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BCSA Publication No. 53/10 Eurocode Load Combinations for Steel Structures
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Eurocode Load Combinations for Steel Structures 2010

Sep 21, 2014

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Page 1: Eurocode Load Combinations for Steel Structures 2010

BBCCSSAA PPuubblliiccaattiioonn NNoo.. 5533//1100

EEuurrooccooddee LLooaaddCCoommbbiinnaattiioonnss ffoorr SStteeeell SSttrruuccttuurreess

Page 2: Eurocode Load Combinations for Steel Structures 2010

BBCCSSAA PPuubblliiccaattiioonn NNoo.. 5533//1100

EEuurrooccooddee LLooaaddCCoommbbiinnaattiioonnss ffoorr SStteeeell SSttrruuccttuurreess

Page 3: Eurocode Load Combinations for Steel Structures 2010

Apart from any fair dealing for the purpose of research or privatestudy or criticism or review, as permitted under the CopyrightDesign and Patents Act 1988, this publication may not bereproduced, stored or transmitted in any form by any meanswithout the prior permission of the publishers or in the case ofreprographic reproduction only in accordance with the terms of thelicences issued by the UK Copyright Licensing Agency, or inaccordance with the terms of licences issued by the appropriateReproduction Rights Organisation outside the UK.

Enquiries concerning reproduction outside the terms stated hereshould be sent to the publishers, The British ConstructionalSteelwork Association Ltd. at the address given below.

Although care has been taken to ensure, to the best of ourknowledge, that all data and information contained herein areaccurate to the extent that they relate to either matters of fact oraccepted practice or matters of opinion at the time of publication,The British Constructional Steelwork Association Limited, theauthors and the reviewers assume no responsibility for any errorsin or misinterpretations of such data and/or information of any lossor damages arising or related to their use.

Publications supplied to members of the BCSA at a discount arenot for resale by them.

The British Constructional Steelwork Association Ltd.4, Whitehall Court, Westminster, London SW1A 2ESTelephone: +44(0)20 7839 8566 Fax: +44(0)20 7976 1634Email: [email protected]: www.steelconstruction.org

Publication Number 53/10First Edition December 2010

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

The British Constructional Steelwork Association Limited (BCSA)is the national organisation for the steel construction industry: itsMember companies undertake the design, fabrication and erectionof steelwork for all forms of construction in building and civilengineering. Associate Members are those principal companiesinvolved in the direct supply to all or some Members ofcomponents, materials or products. Corporate Members areclients, professional offices, educational establishments etc.,which support the development of national specifications, quality,fabrication and erection techniques, overall industry efficiency andgood practice.

The principal objectives of the Association are to promote the useof structural steelwork; to assist specifiers and clients; to ensurethat the capabilities and activities of the industry are widelyunderstood and to provide members with professional services intechnical, commercial, contractual, quality assurance and healthand safety matters. The Association’s aim is to influence thetrading environment in which member companies have to operatein order to improve their profitability.

A current list of members and a list of current publications andfurther membership details can be obtained from:

The British Constructional Steelwork Association Limited4, Whitehall Court, Westminster, London SW1A 2ESTel: +44(0)20 7839 8566, Fax: +44(0)20 7976 1634Email: [email protected]: www.steelconstruction.org

2

TThhee BBrriittiisshh CCoonnssttrruuccttiioonnaall SStteeeellwwoorrkk AAssssoocciiaattiioonn LLiimmiitteedd

EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

One of the most challenging aspects of the Eurocodes is gaining athorough understanding of the loading and load combination forpractical buildings. This challenge is not technical but primarily onerelated to the way the information is presented and the terminologyused in the Eurocodes. The presentation and terminology used inthe Eurocodes are very different to that found in British Standardssuch as BS 5950. The Eurocodes have a preference formathematical formulae over tables and graphs and some of theexplanations are brief.

The principal aim of this publication is to provide the reader withstraightforward guidance on the loading and load combinations forboth the serviceability and ultimate limit states for the followingbuilding types:

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

Chapter 1 gives a brief introduction to EN 1990 Basis of designand EN 1991 Actions on structures together with simpleexplanations of the design situations presented in EN 1990.Chapter 2 is a list of abbreviations, definitions and symbols andagain simple, easy to understand explanations are given. Chapter3 gives a comprehensive description of the load combinations forboth the Ultimate and Serviceability Limit States, together with alist of the load combination factors which are used to account forthe reduced probability of the simultaneous occurrence of two ormore variable loads. These values are based on therecommendations given in the UK National Annex for EN 1990.

Chapter 4 sets out the load combinations for both simple andmoment resisting frames. Information is given on frameclassification (i.e. braced or unbraced), frame imperfections andthe use of the equivalent horizontal force (EHF) (a generalapproach that replaces imperfections with a system of notionalhorizontal forces). Reduction factors for the number of storeys andfloor area are also described together with pattern loading andoverturning. Section 4.2 concentrates on the load combinations forsimple construction while section 4.3 identifies the differencesbetween simple and continuous construction. Chapter 4 concludeswith a worked example that illustrates the application of the loadcombinations equations given in EN 1990 for a three storey high,simple braced frame.

Chapter 5 sets out the application of EN 1990 to industrialbuildings with and without crane loads and illustrates the approachwith 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

Chapter 6 is a list of references where further guidance onapplying the Eurocodes to steel and composite structures is given.

