Load Combinations Book EC3

Eurocode Load Com binations for Ste el S truct ure s

B C S A P u b l i c a t i o n N o . 5 3/ 10

Euro code Loa d Comb inations for S te el S tructure s

B C S A P u b l i c a t i on N o . 5 3 / 1 0

EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

T h e B r it is h Co n s t r u ct i o n a l Ste e l wo rk Asso c i ati o n L i mi te d Apart from any fair dealing for the purpose of research or private study or criticism or review, as permitted under the Copyright Design and Patents Act 1988, this publication may not be reproduced, stored or transmitted in any form by any means without the prior permission of the publishers or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the UK Copyright Licensing Agency, or in accordance with the terms of licences issued by the appropriate Reproduction Rights Organisation outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to the publishers, The British Constructional Steelwork Association Ltd. at the address given below. Although care has been taken to ensure, to the best of our knowledge, that all data and information contained herein are accurate to the extent that they relate to either matters of fact or accepted practice or matters of opinion at the time of publication, The British Constructional Steelwork Association Limited, the authors and the reviewers assume no responsibility for any errors in or misinterpretations of such data and/or information of any loss or damages arising or related to their use. Publications supplied to members of the BCSA at a discount are not for resale by them. The British Constructional Steelwork Association Ltd. 4, Whitehall Court, Westminster, London SW1A 2ES Telephone: +44(0)20 7839 8566 Fax: +44(0)20 7976 1634 Email: [email protected] Website: www.steelconstruction.org Publication Number First Edition

53/10 December 2010

ISBN-10 1-85073-063-6 ISBN-13 978-1-85073-063-7 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library © The British Constructional Steelwork Association Ltd

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The British Constructional Steelwork Association Limited (BCSA) is the national organisation for the steel construction industry: its Member companies undertake the design, fabrication and erection of steelwork for all forms of construction in building and civil engineering. Associate Members are those principal companies involved in the direct supply to all or some Members of components, materials or products. Corporate Members are clients, professional offices, educational establishments etc., which support the development of national specifications, quality, fabrication and erection techniques, overall industry efficiency and good practice. The principal objectives of the Association are to promote the use of structural steelwork; to assist specifiers and clients; to ensure that the capabilities and activities of the industry are widely understood and to provide members with professional services in technical, commercial, contractual, quality assurance and health and safety matters. The Association’s aim is to influence the trading environment in which member companies have to operate in order to improve their profitability. A current list of members and a list of current publications and further membership details can be obtained from: The British Constructional Steelwork Association Limited 4, Whitehall Court, Westminster, London SW1A 2ES Tel: +44(0)20 7839 8566, Fax: +44(0)20 7976 1634 Email: [email protected] Website: www.steelconstruction.org


F or e wo r d One of the most challenging aspects of the Eurocodes is gaining a thorough understanding of the loading and load combination for practical buildings. This challenge is not technical but primarily one related to the way the information is presented and the terminology used in the Eurocodes. The presentation and terminology used in the Eurocodes are very different to that found in British Standards such as BS 5950. The Eurocodes have a preference for mathematical formulae over tables and graphs and some of the explanations are brief. The principal aim of this publication is to provide the reader with straightforward guidance on the loading and load combinations for both the serviceability and ultimate limit states for the following building types: • • • •

Multi-storey buildings – Simple construction Multi-storey buildings – Continuous construction Portal frames without cranes Portal frames with cranes

Chapter 6 is a list of references where further guidance on applying the Eurocodes to steel and composite structures is given. It is intended to update this publication and BCSA would appreciate any observations, particularly on inaccuracies and ambiguities, or proposals on alternative approaches or on any other matters which should be included in future editions. The British Constructional Steelwork Association Ltd. 4, Whitehall Court, Westminster, London SW1A 2ES Telephone: +44(0)20 7839 8566 Fax: +44(0)20 7976 1634 Email: [email protected] Website: www.steelconstruction.org This publication was prepared by: Dr L. Gardner Imperial College Mr. P. J. Grubb Consultant

Chapter 1 gives a brief introduction to EN 1990 Basis of design and EN 1991 Actions on structures together with simple explanations of the design situations presented in EN 1990. Chapter 2 is a list of abbreviations, definitions and symbols and again simple, easy to understand explanations are given. Chapter 3 gives a comprehensive description of the load combinations for both the Ultimate and Serviceability Limit States, together with a list of the load combination factors which are used to account for the reduced probability of the simultaneous occurrence of two or more variable loads. These values are based on the recommendations given in the UK National Annex for EN 1990. Chapter 4 sets out the load combinations for both simple and moment resisting frames. Information is given on frame classification (i.e. braced or unbraced), frame imperfections and the use of the equivalent horizontal force (EHF) (a general approach that replaces imperfections with a system of notional horizontal forces). Reduction factors for the number of storeys and floor area are also described together with pattern loading and overturning. Section 4.2 concentrates on the load combinations for simple construction while section 4.3 identifies the differences between simple and continuous construction. Chapter 4 concludes with a worked example that illustrates the application of the load combinations equations given in EN 1990 for a three storey high, simple braced frame. Chapter 5 sets out the application of EN 1990 to industrial buildings with and without crane loads and illustrates the approach with the following examples: • • • •

Serviceability Limit State – Single span portal frame Ultimate Limit State – Single span portal frame Serviceability Limit State – Single span portal frame with overhead crane Ultimate Limit State – Single span portal frame with overhead crane

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C on t e n t s 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Introduction to EN 1990 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Introduction to EN 1991 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2. ABBREVIATIONS, DEFINITIONS AND SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Symbols (Greek letters) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3. COMBINATIONS OF ACTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1 Ultimate limit states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Serviceability limit states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4. MULTI-STOREY BUILDINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.1.1 Classification of frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.1.2 Frame imperfections and equivalent horizontal forces (EHF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.1.3 Second order (P-∆) effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.1.4 Reduction factors for number of storeys (αn) and floor area (αA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.1.5 Pattern loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.1.6 Dead loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.1.7 Overturning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2 Braced frames (simple construction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2.1 ULS load combinations based on Equation 6.10 with αcr > 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2.2 ULS load combinations based on Equation 6.10 with αcr < 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2.3 ULS load combinations based on Equations 6.10a and 6.10b with αcr > 10 . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2.4 ULS load combinations based on Equations 6.10a and 6.10b with αcr < 10 . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2.5 SLS load combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.3 Moment resisting frames (continuous construction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5. INDUSTRIAL BUILDINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.1.1 EN 1991-1-3: 2003 - Snow loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.1.2 EN 1991-1-4: 2003 - Wind loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.1.3 Frame imperfections and second order P-Δ effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2 Portal frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2.1 Serviceability limit state design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2.2 SLS design example for a single span portal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2.3 Ultimate limit state design (STR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.2.4 ULS design example for a single span portal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.3 Portal frames with cranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.3.1 Serviceability limit state design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.3.2 SLS design example for a single span portal with overhead crane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.3.3 Ultimate limit state design (STR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.3.4 ULS design example for a single span portal with overhead crane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 6. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

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1 . I n t ro d u ct i o n 1.1 Background

Implementation of the structural Eurocodes is underway. The primary challenges are perceived to be related not to the technical content, but rather to the presentation and terminology of the documents, since this is very different to that found in existing UK structural design codes. Immediate differences may be observed in the preference for mathematical formulae over tables and graphs, brevity of explanations and axis conventions. The intention of this guide is to provide straightforward guidance on combinations of actions (load combinations) for the two principal types of steel structure – multi-storey buildings and industrial buildings. Further guidance on applying the Eurocodes to steel and composite structures is given in [1], [2], [3]. Each Eurocode document is accompanied by a National Annex. The National Annex contains nationally determined parameters (NDPs), which are values left open by the Eurocode for definition by the country in which the building is to be constructed. Equation numbers employed in this guide, unless prefixed by the letter D, follow the equation numbering of EN 1990.

1.2 Introduction to EN 1990

EN 1990: Eurocode – Basis of structural design is the primary Eurocode document in that it establishes the common principles and requirements that apply to all aspects of structural design to the Eurocodes. Combinations of actions for all structures are set out in EN 1990. This section provides a brief introduction to the code. EN 1990 considers ultimate and serviceability limit states, the former being associated with the safety of people and the structure, while the latter concerns the functioning and appearance of the structure and the comfort of people. For ultimate limit states, checks should be carried out for the following, as relevant: • EQU: Loss of static equilibrium of the structure or any part of the structure. • STR: Internal failure or excessive deformation of the structure or structural members. • GEO: Failure or excessive deformation of the ground. • FAT: Fatigue failure of the structure or structural members. In the context of structural steelwork in buildings, EQU (to assess overturning and sliding as a rigid body) and STR (to determine forces and moments in structural members under various load combinations) are of primary concern. EN 1990 also emphasises, in Section 3, that all relevant design situations must be examined. Design situations are classified as follows, the first two being the ‘fundamental’ ones: • Persistent design situations, which refer to conditions of normal use. • Transient design situations, which refer to temporary conditions, such as during execution (construction) or repair. • Accidental design situations, which refer to exceptional conditions such as fire, explosion or impact.

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• Seismic design situations, which refer to conditions where the structure is subjected to seismic events. In Clause 4.1.1(1) of EN 1990, actions (imposed loads and deformations) are classified by their variation with time, as permanent, variable or accidental. Permanent actions (G) are those that essentially do not vary with time, such as the self-weight of a structure and fixed equipment; these have generally been referred to as dead loads in previous British Standards. Variable actions (Q) are those that can vary with time, such as imposed loads, wind loads and snow loads; these have generally been referred to as live loads in previous British Standards. Accidental actions (A) are usually of short duration, but high magnitude, such as explosions and impacts. Classification by variation with time is important for the establishment of combinations of actions.

