪ ⎠⎟ 3 ⎪ ⎩ ⎝

(a) Weak storey

(b) Soft storey Wn A Storey weight

Wn-1 Wn-2 W3 W2

A/L > 0.25 L

W1 Wi > 2.0 Wi+1 (or, 2.0Wi−1 ) (c) Mass irregularity A

A A/L > 0.1

A/L > 0.15 L (d) Vertical

A

geometric irregularity

Figure 2.2: Different types of vertical irregularity

28

L

A


∆2 >

1.2(∆1 + ∆ 2 ) 2

∆2

∆1

EQ (a) Torsional

Irregularity

A L

L A

A A/L > 0.15 (b) Re-entrant Corner

Lateral load resisting system

Y

Opening Area, A2

θ X

A2 > 0.5 A

Total floor area, A (c) Non-parallel

System

(d) Diaphragm Discontinuity

Figure 2.3: Different types of plan irregularity

29


Table 2.11 (contd.): Evaluation statements − Moment resisting frames

Statements (Figure 2.4 and Figure 2.5)

C / NC / NA

Beam bar splices: The lap splices for the longitudinal

reinforcement shall not be located within 2d from the joint face and within L/4 from the location of potential plastic hinges. (Clause 6.3.5, IS 13920: 1993) Stirrup spacing: All beams shall have stirrups spaced at or less than d/2 throughout their length. At potential hinge location, stirrups

shall be spaced at or less than the minimum of 8db or d/4. (Clause 6.3.5, IS 13920: 1993) Bent-up bars: Bent-up longitudinal steel shall not be used for shear

reinforcement. (Clause 6.3.4, IS 13920: 1993) Joint reinforcing: Column ties shall be extended at their typical

spacing through all beam column joints. (Clause 8.1, IS 13920: 1993) Deflection compatibility: Secondary components shall have the

shear capacity to develop the flexural strength of the elements. No flat slab frames: The lateral-force-resisting system shall not be

a frame consisting of columns and a flat slab/plate without beams. Prestressed frame elements: The lateral-load-resisting frames shall

not include any prestressed elements. Diaphragm reinforcement: There shall be tensile capacity to

develop the strength of the diaphragm at re-entrant corners or other locations of irregularities. There shall be reinforcement around all diaphragm openings larger than 50% of the gross enclosed diaphragm area. (Table 4, IS 1893: 2002) Anchorage: Stirrups should have 135 degree hook* with 10-

diameter extension (but not less than 75 mm) at each end, embedded in the confined core

*

It is noted that unless the bend angle is mentioned as 135 degree and there is adequate extension beyond the bend, the hook will be considered as “non-compliant”.

30


Table 2.12: Evaluation statements − Shear walls

Statements

C / NC / NA

Shearing stress check: The building satisfies the quick check of

shearing stress in the shear walls. (Section 2.4.2) Reinforcing steel: The area of reinforcing steel for concrete walls

shall be greater than 0. 25% of the gross area of the wall along both the longitudinal and transverse axes and the maximum spacing of bars shall not exceed lw/5, 3tw and 450 mm. (Clauses 9.1.4 and 9.1.7, IS 13920: 1993) Coupling beams: The stirrups shall be spaced at or less than 100

mm and shall be anchored into the core with 135° hooks. (Clause 9.5.2, IS 13920: 1993) Diaphragm openings at shear walls: Diaphragm openings

immediately adjacent to the shear walls shall be less than 25% of the wall length.

Table 2.13: Evaluation statements − Connections

Statements Column connection: All column reinforcement shall be dowelled

into the foundation. (Clause 7.4.2, IS 13920: 1993) Wall connection: Wall reinforcement shall be dowelled into the

foundation. Transfer to shear walls: Diaphragms shall be reinforced and

connected for transfer of loads to the shear walls. Lateral load at pile caps: Pile caps shall have top reinforcement

and piles shall be anchored to the pile caps.

31

C / NC / NA


Table 2.14: Evaluation statements − Geological site hazards

Statements

C / NC / NA

Liquefaction: Liquefaction susceptible, saturated, loose granular

soils that could jeopardise the building’s seismic performance shall not exist in the foundation soils at depths within 15 m under the building. Slope failure: The building site shall be sufficiently remote from

potential earthquake induced slope failures or rock falls to be unaffected by such failures or shall be capable of accommodating any predicted movements without failure. Surface fault rupture: Surface fault rupture and surface

displacement at the building site is not anticipated.

Table 2.15: Evaluation statements − Foundations

Statements Foundation performance: There shall be no evidence of excessive

foundation movement such as settlement or heave that would affect the integrity or strength of the structure. Deterioration: There shall not be evidence that foundation elements

have deteriorated due to corrosion, sulphate attack, material breakdown, or other reasons in a manner that would affect the integrity or strength of the structure. Overturning: The ratio of the effective horizontal dimension, at the

foundation level of the lateral-force-resisting system, to the building height (base/height) shall be greater than 0.6 Sa/g. Ties between foundation elements: The foundation shall have ties

adequate to resist seismic forces where footings, piles, piers are not restrained by beams, slabs, or soils classified as Type I.

32

C / NC / NA


Lapping in middle half of the column

Spacing

≤ 150mm

Spacing ≤ B/4 or 100mm ≥ 75mm

Figure 2.4: Reinforcement detailing for column as per IS 13920: 1993

Spacing ≤ 8db or d/4 Spacing ≤ d/2

At least 2 bars at top and 2 bars at bottom should go full length of the beam.

2d

2d

Lapping prohibited in regions where longitudinal bars can yield in tension Figure 2.5: Reinforcement detailing for beam as per IS 13920: 1993

33


2.6

DECISION FOR DETAILED EVALUATION

In this chapter the steps to be taken in order to carry out a preliminary evaluation of seismic vulnerability of a given building have been outlined. At the end of the preliminary evaluation a decision has to be taken whether to probe further and carry out more rigorous detailed evaluation (described in Chapters III and IV). Strictly, if the given building passes all the quick checks and satisfies all the evaluation statements, detailed evaluation is not called for. Nevertheless it is good practice to go ahead with the detailed evaluation, if an absolute confirmation regarding safety and code compliance is desired. It may be noted that almost every building out of 40 buildings randomly chosen for study under DST project was found to be deficient in some manner or other during the stage of preliminary evaluation. It is possible, as seen in some instances of the case studies carried out, that a building found deficient in preliminary evaluation performs satisfactory (without need for any retrofit) in the detailed evaluation. Thus, the preliminary evaluation serves as a useful screening test for seismic evaluation and its outcome is generally conservative.

34


CHAPTER III EVALUATION BASED ON LINEAR ANALYSIS

3.1

INTRODUCTION

When a building fails to comply with the preliminary evaluation criterion, a detailed structural analysis of the building should be carried out. Detailed analysis includes developing a computational model on which linear / non-linear, static / dynamic analysis is performed. Because of the difficulties and uncertainties in non-linear dynamic analysis, this is not recommended in normal design practice. This manual is confined to the other types of analysis.

This chapter briefly

explains the linear static and linear dynamic analyses as recommended in the code (IS 1893: 2002). The main purpose of these analyses, from the seismic evaluation perspective, is to check the demand-to-capacity ratios of the building components and thereby ascertain code compliance. The non-linear static analysis (pushover analysis) is explained in the next chapter. Some of the important modelling issues will also be discussed in this chapter.

35


3.2

COMPUTATIONAL MODEL

Modelling a building involves the modelling and assemblage of its various loadcarrying elements. A model must ideally represent the complete three dimensional (3D) characteristics of the building, including its mass distribution, strength, stiffness and deformability. Modelling of the material properties and structural elements is discussed below.

3.2.1 Material properties

The material properties of concrete include mass, unit weight, modulus of elasticity, Poisson’s ratio, shear modulus and coefficient of thermal expansion. The short-term modulus of elasticity (Ec) of concrete, as per IS 456: 2000, is given by Ec = 5000 f ck

(3.1)

where f ck ≡ characteristic compressive strength of concrete at 28-days in MPa. For the steel rebar, the properties required are yield stress (fy) and modulus of elasticity (Es). For assigning the material properties, the procedure outlined in section 2.2 shall be followed. As the characteristic strength is a 5 percentile value of the actual strength, the strength in analysis may be increased by the factors suggested in Table 3.1 for seismic evaluation purpose. This is done to estimate the expected capacities of the members. Table 3.1: Factors to estimate the expected strength Material property

Factor

Concrete compressive strength (fck)

1.50

Steel yield stress (fy)

1.00

36

Chapter III – Evaluation based on Linear Analysis

However, the expected values need to be further modified to for the uncertainty regarding the present condition of the material. A “knowledge factor” (mk) is used to account for this uncertainty. Proposed values of the knowledge factor are shown in Table 3.2. Table 3.2: Knowledge factors∗ No

Description of available information

mk

1

Original construction documents, including material testing

1.0

report 2

Documentation as in (1) but no material testing undertaken

0.9

3

Documentation as in (2) and minor deteriorations of

0.8

original condition 4

Incomplete but usable original construction documents

0.7

5

Documentation as in (4) and limited inspection and material

0.6

test results with large variation. 6

3.2.2

Little knowledge about the details of components

0.5

Structural element model

3.2.2.1

Beams and columns

Beams and columns should be modelled by 3D frame elements. While modelling the beams and columns, the important properties to be assigned are cross sectional dimensions, reinforcement details and the types of material used. Plinth beams should also be modelled as frame elements. The moment of inertia of a section should be modelled properly to account for the effect of cracking and the contribution of the flanges for T- or L- beam. The suggested effective moment of inertia (Ieff) for the beams including the effect of cracking and flanges are listed in Table 3.3

∗

The table is adopted from “IITK-GSDMA guidelines for seismic evaluation and strengthening of buildings” prepared by Indian Institute of Technology Kanpur.

37


Table 3.3: Effective moment of inertia for the beam sections∗ Beam Sections

Ieff

Rectangular

0.5 Ig

T - section

0.7 Ig

L - section

0.6 Ig

Here, the gross section moment of inertia (Ig) should be calculated considering the rectangular area only as shown in Figure 3.1.

In the case of columns, the

reduction in stiffness due to cracking is reduced by the presence of axial compression. The suggested moment of inertia for column is: Ieff ≡ 0.7 Ig

T-Beam

L-Beam

Figure 3.1: Rectangular area for the calculation of Ig

Total Length Clear Length Beam

End Offsets Column

Figure 3.2: Use of end offsets at beam-column joint

∗

Factors recommended here are adapted from Paulay and Priestley (1991)

38


3.2.2.2

Beam-column joints

The beam-column joints should be modelled by giving end-offsets to the frame elements, to obtain the moments and forces at the beam and column faces. The beam-column joints can be assumed to be rigid (Figure 3.2).

3.2.2.3

Slabs

The slabs need not be modelled by plate elements to simplify modelling. The structural effect of slabs due to their in-plane stiffness can be taken into account by assigning ‘diaphragm’ action at each floor level. The weight of a slab can be modelled separately as triangular and trapezoidal loads on the supporting beams. In case of large openings or projections in slabs, different portions of the floor may have differential translations, and in such cases, diaphragm action should be assigned separately to the different sections.

3.2.2.4

Appendages

The effects of all significant appendages (for example, water tanks, stairways, cantilever slabs) should be included in the model. Stairway slabs can be modelled as inclined equivalent frame elements, with hinges at the ends. For water tanks and cantilever slabs, the masses are lumped on the supporting elements.

3.2.2.5

Walls (structural and non structural)

Structural walls such as shear walls and walls in building core, which are integrally connected to the floor slabs, can be modelled using equivalent wide column elements. The ‘master’ node of the column element can be at the centre of gravity of the shear wall or core and it should be connected to the ‘slave’ nodes of the adjacent beams by rigid links (Figure 3.3). Non-structural walls such as infill walls have weight and in-plane stiffness. They influence the behaviour of the building under lateral load. The weight of an infill wall should be incorporated

39


separately as a uniform load on the supporting beam. The stiffness contribution of an infill wall can be modelled using a simplified ‘equivalent strut’ approach. Calculation of the properties of the equivalent strut is explained in Appendix B.

When the stiffness contribution of the infill walls is included, the natural period of the building is reduced and the base shear increases. But, the moments in the beams and columns may reduce due to the ‘truss’ action of the equivalent struts. During an earthquake, the infill walls may fail due to out-of-plane bending. This will increase the moments in the beams and columns. To calculate the demands in the beams and columns, two extreme cases can be modelled. In the first model, the lateral stiffness due to the significant infill walls is modelled by the equivalent struts. In the second model, the stiffness is ignored. However, the weight of the infill walls on the supporting beams should be considered in both the models.

(a) Shear Wall

Beam Rigid Links

Master Node

Slave Node (b) Core Wall Figure 3.3: Modelling of shear wall and core wall

40


3.2.3

Modelling of Column Ends at foundation

The column end at foundation can be modelled by considering the degree of fixity provided by the foundation. Depending on the type of footing the end condition may be modelled as follows: i)

Isolated footing: A hinge is to be provided at the column end at the bottom

of the foundation. However, when it is founded on hard rock, the column end may be modelled as fixed, with the level of fixity at the top of the footing. ii)

Raft foundation: The column ends are to be modelled as fixed at the top of

the raft. iii)

Combined footing: Engineering judgement must be exercised in modelling

the fixity provided by the combined footings.

If the footings are

adequately restrained by tie beams, the column ends can be modelled as fixed. iv)

Single pile: Fixity of column is recommended at a depth of five to ten

times the diameter of pile, depending upon the type of soil, from the top of pile cap. v)

Multiple piles: Assume fixity of column at top of the pile cap.

3.2.4

Load Combinations

The analysis results are to be for the following load combinations (IS 1893: 2002): COMB1 = 1.5(DL+IL) COMB2 = 1.2(DL+IL+EL) COMB3 = 1.2(DL+IL − EL) COMB4 = 1.5(DL+EL) COMB5 = 1.5(DL − EL) COMB6 = 0.9DL+1.5EL COMB7 = 0.9DL − 1.5EL

41


Here, DL ≡ Dead load, IL ≡ Live load, and EL ≡ Earthquake Load. The dead load and the live load are taken as per IS 875, 1987. When the lateral load resisting elements are not orthogonally oriented, the design forces along two horizontal orthogonal directions (X- and Y-) should be considered. One method to consider this is the following. (a)

100% of the design forces in X-direction and 30% of the design forces in Ydirection.

(b)

100% of the design forces in Y-direction and 30% of the design forces in Xdirection.

An alternative method to consider the effect of the forces along X- and Ydirections is the square root of the sum of the squares (SRSS) basis. EL = ELx 2 + ELy 2

(3.2)

The vertical component is considered only for special elements like horizontal cantilevers in Zones IV and V. The maximum value of a response quantity from the above load combinations gives the demand.

3.3

LINEAR ANALYSIS METHODS

The two different linear analysis methods recommended in IS 1893: 2002 are explained in this Section. Any one of these methods can be used to calculate the expected seismic demands on the lateral load resisting elements.

3.3.1

Equivalent static method

In the equivalent static method, the lateral force equivalent to the design basis earthquake is applied statically. The equivalent lateral forces at each storey level are applied at the design ‘centre of mass’ locations. It is located at the design eccentricity from the calculated ‘centre of rigidity (or stiffness)’.

42


Centre of mass

3.3.1.1

The centre of mass is the point where the total mass of the floor level is assumed to be lumped. The centre of mass can be calculated for each floor by taking moments of the axial forces (from gravity load analysis of that floor only) in the columns about an assumed reference axis. CMx

=∑

Wi xi

∑W

;

CMy = ∑

Wi yi

∑W

i

(3.3)

i

where CMx

≡ coordinate of the centre of mass along x-direction

CMy

≡ coordinate of the centre of mass along y-direction

∑W

≡ sum of the weights of all components

i

∑W x ≡ sum of the moments of weights about an assumed reference axis along i i

X- direction

∑W y i

i

≡ sum of the moments of weights about an assumed reference axis along

Y-direction

3.3.1.2

Centre of rigidity of storey

The centre of rigidity is the point through which the resultant of the restoring forces in a storey acts. The centre of rigidity for each storey should be found out separately. There are different procedures to calculate the centre of rigidity. One of the procedures is explained below.

The columns of the storey are assumed to be fixed at the bottom. A unit force along X-direction and a unit moment about Z- axis (vertical axis) are applied at a certain test point in the top of the storey and the corresponding rotations are noted down. The distance of the centre of rigidity from the test point, along Y- direction, is calculated from the ratio of the two rotations. Similarly the distance along Xdirection is found out by applying a unit force along Y- direction and a unit moment.

43


Let the co-ordinates of the test point be (x, y). Let (θz)x, (θz)y and (θz)z be the rotations about the Z-axis for the unit loads along X- and Y- directions and unit moment about Z-axis, respectively. The co-ordinates of the centre of rigidity is given as CRx,= x+x1, CRy = y+y1, where x1 = -(θz)x/(θz)z

(3.4a)

y1 = (θz)x/(θz)z

(3.4b)

The static eccentricity of the centre of mass with respect of centre of rigidity is given as follows.

3.3.1.3

esix = CMx−CRx

(3.5a)

esiy = CMy−CRy

(3.5b)

Effect of torsion

The design eccentricity of the centre of mass (edix, ediy) is calculated considering a dynamic amplification factor and an additional eccentricity of 5% of the dimension of the building perpendicular to the direction of the seismic force. For either of X- or Y- directions, edi = 1.5esi + 0.05bi

(3.6a)

or, edi = esi − 0.05bi

(3.6b)

There can be four possible locations of the design centre of mass. To reduce computation, only two diagonal locations can be considered.

3.3.1.4

Seismic weight

The seismic weight of each floor of the structure includes the dead load and fraction of the live load (as per Table 8 of IS 1893: 2002) acting on the floor. The weight of the columns and walls (up to the tributary height) are to be included. The tributary height is between the centreline of the storey above and centre line of the storey below.

44


3.3.1.5

Lumped mass

The lumped mass is the total mass of each floor that is lumped at the design centre of mass of the respective floor. The total mass of a floor is obtained from the seismic weight of that floor.

3.3.1.6

Calculation of lateral forces

The base shear (V = VB) is calculated as per Clause 7.5.3 of IS 1893: 2002. VB = AhW

(3.7)

⎛ Z ⎞ I Sa Ah = ⎜ ⎟ ⎝2⎠ R g

(3.8)

where W ≡ seismic weight of the building, Z ≡ zone factor, I ≡ importance factor, R ≡ response reduction factor, Sa /g ≡ spectral acceleration coefficient determined

from Figure 3.4, corresponding to an approximate time period (Ta) which is given by

Ta = 0.075h0.75 for RC moment resisting frame without masonry infill Ta =

0.09h for RC moment resisting frame with masonry infill d

(3.9a) (3.9b)

The base dimension of the building at the plinth level along the direction of lateral forces is represented as d (in metres) and height of the building from the support is represented as h (in metres). The response spectra functions can be calculated as follows:

For Type I soil (rock or hard soil sites):

⎧ ⎪1 + 15T 0.00 ≤ T ≤ 0.10 Sa ⎪ 0.10 ≤ T ≤ 0.40 = ⎨2.50 g ⎪ 1 ⎪ 0.40 ≤ T ≤ 4.00 ⎩T

For Type II soil (medium soil):

⎧ ⎪1 + 15T 0.00 ≤ T ≤ 0.10 Sa ⎪ 0.10 ≤ T ≤ 0.55 = ⎨2.50 g ⎪ 1.36 ⎪ 0.55 ≤ T ≤ 4.00 ⎩ T

45


⎧ ⎪1 + 15T 0.00 ≤ T ≤ 0.10 Sa ⎪ 0.10 ≤ T ≤ 0.67 = ⎨2.50 g ⎪ 1.67 ⎪ 0.67 ≤ T ≤ 4.00 ⎩ T

For Type III soil (soft soil):

Spctral Acceleraion Coefficient (S a/g)

3.0 2.5

Type III (Soft Soil) Type II (Medium Soil)

2.0

Type I (Rock,or Hard Soil) 1.5 1.0 0.5 0.0 0.0

1.0

2.0

3.0

4.0

Period (s)

Figure 3.4: Response spectra for 5 percent damping (IS 1893: 2002) W3

W2 h3 W1

h2 h1

Figure 3.5: Building model under seismic load

46


The design base shear is to be distributed along the height of building as per Clause 7.7.1 of IS 1893: 2002. The design lateral force at floor i is given as follows Qi = VB

Wi hi2

(3.10)

n

∑W h j =1

2 i i

Here Wi ≡ Seismic weight of floor i, hi ≡ Height of floor measured from base, n ≡ Number of storeys in the building equal to the number of levels at which masses is located (Figure 3.5).

3.3.2

Response spectrum analysis

The equations of motion associated with the response of a structure to ground motion are given by: (t ) + Cu (t ) + Ku(t ) = m x ugx (t ) + m x ugy (t ) + m x ugz (t ) Mu

(3.11)

Here, M is the diagonal mass matrix, C is the proportional damping matrix, K is the stiffness matrix, u , u and u are the relative (with respect to the ground) acceleration, velocity and displacement vectors, respectively, mx, my, and mz are the unit acceleration loads and ugx , ugy and ugz are the components of uniform ground acceleration.

The objective of response spectrum analysis is to obtain the likely maximum response from these equations. The earthquake ground acceleration in each direction is given as a response spectrum curve*. According to IS 1893: 2002, high rise and irregular buildings must be analysed by the response spectrum method. However, this method of linear dynamic analysis is also recommended for regular buildings.

*

The response spectrum is a plot of the maximum response (maximum displacement, velocity, acceleration or any other quantity of interest) to a specified load function for all possible single degree-of-freedom systems. The abscissa of the spectrum is the natural period (or frequency) of the system and the ordinate is the maximum response. It is also a function of damping. Figure 3.3 shows the design response spectra given in IS 1893: 2002 for a 5% damped system.

47


Response spectrum analysis is performed using mode superposition, where free vibration modes are computed using eigenvalue analysis. The maximum modal response (λk) of a quantity (considering the mass participation factor) is obtained for each mode of all the modes considered. Sufficient modes (r) to capture at least 90% of the participating mass of the building (in each of the orthogonal horizontal directions), have to be considered in the analysis. The modal responses of all the individual modes are then combined together using either the square root of the sum of the squares (SRSS) method or complete quadratic combination (CQC) method. The SRSS method is based on probability theory and is expressed as follows. λ=

r

∑ (λ k =1

k

)2

(3.12)

If the building has very closely spaced modes then the CQC method is preferable.

The base shear is calculated for response spectrum analysis in the following manner. The Sa/g value corresponding to each period of all the considered modes is first calculated from Figure 3.4. The base shear corresponding to a mode is then calculated as per Section 3.3.1.5.

Each base shear is multiplied with the

corresponding mass participation factor and then combined as per the selected mode combination method, to get the total base shear of the building. If the base shear calculated from the response spectrum analysis (VB ) is less than the design base shear (VB ) calculated from Equation 3.7, then as per IS 1893: 2002, all the response quantities (member forces, displacements, storey shears and base reactions) have to be scaled up by the factor VB / VB .

3.4

EVALUATION RESULTS

The demands (moments, shears and axial forces) obtained at the critical sections from the linear analyses are compared with the capacities of the individual

48


elements. The capacities of RC members are to be calculated as per IS 456: 2000, incorporating the appropriate “knowledge factors” (Table 3.2). The demand-tocapacity ratio (DCR) for each element should be less than 1.0 for code compliance.

DCR = AB/AC Pu

B C

A

Muy

Mux

Figure 3.6: Demand to capacity ratio for column flexure

For a beam, positive and negative bending moment demands at the face of the supports and the positive moment demands at the span need to be compared with the corresponding capacities. For a column, the moment demand due to bi-axial bending under axial compression must be checked using the P-Mx-My surface (interaction surface), generated according to IS 456: 2000. The demand point is to be located in the P-Mx-My space and a straight line is drawn joining the demand point to the origin. This line (extended, if necessary) will intersect the interaction surface at the capacity point. The ratio of the distance of the demand point (from the origin) to the distance of the capacity point (from the origin) is termed as the DCR for the column (Figure 3.6).

49


wu = 1.2 (wDL + wLL)

ln

EL

1.4 M+uR, left 1.4 M –uR, right plastic hinge

1.4 M –uR, left

EL

1.4 M +uR, right plastic hinge

(a) Loading on beam 1.4(M+uR, left + M –uR, right)/ln

0.5 wu ln 0.5 wu ln

(b) Shear force demand in beam (sway to right) 1.4(M –uR, left + M +uR, right)/ln 0.5 wu ln 0.5 wu ln

(c) Shear force demand in beam (sway to left)

Figure 3.7: Calculation of shear force demand in beams

The shear demand should be calculated as per IS 13920: 1993 recommendations. For beam, the shear demand will be the larger of the shear force from analysis and the shear force corresponding to the beam reaching its flexural capacity (formation of moment hinges at both ends of the beam). This concept is called the capacity based design.

50


The shear demands (Vu) at the support faces (left or right) are obtained as follows (Clause 6.3.3, IS 13920: 1993). Vu , left = 0.5wu ln + 1.4 ( M uR− ,left + M uR+ ,right ) ln

(3.13a)

Vu , right = 0.5wu ln + 1.4 ( M uR+ ,left + M uR− ,right ) ln

(3.13b)

Here, ln is the clear span, and wu is the factored load as shown in the Figure 3.7. The factor 1.4 is intended to account for the higher flexural capacity than the calculated value. The flexural capacity is higher because the actual yield strength of the steel is higher than the characteristic strength and the steel undergoes strain hardening.

Similarly for the columns, the shear demand should be calculated as the larger of the shear force from analysis and the shear force in the column corresponding to the beams (framing into the column) reaching their flexural capacities. The shear demand (Vu) is given by the following expression (Clause 7.3.4, IS 13920: 1993). Vu = 1.4 ( M uR ,b1 + M uR ,b 2 ) hst

(3.14)

Here, MuR, b1 and MuR, b2 are the factored moments of resistance of beam ends ‘1’ and ‘2’ framing into the column from opposite faces, and hst is the storey height (Figure 3.8).

The shear demands for beams and columns should be checked with the corresponding shear capacities. The shear capacities for beams and columns can be calculated using the procedure outlined in Appendix C.

The axial force demands for the ‘equivalent struts’ should be compared with their capacities. The capacity of the equivalent strut can be calculated according to Appendix B.

The storey drift for every storey due to the design lateral force, with partial load factor of 1.0, should satisfy the limitation of 0.4% of the storey height (Clause 7.11.1, IS 1893: 2002).

51


Vu 1.4MuR, b2 hst 1.4MuR, b1 Vu

Figure 3.8: Shear force demand in columns

52


CHAPTER IV EVALUATION BASED ON NONLINEAR PUSHOVER ANALYSIS

4.1.

INTRODUCTION

Pushover analysis is a static, nonlinear procedure in which the magnitude of the lateral loads is incrementally increased, maintaining a predefined distribution pattern along the height of the building. With the increase in the magnitude of the loads, weak links and failure modes of the building are found.

Base Shear (V)

∆

Base Shear (V) Roof Displacement (∆) a) Building model

b) Pushover curve

Figure 4.1: Pushover analysis

53


Pushover analysis can determine the behaviour of a building, including the ultimate load and the maximum inelastic deflection. Local nonlinear effects are modelled and the structure is pushed until a collapse mechanism is developed (Figure 4.1). At each step, the base shear and the roof displacement can be plotted to generate the pushover curve. It gives an idea of the maximum base shear that the structure is capable of resisting. For regular buildings, it can also give a rough idea about the global stiffness of the building.

4.2

CAPACITY SPECTRUM, DEMAND SPECTRUM AND PERFORMANCE POINT

Instead of plotting the base shear versus roof displacement, the base acceleration can be plotted with respect to the roof displacement (capacity spectrum) (Figure 4.2). The spectral acceleration and spectral displacement, as calculated from the linear elastic response spectrum for a certain damping (initial value 5%), is plotted in the Acceleration Displacement Response Spectrum (ADRS) format. With increasing non-linear deformation of the components, the equivalent damping and the natural period increase.

The spectral acceleration and

displacement values can be modified from the 5% damping curve by multiplying a factor corresponding to the effective damping (Table 3, IS 1893: 2002). Thus, the instantaneous spectral acceleration and displacement point (demand point) shifts to a different response spectrum for higher damping. The locus of the demand points in the ADRS plot is referred to as the demand spectrum. The demand spectrum corresponds to the inelastic deformation of the building. The ‘performance point’ is the point where the capacity curve crosses the demand curves. If the performance point exists and the damage state at this point is acceptable, the structure satisfies the target performance level.

54

Chapter IV – Evaluation based on Non-Linear Push-Over Analysis

Spectral Acceleration

Initial Structural Period

5% Damping (Initial) 10% Damping

Performance Point

15% Damping

Capacity Spectrum

Demand Spectrum

Spectral Displacement

Figure 4.2: Demand and capacity spectra It must be emphasised that the pushover analysis is approximate in nature and is based on a statically applied load. It estimates an envelope curve of the behaviour under the dynamic load. It must be used with caution while interpreting the actual behaviour under seismic load.

4.3.

PUSHOVER ANALYSIS PROCEDURE

Pushover analysis involves the application of increasing lateral forces or displacements to a nonlinear mathematical model of a building. The nonlinear load-deformation behaviour of each component of the building is modelled individually. In a force-controlled push, the forces are increased monotonically until either the total force reaches a target value or the building has a collapse mechanism. In a displacement-controlled push, the displacements are increased monotonically until either the displacement of a predefined control node in the building exceeds a target value or the building has a collapse mechanism. For

55


convenience, the control node can be taken at the design centre of mass of the roof of the building. The target displacement is intended to represent the maximum displacement likely to be experienced during the earthquake. Initially, the gravity loads are applied in a force-controlled manner till the total load reaches the target value. The target value can be same as the design gravity load for the linear analysis. Next, the lateral loads are applied in the X- or Ydirection, in a displacement controlled manner. The direction of monitoring of the behaviour is same as the push direction. The effect of torsion can be considered. As the displacement is increased, some beams, columns and ‘equivalent struts’ may undergo in-elastic deformation.

The non-linear in-elastic behaviour in

flexure, shear or axial compression is modelled through assigning appropriate loaddeformation properties at potential plastic hinge locations. The development of the load-deformation properties is explained in Appendices C, D and E.

4.3.1

Seismic Load Distribution

Pushover analysis requires the seismic load distribution with which the structure will be displaced incrementally. Frequently, an inverted triangular shape or the first mode shape is used. The importance of the load distribution increases for tall buildings, whose earthquake response is not dominated by a single mode shape. For such buildings, the load distribution based on the first mode shape may seriously underestimate the loads on the intermediate floor levels. This manual recommends the load distribution pattern given in IS 1893: 2002 for low to midrise buildings (Equation 3.10). Pushover analysis should be performed separately for the two orthogonal directions in order to study the performance of the building in both the directions. There are therefore three pushover cases for evaluating a building. 1. Gravity push, which is used to apply gravity load. 2. Push1 is the lateral push in X-direction, starting at the end of gravity push. 3. Push2 is the lateral push in Y-direction, starting at the end of gravity push.

56


4.3.2 Load-Deformation Behaviour of Elements In pushover analysis, it is necessary to model the non-linear load-deformation behaviour of the elements.

Beams and columns should have moment versus

rotation and shear force versus shear deformation hinges.

For columns, the

rotation of the moment hinge can be calculated for the axial load available from the gravity load analysis. All compression struts have to be modelled with axial load versus axial deformation hinges. There are two approaches for specifying the hinge properties. (i)

Distributed plasticity model

(ii)

Point plasticity model.