It is intended to update this publication and BCSA wouldappreciate any observations, particularly on inaccuracies andambiguities, or proposals on alternative approaches or on anyother matters which should be included in future editions.

The British Constructional Steelwork Association Ltd.4, Whitehall Court, Westminster, London SW1A 2ESTelephone: +44(0)20 7839 8566 Fax: +44(0)20 7976 1634Email: [email protected]: www.steelconstruction.org

This publication was prepared by:Dr L. Gardner Imperial CollegeMr. P. J. Grubb Consultant

3

FFoorreewwoorrdd

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

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1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Introduction to EN 1990 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Introduction to EN 1991 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2. ABBREVIATIONS, DEFINITIONS AND SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Symbols (Greek letters) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3. COMBINATIONS OF ACTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.1 Ultimate limit states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2 Serviceability limit states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4. MULTI-STOREY BUILDINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.1.1 Classification of frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.1.2 Frame imperfections and equivalent horizontal forces (EHF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.1.3 Second order (P-∆) effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.1.4 Reduction factors for number of storeys (αn) and floor area (αA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.1.5 Pattern loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.1.6 Dead loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.1.7 Overturning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.2 Braced frames (simple construction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2.1 ULS load combinations based on Equation 6.10 with αcr > 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2.2 ULS load combinations based on Equation 6.10 with αcr < 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2.3 ULS load combinations based on Equations 6.10a and 6.10b with αcr > 10 . . . . . . . . . . . . . . . . . . . . . . . . 144.2.4 ULS load combinations based on Equations 6.10a and 6.10b with αcr < 10 . . . . . . . . . . . . . . . . . . . . . . . . 154.2.5 SLS load combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.3 Moment resisting frames (continuous construction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5. INDUSTRIAL BUILDINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.1.1 EN 1991-1-3: 2003 - Snow loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195.1.2 EN 1991-1-4: 2003 - Wind loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195.1.3 Frame imperfections and second order P-Δ effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.2 Portal frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.2.1 Serviceability limit state design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.2.2 SLS design example for a single span portal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.2.3 Ultimate limit state design (STR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.2.4 ULS design example for a single span portal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.3 Portal frames with cranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.3.1 Serviceability limit state design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.3.2 SLS design example for a single span portal with overhead crane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.3.3 Ultimate limit state design (STR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.3.4 ULS design example for a single span portal with overhead crane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

6. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

CCoonntteennttss

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

1.1 Background

Implementation of the structural Eurocodes is underway. Theprimary challenges are perceived to be related not to the technicalcontent, but rather to the presentation and terminology of thedocuments, since this is very different to that found in existing UKstructural design codes. Immediate differences may be observedin the preference for mathematical formulae over tables andgraphs, brevity of explanations and axis conventions. Theintention of this guide is to provide straightforward guidance oncombinations of actions (load combinations) for the two principaltypes of steel structure – multi-storey buildings and industrialbuildings. Further guidance on applying the Eurocodes to steeland 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 definitionby the country in which the building is to be constructed.

Equation numbers employed in this guide, unless prefixed by theletter D, follow the equation numbering of EN 1990.

1.2 Introduction to EN 1990

EN 1990: Eurocode – Basis of structural design is the primaryEurocode document in that it establishes the common principlesand requirements that apply to all aspects of structural design to theEurocodes. Combinations of actions for all structures are set out inEN 1990. This section provides a brief introduction to the code.

EN 1990 considers ultimate and serviceability limit states, theformer being associated with the safety of people and thestructure, while the latter concerns the functioning and appearanceof 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 thestructure.

• STR: Internal failure or excessive deformation of the structure orstructural 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 assessoverturning and sliding as a rigid body) and STR (to determineforces and moments in structural members under various loadcombinations) are of primary concern.

EN 1990 also emphasises, in Section 3, that all relevant designsituations must be examined. Design situations are classified asfollows, the first two being the ‘fundamental’ ones:

• Persistent design situations, which refer to conditions of normaluse.

• Transient design situations, which refer to temporary conditions,such as during execution (construction) or repair.

• Accidental design situations, which refer to exceptionalconditions such as fire, explosion or impact.

• Seismic design situations, which refer to conditions where thestructure is subjected to seismic events.

In Clause 4.1.1(1) of EN 1990, actions (imposed loads anddeformations) are classified by their variation with time, aspermanent, variable or accidental. Permanent actions (G) arethose that essentially do not vary with time, such as the self-weightof a structure and fixed equipment; these have generally beenreferred to as dead loads in previous British Standards. Variableactions (Q) are those that can vary with time, such as imposedloads, wind loads and snow loads; these have generally beenreferred to as live loads in previous British Standards. Accidentalactions (A) are usually of short duration, but high magnitude, suchas explosions and impacts. Classification by variation with time isimportant 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 relevantto this publication.

Table 1.1: Parts of EN 1991

EN 1991 Part Action type

EN 1991-1 General actionsEN 1991-2 Traffic loads on bridgesEN 1991-3 Actions induced by cranes and machineryEN 1991-4 Silos and tanks

EN 1991-1 is sub-divided into seven sub-parts, which providedesigners with most of the information required to determine eachindividual action on a structure. The seven sub-parts are given inTable 1.2, with EN 1991-1-1, EN 1991-1-3, EN 1991-1-4 and EN1991-1-7 being of particular relevance to this publication.