1.3 Introduction to EN 1991

EN 1991 Eurocode 1 – Actions on structures comprises four parts, as given in Table 1.1. EN 1991-2 and EN 1991-4 are not relevant to this publication. Table 1.1: Parts of EN 1991 EN 1991 Part EN EN EN EN

1991-1 1991-2 1991-3 1991-4

Action type

General actions Traffic loads on bridges Actions induced by cranes and machinery Silos and tanks

EN 1991-1 is sub-divided into seven sub-parts, which provide designers with most of the information required to determine each individual action on a structure. The seven sub-parts are given in Table 1.2, with EN 1991-1-1, EN 1991-1-3, EN 1991-1-4 and EN 1991-1-7 being of particular relevance to this publication. Table 1.2: Sub-parts of EN 1991-1 EN 1991-1 Part EN EN EN EN EN EN EN

1991-1-1 1991-1-2 1991-1-3 1991-1-4 1991-1-5 1991-1-6 1991-1-7

Action type

Densities, self weight and imposed loads Actions on structures exposed to fire Snow loads Wind actions Thermal actions Actions during execution (construction) Accidental actions (impact and explosions)

EN 1991-1-1 is similar to BS 6399-1 and, since most structural designers are familiar with this document, the change to EN 19911-1 will be relatively straightforward. EN 1991-1-3 is used to determine snow loads and, although some of the terminology is unfamiliar, when read with the UK National Annex to EN 1991-1-3, is very similar to BS 6399-3. The snow map in the UK National Annex is zoned with altitude adjustments, as opposed to that in BS 6399-3, which had isopleths, and it benefits from better analysis of the latest data from the metrological office [4].


EN 1991-1-4, covering wind loading, is different to previous UK codes in that the basic wind velocity is based on a 10-minute mean wind speed, as opposed to the hourly mean wind speed in BS 6399-2 and the 3-second gust of CP3-V-2. The term topography has been replaced by orography, but most designers will adapt quickly to the changes. There are a number of perceived omissions [5] from the Eurocode when compared to BS 6399-2, but it is anticipated that the British Standard, or maybe a stripped down version, may be used as a source of non-conflicting, complementary information [5]. EN 1991-1-4 requires that elective dominant openings are considered to be closed for the persistent design situation (i.e. normal use), but open during severe wind storms as an accidental design situation; this is consistent with the guidance given in BRE Digest 436 [6].

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2 . A b b re v i at i o n s , de f i n i t io n s a n d s ym b o l s The terminology adopted in the Eurocodes will be unfamiliar to the majority of designers and may prove an obstacle to the rapid uptake of the Eurocodes. Most of the definitions given in the Eurocodes derive from:

Characteristic: The typical value of a parameter to be used in design.

• ISO 2394 (1998) General principles on reliability for structures • ISO 3898 (1997) Basis for design of structures – Notations – General symbols • ISO 8930 (1987) General principles on reliability for structures – List of equivalent terms

Combinations of actions: The combination of different sources of load acting simultaneously for the verification of structural reliability for a given limit state.

EN 1990 provides a basic list of terms and definitions which are applicable to all the other Eurocode parts, thus ensuring a common basis for the structural Eurocodes. This section has been provided to help to explain some of the key abbreviations, definitions and symbols used in the structural Eurocodes.

2.1 Abbreviations B EHF EN EQU FAT

GEO

I N NA NCCI P STR

Rules applicable only to buildings Equivalent Horizontal Force European Standard Associated with the loss of static equilibrium Associated with fatigue failure of the structure or structural members Associated with failure or excessive deformation of the ground Informative Normative National Annex Non-Conflicting Complementary Information Principles Associated with internal failure or excessive deformation of the structure or structural members

2.2 Definitions

Attention is drawn to the following key definitions, which may be different from current national practice: Accidental action: An exceptional loading condition usually of high magnitude but short duration such as an explosion or impact.

Action: A load, or imposed deformation to which a structure is subjected (e.g. temperature effects or settlement).

Application rules: Clauses marked ‘P’ in the Eurocodes are principles, which must be followed. Clauses not marked ‘P’ are application rules which, when followed, satisfy the principles. Alternative design rules may be adopted. Application rules make up the bulk of the codes and give the values and formulae to be used in the design. Capacity: The ability to conform to a limit state, e.g. bearing capacity.

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Co-existence: Eurocodes being in force in parallel with national codes.

Conformity: Compliance with standards.

Design resistance: The capacity of the structure or element to resist the design load. Effects of actions: Internal moments and forces, bending moments, shear forces and deformations caused by actions.

Execution: All activities carried out for the physical completion of the work including procurement, the inspection and documentation thereof. The term covers work on site; it may also signify the fabrication of components off site and their subsequent erection on site. Fatigue: A mode of failure in which a member ruptures after many applications of load.

Fundamental combinations: Combinations of actions for the persistent or transient design situations.

Frequent: Likely to occur often, but for a short duration on each occasion. Informative: For information, not a mandatory requirement – see normative.

Load arrangement: Identification of the position, magnitude and direction of the loads (loading pattern). Load case: Compatible loading arrangements considered simultaneously Load combination: See ‘Combinations of actions’.

National Annex: The document containing nationally determined parameters (NDPs). This is an essential supplement without which the Eurocode cannot be used. NDPs: Values left open in a Eurocode for definition in the country concerned. Non-Contradictory Complementary Information: Permitted additional information and guidance. Normative: Mandatory, having the force of a Standard.

Persistent: Likely to be present for most of the design life.


Principles: Clauses marked ‘P’ define structural performance that must be achieved. Quasi-: Being partly or almost.

Quasi-permanent action: An action that applies for a large fraction of the design life. Quasi-static: The static equivalent of a dynamic action.

Reference period: Any chosen period, but generally the design life.

Reliability: The mathematical probability of a structure fulfilling the design requirements.

Transient: Likely to be present for a period much shorter than the design life but with a high probability of occurring. Verify: Check the design output to make sure it complies.

2.3 Symbols (Greek letters)

The following Greek letters are used in EN 1990 and this document: α (alpha) αA αn αcr

γ (gamma) γG γQ ψ (psi) ψ0 ψ1 ψ2

ξ (xi)

Σ (sigma)

Reduction factor for area Reduction factor for number of storeys Factor by which the design loads FEd would have to be increased to cause global elastic instability at the load Fcr (i.e. αcr = Fcr/FEd) Partial factor Partial factor for permanent actions Partial factor for variable actions

Factor for combination value of a variable action Factor for frequent value of a variable action Factor for quasi-permanent value of a variable action Reduction factor Summation

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3 . C om bi n at i o n s o f a ct i o n s Combinations of actions, generally referred to as load combinations, are set out for all structures in Clause 6.4.3.2 of EN 1990. They are presented not simply as a series of multiplication factors to be applied to the various loading components, but instead in an unfamiliar algebraic format, which requires explanation. In Sections 4 and 5 of this guide, the provisions of the code are explained and presented in a format that is more familiar to UK engineers.

3.1 Ultimate limit states

Combinations of actions are defined in Clause 6.4.3 of EN 1990 for the four design situations: persistent, transient, accidental and seismic. Combinations of actions for the persistent (i.e. final usage of complete structure) and transient (e.g. construction) design situations are referred to as fundamental combinations. This guide focuses on the fundamental combinations, though combinations of actions for accidental design situations are also considered in Section 5 for portal frames. For each of the selected design situations, combinations of actions for persistent or transient design situations (fundamental combinations) at ultimate limit states (other than fatigue) may be derived either from Equation 6.10 of EN 1990 or from Equations 6.10a and 6.10b. The UK National Annex has elected to allow the use of either approach, though it should be noted that Equations 6.10a and 6.10b will provide more favourable combinations of actions (i.e. lower load factors). Furthermore, unless there is an unusually high ratio of dead load Gk to imposed load Qk (i.e. Gk > 4.5Qk), only Equation 6.10b need be considered for strength (STR) verifications. For verifying equilibrium (e.g. assessing sliding or overturning as a rigid body), only Equation 6.10 may be applied. The load combination expressions, as they appear in Eurocode, are provided below:

γG,jGk,j “+” γPP “+” γQ,1Qk,1 “+” Σ γQ,iψ0,iQk,i Σ j≥1 i>1

γG,jGk,j “+” γPP “+” γQ,1 ψ0,1Qk,1 “+” Σ γQ,iψ0,iQk,i Σ j≥1 i>1 ξγG,jGk,j “+” γPP “+” γQ,1Qk,1 “+” Σ γQ,iψ0,iQk,i Σ j≥1 i>1 where

“+” Σ ψ0 ξ γG γP γQ P

(6.10) (6.10a) (6.10b)

implies ‘to be combined with’ implies ‘the combined effect of’ is a combination factor, discussed below is a reduction factor for unfavourable permanent actions G, discussed below is a partial factor for permanent actions is a partial factor for prestressing actions is a partial factor for variable actions represents actions due to prestressing

Ignoring prestressing actions, which are generally absent in conventional steel structures, each of the combination expressions contains:

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• Permanent actions Gk,1, Gk,2, … • A leading variable action Qk,1 • Accompanying variable actions Qk,2, Qk,3, …

The latter may be characterised as either ‘main’ or ‘other’ accompanying variable actions; main accompanying variable actions being factored by γQ,1 and other accompanying variable actions being factored by γQ,i. However, since the recommended value (Eurocode and UK National Annex) of both γQ,1 and γQ,i is 1.5, no distinction is needed in practice, and no further distinction will be made in this guide. In general, unless it is clearly not a critical combination, each variable action should be considered as the leading variable action, in turn. Clause 6.1 (2) of EN 1990 states that actions that cannot occur simultaneously, for example due to physical reasons, should not be considered together in combination.