In the first model, the zone of yielding (plastification) is assumed to be spread over a certain length (‘length of the plastic hinge’). In the second model, the zone of yielding is assumed to be concentrated at a specific point in the element. The calculation of the various hinge properties based on the point plasticity model is explained in Appendix C. An idealised load-deformation curve is shown in Figure 4.3. It is a piece-wise linear curve defined by five points as explained below. (i)

Point ‘A’ corresponds to the unloaded condition.

(ii)

Point ‘B’ corresponds to the onset of yielding.

(iii)

Point ‘C’ corresponds to the ultimate strength.

(iv)

Point ‘D’ corresponds to the residual strength. For the computational stability, it is recommended to specify non-zero residual strength.

In

absence of the modelling of the descending branch of a load-deformation curve, the residual strength can be assumed to be 20% of the yield strength. (v)

Point ‘E’ corresponds to the maximum deformation capacity with the residual strength. To maintain computational stability, a high value of

57


deformation capacity equal to 15∆y can be assumed, where ∆y is the deformation at the onset of yielding.

4.4

PERFORMANCE BASED ANALYSIS

The traditional approach to seismic design of a building is a force-based design. The design lateral forces on the building are determined using the response spectrum. The building is subsequently analysed to determine the member forces. The members are designed to withstand those forces. In this approach, there is no measure of the deformation capability of a member or of the building. At best, an elastic drift is computed under the design forces and checked against an elastic drift limit. Alternatively, an inelastic drift is estimated from the calculated elastic drift by multiplying the later by a factor and checking the inelastic drift against an inelastic drift limit. The performance based analysis is based on quantifying the deformations of the members and the building as a whole, under the lateral forces of an earthquake of a certain level of seismic hazard. The deformations or strains are better quantities to assess damage than stresses or forces. Since the deformations are expected to go beyond the elastic values, a performance-based analysis requires a nonlinear lateral load versus deformation analysis. The performance based analysis gives the analyst more choices of ‘performance’ of the building as compared to the limit states of collapse and serviceability in a design based on limit state method.

4.4.1

Performance Objective

The seismic performance of a building is measured by the state of damage under a certain level of seismic hazard. The state of damage is quantified by the drift of the roof and the deformation of the structural elements. Before the analysis of a building, a target performance level of the building and a level of seismic hazard are selected.

A performance objective of an analysis constitutes the target

58


building performance level under the selected level of seismic hazard.

The

selection of the two levels is based on recommended guidelines for the type of the building, economic considerations and engineering judgment. The purpose of developing a performance objective is to have a uniform risk in similar buildings.

4.4.2 Performance Levels of Structure and Elements A building performance level is a combination of the performance levels of the structure and the non-structural components. The performance levels are discrete damage states identified from a continuous spectrum of possible damage states. The structural performance levels are as follows. i)

Immediate Occupancy (IO)

ii)

Life Safety (LS)

iii)

Collapse Prevention (CP).

The three levels are arranged according to decreasing performance of the lateral load and vertical load resisting systems. A target performance is defined by a typical value of the roof drift, as well as limiting values of the deformation of the structural elements.

To determine whether a building meets a specified

performance objective, response quantities from the pushover analysis should be compared with the limits for each of the performance level. Typical values of roof drifts for the three performance levels are as follows (FEMA 356). i)

Immediate Occupancy: Transient drift is about 1% with negligible permanent drift.

ii)

Life Safety: Transient drift is about 2% with 1% permanent drift.

iii)

Collapse Prevention: 4% inelastic drift, transient or permanent.

The performance levels of a structural element are specified in the loaddeformation curve (Figure 4.3). The values of the levels can be obtained from test results. In absence of test data, the following values may be adopted (ATC 40).

59


i)

Immediate Occupancy: 0.2∆ from Point B

ii)

Life Safety: 0.5∆ from Point B.

iii)

Collapse Prevention: 0.9∆ from Point B.

Here, ∆ is the length of the plastic plateau. The above recommendation is shown in Fig. 4.3.

IO

Load

Py

CP

LS

B 0.2∆ 0.5∆ 0.9∆ ∆ ∆

0.2Py

D

E

A

Deformation Figure 4.3: Performance Level 4.4.3 Seismic Hazard Levels

In a probabilistic method, an earthquake level is defined with a probability of exceedance in a specified period.

The following three levels are commonly

defined for buildings with a design life of 50 years (FEMA 356). i)

Serviceability earthquake: 50% probability of exceedance in 50 years.

ii)

Design basis earthquake (DBE): 10% probability of exceedance in 50 years.

iii)

Maximum considered earthquake (MCE): 2% probability of exceedance in 50 years.

In IS 1893: 2002, the zone factor Z corresponds to MCE. The values of Z were evaluated based on a deterministic method. It cannot be directly related to the definitions given above. A simplistic method was adopted to define the DBE. The

60


DBE is defined as ½ MCE and hence, Z/2 is substituted in place of Z. A partial load factor of 1.5 is applied to DBE in the load combinations.

4.4.4 Selection of Performance Objective

A performance objective of an analysis is the selection of a building performance level under a selected earthquake level. If the objective includes two building performance levels under two earthquake levels, then it is a dual level performance objective.

Similarly, there can be multiple level performance

objectives. A basic safety objective (BSO) is defined as the dual requirement of Life Safety under DBE and Collapse Prevention under MCE. The aim of BSO is to have a low risk of life threatening injury during a moderate earthquake (as defined by DBE) and to check the collapse of the vertical load resisting system during a severe earthquake (as defined by MCE). For analysis of multi-storeyed buildings in India, Collapse Prevention under MCE can be selected. It is a partial performance objective as per FEMA 356. Unless the earthquake level of DBE as per IS 1893: 2002 is comparable to the level defined based on the probabilistic method, it is not prudent to check Life Safety under DBE. Of course checking only one performance level will not meet the damage control requirement for frequent earthquakes.

4.5

EVALUATION RESULTS

The output from the pushover analysis contains the pushover curve, the demand and capacity spectra curves and their tabulated values. The pushover curve reveals the base shear capacity and the inelastic roof displacement. A global ductility can be calculated as the ratio of the roof displacement at ultimate base shear to the roof displacement at the onset of yielding. From the demand and capacity spectra curves, the existence of the performance point can be noted. If the performance point does not exist, the structure fails to achieve the target performance level. If

61


the performance point is achieved at a roof drift which is substantially higher than the typical value of the selected performance level, then the performance of the building is unsatisfactory. The other results of interest from the pushover analysis are the deflected shape, the formation of hinges with increasing load and the performance levels of the hinges at the performance point (if exists). The deflected shape and the concentration of hinges in a storey can reveal a soft storey mechanism. The collapse of a building is not physically shown in the deflected shape. From the displacement values of the centres of mass of the storeys, the inelastic drift profile can be plotted. This can also reveal a soft storey mechanism. The number of hinges formed in the beams and columns at the performance point (or at the point of termination of the pushover analysis) and their performance levels can be used to study the vulnerability of the building. The vulnerability can be quantified using the concept of ‘vulnerability index’. Appendix D explains the calculation of ‘vulnerability index’.

62


CHAPTER V SEISMIC RETROFIT

5.1

INTRODUCTION

The strengthening and enhancement of the performance of deficient structural elements in a structure or the structure as a whole is referred to as retrofitting. Retrofitting of a building is not same as repair or rehabilitation. Repair refers to partial improvement of the degraded strength of a building after an earthquake. In effect, it is only a cosmetic enhancement.

Rehabilitation is a functional

improvement, wherein the aim is to achieve the original strength of a building after an earthquake. Retrofitting means structural strengthening of a building to a pre-defined performance level, whether or not an earthquake has occurred. The seismic performance of a retrofitted building is aimed higher than that of the original building. The present report does not cover the repair techniques for a damaged building or distressed elements.

A survey of existing residential buildings reveals that many buildings are not adequately designed to resist earthquakes. In the recent revision of the Indian earthquake code (IS 1893: 2002), many regions of the country were placed in higher seismic zones. As a result many buildings designed prior to the revision of the code may fail to perform adequately as per the new code. It is therefore

63


recommended that the existing deficient buildings be retrofitted to improve their performance in the event of an earthquake and to avoid large-scale damage to life and property.

5.2

GOALS OF RETROFIT

The goals of seismic retrofitting of a building can be summarized as follows (IS 13935: 1993; White, 1995). 1. Giving unity to the structure. 2. Eliminating sources of weakness or features that produce concentration of stresses in members. 3. Enhancing the redundancy of the lateral load resisting systems, thereby eliminating the possibility of progressive collapse. 4. Increasing the lateral strength and stiffness of the building. 5. Increasing the ductility (energy absorption) and damping (energy dissipation). Avoiding the possibility of brittle modes of failure. 6. The retrofit scheme should be cost effective, should consistently and reliably achieve the intended performance objective.

5.3

DEFINITIONS

i)

Retrofit strategy

The options available for retrofitting individual elements or the building as a whole is termed as retrofit strategies.

ii)

Retrofit scheme

A combination of several retrofit strategies is termed as a retrofit scheme for a building.

64

Chapter V – Seismic Retrofit

iii)

Retrofit programme

The complete process involved in retrofit of a building is termed as a retrofit programme.

5.4

STEPS OF RETROFIT

A retrofit programme consists of the following steps (Basu, 2002). i)

Seismic evaluation

The evaluation of a building involves data collection, visual inspection, in-situ testing, examination of as-built information and structural analysis. The structural analysis can be linear static (equivalent static method), linear dynamic (response spectrum analysis or time-history analysis), nonlinear static (pushover analysis) and nonlinear dynamic (nonlinear time-history analysis).

If the demand-to-

capacity ratios of the components are greater than one or if the building fails to achieve the target performance level, then retrofit becomes necessary.

ii)

Decision to retrofit

Based on the extent of deficiency of the building, the economic viability, the expected durability of the upgraded building and the availability of the materials, a decision is taken whether to repair, retrofit or demolish the building.

iii)

Selection and design of the retrofit scheme

The selection of the retrofit strategies from the options available and their design, influence the decision to retrofit. Hence, knowledge of the retrofit strategies is essential. The design and the detailing should address the transfer of load and the compatibility of deformation between the existing elements, modified elements and the new elements as per the assumptions in the analysis.

iv)

Verification of the retrofit scheme

Structural analysis is necessary to justify the selected retrofit scheme. Alteration of the load path, redistribution of the member forces and the changes in the failure

65


modes after retrofitting, need to be studied. The increase in strength at the cost of a ductile failure mode changing to brittle is not desirable. The selection and design of the retrofit scheme may need to be revised accordingly.

v)

Construction

The effectiveness of the retrofit scheme greatly depends on the quality of execution.

Hence, the proper execution as per the suggested detailing and

specifications is imperative.

vi)

Monitoring

Monitoring the performance of the retrofitted building is necessary to detect any defect or remaining deficiency. This will lead to a refinement of the design guidelines and the specifications for future retrofit projects.

5.5

PERFORMANCE OBJECTIVES

For seismic retrofit of buildings, a performance-based analysis is preferred whenever the necessary tools for the analysis are available. The decision to retrofit and the choice of retrofit strategies are open-ended tasks, as compared to seismic design of a new building. The performance-based analysis is a rational method that aids the decision-making and selection of retrofit strategies in a retrofit programme of a building.

The definitions of performance levels are

explained in Chapter 4.

A performance objective in a performance-based analysis is the selection of a building performance level under a selected earthquake level. The selection of a performance objective in a retrofit programme is guided by the benefit from improved safety, economic decisions, available technical expertise, inconvenience during the intervention and other considerations. Depending upon the importance of the structure, the building performance levels and earthquake levels are chosen. For example, hospital buildings, relief and rescue centres, police stations, fire

66


stations etc. should be functional immediately after an earthquake. For retrofit of multi-storeyed buildings in India, Collapse Prevention (CP) under maximum credible earthquake (MCE) can be selected, as explained in Chapter 4.

A structure with a trial retrofit scheme needs to be re-analysed to check its performance. If a performance point is achieved satisfying the above objective, then the retrofit scheme is satisfactory. But for severely deficient structure a performance point may not be achieved with an acceptable retrofit scheme. There may be partial increase in strength and ductility. This can be accepted as a reduced performance objective as compared to the basic safety objective.

5.6

RETROFIT STRATEGIES

Retrofit strategy refers to options of increasing the strength, stiffness and/or ductility of the elements or of the whole building. For a building, a combination of retrofit strategies may be selected under a retrofit scheme. Retrofit strategies may be broadly classified as local strategies and global strategies. Retrofit of individual members or elements is referred to as local retrofit, whereas the retrofit of the building as a whole is termed as global retrofit. This classification need not be watertight and strategies falling in either group are expected.

It may be

necessary to combine both local and global retrofit strategies for an effective retrofit scheme.

5.6.1 Global Strategies

The global retrofit strategies are applied to improve the overall behaviour of a building. If a building has inadequate strength to resist lateral forces, it exhibits inelastic behaviour at very low levels of ground shaking. Analysis of such a building indicates large demand-to-capacity ratios in the components throughout the structure. By providing supplemental elements to the building’s lateral force resisting system, it is possible to raise the threshold of ground motion at which the

67


onset of damage occurs. Addition of shear walls and braced frames, for example, is effective for this purpose.

Reduction of plan and vertical irregularities,

reduction of mass and improving the connections between the elements are other global retrofit strategies.

In buildings with a large number of deficiencies, it is usually more economical to try a global retrofit strategy first and then if further strengthening becomes necessary, local retrofit strategies can be adopted.

5.6.2 Local Strategies

Local strengthening allows the under-capacity elements or connections to resist the demands predicted by the analysis, without significantly affecting the overall response of the structure. This scheme tends to be economical when only a few of the building’s elements are deficient. The local retrofit strategies discussed here include strengthening of beams, columns, joints, walls and footings.

5.6.3 Energy Dissipation and Base Isolation

A number of technologies are available to allow the energy imparted to a structure to be dissipated through the action of special devices such as viscous fluid dampers, yielding plates or friction pads. These are called energy dissipation devices.

Base isolation produces a system with a fundamental response that consists of nearly a rigid body translation of the structure above the bearings. Most of the displacement induced in the isolated system by the ground motion occurs within the compliant bearings, which are specifically designed for the large displacements.

Most bearings also have excellent energy dissipation

characteristics.

68


The cost of energy dissipation and base isolation systems is high and at present their use is limited to important structures like hospitals and monumental structures in India. These devices are not covered in this manual.

5.6.4

Mitigating Geological Hazards

Some of the geological hazards are fault rupture, liquefaction, differential compaction, landslide and earthquake induced tsunamis or flood. Mitigation of geological hazards generally is expensive. Some schemes for the mitigation of these hazards are described in FEMA 356 (2000).

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CHAPTER VI BUILDING DEFICIENCIES

6.1

INTRODUCTION

Seismic retrofit of an existing building most often is more challenging than designing a new one. The first step of seismic evaluation aims at detecting the deficiencies of the building. It is a crucial step in a successful retrofit programme and is analogous to the diagnosis of a patient. This chapter highlights some common deficiencies observed in multi-storeyed reinforced concrete (RC) framed buildings in India. Substantial part of the material is from the buildings evaluated under the project “Seismic Evaluation and Retrofit of Existing Multi-storeyed Buildings” and from reports on Bhuj earthquake (Sinha and Shaw, 2001; Murty et al., 2002). The regional distribution of the buildings studied is shown in Figure 6.1. Although the observations were made in the buildings studied, similar construction practices are noticed in other parts of the country. The building deficiencies can be broadly classified as Local Deficiencies and Global Deficiencies.

70


Delhi Guwahati

Ahmedabad Mumbai

Vellore

Chennai

Trivandrum

Figure 6.1: Regions where buildings were surveyed

6.2

GLOBAL DEFICIENCIES

Global deficiencies refer to the deficiencies of the building as a whole. Certain structural design concepts that may work adequately in non-seismic areas perform poorly when subjected to earthquake motions. Examples are frame structures with strong beams and weak columns, or frame structures employing open ground storeys. For either case, a single storey sway mechanism can develop under lateral loading. Global deficiencies can broadly be classified as plan irregularities and vertical irregularities, as per IS 1893 (Part I): 2002. The items left out are listed under miscellaneous deficiencies.

72

Chapter VI – Building Deficiencies

6.2.1 Plan Irregularities Some of the observed plan irregularities are as follows. a. Torsional Irregularity Torsional irregularity is to be checked when the diaphragm is rigid. Torsional irregularity arises due to the eccentricity between the centre of stiffness and centre of mass of each floor.

Poor layout of structural walls leads to significant

eccentricity. Even for a symmetric building, if the aspect ratio of length to width is large, there can be torsional irregularity. Under lateral loads, the torsional response modes will dominate, and large displacement demands will be placed on the vertical elements farthest from the centre of rigidity, for example the corner columns. The large cyclic motions would typically put reversed biaxial displacement demands on these columns. Even well detailed columns will typically fail under such extreme loading conditions. Eccentric mass, for example due to overhead tanks or swimming pools, aggravates the torsional irregularity.

Figure 6.2: A building with diaphragm discontinuity and re-entrant corners

73


b. Re-entrant Corners To accommodate multiple dwelling units in one level and to have large number of windows, re-entrant corners are frequently seen in apartment buildings (Figure 6.2). The layouts with re-entrant corners result in high demands in the corner columns and in the corners of the diaphragms. c. Diaphragm Discontinuity Diaphragm discontinuity is observed when a stair case or a lift well is located at the middle of the building. The connection of the two halves of the diaphragms is inadequate (Figure 6.2). Staggered floors with absence of collector elements also cause diaphragm discontinuity.

Figure 6.3: Examples of plan and vertical irregularities

74


d. Out-of-Plane Offset Out-of-plane offsets of the lateral force resisting elements cause discontinuities in the load path. Often columns in the ground storey are set back from the columns above to reduce the built-up area (Figure 6.3). The floating columns above the ground storey are supported on transfer cantilever beams. This leads to out-ofplane offset when the direction of the lateral load is perpendicular to the direction of the offset. e. Non-parallel Systems Non-parallel system is defined to exist when some of the vertical lateral force resisting elements are not parallel to or symmetric about the orthogonal axes of the lateral force resisting system.

6.2.2 Vertical Irregularities a. Stiffness Irregularity The non-uniformity of the stiffness along the height of the building is referred to as stiffness irregularity. To facilitate parking of vehicles, infill walls are avoided in the ground storeys of residential buildings (Figure 6.3). Also, open shop front demands the absence of infill walls in the front side of the ground storey. This leads to a soft storey, resulting in a sway mechanism under lateral load. Inelastic deformations will concentrate in this storey, with the remainder of the structure staying in the elastic range of response. The transfer beam in the first floor is stronger than the columns beneath, thus creating a situation of strong-beam–weakcolumn joints.

Even well detailed columns will lose strength, stiffness, and

energy absorption capacity due to the concentrated inelastic demand placed on this single storey. Thus, collapse of the building is likely under moderate to severe earthquake. Although lack of infill walls at the ground storey is due to functional requirement, it needs special design of the columns. The absence of plinth beams increases the vulnerability of the ground storey columns.

75


b. Mass Irregularity Mass irregularity may be caused by variation of mass between floors. c. Vertical Geometric Irregularity To avoid the monotony of a box type of structure, setback towers are provided. But this may create a vertical geometric irregularity. d. Weak Storey The open ground storeys frequently observed are examples of weak storeys. e. In-Plane Discontinuity If the in-plane offset of a lateral force resisting element is greater than the length of the element, an in-plane discontinuity exists. For a column set back in the ground storey, although the offset is less than the length of the column, it is a case of in-plane discontinuity when the direction of lateral load coincides with the direction of offset.

6.3

LOCAL DEFICIENCIES

Local deficiencies are element deficiencies that lead to the failure of individual elements of the building such as crushing of columns, flexural and shear failure of beams, columns and shear walls etc. Unaccounted loads, inadequate confinement, unauthorized alterations, poor quality of construction, poor detailing, lack of anchorage of reinforcement, inadequate shear reinforcement, insufficient cover, inadequate compaction and curing etc. and environmental deterioration are reasons for local deficiencies. The observed deficiencies of the elements are described next.

76


6.3.1 Columns Columns are the primary gravity-load carrying members for most RC buildings. Therefore, column failures have led to catastrophic collapses during the past earthquakes.

Buildings designed only for gravity loads may have several

inadequacies for seismic loads. The common deficiencies are discussed below. a. Inadequate Shear Capacity Typical gravity and wind load designs normally result in a design shear force significantly lower than the shear force that can develop in a column during seismic loading. Hence, columns in the buildings not designed for seismic forces have inadequate shear capacity. The cross-sectional dimension of a column is frequently limited to 230 mm to flush it with the wall. This may be inadequate for seismic loading. Another common problem is artificial “shortening” of columns by adding partial height partition walls that restrict the movement of the lower part of the columns. The resulting short columns are stiff and attract much higher shear forces than they were designed to carry. b. Inadequate Confinement of Column Core Although the frame structures are supposed to be designed using the strongcolumn–weak-beam concept, the use of deep spandrel beams in the first floor leads to stronger beams compared to the columns. The ground storey columns often form plastic hinges during strong seismic loading. The concrete core in a plastic hinging region must be adequately confined to prevent loss of the shear and flexural strength of the column. The confinement requirement in a column is more stringent because of the high axial load and shear that typically need to be carried through the plastic hinging region. Frequently, 6 mm diameter ties are placed at 200 to 225 mm spacing in the plastic hinging region. The ends of the ties have 90º hooks with inadequate hook length instead of 135º hooks. Although in the drawings the hook end is shown to be bent to about 135º, in practice 90º hooks are provided. These hooks open, leading to loss of confinement. There are

77


numerous examples of failure of poorly confined columns during the Bhuj earthquake. c. Faulty splicing of rebar It is a common practice in gravity load design to provide the column splice just above the floor and that too designed for compression only (Figure 6.4). The column may be subjected to large moments or subjected to tension under seismic loading (especially when infill walls are added and the column serves as a boundary element for the wall), resulting in pull-out of the rebar.

Figure 6.4: Examples of lack of seismic detailing (ATC 40, 1996) d. Inadequate Capacity under Biaxial Loading The problems of shear strength and confinement are more severe in corner columns, especially if the building has significant eccentricity between the centre of mass and the centre of rigidity. Corner columns need to have a higher degree of confinement if they are to survive the biaxial loading demands that are likely to occur in them.

78


6.3.2 Beams and Beam-Column Joints Deficiencies in beams and beam-column joints are frequently related to the inadequate transverse reinforcement for shear strength and confinement. Although the failures are local and may not lead to collapse, they affect the performance of the building. a. Inadequate Shear Capacity and Lack of Confinement During severe seismic loading, plastic hinges will develop at the ends of the beam. The shear in the beam during the formation of these hinges can be significantly higher than the shear force the beam was designed for, leading to a shear failure. The stirrups usually are not designed to resist the shear corresponding to the development of the beam flexural capacity (capacity based design). However, a more common problem is inadequate transverse confinement in the beam hinging zones. The stirrups may not be closed stirrups. As the plastic hinge “works” during the earthquake, the lack of adequate confinement will result in a steady loss of the shear strength and stiffness in the hinging zone. b. Inadequate Amount and Anchorage of Bottom Rebar The connections can suffer a significant loss of stiffness due to inadequate amount and anchorage capacity of the bottom longitudinal bars. The bottom bars at supports are not designed for tension in a gravity load design. There are instances when they are not laid continuous through the joint (Figure 6.4). Improper anchor detail of the main reinforcement can lead to pullout of the bars. For exterior columns, the beam rebar may not be bent properly with adequate hook length to confine the concrete.

6.3.3 Slabs The slab is assumed to act as a rigid diaphragm. In order to achieve this, it is necessary to provide additional reinforcement at the edges of the slab. These are

79


known as the drag and chord reinforcements. None of the buildings that were studied under the project had such reinforcement.

6.3.4 Unreinforced Masonry Walls Unreinforced masonry infill walls are common in RC frames. They are weak in out-of-plane bending. Their failure may also occur due to crushing of the corners or due to in-plane shear along the joints of the masonry units. Some times low quality mud mortar is used in the joints. The failure of the masonry infill leads to reduction in stiffness and additional load and deformation demand on the frame. This situation is critical if the columns were designed considering the performance of the infill.

6.3.5 Precast Elements The major issue for precast concrete construction is proper connections between the various components of the structure in order to establish a load path from the floor masses to the foundation. Failures have been reported in several school buildings in Gujarat. The seismic forces to be transmitted through the connections were not properly anticipated, resulting in failure.

6.3.6

Deficient Construction

Traditional practice of volume batching that disregards the moisture content of the aggregates, and pouring of additional water to attain workability lead to poor quality of concrete. Lack of proper compaction due to inadequate or excessive vibration, results in honeycombed or layered concrete. To reuse the column formwork, the top of the columns is cast separately along with the beams. The concrete is poured from the top of the beam-column joints. The congestion of reinforcement and inadequate vibration cause weak concrete in the potential hinging zone of the columns. The side face cover may be inadequate due to

80


forced placement of the reinforcement cage within the formwork. This leads to the corrosion of the rebar.

6.4

MISCELLANEOUS DEFICIENCIES

6.4.1 Deficiencies in Analysis If a building is designed only as a gravity load resisting system, then there can be severe deficiencies in the lateral load resistance.

When the infill walls are

neglected in the analysis of a building, the calculated time period is high and the design base shear is low. Hence, the effect of infill on the frame needs to be carefully investigated. Many of the multi-storeyed buildings are built without adequate geotechnical data. If a site has soft soil (Type III) and the building is designed with the assumption of hard soil (Type I) or medium soil (Type II), then the design base shear is lower than the recommended value. The amplification and attenuation of the ground shaking are neglected. When the site is close to a strike slip fault, constructive interference of the earthquake waves leads to higher ground shaking. This is termed as the near-source effect. When this effect is not considered, the design base shear is further low. The loss of stiffness during an earthquake and the consequent lengthening of the building period, may lead to an increase in the displacement response.

The

increased displacements mean higher eccentricity of the vertical loads, which can lead to collapse of the building if P-∆ effect has not been accounted for in the analysis.

81


6.4.2 Lack of integral action The building performance is degraded due to the lack of integral action of the lateral load resisting elements. The moment resisting frames are not well defined in the building plan. Advantage is not taken of the elevator core walls due to lack of connection with the building frame. The slabs are not provided with collector elements or chord and drag reinforcement, which are required for a diaphragm action. In such a case, the analysis is unconservative if the diaphragm action is assumed.

6.4.3 Failure of stair slab If the stair slab is simply supported without adequate bearing length, a collapse of the slab closes the escape route for the residents.

6.4.4 Pounding of buildings A thermal expansion joint between segments of a building or inadequate space between adjacent buildings is inadequate to act as a seismic joint. When the space is not adequate, the buildings may ‘pound’ against each other as they respond to the earthquake excitation. Buildings are not designed to absorb pounding loads from adjacent structures. Also, these impulsive pounding forces can significantly alter the dynamic response of the buildings and can cause collapse of the buildings. Such cases were observed in the Bhuj earthquake.

6.4.5 Geotechnical aspects For buildings on firm soil, the loss of stiffness may lead to reduction in the displacement response or at least no increase, because the period of the structure tends to lengthen. However, for buildings on soft soils this loss of stiffness and lengthening of the building period may lead to an increase in the displacement

82


response. The increased displacements can lead to collapse of the building. The discussion of soil failure is beyond the scope of this manual.

6.4.6 Inadequate detailing and documentation It was observed from the buildings studied that the documentation of design procedure, the code that was followed, geotechnical and architectural information was extremely poor. The detailing of rebar at the joints and at the splices was incomplete. Any evaluation of a building without these information is subjected to postulation and hence questionable.

83


CHAPTER VII GLOBAL RETROFIT STRATEGIES

7.1

INTRODUCTION

Buildings behave poorly in earthquakes because the existing lateral load resisting components do not have adequate strength and ductility (energy absorption capacity). Stiffening the structure by providing additional lateral load resisting elements, thereby reducing the lateral deformation, is an effective method of improving the performance of a building. Stiffening of the structure can be achieved by the construction of new braced frames, infill walls or shear walls. Reductions of irregularities or mass in a building are other methods of global retrofit.

The global retrofit strategies are described under the following

categories. 1. Structural stiffening 2. Reduction of irregularities 3. Reduction of mass.

7.2

STRUCTURAL STIFFENING

Structural stiffening can be achieved by the following methods.

84


1. Addition of infill walls 2. Addition of shear walls 3. Addition of steel braces

7.2.1

Addition of Infill Walls

The effect of adding infill walls and braces on the load versus deformation behaviour of reinforced concrete frames is shown schematically in Figure 7.1.

Figure 7.1: Effect of adding infill walls and braces (Sugano, 1981)

The following are the different types of infill walls commonly used in residential buildings. •

Masonry Infill Wall

•

Cast-In-Place RC Infill Wall

•

Precast Concrete Infill Wall

Steel infill panels have been investigated experimentally. The modelling of infill walls is usually done by the equivalent strut method. The details of modelling of masonry infill walls are given in Appendix B.

86

Chapter VII – Global Retrofit Strategies

7.2.2 Addition of shear walls

The addition of new shear walls is used to control excessive displacements in buildings. Critical design issues involved in the addition of shear walls are as follows (White, 1995). •

Determining the adequacy of existing floor and roof slabs to carry the seismic forces.

•

Transfer of diaphragm shears into the new shear walls through dowels.

•

Adding new collector and drag members to the diaphragms.

•

Reactions of the new shear walls on existing foundations.

The collector and drag members connect shear walls and frames to mobilise their lateral load resistance simultaneously.

The reactions of new shear walls on

existing foundations may cause serious problems to the foundations. This is a strong disadvantage of adding shear walls. Another disadvantage is the closing of formerly open spaces, which can have negative impact on interior building uses or exterior appearance. The modelling of shear walls is given in Chapter 3.

7.2.3

Addition of steel braces

The seismic strength and stiffness of framed structures can be efficiently and economically increased using steel braces or shear walls. Usually steel braces are used in steel buildings. However, in recent years steel braces have been used in RC buildings because of ease of construction and high strength to weight ratio. Braces reduce flexure and shear demands on beams and columns and transfer the lateral loads as axial loads (truss action).

The advantages of retrofitting an RC frame by steel braces are as follows. •

They block less floor space.

•

Due to the efficiency of braces as axially loaded members, they are economical.

87


•

In a retrofit scheme, they are easy to use with minimal disruption to functional use.

•

The requirement of strength and stiffness can be achieved with steel braces.

•

The braces add very little to the existing mass to the building.

•

The braces can be efficiently connected to existing RC frames using bolts.

A background and the application of steel braces are given in Appendix E.

7.3

REDUCTION OF IRREGULARITIES

The plan and vertical irregularities are common causes of undesirable performance under an earthquake.

In a linear analysis, the irregularities are

reflected in the distribution of structural displacements and Demand-to-Capacity Ratios (DCRs) in the elements. In a nonlinear analysis, in addition to the above, the irregularities are reflected in the inelastic deformation demands. If the values of displacements, DCRs, or inelastic deformation demands predicted by the analyses are unbalanced, with large concentrations of high values within one storey or at one side of a building, then an irregularity exists. Such irregularities are often, but not always, caused by the presence of a discontinuity in the building, for example, termination of a wall above the ground storey. Removal of the irregularity may be sufficient to reduce demands to acceptable levels.

Among plan irregularities, torsional irregularities can be corrected by the addition of moment frames, braced frames, or shear walls to balance the distribution of stiffness and mass within a storey. Eccentric masses can be relocated. Seismic joints can be created to transform an irregular building into multiple regular structures. Partial demolition can also be an effective corrective measure for irregularities, although this may have significant impact on the appearance and utility of the building.