Table 1.2: Sub-parts of EN 1991-1

EN 1991-1 Part Action type

EN 1991-1-1 Densities, self weight and imposed loadsEN 1991-1-2 Actions on structures exposed to fireEN 1991-1-3 Snow loadsEN 1991-1-4 Wind actionsEN 1991-1-5 Thermal actions EN 1991-1-6 Actions during execution (construction)EN 1991-1-7 Accidental actions (impact and explosions)

EN 1991-1-1 is similar to BS 6399-1 and, since most structuraldesigners are familiar with this document, the change to EN 1991-1-1 will be relatively straightforward.

EN 1991-1-3 is used to determine snow loads and, although someof the terminology is unfamiliar, when read with the UK NationalAnnex to EN 1991-1-3, is very similar to BS 6399-3. The snow mapin the UK National Annex is zoned with altitude adjustments, asopposed to that in BS 6399-3, which had isopleths, and it benefitsfrom better analysis of the latest data from the metrological office [4].

6

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

EN 1991-1-4, covering wind loading, is different to previous UKcodes in that the basic wind velocity is based on a 10-minute meanwind speed, as opposed to the hourly mean wind speed in BS6399-2 and the 3-second gust of CP3-V-2. The term topographyhas been replaced by orography, but most designers will adaptquickly to the changes. There are a number of perceivedomissions [5] from the Eurocode when compared to BS 6399-2,but it is anticipated that the British Standard, or maybe a strippeddown version, may be used as a source of non-conflicting,complementary information [5]. EN 1991-1-4 requires that electivedominant openings are considered to be closed for the persistentdesign situation (i.e. normal use), but open during severe windstorms as an accidental design situation; this is consistent with theguidance given in BRE Digest 436 [6].

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

The terminology adopted in the Eurocodes will be unfamiliar to themajority of designers and may prove an obstacle to the rapiduptake of the Eurocodes. Most of the definitions given in theEurocodes derive from:

• 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

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

2.1 Abbreviations

B Rules applicable only to buildingsEHF Equivalent Horizontal ForceEN European StandardEQU Associated with the loss of static equilibriumFAT Associated with fatigue failure of the structure or

structural membersGEO Associated with failure or excessive deformation of the

groundI Informative N NormativeNA National AnnexNCCI Non-Conflicting Complementary InformationP PrinciplesSTR 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 bedifferent from current national practice:

Accidental action:An exceptional loading condition usually of high magnitude butshort 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 mustbe followed. Clauses not marked ‘P’ are application rules which,when followed, satisfy the principles. Alternative design rulesmay be adopted. Application rules make up the bulk of thecodes 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.

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

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

Combinations of actions:The combination of different sources of load actingsimultaneously for the verification of structural reliability for agiven limit state.

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 forcesand deformations caused by actions.

Execution:All activities carried out for the physical completion of the workincluding procurement, the inspection and documentation thereof.The term covers work on site; it may also signify the fabricationof components off site and their subsequent erection on site.

Fatigue:A mode of failure in which a member ruptures after manyapplications of load.

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

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 theEurocode cannot be used.

NDPs:Values left open in a Eurocode for definition in the countryconcerned.

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.

8

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Principles:Clauses marked ‘P’ define structural performance that must beachieved.

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 designrequirements.

Transient:Likely to be present for a period much shorter than the design lifebut 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 Reduction factor for areaαn Reduction factor for number of storeysαcr Factor by which the design loads FEd would have

to be increased to cause global elastic instability atthe load Fcr (i.e. αcr = Fcr/FEd)

γ (gamma) Partial factorγG Partial factor for permanent actionsγQ Partial factor for variable actions

ψ (psi)ψ0 Factor for combination value of a variable actionψ1 Factor for frequent value of a variable actionψ2 Factor for quasi-permanent value of a variable

action

ξ (xi) Reduction factor

Σ (sigma) Summation

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Combinations of actions, generally referred to as loadcombinations, are set out for all structures in Clause 6.4.3.2 of EN1990. They are presented not simply as a series of multiplicationfactors to be applied to the various loading components, butinstead in an unfamiliar algebraic format, which requiresexplanation. In Sections 4 and 5 of this guide, the provisions of thecode are explained and presented in a format that is more familiarto UK engineers.

3.1 Ultimate limit states

Combinations of actions are defined in Clause 6.4.3 of EN 1990 forthe four design situations: persistent, transient, accidental andseismic. Combinations of actions for the persistent (i.e. final usageof complete structure) and transient (e.g. construction) designsituations are referred to as fundamental combinations. This guidefocuses on the fundamental combinations, though combinations ofactions for accidental design situations are also considered inSection 5 for portal frames.

For each of the selected design situations, combinations of actionsfor persistent or transient design situations (fundamentalcombinations) at ultimate limit states (other than fatigue) may bederived either from Equation 6.10 of EN 1990 or from Equations6.10a and 6.10b. The UK National Annex has elected to allow theuse of either approach, though it should be noted that Equations6.10a and 6.10b will provide more favourable combinations ofactions (i.e. lower load factors). Furthermore, unless there is anunusually 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 oroverturning as a rigid body), only Equation 6.10 may be applied.The load combination expressions, as they appear in Eurocode,are provided below:

Σ γG,jGk,j “+” γPP “+” γQ,1Qk,1 “+” Σ γQ,iψ0,iQk,i (6.10)j≥1 i>1

Σ γG,jGk,j “+” γPP “+” γQ,1 ψ0,1Qk,1 “+” Σ γQ,iψ0,iQk,i (6.10a)j≥1 i>1

Σ ξγG,jGk,j “+” γPP “+” γQ,1Qk,1 “+” Σ γQ,iψ0,iQk,i (6.10b)j≥1 i>1

where “+” implies ‘to be combined with’Σ implies ‘the combined effect of’ψ0 is a combination factor, discussed belowξ is a reduction factor for unfavourable permanent

actions G, discussed belowγG is a partial factor for permanent actionsγP is a partial factor for prestressing actionsγQ is a partial factor for variable actionsP represents actions due to prestressing

Ignoring prestressing actions, which are generally absent inconventional steel structures, each of the combination expressionscontains:

• 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 variableactions being factored by γQ,1 and other accompanying variableactions being factored by γQ,i. However, since the recommendedvalue (Eurocode and UK National Annex) of both γQ,1 and γQ,i is1.5, no distinction is needed in practice, and no further distinctionwill be made in this guide.

In general, unless it is clearly not a critical combination, eachvariable action should be considered as the leading variableaction, in turn. Clause 6.1 (2) of EN 1990 states that actions thatcannot 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 onTables 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 1990applies to verification of static equilibrium (EQU) of buildingstructures, Table NA.A1.2(B) applies to the verification of structuralmembers (STR) in buildings, and Table NA.A1.2(C) relates to anyverifications involving geotechnical actions, such as piles andfootings (which are not considered in this guide).

In clause 6.4.3.1(4) of EN 1990 a distinction is made betweenfavourable and unfavourable actions. For permanent actions, theupper characteristic (superior) value Gkj,sup should be used whenthat action is unfavourable, and the lower characteristic (inferior)value Gkj,inf should be used when that action is favourable. Thisclause allows the designer to consider a permanent action aseither favourable or unfavourable, in separate load combinations.As stated in EN 1990, this approach is only necessary where theresults of verification are sensitive to variations in the magnitude ofa permanent action from place to place in a structure. This idea isconsidered in more detail in Reference [7] with a continuous beamexample. All variable actions should generally be present within aload combination unless they have a favourable influence, in whichcase they are assigned a partial factor γQ of zero, effectivelyexcluding them.

Table 3.1: Design values of actions for equilibrium (EQU)

Persistent and Permanent actions Leading Accompanyingtransient design Unfavourable Favourable variable variablesituations 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) usingEquation 6.10

Persistent and Permanent actions Leading Accompanyingtransient design Unfavourable Favourable variable variablesituations action actions

Eq. 6.10 1.35 Gkj,sup 1.0 Gkj,inf 1.5 Qk,1 1.5ψ0,i Qk,i

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Table 3.3: Design values of actions for strength (STR) usingEquations 6.10a and 6.10b

Persistent and Permanent actions Leading Accompanyingtransient design Unfavourable Favourable variable variablesituations action actions

Eq. 6.10a 1.35 Gkj,sup 1.0 Gkj,inf 1.5ψ0,i Qk,iEq. 6.10b ξ×1.35Gkj,sup 1.0 Gkj,inf 1.5 Qk,1 1.5ψ0,i Qk,i

The ξ factor that appears in Equation 6.10b of EN 1990 is areduction factor for unfavourable permanent actions G. The UKNational Annex sets the ξ factor equal to 0.925. When combinedwith γG in Equation 6.10b the effect is to reduce the overall factorfrom 1.35 to 1.25. In applying Equation 6.10a all vaiable actionsare termed ‘accompanying’ (the largest of which is the main‘accompanying action’), whereas in applying Equation 6.10b themost significant variable action is termed the ‘leading variableaction’, 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 inEN 1990. The purpose of ψ0 is to take account of the reducedprobability of the simultaneous occurrence of two or more variableactions. ψ factors are discussed in Section 4.1.3 of EN 1990.Values for ψ factors for buildings in the UK are given in TableNA.A1.1 of BS EN 1990. In general, these factors are the sameas those recommended in Table A1.1 of EN 1990, but with someexceptions. For example, ψ0 is 0 for imposed loading on roofs and0.6 for wind loading on buildings in EN 1990, whereas the UKNational Annex gives values of 0.7 for imposed loading on roofsand 0.5 for wind loading. Selected values of ψ0 from the UKNational Annex are given in Table 3.4. Values of ψ1 and ψ2 fromthe UK National Annex are also provided in Table 3.4, but onlyfeature in serviceability or accidental combinations.

Table 3.4: Values of ψ factors for buildings

Action ψ0 ψ1 ψ2Imposed loads in buildings, category (see EN 1991-1-1)Category A: domestic, residential areas 0.7 0.5 0.3Category B: office areas 0.7 0.5 0.3Category C: congregation areas 0.7 0.7 0.6Category D: shopping areas 0.7 0.7 0.6Category E: storage areas 1.0 0.9 0.8Category F: traffic area, vehicle weight ≤ 30 kN 0.7 0.7 0.6Category G: traffic area,

30 kN < vehicle weight ≤ 160 kN 0.7 0.5 0.3Category H: roofs 0.7 0 0Snow loads on buildings (see EN 1991-1-3)

– for sites located at altitude H > 1000 m above sea level 0.7 0.5 0.2

– for sites located at altitude H ≤ 1000 m above sea level 0.5 0.2 0

Wind loads on buildings (see EN 1991-1-4) 0.5 0.2 0Temperature (non fire) in buildings (see EN 1991-1-5) 0.6 0.5 0

3.2 Serviceability limit states

For serviceability limit states, guidance on combinations of actionsis given in Clauses 6.5.3 and A1.4 of EN 1990. Three groups ofcombinations are identified: characteristic, frequent and quasi-permanent.