Tables 3.1 to 3.3 set out values for the partial factors (γG and γQ) for permanent and variable actions. These tables are based on Tables NA.A1.2(A) and (B) of the UK National Annex to EN 1990. Note that Table NA.A1.2(A) of the UK National Annex to EN 1990 applies to verification of static equilibrium (EQU) of building structures, Table NA.A1.2(B) applies to the verification of structural members (STR) in buildings, and Table NA.A1.2(C) relates to any verifications involving geotechnical actions, such as piles and footings (which are not considered in this guide). In clause 6.4.3.1(4) of EN 1990 a distinction is made between favourable and unfavourable actions. For permanent actions, the upper characteristic (superior) value Gkj,sup should be used when that action is unfavourable, and the lower characteristic (inferior) value Gkj,inf should be used when that action is favourable. This clause allows the designer to consider a permanent action as either favourable or unfavourable, in separate load combinations. As stated in EN 1990, this approach is only necessary where the results of verification are sensitive to variations in the magnitude of a permanent action from place to place in a structure. This idea is considered in more detail in Reference [7] with a continuous beam example. All variable actions should generally be present within a load combination unless they have a favourable influence, in which case they are assigned a partial factor γQ of zero, effectively excluding them. Table 3.1: Design values of actions for equilibrium (EQU)

Persistent and Permanent actions Leading Accompanying transient design Unfavourable Favourable variable variable situations action actions Eq. 6.10

1.10 Gkj,sup

0.9 Gkj,inf

1.5 Qk,1 1.5ψ0,i Qk,i (0 when favourable)

Table 3.2: Design values of actions for strength (STR) using Equation 6.10

Persistent and Permanent actions Leading Accompanying transient design Unfavourable Favourable variable variable situations action actions Eq. 6.10

1.35 Gkj,sup

1.0 Gkj,inf

1.5 Qk,1

1.5ψ0,i Qk,i


Table 3.3: Design values of actions for strength (STR) using Equations 6.10a and 6.10b Persistent and Permanent actions Leading Accompanying transient design Unfavourable Favourable variable variable situations action actions Eq. 6.10a Eq. 6.10b

1.35 Gkj,sup

1.0 Gkj,inf

ξ×1.35Gkj,sup 1.0 Gkj,inf

1.5ψ0,i Qk,i

1.5 Qk,1 1.5ψ0,i Qk,i

The ξ factor that appears in Equation 6.10b of EN 1990 is a reduction factor for unfavourable permanent actions G. The UK National Annex sets the ξ factor equal to 0.925. When combined with γG in Equation 6.10b the effect is to reduce the overall factor from 1.35 to 1.25. In applying Equation 6.10a all vaiable actions are termed ‘accompanying’ (the largest of which is the main ‘accompanying action’), whereas in applying Equation 6.10b the most significant variable action is termed the ‘leading variable action’, and all others (i>1) are simply ‘accompanying’. The combination factor ψ0 that appears in each of Equations 6.10, 6.10a and 6.10b is one of three ψ factors (ψ0, ψ1 and ψ2) used in EN 1990. The purpose of ψ0 is to take account of the reduced probability of the simultaneous occurrence of two or more variable actions. ψ factors are discussed in Section 4.1.3 of EN 1990. Values for ψ factors for buildings in the UK are given in Table NA.A1.1 of BS EN 1990. In general, these factors are the same as those recommended in Table A1.1 of EN 1990, but with some exceptions. For example, ψ0 is 0 for imposed loading on roofs and 0.6 for wind loading on buildings in EN 1990, whereas the UK National Annex gives values of 0.7 for imposed loading on roofs and 0.5 for wind loading. Selected values of ψ0 from the UK National Annex are given in Table 3.4. Values of ψ1 and ψ2 from the UK National Annex are also provided in Table 3.4, but only feature in serviceability or accidental combinations. Table 3.4: Values of ψ factors for buildings

Action

Imposed loads in buildings, category (see EN 1991-1-1)

Category A: domestic, residential areas

ψ0 0.7

ψ1 0.5

ψ2 0.3

Category B: office areas

0.7

0.5

0.3

Category D: shopping areas

0.7

0.7

0.6

Category C: congregation areas Category E: storage areas

0.7 1.0

Category F: traffic area, vehicle weight ≤ 30 kN 0.7

Category G: traffic area, 30 kN < vehicle weight ≤ 160 kN

0.7 0.9 0.7

– for sites located at altitude H > 1000 m above sea level

0.7

0.5

0.2

Wind loads on buildings (see EN 1991-1-4)

0.5

0.2

0

0.6

0.5

0

– for sites located at altitude H ≤ 1000 m above sea level

Temperature (non fire) in buildings (see EN 1991-1-5)

0.5

0

0.2

Gk, j “+” P “+” Qk,1 “+” Σ ψ0,iQk,i Σ i>1 j≥1

(6.14b)

The frequent combination is given by Equation 6.15b of EN 1990 and is normally used for reversible limit states including excessive temporary (elastic) deformations or vibrations.

Gk, j “+” P “+” ψ1,1Qk,1 “+” Σ ψ2,iQk,i Σ j≥1 i>1

(6.15b)

The quasi-permanent combination is given by Equation 6.16b of EN 1990 and is normally used for reversible limit states where long term effects are important (e.g. shrinkage, relaxation or creep). This is rarely applicable for steel structures.

Gk, j “+” P “+” Σ ψ2,iQk,i Σ j≥1 i>1

(6.16b)

The UK National Annex to EN 1993-1-1 (Clauses NA.2.23 and NA.2.24) states that vertical and horizontal deflections may be checked using the characteristic combination with variable loads only (i.e. permanent loads should not be included). Deflection limits are also provided, which are similar to those given in BS 5950. The basis for employing the characteristic combination is that excessive deflections may cause permanent local damage to connected parts or finishes (i.e. irreversible limit states), even though the steel members themselves will generally remain elastic. The designer may also wish to check total deflections, and may also wish to consider whether the frequent combination is applicable.

0.6 0.3

0.7

The characteristic combination is given by Equation 6.14b of EN 1990 and is normally used for irreversible limit states, such as permanent local damage or permanent unacceptable deformations.

0.8

0.5

Snow loads on buildings (see EN 1991-1-3)

For serviceability limit states, guidance on combinations of actions is given in Clauses 6.5.3 and A1.4 of EN 1990. Three groups of combinations are identified: characteristic, frequent and quasipermanent.

0.6

0.7

Category H: roofs

3.2 Serviceability limit states

0

0

11


4 . M u l t i - s t or e y b u i l di n g s In this section, Eurocode load combinations for multi-storey buildings are set out. General guidance for both simple and moment resisting frames is given in Section 4.1, since, in principle, load combinations are the same for both types of structure. However, differences in treatment often arise due to differences in sway stiffness, member interaction etc. and hence, specific guidance and examples for simple and moment resisting frames is provided in Sections 4.2 and 4.3, respectively.

4.1 General

4.1.1 Classification of frames Structural frames may be classified with regards to their lateral load resisting system and sway stiffness. Concerning the lateral load resisting system, a frame may be regarded as either braced or unbraced. As a guide, for a frame to be classified as ‘braced’, it should contain a bracing system with lateral stiffness of at least five times that of the unbraced frame [8], which will be the case in braced simple construction. Bracing systems using wire ties (as opposed to open or hollow sections) may result in the frame being classified as ‘unbraced’. Sway stiffness is commonly achieved through the provision of a suitable bracing system or by utilising the inherent bending resistance of a rigid frame. Adequate sway stiffness is important because it limits the lateral deflections of the frame and hence controls second order (P-Δ) effects. Sway stiffness is assessed in EN 1993-1-1 in a similar way as it is in BS 5950, through the αcr parameter (equivalent to λcr in BS 5950), which represents the factor by which the vertical design loading would have to be increased to cause overall elastic buckling of the frame (Clause 5.2.1(3) of EN 1993-1-1). A simplified means of determining αcr for regular frames is also given in Equation 5.2 of EN 1993-1-1. Regardless of the frame type, if αcr is greater than 10, the sway stiffness is deemed sufficiently large for second order effects to be ignored. Conversely, if αcr is less than 10, second order effects may no longer be ignored. Second order effects are discussed further in Section 4.1.3. 4.1.2

Frame imperfections and equivalent horizontal forces (EHF) Frame imperfections may be incorporated directly into the structural analysis by defining an initial sway for the frame. However, the more general approach is to replace this geometric imperfection with a system of equivalent horizontal forces (EHF), referred to as notional horizontal loads in BS 5950. Whereas in BS 5950, equivalent horizontal forces were only required in the vertical load case, in the Eurocodes it is deemed that since frame imperfections are inherently present, they should be included in all ULS load combinations. This appears entirely rational. EHF are not required in SLS load combinations. The EHF should be determined separately for each load combination since they depend on the level of design vertical loads. For each storey, the EHF may be calculated as the design vertical load for that storey (not the cumulative vertical load) multiplied by 1/200 (i.e. 0.5%). Depending on the height of the structure and the number of columns in a row, reductions to this basic value of 1/200 are possible, as detailed in Clause 5.3.2(3) of EN 1993-1-1. If horizontal loads (HEd) exceed 15% of vertical loads (VEd) these

12

sway imperfections may be disregarded, and EHF ignored – this would more oftern apply to low rise buildings. 4.1.3 Second order (P-Δ) effects Second order effects relate to the increase in member forces and moments that occur as a result of deformation of the structure under load. As outlined in Section 4.1.1, second order (P-Δ) effects need not be considered provided the frame is sufficiently stiff (i.e. sway deformation under the design loading is relatively small) – this is deemed to be the case for elastic analysis when αcr > 10, and similarly, according to the UK National Annex, for plastic analysis of clad frames when the additional stiffening effect of the cladding has been neglected. In cases where αcr is less than 10, the designer is presented with a number of options. These include enhancement of the stability system such that αcr is raised above 10 and hence second order effects may be ignored, making allowance for second order effects by approximate means (amplified sway method or effective length method, both of which were allowed in BS 5950), or making allowance for second order effects by performing a second order structural analysis enabling and accounting for deformation of the structure under load. It should be noted that if αcr is less than 3, then an accurate second order analysis must be performed (Clause 5.2.2(5) of EN 1993-11). The aforementioned is summarised in Table 4.1. Table 4.1: Summary of analysis methods and treatment of second order effects

Limits on αcr Analysis method αcr > 10

10 > αcr > 3 αcr < 3

First order analysis

Result

Second order effects ignored

First order analysis plus Second order effects amplified sway method or allowed for by effective length method approximate means Second order analysis

Second order effects allowed for more accurately

The most common approximate treatment of second order effects in multi-storey buildings, which may be applied provided that αcr >3, is the so called ‘amplified sway method’. In this method, account for second order effects is made by amplifying all lateral loading on the structure (typically wind loads and EHF) by a factor, referred to in the UK National Annex to EN 1993-1-1 as kr, which is related to the sway stiffness of the structure through Equation D4.1 (Equation 5.4 of EN 1993-1-1). kr =

4.1.4

1 1-1/αcr

(D4.1)

Reduction factors for number of storeys (αn) and floor area (αA) As the number of storeys in a building increase, the likelihood that all floors will be loaded to the full design level decreases. Similarly, large floor areas will seldom be subjected to the full design loading uniformly. To reflect this, reduction factors for imposed loads may be applied for the design of floors, beams and roofs and for the design of columns and walls. For the design of individual floors,


beams and roofs, the area reduction factor αA may be applied. For the design of columns and walls, the reduction factor αn for the number of storeys may be applied. The reduction factor αn relates to the number of floors supported by the column section under consideration, and may be applied to the total imposed load being carried. If, for a given column or wall, αA < αn, then αA may be used in place of αn, but αA and αn may not be used together (Clause NA.2.6). Reduction factors αA for imposed loads on floors and accessible roofs are provided in Clause NA.2.5 of the UK National Annex to EN 1991-1-1 (see Equation D4.2), and replace those given in Clause 6.3.1.2(10) of EN 1991-1-1. αA = 1.0 – A/1000 ≥ 0.75

(D4.2)

Figure 4.1: Pattern loading for continuous floor beams

γGGk

γGGk + γQQk

Storey under consideration

(a) Applies to span (sagging) moments

where A is the area (m2) supported.