88

Chapter VII – Global Retrofit Strategies

For vertical irregularities, portions of the building that create the irregularity, such as setback towers, can be removed. Discontinuous components such as columns or walls can be extended beyond the zone of discontinuity. As mentioned earlier, walls or braces can alleviate the deficiency of soft and weak storey.

7.4

REDUCTION OF MASS

Two of the primary characteristics that control the amount of lateral force and deformation induced in a building by ground motion are its stiffness and mass. Reductions in mass result in direct reductions in both the force and deformation demands produced by earthquakes, and therefore, can be used in lieu of structural strengthening and stiffening. Mass can be reduced through demolition of upper storeys, replacement of heavy cladding and interior partitions, or removal of heavy storage and equipment loads, or change in the use of the building.

89


CHAPTER VIII LOCAL RETROFIT STRATEGIES

8.1

INTRODUCTION

Local retrofit strategies include strengthening of beams, columns, slabs, beamcolumn or slab-column joints (for flat plates), walls and foundations.

Local

strengthening allows one or more under-strength elements or connections to resist the demands predicted by the analysis. In the following sections, the local retrofit strategies are grouped according to the type of elements. Some of the solved examples were taken from the buildings analysed under the project.

8.2

COLUMN STRENGTHENING

Column strengthening techniques include the following. 1. Concrete jacketing 2. Steel jacketing 3. Fibre reinforced polymer wrapping The design should specify to what extent the load on a column should be released during the retrofit construction.

90


8.2.1 Concrete Jacketing Concrete jacketing is a popular method of column retrofit. This involves addition of a thick layer of reinforced concrete (RC) in the form of a jacket, using longitudinal reinforcement and closely spaced ties with seismic detailing (Figure 8.1).

Figure 8.1: Concrete jacketing (Basu, 2002)

The method is comparatively straightforward and increases both strength and ductility. But, the composite deformation of the existing and the new concrete requires adequate dowelling to the existing column. The mix design of the new concrete, surface preparation of the existing column and choice of appropriate bonding material are also important. Also, the additional longitudinal bars need to be anchored to the foundation and should be continuous through the slab. The use of ferrocement jacket increases the shear strength and the ductility of RC columns.

92

Chapter VIII – Local Retrofit Strategies

The disadvantages of concrete jacketing are listed below. a. Drilling of holes. b. Increase in the size of the column. c. Placement of ties at the beam-column joints Analysis of Strengthened Columns a. Flexural Capacity The analysis of a strengthened column can be performed by the traditional method of interaction curves.

To get the moment versus curvature behaviour, the

equations of equilibrium and compatibility and the constitutive relationships have to be satisfied. The analysis assumes that there is perfect bond between the new and old concrete. An adequately confined core can be modelled with the stress versus strain relationship of confined concrete. An example of a deficient existing section from Building A08 (located in Zone V) and the retrofitted section is presented. The existing section is 350×600mm, with 4-25mm diameter and 12-20mm diameter longitudinal bars and 8mm diameter ties at 100mm on centre (Figure 8.2). The grade of concrete is M15 and the grade of steel is Fe 415. Y

4-25 Φ and 12-20 Φ 600 X

X

8Φ @ 100 mm c/c

Y

350

Figure 8.2: Existing cross-section

93


The section is analysed about X-X and Y-Y axes separately. The flexural strength of the section is adequate about X-X but it is inadequate about Y-Y. A concrete jacket is added with 75 mm thick concrete all around, 12-12 mm diameter longitudinal bars and 8 mm diameter ties at 100 mm on centre (Figure 8.3).

Y 75

4-25Φ and 12-20Φ X 750

600

12-12Φ

X

8Φ @ 100 mm c/c 8Φ @ 100 mm c/c 75 75

350

75

500 Y

Figure 8.3: Retrofitted cross-section

In the analysis, the concrete grade and the steel grade of the jacket were retained same as those of the existing section. The dowels connecting the existing and the new concrete are not shown in the figure. The number of dowels should be low to have minimal drilling into the existing section. The interaction curves for the existing and the retrofitted sections are shown in Figure 8.4. The moment versus curvature curves, in presence of axial loads, are shown in Figure 8.5.

94


5000

Axial load (kN)

4000

3000

2000

1000

0 0

100

200

300

400

500

Moment (kN m) Existing about Y-Y Retrofitted about X-X

Existing about X-X Demand about Y-Y

600

700

Demand about X-X Retrofitted about Y-Y

Figure 8.4: Interaction curves for the existing and the retrofitted sections

700 600

Moment (kN m)

500 400 300 200 100 0 0

0.00002

0.00004

0.00006

0.00008

0.0001

Curvature (rad) Exisiting

Retrofitted

Figure 8.5: Moment versus curvature curves for the existing and the retrofitted sections

95

0.00012


It is observed that the increase in flexural strength can be substantial with a concrete jacket. Along with the increase in strength and stiffness, the ductility is retained in the section after retrofit. The additional stirrups are provided to meet the shear demand. b. Confinement The ends of a column are to be confined because of the potential plastic hinge formation. Special confining reinforcement is required throughout the length of plastic hinges in each end.

The required amount of special confining

reinforcement as per IS 13920: 1993 is given below. For a circular column A sh = 0.09 S Dc

f ck ⎛ Ag ⎞ − 1.0 ⎟ ⎜ fysp ⎝ Ac ⎠

(8.1)

where, Ash

total area of the bar cross sections of spiral or circular hoops

S

pitch of spiral or spacing of hoops

Dc

diameter of core measured to the outside of the spiral or hoop

fck

cube compressive strength of the concrete

fysp

yield strength of steel of hoop or spiral

Ag

gross area of the column cross section

Ac

area of the concrete core = π×Dc2/4.

For a rectangular column, A sh = 0.18 S h

f ck ⎛ Ag ⎞ − 1.0 ⎟ ⎜ fysp ⎝ Ac ⎠

(8.2)

Here, h is the longer dimension of the rectangular confining hoop measured to its outer face. It shall not exceed 300mm. Paulay and Priestley (1992) proposed an equation which incorporates the effect of the axial load on the amount of confining steel for the required curvature ductility.

96


For a rectangular column, ⎛ f ' Ag ⎛ Pu ⎞⎞ Ash = S Dc ⎜ K c − 0.08 ⎟ ⎟ ⎜ ' ⎜ fysp Ac f Ag ⎟ ⎝ c ⎠⎠ ⎝

(8.3)

Here,

f c/ = cylinder compressive strength ≈ 0.8 fck k = 0.35 for a required curvature ductility of µΦ = 20 k = 0.25 for µΦ = 10. Other values can be calculated by interpolation or extrapolation. Pu = design load in the column. The required amount of additional stirrups for confinement (Ash,add) can be calculated as follows. A sh,add = A sh - A sh,pro

(8.4)

Here, Ash,pro is the area of confining reinforcement provided in the existing column. c. Shear Capacity The shear resistance (VuR) of a column can be expressed as follows. VuR =Vc +Vs

(8.5)

where, Vc is the concrete contribution and Vs is the steel contribution. The shear strength enhancement by jacket is included as an additional term Vj to the shear resistance.

VuR = Vc +Vs +Vj

(8.6)

The design capacity VuR is to be greater than the demand Vu .

VuR ≥ Vu

97

(8.7)


Here, Vu is the maximum value that is obtained from analysis with different load combinations and the shear force corresponding to the development of the flexural strengths of the connected beams (as per IS 13920: 1993). Thus, the required strength from the jacket is ∴ Vj ≥ Vu - Vc - Vs

(8.8)

The concrete contribution in a rectangular column is given as Vc = δ τ c bd

(8.9)

where, the enhancement in shear capacity due to the axial load is given by the factor δ. 3 Pu ⎞ ⎛ δ = ⎜0 + ≤ 0.5 Ag fck ⎟⎠ ⎝

(8.10)

The design shear stress of concrete (τc) is available from Table 19 of IS 456: 2000. The breadth (b) and the effective depth (d) can be taken for the retrofitted section. For a circular section, a similar expression is used. The steel contribution is as follows. Vs = 0.87fy Asv

d cot θ sv

Here, Asv

Cross sectional area of ties

sv

Spacing

fy

Yield stress of ties

d

Effective depth of section

θ

Inclination of cracks to the column axis.

Usually θ is assumed to be 45°. This means cot θ = 1.

98

(8.11)


The expression of Vj is similar to Vs. The additional steel tie or spiral contribution is as follows. Vj = 0.87fy Asv add

d cot θ sv

(8.12)

Here, Asv,add is the total area of the additional stirrups. The expressions for circular ferrocement jackets consider the area of the wire mesh.

Vj =

0.125 π 2 dw 2 fyj n D' gw

(8.13)

Here, n

Number of layers of wire mesh.

dw

Diameter of wire mesh.

gw

Grid spacing.

fyj

Allowable stress of steel in wire mesh, taken to be 0.4 fy, where fy is the yield stress.

D'

8.2.2

Core diameter of jacketed section.

Steel Jacketing

Steel jacketing refers to encasing the column with steel plates and filling the gap with non-shrink grout (Figure 8.6). Steel jacketing was originally developed for circular columns. Steel jacketing is an effective method to remedy deficiencies such as inadequate shear strength and inadequate splices of longitudinal bars at critical locations, by providing confinement. The jacket is effective in passive confinement, that is, confining stress is induced in the concrete as it expands laterally.

The jacket can be considered equivalent to continuous hoop

reinforcement. In most cases increase in strength and ductility due to confinement alone may be adequate, so that composite action may not be necessary.

99


Figure 8.6: Steel jacketing (Seth, 2002)

If the flexural capacity of the original column is adequate, gaps are left at the top and bottom of the jacket to avoid the following a. The possibility of the jacket acing as compression reinforcement by bearing against the supporting member at large drift angles b. The increase of the stiffness of the column and hence, of the induced shear force. When the jacketing steel is also needed for additional composite strength it is necessary to provide continuity at the ends. For rectangular columns, the recommended procedure is to use an oval jacket, which provides a continuous confining action similar to that of a circular spiral. The space between the jacket and columns is filled with concrete. For bridges, rectangular columns so retrofitted have performed exceptionally well in flexure and shear. Attempts to retrofit rectangular columns using rectangular jackets have been less successful even when the jackets were extensively stiffened. This is because the confining action of the rectangular jackets can only be developed as a consequence of lateral bending of the jacket sides, which is a very flexible action in comparison to the hoop tension action developed in an oval jacket. The steel plates of a rectangular jacket need to be anchored to the column by means of shear

100


lugs or studs in order to enhance their effectiveness in providing confinement or in the composite action. Alternatively, steel jackets can also be made of vertical angles, plates or channel shapes, tied together by welded transverse steel bands or lattice bars. When found adequate, the plates are attached to the column by epoxy-grouted bolts or by epoxy bond. The jacketing may not be needed over the full length of the column, if the shear strength of the original column is sufficient in the unjacketed portions. Analysis of Strengthened Columns The required shear strength from the jacket (Vj) can be calculated as given for columns strengthened with concrete jackets.

Regarding Vj, for rectangular

columns, Aboutaha et al. (1999) considered the jacket to act as a series of independent square ties of thickness and spacing tsj, where tsj is the jacket thickness. Vj =Asj

fsj dsj ssj

(8.14)

Here, Asj is the total area of the assumed square tie, Asj = tsj2 (expected to be 2tsj2), fsj is the allowable stress of the jacket, dsj is the height of the jacket and ssj is the spacing between the square ties, ssj = tsj. It was assumed that the shear cracks are inclined at 45º to the column axis and the allowable stress in the jacket is fsj = fysj/2, where fysj is the ‘yield’ stress. The required thickness tsj can be calculated from the required value of Vj.

8.2.3 Fibre Reinforced Polymer (FRP) Wrapping

Fibre Reinforced Polymer (FRP) is a composite material consisting of a matrix of polymeric material reinforced with unidirectional or multi-directional fibres. Fibres can be classified as glass fibre reinforced polymers (GFRP), carbon fibre reinforced polymers (CFRP) and aramid fibre reinforced polymers (AFRP). Glass

101


fibre has been the predominant fibre for applications in India, because of the economical balance of cost and strength properties. FRP is mechanically different from steel since it is anisotropic, linear elastic and is usually of higher strength with a lower modulus of elasticity than steel. FRP has desirable physical properties over steel, like corrosion and fatigue resistance and high tensile strength (up to ~3000 MPa compared to ~400 MPa of steel) to weight ratio. FRP sheets are thin, light and flexible enough to be inserted behind pipes, electrical cables and other service ducts, thus facilitating installation. FRP jackets are used in the retrofitting of columns. There is no significant increase in the size of the column. In addition to passive confinement, a degree of active confinement is achieved by pressure grouting between the jacket and column. The main drawback of FRP is the high cost. Unlike steel, FRP is a brittle material, which must be accounted for in design. The performance of bond between FRP sheets and concrete over a long period of time is yet to be established. The other disadvantages are susceptibility of FRP to moisture and chemicals, degradation of properties at high temperatures, as in the case of fire, and the damage from ultraviolet light. External FRP jackets with horizontally oriented fibres can enhance both the shear capacity and the ductility of columns against seismic forces. Under shear forces, the tensile stresses in FRP contribute to the over all shear resistance of columns, similar to its effect in shear strengthening of beams. Under flexure, the FRP provides confinement, which enhances the strength and ultimate strain of concrete.

The enhancement to the ultimate concrete strain is particularly

important for seismic retrofit as it allows a much greater ductility level to be achieved in inelastic deformations. For shear strengthening, the FRP jacket is generally required to cover the entire column height.

For plastic hinge

confinement and for lap splice clamping, the FRP jacket is only needed in the plastic hinge and near by regions.

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8.3

BEAM STRENGTHENING

Beam strengthening techniques include the following. 1. Concrete jacketing 2. Steel plating 3. Fibre reinforced polymer (FRP) wrapping 4. Use of FRP bars 5. External Prestressing

8.3.1 Concrete Jacketing

Concrete jacketing is one of the traditional methods of retrofit. Jacketing can be effectively used to retrofit common deficiencies in beams such as discontinuity of bottom bars at the supports and to increase the shear capacity. Several options are available for adding concrete (Figure 8.7).

Figure 8.7: Concrete jacketing (IS 13935: 1993)

There are some disadvantages in this traditional retrofit strategy. First, addition of concrete increases the size and weight of the beam. Second, the new concrete requires proper bonding to the existing concrete. In the beam soffit, bleed water from the new concrete creates a weak cement paste at the interface. Third, the

103


effects of drying shrinkage must be considered as it induces tensile stress in the new concrete. Instead of regular concrete, fibre reinforced concrete can be used for retrofit. For the proper confinement of concrete and formation of plastic hinges, it is essential to provide stirrups at close intervals especially near the supports. This involves drilling of holes in the slab or in the beam or in both, at fairly close intervals. Drilling of holes in the beam may lead to micro-cracking and hence, weakening of the beam. The surface of the beam is usually roughened for better bonding with the new concrete. Recently, some patented cements are available to avoid hacking the surface. In case the depth of the transverse beam is equal to the depth of the beam to be retrofitted, or the width of the column is greater than that of the beam, drilling becomes unavoidable.

However, the engineer must endeavour to

minimise the amount of drilling in concrete, especially in the regions where there is congestion of reinforcement. It is imperative that the strength of the column must be greater than that of the beam as per capacity based design. Also, the joint should not become weaker than the beam after retrofit. The analysis of a strengthened beam can be performed by the traditional method of beam analysis. To obtain the enhanced moment versus curvature behaviour, the equations of equilibrium and compatibility and the constitutive relationships have to be satisfied. The analysis assumes that there is perfect bond between the new and old concrete. Analysis of Strengthened Beams An example of a beam section deficient in flexure in an existing building and the retrofitted section is presented. The existing section is 250×600mm, with 4-16mm diameter bars at the bottom and 4-16mm and 2-12mm diameter bars at the top, near the support. The section is deficient both for the positive (sagging) and negative moments, as shown in Table 8.1.

104


Table 8.1: Moment demands and capacities of example section

MuR+ (kN-m)

Mu+

MuR− (kN-m)

Mu−

kN-m

Existing

After retrofit

kN-m

Existing

After retrofit

253

152

267

261

194

267

Here, Mu represents the factored demand and MuR represents the ultimate resistance (capacity). The size of the retrofitted section is 350×650mm, with 316mm diameter bars as additional reinforcement at the bottom and 2-10 mm and 2-12 mm diameter bars as additional reinforcement at the top (at the level of the soffit of the slab). The capacities after retrofit are also shown in the table. The moment curvature behaviour is shown in Figure 8.8.

300

Moment (kN-m)

250 200 150 100 50 0 0

5

10

15

20

25

30

35

40

45

curvature x 10e-3 (1/m) Existing

After retrofit

Figure 8.8: Moment versus curvature for positive moment

It is observed that with the increase in strength and stiffness, the reduction in the ductility after retrofit is marginal. It is important to note that with the increase in

105


flexural capacity, the shear demand (based on the flexural capacity) also increases. Additional stirrups are provided to meet the shear demand.

8.3.2

Steel Plating

The technique of gluing mild steel plates to beams is often used to improve their flexural and shear capacities. It increases the strength and stiffness of the beams and subsequently, reduces the crack width. The addition of steel plate is simple and rapid to apply, does not reduce the storey clear height significantly and can be applied while the building is in use. Gluing plates requires adequate smearing of adhesive on the existing surfaces. The cost is governed by that of the plates, epoxy and labour. Glued plates are prone to premature debonding which can severely limit the application of this technique. Providing bolts at the ends may reduce the debonding, but it involves drilling into the existing concrete. The advantages of steel plating are the following (Barnes, 2001). 1. Increase in strength and stiffness. 2. Increase in serviceability (lower deflection and reduced crack width). 3. It is possible to strengthen the structure while in use. 4. Relatively small increase in the size and weight of the existing section. 5. Accessibility for inspection and maintenance. The disadvantages of steel plating are 1. Corrosion of the external plate. 2. Transporting, handling and installing the plates. 3. Cost of the steel plates. Plating may be done either on the tension-face or on the side-face of the beams. Tension-face plates are mechanically efficient as they act at the furthest extremity from the compression zone and hence, accomplish the highest increase in flexural strength and stiffness. Side-face plating increases the shear capacity and to a

106


limited extent, flexural capacity. A combination of the above methods is also done. a. Tension-Face Plated Beams Steel plates or sheets are attached to the tension face of beams to increase the flexural strength.

Unlike concrete jackets, the plates are prone to premature

debonding. Failure in plated beams occurs due to the debonding of concrete cover. There are four mechanisms of debonding of tension-face plated beams (Oehlers and Moran, 1990). 1. Flexural peeling, 2. Shear peeling, 3. Reverse peeling and 4. Adhesive failure. The peeling refers to the delamination of concrete cover. It has been observed from experiments conducted on tension-face plated simply supported beams with 2-point loading that when the moment to shear (M/V) ratio is high, flexural peeling initiates at the end of the plates. For intermediate M/V ratios, a combination of shear and flexural peeling occurs. In specimens with low M/V ratios, shear failure of the beam and debonding of the plate due to shear are observed. The flexural peeling is induced by increasing curvature. It is a gradual failure mode. The shear peeling is induced by the formation of diagonal shear cracks and the peeling is rapid. After the ultimate moment is reached, due to the rapid loss of longitudinal strain in the plate, cracks can propagate in the reverse direction (towards the support). The reverse peeling occurs only after the ultimate moment is reached and hence it is not considered as a failure mode. The adhesive failure is due to bad preparation of the concrete surface, or use of poor quality adhesive, or bad workmanship. The failure occurs at the interface of the glue line as compared to the flexural or shear peeling of the cover concrete.

107


Of late, the adhesive failure is not significant due to the good quality of adhesives available. Analysis of Tension-face Plated Beams Near the location of plate cut-off, substantial normal stress (also termed as ‘peeling’ stress) and shear stress generate at the interface due to the sudden change in the cross-section from plated to unplated. This cannot be predicted by flexural theory. Roberts and Hazi-Kazemi (1989) explained this phenomenon by theory of elasticity. Figure 8.9 shows a schematic representation of the stresses at the location of plate cut-off.

RC Beam

Steel Plate Shear Stress

Normal Stress

Shear Stress Normal Stress

Tension

Distance along plate

Compression

Figure 8.9: Shear and normal stresses at location of plate cut-off

Due to the high normal stress, the plate starts to peel at the location of cut-off. When thick plates are used, the plate separation precedes the plate yielding. When the tensile capacity of concrete is exceeded, a diagonal crack develops. The formation of the diagonal crack magnifies the effect of peeling and the crack

108


extends rapidly to the bottom of tensile reinforcement. This relieves the bond stresses at the end of the plate. The location of peeling of the plate ‘moves’ inwards into the region of higher moment. The process continues till the cover concrete peels substantially (Ali and Oehlers, 2002). In choosing the thickness of the steel plate, it is necessary to ensure that the section does not become over-reinforced. The ultimate strength analysis was proposed by Roberts (1989) and later modified by Ziraba et al. (1994). It is based on satisfying the equilibrium and compatibility equations and the constitutive relationships. It models the adhesive failure due to the stress concentration at the location of plate cut-off. The essential features of the model are as follows. 1. The steel plate is assumed to act integrally with the concrete beam. Conventional beam theory is used to determine the flexural capacity. 2. The normal and shear stresses are calculated to check the failure of the adhesive. The concrete stress block is modified as per IS 456: 2000. The stresses and strains distribution of a tension-face plated beam is shown in Figure 8.10.

b 0.0035

0.447 fck

C

xu hp

hs

D

dc dp

st

bp

pt

Strains

fst

Tst

fpt

Tpt

Stresses

Figure 8.10: Strains and stresses in a plated beam

109

Forces


The depth of neutral axis (xu) can be found out from the equilibrium equation as follows.

xu =

f st Ast + f pt b p d p 0.36 f ck b

(8.15)

The ultimate moment capacity (MuR) of the plated section is given by the following expression. M uR = 0.36 f ck b x u ( h s -0.416 x u ) + f pt b p d p ( d c + d p 2 )

(8.16)

Here, b, D, hs - Width, overall depth and effective depth of the original section bp, dp, hp - Width, thickness and effective depth of the steel plate fck

- Characteristic cube strength (MPa)

fst, fpt

- Stress in internal reinforcement and external plate, corresponding

to the strains εst and εpt. These can be calculated from the compatibility equations. The width of the plate is limited to the width of the beam. The limit on the thickness of the plate is such that the section does not become over-reinforced. The adhesive failure is checked by the following equation. τ 0 + σ 0 tan28D ≤ c all

(8.17)

τ0 = CR1 V0 Here, τ0 and σ0 are the expressions for shear and normal stresses at the interface at adhesive failure. The allowable coefficient of cohesion is denoted as call. The expression for peak shear stress τ0 is

⎛C V ⎞ τ 0 = α1 f t ' ⎜ R1 ' 0 ⎟ ⎝ fc ⎠

110

5/4

(8.18)


where, V0

- Shear force at the location of plate cut-off

α1

- Empirical regression constant (α1 = 35)

fc'

- Cylinder compressive strength

ft'

- Tensile strength of concrete.

CR1 is a constant given by the following expression.

⎡ ⎛ K s CR1 = ⎢1+ ⎜ ⎜ ⎢ ⎝ E p bp d p ⎣

1/2 ⎞ * ⎤ bp d p (h p - x u ) ⎟⎟ a ⎥ I b ⎥ cr a ⎠ ⎦

Here, a*

M0 / V0 at plate cut-off location

Icr

Moment of inertia of equivalent transformed cracked steel section

Ks

Shear stiffness of the adhesive layer (= Ga ba/da)

Ga, ba, da Shear modulus, width and thickness of the adhesive layer. Ep

Elastic modulus of the plate

The expression for the peak shear stress σ0 is

σ0 = α 2 CR2 τ0

(8.19)

CR2 is a constant given by the following expression.

CR2

⎛ Kn = dp ⎜ ⎜ 4 E p Ip ⎝

1/4

⎞ ⎟⎟ ⎠

where, α2

Empirical regression coefficient (α2 = 1.1)

Ip

Moment of inertia of the steel plate about its centroid

Kn

Normal stiffness of adhesive layer (= Ea ba/da)

Ea

Elastic modulus of adhesive.

111


The retrofit of a beam deficient in flexure under gravity loads is illustrated below. A rectangular beam of length 4500mm and dimensions 230×400mm is reinforced with 3-12mm bars at the top and bottom. The existing capacity is 40.9 kN-m and the required capacity is 50.6 kN-m. Grade of concrete is M20 and grade of reinforcing steel is Fe 415. The beam is retrofitted with a plate of grade Fe 250. The beam is propped before plating so that after the prop is released, the strengthened section carries the required moment. Step 1: Flexural design. A steel sheet of 150mm width and 1mm thickness is plated to the soffit of the beam. Equating the compression and the tensile forces, xu = 55.3mm. The positive moment capacity of the beam is 52.6kN-m. Step 2: Interface stresses. The properties of the adhesive used are given below. Shear modulus of adhesive Ga

80N/mm2

Young’s modulus of adhesive Ea

250N/mm2

Allowable coefficient of shear cohesion call 2.6N/mm2 Icr is the section modulus of the cracked, equivalent transformed steel section about the neutral axis (NA). The top reinforcement is very close to the NA and is hence ignored in the calculation of Icr.

⎛E Icr = ⎜ c ⎜ Ep ⎝

Ec

⎞ b x 3u 2 2 + A s ( h s -x u ) + A p ( h p -x u ) ⎟⎟ ⎠ 3

5000√20 =

22,360N/mm2

Ep

200,000N/mm2

Area of tension steel Ast

340mm2

Effective depth hs

360mm

Area of steel sheet Ap = 150×1

150mm2

112


Depth of steel sheet dp = 400+1/2

400.5mm

3

2 2 ⎛ 22.36 ⎞ 230×55.3 Icr = ⎜ + 340 ( 360-55.3) + 150 ( 400.5-55.3) ⎟ 3 ⎝ 200 ⎠ = 50.89×106 mm 4

Moment of inertia of the steel sheet about its centroid is Ip. Ip = 150×13/12 =

12.5mm4

Thickness of the adhesive da

1mm

Shear stiffness of the adhesive

Ks = Ga(ba/da) = 80×150/1 = 12,000N/mm2

Normal stiffness of the adhesive

Kn = Ea(ba/da) = 250×150/1 = 37,500N/mm2

CR2

1/4

⎛ Kn = dp ⎜ ⎜ 4 E p Ip ⎝

⎞ ⎟⎟ ⎠

1/4

37500 ⎛ ⎞ = 1× ⎜ ⎟ ⎝ 4×200000×12.5 ⎠

= 0.2475

Figure 8.11 shows the tension-face plated beam of span l subjected to a uniformly distributed load w per m. Here, 'a' refers to the distance from the point of zero moment (in this case, the supports) to the edge of the plate. w /m

a

a

l - 2a

BMD M0

M0

wl2/8 V0

wl/2 V0

wl/2 SFD

Figure 8.11: Bending moment and shear force diagrams

113


The plate must be terminated at such a point that the limits of interface stresses are not exceeded. ⎛ wl wa 2 ⎞ w 2 Moment at the point of curtailment M 0 = ⎜ a ⎟ = ( la-a ) 2 2 2 ⎝ ⎠

The shear at the point of curtailment of the plates V0 =

a* =

wl ⎛ l -2a ⎞ w ⎜ ⎟ = ( l -2a ) 2 ⎝ l ⎠ 2

M0 la - a 2 = V0 l - 2a

Using the expression for CR1, a* and V0, ⎡⎧ ⎛ Ks ⎪ ⎢ CR1V0 = ⎨1+ ⎜ ⎜ ⎢ E b d ⎣ ⎪⎩ ⎝ p p p

⎛C V ⎞ Peak shear τ 0 = α f ⎜ R1 ' 0 ⎟ ⎝ fc ⎠

1/2 ⎤ ⎞ ⎛ la-a 2 ⎞ ⎫⎪ b p d p w ⎥ (h p - x u ) ( l -2a ) ⎟⎟ ⎜ ⎟⎬ ⎥ 2 ⎠ ⎝ l -2a ⎠ ⎪⎭ Icr ba ⎦

(8.20)

5/4

' 1 t

⎛ τ ⎞ ⇒ CR1V0 = ⎜ 0 ' ⎟ ⎝ α1 f t ⎠

4/5

(8.21)

f c'

fc' and ft' are the cylinder strength and tensile strength of concrete. The expression for limiting the interface stresses is as follows. τ 0 + σ 0 tan 28o ≤ call and σ 0 = α 2 CR2 τ 0

(

)

Hence, the limiting case is τ 0 1+α 2 CR2 tan28o = call

∴ τ0 =

call 1+α 2 CR2 tan28o

This expression for τ0 can be substituted in equation (8.21). expression is as follows.

114

The resulting


⎡ ⎤ call ⎥ CR1V0 = ⎢ ⎢⎣ 1+α 2 CR2 tan28o α1f t' ⎥⎦

(

)

4/5

f c'

(8.22)

Equation (8.20) when equated with (8.22) results in a cubic equation in 'a', the maximum distance of plate cut-off from the supports. The equation can be solved by trial and error. The maximum distance of plate cut-off (amax) must not exceed three times the depth of the beam. 1/2 ⎡ ⎪⎧ ⎛ ⎤ 20,000 150×1 ⎞ ⎛ 4500a-a 2 ⎞ ⎪⎫ ⎢ ⎨1+ ⎜ ⎥ (400.5-55.28) ⎟⎬ ⎟ ⎜ 6 ⎢⎣ ⎩⎪ ⎝ 200,000×150×1 ⎠ ⎝ 4500-2a ⎠ ⎭⎪ 50.89×10 ×150 ⎥⎦

⎛ ⎞ 20 2.6 ⎟ × ( 4500-2a ) = ⎜⎜ o ⎟ 2 1+1.1×0.2812 tan28 35×3.13 ⎝ ⎠

(

4/5

)

( 0.8×20 )

Solving the equation by trial and error, 'a' = 70.6mm. The curtailment by 70mm on either side would not result in any appreciable economy. However, in case of beams of longer span and with higher loads, curtailment of plates or sheets becomes necessary. Step 3: Shear strength Steel plating enhances the shear capacity of the section.

However, as a

conservative measure, the increase in shear capacity may be ignored. If the beam does not possess sufficient shear capacity, side-face plating becomes necessary. Some authors contend that adhesive failure in plated beams is not of great significance since the quality of adhesives presently available is good. Oehlers and Moran proposed an empirical expression for the ultimate moment capacity due to flexural peeling (Oehlers and Moran, 1990). The expression was based on a number of experiments conducted on simply supported beams with 2point loading, with plates terminated in regions of constant moment.

115


b. Side-Face Plated Beams Steel plates are attached to the side face of a beam to increase the shear strength. Here also there may be premature failure before reaching the intended strength. The failure modes of side-face plated beams are as follows. i.) Fracture of bolts The bolts may fracture if the slip at the beam–plate interface is large. ii.) Buckling of Plates The side-face plates may buckle under diagonal compression. Design rules were developed for buckling of plates in both elastic and yielded states (Smith, 1999). iii.) Splitting of concrete The bolts can cause splitting of concrete due to bearing of the bolts against the concrete. Analysis of Side-face Plated Beams Barnes et al. (2001) derived expressions for the enhancement of shear capacity of side-face plated simply supported beams subjected to 2-point loading.