The characteristic combination is given by Equation 6.14b of EN1990 and is normally used for irreversible limit states, such aspermanent local damage or permanent unacceptabledeformations.

Σ Gk,j “+” P “+” Qk,1 “+” Σ ψ0,iQk,i (6.14b)j≥1 i>1

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

Σ Gk,j “+” P “+” ψ1,1Qk,1 “+” Σ ψ2,iQk,i (6.15b)j≥1 i>1

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

Σ Gk,j “+” P “+” Σ ψ2,iQk,i (6.16b)j≥1 i>1

The UK National Annex to EN 1993-1-1 (Clauses NA.2.23 andNA.2.24) states that vertical and horizontal deflections may bechecked using the characteristic combination with variable loadsonly (i.e. permanent loads should not be included). Deflectionlimits are also provided, which are similar to those given in BS5950. The basis for employing the characteristic combination isthat excessive deflections may cause permanent local damage toconnected parts or finishes (i.e. irreversible limit states), eventhough the steel members themselves will generally remainelastic. The designer may also wish to check total deflections, andmay also wish to consider whether the frequent combination isapplicable.

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In this section, Eurocode load combinations for multi-storeybuildings are set out. General guidance for both simple andmoment 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 insway stiffness, member interaction etc. and hence, specificguidance and examples for simple and moment resisting frames isprovided in Sections 4.2 and 4.3, respectively.

4.1 General

4.1.1 Classification of framesStructural frames may be classified with regards to their lateralload resisting system and sway stiffness. Concerning the lateralload resisting system, a frame may be regarded as either bracedor unbraced. As a guide, for a frame to be classified as ‘braced’,it should contain a bracing system with lateral stiffness of at leastfive times that of the unbraced frame [8], which will be the case inbraced simple construction. Bracing systems using wire ties (asopposed to open or hollow sections) may result in the frame beingclassified as ‘unbraced’.

Sway stiffness is commonly achieved through the provision of asuitable bracing system or by utilising the inherent bendingresistance of a rigid frame. Adequate sway stiffness is importantbecause it limits the lateral deflections of the frame and hencecontrols second order (P-Δ) effects. Sway stiffness is assessed inEN 1993-1-1 in a similar way as it is in BS 5950, through the αcrparameter (equivalent to λcr in BS 5950), which represents thefactor by which the vertical design loading would have to beincreased to cause overall elastic buckling of the frame (Clause5.2.1(3) of EN 1993-1-1). A simplified means of determining αcr forregular 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 swaystiffness is deemed sufficiently large for second order effects to beignored. Conversely, if αcr is less than 10, second order effectsmay no longer be ignored. Second order effects are discussedfurther in Section 4.1.3.

4.1.2 Frame imperfections and equivalent horizontalforces (EHF)

Frame imperfections may be incorporated directly into thestructural analysis by defining an initial sway for the frame.However, the more general approach is to replace this geometricimperfection with a system of equivalent horizontal forces (EHF),referred to as notional horizontal loads in BS 5950. Whereas in BS5950, equivalent horizontal forces were only required in thevertical load case, in the Eurocodes it is deemed that since frameimperfections are inherently present, they should be included in allULS load combinations. This appears entirely rational. EHF arenot required in SLS load combinations. The EHF should bedetermined separately for each load combination since theydepend on the level of design vertical loads. For each storey, theEHF 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 ofcolumns in a row, reductions to this basic value of 1/200 arepossible, as detailed in Clause 5.3.2(3) of EN 1993-1-1. Ifhorizontal loads (HEd) exceed 15% of vertical loads (VEd) these

sway imperfections may be disregarded, and EHF ignored – thiswould more oftern apply to low rise buildings.

4.1.3 Second order (P-Δ) effectsSecond order effects relate to the increase in member forces andmoments that occur as a result of deformation of the structureunder load. As outlined in Section 4.1.1, second order (P-Δ)effects need not be considered provided the frame is sufficientlystiff (i.e. sway deformation under the design loading is relativelysmall) – this is deemed to be the case for elastic analysis when αcr> 10, and similarly, according to the UK National Annex, for plasticanalysis of clad frames when the additional stiffening effect of thecladding has been neglected. In cases where αcr is less than 10,the designer is presented with a number of options. These includeenhancement of the stability system such that αcr is raised above10 and hence second order effects may be ignored, makingallowance for second order effects by approximate means(amplified sway method or effective length method, both of whichwere allowed in BS 5950), or making allowance for second ordereffects by performing a second order structural analysis enablingand accounting for deformation of the structure under load. Itshould be noted that if αcr is less than 3, then an accurate secondorder analysis must be performed (Clause 5.2.2(5) of EN 1993-1-1). The aforementioned is summarised in Table 4.1.