Reduction factors αn for imposed loads from several storeys used for calculating column forces are defined in Clause 6.3.1.2(11) and by Equation 6.2 of EN 1991-1-1. Revised expressions are provided in the UK National Annex (Clause NA.2.6 and Equation NA.2), as given by Equations D4.3 to D4.5 below. These reduction factors may be applied to the total imposed load experienced by a given column, but may only be employed when the imposed load is the leading variable action in a load combination. When the imposed load is an accompanying action, either ψ0 or αn may be applied, but not both. αn = 1.1 – n/10 for 1 ≤ n ≤ 5

(D4.3)

αn = 0.5

for 5 < n ≤ 10

(D4.4)

for n > 10

(D4.5)

αn = 0.6

4.1.5 Pattern loading For the design of floors within one storey and for the design of roofs, EN 1991-1-1 Clause 6.2.1(1) states that pattern loading should be considered for continuous construction, though the storeys other than the one under consideration may be assumed to be uniformly loaded (Clause 6.2.1 of EN 1991-1-1). Pattern loading need not be considered for simple construction. The two loading patterns indentified in Clause AB.2 of EN 1993-1-1 for continuous floor beams to assess (a) the span moments and (b) support moments for the storey under consideration are shown in Figures 4.1(a) and (b), respectively. In Figure 4.1(a), alternative spans carry the design permanent and variable load (γGGk + γQQk) while other spans carry only the design permanent load ( γGGk). In Figure 4.1(b), two adjacent spans carry the design permanent and variable load (γGGk + γQQk) while all other spans carry only the design permanent load ( γGGk).

γGGk

γGGk + γQQk

Storey under consideration

(b) Applies to support (hogging) moments

For the design of columns or walls loaded from several storeys (2 or more) the total imposed floor load on each storey should be assumed to be uniformly distributed (Clause 6.2.2(1) of EN 1991-1-1). 4.1.6 Dead loads In load combinations, the total self-weight of the structure and nonstructural components should be taken as a single action (Clause 3.2(1) of EN 1991-1-1). Permanent roof loads and floor loads may therefore be treated as a single action Gk in load combinations.

4.1.7 Overturning Overturning of a structure as a rigid body is independent of its lateral load resisting system and sway stiffness. It is solely a matter of equilibrium (EQU), for which only Equation 6.10 of EN 1990 should be applied. The critical load combination for general multi-storey buildings emerges on the basis of maximising the overturning moment due to the horizontal loading (wind and EHF) and minimising the restoring moment due to the vertical loading. It is generally appropriate to consider only a single value for dead loading, but the concept of upper (superior) Gk,sup and lower (inferior) Gk,inf characteristic values should be considered where sensitivity to variability in dead loads is very high (Clause A1.3.1 of EN 1990). For the overturning load case, a factor of 0.9 is applied to the dead load (where it is contributing to the restoring moment) and factor of 1.5 is applied to the wind load, as the leading variable action. The wind load has been denoted Wk in this document. Equivalent horizontal forces are included, as in all ULS combinations, but these are not factored (again) since they are already based on factored loading. Thus, the overturning load combination is given by Equation D4.6.

13


0.9Gk “+” 1.5Wk “+” EHF

(D4.6)

As noted in Section 4.1.2, the EHF may be calculated as 0.5% (with some scope for reduction) of the load on each storey, and are thus dependant upon the load combination being considered.

4.2 Braced frames (simple construction)

In terms of ease of analysis and design, there are a number of advantages associated with simple construction. The structural members can, largely, be designed in isolation, with the beams considered as simply-supported members carrying the vertical loading and the columns as pin ended compression members with a nominal moment arising from the eccentric beam reactions. A bracing system will typically be employed to resist the horizontal loading, though note that columns forming part of the bracing system will also attract axial forces arising from the horizontal loading (wind loads and EHF), as described in Reference [5]. 4.2.1

ULS load combinations based on Equation 6.10 with αcr > 10 For frames with αcr > 10, second order effects need not be considered. Assuming all loads to be always unfavourable (i.e. causing an increase in member forces or moments), two basic load combinations, given by Equations D4.7 and D4.8, arise from Equation 6.10. In Equation D4.7, imposed load is assumed to be the leading variable action and hence attracts a load factor of 1.5, whilst the wind load is reduced by a combination factor ψ0 of 0.5 (to give a load factor = 0.5 × 1.5 = 0.75). In Equation D4.8, wind load is considered as the leading variable action with a load factor of 1.5, thus the imposed load is reduced by a combination factor ψ0 of 0.7 (applicable in all cases except for storage areas), to give a load factor = 0.7 × 1.5 = 1.05). It is assumed throughout this section that imposed loading on the roofs of multi-storey buildings will be greater than the snow loading, thus attracting a combination factor ψ0 = 0.7, rather than ψ0 = 0.5, which applies to snow loading (at altitudes of less than 1000 m). Note, as discussed in Section 4.1.2 of this guide, that the EHF should be determined separately for each load combination. 1.35Gk “+” 1.5Qk “+” 0.75Wk “+” EHF

1.35Gk “+” 1.05Qk “+” 1.5Wk “+” EHF

(D4.7) (D4.8)

Equation D4.7 would generally govern the design of the beams and columns, whilst Equation D4.8 would be expected to be more critical for the bracing members. The imposed load in Equation D4.7 may be reduced by the area reduction factor αA, given by Equation D4.2, for the design of the beams. For column design, the imposed load may be reduced by the reduction factor for number of storeys αn (that the column under consideration is supporting) or the reduction factor for area αA, whichever is the more beneficial. Note that the imposed load reduction factors may only be applied in combinations where the imposed loading is the leading variable action (Equation D4.7). Pattern loading need not be considered for column design (see Section 4.1.5). Other load combinations arise by considering that the variable actions may be favourable (i.e. causing a reduction in member

14

forces or moments). A good example of this is the uplift case, where imposed load is clearly favourable since it opposes the uplift. The imposed load therefore has a load factor of zero for the uplift case, whilst the dead load has a load factor of 1.0. This results in Equation D4.9. 1.00Gk “+” 1.5Wk “+” EHF

(D4.9)

1.35Gk “+” 1.5Qk “+” EHF

(D4.10)

The wind load itself may also be favourable, for example where uplift results in reduced columns loads. Assuming wind load to be favourable leads to the load combination given by Equation D4.10.

4.2.2

ULS load combinations based on Equation 6.10 with αcr < 10 For frames with αcr < 10, second order effects must be considered. This may be avoided by appropriate reconfiguration of the bracing system in order to increase the sway stiffness of the structure and hence ensure αcr ≥ 10, though this may be uneconomical. Otherwise, account must be made of second order effects. For αcr < 3, an accurate second order analysis is required, whilst for regular frames with αcr ≥ 3 approximate methods to allow for second order effects may be employed, the most common of which is the amplified sway method. In this case, load combinations will be the same as those defined in Section 4.2.1, except that all horizontal loads (Wk + EHF) and other possible sway effects (e.g. arising from asymmetric loading) will be multiplied by kr (Equation D4.1). Note that kr is derived from αcr, which is in turn dependant on the loading FEd on the structure, so, as for EHF, kr should be determined separately for each load combination. 4.2.3

ULS load combinations based on Equation 6.10a and 6.10b with αcr > 10 Employing Equations 6.10a and 6.10b of EN 1990, and adopting the same approach as described in Section 4.1.1, three load combinations arise when all loads are assumed to be unfavourable, as given by Equations D4.11 to D4.13. Note that Equation D4.11 arises from Equation 6.10a where all variable actions are reduced by the combination factor ψ0, while Equations D4.12 and D4.13 emerge from Equation 6.10b, and have a lower dead load factor of 1.25 due to the introduction of the ξ factor (see Section 3.1). 1.35Gk “+” 1.05Qk “+” 0.75Wk “+” EHF

1.25Gk “+” 1.5Qk “+” 0.75Wk “+” EHF

1.25Gk “+” 1.05Qk “+” 1.5Wk “+” EHF

(D4.11) (D4.12) (D4.13)

Of the above three combinations, Equation D4.11 will only govern on the rare occasions where the dead load is significantly larger than the imposed load. For the uplift combination, given by Equation D4.14, the wind load is the leading variable action, attracting a load factor of 1.5, and the imposed load is absent since it is favourable. Note that Equation D4.14 is the same as D4.9, showing that the uplift load combination is the same whether derived from Equation 6.10 or Equations 6.10a and 6.10b.


1.00Gk “+” 1.5 Wk “+” EHF

(D4.14)

1.25Gk “+” 1.5Qk “+” EHF

(D4.15)

Similarly, the wind favourable case results in Equation D4.15.

Equations D4.12 to D4.15 represent the four basic load combinations for multi-storey frames. For economy, it is recommended that these load combinations (Equations D4.11 to D4.15 all emerging from Equation 6.10b) be used in preference to those arising from Equation 6.10 (Equations D4.7 to D4.10). 4.2.4

ULS load combinations based on Equations 6.10a and 6.10b with αcr < 10 As described in Section 4.2.2, when αcr < 10, second order effects must be considered. If the amplified sway method is employed, load combinations will be the same as those given in Equations D4.11 to D4.15, except that all horizontal loads (wind and equivalent horizontal forces) and other sway effects are multiplied by the factor kr, which, as noted in Section 4.2.2 is load combination dependant. 4.2.5 SLS load combinations As outlined in Section 3.2, the UK National Annex to EN 1993-1-1 states that vertical and horizontal deflections may be checked using the characteristic combination with variable loads only (i.e. permanent loads should not be included). The characteristic combination is defined by Equation 6.14b of EN 1990, where the leading variable action is unfactored (i.e. taken as its characteristic value) and all accompanying variable actions are reduced by the combination factor ψ0.