The

formulation is based on satisfying the equilibrium of forces and compatibility of deformations in the shear span region of a beam. The forces of the free body at ultimate are shown in Figure 8.12. The inclined section is due to the diagonal cracking from the support to the edge of the loading point. The notations used are given below. a'

- Effective length of the shear span

db

- Effective depth of the side-face plate

Pc

- Compressive force across the compression zone

Pst

- Tensile force in the bottom reinforcement

Pu

- Ultimate load

St

- Principal tensile force perpendicular to the failure plane

Vc

- Shear force across the compression zone

116


Vd

- Shear force across the bottom reinforcement

xs

- Depth of the compression zone under the bearing plate

Z1, Z2 - Lever arm of the side-face plate and bond length function α

- Angle of inclination of the cracked section, ≥ 30°.

a'

da d'

Vc

xs

Pc

d

D

Bolted Plate

db

Bonded Plate

Z2

O Z1

db St

bl Vd

Pst

Pu / 2

Figure 8.12: Stress-distribution in a side-face plated beam

For bonded plates, db is taken up to the bottom of the plate, whereas for a bolted plate, db is taken up to midway between the lower row of bolts and bottom of the plate. Applying equilibrium to the inclined section, the following equations can be derived. 1. Vertical equilibrium Pu = St cos α + Vc + Vd 2

(8.23)

2. Horizontal equilibrium

Pc = St sin α + Pst

117

(8.24)


3. Moment equilibrium about hinge 'O' ⎛ d - xs ⎞ Pu a' = Pc ( 0.5 x s ) + Pst ( d - x s ) + St Z1 + Vd ⎜ ⎟ 2 ⎝ tan α ⎠

(8.25)

For developing the displacement compatibility equations, the shear deformation of the panel is related to the extension of the bottom bars. The strain in the bars due to flexure is neglected.

Compatibility of deformation between the plate and

concrete is assumed up to shear failure.

O

A

Figure 8.13: Compatibility of panel deformations

The strain compatibility is shown in Figure 8.13 and is expressed as ε st = ε pt cos α

(8.26)

(An accurate expression of the transformation of strain is εst = εpt cos2α + εpc sin2α) Here, εst

Strain in the tension bars, corresponding to deformation δh

118


εpt

Diagonal tensile strain in the plate corresponding to deformation δt.

εpc

Diagonal compressive strain in the plate.

In the above derivation, any deformation of the adhesive layers is neglected. Expressing the strains in terms of forces, the compatibility equation can be written as Pst = St cos α

A st E s ⎛ d -x β1 t p ⎜ b s ⎝ sin α

⎞ ⎟ Ep ⎠

(8.27)

where, Ep

Elastic modulus of the plate

tp

Total thickness of the plate

β1

Factor to consider the parabolic strain distribution across the plate, when it is not accounted for in the expression of St.

The value of St depends upon the relative capacities of the following. 1. The concrete-plate composite section at the tensile splitting of the concrete 2. Ultimate tensile capacity of the plate 3. Capacity at the tensile failure of the concrete at the adhesive-concrete interface. The thickness of the plates should be adequate to avoid Case 1. For Case 2, the plate force St is given by the yielding of the plates. ⎛d -x ⎞ St = N f yp t p ⎜ b s ⎟ ⎝ sinα ⎠

(8.28)

Here, N is the number of side-face plates. The value of β1 is equal to 0.67. For Case 3, it is assumed that the failure occurs due to the concrete failing under tension over the bonded area. The corresponding plate force St is given as below.

119


⎛d -x ⎞ St = N ( 0.67 Z2 fct ) ⎜ b s ⎟ ⎝ sinα ⎠

(8.29)

where, Z2 is the length of the bonded interface (Figure 8.12) and fct is the direct tensile strength of concrete. Assuming α = 45o, Z2 is equated to the lever arm Z1 = ½(db − xs)/sinα. The value of β1 is equal to 1. The value of St for bonded plates is the lower of the above two expressions. For bolted plates, only the value of St from Case 2 is used. It will govern provided there is no shear or bearing failure of the bolts. The final stages of diagonal splitting are characterized by failure of the compression zone beneath the point load (Figure 8.14).

Pu 2

Pu 2

bl

xs

45o

xs

A (bl + xs)

Vc

45o

O

v h

2

1

h

v

Stress state at point A

Mohr's circle for stress at point A

Figure 8.14: Stress distribution beneath the point load

120


This occurs with either crushing of the concrete at the compression limit Pc,max or splitting of the concrete at the shear limit Vc,max. These limits are calculated from the state of stresses in the compression zone. The average values of the stresses over the depth of the compression zone are used in the following formulation. The tensile principal stress (σ2) is close to zero and the compressive principal stress (σ1) is limited to fck. Assuming σ1 = fck and σ2 = 0 in the Mohr’s circle, the normal and shear stresses at half the depth of the compression zone (0.5 xs) at ultimate can be calculated as follows.

σv =

( Pu 2 ) - Vc b ( bl + x s )

σ h = f cu -σ v

2θ = cos -1

τ=

(8.30) (8.31)

σh - σv f cu

f st sin 2θ 2

(8.32)

The limiting value of the compression (Pc,max) is given as

Pc, max = σ h ( x s b ) + Asc ( f yc - σ h )

(8.33)

Here, any contribution from the plates is neglected. In calculating the limiting value of the shear (Vc,max), a transformed concrete section is used.

Vc, max = τ ( b x s + Asc ( m -1) )

(8.34)

The effect of the compression bars on the shear capacity of the compression zone can be neglected.

A nominal value of the dowel force across the tension

reinforcement (Vd) is given based on the transformed concrete section.

121


An algorithm was provided to solve the above equations and calculate the ultimate load Pu. The depth of the compression zone (xs) is assumed. The value of xs should be greater than da, the depth of the upper edge of the plates. The values of St, Pst, Pc, Vc and Pu are calculated from the equations provided. The value of xs can be modified till either Pc = Pc,max or, Vc = Vc,max. The shear strength is equal to Pu/2. Material safety factors can be incorporated in fyp and fck. To apply the above procedure to uniformly distributed loads and continuous beams, the equilibrium equations need to be modified.

8.3.3 Fibre reinforced polymer (FRP) plating

RC beams can be strengthened using epoxy bonded FRP plates or fabrics. The advantages of using FRP are ease of fabrication and bonding, corrosion resistance and lightweight. In the case of FRP plated beams, in addition to the usual failure modes such as crushing of concrete, yielding of steel and rupture of FRP, local failure may occur in the concrete beam due to stress concentration at the cut-off point.

An analysis procedure for beams strengthened with FRP plates was

suggested by Saadatmanesh and Malek (1998).

8.3.4 Use of FRP bars

FRP has been used not only as sheets, but also as reinforcing bars. FRP bars can be attached to the web of a beam for shear strengthening (Lorenzis and Nanni, 2001, 2002). These near-surface mounted bars can be anchored to the flange of the beam. The failure generates from the debonding of the bars due to splitting of the epoxy paste in the grooves.

8.3.5 External Prestressing

Post-tensioned reinforcement is used to increase flexural capacity or to replace damaged prestressed strands. Prior to post-tensioning, any flexural cracks must be

122


epoxy grouted for uniform distribution of compression force. Post-tensioning provides the ability to relieve overstressed conditions, reduce excessive deflection and convert discontinuous members into continuous members.

8.4

BEAM-COLUMN JOINT STRENGTHENING

Under seismic excitation, the beam-column joint region is subject to horizontal and vertical shear forces whose magnitudes are generally many times higher than in the interior region of the beam or column. Hence, the joint should be carefully detailed to meet the shear strength requirements. The following are the most common methods of retrofit of joints. 1. Concrete jacketing 2. Concrete fillet 3. Steel jacketing 4. Steel plating 5. Fibre Reinforce Polymer (FRP) jacketing

8.4.1 Concrete Jacketing

Concrete jacketing is a common method of retrofitting a joint. Stoppenhagen et al. (1995) strengthened the joints by placing horizontal ties through drilled holes in the beam. Placement of such ties is difficult in existing buildings.

8.4.2 Concrete Fillet

Bracci et al. (1995) suggested the use of a concrete fillet at the beam-column joint to shift the potential hinge region away from the column face to the beam-slab near the end of the fillet.

123


8.4.3

Steel Jacketing

Steel jacketing helps the beam-column joint in transferring moments. The jacket provides increased flexural strength to the beam, especially where adequate bottom reinforcement may not be present if the frame was designed for gravity loads only. In a joint, the beam jacket needs to be connected to the column jacket. Steel jackets can also enhance the shear strength and ductility of beams through added strength of steel as well as through confinement of existing concrete.

8.4.4

Steel Plating

Steel plating is simpler as compared to steel jacketing, where plates in the form of brackets are attached to the soffits of the beams and sides of the column. The moment and plastic rotation capacities in beams with discontinuous bottom steel can be improved by the use of steel plates. The retrofitted interior joint performs well because: a) the pullout of the discontinuous bottom reinforcement is prevented, b) the damage is transferred from the embedment zone to other parts of the joint region, c) the column shear strength is enhanced and d) the deterioration rate of the joint region under cyclic loadings is reduced.

This approach is

unobtrusive, easy to implement and permits strengthening of exterior joints in buildings without having to break the exterior facade.

8.4.5

FRP Jacketing

The bond-slip of the longitudinal reinforcement in a joint reduces the flexural capacity. FRP sheets have been used to strengthen beam-column joints with bond-slip as well as a replacement for inadequately anchored bars. In order to prevent debonding of the fabric from concrete, mechanical anchors or FRP wraps should be provided.

124


8.5

WALL STRENGTHENING

A concrete shear wall can be strengthened by adding new concrete with adequate boundary elements (bolster columns). For the composite action, dowels need to be provided between the existing and new concrete (Figure 8.15). The analysis of a building with strengthened shear walls can be preformed using the equivalent properties of the wall.

The use of vertical and diagonal steel strips were

experimentally investigated by Taghdi et al., 2000.

Figure 8.15: Strengthening of a shear wall using concrete (Seth, 2002)

Retrofitting of a masonry infill wall is necessary when the failure of an infill wall is a hazard. For example, the failure of infill walls in higher storeys facing a busy footpath or above shop-fronts can lead to severe injury. IS 13935: 1993 gives guidelines for repair and strengthening of walls using grout and wire mesh. FRP or steel sheets can be used to strengthen walls for out-of-plane bending. Retrofitting by steel sheets involves epoxy bonding of thin sheets on both sides of the wall and addition of triangular corner plates in all the corners of the two sides (Ramesh, 2003). This strategy increases the strength, stiffness and ductility of the wall and the resistance to out-of-plane bending. FRP has been used in the strengthening of infill walls. The FRP sheets can be bonded over the full area or diagonally on both sides with triangular corner plates

125


(Ravichandran, 2003). In walls where the FRP sheet was bonded on the plastered surface, spalling of the plaster made the FRP strengthening ineffective. The sheets are more effective when they are bonded on the unplastered surface.

8.6

FOOTING STRENGTHENING

Figure 8.16: Strengthening of a footing (Basu, 2002)

The following measures may be effective in the rehabilitation of shallow footings. 1. New isolated or spread footings may be added to existing structures to support new structural elements such as shear walls or frames. 2. Existing spread footings may be enlarged to increase the capacity as shown in Figure 8.16. 3. Existing spread footings may be underpinned to increase bearing or uplift capacity. Underpinning improves bearing capacity by lowering the depth of the footing. 4. Uplift capacity may be improved by increasing the resisting soil mass above the footing or by using anchor piles.

126


5. Providing interconnection with grade beams, RC grade slab or ties helps to mitigate differential lateral displacement of the footings. The design of the strengthening of the footing is based on the conventional analysis of footings.

127


CHAPTER IX CASE STUDY I

9.1

BUILDING DESCRIPTION

The present case study is an example of a residential building in Zone III. The deficiency is due to open ground storey and shear carrying capacity of columns. A retrofit scheme using non-buckling braces is illustrated. 9.1.1 Data collection and condition assessment of building The chosen building is a seven storey residential building located in Seismic Zone III. Table 9.1 presents a summary of the building parameters. The building is symmetric about X-axis. The ground floor of the building has parking provision. Table 9.1(a): Building survey data sheet - General data S.No. 1

Description

Information

Address of the building • • • • •

CS1 Ahmedabad Gujarat

Name of the building Plot number Locality/Town ship District State

129


2

Name of owner

-

3

Name of builder

-

4


-

5


-

6

Use of building

Residential

7

Number of storeys above ground level

6

8

Number of basements below ground level Type of structure

-

• Load bearing wall • RC frame • RC frame and shear wall Steel frame

RC frame

9

10

Soil data Medium

• Type of soil Design safe bearing capacity 11

(assumed)

Dead loads (unit weight adopted) • Earth • Water • Brick masonry • Plain cement concrete • Floor finish Other fill materials

12

20kN/m3 1kN/m2

Imposed (live)loads 2 kN/m2 1.5 kN/m2

• Floor loads Roof loads 13

Cyclone/Wind -

• Speed Design pressure intensity 14

History of past earthquakes and tremors

-

15

Seismic zone

III

16


1

17


0.16

18


3

130

Chapter IX – Case Study I

19


Table 9.6

20

Design Horizontal acceleration spectrum value (Ah)

Table 9.6

21

Seismic designed lateral force (percentage of weight 6.7% of building)

22


-

Table 9.1(b): Building survey data sheet - Building data (moment resisting frame) S.No. 1

Description

Information

2

Number of basements

Regular frames -

3

Number of floors

6

4

Horizontal floor system • Beams and slabs • Waffle slab • Ribbed floor • Flat slab with drops • Flat plate without drops Soil data • Type of soil • Recommended foundation - Independent footings - Raft - Piles • Recommended bearing capacity • Recommended type, length, diameter and load capacity of piles • Depth of water table • Chemical analysis of ground water • Chemical analysis of soil Foundations • Depth below ground level • Type − Independent − Interconnected − Raft − Piles System of interconnecting foundations • Plinth beams • Foundation beams

5

6

7

Type of building

131

Beams slabs

and

Medium Independent footings

1.5m Independent

Plinth beams


8 9 10 11 12

13 14 15

16

Grades of concrete used Method of analysis Computer software used Torsion included Base shear a) Based on approximate fundamental period b) Based on dynamic analysis c) Ratio of a/b Distribution of seismic forces along the height of building The columns of soft ground storey specially designed Clear minimum cover provided in • Footing • Column • Beams • Slabs • Walls Ductile detailing of RC frame • Type of reinforcement used • Minimum dimension of beams • Minimum dimension of columns • Minimum percentage of reinforcement of beams at any cross section • Spacing of transverse reinforcement at any section of beam • Spacing of transverse reinforcement in 2d length of beam near the ends • Ratio of capacity of beams in shear to capacity of beams in flexure • •

• • •

Maximum percentage of reinforcement in column Confining stirrups near ends of columns and in beam-column joints − Diameter − Spacing Ratio of shear capacity of columns to maximum seismic shear in the storey Column bar splices location and spacing of hoops in the splice Beam bar splices location and spacing of hoops in the splice

132

M20 2960kN 939kN 3.15 Parabolic No 40mm 30mm 25mm 15mm Fe 415 230mm 230mm 0.26% 200mm 100mm less than 1 in many sections 1.2% -

Section 9.2.2 -


Figure 9.1: Architectural plan for typical floor level of the building. 133


9.1.2 Structural system and members

9.1.2.1

Foundation

The foundation system is isolated footing. Depth of the foundation is 1.5m from ground level.

9.1.2.2

Structural system

It is a RC framed structure. The concrete slab thickness is 115 mm except for some locations where it is 120 mm. Figure 9.2 shows the slab layout at a typical floor level and their details are given in Table 9.2. The external walls are 230mm thick and partition walls inside the building are 115mm thick. Figure 9.3 shows the column layout and Table 9.3 shows the reinforcement details of the column sections at a typical floor. Table 9.2: Details of slabs at typical floor level Slab Thickness Mark (mm) S1 115 S2 115 S3 120 S4 115 S5 120 S6 120

Reinforcement (mm) Short Span Long Span Y8 @ 150 c/c Y8 @ 150 c/c Y8 @ 125 c/c Y8 @ 125 c/c Y8 @ 150 c/c Y8 @ 150 c/c Y8 @ 150 c/c Y8 @ 150 c/c Y8 @ 150 c/c Y8 @ 150 c/c Y8 @ 175 c/c Y8 @ 175 c/c

Remarks One Way Two Way Two Way Two Way Two Way Two Way

Table 9.3: Details of column reinforcements Longitudinal Reinforcement (mm)

Transverse Reinforcement (mm)

8Y12

2 LGD 6φ @ 150c/c

C1

Size (mm) Width × Depth Above Below Plinth Plinth 230 × 450 300 × 533

C2

230 × 533

300 × 610

4Y16 + 4Y12

2 LGD 6φ @ 150c/c

C3

230 × 533

300 × 610

8Y16

2 LGD 6φ @ 150c/c

C4

230 × 610

300 × 686

4Y20 + 4Y16

2 LGD 6φ @ 150c/c

C5

230 × 610

300 × 686

6Y20 + 4Y16

3 LGD 6φ @ 150c/c

Column ID

134


C6

230 × 610

300 × 686

12Y20

3 LGD Y8 @ 250c/c

C7

230 × 685

300 × 762

14Y20

3 LGD Y8 @ 200c/c

Figure 9.4 shows the layout of beam sections at a typical floor level and Figure 9.5 shows the layout of beam elements. All floors have identical beam sections. Table 9.4 shows the beam section assigned to different beam elements. Table 9.4: Details of beam reinforcements Longitudinal Reinforcement at Transverse support (mm2) Reinforcement (mm) Top Bottom

Beam Section

Size (mm) Width × Depth

B6

230 × 457

703.7

339.3

B7 B8 B9 B10 B11 B15 B16 B17 B19 B21 B22 B25 B26 B27 B35

230 × 457 230 × 457 230 × 457 230 × 457 230 × 457 230 × 230 230 × 457 115 × 571 230 × 381 230 × 457 230 × 495 230 × 381 230 × 267 230 × 381 230 × 381

414.0 502.0 615.5 816.0 615.8 502.0 703.7 100.5 414.5 753.0 502.5 515.0 615.5 615.0 414.0

306.0 402.0 603.2 515.2 100.5 226.0 339.3 100.5 339.3 716.3 339.0 515.0 402.0 314.0 339.0

135

Y8@100c/c Y8@127c/c Y8@127c/c Y8@100c/c Y8@127c/c Y8@100c/c Y8@150c/c Y8@127c/c Y8@127c/c Y8@127c/c Y8@100c/c Y8@100c/c Y8@127c/c Y8@100c/c Y8@127c/c Y8@150c/c


Figure 9 2: Slab section layout of typical floor level. 136


Figure 9.3: Column section and their orientation layout of typical storey. (Section ‘Cn’ and ‘CCn’ are having same properties but different orientation) 137


Figure 9.4: Beam section layout of typical floor level. 138


Figure 9.5: Beam element layout of typical floor level. (‘N’ indicates the story level e.g. 3B46 element indicates third floor level) 139


Figure 9.6: Lateral load resisting frames along X-direction. 140


Figure 9.7: Lateral load resisting frames along Y-direction. 141


9.2

PRELIMINARY EVALUATION

The preliminary evaluation was done as per the method in Chapter 2. 9.2.1 Rapid Visual Screening The rapid visual screening results shown in Table 9.5 indicate the requirement of detailed analysis. Both MRF and URM - INF were considered, as the building is primarily moment resisting framed building with un-reinforced masonry infill. Table 9.5: Rapid Visual Screening data collection Region of Seismicity Building Type Basic Score Mid rise High rise Vertical irregularity

Plan irregularity Pre-code Post-benchmark Soil Type I Soil Type II Soil Type III Final Score Comments

High Seismicity (Zone V) URM MRF SW INF 2.5 2.8 1.6 +0.4 +0.4 +0.2 +0.6 +0.8 +0.3

Moderate Seismicity (Zone IV) URM MRF SW INF 3.6 3.0 3.2 +0.2 +0.4 +0.2 +0.5 +0.8 +0.4

-1.5

-1.0

-1.0

-2.0

-0.5 -1.2 +1.4 -0.4 -0.6 -1.2

-0.5 -1.0 +2.4 -0.4 -0.6 -0.8

-0.5 -0.2 N/A -0.4 -0.4 -0.8

-2.0

-1.5

-2.0

-2.0

-0.5 -0.5 -0.5 -0.8 -0.8 -0.8 -1.0 -0.4 -1.0 N/A N/A N/A +1.2 +1.6 N/A +0.6 +0.4 N/A -0.6 -0.8 -0.6 -0.6 -0.4 -0.4 -1.4 -0.8 -0.8 -1.0 -1.2 -1.0 -1.6 -1.6 -1.6 -2.0 -2.0 -2.0 -0.5 -0.4 Final Score is less than the cut-off score of 2.0, so detailed analysis required

9.2.2 Quick Checks for strength and stiffness

9.2.2.1

-2.0

Low Seismicity (Zone II & Zone III) URM MRF SW INF 4.4 4.8 4.4 +0.4 -0.2 -0.4 +1.0 0.0 -0.4

Column Shear

The calculation details are given in the Table 9.6.

142


Table 9.6: Average column shear stress Floor No

nf

nc

Ac (m2)

Vj (kN)

τavg(MPa)

Remarks

B G 1 2 3 4 5 6

7 7 7 7 7 7 7 7

32 32 32 32 32 32 32 32

6.27 4.24 4.24 4.24 4.24 4.24 4.24 4.24

1685 1685 1669 1614 1494 1289 979 540

0.344 0.509 0.504 0.487 0.451 0.389 0.296 0.163

< 0.4 > 0.4 > 0.4 > 0.4 > 0.4 > 0.4 > 0.4 > 0.4

9.2.2.2

Shear stress in shear wall

Not applicable to this building.

9.2.2.3


The details are given in the Table 9.7. Table 9.7 Details of axial stress in column

X dir Y dir

Left Right Left Right

Vb(kN)

nf

h(m)

L(m)

P(kN)

Axial stress

1685 1275 1685 1392

6 4 5 5

23.55 23.55 23.55 23.55

14.25 10.64 17.78 17.78

290 441 279 230

2.37 3.60 2.28 1.88

Permissible limit is 0.24fck i.e. 0.24 x 20 = 4.8 N/mm2. Calculated axial stresses are within the permissible limit.

9.2.2.4

Frame Drift

Since dimensions of columns are not changed from storey to storey in this building, the Drift Ratio (DR) is calculated for ground storey and the first storey only. Ground storey height is 3.45m and other storey height is 3.0. The DR value is observed to be very less in the building i.e. 1.3×10-5 for ground storey and

143


1.15×10-6 for first storey. The limiting value of DR is 0.015. Hence, the storey drifts are within the limit.

9.2.2.5

Strong column – weak beam

In the strong direction of the columns (about major axis) ∑ Moment capacities of the columns = 496 kNm 1.2 ∑ Moment capacities of the beams = 135 kNm. In the weak direction of the columns (about minor axis) ∑ Moment capacities of the columns = 196 kNm 1.2 ∑ Moment capacities of the beams = 216 kNm. The strong column and weak beam criteria is satisfied in the strong direction, but not in the weak direction. 9.2.3 Evaluation statements

Table 9.8: Evaluation statements Building system

C / NC / NA C

Load path:

NA

Adjacent buildings:

C

Mezzanines:

NA

No deterioration of concrete: Vertical irregularities

C / NC / NA C

No weak storey:

NC

No soft storey:

C

No mass irregularity:

NC

No vertical geometric irregularity:

C

No vertical discontinuities: Plan Irregularities

144

C / NC / NA


No Torsion irregularity:

NC

No diaphragm discontinuity:

NC

No re-entrant corners:

NC

No out of plane offsets:

C

No non-parallel system:

C

Moment resisting frames

C / NC / NA

Redundancy:

C

No interfering wall:

C NC

Shearing stress check: Axial stress check:

C

Drift check:

C

No short captive columns:

C

No shear failures:

NC

Strong column-weak beam:

NC

Column bar splices:

NA

Column tie spacing:

NA C

Beam bars: Beam bar splices:

NA

Stirrup spacing:

NC

Bent-up bars:

NC

Joint reinforcing:

NC

Deflection compatibility:

C

No flat slab frames:

C

Prestressed frame elements:

C

Diaphragm reinforcement:

C Shear walls

C / NC / NA

Shearing stress check:

NA

Reinforcing steel:

NA

145


Coupling beams:

NA

Diaphragm openings at shear walls:

NA

Connections

C / NC / NA C

Column connection: Wall connection:

NA

Transfer to shear walls:

NA

Lateral load at pile caps:

NA

Geologic site hazards

C / NC / NA

No Liquefaction:

NA

No slope failure:

NA

No surface fault rupture:

NA Foundations

C / NC / NA C

Foundation performance: Deterioration:

NA

Overturning:

C NA

Ties between foundation elements:

Table 9.8 shows that the statements are non-compliant (NC) for most of the cases because of poor detailing. There is no vertical or plan irregularity in the building.

146


9.3

EVALUATION BASED ON LINEAR ANALYSIS

The building modelled and analysed as per the guidelines given in Chapter 3. 9.3.1 Material Properties The material properties considered for the analysis are given in Table 9.9. Table 9.9: Materials properties Material Concrete (M 20) Reinforcing Steel (Fe 415) Brick infill

Characteristic Strength (MPa) 20 415 1.65

Modulus of Elasticity (MPa) 22360 2 × 105 1237.5

Figure 9.8: 3D computer model of the structure.

147


9.3.2

Structural Element Model

9.3.2.1

Infill Walls

Figure 9.9 shows the location of infill walls that were modelled as equivalent struts. The calculated strut parameters are shown in Table 9.10. Table 9.10: Strut parameters Strut

9.3.3

Equivalent Thickness Strength Yield Deformation Width (m) (m) (kN) (mm)

S1

1.42

0.230

358

2.90

S2

1.21

0.230

435

4.98

S3

1.49

0.115

215

3.35

S4

1.31

0.230

353

2.99

S5

1.54

0.230

443

3.31

S6

1.54

0.230

457

4.25

S7

1.29

0.115

267

5.78

S8

1.48

0.115

213

4.15

S9

0.93

0.230

348

4.07

S10

1.11

0.115

173

2.99

S11

1.12

0.230

324

3.03

S12

1.09

0.230

318

3.06

S13

1.09

0.230

318

3.28

S14

1.36

0.230

348

2.98

Modelling of column ends at foundation

The foundation for the building is made up isolated footings. In the model, hinges were assumed at the column ends at the bottom of footings. The effect of soilstructure interaction was ignored in the analyses.

148


Figure 9: Location of infill walls 149


9.3.4 Design centres of mass Since there is a discontinuity of the diaphragm in the building, two separate diaphragms were considered at every floor level. Tables 9.11 and 9.12 give the centres of masses and rigidity of the building for the equivalent static method. Table 9.13 and Table 9.14 give the values for the response spectrum method. edi1

= 1.5esi + 0.05b = esi + 0.05b = esi – 0.05b

edi2

(for the equivalent static method) (for the response spectrum method) (for both the methods)

Table 9.11: Centres of mass and rigidity for the equivalent static method (Without infill stiffness) Floor

CM X

CR Y

X

esi Y

edi1

X

edi2 X

DCM

Y

X

Y

Y

X

Y

0.00 0.00 0.00

1.12 1.10 3.29

0.90 0.90 0.90

-0.57 -0.90 8.56 9.21 -0.58 -0.90 8.59 9.21 0.88 -0.90 6.92 9.21

0.00 0.00 0.00

4.12 4.09 3.98

0.90 0.90 0.90

1.68 1.66 1.59

Left 9.68 10.11 9.90 10.11 0.22 1 2 to 6 9.69 10.11 9.90 10.11 0.21 10.21 10.11 11.88 10.11 1.67 7

Right 25.28 10.11 22.96 10.11 2.32 1 2 to 6 25.26 10.11 22.96 10.11 2.30 25.19 10.11 22.96 10.11 2.23 7

-0.90 29.40 9.21 -0.90 29.35 9.21 -0.90 29.17 9.21

Table 9.12: Structural parameters and Design Centre of Masses for Equivalent static method (with infill stiffness) Floor

CM X

CS Y

X

esi Y

X

edi1

edi2 X

DCM

Y

X

Y

Y

X

Y

0.00 0.00 0.00

1.41 3.05 4.91

0.90 0.90 0.90

-0.37 -0.90 8.68 9.21 0.72 -0.90 8.15 9.21 1.96 -0.90 8.05 9.21

0.31 0.00 0.00

1.81 3.64 4.39

1.37 0.90 0.90

0.14 1.36 1.86

Left 9.68 10.11 10.10 10.11 0.42 1 2 to 6 9.69 10.11 11.20 10.11 1.51 10.21 10.11 12.96 10.11 2.75 7

Right 25.28 10.11 24.50 9.80 0.78 1 2 to 6 25.26 10.11 23.26 10.11 2.00 25.19 10.11 22.69 10.11 2.50 7

150

-0.59 26.31 11.17 -0.90 26.90 9.21 -0.90 27.08 9.21


Table 9.13: Structural parameters and Design centre of masses for Response spectrum method (without infill stiffness) Floor

CM X

CS Y

X

edi1

esi Y

X

edi2 X

DCM

Y

X

Y

Y

X

Y

0.00 0.00 0.00

1.01 1.00 2.46

0.90 0.90 0.90

-0.57 -0.90 8.89 9.21 -0.58 -0.90 8.90 9.21 0.88 -0.90 9.42 9.21

0.00 0.00 0.00

2.96 2.94 2.87

0.90 0.90 0.90

1.68 1.66 1.59

Left 9.68 10.11 9.90 10.11 0.22 1 2 to 6 9.69 10.11 9.90 10.11 0.21 10.21 10.11 11.88 10.11 1.67 7

Right 25.28 10.11 22.96 10.11 2.32 1 2 to 6 25.26 10.11 22.96 10.11 2.30 25.19 10.11 22.96 10.11 2.23 7

-0.90 25.92 9.21 -0.90 25.90 9.21 -0.90 25.83 9.21

Table 9.14: Structural parameters and Design centre of masses for Response spectrum method (without infill stiffness) Floor

CM X

CS Y

X

esi Y

edi1

X

edi2 X

DCM

Y

X

Y

Y

X

Y

0.00 0.00 0.00

1.20 2.30 3.54

0.90 0.90 0.90

-0.37 -0.90 8.89 9.21 0.72 -0.90 8.90 9.21 1.96 -0.90 9.42 9.21

0.31 0.00 0.00

1.42 2.64 3.14

1.21 0.90 0.90

0.14 1.36 1.86

Left 9.68 10.11 10.10 10.11 0.42 1 2 to 6 9.69 10.11 11.20 10.11 1.51 10.21 10.11 12.96 10.11 2.75 7

Right 25.28 10.11 24.50 9.80 0.78 1 2 to 6 25.26 10.11 23.26 10.11 2.00 25.19 10.11 22.69 10.11 2.50 7

-0.59 25.92 11.0 -0.90 25.90 9.21 -0.90 25.83 9.21

9.3.5 Equivalent static analysis 9.3.5.1

Design Base Shear

Table 9.15 shows the calculations of base shear for the left and right portions of the building for both without infill stiffness and with infill stiffness cases. Typical seismic load distribution for left portion of building with infill stiffness in Xdirection is shown in the Table 9.16. (Base shear is 1685kN)

151


Table 9.15: Details of calculations for base shear of the building Width of Time Building Period ('d' in m) (s) Without Infill Stiffness

With Infill Stiffness

Left

Right

Sa/g

ah

Base Weight Shear (kN) (kN)