Table 4.1: Summary of analysis methods and treatment ofsecond order effects

Limits on αcr Analysis method Result

αcr > 10 First order analysis Second order effects ignored

10 > αcr > 3 First order analysis plus Second order effects amplified sway method or allowed for byeffective length method approximate means

αcr < 3 Second order analysis Second order effects allowed for moreaccurately

The most common approximate treatment of second order effectsin 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 lateralloading 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, whichis related to the sway stiffness of the structure through EquationD4.1 (Equation 5.4 of EN 1993-1-1).

kr = 1 (D4.1)1-1/αcr

4.1.4 Reduction factors for number of storeys (αn) andfloor area (αA)

As the number of storeys in a building increase, the likelihood thatall floors will be loaded to the full design level decreases. Similarly,large floor areas will seldom be subjected to the full design loadinguniformly. To reflect this, reduction factors for imposed loads maybe applied for the design of floors, beams and roofs and for thedesign of columns and walls. For the design of individual floors,

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beams and roofs, the area reduction factor αA may be applied. Forthe design of columns and walls, the reduction factor αn for thenumber of storeys may be applied. The reduction factor αn relatesto the number of floors supported by the column section underconsideration, and may be applied to the total imposed load beingcarried. If, for a given column or wall, αA < αn, then αA may beused 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 accessibleroofs are provided in Clause NA.2.5 of the UK National Annex toEN 1991-1-1 (see Equation D4.2), and replace those given inClause 6.3.1.2(10) of EN 1991-1-1.

αA = 1.0 – A/1000 ≥ 0.75 (D4.2)

where A is the area (m2) supported.

Reduction factors αn for imposed loads from several storeys usedfor calculating column forces are defined in Clause 6.3.1.2(11) andby Equation 6.2 of EN 1991-1-1. Revised expressions areprovided in the UK National Annex (Clause NA.2.6 and EquationNA.2), as given by Equations D4.3 to D4.5 below. These reductionfactors may be applied to the total imposed load experienced by agiven column, but may only be employed when the imposed loadis the leading variable action in a load combination. When theimposed load is an accompanying action, either ψ0 or αn may beapplied, but not both.

αn = 1.1 – n/10 for 1 ≤ n ≤ 5 (D4.3)

αn = 0.6 for 5 < n ≤ 10 (D4.4)

αn = 0.5 for n > 10 (D4.5)

4.1.5 Pattern loadingFor the design of floors within one storey and for the design ofroofs, EN 1991-1-1 Clause 6.2.1(1) states that pattern loadingshould be considered for continuous construction, though thestoreys other than the one under consideration may be assumedto be uniformly loaded (Clause 6.2.1 of EN 1991-1-1). Patternloading need not be considered for simple construction. The twoloading patterns indentified in Clause AB.2 of EN 1993-1-1 forcontinuous floor beams to assess (a) the span moments and (b)support moments for the storey under consideration are shown inFigures 4.1(a) and (b), respectively. In Figure 4.1(a), alternativespans carry the design permanent and variable load (γGGk + γQQk)while other spans carry only the design permanent load ( γGGk). InFigure 4.1(b), two adjacent spans carry the design permanent andvariable load (γGGk + γQQk) while all other spans carry only thedesign permanent load ( γGGk).

Figure 4.1: Pattern loading for continuous floor beams

(a) Applies to span (sagging) moments

(b) Applies to support (hogging) moments

For the design of columns or walls loaded from several storeys (2 ormore) the total imposed floor load on each storey should be assumedto be uniformly distributed (Clause 6.2.2(1) of EN 1991-1-1).

4.1.6 Dead loadsIn load combinations, the total self-weight of the structure and non-structural components should be taken as a single action (Clause3.2(1) of EN 1991-1-1). Permanent roof loads and floor loads maytherefore be treated as a single action Gk in load combinations.

4.1.7 OverturningOverturning of a structure as a rigid body is independent of itslateral load resisting system and sway stiffness. It is solely amatter of equilibrium (EQU), for which only Equation 6.10 of EN1990 should be applied. The critical load combination for generalmulti-storey buildings emerges on the basis of maximising theoverturning moment due to the horizontal loading (wind and EHF)and minimising the restoring moment due to the vertical loading. Itis generally appropriate to consider only a single value for deadloading, but the concept of upper (superior) Gk,sup and lower(inferior) Gk,inf characteristic values should be considered wheresensitivity to variability in dead loads is very high (Clause A1.3.1 ofEN 1990). For the overturning load case, a factor of 0.9 is appliedto 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 variableaction. The wind load has been denoted Wk in this document.Equivalent horizontal forces are included, as in all ULScombinations, but these are not factored (again) since they arealready based on factored loading. Thus, the overturning loadcombination is given by Equation D4.6.

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γGGk γGGk + γQQkStorey under consideration

γGGk γGGk + γQQkStorey under consideration

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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 arethus 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 ofadvantages associated with simple construction. The structuralmembers can, largely, be designed in isolation, with the beamsconsidered as simply-supported members carrying the verticalloading and the columns as pin ended compression members witha nominal moment arising from the eccentric beam reactions. Abracing system will typically be employed to resist the horizontalloading, though note that columns forming part of the bracingsystem will also attract axial forces arising from the horizontalloading (wind loads and EHF), as described in Reference [5].

4.2.1 ULS load combinations based on Equation 6.10 withαcr > 10

For frames with αcr > 10, second order effects need not beconsidered. Assuming all loads to be always unfavourable (i.e.causing an increase in member forces or moments), two basicload combinations, given by Equations D4.7 and D4.8, arise fromEquation 6.10. In Equation D4.7, imposed load is assumed to bethe 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, windload is considered as the leading variable action with a load factorof 1.5, thus the imposed load is reduced by a combination factorψ0 of 0.7 (applicable in all cases except for storage areas), to givea load factor = 0.7 × 1.5 = 1.05). It is assumed throughout thissection that imposed loading on the roofs of multi-storey buildingswill be greater than the snow loading, thus attracting a combinationfactor ψ0 = 0.7, rather than ψ0 = 0.5, which applies to snow loading(at altitudes of less than 1000 m). Note, as discussed in Section4.1.2 of this guide, that the EHF should be determined separatelyfor each load combination.