Assuming all loads to be unfavourable, the resulting SLS combinations are given by Equations D4.16 (where imposed load is taken as the leading variable action) and D4.17 (where wind load is taken as the leading variable action). 1.00Qk “+” 0.50Wk

1.00Wk “+” 0.70Qk

(D4.16) (D4.17)

For cases where the influence of horizontal loading on vertical deflections is deemed insignificant, or for cases where wind load is favourable (e.g. suction on a roof may reduce deflections), Equation D4.16 reduces simply to Equation D4.18 (i.e. checking vertical deflections under unfactored imposed loading only). 1.00Qk

(D4.18)

1.00Wk

(D4.19)

For cases where the influence of vertical loading on horizontal deflections is deemed insignificant, or for cases where vertical loading is favourable, Equation D4.17 reduces to Equation D4.19 (i.e. checking horizontal deflections under unfactored wind loading only).

Deflection limits are also provided in the National Annex to EN 1993-1-1 in Clauses NA.2.23 and NA.2.24. The deflection limits of

relevance to multi-storey buildings, which are the same as those given in BS 5950, are presented in Tables 4.2 and 4.3. Table 4.2: Vertical deflection limits

Vertical deflection

Limit

Beam carrying plaster or other brittle finish

Span/360

Cantilevers

Other beams (except purlins and sheeting rails) Table 4.3: Horizontal deflection limits Horizontal deflection

In each storey of a building with more than one storey

Length/180 Span/200

Limit

Height of that storey/300

As 4.1.2 if horizontal loads (HEd) exceed 15% of vertical loads (VEd) the EHF can be ignored. This is most likely to be the case in Equations D4.17 and D4.19.

4.3 Moment resisting frames (continuous construction)

For the case of simple braced frames, the members can essentially be designed in isolation. For moment resisting frames, the structure is not statically determinate, there is interaction between the members and this simplification may not generally be made. Unbraced (moment resisting) frames are also generally less stiff laterally than braced frames, and are therefore more likely to require consideration of second order effects. However, the basic load combinations derived for simple frames in Section 4.2 are equally applicable to moment resisting frames. It is therefore recommended that, as for simple frames, the ULS load combinations for moment resisting frames be based on Equations 6.10a and 6.10b. This results in five load combinations given by Equations D4.11 to D4.15, of which D4.11 is unlikely to govern except in cases of an unusually high ratio of dead to imposed loading. SLS load combinations are given by Equations D4.16 to D4.19.

4.4 Example

The following example illustrates application of the above load combinations (from Equations 6.10a and 6.10b) to a simple braced frame. The general case considered is set out in Figure 4.2, where the loads shown are unfactored (characteristic values). The following notation is used: Gkr = permanent actions on roof; Gkf = permanent actions on floors; Qkr = imposed load on roof; Qkf = imposed load on floors; Wk = wind loads. Frames are spaced at 6 m centres and every third frame is braced (in the configuration shown in Figure 4.2). For the equilibrium check only, lateral forces, together with overturning and restoring moments, are shown per frame. Throughout the remainder of the example, lateral forces are shown per braced frame. It is assumed that αcr > 10, so second order effects are neglected. Imposed load reduction factors have not been considered. EHF have been calculated on the basis of 1/200 of the total vertical load for each storey.

15


Figure 4.2: Unfactored loading on example frame Wk = 0.63 kN/m2

Gkr = 3.5 kN/m2 Qkr = 1.5 kN/m2

3.6 m

kN/m2

Gkf = 3.5 Qkf = 5 kN/m2

3.6 m

Gkf = 3.5 kN/m2 Qkf = 5 kN/m2

6m

3.6 m

6m

6m

EHF = 10.0 kN Wind = 21.9 kN EHF = 19.2 kN Wind = 43.7 kN

Wk = 0.2 kN/m2

Wk = 0.7 kN/m2

Gkf = 3.5 kN/m2 Qkf = 5 kN/m2

Figure 4.4: Total factored ULS loading arising from Equation D4.12

3.6 m

Figures 4.3 to 4.7 present the total factored design loading on the structure arising from the five load combinations defined by Equations D4.11 to D4.15, respectively.


qEd = 36.9 kN/m

qEd = 71.3 kN/m qEd = 71.3 kN/m qEd = 71.3 kN/m

Bracing FEd

External column FEd

Internal column FEd

Design loading in key members:

1.25Gk “+” 1.5Qk “+” 0.75Wk “+” EHF

qEd = 36.9 kN/m

Roof design UDL

qEd = 71.3 kN/m

Floor design UDL

FEd = 752.0 kN

External column Bracing

Internal column (unbraced frame) Internal column (braced frame) Figure 4.3: Total factored ULS loading arising from Equation D4.11 EHF = 9.4 kN Wind = 21.9 kN EHF = 16.2 kN Wind = 43.7 kN EHF = 16.2 kN Wind = 43.7 kN EHF = 16.2 kN Wind = 43.7 kN

qEd = 35.0 kN/m

qEd = 59.9 kN/m

qEd = 59.9 kN/m

Bracing FEd

External column FEd

Internal column FEd


1.35Gk “+” 1.05Qk “+” 0.75Wk “+” EHF Roof design UDL

Floor design UDL External column Bracing

Internal column (unbraced frame) Internal column (braced frame)

16

qEd = 35.0 kN/m qEd = 59.9 kN/m FEd = 643.5 kN

FEd = 246.1 kN (tension) FEd = 1287.1 kN FEd = 1577.9 kN

FEd = 1504.0 kN FEd = 1807.1 kN

Figure 4.5: Total factored ULS loading arising from Equation D4.13


qEd = 59.9 kN/m

FEd = 257.5 kN (tension)


qEd = 30.0 kN/m


Bracing FEd

External column FEd

Internal column FEd


1.25Gk “+” 1.05Qk “+” 1.5Wk “+” EHF Roof design UDL






Figure 4.6: Total factored ULS loading arising from Equation D4.14 EHF = 4.1 kN Wind = 43.7 kN EHF = 5.7 kN Wind = 87.5 kN EHF = 5.7 kN Wind = 87.5 kN EHF = 5.7 kN Wind = 87.5 kN

qEd = 15.3 kN/m


Bracing FEd

External column FEd

Internal column FEd

Design loading in key members: 1.00Gk “+” 1.5Qk “+” EHF Roof design UDL Bracing



Wind = 14.6 kN

FEd = 381.7 kN (tension)

Wind = 29.2 kN

FEd = 470.0 kN FEd = 920.2 kN

Wind = 29.2 kN

Figure 4.7: Total factored ULS loading arising from Equation D4.15 EHF = 10.7 kN qEd = 39.8 kN/m Wind = 0.0 kN EHF = 19.2 kN Wind = 0.0 kN

Figure 4.8: SLS loading arising from Equation D4.16

Wind = 29.2 kN

FEd = 235.0 kN

External column

Serviceability load combinations, as defined by Equations D4.16 to D4.19, are shown in Figures 4.8 to 4.11, respectively.

qEd = 15.3 kN/m qEd = 21.0 kN/m

Floor design UDL

From Figures 4.3 to 4.7, it may be seen that the maximum loadings in different members often arise from different load combinations. For the case considered (Figure 4.2), the maximum design UDL on the roof and floors arise from Equation D4.15 (1.25Gk “+” 1.5Qk “+” EHF), as does the maximum external column load and the maximum internal column load (for the unbraced frames in the structure). The maximum force in the bracing members results from Equation D4.13 (1.25Gk“+” 1.05Qk “+” 1.5Wk “+” EHF), while the maximum internal column load (for the braced frames in the structure) arises from Equation D4.12 (1.25Gk “+” 1.5Qk “+” 0.75Wk “+” EHF).

qEd = 71.3 kN/m

qEd = 7.1 kN/m


Summary of SLS loading: 1.00Qk “+” 0.5Wk Roof SLS UDL

Floor SLS UDL

qEd = 71.3 kN/m

Lateral SLS load at roof level

Lateral SLS load at levels 1, 2 and 3

qEd = 71.3 kN/m

Bracing FEd

External column FEd

Internal column FEd

qEd = 7.1 kN/m

qEd = 30.0 kN/m HEd = 14.6 kN HEd = 29.2 kN

Design loading in key members: 1.25Gk “+” 1.5Qk “+” EHF Roof design UDL





17


Figure 4.9: SLS loading arising from Equation D4.17 Wind = 29.2 kN Wind = 58.3 kN Wind = 58.3 kN Wind = 58.3 kN

qEd = 2.5 kN/m

qEd = 21.0 kN/m qEd = 21.0 kN/m

Wind = 58.3 kN

qEd = 21.0 kN/m

Wind = 58.3 kN

qEd = 2.5 kN/m

Roof SLS UDL

qEd = 21.0 kN/m

Floor SLS UDL



HEd = 29.2 kN HEd = 58.3 kN


Wind = 0.0 kN Wind = 0.0 kN

qEd = 9.0 kN/m

qEd = 30.0 kN/m


Floor SLS UDL


qEd = 0.0 kN/m

Floor SLS UDL



HEd = 29.2 kN HEd = 58.3 kN

From Figures 4.8 to 4.11 it may be observed that Equation D4.18 (1.00Qk “+” EHF) is critical for vertical deflections of the beams, and Equation D4.17 (1.00Wk “+” 0.7Qk “+” EHF) governs for horizontal deflections of the frame at levels 1, 2 and 3 but at roof level Equation D4.19 (1.00Wk “+” EHF) governs.