X dir

N/A

0.80

1.70

0.045

25271

1143

Y dir

N/A

0.80

1.70

0.045

20876

944

X dir

15.78

0.53

2.50

0.067

25271

1685

Y dir

17.78

0.50

2.50

0.067

25271

1685

X dir

12.74

0.59

2.29

0.061

20876

1275

Y dir

17.78

0.50

2.50

0.067

20876

1392

Table 9.16: Typical distribution of lateral force over the height of the building Floor No. Water tank 6 5 4 3 2 1 G

9.3.6

Seismic Weight, Wi (kN)

Height, hi (m)

Lateral Force, Qi (kN)

422

23.55

84

2767

21.45

457

3592

18.45

438

3626

15.45

310

3691

12.45

205

3720

9.45

119

3716

6.45

55

3737

3.45

16

Response spectrum analysis

The various fundamental time periods and the spectral acceleration coefficients for the building are given in Table 9.17. The comparison is shown in Figure 9.10. Table 9.18 represents the period and the predominant direction of vibration for the first five modes of the building, with and without the infill stiffness. The table also shows the mass participation for each of the five modes. The first five modes were considered in the dynamic analysis, which give more than 90% mass participation in both of the horizontal directions. Figure 9.11 shows the first three mode shapes

152


of the building. The base shear for the equivalent static method and the response spectrum methods are given in Table 9.19. Table 9.17: Comparison of fundamental time periods IS 1893: 2002 Without Infill Stiffness


X dir Y dir

Computational model

T (s)

Sa/g

T (s)

Sa/g

X dir

0.80

1.70

1.64

0.82

Y dir

0.80

1.70

1.52

0.89

Left

0.53

2.50

Right

0.50

2.50

Left

0.59

2.29

1.23

1.10

Right

0.50

2.50

Table 9.18: Time periods and mass participation factors for the first five modes Mode 1 2 3 4 5

Without infill stiffness Mass Participation (%) T (s) ux uy

With infill stiffness Mass Participation (%) T (s) ux uy

1.64

86.74

0.03

1.23

7.94

31.39

1.52

0.07

89.95

1.14

39.62

47.87

1.30

1.87

0.44

1.09

46.36

16.59

0.54

8.59

0.00

0.39

0.24

1.66

0.49

0.01

6.99

0.35

5.23

0.24

97.28

97.41

99.39

97.75

Total

Table 9.19: Comparison of base shear Without infill stiffness Vx (kN) Vy (kN)

With infill stiffness Vx (kN) Vy (kN)

Equivalent Static

(V )

2086

2086

2960

3077

(VB )

913

1013

939

862

VB / VB

2.28

2.06

3.15

3.57

B

Response Spectrum

153


3

a /g)

IS 1893 (Without infill stiffness) IS 1893 (With infill stiffness)

2.5

Computaional (w ithout inf ill stiffness)

Spectral accelaration ( S

Computational (w ith inf ill stiffness)

2

1.5

1

0.5

0 0

0.5

1

1.5

2

2.5

3

3.5

4

Time period (s)

Figure 9.10: Comparison of time periods of the building models

Figure 9.11(a): First mode shape of the building (without infill stiffness)

154


Figure 9.11(b): Second mode shape of the building (without infill stiffness)

Figure 9.11(c): Third mode shape of the building (without infill stiffness)

155


Figure 9.11(d): First mode shape of the building (with infill stiffness)

Figure 9.11(e): Second mode shape of the building (with infill stiffness)

156


Figure 9.11(f): Third mode shape of the building (with infill stiffness) 9.3.7 Evaluation results Since the torsional mode is predominant for the model with infill stiffness, the response spectrum method is important. The response spectrum analysis results show that a number of elements do not satisfy the Demand-to-Capacity Ratios (DCR). The deficient beam sections are given in Tables 9.20, 9.21 and 9.22. The deficient column sections are given in Tables 9.23 and 9.24. The percentage of deficient elements is the ratio of number of elements with DCR greater than 1, to the total number of elements for the particular type of section. Table 9.20: Evaluation results for flexure in beams (without infill stiffness) Percentage Capacity (kN-m) Demand (kN-m) DCR Sl. of deficient Section No. M(-ve) M(+ve) M(-ve) M(+ve) M(+ve) M(-ve) elements 1

B3

-54

15

-50

5

0.93

0.30

0

2

B6

-50

60

-260

214

5.20

3.57

74

3

B7

-60

45

-201

176

3.34

3.90

67

157


4

B8

-73

59

-237

166

3.25

2.82

83

5

B9

-89

87

-292

114

3.28

1.31

77

6

B10

-116

75

-301

164

2.59

2.19

73

7

B11

-82

25

-258

166

3.14

6.66

100

8

B15

-30

15

-78

52

2.58

3.50

78

9

B16

-96

49

-87

25

0.90

0.51

0

10

B17

-19

19

-91

68

4.80

3.60

75

11

B19

-49

40

-207

80

4.23

2.00

78

12

B21

-109

103

-244

148

2.24

1.44

100

13

B22

-79

54

-331

194

4.18

3.59

72

14

B25

-60

60

-148

52

2.47

0.87

60

15

B26

-46

31

-114

55

2.48

1.77

81

16

B27

-70

37

-194

84

2.77

2.28

55

17

B35

-49

40

-157

59

3.21

1.48

64

Table 9.21: Evaluation results for flexure in beams (with infill stiffness) Capacity (kN-m) Demand (kN-m) Sl Section No. M(-ve) M(+ve) M(-ve) M(+ve)

(+ve)

(-ve)

Percentage of deficient elements

DCR

1

B3

-54

15

-79

7

1.45

0.48

21

2

B6

-50

60

-486

378

9.71

6.31

93

3

B7

-60

45

-271

104

4.52

2.30

88

4

B8

-73

59

-332

296

4.55

5.02

95

5

B9

-89

87

-446

207

5.01

2.38

99

6

B10

-116

75

-411

243

3.54

3.24

88

7

B11

-82

25

-382

311

4.66

12.42

100

8

B15

-30

15

-132

75

4.40

5.00

89

9

B16

-96

49

-136

21

1.41

0.44

7

10

B17

-19

19

-143

46

7.52

2.44

100

11

B19

-49

40

-303

89

6.19

2.23

98

12

B21

-109

103

-325

300

2.98

2.91

100

13

B22

-79

54

-293

200

3.71

3.70

94

14

B25

-60

60

-225

82

3.75

1.37

71

15

B26

-46

31

-136

93

2.95

2.99

100

16

B27

-70

37

-57

93

0.82

2.51

52

17

B35

-49

40

-214

64

4.37

1.61

86

158


Table 9.22: Evaluation results for shear in beams Sl. Capacity Section No. (kN-m)

Demand (kN-m)

from Flexure Capacity WOIS WIS WOIS WIS

Analysis WoIS

WIS


DCR

1

B6

68

246

428

112

3.62

6.30

43

48

2

B9

68

187

257

132

2.75

3.78

62

78

3

B10

54

98

146

131

2.43

2.71

73

85

4

B11

68

96

129

99

1.46

1.89

12

15

5

B12

54

48

93

55

1.02

1.72

6

6

6

B15

45

207

257

52

4.61

5.71

19

24

7

B17

25

223

325

21

8.94

12.99

34

43

8

B19

54

132

161

84

2.45

2.98

46

56

9

B22

54

144

164

111

2.66

3.04

44

52

10

B25

54

119

89

86

2.20

1.65

43

41

11

B27

54

178

246

94

3.29

4.56

21

38

12

B35

45

264

457

94

5.88

10.15

32

43

Table 9.23: Evaluation results for flexure in columns Sl. No.

Percentage of deficient elements WOIS WIS

DCR

Section

WOIS

WIS

1

CC1

4.10

6.35

83

88

2

CC3

3.71

5.97

73

81

3

CC4

5.32

6.72

72

71

4

CC5

3.74

6.77

73

72

5

C1

3.58

5.82

67

85

6

C2

4.77

8.91

64

59

7

C3

4.34

9.44

66

67

8

C4

5.31

10.32

69

90

9

C5

3.23

8.74

71

83

10

C6

3.70

9.03

54

62

11

C7

3.94

9.60

56

65

Table 9.24: Evaluation results for shear in columns Sl. No.

Section

1

CC1

Capacity (kN)

DCR

V2

V3

WOIS V2 V3

136

72

0.50

159

0.60

WIS V2 V3 0.71

1.49


WOIS

WIS

0

6


2

CC3

166

79

0.69

0.63

0.86

1.17

0

6

3

CC4

194

85

1.05

1.77

1.09

2.65

6

15

4

CC5

198

89

0.68

0.79

1.01

1.08

5

C1

71

136

0.55

0.49

0.65

0.71

0 0

6 0

6

C2

77

163

0.89

0.50

0.83

1.10

0

6

7

C3

79

167

0.75

0.71

0.90

1.33

0

7

8

C4

85

194

0.54

0.72

1.05

1.34

0

7

9

C5

88

199

0.88

0.52

0.93

1.31

0

7

10

C6

92

202

0.59

0.67

0.85

1.57

0

6

11

C7

98

230

0.77

0.64

2.08

1.35

0

8

The above results show that the beams are having lesser capacities than the corresponding demands in both flexure and shear. The columns are having lesser capacities than the demands in flexure. For shear, many columns are adequate along the major dimension, but many are deficient along the minor dimension. Major portion of the failure is observed in the ground, first and second storeys. The storey displacements along the X- and Y- directions are presented in Figures 9.12(a) and 9.12(b). The deflection profiles for the cases of without infill stiffness and with infill stiffness are plotted in the same graph for comparison. Since the basement height is not same as storey height, the change in the profile at basement level can be ignored. The calculated inter storey drifts are shown in Figures 9.13(a) and 9.13(b).

160


8 7

Storey Level

6 5 4 3 2 1 0 0

0.02

0.04

0.06

0.08

Displacement

Figure 9.12(a): Displacements along X-direction

8 7

Storey Level

6 5 4 3 2 1 0 0

0.02

0.04

0.06

0.08

Displacement

Without Infill Stiffness


Figure 9.12(b): Displacements along Y-direction

161


7 6

Storey Level

5 4 3 2 1 0

0.1

0.2

0.3

0.4

0.5

0.6

Inter Storey Drift (%)

Figure 9.13(a): Inter storey drift along X-direction of building

7 6

Storey Level

5 4 3 2 1 0

0.2

0.4

0.6

0.8




Figure 9.13(b): Inter storey drift along Y-direction of building

162


9.4

EVALUATION BASED ON NONLINEAR PUSHOVER ANALYSIS

The analysis was done as per the method in Chapter 4. Since the building is irregular, 30 percent of lateral push was applied along with the push in the main direction. 9.4.1

Pushover curves

Pushover curves for the building with and without infill stiffness in X- and Ydirections are shown in Figure 9.14 and 9.15. The base shear from the equivalent static method is also plotted to compare the capacity with the demand based on linear analysis. The capacity from the pushover analysis is observed to be little higher than the demand. The pushover curve is almost linear and it terminates abruptly due to the formation of shear hinges in the columns.

3500

VB 3000

Base Shear (kN)

2500

VB 2000 1500 1000 500 0 0

0.02

0.04

0.06

0.08

0.1

Roof displacement (m)



Figure 9.14: Pushover curves for the building in X-direction.

163


9.4.2 Capacity spectrum, demand spectrum and performance point Pushover analyses in either direction failed to give a performance point for both the models, with and without infill stiffness. The demand and capacity spectrum for the lateral push along the two orthogonal directions are shown in Figures 9.16 and 9.17. Many equivalent struts in the first and second storeys failed before the formation of the mechanism. 9.4.3 Displacements and inter storey drifts The displacements at ultimate are plotted in Figures 9.18 and 9.19. The inter storey drifts corresponding to the displacement profiles are shown in Figures 9.20 and 9.21.

4000 3500

VB

Base Shear (kN)

3000 2500

VB

2000 1500 1000 500 0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Roof displacement (m)



Figure 9.15: Pushover curves for the building in Y-direction.

164


X - Direction Y - Direction Figure 9.16: Demand and capacity spectra (without infill stiffness)

X - Direction Y - Direction Figure 9.17: Demand and capacity spectrum (with infill stiffness)

165


9 8 7 Storey Level

6 5 4 3 2 1 0 0

0.02

0.04

0.06

0.08

0.1

Displacement



Figure 9.18: Displacement along X-direction.

9 8 7 Storey Level

6 5 4 3 2 1 0 0

0.01

0.02

0.03

0.04

0.05

0.06

Displacement



Figure 9.19: Displacement along Y-direction.

166


7

Storey Level

6 5 4 3 2 1 0

0.1

0.2

0.3

0.4

0.5




Figure 9.20: Inter storey drifts for the building in X-direction.

7

Storey Level

6 5 4 3 2 1 0

0.1

0.2

0.3

0.4




Figure 9.21: Inter storey drifts for the building in Y-direction.

167


9.4.4

Vulnerability Index

Since the failure hinges are shear hinges, the value of vulnerability index is very less. So, the damage in the building cannot be predicted by vulnerability index. 9.4.5 Summary of the results

(i)

Linear analysis results show that almost all beam and column sections are weak in flexure and shear. Pushover analysis also reveals the same weakness of the structure and failed to give a performance point for both the models, with and without infill stiffness.

(ii)

Building is not satisfying drift requirements under design lateral force.

(iii)

Inter storey drifts in ground storey is high in both linear and nonlinear analysis for with infill strut case.

168


9.5

RETROFITTING

9.5.1 Retrofitting Since there is a severe global deficiency of a soft storey, a global retrofit strategy is tested. In the ground storey, non-buckling braces are placed to stiffen the storey. In the first and second storeys, the infill walls are replaced with nonbuckling braces at certain locations. Figure 9.25 shows the bracing locations in the ground and the first two storeys. The modelling of the load-deformation behaviour of the non-buckling braces is based on Appendix E.

Along with the

global retrofit, the shear capacities of columns in the lower three storeys at locations A, B and C and beams in the first and second floors at location D and E need to be increased by 30%. To achieve a performance point, the required number of braces is high. Also, introduction of the braces in the ground storey reduces the functionality of the space. The proposed retrofit scheme is for illustration of the change in behaviour of the structure. The pushover curves in both X- and Y- directions are shown in Figure 9.22. The base shear capacity of the building has increased after the

7000

8000

6000

7000

5000

B ase Sh ear (kN )

B ase Sh ear (kN)

retrofitting with braces.

4000 3000

VB

2000 1000 0 0.00

6000 5000 4000 3000

VB

2000 1000

0.05

0.10

0.15

0 0.00

0.05

0.10

Roof dis place m e nt (m )

Roof dis place m e nt (m )

X - Direction

Y - Direction

Figure 22: Pushover curve along X and Y direction.

169

0.15


Figure 23: Demand and Capacity spectra for lateral push along X-direction

Figure 24: Demand and Capacity spectra for lateral push along Y-direction.

170


The demand and capacity spectra for the lateral push along X- and Y- directions are shown in Figures 23 and 24. The building has achieved performance points in both the directions. The building experiences a drift about 0.5% at the performance point, which is acceptable. The inter storey drifts are within the permissible limits at the performance point.

171


C

E

A D B

Figure. 25: Location of non-buckling braces at first storey level (Braces are shown by dotted lines are additional braces in Ground storey)

172


CHAPTER X CASE STUDY II

10.1 INTRODUCTION The present case study is an example of a residential building in Zone V. The deficiency due to open ground storey is highlighted.

A retrofit scheme with

addition of infill walls and concrete jacketing is illustrated.

10.2

DATA COLLECTION AND CONDITION ASSESSMENT OF

BUILDING The building is a five storey residential building located in Zone V. Tables 10.1 and 10.2 present a summary of the building parameters. The building is symmetric in both the directions. The ground storey of the building is an open ground storey to accommodate car parking.

Figure 10.1 shows a typical floor plan of the

building.

173


Figure 10.1: Typical floor plan of the building

Table 10.1: Building survey data sheet: General data S.No

Description

Information

Notes

. 1



CS2 Guwahati Assam

2

Name of owner

−

3

Name of builder

−

4


−

5


−

6

Use of building

Residential

7

5

9


10

Soil data

8

• •

Type of soil Design safe bearing capacity

174

0 RC frame Medium Not Available

(Assumed)

Chapter X – Case Study II


Information

Notes

11

Dead loads (unit weight adopted)

12

• Earth • Water • Brick masonry • Plain cement concrete • Floor finish • Other fill materials Imposed (live)loads

13

• Floor loads • Roof loads Cyclone/Wind

2 kN/m2 1.5 kN/m2 −

15

• Speed • Design pressure intensity History of past earthquakes and tremors Seismic zone

Earthquake Prone Area V

IS 1893: 2002

16


1.0

IS 1893: 2002

17


0.36

IS 1893: 2002

18


3.0

IS 1893: 2002

19


0.38 s

IS 1893: 2002

20 21

Design Horizontal acceleration 0.15 spectrum value (Ah) Seismic design lateral force 2878 kN

22


14

10 kN/m3 20 kN/m3 25 kN/m3 18 kN/m3

IS: 875 Part 1

IS: 875 Part 2

IS 1893: 2002

−

Table 10.2: Building survey data sheet: Building Data (moment resisting frame) S.No. Description

Information

1

Type of building

2

Number of basements

Regular frames with open ground storey −

3

Number of floors

5

4

Horizontal floor system

Beams slabs

175

and

Notes



6

7

8 9 10 11 12

13 14 15

16

Information

Soil data • Type of soil • Recommended foundation • Recommended bearing capacity • Recommended type, length, diameter and load capacity of piles • Depth of water table • Chemical analysis of ground water • Chemical analysis of soil Foundations • Depth below ground level • Type System of interconnecting foundations • Plinth beams • Foundation beams Grades of concrete used in different parts of building Method of analysis Computer software used Torsion included Base shear a) Based on approximate fundamental period b) Based on dynamic analysis c) Ratio of a/b Distribution of seismic forces along the height of building The columns of soft ground storey specially designed Clear minimum cover provided in • Footing • Column • Beams • Slabs • Walls Ductile detailing of RC frame

176

Notes

Medium (assumed)

− − − 0.7 m Pile No interconnection

Groups of multiple pile

M15 − − − IS 1893: 2002 2878 kN 1768 kN 1.63 Parabolic

IS 1893: 2002

−

IS 1893: 2002

Not Available



Information

Ductile detailing of RC frame • Type of reinforcement used • Minimum dimension of beams • Minimum dimension of columns • Minimum percentage of reinforcement of beams at any cross section • Spacing of transverse reinforcement at any section of beam • Spacing of transverse reinforcement in 2d length of beam near the ends • Ratio of capacity of beams in shear to capacity of beams in flexure • Maximum percentage of reinforcement in column • Confining stirrups near ends of columns and in beamcolumn joints − Diameter − Spacing • Ratio of shear capacity of columns to maximum seismic shear in the storey • Column bar splices location and spacing of hoops in the splice • Beam bar splices location and spacing of hoops in the splice

177

Fe 415 150 × 500 400 × 450 1.072 100 mm c/c 75 mm c/c − 1.77

6 mm 100 mm 1.04

Not Available Not Available

Notes


10.3

STRUCTURAL SYSTEM AND MEMBERS

10.3.1 Foundation The foundation system is pile foundation with groups of 4 or 6 under reamed piles. Each pile is of 300 mm diameter reinforced with 6Y12 longitudinal bars and Y6 links @ 175 c/c ties. Piles are more than 11m deep under the ground level as per the drawing.

nB1 nB5

nB12

nB4

nB12

nB3

nB10 nB8

nB13

nB13

nB6

nB5

nB5 nB13

nB6 nB12

nB11

nB15 nB9 nB7

nB5

nB5

nB5

nB5

nB7

nB10

nB8

nB10

nB5

nB5

nB4

nB9

nB1

nB5

nB15

nB5

nB5

nB5

Y

nB5

nB2

nB11

nB10

nB1

nB6

nB12 nB1

X

Figure 10.2: Floor (all floors other than top floor) framing plan – Beam location (Prefix ‘n’ represents floor number)

10.3.2 Structural system It is a RC framed structure. The concrete slab is 150mm thick at every floor level. The wall thickness is 120 mm for both the exterior and interior infill walls. The floor plan is same up to fourth floor while at the roof level few beams are absent. The beam layouts for the first four floors and the roof are shown in Figures 10.2 and 10.3, respectively. Figure 10.4 shows the column location. The size and

178


reinforcement details for beam and column sections (at beam and column faces) are given in Tables 10.3 and 10.4, respectively.

Figure 10.5 shows the

reinforcement details of different column sections.

5B12

5B11

5B15

5B5

5B10

5B5 5B5

5B10

5B7 5B13

5B4

5B12

5B10

5B5 5B3

5B8

5B5

5B6 5B13

5B10

5B13

5B5

5B8

5B9

5B5

5B7

5B9 5B10

5B5

5B4 5B5

5B11

5B15

5B5

5B5

5B10

5B2

5B5

5B1

5B1

Figure 10.3: Roof floor framing plan – Beam location (Roof)

nC25

nC24

nC23

nC22 nC20

nC18

nC16

nC9

nC1

nC2

nC17

nC13

nC12 nC8

nC21

nC19

nC15

nC14

nC28

nC27

nC26

nC6 nC3

nC7

nC10 nC4

nC11 nC5

Figure 10.4: Column location (Prefix ‘n’ represents floor number)

179


Table 10.3: Details of beam sections at column faces Beam Number B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15 B16 B17 B18 B19

Size (mm) 150 × 500 300 × 500 200 × 450 250 × 500 250 × 500 150 × 500 300 × 500 250 × 500 250 × 500 150 × 500 250 × 450 250 × 500 250 × 500 300 × 500 300 × 500 300 × 500 200 × 450 250 × 500 300 × 500

Longitudinal Reinforcement Top Bottom 2Y20 2Y20 6Y20, 1Y16 4Y20 6Y20 4Y20 4Y20, 2Y16 4Y20 4Y16 2Y16 2Y16 2Y16 6Y20 3Y20 4Y20, 2Y16 3Y20 2Y16 3Y16 3Y16 4Y16 6Y20 2Y20 4Y20 2Y20 7Y20 3Y20 6Y20 4Y20 4Y20, 2Y12 4Y20 4Y20, 2Y16 3Y20 4Y20, 2Y12 4Y20 4Y20, 2Y12 3Y20 4Y20, 2Y12 3Y20

Transverse Reinforcement 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c 2Y8 @ 75 c/c

Table 10.4: Details of column sections at the beam faces Column Number

Size (mm)

Longitudinal Reinforcement

Transverse Reinforcement

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11

400 × 450 400 × 450 400 × 450 400 × 500 400 × 500 400 × 500 400 × 450 400 × 450 400 × 500 400 × 500 400 × 500

8Y20 6Y20, 2Y16 4Y20, 4Y16 8Y20 6Y20, 2Y16 4Y20, 4Y16 10Y20 8Y20, 2Y16 10Y20, 2Y16 10Y20 8Y20, 2Y16

6φ @ 100c/c 6φ @ 100c/c 6φ @ 100c/c 6φ @ 100c/c 6φ @ 100c/c 6φ @ 100c/c 6φ @ 100c/c 6φ @ 100c/c 6φ @ 100c/c 6φ @ 100c/c 6φ @ 100c/c

180


400 mm

4Y16

2Y16 C1

C2

4Y16

2Y16 C4

C5

C6 400 mm

400 mm

450 mm

500 mm

400 mm

450 mm

400 mm

500 mm

500 mm

500 mm

C3

400 mm

400 mm

2Y16 C7

C8

2Y16 C9

400 mm

400 mm

500 mm

500 mm

400 mm

450 mm

450 mm

450 mm

400 mm

C10

2Y16

C11

Figure 10.5: Reinforcement details of the columns at the beam faces (Bar diameter is 20 mm if not mentioned)

181


10.4

PRELIMINARY ANALYSIS

The preliminary evaluation was done as per Chapter 2.

10.4.1 Rapid Visual Screening Rapid visual screening results, shown in Table 10.5, indicate the requirement of detailed analysis. Both MRF and URM-INF were considered as the building is a moment resisting framed building with un-reinforced masonry infill.

Table 10.5: Rapid visual screening data Region of Seismicity

High Seismicity Moderate Seismicity Low Seismicity (Zone V) (Zone IV) (Zone II and III) URM URM URM Building Type MRF SW MRF SW MRF SW INF INF INF Basic Score √

2.5

2.8

1.6

3.0

3.6

3.2

4.4

4.8

4.4

Mid rise √ +0.4

+0.4

+0.2

+0.2

+0.4

+0.2

+0.4

-0.2

-0.4

High rise

+0.8

+0.3

+0.5

+0.8

+0.4

+1.0

0.0

-0.4

-1.0

-1.0

-2.0

-2.0

-2.0

-1.5

-2.0

-2.0

-0.5

-0.5

-0.5

-0.5

-0.5

-0.8

-0.8

-0.8

+0.6

Vertical -1.5 irregularity √ Plan -0.5 irregularity Pre-code

-1.2

-1.0

-0.2

-1.0

-0.4

-1.0

N/A

N/A

N/A

Postbenchmark

+1.4

+2.4

N/A

+1.2

+1.6

N/A

+0.6

+0.4

N/A

Soil Type I

-0.4

-0.4

-0.4

-0.6

-0.8

-0.6

-0.6

-0.4

-0.4

Soil Type II √ -0.6

-0.6

-0.4

-1.0

-1.2

-1.0

-1.4

-0.8

-0.8

Soil Type III

-1.2

-0.8

-0.8

-1.6

-1.6

-1.6

-2.0

-2.0

-2.0

Final Score

0.8

Comments

0.4 Final Score is less than the cut-off score of 2.0

182


10.4.2 Quick Checks for Strength and Stiffness The fundamental periods of the building are Tax = 0.28s. and Tay = 0.36s. The

spectral acceleration coefficient (Sa/g) corresponding to each of the periods is 2.5. For a building is in Zone V, Z = 0.36. For an ordinary moment resisting frame, R = 3. Horizontal seismic co-efficient, Ah =

ZIS a 0.36 ×1.0 × 2.5 = = 0.15 . 2 Rg 2×3

For residential building, I = 1.0. Design seismic base shear, VB = Ah×W. W = 19190 kN (calculated later) Therefore, VB = 0.15×19190 kN ≅ 2878 kN. Table 10.6 shows the distribution of the base shear over the height of the building.

Table 10.6: Distribution of lateral force over the height of the building

Floor No 1 2 3 4 5 10.4.2.1

Seismic Weight, Wi (kN) 4250 4110 4110 4110 2610

Height, hi (m)


3 6 9 12 15

65 251 564 1003 995

Column Shear

Tables 10.7 and 10.8 show the column shear stresses at each storey along X- and Y- directions, respectively. The lateral load resisting frames along X- and Ydirections are shown in Figure 10.6 and 10.7, respectively. The beams are having eccentric connection at the columns. This was neglected in the computational model.

183


Table 10.7: Average column shear stress in X-direction

Floor No

nf

nc

Ac (m2)

V j (kN)

vavg (MPa)

Remarks

1 2 3 4 5

9 9 9 9 9

24 24 24 24 24

4.6 4.6 4.6 4.6 4.6

2878 2813 2562 1998 995

1.00 0.98 0.89 0.69 0.35

> 0.4 > 0.4 > 0.4 > 0.4 < 0.4

Table 10.8: Average column shear stress in Y-direction

Floor No

nf

nc

Ac (m2)

V j (kN)

vavg (MPa)

Remarks

1 2 3 4 5

8 8 8 8 8

18 18 18 18 18

3.48 3.48 3.48 3.48 3.48

2878 2813 2562 1998 995

1.49 1.46 1.33 1.03 0.51

> 0.4 > 0.4 > 0.4 > 0.4 > 0.4

Figure 10.6: Lateral load resisting frames along X-direction

184


Figure 10.7: Lateral load resisting frames along Y-direction

10.4.2.2


Not applicable for this building. 10.4.2.3


Details of the column axial stress calculation are given in Table 10.9.

The

allowable axial stress in column is 0.24 fck = 0.24×15 MPa = 3.6 MPa. Table 10.9 Details of axial stress in column

Vb(kN)

nf

h (m)

L (m)

P (kN)

Axial stress

X-direction.

2878

9

15

5.92

506.4

2.81 MPa

Y-direction.

2878

8

15

3.60

936.8

4.68 MPa

The column axial stress is more than the allowable stress when the load is in Ydirection.

185


10.4.2.4

Frame Drift

The calculation details for the storey drift for X- and Y- directions are shown in Tables 10.10 and 10.11, respectively. The allowable drift ratio in any storey is 0.015. For most of the storeys, the drifts are more than 0.015. Table 10.10: Frame Drift Ratio along X-direction

Storey 1 2 3 4 5

Storey Height (m) 3 3 3 3 3

Vc (kN) 200 196 178 138 70

DR 0.016 0.016 0.014 0.011 0.006

Table 10.11: Frame Drift Ratio along Y-direction

Storey 1 2 3 4 5

10.4.2.4

Storey Height (m) 3 3 3 3 3

Vc (kN) 298 292 266 206 102

Strong column – Weak beam

In the strong direction of the columns (about major axis) ∑ Moment capacities of the columns = 484 kNm 1.2 ∑ Moment capacities of the beams = 536 kNm. In the weak direction of the columns (about minor axis) ∑ Moment capacities of the columns = 328 kNm 1.2 ∑ Moment capacities of the beams = 408 kNm. The strong column and weak beam criteria is not satisfied.

186

DR 0.022 0.021 0.019 0.015 0.007


10.4.3 Evaluation Statements

The evaluation statements are presented in Table 10.12. A number of statements are non-compliant because of the presence of open ground storey and poor reinforcement detailing.

Table 10.12: Evaluation statements

Building system

C / NC / NA

Load path:

C

Adjacent buildings:

−

Mezzanines:

C

No deterioration of concrete:

−

Vertical irregularities No weak storey:

NC

No soft storey:

NC


C


C

No vertical discontinuities:

C

Plan Irregularities No Torsion irregularity:

C


C


C


C


C

Moment resisting frames Redundancy:

NC


C


NC

187


Table 10.12 (contd.): Evaluation statements

Moment resisting frames Axial stress check:

NC

Drift check:

NC

Short captive columns:

C

No shear failures:

C


NC

Column bar splices:

NC

Column tie spacing:

C

Beam bars:

C

Beam bar splices:

NC

Stirrup spacing:

C

Bent-up bars:

C

Joint reinforcing:

NC


C


C


C


NC

Anchorage:

NC Shear walls


NA

Reinforcing steel:

NA

Coupling beams:

NA

Diaphragm openings at shear walls:

NA

Connections Column connection:

C

Wall connection / Transfer to shear walls: Lateral load at pile caps:

NA C

188


Table 10.12 (contd.): Evaluation statements

Geologic site hazards Liquefaction / Slope failure / Surface fault rupture

NA

Foundations Foundation performance:

−

Deterioration:

−

Overturning:

C


10.5

NC

DETAILED EVALUATION BASED ON LINEAR ANALYSIS

The detailed evaluation based on the linear analysis was done as per the procedure in Chapter 3.

10.5.1

Material Properties

The material properties considered for the analysis are given in Table 10.13.

Table 10.13: Materials properties

Material

Characteristic Strength

Modulus of Elasticity

Concrete (M 15)

15 MPa

19365 MPa

Reinforcing Steel (Fe 415)

415 MPa

2 × 105 MPa

Brick infill

10.5.2

1237.5


Figure 10.8 shows the 3D model of the building.