1.35Gk “+” 1.5Qk “+” 0.75Wk “+” EHF (D4.7)

1.35Gk “+” 1.05Qk “+” 1.5Wk “+” EHF (D4.8)

Equation D4.7 would generally govern the design of the beamsand columns, whilst Equation D4.8 would be expected to be morecritical for the bracing members. The imposed load in EquationD4.7 may be reduced by the area reduction factor αA, given byEquation D4.2, for the design of the beams. For column design,the imposed load may be reduced by the reduction factor fornumber of storeys αn (that the column under consideration issupporting) or the reduction factor for area αA, whichever is themore beneficial. Note that the imposed load reduction factors mayonly be applied in combinations where the imposed loading is theleading variable action (Equation D4.7). Pattern loading need notbe considered for column design (see Section 4.1.5).

Other load combinations arise by considering that the variableactions may be favourable (i.e. causing a reduction in member

forces or moments). A good example of this is the uplift case,where imposed load is clearly favourable since it opposes theuplift. The imposed load therefore has a load factor of zero for theuplift case, whilst the dead load has a load factor of 1.0. Thisresults in Equation D4.9.

1.00Gk “+” 1.5Wk “+” EHF (D4.9)

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

1.35Gk “+” 1.5Qk “+” EHF (D4.10)

4.2.2 ULS load combinations based on Equation 6.10 withαcr < 10

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

4.2.3 ULS load combinations based on Equation 6.10a and6.10b with αcr > 10

Employing Equations 6.10a and 6.10b of EN 1990, and adoptingthe same approach as described in Section 4.1.1, three loadcombinations arise when all loads are assumed to beunfavourable, as given by Equations D4.11 to D4.13. Note thatEquation D4.11 arises from Equation 6.10a where all variableactions are reduced by the combination factor ψ0, while EquationsD4.12 and D4.13 emerge from Equation 6.10b, and have a lowerdead load factor of 1.25 due to the introduction of the ξ factor (seeSection 3.1).

1.35Gk “+” 1.05Qk “+” 0.75Wk “+” EHF (D4.11)

1.25Gk “+” 1.5Qk “+” 0.75Wk “+” EHF (D4.12)

1.25Gk “+” 1.05Qk “+” 1.5Wk “+” EHF (D4.13)

Of the above three combinations, Equation D4.11 will only governon the rare occasions where the dead load is significantly largerthan the imposed load. For the uplift combination, given byEquation D4.14, the wind load is the leading variable action,attracting a load factor of 1.5, and the imposed load is absent sinceit is favourable. Note that Equation D4.14 is the same as D4.9,showing that the uplift load combination is the same whetherderived from Equation 6.10 or Equations 6.10a and 6.10b.

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1.00Gk “+” 1.5 Wk “+” EHF (D4.14)

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

1.25Gk “+” 1.5Qk “+” EHF (D4.15)

Equations D4.12 to D4.15 represent the four basic loadcombinations for multi-storey frames. For economy, it isrecommended that these load combinations (Equations D4.11 toD4.15 all emerging from Equation 6.10b) be used in preference tothose arising from Equation 6.10 (Equations D4.7 to D4.10).

4.2.4 ULS load combinations based on Equations 6.10aand 6.10b with αcr < 10

As described in Section 4.2.2, when αcr < 10, second order effectsmust be considered. If the amplified sway method is employed,load combinations will be the same as those given in EquationsD4.11 to D4.15, except that all horizontal loads (wind andequivalent horizontal forces) and other sway effects are multipliedby the factor kr, which, as noted in Section 4.2.2 is loadcombination dependant.

4.2.5 SLS load combinationsAs outlined in Section 3.2, the UK National Annex to EN 1993-1-1states that vertical and horizontal deflections may be checkedusing the characteristic combination with variable loads only (i.e.permanent loads should not be included). The characteristiccombination is defined by Equation 6.14b of EN 1990, where theleading variable action is unfactored (i.e. taken as its characteristicvalue) and all accompanying variable actions are reduced by thecombination factor ψ0.

Assuming all loads to be unfavourable, the resulting SLScombinations are given by Equations D4.16 (where imposed loadis taken as the leading variable action) and D4.17 (where windload is taken as the leading variable action).

1.00Qk “+” 0.50Wk (D4.16)

1.00Wk “+” 0.70Qk (D4.17)

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

1.00Qk (D4.18)

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

1.00Wk (D4.19)

Deflection limits are also provided in the National Annex to EN1993-1-1 in Clauses NA.2.23 and NA.2.24. The deflection limits of

relevance to multi-storey buildings, which are the same as thosegiven in BS 5950, are presented in Tables 4.2 and 4.3.

Table 4.2: Vertical deflection limits

Vertical deflection LimitCantilevers Length/180Beam carrying plaster or other brittle finish Span/360Other beams (except purlins and sheeting rails) Span/200

Table 4.3: Horizontal deflection limits

Horizontal deflection LimitIn each storey of a building with more Height of than one storey 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 inEquations D4.17 and D4.19.