Summary of SLS loading: Roof SLS UDL

qEd = -3.8 kN/m

Roof SLS UDL

Figure 4.12: Loading per frame for EQU overturning check

qEd = 30.0 kN/m

1.00Qk

1.00Wk

For checking against overturning (EQU), only Equation 6.10 may be applied, resulting in the load combination given by Equation D4.6, illustrated for the example frame in Figure 4.12. Note that loads, together with the overturning and restoring moments, are shown per frame in Figure 4.12.

qEd = 30.0 kN/m


qEd = -3.8 kN/m

Summary of SLS loading:

1.00Qk “+” 0.7Qk

Wind = 0.0 kN

Wind = 29.2 kN Wind = 58.3 kN

Summary of SLS loading:

Wind = 0.0 kN


qEd = 9.0 kN/m

qEd = 30.0 kN/m HEd = 0.0 kN HEd = 0.0 kN


qEd = 13.2 kN/m


Equilibrium assessment: 0.9Gk “+” 1.5Wk “+” EHF

Overturning moment per frame Restoring moment per frame

18

M = 893.7 kNm

M = 11330 kNm


5 . In d u s t r i al bu i l d i n gs 5.1 General

Although industrial buildings can be designed to support mezzanine floors and cranes, they are primarily loaded by their self weight, service loads, imposed loads or snow loads and wind loads. Service loads tend to be ‘project specific’ but a nominal value of around 0.05 kN/m2 should always be considered in structural design to allow for loads from nominal lighting. This value will increase if more substantial services such as sprinkler systems or air-conditioning are incorporated. The self weights of false ceilings over intermediate floors are often also treated as service loads. Snow loads and wind loads are site specific and are influenced by the geometry of the structure and its orientation. Snow loads are determined by reference to EN 1991-1-3 and its UK National Annex. Wind loads are determined by reference to EN 1991-1-4 and its UK National Annex, but designers might also like to refer to Reference [5]. Clause 3.3.2 (1) of EN 1991-1-1 states that on roofs, imposed loads and snow loads or wind loads should not be applied together simultaneously. This implies (1) that snow load and imposed load should not appear together in any given load combination, and (2) that imposed load and wind load should not appear together in any given load combination. The basis for this clause is that it would be unreasonable to consider that maintenance would be undertaken in severe weather conditions. The first implication is in line with current practice in the UK, where, for roofs that are not accessible except for normal maintenance and repair, the loading would typically be taken as the larger of an imposed load of 0.6 kN/m2 or the snow load (i.e. the imposed loads and snow loads are not applied simultaneously). The same value of 0.6 kN/m2 is also recommended for roof slopes less than 30º in Table NA.7 of the UK National Annex to EN 1991-1-1. The second implication is that for cases where the snow load is less than 0.6 kN/m2, then it is only this lesser value that would be applied in combination with the wind load, which, coupled with the fact that the combination factor for snow loading (ψ0 = 0.5) is lower than that for imposed loading (ψ0 = 0.7), may result in significantly lower roof loading (in combination with wind) than is used in current UK practice. It is recommended in this guide that imposed loads and wind loads continue to be considered in combination for the design of portal frames in the UK. Given the different combination factors for snow and imposed loading, the snow load would have to be greater than 1.4 times the imposed load (i.e. greater than 0.84 kN/m2) to be critical in the wind (leading) plus imposed or snow load combination. Where the imposed load or snow load is the leading variable action, the snow load simply needs to exceed the imposed load to become critical.

The concept of ψ factors was introduced in Section 3 and Table 5.1 presents the ψ factors that are relevant to portal frame design. In Table 5.1, Gkc = permanent crane action and Gkc + Qkc = total crane action (from Clause A.2.3 of EN 1991-3 Annex A).

Table 5.1: ψ factors relevant to portal frame structures Imposed loads on roofs

Snow loads at altitude less than or equal to 1000 m Wind loads

Crane loads

ψ0

ψ1

ψ2

0.7

0.0

0.0

0.5

0.2

0.0

1.0

0.9

Gkc/(Gkc+Qkc)

0.5

0.2

0.0

5.1.1 EN 1991-1-3: 2003 - Snow loading In Section 2 of EN 1991-1-3, ‘Classification of actions’, snow loads are classified as variable fixed actions unless otherwise specified in the code. In this section it also states that exceptional snow loads and exceptional snow drifts may be treated as accidental actions, depending on geographical locations. The UK National Annex confirms this in clauses NA.2.4 and NA.2.5 and also states that Annex B should be used to determine the drifted snow load case. This approach is consistent with current UK practice for designers using BS 6399-3 and BRE Digest 439 [9] to determine uniform snow loads and the loads caused by the build up of drifted snow. 5.1.2 EN 1991-1-4: 2003 - Wind loading Wind actions are defined as variable fixed actions. The process for determining wind pressures is based on a 10-minute mean wind velocity and a new map has been provided in the UK National Annex. Designers who have been working with BS 6399-2 will find the approach for determining wind pressures very similar although some terminology has changed. The publication “Designers’ Guide to EN 1991-1-4 Eurocode 1: Actions on structures, general actions part 1-4. Wind actions” [2] is very important in explaining the limitations of the new European Standard. Although wind pressures vary depending on site location, altitude, orientation etc, the pressure and force coefficients depend only on the external shape of the structure. By looking at the overall pressure coefficients, irrespective of the actual site wind pressures, it is possible to determine the critical load cases. The majority of portal frames have roof pitches of 5°, 6° or 10°. Figures 5.1c, 5.1d and 5.1e have been produced for portal frames with these roof pitches and present overall pressure coefficients. Figures 5.1a and 5.1b have been included to show the intermediate steps required to arrive at the figures in 5.1c. Similar intermediate steps have not been included for Figures 5.1d and 5.1e, although some extended expressions have been shown. External pressure coefficients for the walls have been extracted from Table 7.1 of EN 1991-1-4 assuming an h/d ratio ≤ 0.25. Table 7.4a of EN 1991-1-4 cannot be used for roof coefficients; instead, the UK National Annex directs us to use Table 10 of BS 6399-2. Once the basic external coefficients have been established, to comply with the requirements of Clauses 5.3 and 7.2.2 of EN 1991-1-4 two addition factors must be applied to the external force coefficients: 1. The structural factor cscd – for the majority of portal frames the height will be less than 15 m and the value of cscd is taken as 1. 2. For buildings with h/d ≤1, most portal frames, the external wind forces on the windward and leeward faces are multiplied by 0.85.

19


In recent years internal pressures of -0.3 / +0.0 have been adopted by many portal frame designers. This may still be appropriate for large storage buildings with no windows and doors primarily in one face. However, the internal pressure coefficients are now derived from Figure 7.13 of EN 1991-1-4 and are based on relative wall porosity. Within the range of coefficients are the values -0.3 / +0.2 used traditionally by UK engineers. These values have been used in the derivation of the overall force coefficients.

The resulting diagrams show that, for the range of roof pitches considered, the primary condition for wind loading on the roof is suction. If dominant openings are regarded as closed in a storm (elective dominant openings) the maximum uplift for ULS design is always for longitudinal wind (wind blowing directly onto the gable causing suction on all external faces of the portal) with internal pressure as is common with current practice.

-0.6

-0.6

-0.8

-0.8

-0.8

-0.8

Longitudinal Wind 1

-1.2

-0.6

0.3

Longitudinal Wind 1

-0.4

-1.02 -0.3

0.7

0.3

0.595

-0.255

-0.4

-0.255

0.0 0.595

-0.34 -0.255

Transverse Wind 2

Transverse Wind 2

Figure 5.1a: External Pressure Coefficients – Portal frame with 5° roof pitch The above coefficients are now modified by the 0.85 and cscd factors to give:

Figure 5.1b: Modified External Pressure Coefficients – Portal frame with 5° roof pitch

Key Overall coefficients shown thus: Pressure shown as positive values Suction shown as negative values

20

-0.34

Transverse Wind 1

-0.3

0.7

-0.255

-0.51

Transverse Wind 1

0.0

-0.6

-0.6


The same process can be applied to a portal with 6° roof pitch to give: -0.6

-0.6 -0.8

-1.0

-0.8

-0.8

Internal pressure 0.2

-1.0

-0.6

-0.6 -0.8

-0.8

-0.8

-1.0

Longitudinal Wind 1

0.595

0.255

-0.51

-1.02

-0.71

-1.22

0.395

-0.455


-0.54

-0.255

0.7 x 0.85

0.595

-0.21

-0.72

0.895

Internal suction -0.3

0.045

-0.693

-1.186

0.595

0.395

0.2

-0.055


0.395

-0.34 -0.04

0.595

0.895

0.3


0.045

-0.455

-0.3 x 0.85

-0.3

0.595

-0.193

-0.686 0.895

-0.006


-0.389 -0.089

0.045

-0.255

Transverse Wind 1a 0.02 x 0.85

-0.34 -0.14

-0.5

-0.255

-0.41 x 0.85 -0.589

-0.306

-0.493

-0.986

-0.3

0.595

0.395

-0.183

Transverse Wind 2 0.0

-0.8

Transverse Wind 1

0.0

-0.255

-0.506


Transverse Wind 1a 0.0

-0.36 x 0.85

-0.58 x 0.85

-1.16 x 0.85

-0.34

-0.455

0.255

-0.51

-1.0

Longitudinal Wind 1

Transverse Wind 1 -1.02

-0.8


-0.36 x 0.85 -0.506


-0.41 x 0.85 -0.489

-0.455

-0.255


-0.34 -0.04

0.0

-0.3

0.595

0.895

0.317

-0.306 -0.006


-0.389 -0.089

0.045

-0.255

Transverse Wind 2a

Transverse Wind 2a

Figure 5.1c: Wind Pressure Coefficients – Portal frame with 5° roof pitch

Figure 5.1d: Wind Pressure Coefficients – Portal frame with 6° roof pitch

Note: Longitudinal wind 1 gives the maximum overall suction on the roof. Transverse wind 2 gives maximum local suction. Transverse wind 2a causes maximum sidesway.

The above coefficients are typical for internal transverse portal frames in a building. Towards the ends of the structure more onerous coefficients are applicable. However, the intention of these diagrams is purely to eliminate less onerous combinations for later analysis and the overall pattern is similar for the areas with higher coefficients. For final design, local effects must be included, not only for the design of frames, but also for the design of secondary components such as purlins, side rails and claddings.