189


Walls (Structural and non structural): The lift core (surrounded by the staircase) made up of RC walls was ignored in the model as it is not integrally connected either to the floor diaphragms or to the lateral load resistant frames. Figure 10.9 shows the location of infill walls that were modelled as equivalent struts in a typical storey (except ground storey). The ground floor has only three infill walls (1S10, 1S11, 1S12) surrounding the stair case. The calculated strut parameters are shown in Table 10.14

Figure 10.8: 3D computer model of the building

190


Table 10.14: Calculated strut parameters

Width (m)

Strength (kN)

S12, S13, S14

S1

1.65

230

S4, S5. S8, S9

S2

1.70

275

S1, S2, S3, S6, S7, S10, S11

S3

1.50

175

S15, S16

S4

1.40

140

nS14 nS9 nS7

nS3

nS5 nS2

nS6

nS1

nS4

nS11

nS10

nS13 nS8

nS12

nS16

Section

nS15

Equivalent Strut

Figure 10.9: Location of infill walls that were modelled as equivalent strut (Prefix ‘n’ represents storey number)

Modelling of Column Ends at Foundation The foundation system for the building is a pile foundation with groups of 4 or 6 piles. In the model, fixity was considered at the top of the pile caps. The effect of soil-structure interaction was ignored in the analyses.

Design Centre of Masses Tables 10.15 to 10.18 give the centres of masses and rigidity of the building. Only two (CM1 and CM2) of the four calculated centres of mass were considered for analysis.

191


Table 10.15: Structural parameters (with infill stiffness)

Seismic Lumped mass Floor weight (Ton) (kN)

CM (m)

CR (m)

esi (m)

X

Y

X

Y

X

Y

5

2610

266

12.40

6.77

12.54

7.13

0.14

0.36

4

4110

419

12.56

7.14

12.53

7.26

0.03

0.12

3

4110

419

12.56

7.14

12.53

7.26

0.03

0.12

2

4110

419

12.56

7.14

12.53

7.26

0.03

0.12

1

4250

433

12.56

7.14

12.59

7.44

0.03

0.30

Table 10.16: Location of centres of mass (with infill stiffness)

CR (m)

Floor

esi (m)

Design CM1 (m)

Design CM2 (m)

X

Y

X

Y

X

Y

X

Y

5

12.54

7.13

0.14

0.36

11.42

6.79

14.01

8.37

4

12.53

7.26

0.03

0.12

11.30

6.68

13.83

8.14

3

12.53

7.26

0.03

0.12

11.30

6.68

13.83

8.14

2

12.53

7.26

0.03

0.12

11.30

6.68

13.83

8.14

1

12.59

7.44

0.03

0.30

11.36

7.04

13.89

8.59

Table 10.17: Structural parameters (without infill stiffness)

Seismic Lumped mass Floor weight (Ton) (kN)

CM (m)

CR (m)

esi (m)

X

Y

X

Y

X

Y

5

2610

266

12.40

6.77

12.51

7.42

-0.11

-0.65

4

4110

419

12.56

7.14

12.51

7.54

0.05

-0.40

3

4110

419

12.56

7.14

12.51

7.54

0.05

-0.40

2

4110

419

12.56

7.14

12.51

7.54

0.05

-0.40

1

4250

433

12.56

7.14

12.59

7.44

-0.03

-0.30

192


Table 10.18: Location of centre of masses (without infill stiffness)

CR (m)

Floor

Design CM1 (m) X Y

esi (m)

Design CM2 (m) X Y

X

Y

X

Y

5

12.51

7.42

0.11

0.65

11.36

7.37

13.93

9.09

4

12.51

7.54

0.05

0.40

11.30

7.24

13.84

8.84

3

12.51

7.54

0.05

0.40

11.30

7.24

13.84

8.84

2

12.51

7.54

0.05

0.40

11.30

7.24

13.84

8.84

1

12.59

7.44

0.03

0.30

11.36

7.04

13.89

8.59

10.5.3 Equivalent Static Analysis

Design Base Shear: Table 10.19 shows the calculations of base shear of the building for both without infill stiffness and with infill stiffness cases. Seismic load distribution for X-direction is shown in the Table 10.20. Table 10.19 Details of calculations for base shear of the building

Without infill stiffness With infill stiffness

Time Period (s)

Sa/g

Ah

W (kN)

VB (kN)

X-direction

0.59

2.3

0.138

19190

2649

Y-direction

0.59

2.3

0.138

19190

2649

X-direction

28

2.5

0.150

19190

2878

Y-direction

36

2.5

0.150

19190

2878

Table 10.20: Lateral force at different floor levels

Floor no 1 2 3 4 5

W i (kN) 4250 4110 4110 4110 2610

h i (m) 3 6 9 12 15

Qi (kN) With infill stiffness 65 251 564 1003 995

193

Without infill stiffness 60 231 519 923 916


10.5.4 Response Spectrum Analysis

The various fundamental time periods and the spectral acceleration coefficients for the building are given in Table 10.21. The comparison is shown in Figures 10.10 and 10.11. Table 10.22 represents the period and the predominant direction of vibration for the first five modes of the building, with and without the infill stiffness. The table also shows the mass participation for each of the five modes. The first five modes were considered in the dynamic analysis, which give more than 90% mass participation in both of the horizontal directions. Figure 10.12 shows the first three mode shapes of the building. The base shears for the equivalent static method and the response spectrum methods are given in Table 10.23 Table 10.21: Comparison of fundamental time periods

T (s) Sa/g

Empirical formula With infill Without infill stiffness stiffness 0.28 0.59 2.50

2.30

Computational model With infill Without infill stiffness stiffness 0.83 0.96 1.64

1.42

Table 10.22: Time periods and modal participation for the first five modes

Without infill Mode

Natural Period (s)

With infill

Mass Participation (%) X

Y

Natural Period (s)

Mass Participation (%) X

Y

1

0.96

88.78

0.31

0.83

92.91

0.20

2

0.88

0.35

86.81

0.76

0.23

90.51

3

0.43

0.23

0.38

0.39

0.11

0.52

4

0.30

8.05

0.03

0.25

5.39

0.04

5

0.27

0.03

9.55

0.24

0.03

7.07

194


Spectral Acceleration Coefficient (Sa/g)

3.0

Empirical formula

2.5

Computational model

2.0 1.5 1.0 0.5 0.0 0.5

1.0

1.5

Period (s) Figure 10.10: Comparison of fundamental periods (with infill stiffness)

Spectral Acceleration Coefficient (Sa/g)

3.0

Empirical formula

2.5 Computational model

2.0 1.5 1.0 0.5 0.0 0.0

0.5

1.0

1.5

Period (s) Figure 10.11: Comparison of fundamental periods (without infill stiffness)

195


First mode (Translation X)

Second mode (Translation-Y)

Third mode (Rotation-Z) Figure 10.12: First three mode shapes

196


Table 10.23: Comparison of base shears

( )

With infill stiffness Vx (kN) Vy (kN)

Without infill stiffness Vx (kN) Vy (kN)

Equivalent Static VB

2878

2878

2649

2649

Response Spectra (VB )

1768

1871

1463

1576

VB / VB

1.63

1.54

1.81

1.68

10.5.5

Evaluation Results

The equivalent static analysis results show that a number of elements do not satisfy the Demand-to-Capacity Ratios (DCR) for flexure. However the DCR for shear is always less than one for both beams and columns. DCR for a few ground floor beams and columns are given in Tables 10.24 and 10.25, respectively. Table 10.24: Demand-to-Capacity Ratios (DCR) in Beams

Beams 1B1 1B2 1B3 1B4 1B5 1B6 1B7 1B8 1B9 1B10 1B11 1B12 1B13 1B14 1B15 1B16 1B17

Without infill stiffness With infill stiffness DCR in Flexure DCR in Shear DCR in Flexure DCR in Shear 1.4 0.3 1.5 1.1 1.5 1.5 1.1 1.5 0.3 1.4 1.5 1.7 1.4 1.2 1.2 1.4 1.7

0.6 0.3 0.9 0.5 0.9 0.9 0.5 0.9 0.3 0.6 0.7 0.8 0.6 0.5 0.5 0.6 0.8

197

1.1 0.3 1.2 0.9 1.2 1.2 0.9 1.2 0.3 1.1 1.3 1.4 1.2 1.0 1.0 1.1 1.4

0.5 0.3 0.8 0.4 0.8 0.8 0.4 0.8 0.3 0.5 0.6 0.7 0.6 0.4 0.5 0.6 0.7


Table 10.25: Demand-to-Capacity Ratios (DCR) in columns

Without infill stiffness Columns

DCR in Flexure

1C1 1C2

1.1 1.4 1.3 1.5 1.2 1.2 1.5 1.4 1.4 1.4 1.9 1.4 1.6 1.5 1.4 1.1 1.5 1.3 1.4 1.4 1.2 1.3 1.3 1.4 1.5 1.0

1C3 1C4 1C5 1C6 1C7 1C8 1C9 1C10 1C11 1C12 1C13 1C14 1C15 1C16 1C17 1C18 1C19 1C20 1C21 1C22 1C23 1C24 1C25 1C26

DCR in Shear V2 V3 0.4 0.1 0.6 0.2 0.3 0.9 0.4 0.1 0.2 0.8 0.4 0.7 0.4 0.7 0.6 0.5 0.2 0.8 0.4 0.1 0.2 0.7 0.3 0.9 0.6 0.6 0.4 0.9 0.5 0.2 0.1 0.2 0.4 0.7 0.2 0.1 0.5 0.9 0.6 0.2 0.3 0.1 0.4 0.2 0.2 0.5 0.4 0.7 0.3 0.5 0.6 0.7

With infill stiffness DCR in Flexure 1.6 1.4 1.5 1.4 2.1 1.8 1.9 1.8 1.8 2.1 2.6 1.6 1.8 1.5 1.7 2.1 2.3 1.5 1.7 1.7 2.3 1.4 1.5 1.6 1.5 1.7

DCR in Shear V2 V3 0.3 0.7 0.5 0.7 0.3 0.9 0.9 0.1 0.2 0.8 0.6 0.2 0.3 0.7 0.5 0.5 0.4 0.8 0.9 0.8 0.2 0.7 0.1 0.5 0.6 0.6 0.3 0.7 0.7 0.2 0.5 0.2 0.8 0.7 0.4 0.7 0.4 0.9 0.6 0.2 0.2 0.1 0.4 0.2 0.4 0.4 0.6 0.7 0.4 0.5 0.6 0.6

The storey drifts are shown in Figure 10.13. The values satisfy the IS 1893: 2002 limit of 0.4%.

198


5

Storey Level

4 3 2 1 0 0.0

0.1

0.2

0.3

0.4

Storey Drift (%) (a) Considering infill stiffness 5

Storey Level

4 3 2 1 0 0.0

0.1

0.2

0.3

0.4

Storey Drift (%) (b) Without considering infill stiffness Figure 10.13: Storey drift under design seismic lateral force

199


10.6


The analysis was done as per the method in Chapter 4.

10.6.1

Pushover Curve

Pushover curves for the building with and without infill stiffness in X- and Ydirections are shown in Figure 10.14 and 10.15.

The base shear from the

equivalent static method is also plotted to compare the capacity with the demand based on linear analysis. The capacity from the pushover analysis is observed to be little higher than the demand.

Without infill stiffness

With infill stiffness

4000

Base Shear (kN)

3000

2000

1000

0 0

0.02

0.04

0.06

Roof Displacement (m) Figure 10.14: Pushover curve along X-direction

200

0.08




4000

Base Shear (kN)

3000

2000

1000

0 0

0.02

0.04

0.06

0.08

Roof Displacement (m) Figure 10.15: Pushover curve along Y-direction 10.6.2

Capacity Spectrum, Demand Spectrum and Performance Point

Pushover analyses in either direction failed to give a performance point for both the models, with and without infill stiffness. The demand and capacity spectra for the lateral push along the two orthogonal directions are shown in Figures 10.16 to 10.19.

10.6.3

Displacements and Storey Drifts

The displacements at ultimate are plotted in Figures 10.20 and 10.21. The interstorey drifts corresponding to the displacement profiles are shown in Figures 10.22and 10.23. These figures show the soft storey mechanism.

201


Spectral Acceleration (Sa/g)

1.0

0.8

0.6

0.4

0.2

0.0 0.0

0.1

0.2

0.3

0.4

0.5

Spectral Displacement (m)

Figure 10.16: Capacity Spectrum along X-direction (with infill stiffness)


1.0

0.8

0.6

0.4

0.2

0.0 0.0

0.1

0.2

0.3

0.4

0.5


Figure 10.17: Capacity Spectrum along Y-direction (with infill stiffness)

202



1.0

0.8

0.6

0.4

0.2

0.0 0.0

0.1

0.2

0.3

0.4

0.5


Figure 10.18: Capacity Spectrum along X-direction (without infill stiffness)


1.0

0.8

0.6

0.4

0.2

0.0 0.0

0.1

0.2

0.3

0.4

0.5


Figure 10.19: Capacity Spectrum along Y-direction (without infill stiffness)

203


5

Storey Level

4

3

2

1

0 0

20

40

60

80

100

Displacement (mm)

Figure 10.20: Displacement along X-direction (with infill stiffness)

5

Storey Level

4

3

2

1

0 0

20

40

60

80

100

Displacement (mm)

Figure 10.21: Displacement along X-direction (without infill stiffness)

204


5

Storey Level

4

3

2

1

0 0.0

0.5

1.0

1.5

2.0

2.5

Storey Drift

Figure 10.22: Storey drift along X-direction (with infill stiffness)

5

Storey Level

4

3

2

1

0 0.0

0.5

1.0

1.5

2.0

2.5

Storey Drift

Figure 10.23: Displacement along X-direction (without infill stiffness)

205


10.6.4

Vulnerability Index

The vulnerability indices of the building and vulnerability indices of storeys are separately calculated in both X- and Y- directions, for with and without infill stiffness cases, according to Appendix D.

The vulnerability indices of the

buildings are given in Tables 10.26 and 10.27. The indices of storeys are given in Tables 10.28 and 10.29. Table 10.26: Vulnerability index of buildings (with infill stiffness)

Xdirection

Ydirection

Location

B-IO

IO-LS

LSCP

CP-C

C-D

D-E

>E

Column

0

0

46

0

1

5

4

Beam

0

0

0

0

0

0

3

Column

0

0

28

0

0

2

9

VIbldg 0.069

0.066 Beam

0

0

0

0

0

0

15

Table 10.27: Vulnerability index of buildings (without infill stiffness) Location Yielded Xdirection

Ydirection

Column

B-IO

IO-LS

LS-CP

CP-C

C-D

D-E

>E

0

0

21

0

0

1

1

VIbldg 0.042

Beam

0

0

0

0

0

0

14

Column

0

0

11

0

0

1

0 0.087

Beam

0

0

0

206

0

0

0

65


Table 10.28: Vulnerability indices of storeys (with infill stiffness) in X-direction Storey Level B-IO

1

2

3

4

5

0

0

0

0

0

IO-LS

0

0

0

0

0

LS-CP

46

0

0

0

0

CP-C

0

0

0

0

0

C-D

1

0

0

0

0

D-E

5

0

0

0

0

>E

2

2

0

0

0

VIstorey

0.656

0.036

0

0

0

Table 10.29: Vulnerability indices of storeys (with infill stiffness) in Ydirection Storey Level B-IO

1

2

3

4

5

0

0

0

0

0

IO-LS

0

0

0

0

0

LS-CP

28

0

0

0

0

CP-C

0

0

0

0

0

C-D

1

0

0

0

0

D-E

2

0

0

0

0

>E

4

4

1

0

0

VIstorey

0.438

0.071

0.018

0

0

10.7

SUMMARY OF THE RESULTS

(i)

Linear analysis results show that a number of beams and columns are deficient in flexure.

(ii)

However, all the beam and column sections have adequate shear capacity.

(iii)

Building complies with the drift requirement under design lateral force.

(iv)

Pushover analyses in either direction fail to give a performance point before the collapse. So the performance is not acceptable. Building needs to be retrofitted.

10.8

RETROFIT

207


The selected retrofit scheme consists of global and local retrofit strategies. For the global strategy, full brick walls (230 mm) were continued in the ground storey at a few symmetrical locations of the building. Figure 10.24 shows the locations of the new walls. This will cause least intervention in the functional requirement of car parking. For the local strategy, all the ground storey columns were strengthened by concrete jacketing. The modelling of the load-deformation behaviour of the jacketed column is based on Chapter 8. The pushover curves in Y-directions for the retrofitted building are shown in Figure 10.25. The pushover analyses in both the directions give performance points. The building experiences a drift of about 1.0% at the performance point, which is acceptable. The demand and capacity spectra for the lateral push along X- and Y- directions are shown in Figures 10.26 and 10.27. The scheme increases the stiffness of the building only marginally. Figure 10.28 shows the comparison of the fundamental periods and the corresponding spectral acceleration coefficients for the existing and the retrofitted models of the building.

Figure 10.24: Locations of infill walls and column jacketing in ground storey

208


Existing

Retrofitted

8000

Base Shear (kN)

6000

4000

2000

0 0.00

0.04

0.08

0.12

0.16

0.20

Roof Displacement (m)

Figure 10.25: Comparison of pushover curves along Y-direction


1.0

0.8

0.6

0.4

0.2

0.0 0.0

0.1

0.2

0.3

0.4


Figure 10.26: Capacity spectrum along X-direction

209

0.5


0.8

0.6

0.4

0.2

0.0 0.0

0.1

0.2

0.3

0.4


Figure 10.27: Capacity spectrum along Y-direction

3

Spectral Accelaration Coefficient (Sa/g)


1.0

Retrofitted 2

Existing

1

0 0.0

0.5

1.0

1.5

Period (s) Figure 10.28: Comparison of the fundamental period

210

0.5


CHAPTER XI CASE STUDY III

11.1 INTRODUCTION The present case study is an example of an office building in Zone III. The deficiency due to inadequate shear reinforcement is highlighted. A retrofit scheme with shear strengthening is illustrated.

11.2

DATA COLLECTION AND CONDITION ASSESSMENT OF

BUILDING

Figure 11.1: Typical floor plan of the building (The dotted area is terminated above ground floor)

211


The building is a six storey office building with a basement, located in Zone III. Tables 11.1 and 11.2 present a summary of the building parameters. The building is symmetric in both X- and Y-directions. The basement is for parking. Figure 11.1 shows a typical floor plan of the building. Table 11.1: Building survey data sheet: General data S.No

Description

Information

Notes

. 1



B7 Calicut Kerala

2

Name of owner

−

3

Name of builder

−

4


−

5


−

6

Use of building

Office

7

6

9


10

Soil data

11

• Type of soil • Design safe bearing capacity Dead loads (unit weight adopted)

8

12

• Earth • Water • Brick masonry • Plain cement concrete • Floor finish • Other fill materials Imposed (live)loads • Floor loads • Roof loads

212

1 RC frame Medium Not Available

10 kN/m3 20 kN/m3 25 kN/m3 18 kN/m3

4 kN/m2 1.5 kN/m2

(Assumed)

IS 875 Part 1

IS 875 Part 2

Chapter XI – Case Study III


Information

Notes

13

Cyclone/Wind

−

14 15

• Speed • Design pressure intensity History of past earthquakes and tremors Seismic zone

Earthquake Prone Area III

IS 1893: 2002

16


1.0

IS 1893: 2002

17


0.16

IS 1893: 2002

18


3.0

IS 1893: 2002

19


0.49

IS 1893: 2002

20 21

Design Horizontal acceleration 0.067 spectrum value (Ah) Seismic design lateral force 2150 kN

22


IS 1893: 2002

−

Table 11.2: Building survey data sheet: Building Data (moment resisting frame) S.No. Description

Information

1

Type of building

2

Number of basements

Regular frames −

3

Number of floors

7

4

Horizontal floor system

Beams slabs

5

Soil data Medium • Type of soil • Recommended foundation • Recommended bearing capacity • Recommended type, length, diameter and load capacity of piles • Depth of water table • Chemical analysis of ground − water − • Chemical analysis of soil

213

Notes

and Assumed



7

8 9 10 11 12

13 14 15

16

Information

Foundations • Depth below ground level • Type System of interconnecting foundations • Plinth beams • Foundation beams Grades of concrete used in different parts of building Method of analysis Computer software used Torsion included Base shear a) Based on approximate fundamental period b) Based on dynamic analysis c) Ratio of a/b Distribution of seismic forces along the height of building The columns of soft ground storey specially designed Clear minimum cover provided in • Footing • Column • Beams • Slabs • Walls Ductile detailing of RC frame • Type of reinforcement used • Minimum dimension of beams • Minimum dimension of columns • Minimum percentage of reinforcement of beams at any cross section • Spacing of transverse reinforcement at any section of beam • Spacing of transverse reinforcement in 2d length of beam near the ends

214

− Pile No inter connection

Notes

Pile groups

M20 − − − IS 1893: 2002 2150 891 2.31 Parabolic

IS 1893: 2002

−

IS 1893: 2002

Not Available

Fe 415 200 × 750 300 × 450 0.536 250 mm c/c 150 mm c/c



11.3

Information

Ductile detailing of RC frame • Ratio of capacity of beams in shear to capacity of beams in flexure • Maximum percentage of reinforcement in column • Confining stirrups near ends of columns and in beamcolumn joints − Diameter − Spacing • Ratio of shear capacity of columns to maximum seismic shear in the storey • Column bar splices location and spacing of hoops in the splice • Beam bar splices location and spacing of hoops in the splice

Notes

− 1.54

8 mm 200 mm 2.51 Not Available Not Available

STRUCTURAL SYSTEM AND MEMBERS:

11.3.1 Foundation

The foundation system is pile foundation. The depths of the pile bottoms vary between 21m to 30m, depending up on the soil strata.

11.3.2 Structural system

It is a RC framed structure. The concrete slab thickness is 120 mm except for some locations where it is 150 mm. Waist slab for the staircase is 150 mm thick. The external walls are 230mm thick and no partition walls are present inside the building. The floor plan is similar for basement and ground floor. One corner is

215


terminated above the ground floor. Figure 11.2 shows the column layout at a typical floor and Table 11.3 shows the reinforcement details of the columns sections. Figure 11.3 shows the beam layout at a typical floor level. All floors have identical beam sections. It can be noted from Table 11.3 that most of the columns are of rectangular cross section with very high aspect ratio. However columns are oriented in such a way that strength and stiffness in both X- and Ydirection are comparable. Table 11.3: Details of column reinforcements Column ID

Size (mm) Width x Depth

Longitudinal Reinforcement (mm)


AC1

300 × 450

8Y16

2×2 LGD Y8 @ 200c/c

AC2

300 × 600

8Y20 + 2Y12

2×6 LGD Y8 @ 200c/c

AC3

300 × 750

8Y20 + 2Y12

2×6 LGD Y8 @ 200c/c

AC4

300 × 900

12Y20 + 2Y16

2×8 LGD Y8 @ 200c/c

AC7

700 × 700

14Y20

6×6 LGD Y8 @ 200c/c

AC3

AC2

AC3

AC3

AC7

AC7

AC4

AC2

AC7

AC7

AC4

AC3

AC7

AC7

AC3

AC4

AC4

AC4

AC3

AC3

AC4

AC1

Figure 11.2(a): Column section and their orientation layout (basement and ground storey)

216


AC3

AC3

AC2

AC3

AC3

AC7

AC7

AC4

AC2

AC7

AC7

AC4

AC3

AC7

AC7

AC3

AC3

AC4

AC4

AC4

AC4

Figure 11.2(b): Column section and their orientation layout of typical storey. (1st to 5th storey) AB5

AB5

AB20

AB18

AB8

AB15

AB18

AB18

AB15

AB16

AB1

AB9

AB10

AB38

AB11

Figure 11.3: Beam section layout of typical floor level. (Dotted beams are not present above first floor level) Table 11.4 shows the reinforcement details of the beam sections. It can be noted that all of the beams have b/d ratio more than 3.0.

217


Table 11.4: Details of beam reinforcements Beam section AB1 AB5 AB8 AB9 AB10 AB11 AB15 AB16 AB18 AB20 AB38

Size (mm) Width × Depth 200 × 750 250 × 750 250 × 750 250 × 750 250 × 750 250 × 750 250 × 750 250 × 750 250 × 750 250 × 750 250 × 750

Longitudinal Reinforcement at support (mm2) Top

Bottom


2Y16 6Y25 3Y32+2Y25 2Y32+2Y25 5Y25 3Y25, 2Y25 2Y16+2Y20 4Y20 2Y16+2Y20 2Y20+2Y25 2Y32+2Y25

2Y16 4Y25 4Y25 3Y25 4Y25 2Y25 4Y20 2Y20+1Y16 3Y20 3Y20 2Y20+2Y25

Y8@250c/c Y8@150c/c Y8@200c/c Y8@150c/c Y8@150c/c Y10@200c/c Y8@150c/c Y8@150c/c Y8@200c/c Y8@200c/c Y8@150c/c

The lateral load resisting frames in the building are identified. Figures 11.4 (a) and 11.4(b) show the frames along X-direction and Y-directions, respectively. The beams are having eccentric connection at the columns. This was neglected in the computational model.

Figure 11.4(a): Load resisting frames along X-direction

218


Figure 11.4(b): Load resisting frames along Y-direction

11.4

PRELIMINARY ANALYSIS

The preliminary evaluation was done as per the method in Chapter 2.

11.4.1 Rapid Visual Screening Rapid visual screening results shown in Table 11.5 indicate the requirement of detailed analysis. Both MRF and URM-INF were considered as the building is a moment resisting framed building with un-reinforced masonry infill.

219


Table 11.5: Rapid visual screening data Region of Seismicity

High Seismicity Moderate Seismicity Low Seismicity (Zone V) (Zone IV) (Zone II and III) URM URM URM Building Type MRF SW MRF SW MRF SW INF INF INF Basic Score √

2.5

2.8

1.6

3.0

3.6

3.2

4.4

4.8

4.4

Mid rise

+0.4

+0.4

+0.2

+0.2

+0.4

+0.2

+0.4

-0.2

-0.4

High rise √ Vertical irregularity Plan irregularity

+0.6

+0.8

+0.3

+0.5

+0.8

+0.4

+1.0

0.0

-0.4

-1.5

-1.0

-1.0

-2.0

-2.0

-2.0

-1.5

-2.0

-2.0

-0.5

-0.5

-0.5

-0.5

-0.5

-0.5

-0.8

-0.8

-0.8

Pre-code √ Postbenchmark

-1.2

-1.0

-0.2

-1.0

-0.4

-1.0

N/A

N/A

N/A

+1.4

+2.4

N/A

+1.2

+1.6

N/A

+0.6

+0.4

N/A

-0.4

-0.4

-0.4

-0.6

-0.8

-0.6

-0.6

-0.4

-0.4

Soil Type II √ -0.6

-0.6

-0.4

-1.0

-1.2

-1.0

-1.4

-0.8

-0.8

Soil Type III

-0.8

-0.8

-1.6

-1.6

-1.6

-2.0

-2.0

-2.0

Soil Type I

-1.2

Final Score Comments

1.5

1.6

Final Score is less than the cut-off score of 2.0

11.4.2 Quick Checks for Strength and Stiffness Fundamental period of the building: Tax = 0.55s. and Tay = 0.49 s.

Sa/g = 2.50. Z = 0.16; R = 3; I = 1.0 Ah =

ZIS a 0.16 × 1.0 × 2.50 = = 0.067 2 Rg 2×3

VB = Ah×W. = 0.067×32257 kN ≅ 2128.96 kN. Table 11.6 shows the distribution of the base shear over the height of the building. These were calculated using IS 1893: 2002 recommended parabolic distribution methods.

220


Table 11.6: Distribution of lateral force over the height of the building

Seismic Weight, Wi (kN) 4901 4652 4709 4707 4979 4883 3426

Floor No G 1 2 3 4 5 6 11.4.2.1

Height, hi (m)


3.60 6.60 10.2 13.8 17.4 21.0 24.6

19 59 143 261 438 627 604

Column Shear

Table 11.7 shows the column shear stress at each storey. Table 11.7: Average column shear stress

Storey No

nf

nc

Ac (m2)

B G 1 2 3 4 5

5 5 5 5 5 5 5

22 22 21 21 21 21 21

6.585 6.585 6.585 6.585 6.585 6.585 6.585

10.4.2.2

Vj

vavg

(kN)

(MPa)

2580.52 2462.04 2270.40 1979.46 1594.63 1080.25 479.69

0.507 0.484 0.446 0.389 0.313 0.212 0.094

Remarks >0.4 >0.4 >0.4 <0.4 <0.4 <0.4 <0.4


Not applicable for this building. 10.4.2.3


The details of the column axial stress calculations are given in Table 11.8. The average axial stresses in column is within the allowable axial stress of 0.24 fck ( = 0.24×20 MPa = 4.8 MPa).

221


Table 11.8 Details of axial stress in column

Vb(kN)

nf

h (m)

L (m)

P (kN)

Axial stress

X-direction.

2150

5

24.6

15.95

442

0.9 MPa

Y-direction.

2150

4

24.6

20.6

428.8

0.9 MPa

11.4.2.4

Frame Drift

The calculation detail for the storey drift is shown in Tables 11.9. The frame drift ratio at each storey level is considerably less than the allowable drift. Table 11.9: Frame Drift Ratio along X-direction

Storey B G 1 2 3 4 5 11.4.2.5

Storey Height (m) 3.6 3.0 3.6 3.6 3.6 3.6 3.6

Vc (kN) 653.7 835.5 731.9 694.1 633.7 461.6 532.2

Strong column – Weak beam

In the strong direction of the columns (about major axis) ∑ Moment capacities of the columns = 1974 kNm 1.2 ∑ Moment capacities of the beams = 2054 kNm. In the weak direction of the columns (about minor axis) ∑ Moment capacities of the columns = 1974 kNm 1.2 ∑ Moment capacities of the beams = 691 kNm. The strong column and weak beam criteria is not satisfied.

222

DR 0.00092 0.00092 0.00103 0.00097 0.00089 0.00064 0.00074


11.4.3 Evaluation Statements

The evaluation statements are presented in Table 11.10. A number of statements are non-compliant because poor reinforcement detailing.


Building system

C / NC / NA

Load path:

C

Adjacent buildings:

− NA

Mezzanines:

−

No deterioration of concrete: Vertical irregularities No weak storey:

C

No soft storey:

C


C


C

No vertical discontinuities:

C

Plan Irregularities No Torsion irregularity:

C


C


C


C


C

Moment resisting frames Redundancy:

C


C NC

Shearing stress check: Axial stress check:

C

Drift check:

C

223



Moment resisting frames

C / NC / NA C

No short captive columns: No shear failures:

NC


NC

Column bar splices:

NC C

Beam bars: Beam bar splices:

NC

Stirrup spacing:

NC C

Bent-up bars: Joint reinforcing:

NC


NC


NA


NA


C

Shear walls Shearing stress check:

NA

Reinforcing steel:

NA

Coupling beams / Diaphragm openings at shear walls

NA

Connections C

Column connection: Wall connection / Transfer to shear walls:

NA C

Lateral load at pile caps: Geologic site hazards No Liquefaction/ No slope failure/ No surface fault rupture:

−

Foundations Foundation performance:

−

Deterioration:

−

Overturning:

C


C

224


11.5

DETAILED EVALUATION BASED ON LINEAR ANALYSIS

The detailed evaluation based on the linear analysis was done as per the procedure outlined in Chapter 3.

11.5.1

Material Properties

The material properties considered for the analysis are given in Table 11.11. Table 11.11: Materials properties

Material

Characteristic Strength (MPa)

Concrete Reinforcing Steel Brick infill

20 MPa 415 MPa 1.65

11.5.2

Modulus of Elasticity (MPa) 19365 MPa 2 × 105 MPa 1237.5


Figure 11.5 shows the 3D model of the building.

Figure 11.5: 3D computer model of the structure.