Key Overall coefficients shown thus: -0.3 Pressure shown as positive values Suction shown as negative values

21


-0.65

-0.65 -0.8

-0.85

-1.0

-0.85


-1.0

-0.8

Longitudinal Wind 1

0.7 x 0.85

-0.6 x 0.85

-0.5 x 0.85

-1.00 x 0.85

-0.625

-1.05

-0.71


0.395

-0.45 x 0.85 -0.583 -0.455

-0.3 x 0.85

Transverse Wind 1

0.595

-0.51

-0.425

-0.85

-0.125

-0.55

0.895


-0.21

-0.383 -0.083

0.045

-0.255

Transverse Wind 1a -0.51

0.1 x 0.85 0.595

0.395

-0.115


-0.71

-0.455

-0.255

-0.51

0.595

0.895

0.385


-0.21

Combinations of actions for portal frames are considered in this Section. Additional considerations for cranes are introduced in Section 5.3. The serviceability limit state is treated first since this is likely to govern the design of this form of construction. 5.2.1 Serviceability limit state design For the serviceability limit state, the UK National Annex to EN 1993-1-1 states that deflections may be checked using the characteristic combination of loading and considering variable loads only, as discussed in Section 3.2. Assuming that for steel portal frame structures the dead load can be accurately determined and that the combined dead and service loads can be treated as one dead load:

Wk Ad

6.14b


5.2 Portal frames

Gksup Gkinf Qk

-0.383 -0.583

more general approach is to apply equivalent horizontal forces (EHF). For more information on this and P-∆ effects refer to Sections 4.1.2 and 4.1.3 of this publication. Subject to a number of geometrical restraints, the UK National Annex to EN 1993-1-1 (Clause NA.2.9) allows that second order effects may be ignored in the plastic design of portal frames under gravity loading only provided αcr ≥ 5.

-0.383 -0.083

0.045

-0.255

Transverse Wind 2a

= = = = =

Dead load + Service load Dead load Imposed load (or uniform snow load if greater than 0.6 kN/m2) Wind load - three load cases as identified earlier Load from snow build-up or drift (accidental load condition)

1.00Qk “+” 0.50Wk (pressure) “+” EHF 0.70Qk “+” 1.00Wk (pressure) “+” EHF 0.00Qk “+” 1.00Wk (suction) “+” EHF

5.2.2 SLS design example for a single span portal Consider a 25 m span portal frame, 6 m to eaves and in 6 m bays with a 6° roof pitch. The structure is assumed to be clad with composite sheeting supported by purlins and side rails at 1.8 m maximum centres.

Key Overall coefficients shown thus: -0.15 Pressure shown as positive values Suction shown as negative values Figure 5.1e: Wind Pressure Coefficients – Portal frame with 10° roof pitch


22

5.1.3 Frame imperfections and second order P-∆ effects Frame imperfections may be incorporated directly into the structural analysis by defining an initial sway for the frame. The

Figure 5.2: Typical clear span portal frame Dead load: Cladding Purlins (0.046 × 1.25/1.8)

(1.25 factor to allow for purlin sleeves)

Rafter (0.54 × 1.1 / 6.0)

(1.10 factor to allow for rafter haunches)

Dead load on slope Slope factor (6° slope) Dead load on plan

0.150 kN/m2 0.032 kN/m2 0.099 kN/m2 0.281 kN/m2 1.0055 0.283 kN/m2


Gksup = Dead + Service load = 0.283 + 0.150 = 0.433 kN/m2

3. Identify the wind case that results in the maximum eaves displacement (side sway). This is likely to be transverse wind with pressure on the windward slope and suction on the leeward slope. 4. Use the wind load cases identified in steps 2 and 3 of this procedure in equation 6.14b to identify maximum displacements. 5. If frame is unsymmetrical in any way the designer should apply the wind load in the direction to maximise the sway effect.

Gkinf = Dead = 0.283 kN/m2 Qk

Wk Ad

= Imposed load = 0.600 kN/m2

= Wind load: Wind pressure = 0.500 kN/m2; Wind suction = -0.800 kN/m2

5.2.3 Ultimate limit state design (STR) For the ultimate limit state, Equations 6.10 or 6.10a and 6.10b from EN 1990 are to be considered, as introduced in Section 3.1.

= Load from snow build-up or drift = 0.550 kN/m2

Applying the loads for the example to the set of serviceability equations yields the design loads as summarised in Table 5.2. The values of the EHF will vary with the load combination and may, when HEd ≥ 0.15 VEd, be ignored. The bold figures identify the critical load combinations. Table 5.2: Load combinations for the serviceability limit state

Load (kN/m2)

Equation 6.14b

Qk = 0.600

0.600 0.420 0.000

Wk (pressure) = +0.500 Wk (suction) = -0.800 0.250 0.500 -0.800

Ad = 0.550

Design load (kN/m2)

0.000 0.000 0.000

0.850 0.920 -0.800

The normal roof pitch for portal frame structures in the UK is in the range 5-15°. In this range it is unlikely that the roof will be subjected to wind pressure throughout the span. Hence, all three combinations to Equation 6.14b must be considered. Now consider the same example, but removing the load condition of pressure on the roof – the load combinations of Table 5.2a emerge. Table 5.2a: Load combinations for the serviceability limit state (no uniform roof pressure) Load (kN/m2)

Equation 6.14b

Qk = 0.600

0.600 0.000

Wk (suction) = -0.800 0.000 -0.800

Ad = 0.550

0.000 0.000

Design load (kN/m2) 0.600 -0.800

The designer must be aware of the possible number of wind load cases to be considered, the above matrix simply presents these as uniform suction or pressure on the roof. In reality the loading pattern is more complex than this and the following procedure may be of use. Suggested procedure: 1. Carry out an elastic analysis for each individual serviceability load case. 2. Identify the wind case for maximum suction on the rafter. (This is generally longitudinal wind with internal pressure)

The relevant ψ factors are given in Table 5.1 above. With the following loading,

Gksup = Dead load + Service load

Gkinf = Dead load Qk

Wk

Ad

= Imposed load (or uniform snow load if greater than 0.6 kN/m2)

= Wind load – 5 load cases, 2 of which can be discarded after SLS analysis

= Load from snow build-up or drift (accidental load condition)

if the typical load cases that were considered for the serviceability limit state are now considered for ultimate limit state with the following possible load combinations result: 6.10

6.10a

6.10b

1.35Gksup “+” 1.50Qk “+” 0.00Qk + EHF 1.35Gksup “+” 1.50Qk “+” 0.75Wk (pressure) + EHF 1.35Gksup “+” 1.05Qk “+” 1.50Wk (pressure) + EHF 1.00Gkinf “+” 0.00Qk “+” 1.50Wk (suction) + EHF 1.35Gksup “+” 1.05Qk “+” 0.00Wk + EHF 1.35Gksup “+” 1.05Qk “+” 0.75Wk (pressure) + EHF 1.00Gkinf “+” 0.00Qk “+” 0.75Wk (suction) + EHF 1.25Gksup 1.25Gksup 1.25Gksup 1.00Gkinf

“+” 1.50Qk “+” 0.00Wk “+” 1.50Qk “+” 0.75Wk (pressure) “+” 1.05Qk “+” 1.50Wk (pressure) “+” 0.00Qk “+” 1.50Wk (suction)

+ + + +

EHF EHF EHF EHF

Accidental 6.11b 1.00Gksup “+” 0.00Qk “+” 0.00Wk “+” 1.00Ad “+” EHF

Note that, as recommended in Section 5.1 of this guide, imposed load is being considered in combination with wind, and that if the snow load were to exceed 1.4 times the imposed loading, then the factor of 1.05 (with ψ0 = 0.7) currently applying to the imposed loading would become 0.75 (with ψ0 = 0.5) applying to the snow loading. Each of the above load combinations should be analysed with the relevant equivalent horizontal force, noting that the equivalent horizontal force is 0.5% of the vertical reaction at the column base and therefore includes the self weight of any cladding carried by the column, as well as the effects of the wind. The above ultimate limit state load combinations are implemented in the design example started earlier for the serviceability limit state. Substituting the loadings for the example into these equations yields the design loads as summarised in Table 5.3. The bold figures identify the critical load combinations, assuming that the designer will opt for Equations 6.10a and 6.10b at ULS.

23


Table 5.3a: Simplified ULS load combinations (no uniform roof pressure)

5.2.4 ULS design example for a single span portal Gksup = Dead + Service load = 0.283 + 0.150 = 0.433 kN/m2 Gkinf = Dead = 0.283 kN/m2 Qk

Wk Ad

= Imposed = 0.600 kN/m2

Equation 6.10b 0.541 0.283

= Wind load: Wind pressure = 0.500 kN/m2; Wind suction = -0.800 kN/m2

Equation 6.11b 0.433


Table 5.3: ULS load combinations Load (kN/m2) Equation 6.10

Gksup = 0.433 Gkinf = 0.283

Qk = Wk (pressure) 0.600 = +0.500 Wk (suction) = -0.800

Ad = 0.550

0.630 0.630 0.000

0.000 0.000 0.000

Design load (kN/m2)

0.900 0.900 0.630 0.000

0.000 0.375 0.750 -1.200

0.000 0.000 0.000 0.000

1.485 1.860 1.965 -0.917

Equation 6.10b 0.541 0.541 0.541 0.283

0.900 0.900 0.630 0.000

0.000 0.375 0.750 -1.200

0.000 0.000 0.000 0.000

1.441 1.816 1.921 -0.917

Equation 6.11b 0.433

BS5950-1:

0.000

0.000 0.375 -0.600

0.100

0.550

1.40 Gk + 1.60 Qk = 1.566 kN/m2 1.00 Gk - 1.40 Wk = -0.837 kN/m2 1.20 (Gk + Qk + Wk) = 1.840 kN/m2

1.215 1.590 -0.317

1.083

Notes: 1. No reduction in loading can be applied on the basis of area since such reduction only applies to roofs with access. 2. For shallow pitched portals there is no pressure on the whole rafter and since suction will reduce the total load it must not be included if the most onerous design combination is to be considered.

Portal frame designers will generally set out to provide the most economic frame solution and, given the choice of 6.10 or 6.10a and 6.10b the design loads to be considered in 6.10 are more onerous and therefore are likely to be ignored. It would appear that there are more combinations to consider if we apply 6.10a and 6.10b but, by observation, 6.10b combinations are more onerous than those of 6.10a, other than for a high ratio of dead to imposed load (see Section 3.1) which is particularly unlikely for this form of construction. As shown in Figures 5.1, positive pressure on the whole roof does not occur for normal portal frame roof pitches. If this pressure is removed from the example, the design loads in Table 5.3a result.