225


Infill Walls Figure 11.6 shows the location of infill walls that were modelled as equivalent struts. The calculated strut parameters are shown in Table 11.12 STR3

STR6

STR3

STR2 STR1

Y

STR3

STR3

STR2

STR2

STR4

STR4

STR3

STR4

STR5

X

Figure 11.6(a): Location of infill walls (at the ground storey) STR4

STR3

STR2 STR1

Y

STR3

STR3

STR2

STR2

STR6

STR4

STR4

STR5

X

Figure 11.6(b): Location of infill walls (at the ground storey)

226


STR4

STR6

STR3

STR3

STR2

STR2

STR3

STR2 STR1

STR1

Y

STR2

STR5

STR3

STR4

STR4

X

Figure 11.6(c): Location of infill walls at a typical storey (above ground storey)

Table 11.12: Strut parameters Equivalent Strut

Thickness (m)

Width (m)

Strength (kN)

STR1

0.23

STR2

0.23

1.933 1.502

485.159 455.389

STR3

0..23

2.408

639.265

STR4

0.23

2.023

391.378

STR5

0.23

1.753

326.540

STR6

0.23

1.846

513.724

Modelling of Column Ends at Foundation The foundation system for the building is piles.

In the model, fixity was

considered at the top of the pile caps. The effect of soil-structure interaction was ignored in the analyses.

227


Design centres of mass Tables 11.13(a) to 11.13(d) give the centres of mass and rigidity of the building. Only two (CM1 and CM2) of the four calculated centres of mass were considered for analysis. Table 11.13(a): Centres of mass and rigidity (without infill stiffness)

Floor

Seismic weight (kN)

Lumped mass (Ton)

6

3426.36

5

CM (m)

CR (m)

esi(m)

X

Y

X

Y

X

Y

349.27

7.52

11.33

8.42

11.18

0.90

0.15

4883.30

497.79

7.49

11.48

8.59

11.18

1.10

0.30

4

4978.94

507.54

7.49

11.59

8.59

11.18

1.10

0.41

3

4706.50

479.77

7.52

11.51

8.47

11.18

0.95

0.33

2

4708.90

480.01

7.55

11.47

8.47

11.18

0.92

0.29

1

4652.10

474.22

7.55

11.45

8.42

11.15

0.87

0.30

G

4900.50

499.54

7.62

11.37

8.63

10.99

1.00

0.38

Table 11.13(b): Structural parameters and design CM (with infill stiffness) CR (m)

Floor

Design CM1 (m)

esi(m)

Design CM2 (m)

X

Y

X

Y

X

Y

X

Y

6

8.42

11.18

0.90

0.15

9.66

12.58

5.38

10.08

5

8.59

11.18

1.10

0.30

9.94

12.97

5.04

10.00

4

8.59

11.18

1.10

0.41

9.94

13.23

5.04

9.95

3

8.47

11.18

0.95

0.33

9.75

13.02

5.30

9.99

2

8.47

11.18

0.92

0.29

9.73

12.93

5.36

10.01

1

8.42

11.15

0.87

0.30

9.65

12.92

5.44

9.97

G

8.63

10.99

1.00

0.38

9.92

12.97

5.32

9.77

228


Table 11.13(c): Structural parameters and design CM (without infill stiffness) Seismic weight (kN)

Lumped mass (Ton)

X

Y

X

Y

X

Y

6

3426.36

349.27

7.52

11.33

7.57

11.15

0.05

0.18

5

4883.30

497.79

7.49

11.48

7.66

11.16

0.17

0.32

4

4978.94

507.54

7.49

11.59

7.62

11.17

0.13

0.42

3

4706.50

479.77

7.52

11.51

7.56

11.17

0.04

0.34

2

4708.90

480.01

7.55

11.47

7.56

11.17

0.02

0.30

1

4652.10

474.22

7.55

11.45

7.73

11.10

0.18

0.35

G

4900.50

499.54

7.62

11.37

8.08

11.30

0.46

0.07

Floor

CM (m)

CR (m)

esi(m)

Table 11.13 (d): Structural parameters and design CM (with infill stiffness)

esi (m)

CR (m)

Floor

Design CM1 (m) X Y

Design CM2 (m) X Y

X

Y

X

Y

6

7.57

11.15

0.05

0.18

8.39

12.63

6.65

10.03

5

7.66

11.16

0.17

0.32

8.54

12.99

6.45

9.98

4

7.62

11.17

0.13

0.42

8.48

13.25

6.51

9.93

3

7.56

11.17

0.04

0.34

8.38

13.04

6.67

9.97

2

7.56

11.17

0.02

0.30

8.37

12.94

6.72

9.99

1

7.73

11.10

0.18

0.35

8.62

13.00

6.47

9.90

G

8.08

11.30

0.46

0.07

9.11

12.50

6.14

10.23

10.5.3 Equivalent Static Analysis

Design Base Shear: Design lateral forces at each storey level are applied at the centre of mass locations independently in two horizontal directions. Table 11.14 shows lateral force distribution at different storey level.

229


Table 11.14: Typical distribution of lateral force over the height of the building

Lateral Force, Qi (kN) With infill Without infill Stiffness stiffness X Y

Floor no

Seismic weight, Wi (kN)

Height, hi (m)

6

3426.36

24.60

603.63

592.36

396.38

5

4883.30

21.00

626.93

615.23

411.68

4

4978.94

17.40

438.84

430.65

288.16

3

4706.50

13.80

260.93

256.06

171.34

2

4708.90

10.20

142.62

139.96

93.65

1

4652.10

6.60

58.99

57.89

38.74

G

4900.50

3.60

18.49

18.14

12.14

11.5.4 Response Spectrum Analysis

Table 11.15 shows the comparison of the fundamental periods and the spectral accelerations for the building. Figure 11.7 shows the position of the periods in the response spectrum. Table 11.15: Comparison of fundamental time periods

Empirical formula

Computational model





T (s)

0.49

0.83

1.06

1.28

Sa/g

2.50

1.64

1.28

1.07

Table 11.26 represents the period and the predominant direction of vibration for the first five modes of the building, with and without the infill stiffness. The table also shows the mass participation for each of the five modes. The first five modes were considered in the dynamic analysis, which give more than 90% mass participation in both of the horizontal directions. Figure 11.8 shows the first three mode shapes of the building. The base shear for the equivalent static method and the response spectrum methods are compared in Table 11.17

230


3.0

Empirical formula

Spectral Accelaration Coefficient (Sa/g )

Spectral Accelaration Coefficient (Sa/g )

3.0 2.5

Computational model

2.0 1.5 1.0 0.5 0.0

Empirical formula

2.5 2.0

Computational model

1.5 1.0 0.5 0.0

0.0

0.5

1.0

1.5

0.0

0.5

Period (s)

1.0

1.5

Period (s)

(a) with infill stiffness

(b) without infill stiffness

Figure 11.7: Comparison of time periods of the building models Table 11.16: Time Period and Modal Participation Ratio for the first five modes

Without infill stiffness Mass Participation (%) T (s) Ux Uy 1.27 6.12 70.27 1.20 69.99 6.53 0.60 0.31 1.16 0.41 0.42 11.50 0.38 13.54 0.37

Mode 1 2 3 4 5

With infill stiffness T (s) 1.06 0.92 0.39 0.33 0.30

Mass Participation (%) Ux 74.89 0.18 0.08 15.10 0.07

Uy 0.18 78.29 1.35 0.07 11.19

Table 11.17: Comparison of base shear



Vx

Vy

Vx

Vy

2150

2110

1412

1412

(VB )

891

1030

745

693

VB / VB

2.37

2.05

2.88

3.10

Equivalent static

(V ) B

Response spectrum

231


`

(a) First Mode

(b) Second Mode

(c) Third Mode

Figure 11.8: First mode shape of the building (without infill stiffness)

11.5.5

Evaluation results

The analysis results show that a number of frame sections are deficient. Tables 11.18 and 11.19 shows the DCR for a few column and beam sections, respectively.

232


Table 11.18: Demand-to-Capacity Ratios (DCR) in columns

Without infill stiffness Columns

DCR in Flexure

GAC1 GAC2 GAC3

1.3 1.2 1.2

DCR in Shear V2 V3 0.3 0.6 0.4 0.5 0.4 0.3

GAC4 GAC7 1AC1 1AC2

1.9 1.6 1.8 2.1

0.5 0.5 0.4 0.6

1AC3 1AC4 1AC7 2AC1

1.9 2.2 2.4 1.9

2AC2

1.6

With infill stiffness DCR in Flexure 2.6 3.1 3.2

DCR in Shear V2 V3 0.4 0.7 0.8 0.6 0.7 0.6

0.6 0.4 0.5 0.8

2.1 2.5 2.4 2.8

0.7 0.5 0.6 0.4

0.9 0.7 0.6 0.3

0.3 0.4 0.5 0.3

0.8 0.5 0.4 0.6

2.6 2.7 2.9 2.4

0.4 0.4 0.5 0.5

0.7 0.9 0.4 0.8

0.4

0.2

2.5

0.6

0.3

Table 11.19: Demand-to-Capacity Ratios (DCR) in Beams

Beams GAB1 GAB5

Without infill stiffness DCR in DCR in Shear Flexure 1.05 1.37 1.04 4.48

With infill stiffness DCR in DCR in Shear Flexure 2.20 1.17 3.40 3.20

GAB8 GAB9 GAB10 GAB11

1.26 0.39 0.23 1.09

4.30 3.09 3.07 2.54

3.45 0.74 0.65 2.21

5.21 2.50 4.10 1.56

GAB15 GAB16 GAB18 GAB20

0.09 0.05 0.01 0.29

1.99 1.38 1.22 1.55

0.12 0.09 0.09 0.54

2.00 1.10 1.01 1.47

GAB38 1AB1 1AB5 1AB8

0.53 1.03 1.07 1.16

2.42 1.20 4.82 4.14

0.70 2.07 2.60 2.25

2.31 1.68 2.51 3.27

233


The storey drift for every storey is within the code limit of 0.4%. Figure 11.9 shows the storey drifts in X-direction.

6 5

Storey Level

4 3 2 1 G0 B -1

0.00

0.03

0.06

0.09

0.12

0.15

Storey Drift

Figure 11.9: Storey drifts along X-direction for design seismic base shear 10.6


The analysis was done as per the method in Chapter 4.

10.6.1

Pushover Curve

Figure 11.10 shows the pushover curves for the building with and without infill stiffness. The building has sufficiently large strength and stiffness at the global level when infill stiffness was modelled, but it does not show desired strength and stiffness when the infill stiffness was ignored.

11.6.2

Capacity spectrum, demand spectrum and performance point

Pushover analyses in either direction failed to give a performance point for both the models, with and without infill stiffness. The demand and capacity spectrum

234


for the lateral push along the two orthogonal directions are shown in Figures 11.11(a) to 11.11(d).

Without Infill Stiffness (WOS)

With Infill Stiffness (WS)

4500

Base Shear (kN)

4000 3500 3000 2500 V (WS) B 2000 1500

VB (WOS)

1000 500 0 0.00

0.01

0.02

0.03

0.04

0.05


Figure 11.10: Pushover curves (X- direction)

Spectral Acceleration/g

0.45

0.30

0.15

0.00 0.00

0.05

0.10

0.15


Figure 11.11(a): Demand and Capacity spectra for lateral push along X-direction (without infill stiffness)

235



0.45

0.30

0.15

0.00 0.00

0.05

0.10

0.15


Figure 11.11(b): Demand and capacity spectra for lateral push along Y-direction (Without infill stiffness)


0.45

0.30

0.15

0.00 0.00

0.05

0.10

0.15


Figure 11.11(c): Demand and capacity spectra for lateral push along X-direction (With infill stiffness)

236



0.45

0.30

0.15

0.00 0.00

0.05

0.10

0.15


Figure 11.11(d): Demand and capacity spectra for lateral push along Y-direction (With infill stiffness) 11.6.3

Displacements and inter-storey drifts

The inter-storey drifts corresponding to the displacement profiles are shown in Figures 11.12(a) and 11.12(b). 6 5

Storey Level

4 3 2 1 G0 B -1

0.00

0.07

0.14

0.21

0.28

0.35

Storey Drift

Figure 11.12(a): Maximum storey drift along X-direction (with infill stiffness)

237


6 5

Storey Level

4 3 2 1 G0 B -1

0.00

0.07

0.14

0.21

0.28

0.35

Storey Drift

Figure 11.12(b): Maximum inter-storey drift along Y-direction (with infill

stiffness)

10.6.4

Vulnerability Index

The vulnerability indices of the building and vulnerability indices of the stories are separately calculated in both X- and Y- directions, for with and without infill stiffness cases, according to Appendix D. Vulnerability index of the buildings are given in Tables 10.20(a) and 10.20(b).

The indices of storeys are given in

Tables 10.21(a) and 10.21(b). Table 10.20(a): Vulnerability index of buildings (with infill stiffness)

Location Yielded

B-IO

IO-LS

LS-CP

CP-C

C-D

D-E

>E

Column Xdirection Beam

0

0

0

0

0

0

0

8

2

1

1

0

2

0

Column Ydirection Beam

13

4

0

0

0

0

0

58

2

1

11

0

2

16

238

VIbldg 0.006

0.050


Table 10.20(b): Vulnerability index of buildings (without infill stiffness)

Location Yielded

B-IO

IO-LS

LS-CP

CP-C

C-D

D-E

>E

Column Xdirection Beam

3

0

0

0

0

0

0

19

3

3

3

0

3

32

16

0

0

0

0

0

0

44

1

3

7

0

1

18

Column Ydirection Beam

VIbldg 0.053

0.043

Table 10.21(a): Vulnerability index of stories (with infill stiffness) in X direction

Storey Level

1

2

3

4

5

6

7

B-IO

0

0

0

0

0

0

0

IO-LS

0

0

0

0

0

0

0

LS-CP

0

0

0

0

0

0

0

CP-C

0

0

0

0

0

0

0

C-D

0

0

0

0

0

0

0

D-E

0

0

0

0

0

0

0

>E

0

0

0

0

0

0

0

VIstorey

−

−

−

−

−

−

−

Table 10.21(b): Vulnerability index of stories (with infill stiffness) in Y direction

Storey Level

1

2

3

4

5

6

7

B-IO

7

3

1

0

1

1

0

IO-LS

3

1

0

0

0

0

0

LS-CP

0

0

0

0

0

0

0

CP-C

0

0

0

0

0

0

0

C-D

0

0

0

0

0

0

0

D-E

0

0

0

0

0

0

0

>E

0

0

0

0

0

0

0

VIstorey

0.045

0.018

0.003

0

0.003

0.003

0

239


11.7

SUMMARY OF THE RESULTS

(i)

The linear analysis results show that almost all the beam and column sections are safe in flexure. But a few column sections and all beam sections are deficient in shear. Pushover analysis also reveals the same weakness of the structure.

(ii)

The building complies with the drift requirement.

(iii)

All the pushover analyses failed to give a performance point, except for Ydirection with infill stiffness. So the performance is not acceptable. The building needs to be retrofitted.

11.8

RETROFIT

A global retrofit strategy of placing walls inside the office space was not possible. So, a local retrofit strategy was adopted. Two beam sections, AB5 and AB8, were retrofitted to take additional 25% shear force. Figure 11.13 shows the location of these beams in a typical floor. The beam sections can be retrofitted by concrete jacketing or glass fibre reinforced polymer wrapping. AB 5

AB 5

AB 8

Figure 11.13: Location of retrofitted beams

240


The shear strengthening is modelled in the structure by changing the shear hinge properties. The re-analysis of the retrofitted structure shows that the building achieves desirable performance in either direction. The drift at the performance point is about 0.25% which is acceptable. Figures 11.14 (a) and 11.14(b) show the pushover curves along X- and Y-directions, respectively. Figures 11.15(a) and 11.15 (b) shows the demand and capacity spectra for the retrofitted building along X- and Y- directions, respectively. 6000

Base Shear (kN)

5000

4000

3000

2000

1000

0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08


Figure 11.14(a): Pushover curves along X-direction for the retrofitted building

7000 6000

Base Shear (kN)

5000 4000 3000 2000 1000 0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08


Figure 11.14(b): Pushover curves along Y-direction for the retrofitted building

241



0.45

0.30

0.15

0.00 0.00

0.05

0.10

0.15


Figure 11.15(a): Demand and capacity spectra for push along X-direction


0.45

0.30

0.15

0.00 0.00

0.05

0.10

0.15


Figure 11.15(b): Demand and capacity spectra for push along Y-direction

242


APPENDIX A MAPPING OF SOIL TYPE

The three soil types used in the data collection form of FEMA 154 are C, D and E. The soil types are mapped to soil Types I, II and III as given in IS 1893: 2002, by Table A1. Table A1: Mapping of soil types UBC 1997 Soil Type

IS 1893: 2002 Criteria

Soil Type

A– Hard rock B – Rock C – Dense soil and soft rock

Criteria

vs > 1500 m/s 760 m/s < vs ≤ 1500 m/s 360 m/s < vs ≤ 760 m/s, Type I N > 30 or, N > 50, (Rock or hard soil) or, su > 100 kPa D – Stiff Soil 180 m/s ≤ vs ≤ 360 m/s, Type II 10 ≤ N ≤30 or, 15 < N ≤ 50, (Medium soil) or, 50 kPa< su ≤ 100 kPa E – Soft Soil vs < 180 m/s, Type III N<10 or, a profile with more than (Soft soil) 3.05 m of soft clay F – Poor Soil Requires site specific evaluation N: Standard penetration count, su: Un-drained shear strength, vs: Shear wave velocity.

A1


APPENDIX B MODELLING OF MASONRY INFILL WALLS

B.1

MODELLING OF MASONRY INFILL

For an infill wall located in a lateral load-resisting frame, the stiffness and strength contribution of the infill has to be considered. Non-integral infill walls subjected to lateral load behave like diagonal struts. Thus an infill wall can be modelled as an equivalent ‘compression only’ strut in the building model. The concept is shown in Figure B1. It is a trussed frame model. Rigid joints connect the beams and columns, but pin joints connect the equivalent struts to the beam-to-column junctions. This section explains the procedure based on Smith and Carter (1969) to calculate the modelling parameters (effective width, elastic modulus and strength) of an equivalent strut.

The length of the strut is given by the diagonal distance (d) of the panel (Figure B1c) and its thickness is equal to the thickness of the infill wall. The elastic modulus of the strut is equated to the elastic modulus of masonry (Em). As per IBC: 2000, Em is given as Em = 750 f m/

B1

(B.1)


where f m/ is the specified compressive strength of the masonry in MPa. The value of f m/ can be obtained by prism tests. As per FEMA 356 (2000), Em is given as Em = 550 f m/ . For the estimation of width (w) of the strut, a simple expression can be adopted (Ramesh, 2003). w

= 1.477 + 0.0356λ h − 0.912 ( R / Rc ) w′

(B.2)

Here, the instantaneous value of w is expressed in terms of a parameter w/. The expression of w/ is given as

⎛ w ' ⎞ 0.43sin 2θ ⎜ ⎟= λh ⎝d ⎠

Length of contact

(B.3)

d

(a) Infill frame

(b) Deformed shape

(c) Equivalent strut

Figure B1: Behaviour of Infill Frames

The expressions are functions of λh, a non-dimensional quantity. Here, λ is the relative stiffness of the infill to the frame. It is calculated as follows.

λ=

4

Emt sin 2θ 4 Ec I c h '

Here, Ec ≡ Modulus of elasticity of concrete in the column

h ≡ Height of column (between centrelines of beams)

B2

(B.4)

Appendix B – Modelling of Masonry Infill Walls

h' ≡ Clear height of infill wall Ic ≡ Moment of inertia of the column section (lower of the two bounding columns)

l ≡ Length of beam (between centrelines of columns) t ≡ Thickness of infill wall

θ ≡ Slope of the infill diagonal to the horizontal = tan −1 (h / l ) R ≡ Instantaneous diagonal load in the strut Rc ≡ Compressive strength of the strut

Figure B2: Infilled Frame

B.2

EFFECT OF OPENINGS:

In the presence of an opening, a simplified procedure was proposed by Al-Char (2002). The effect of the opening is accounted for by reducing the effective width, as per the following equation.

wopen = ρ w × w

(B.5)

where, ρw ≡ Reduction factor for openings The corresponding equivalent strut is assumed to act in the same manner as for an infill without opening. The reduction factor ρw is calculated from the following equation. ρ w = 0.6 Ar 2 -1.6 Ar + 1

B3

(B.6)


where, Ar = ratio of opening area to the gross area of the panel If Area of opening is greater than or equal to 60 percent of gross area of panel, then the infill may be neglected. Reducing the strut width to account for an opening does not represent the stress distribution in the infill properly. Yet, this method was proposed based on its simplicity.

Mondal (2003) suggested the

following equation to consider the reduction in effective width in the presence of an opening.

ρ w = 1 − 1.25 Ar

B.3

(B.7)

STRENGTH OF EQUIVALENT STRUT

The strength of the equivalent strut is governed by the lowest of the failure loads corresponding to the following failure modes. a) Local crushing of the infill at one of the loaded corners. b) Shear cracking along the bedding joints of the brickwork.

The diagonal tensile cracking need not be considered as a failure mode, as higher load can be carried beyond tensile cracking

B.3.1

Local Crushing Failure

The diagonal load causing local crushing (Rc) is given by the following equation (Smith and Carter, 1969).

Rc = α c t sec θ f m

(B.8)

The length of contact at the column (αc) at the compression diagonal corner is calculated using the following formula.

αc h

=

π 2λ h

Other variables are as defined earlier.

B4

(B.9)

Appendix B – Modelling of Masonry Infill Walls

B.3.2

Shear Failure

Following relationship of Rs proposed by Govindan (1986) using the curves given by Smith and Carter (1969) is chosen, as it is simple and non-dimensional. RS = 1.65(l '/ h ')0.6 (λ h ) −0.05( l '/ h ')0.5 f 'bs ht

(B.10)

Where, f bs′ = The bond shear strength between the masonry and mortar. It is varies from 0.24 MPa for low strength mortar to 0.69 MPa for high strength mortar (Ramesh 2003). Again to be in conservative side f bs′ is taken as 0.24 in the calculation.

B5


APPENDIX C MODELLING OF PLASTIC HINGES

C.1

FLEXURAL HINGES FOR BEAMS AND COLUMNS

C.1.1

Stress-Strain Characteristics of Concrete

The stress-strain curve of concrete in compression forms the basis of analysis and design of any reinforced concrete section. Such curves are usually prescribed in design codes and give details of the shape of the curve (often idealised as parabolic in the initial ascending portion, and thereafter linearly descending or flat). The ultimate peak strength (and corresponding strain level, usually 0.002) and the ultimate compressive strain (in the range 0.003 to 0.004) are also specified. However, the maximum compressive strength and strain gets enhanced when the concrete is confined, and details of such effects are not available in the prevailing codes. The characteristic and design stress−strain curves specified by the IS 456: 2000, for concrete in flexural compression are depicted in Figure C1. The maximum stress in the ‘characteristic’ curve is restricted to 0.67 f ck . The curve consists of a parabola in the initial region up to a strain of 0.002 (where the slope becomes

C1


zero), and a straight line thereafter, at a constant stress level of 0.67 f ck up to an ultimate strain of 0.0035. For the purpose of limit states design, the appropriate partial safety factor γ c has to be applied, and γ c is equal to 1.5 for the consideration of ultimate limit states. Thus, the ‘design curve’ is obtained by simply scaling down the ordinates of the characteristic curve — dividing by γ c [Figure C1]. Accordingly, the maximum design stress becomes equal to 0.447 f ck , and the formula for the design compressive stress f c corresponding to any strain ε c ≤ 0.0035 is given by:

⎧ ⎡ ⎛ ε c ⎞ ⎛ ε c ⎞2 ⎤ 0.447 f ⎪ ck ⎢ 2 ⎜ ⎟−⎜ ⎟ ⎥ for ε c <0.002 fc = ⎨ ⎢⎣ ⎝ 0.002 ⎠ ⎝ 0.002 ⎠ ⎥⎦ ⎪ for 0.002 ≤ ε c ≤ 0.0035 ⎩ 0.447 f ck

Stress

0.67fck

characteristic curve

0.447fck

0

(C1)

design curve

0.001

0.002

0.003

εcu = 0.0035

Strain

Figure C1: Characteristic and design stress-strain curves for concrete – IS 456

C2

Appendix C – Modelling of Plastic Hinges

The IS 456: 2000 model does not truly reflect the actual stress-strain behaviour in the post-peak region, as (for convenience in calculations) it assumes a constant stress in this region (strains between 0.002 and 0.0035). In reality, as evidenced by experimental testing, the post-peak behaviour is characterised by a descending branch, which is attributed to ‘softening’ and micro-cracking in the concrete. Also, the IS code model does not account for strength enhancement and ductility due to confinement. The British code [BS 8110] model of stress-strain curve is similar to IS 456: 2000 model. ACI 318M-02 recognizes the inelastic stress distribution of concrete at high stress. As maximum stress is approached, the stress is approached, the stress-strain relationship for concrete is not a straight line but some form of curve (stress is not proportional to strain). The general shape of a stress-strain curve is primarily a function of concrete strength and consists of a rising curve from zero to a maximum at compressive strain between 0.0015 to 0.002 followed by a descending curve to an ultimate strain (crushing of concrete) ≡ 0.003. The ACI code assumes relationship between concrete compressive stress distribution and concrete strain to be rectangular.

Confined concrete

' f cc

First hoop fracture

Unconfined concrete

' f co

Ec Esec εt εco 2εco εsp ft'

Assumed for cover concrete εcc

εcu

Figure C2: Stress-strain curves for concrete – Mander, Priestley, and Park (1988) Mander, Priestley, and Park (1988) proposed a stress-strain model for concrete subjected uniaxial compressive loading and confined by transverse reinforcement

C3


(Figure C2). The concrete section may contain any general type of confining steel: either spiral or circular hoops; or rectangular hoops with or without supplementary cross ties. These cross ties can have either equal or unequal confining stresses along each of the transverse axes. The salient strain locations in the model (Figure C2) are given by the ultimate compressive strain (εcu), and the strains corresponding to the peak strength, viz., εcc in the case of confined concrete and εco (usually 0.002) in the case of ' unconfined concrete. The corresponding peak strengths are f cc in the case of

' in the case of unconfined concrete. The following confined concrete and f co

expressions for critical strains have been proposed:

ε cu = 0.004 + ⎡

1.4 ρ s f yhε sm

f 'cc ⎛ f 'cc ⎞ ⎤ − 1⎟ ⎥ ' ⎝ f co ⎠ ⎥⎦

ε cc = ε co ⎢1 + 5 ⎜ ⎣⎢

(C2)

(C3)

where ρ s = volumetric ratio of confining steel, f yh = grade of the stirrup reinforcement, and ε sm = steel strain at maximum tensile stress. ' The following expression is proposed for f cc in the case of circular sections or

rectangular sections with effective confining stress f l ' applied equally in the two orthogonal directions. The influence of various types of confinement is taken into account by defining an effective lateral confining stress, which is dependent on the configuration of the transverse and lateral reinforcement. ⎛ 7.94 f l ' fl ' ⎞ −2 ' ⎟ f cc = f 'co ⎜ −1.254 + 2.254 1 + ⎜ f 'co f co ⎟⎠ ⎝ '

1 fl ' = ke ρ s f yh 2

(C4)

(C5)

where ke is the “confinement effectiveness coefficient”, having a typical value of 0.95 for circular sections and 0.75 for rectangular sections. In the more general

C4


case of a rectangular section with unequal lateral confining stresses in the X- and ' ' / f co (Figure C3). Y- directions, a chart has been proposed to calculate f cc

A single equation is proposed to generate the stress fc corresponding to any given strain εc: fc = where x =

f 'cc x r r −1 + x r

(C6)

εc Ec f' ; r= ; Ec = 5000 f 'co ; Esec = cc . ε cc Ec − Esec ε cc K=

Largest Effective Confining Stress ratio f 'lx /f 'co

1.0

f ' cc f 'co

1.5

2.0

0.0

0.1

0.2

0.3 0.0

0.1

0.2

0.3

Smallest Effective Confining Stress ratio f 'ly /f 'co

Figure C3: Confined strength determination from lateral confining stresses for

rectangular sections This model has the following advantages: (a)

A single equation defines both the ascending and descending branches of stress-strain curve.

(b)

The model can also be used for unconfined concrete sections.

C5


(c)

The model can be applied to any shape of concrete member section confined by any kind of transverse reinforcement (spirals, cross ties, circular or rectangular hoops).

Fardis et al. (2001), proposed modifications to Mander’s et al. model.

An

expression for f 'cc was proposed to simplify the modelling of Figure C3. 0.85 ⎡ ⎛ 0.5ke ρ s f yh ⎞ ⎤ f cc = f co ⎢1 + 3.7 ⎜ ⎟ ⎥ f 'co ⎢⎣ ⎝ ⎠ ⎥⎦ '

'

(C7)

The expression for ultimate compressive strain has also been modified as follows:

ε cu = 0.004 +

0.6 ρ s f yhε sm f 'cc

(C8)

It is seen that Modified Mander’s (Fardis et al.) model of stress-strain curve is simple to use and gives realistic results. However it can be used only for normalstrength concrete.

C.1.2

Stress-Strain Characteristics of Steel

The ‘characteristic’ and ‘design’ stress−strain curves specified by the Code for various grades of reinforcing steel (in tension or compression) are shown in Figure C4.

C.1.3

Moment-Curvature Relationship

Curvature (φ) is defined as the reciprocal of the radius of curvature (R) at any point along a curved line. When an initial straight beam segment is subject to a uniform bending moment throughout its length, it is expected to bend into a segment of a circle with a curvature φ that increases in some manner with increase in the applied moment (M). Curvature φ may be alternatively defined as the angle

1 dθ ⎞ ⎛ change in the slope of the elastic curve per unit length ⎜ ϕ = = ⎟ . At any R ds ⎠ ⎝ section, using the ‘plane sections remain plane’ hypothesis under pure bending,

C6


the curvature can be computed as the ratio of the normal strain at any point across the depth to the distance measured from the neutral axis at that section (Figure C5). 500

fy

characteristic curve

400 design curve

stress (MPa)

0.87 fy

300

200 Es = 2 × 105 MPa

100

εy = (0.87 fy) Es + 0.002 0 0.000

0.002

0.004

0.006

0.008

strain

Figure C4: Stress-strain relationship for reinforcement – IS 456: 2000

If the bending produces extreme fibre strains of ε1 and ε2 at top and bottom at any section as shown in Figure C5 (compression on top and tension at bottom assumed in this case), then, for small deformations, it can be shown that ϕ =

( ε1 + ε2 ) , D

where D is the depth of the beam. If the beam behaviour is linear elastic, then the moment-curvature relationship is linear, and the curvature is obtained as ϕ=

M EI

(C9)

where EI is the flexural rigidity of the beam, obtained as a product of the modulus of elasticity E and the second moment of area of the section I.

C7


When an RC flexural member is subjected to a gradually increasing moment, its behaviour transits through various stages, starting from the initial uncracked state to the ultimate limit state of collapse. The stresses in the tension steel and concrete go on increasing as the moment increases. The behaviour at the ultimate limit state depends on the percentage of steel provided, i.e., on whether the section is ‘under-reinforced’ or ‘over-reinforced’.

In the case of under-reinforced

sections, failure is triggered by yielding of tension steel whereas in overreinforced section the steel does not yield at the limit state of failure. In both cases, the failure eventually occurs due to crushing of concrete at the extreme compression fibre, when the ultimate strain in concrete reaches its limit. Underreinforced beams are characterised by ‘ductile’ failure, accompanied by large deflections and significant flexural cracking. On the other hand, over-reinforced beams have practically no ductility, and the failure occurs suddenly, without the warning signs of wide cracking and large deflections.

Centre of curvature dθ R

M

ds(1- ε1)

y1 y2

M

ds Neutral Axis

ds(1+ ε2)

Figure C5: Curvature in an initially straight beam section

In the case of a short column subject to uniaxial bending combined with axial compression, it is assumed that equation C9 remains valid and that “plane sections

C8


before bending remain plane”.

However, the ultimate curvature (and hence,

ductility) of the section is reduced as the compression strain in the concrete contributes to resisting axial compression in addition to flexural compression.

C.1.4

Modelling of Moment-Curvature in Confined RC Sections

Using the Modified Mander (Fardis et al.) model of stress-strain curves for concrete and the stress-strain curve for steel as per IS 456: 2000, for a specific confining steel, moment curvature curves can be generated for beams and columns (for different axial load levels).

The assumptions and procedure used in

generating the moment-curvature curves are outlined below. C.1.4.1 1.

Assumptions

The strain is linear across the depth of the section (‘plane sections remain plane’).

2.

The tensile strength of the concrete is ignored.

3.

The concrete spalls off at a strain of 0.0035.

4.

The initial tangent modulus of the concrete, Ec is adopted from IS 456: 2000, as 5000 f ck .

5.

In determining the location of the neutral axis, convergence is assumed to be reached within an acceptable tolerance of 1%.

C.1.4.2 1.

Numerical Algorithm for Moment-Curvature for Beam Sections Assign a value to the extreme concrete compressive fibre strain (normally starting with a very small value).

2.

Assume a value of neutral axis depth measured from the extreme concrete compressive fibre.

3.

Calculate the strain and the corresponding stress at the centroid of tension

and compression reinforcement.

C9


4.

Determine the stress distribution in the concrete compressive region based on the Modified Mander stress-strain model for the given volumetric ratio of confining steel. The resultant concrete compressive force is then obtained by numerical integration of the stress over the entire compressive region.

5.

Calculate the tensile force from the stress in tensile reinforcement and the area of bar and compare with the net compressive force (Resultant concrete force + compressive force in compression reinforcement). If the difference lies within the specified tolerance, the assumed neutral axis depth is adopted. The moment capacity and the corresponding curvature of the section are then calculated.

Otherwise, a new neutral axis is

determined from the iteration (using bisection method) and steps (3) to (5) are repeated until it converges. 6.

Assign the next value, which is larger than the previous one, to the extreme concrete compressive strain and repeat steps (2) to (5).

7.

Repeat the whole procedure until the complete moment-curvature is obtained.

C.1.4.3 1.

Numerical Algorithm for Moment-Curvature for Column Sections Assign a value to the extreme concrete compressive fibre strain (normally starting with a very small value).

2.

Assume a value of neutral axis depth measured from the extreme concrete compressive fibre.

3.

Calculate the strain and the corresponding stress at the centroid of each longitudinal reinforcement bar.

4.

Determine the stress distribution in the concrete compressive region based on the Modified Mander stress-strain model for the given volumetric ratio of confining steel. The resultant concrete compressive force is then obtained by numerical integration of the stress over the entire compressive region.

C10


5.

Calculate the axial force from the equilibrium and compare with the applied axial load. If the difference lies within the specified tolerance, the assumed neutral axis depth is adopted. The moment capacity and the corresponding curvature of the section are then calculated. Otherwise, a new neutral axis is determined from the iteration (using bisection method) and steps (3) to (5) are repeated until it converges.

6.

Assign the next value, which is larger than the previous one, to the extreme concrete compressive strain and repeat steps (2) to (5).

7.

Repeat the whole procedure until the complete moment-curvature is obtained.

C.1.5

Moment-Rotation Parameters

Let us consider a simple cantilever beam AB shown in Figure C6(a) with a concentrated load applied at the free end B. To determine the rotation between the ends an idealized inelastic curvature distribution and a fully cracked section in the elastic region may be assumed. Figures C6(b) and C6(c) represent the bending moment diagram and probable distribution of curvature at the ultimate moment. The rotation between A and B is given by B

θ = ∫ ϕ dx ………………………………………………………..(C10) A

where ϕ is the curvature and dx is an element length of the member i.e., ultimate rotation, θu = ϕ y

l + (ϕu − ϕ y )l p …………………………………(C11) 2

where the yield rotation θ y = ϕ y

l …………………………………………..(C12) 2

or, plastic rotation, θ p = (ϕu − ϕ y ) l p …………………………………………(C13) where ϕu is the ultimate curvature, ϕ y is the yield curvature and l p is the equivalent length of plastic hinge over which plastic curvature is considered to be constant.

C11


The physical definition of the plastic hinge length, considering the ultimate flexural strength developing at the support, is the distance from the support over which the applied moment exceeds the yield moment. The established practice is to consider l p = 0.5 D ……………………………………………………(C14) Panagiotakos and Fardis (2001) proposed the length of plastic hinge as:

l p = 0.12 Ls + 0.014asl db f y ………………………………………..(C15)

B

A l (a)

(b)

lp

ϕu

ϕy (c) Figure C6: (a) cantilever beam, (b) Bending moment distribution, and (c)

Curvature distribution (Park and Paulay 1975) The moment-rotation curve can be idealised as described in Chapter IV, and can be derived from the moment-curvature model. While applying equations C11 and C12 to determine the yield and ultimate rotations, care must be taken to adopt the

C12


correct value of the length l, applicable for cantilever action. In the case of a frame member in a multi-storey frame subject to lateral loads, it may be conveniently assumed that the points of contraflexure are located (approximately) at the mid-points of the beams and columns. In such cases, an approximate value of l is given by half the span of the member under consideration.

C.2

SHEAR HINGES FOR BEAMS AND COLUMNS

Flexural plastic hinges will develop, along with the predicted values of ultimate moment capacity, provided there is no prior failure in shear. In order to prevent this occurrence, design codes prescribe specifications (e.g. ductile detailing requirement of IS 13920: 1993) for adequate shear reinforcement, corresponding to the ultimate moment capacity level. However, in practice, shear failure are commonly seen to occur in beams and columns in the event of a severe earthquake, owing to inadequate shear design. In non-linear analysis, this can be modelled by employing ‘shear hinges’. These hinges should ideally be located at the same points as the flexural hinges near the beam column joints. If the shear hinge mechanism is triggered before the formation of flexural hinge, the moment demand gets automatically restricted and the full flexural hinge may not develop. Shear force-deformation curves to assign shear hinges for beams and columns can be calculated as follows. It is assumed to be symmetric for positive and negative shear forces. A typical force-deformation curve is shown in Figure C7. Yield shear strength (Vy) is calculated by adding strength of the shear reinforcement (Vsy) to the shear strength of the concrete section (Vc) in case of column. But for beam, when it is designed for medium and high ductility, shear strength contribution of concrete is completely ignored as in cracked section

C13


concrete does not provide any shear resistance. Shear resistance carried by shear reinforcement (Vsy) as per clause 40.4 of IS 456: 2000 is. Vsy = 0.87 f y Asv

d sv

(C16)

≡ yield stress of the transverse reinforcement

Where, fy Asv

≡ Total cross sectional area of one stirrup considering all the legs

d

≡ effective depth ≡ Spacing between two stirrup

Shear strength (V)

Sv

Vu = 1.05Vy

Vy

Residual Shear Strength

0.2 Vy ∆y

1.5∆y

∆m=15∆y

Shear deformation (∆)

Figure C7: Typical shear force-deformation curves to model shear hinges

For calculation of Vsy, above formula is used putting 1.00fy instead of 0.87fy for the actual strain hardened reinforcement. Vsy = 1.0 f y Asv

d sv

(C17)

In case of column shear strength in existing construction is calculated by the following expression Vy = Vc + Vsy

(C18)

Shear resistance taken by the concrete (Vc) as given in the clause 40.2.2 of IS 456: 2000 is

C14


Vc = δτ c bd where δ = 1 +

0.85 0.8 f ck ( 1 + 5β − 1) 3Pu ≤ 1.5 and τ c = 6β Ag f ck Here β =

(C19)

0.116 f ck bd ≥ 1.0 100 Ast

For moderate and high ductility of the column section δ = 0 +

3Pu ≤ 0.5 is taken Ag f ck

in calculation (ATC 40)

Shear deformation (∆) is to be calculated using the following formula. ∆=

Yield shear strength R = KV Shear stiffness

(C20)

Yield deformation should be calculated using shear stiffness of un-cracked member as shown in Equation C21 KV =

1 ⎛ G × bW d ⎞ ⎟ f ⎜⎝ l ⎠

(C21)

Where G = Shear modulus of the reinforced concrete section Ag = Gross area of the section l = Length of member f = Factor to account non-uniform distribution of shear stress. For rectangular section, f = 1.2 and for T and I section f = 1.0. Ultimate shear deformation can be calculated using shear stiffness of the cracked member. Shear stiffness for the cracked member can be calculated using the procedure given in Park and Paulay (1975). The expression for shear stiffness of a rectangular section with 450 diagonal cracks and vertical stirrups is given in Equation C22 K v ,45 =

ρv

1 + 4n ρ v

Es bw d

C15

(C22)


Here, ρ v =

Asv E ; n = s and bw = web width sv bw Ec

Similar expression is available for other inclination of cracking and stirrups in Park and Paulay (1975) The ultimate shear strength (Vu) is taken as 5% more than yield shear strength (Vy) and residual shear strength is taken as 20% of the yield shear strength for modelling of the shear hinges as shown in Figure C7. Similarly maximum shear deformation is taken as 15 times the yield deformation. The values were taken as per FEMA recommendations.

C.3

AXIAL HINGES FOR EQUIVALENT STRUTS

The axial load versus deformation behaviour of the equivalent struts under compression can be modelled with axial hinges. In absence for data, an elastic behaviour up to the failure load can be assumed. Any tensile load carrying capacity of the strut is neglected. Figure C8 shows a typical load-deformation relation for the axial hinge in strut. R and ∆y represent the failure load and the corresponding deformation, respectively, of the strut.

The failure load (R) is calculated from the lower of the failure loads corresponding to local crushing and shear cracking. The expressions are given in Appendix B. The deformation corresponding to the failure load can be calculated based on the initial stiffness as follows.

∆y =

R R×d = ……………………………. (C23) ⎛ AE ⎞ w × t × Em ⎜ ⎟ ⎝ d ⎠

Here

Em = elastic modulus of the infill material

C16


t = thickness of infill wall d = length of the strut between the beam-to-column joint nodes w = effective width of the equivalent strut The post peak behaviour is modelled with zero load capacity.

R

Load

IO, LS, CP

∆y Deformation

Figure C8: A typical stress-strain relation for axial hinges in equivalent struts.

C17


APPENDIX D VULNERABILITY INDEX

The vulnerability index is a measure of the damage in a building obtained from the pushover analysis. The vulnerability index is defined as a scaled linear combination (weighted average) of performance measures of the hinges in the components. It is calculated from the performance levels of the components at the performance point or at the point of termination of the pushover analysis.

Table D.1: Weightage factors for performance range Sl

Performance range(i)

Weightage factor(xi)

1

0

2

B – IO

0.125

3

IO – LS

0.375

4

LS – CP

0.625

5

CP – C

0.875

6

C – D, D – E, and >E

1.000

no.

It is mentioned in Appendices C and D that the load-deformation curve for a particular hinge is assumed to be piece-wise linear (Figure D1). The plastic

D1


plateau (B-C) in the load-deformation curve is sub-divided into the performance ranges namely, B-IO, IO-LS, LS-CP, CP-C, C-D, D-E, and >E (also refer Section 4.6). After the pushover analysis, performance ranges of the hinges formed in the component can be noted from the deformed shape output. The number of hinges formed in the beams and columns for each performance range are available from the output. A ‘weightage factor’ (xi) is assigned to each performance range. The proposed values of xi are given in Table D.1. As columns are more important than beams in the global safety of a building, an ‘importance factor’ of 1.5 for column is additionally assigned. The Building vulnerability index (VIbldg) is accordingly given by the following weighted average. VI bldg =

1.5∑ N ic xi + ∑ N ib xi

∑N

c i

(F.1)

+ ∑ N ib

Here, N ic and N ib are the numbers of hinges in columns and beams respectively for the i'th performance range.

The summation ∑ is intended to cover the

performance ranges (i =1, 2, … 6).

0.625 0.375

0.125

B

Load

0.875

IO

C

LS

CP

D

A

E

Deformation

Figure D1: Weightage factor for different level of hinges

D2

Appendix D – Vulnerability Index

VIbldg is measure of the overall vulnerability index for the building. A high value of VIbldg reflects poor performance of the building components (i.e., high risk) as obtained from pushover analysis. But this index may not reflect a soft storey mechanism, in which a performance point may not be achieved. A storey vulnerability index (VIstorey) can be defined to quantify the possibility of a soft/weak storey with the formation of flexural hinges. For each storey the VIstorey is defined as: VI storey

∑N x = ∑N

c i i c i

(D.2)

where N ic is the number of column hinges in the storey under investigation for a particular performance range. In a given building, the presence of soft / weak storey is reflected by a relatively high value of VIstorey for that storey, in relation to other storeys. If the analysis terminates by the formation of shear hinges, then the above definition is not applicable.

D3


APPENDIX E ADDITION OF STEEL BRACES

E.1

TYPES OF BRACING

The braces in a building may be either concentric or eccentric.

Concentric

bracings may be of diagonal or X-brace type as shown in Figure E1. In Xbracings at least one of the members in each floor is under tension and hence it is preferred to diagonal bracings.

The concentric bracings increase the lateral

stiffness of the frame and decrease the lateral drift. However, increase in the stiffness may attract a larger inertia force due to earthquake. Further, while the bracings decrease the bending moments and shear forces in columns, they increase the axial compression and tension in the columns to which they are connected. Since RC columns are strong in compression, it may not pose a problem to retrofit in a RC frame using concentric steel bracings. However, it should be ensured that there is adequate pre-compression in the columns due to gravity loads to offset the tension generated due to earthquakes. The foundation uplift due to this tension should be avoided. Concentric bracings usually have lower energy dissipation capacity, especially under compression range of the cyclic loading. In order to lessen the increase in the lateral stiffness of the frame and improve the energy dissipation capacity, eccentrically braced frames (Figure E2) have been used.

E1


(a) Diagonal CBF

(b) X-braced CBF

Figure E1: Types of Concentric Braced Frame (CBF)

(a) Diagonal EBF

(b) Split-K braced EBF

(c) V-type EBF

Figure E2: Types of Eccentric Braced Frame (EBF)

Due to eccentric connection of the braces to beams, the lateral stiffness of the system depends upon the flexural stiffness of the beams and columns, thus reducing the lateral stiffness of the frame. The vertical component of the bracing

E2

Appendix E – Addition of Steel Braces

force due to earthquake cause transverse concentrated load on the beams at the point of connection of the eccentric bracings. Under this load, plastic hinges are formed in the stub length of the beam, along with large shear. The beam should have adequate ductility to dissipate energy through these plastic hinges. Although eccentrically braced frames attract lesser base shear due to their lesser stiffness compared to concentrically braced frame, they under go larger lateral drift. Further, use of eccentric brace in RC frames is usually not appropriate due to the low plastic hinge deformation capacity and low shear capacity of RC beams. Steel braces have enough ductility in tension to dissipate energy, but are weak in compression. Due to this reason, normally X-bracings are preferred over diagonal bracings in seismic zones. Diagonal bracings can be used in the zones having high intensity of wind particularly in one direction. Diagonal bracings in two bays in each orthogonal direction in plan with opposite slopes in a given storey can be used instead of X bracings.

E.2

CONNECTION OF BRACES TO RC FRAME

The connections are most important in braced frames, especially while retrofitting. Forces in the braces transfer to frame beam-column joints though the connections. The strength, ductility and energy dissipation characteristics of braced frame under earthquake loading are often dictated by connections. Various types of connections (Maheri and Sahebi, 1997 and Maheri and Hadjipour, 2003) are shown in Figure E3. E.2.1 Connection Type I (Figure E3-a) This type of connection is suitable in new construction. While constructing the concrete frame, anchor bolts should be placed at appropriate locations in concrete, and designed to have enough anchorage strength.

The forces in braces are

transferred through gusset plates and end plates to the concrete frame at beam column junction through the anchor bolts.

E3


E.2.2 Connection Type II (Figure E3-b) This type of connection requires special provisions at the concrete beam-column intersection. The corner of the frame is built-up with concrete so that only one connecting plate is used to transfer the brace load directly through the joint. It creates a more direct load path for the transfer of the brace force and provides ample space for anchor bolts.

The connection is suitable when braces are

introduced in frames during construction so that special provisions for the built-up corner can be made at design and construction stages. E.2.3 Connection Type III (Figure E3-c) This type of connection is identical to Type I, except for the method of anchoring end plates into the RC joint. The plates are connected to the concrete members using straight bolts introduced through holes in the members and anchored at the opposite face with a bearing plate and nuts.

In this method the width of

connecting plate and bearing plate is less than or equal to the width of beam or column. Advantage of this method is that bolts can be placed in the concrete even after frame construction. Hence, this method is applicable for retrofit of existing RC frames using steel bracing. E.2.4 Connection Type IV (Figure E3-d) This type of connection is identical to Type III, but for the location of bolts. In the earlier method, the width of the connecting plate and bearing plates are less than the width of beam and column and the bolts were inserted through holes in the members. In this method, the connecting plate and bearing plate project beyond the width of the beam and column. The bolts are outside the members. Hence drilling of holes through the reinforced concrete beam and column is avoided. This method is useful for retrofit of existing RC frames.

E4


Gusset plate

Brace

Connecting

(b) Connecting bolts embedded in concrete directly to joint.

(a) Connecting bolts embedded in concrete.

Bearing plate

(c) Bolts connected by bearing plate through concrete

(d) Bolts connected by bearing plate out side of the section.

Figure E3: Types of connections between brace to concrete frame

E5


E.3

ANALYSIS AND DESIGN OF BRACES

The design of braces is an iterative process, because the forces in the braces depend on the stiffness of the braces. The braces are subjected to alternative tension and compression during the seismic loading and have to be designed for both tension and compression. In X-bracing, at any instant, one brace is subjected to tension while the other is subjected to compression. The stiffness and strength of brace under compression is often neglected in design, and only stiffness of the brace subjected to tension is considered. The braces are designed to resist only tension. The braces can be designed by analysing the frame by any of the following methods •

Equivalent static method. (Linear static analysis)

•

Response spectrum method. (Linear dynamic analysis)

•

Non-linear static method. (Push over method)

An appropriate section for the brace has to be selected satisfying the maximum value of effective slenderness ratio of the IS code. The design forces in a brace from the analysis are used to calculate the required section. If the required section is very different from the initial section, the analysis needs to be performed again with the revised section properties of the brace. This process is repeated until the section is adequate for the forces in the member. In the nonlinear static method, the iterative procedure of selecting the brace sections and modelling the brace is similar to the linear methods. In addition, axial load versus deformation behaviour has to be modelled as axial hinge properties.

E6


Approximate analysis In this method the lateral force resisted by the frame is neglected and hence it is conservative to find the forces in the braces. The following steps may be used to calculate the brace forces rapidly and more conservatively (FEMA 172, 178).

Calculate the time period of building.

Calculate the horizontal seismic coefficient.

Calculate the base shear and distribute the base shear to storeys

Calculate the axial force in the diagonal brace (Fbr) by the following expression.

⎛ Vj ⎞ Lbr Fbr = ⎜ ⎟ ⎝ N br ⎠ s

(E.1)

Here, Vj = Storey shear in jth storey Lbr =

Average length of braces

Nbr = Number of braces in tension and compression, if the braces are designed for compression. Nbr = Number of braces in tension if the effectiveness of compression brace is neglected. s=

Average span of braces.

Behaviour of Braces The common modes of failure of braces system are as follows. •

Tension yielding of gross area of brace.

•

Tension fracture of net area of braces at the end connections.

•

Tension fracture of end gusset plate.

•

Buckling failure under compression of braces between lateral supports.

•

Buckling failure under compression of end gusset plate.

•

Block-shear failure of braces at the end connection.

•

Block-shear failure of end gusset plate.

•

Bolt shear failure.

E7


•

Bearing failure of bolts against the plates.

•

Fracture of fillet welds between gusset plate and connecting end plate.

While conventional braces dissipate considerable energy by yielding under tension (gross area yielding), they buckle under compression without much energy dissipation.

Figure E4-a shows a typical hysteresis plot for a conventional

Stress

concentric brace under cyclic loading (Ikeda and Madhin, 1985).

Axial force

Tension

Displacement

Strain Compression (a). Conventional brace system

(b). X brace system

Figure E4: Behaviour of conventional brace and X bracing under cyclic loading

The strength, stiffness and energy dissipation in compression reduced progressively with each cycle and fracture at the plastic hinge location due to buckling occurred within a few cycles. So single diagonal bracing is not desirable to resist cycling loading under earthquake. X bracing in a single bay or bracing with opposing slopes in multiple bays overcome this disadvantage, because when one brace is under compression, the other is in tension.

Even though the

individual brace behaviour is same as the conventional brace, the over all frame behaviour meets the requirements of cyclic loading. The typical behaviour of Xbracing under cyclic loading is shown in Figure E4-b.

The degradation of

stiffness encountered in conventional braces during one half of the cycle

E8


corresponding to compression is not observed in X-braces. However, lower or zero stiffness (pinching) at the stage of stress reversal is observed due to yielding and plastic elongation of the member under tension and buckling of the member under compression in the previous cycles.

E.4

NON-BUCKLING BRACES

Generally it is not economical to design a building to remain elastic under earthquake loading. Steel members can dissipate considerable energy through inelastic deformations, using the ductility of the material.

The non-buckling

bracing system (Figure E5) is an innovative, patented concept (Indian patent No. 155036, dated April 30, 1981 and United States patent No. 5175972, dated January 5, 1993), which overcomes the problem of buckling and low energy dissipation in regular braces in the compression portion of the cycle.

Sleeve

Grout

Core Figure E5: Non- buckling braces

In this system, the two requirements in the design of compression members (adequate material strength to resist compression and flexural rigidity to avoid buckling) have been bifurcated between the core and sleeve elements. The space between the core and the sleeve is filled with inert filler such as cement grout. The bond between the core and the grout is eliminated to ensure that no part of axial force directly applied on the core element is transferred to the sleeve.

E9


Projection of the core beyond the sleeve is to be designed such that the core does not yield or buckle in that region.

Axial Load

Tension

Axial Deformation

Compression Figure E6: Non-prismatic core element

Extensive experimental and analytical studies have indicated that as long as the sleeve is adequately stiff, the core can be subjected to a compressive strain well beyond the yield stain, without the overall buckling of the strut. Hence the nonbuckling braces can dissipate energy both in tension and compression, as shown in Figure E6. The strength and stiffness of the non-buckling brace can be altered using cores with non-prismatic cross-sections. Two parameters α, β are used to describe the non-prismatic core properties as given below (Figure E7).

Ac

Areduced Lreduced L

Figure E7: Behaviour of non-buckling brace under cyclic loading

E10


α=

A reduced

β=

L reduced

Ac

L

Where, Ac

Total area of core

Areduced

Reduced area of core

L

Full length of core element

Lreduced

Length of the element over which the area of cross section has been reduced

The strength is governed by the value of α, while the stiffness is governed by the values of α and β. Changes in strength and stiffness of bracing lead to changes in base shear and drifts of the building. Buildings can be designed at required performance levels by changing the base shear and drifts of the building. The reduced area of the core (α Ac) is chosen so as to have yield strength of the reduced area equal to the bracing force. The sleeve flexural stiffness is chosen so that its Euler buckling strength is at least 25% greater than the bracing force from analysis. The enlarged area of the core at ends (Ac) is chosen so as to avoid buckling of the core in the projection beyond the sleeve. The length of the core with reduced area (β L) is chosen depending upon the desired lateral stiffness. In the analysis an equivalent prismatic brace, corresponding to the non-prismatic core element, is used to model the brace. The load-deformation behaviour of steel brace in tension is taken from FEMA 273 (1997) and is shown in Figure E8. It consists of a loading curve with the elastic axial stiffness until it reaches its yield capacity (fy = 250 N/mm2, εy = 0.00125). Thereafter, it yields at a constant yield load until the deformation becomes 12

E11


times the yield deformation. At this deformation, the capacity is reduced to 80% of the yield load until the deformation becomes 15 times the yield deformation where the brace is assumed to fracture.

1.2 1

B LS CP

IO

0.8

P/Py

C D

E

0.6 0.4 0.2 0 0

2

4

6

8

10

12

14

16

∆/ ∆y

Figure E8: Steel brace hinge property

Design Example of Non-Buckling Brace Design a non-buckling brace for load of 300kN. Frame inner dimensions are 5m × 3.5m, fy = 300N/mm2, E = 2 × 105N/mm2. Beam size

230 × 350 mm.

Column size

230 × 400 mm.

Design of core Area of core =

P 300000 = =1000mm 2 fy 300

Choose 2 angle sections of ISA 45 × 45 × 6, having area of 507mm2 each. = 1014 mm2.

Total area of core

= 2 × 507

Yield load on core

= 1014 × 300 = 304.2kN

Increase 25% load to design sleeve, other components and connections. Design load

= 1.25 × 304.2 = 380.25kN. ~ 380kN.

E12


Design of core at the end of sleeve Core should not yield and should not buckle at the end of sleeve. P = 380kN. Approximate length = 150 + 30 + 200

= 380mm.

Sleeve Gusset plate

150

Effective length

30

200

= 2 × l = 2 × 380

Load coming on each angle is 380/2

= 760mm. = 190kN.

Each angle can buckle individually. To avoid buckling, area required is

190×103 =1267mm 2 150

Try ISA 90 × 90 × 8 having I

= 32 × 104mm4.

Radius of gyration r

= 17.5 mm.

L 760 = =43.4 σ ac =160.2 N/mm 2 r 17.5 Area required is

190×103 =1186mm 2 <1379mm 2 (provided) 160.2

Design strength due to yielding of gross section The design strength of brace under axial tension Tdg, as governed by yielding of gross section, is given by Tdg =

f y Ag γ m0

=

300×1379 = 358kN > 190kN ( OK ) 1.15

E13


Design strength due to rupture of critical section Tearing strength of net section may be taken as Tdn =

α An fu γ m1

Take α = 0.7, fu = 450N/mm2 An = 1379 - 2 × 21.5 × 8 = 1035mm2

Tdn =

0.7×1035×450 = 326kN >190kN ( OK ) 1

Design of sleeve Effective length of brace is length can be taken as length between to two gusset plate corners. L = 6100 – 2 × 200 = 5700mm.

170 mm

Moment inertia of sleeve I required =

P×L2 380×103 ×57002 = =6.254×106 mm 4 2 2 5 π ×E π ×2×10

Minimum inner dimension required for square tube is 175mm. Minimum inner dimension required for circular tube is 220mm. Sleeve can be designed as square tube or circular tube.

175 mm 220 mm

E14


Thickness required for square tube

(175+2t )

4

= 6.254×106 ×12+ (175 )

1 ⎡ 4 4 175+2t ) - (175 ) ⎤ = 6.254×106 ( ⎦ 12 ⎣

4

2t = 3.4mm. Provide 2mm thick plate for square tube.

Thickness required for circular tube

( 220+2t )

4

π ⎡ 4 4 ( 220+2t ) - ( 220 ) ⎤⎦ = 6.254×106 ⎣ 64

= 6.254×106 ×64/π+ ( 220 )

4

2t = 2.93mm. Provide 2mm thick plate for circular tube. Connection of brace angles to gusset plate Use HSFG bolts of 20mm diameter for the connection. Hole diameter of bolt is 21.5mm. 1.1 Ks µ P0

Slip resistance capacity of the bolt is

1.1 × 1 × 0.45 × 144 = 71.28kN. No. of bolts required for each angles

190/71.3 = 2.66

= 3bolts.

Pitch of bolts

2.5 × 20

= 50mm.

Length of angle required on gusset plate

2 × 50 + 2 × 30

= 160mm.

Design of gusset plate Dimensions of plate to accommodate core (angles) and maintain the load passing through the corners is shown below. Assume thickness of gusset is 30mm.

E15


100

L = 1.2 × l

Dimensions of gusset plate & Modified Thornton width.

Check for compressive strength by modified Thornton method Modified Thornton width

= 110 + 2 × 100 tan45° = 110 + 200 = 310mm.

Effective length for buckling = 1.2 × 198 = 238mm. r=

30 = 8.66mm 12

L 238 = = 27.48 r 8.66 Design compressive stress, fcd for column buckling curve from table 7.4c of IS: 800 revised code is 242.3N/mm2 Load carrying capacity of gusset plate = 310 × 8 × 242.3 = 600.9kN > 380kN. (OK.) Check for tensile strength of gusset plate by Whitmore width concept Whitmore width = 110 + 2 × 100 × tan30° = 226mm. Design strength due to rupture of critical section Tearing strength of net section may be taken as Tdn =

0.7× ( 226-2×21.5 ) ×30×450 α An fu = =1383kN > 380kN ( OK ) γ m1 1.25

E16


Provide 50 x 8 mm stiffeners along free edges and along center line of load path on outer sides of plates. Connection between gusset plate and L-plate Force coming on each gusset plate is 380kN.

Weld

218kN 380kN

3.5m

θ 5.0m

270mm

Cos θ = 5.0 / 6.1 = 0.819 Sin θ = 3.5 / 6.1 = 0.573

312kN

320mm Connection of gusset plate to L-Plate

Welds are designed to resist taking axial load and transferring the force to bolts. Thickness required for vertical weld: t=

311×103 = 7.48mm 2×270×0.7×110

Thickness required for horizontal weld: t=

218×103 = 4.4mm 2×320×0.7×110

Provide 8mm fillet weld for vertical and 6mm fillet weld for horizontal on both sides of plates. Design of bolt connecting frame and L-plate Force in bolt connected to column is 156/4 = 39.0kN. Force in bolt connected to beam is 109/4

= 27.25kN.

Provide 16mm HSFG bold having tensile capacity of 82.9kN. Design of L-plate and back plates Bending moment in the plate = 156 × 0.135 = 21.06kN-m. Thickness required resisting bending moment

E17


Z required is

M 21060000 = = 106.36×103 mm3 f 0.66×300

bt2/6 = 106.36 × 103mm3, b = 320mm Hence, t = 44.6mm.

300mm 50mm 300mm

Check for shear at face of column in back plate Shear stress =

156000 = 9.75N/mm 2 < 0.45f y ( OK ) 320×50

Two plate of L-plate connect by full depth single V-butt weld. Non – prismatic core section Length of core (L)

5300mm.

Full area of core

2758 mm2 (Area of core beyond

sleeve) Area corresponding to yield for given load 1014mm2

α corresponding to yield for given load is 0.368. Initial β value is 0.9. Choose

α values 0.3 and 0.2. β values 0.75 and 0.5

Stiffness can be changed with out changing the strength by changing β value keeping a value constant. This can be observed by braces b, d, f. and c, e, g required stiffness could be obtained by changing β value.

E18


Identifier

α

β

a

0.367

b

Yield load Stiffness (kN)

kN/m

0.90

304

40777

0.30

0.90

248

33573

c

0.20

0.90

165

22625

d

0.30

0.75

248

37846

e

0.20

0.75

165

26019

f

0.30

0.50

248

48035

g

0.20

0.50

165

34692

Bearing

Column L - Plate Gusset plate

Gusset

Beam Bolts Sleeve

Connection model for non-buckling brace and its components

E19

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