24

Qk = 0.600

Wk (suction) = - 0.800

Ad = 0.55

0.630 0.000

0.750 -1.200

0.000 0.000

0.000

0.000

0.550

Design load (kN/m2) 1.921 -0.917 0.983

5.3 Portal frames with cranes

0.585 0.585 0.585 0.283

Equation 6.10a 0.585 0.585 0.283

Gksup = 0.433 Gkinf = 0.283

Load (kN/m2)

The inclusion of one additional imposed load type increases the number of possible load combinations since each imposed load type has to be considered as the leading or main accompanying variable action in turn. The introduction of a crane also increases the horizontal loads (both transverse and longitudinally) to be carried by the structure as the crane will generate horizontal surge loads as it lifts and moves loads around. The crane’s load Qkc considered below may therefore have both vertical and horizontal components. The vertical loads are modified by dynamic factors taken from Table 2.2 of EN 1991-3:2006. 5.3.1 Serviceability limit state design Gksup = Dead load + Service load Gkinf = Dead load Qk

Qkc

Wk Ad

= Imposed load (or uniform snow load if greater than 0.6 kN/m2)

= Crane load (vertical load (including crane self weight) and horizontal surge load) = Wind load (generally suction) - three load cases = Load from snow build-up or drift (accidental load condition)

Other combinations are possible, but those that are most likely to provide the critical design condition are as follows: 6.14b

1.00Qk 0.70Qk 0.70Qk 0.00Qk

“+” “+” “+” “+”

1.00Qkc 1.00Qkc 1.00Qkc 0.00Qkc

“+” “+” “+” “+”

0.50Wk 0.50Wk 1.00Wk 1.00Wk

(pressure) (pressure) (pressure) (suction)

5.3.2 SLS design example for a single span portal with overhead crane Consider the 25 m span portal frame of the previous example with a 24 m span, 5 tonne electric overhead crane. Maximum wheel loads = 40 kN, minimum wheel loads = 12.5 kN. The derivation of the maximum and minimum reactions is shown for vertical loads, but is also applicable to the horizontal loads. How the horizontal loads are transferred to the main structure is dependent on the number of flanges to the wheels supported by the crane rail. If the wheels are double flanged, the horizontal load may be shared between the two crane rails; if the wheels are single flanged, then the horizontal loads are applied to just a single crane beam. The

TYPICAL WELDING PROCEDURE SPECIFICATIONS FOR STRUCTURAL STEELWORK

magnitude of the horizontal load is dependent on factors particular to each project. Assume that the crane is supported centrally on bogies with a 3.6m wheel base. If one wheel is positioned directly on the line of the portal, the second wheel is 3.6m into the span and hence the maximum reaction to the portal is 1+2.4/6.0 = 1.4 times the wheel load. Maximum reaction to portal from simply supported crane beams = 1.4 x 40 = 56 kN, Minimum coincident reaction = 1.4 x 12.5 = 17.5 kN.

5.3.3 Ultimate limit state (STR) The number of load combinations again increases because of the addition of the load from the crane. The individual load cases are as follows: Gksup = Dead load + Service load

Gkinf = Dead load Qk

Qkc

Wk Ad

Figure 5.3: Typical clear span portal frame with travelling overhead crane Gksup = Dead + Service load = 0.283 + 0.150 = 0.433 kN/m2 Gkinf = Dead = 0.283 kN/m2 Qk

Qkc

Wk Ad

= Imposed load = 0.600 kN/m2

= Max / min crane wheel loads = 56.0 / 17.5 kN = Wind load: Wind pressure Wind suction


= 0.500 kN/m2; = -0.800 kN/m2

Substituting the loadings for the example into these equations yields the design loads as summarised in Table 5.4. The bold and shaded figures identify the critical load combinations. Table 5.4: SLS load combinations

Load (kN/m2)

Qk = Wk (pressure) Ad = Design Qkc = 0.600 = +0.500 0.550 load 56.0/ Wk (suction) (kN/m2) 17.5kN = -0.800

Equation 6.14b 0.600 0.420 0.420 0.000

0.250 0.250 0.500 -0.800

0.000 0.850 56.0 / 17.5 0.000 0.670 56.0 / 17.5 0.000 0.920 56.0 / 17.5 0.000 -0.800 0.000

= Imposed load (or uniform snow load if greater than 0.6 kN/m2) = Crane load (vertical load on columns with horizontal surge loads)

= Wind load (generally suction) – three load cases, at least one of which can be discarded after SLS design

= Load from snow build-up or drift (accidental load condition)

When each load combination is considered with respect to Equations 6.10, 6.10a, 6.10b and the accidental condition the following combinations result: [For the accidental combinations, ψ2 = ratio of the permanent crane action and the total crane action = 50/125 = 0.40 (Clause A.2.3 from EN 1991-3 Annex A)]. 6.10 1.35Gksup 1.35Gksup 1.35Gksup 1.35Gksup 1.00Gkinf

“+” “+” “+” “+” “+”

6.10b 1.25Gksup 1.25Gksup 1.25Gksup 1.00Gkinf

“+” “+” “+” “+”

1.50Qk “+” 1.50Qkc “+” 0.00Wk (suction) “+” EHF 1.50Qk “+” 1.50Qkc “+” 0.75Wk (pressure) “+” EHF 1.05Qk “+” 1.50Qkc “+” 0.75Wk (pressure) “+” EHF 1.05Qk “+” 1.50Qkc “+” 1.50Wk (pressure) “+” EHF 0.00Qk “+” 0.00Qkc “+” 1.50Wk (suction) “+” EHF

6.10a 1.35Gksup “+” 1.05Qk “+” 1.50Qkc “+” 0.00Wk (suction) “+” EHF 1.35Gksup “+” 1.05Qk “+” 1.50Qkc “+” 0.75Wk (pressure) “+” EHF 1.00Gkinf “+” 0.00Qk “+” 0.00Qkc “+” 0.75Wk (suction) “+” EHF 1.50Qk 1.05Qk 1.05Qk 0.00Qk

“+” “+” “+” “+”

1.50Qkc 1.50Qkc 1.50Qkc 0.00Qkc

“+” “+” “+” “+”

0.00Wk 0.75Wk 1.50Wk 1.50Wk

(suction) “+” EHF (pressure) “+” EHF (pressure) “+” EHF (suction) “+” EHF

Accidental 6.11b Gksup “+” 1.00Ad “+” 0.00Qk “+” 0.40Qkc “+” 0.00Wk (pressure) “+” EHF Gksup “+” 1.00Ad “+” 0.00Qk “+” 0.90Qkc “+” 0.00Wk (pressure) “+” EHF Gksup “+” 1.00Ad “+” 0.00Qk “+” 0.40Qkc “+” 0.20Wk (pressure) “+” EHF 5.3.4 ULS design example for a single span portal with overhead crane Substituting the loadings for the example into these equations yields the design loads as summarised in Table 5.5. The bold figures identify the critical load combinations.

25


Table 5.5: ULS load combinations

Load (kN/m2)

Equation 6.10

Gksup = 0.433 Gkinf = 0.283

Qk = Wk (pressure) Ad = Design 0.600 = +0.500 0.550 load Wk (suction) (kN/m2) = -0.800

Qkc = 56.0/ 17.5kN

0.585 0.585 0.585 0.585 0.283

0.900 0.900 0.630 0.630 0.000

0.000 0.375 0.375 0.750 -1.200

0.000 0.000 0.000 0.000 0.000

1.485 1.860 1.590 1.965 -0.917

84.0 / 26.25 84.0 / 26.25 84.0 / 26.25 84.0 / 26.25 0.00

Equation 6.10b 0.541 0.541 0.541 0.283

0.900 0.630 0.630 0.000

0.000 0.375 0.750 -1.200

0.000 0.000 0.000 0.000

1.441 1.546 1.921 -0.917

84.0 / 26.25 84.0 / 26.25 84.0 / 26.25 0.00

Equation 6.10a 0.585 0.585 0.283

Equation 6.11b

0.433 0.433

0.630 0.630 0.000

0.000 0.000

0.000 0.375 -0.600

0.000 0.100

0.000 0.000 0.000

0.550 0.550

1.215 1.590 -0.317

0.983 1.083

84.0 / 26.25 84.0 / 26.25 0.000

50.4 / 15.75 22.4 / 7.0

Notes: 1. Transverse wind load cases will cause suction on the roof but will also cause the portal to sway. SLS will identify the load case for maximum sway. 2. EHF to be applied in the same direction as the horizontal surge. 3. Frame may naturally sway therefore important to ensure that the surge load is applied in two alternative directions to find the natural sway and ensure that the EHF does not ‘prop’ the frame.

26


6 . Re fe r e n ce s [1]

Steel Building Design: Introduction to the Eurocodes, SCI Publication P361, The Steel Construction Institute, 2009.

[2]

Steel Building Design: Concise Eurocodes, SCI Publication P362, The Steel Construction Institute, 2009.

[3]

Brown, D. G., King, C. M., Rackham, J. W. and Way, A. (2004).Steel Building Design: Medium Rise Braced Frames. SCI Publication P365. The Steel Construction Institute, 2004.

[4]

Brettle, M., Currie, D.M. (2002) Snow loading in the UK and Eire: Ground snow load map. The Structural Engineer (Vol; 80, Issue: 12).

[5]

Cook, N. (2007). Designers’ Guide to EN 1991-1-4 Eurocode 1: Actions on structures, general actions - Part 1-4. Wind actions. Thomas Telford Ltd.

[6]

Wind loading on buildings, BRE, Digest 436, The Building Research Establishment, 1999.

[7]

Gulvanessian, H., Calgaro J.-A. and Holický, M. (2002). Designers’ Guide to EN 1990 Eurocode: Basis of Structural Design. Thomas Telford Publishing.

[8]

Boissonnade, N., Greiner, R., Jaspart, J. P. and Lindner, J. (2006). Rules for Member Stability in EN 1993-1-1 – Background documentation and design guidelines. ECCS Publication No. 119. ECCS Technical Committee 8 – Stability.

[9]

Roof loads due to local drifting of snow, BRE Digest 439, The Building Research Establishment, 1999.

[10] Guide to evaluating design wind loads to BS 6399-2: 1997, SCI Publication P286, The Steel Construction Institute, 2003.

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Eurocode Load Combinations for Steel Structures B C S A P u b l i c a t i o n N o . 5 3 /1 0

Load Combinations Book EC3

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