4.3 Moment resisting frames (continuousconstruction)

For the case of simple braced frames, the members canessentially be designed in isolation. For moment resisting frames,the structure is not statically determinate, there is interactionbetween the members and this simplification may not generally bemade. Unbraced (moment resisting) frames are also generally lessstiff laterally than braced frames, and are therefore more likely torequire consideration of second order effects. However, the basicload combinations derived for simple frames in Section 4.2 areequally applicable to moment resisting frames.

It is therefore recommended that, as for simple frames, the ULSload combinations for moment resisting frames be based onEquations 6.10a and 6.10b. This results in five load combinationsgiven by Equations D4.11 to D4.15, of which D4.11 is unlikely togovern except in cases of an unusually high ratio of dead toimposed loading. SLS load combinations are given by EquationsD4.16 to D4.19.

4.4 Example

The following example illustrates application of the above loadcombinations (from Equations 6.10a and 6.10b) to a simple bracedframe. The general case considered is set out in Figure 4.2, wherethe loads shown are unfactored (characteristic values). Thefollowing 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 6m centres and every third frame is braced (in the configurationshown in Figure 4.2). For the equilibrium check only, lateral forces,together with overturning and restoring moments, are shown perframe. Throughout the remainder of the example, lateral forces areshown per braced frame. It is assumed that αcr > 10, so secondorder effects are neglected. Imposed load reduction factors havenot been considered. EHF have been calculated on the basis of1/200 of the total vertical load for each storey.

15

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

Figure 4.2: Unfactored loading on example frame

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

Figure 4.3: Total factored ULS loading arising from EquationD4.11

Design loading in key members:1.35Gk “+” 1.05Qk “+” 0.75Wk “+” EHFRoof design UDL qEd = 35.0 kN/mFloor design UDL qEd = 59.9 kN/mExternal column FEd = 643.5 kNBracing FEd = 246.1 kN (tension)

Internal column (unbraced frame) FEd = 1287.1 kNInternal column (braced frame) FEd = 1577.9 kN

Figure 4.4: Total factored ULS loading arising from EquationD4.12

Design loading in key members:1.25Gk “+” 1.5Qk “+” 0.75Wk “+” EHFRoof design UDL qEd = 36.9 kN/mFloor design UDL qEd = 71.3 kN/mExternal column FEd = 752.0 kNBracing FEd = 257.5 kN (tension)

Internal column (unbraced frame) FEd = 1504.0 kNInternal column (braced frame) FEd = 1807.1 kN

Figure 4.5: Total factored ULS loading arising from EquationD4.13

Design loading in key members:1.25Gk “+” 1.05Qk “+” 1.5Wk “+” EHFRoof design UDL qEd = 30.0 kN/mFloor design UDL qEd = 57.8 kN/mExternal column FEd = 609.8 kNBracing FEd = 421.1 kN (tension)

Internal column (unbraced frame) FEd = 1219.7 kNInternal column (braced frame) FEd = 1715.2 kN

16

Gkf = 3.5 kN/m2

Qkf = 5 kN/m2

Gkf = 3.5 kN/m2Qkf = 5 kN/m2

Gkr = 3.5 kN/m2

Qkr = 1.5 kN/m2

Gkf = 3.5 kN/m2Qkf = 5 kN/m2

Wk = 0.63 kN/m2

Wk

= 0.7

kN/m

2

Wk

= 0.2

kN/m

2

6m 6m 6m

3.6m

3.6m

3.6m

3.6m

EHF = 9.4 kNWind = 21.9 kN qEd = 35.0 kN/m

EHF = 16.2 kNWind = 43.7 kN

EHF = 16.2 kNWind = 43.7 kN

EHF = 16.2 kNWind = 43.7 kN

qEd = 59.9 kN/m

qEd = 59.9 kN/m

qEd = 59.9 kN/m

External column FEd

Internal column FEd

Bracing FEd

EHF = 10.0 kNWind = 21.9 kN qEd = 36.9 kN/m

EHF = 19.2 kNWind = 43.7 kN

EHF = 19.2 kNWind = 43.7 kN

EHF = 19.2 kNWind = 43.7 kN

qEd = 71.3 kN/m

qEd = 71.3 kN/m

qEd = 71.3 kN/m

External column FEd

Internal column FEd

Bracing FEd

EHF = 8.1 kNWind = 43.7 kN qEd = 30.0 kN/m

EHF = 15.6 kNWind = 87.5 kN

EHF = 15.6 kNWind = 87.5 kN

EHF = 15.6 kNWind = 87.5 kN

qEd = 57.8 kN/m

qEd = 57.8 kN/m

qEd = 57.8 kN/m

External column FEd

Internal column FEd

Bracing FEd

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

Figure 4.6: Total factored ULS loading arising from EquationD4.14

Design loading in key members:1.00Gk “+” 1.5Qk “+” EHFRoof design UDL qEd = 15.3 kN/mFloor design UDL qEd = 21.0 kN/mExternal column FEd = 235.0 kNBracing FEd = 381.7 kN (tension)

Internal column (unbraced frame) FEd = 470.0 kNInternal column (braced frame) FEd = 920.2 kN

Figure 4.7: Total factored ULS loading arising from EquationD4.15

Design loading in key members:1.25Gk “+” 1.5Qk “+” EHFRoof design UDL qEd = 39.8 kN/mFloor design UDL qEd = 71.3 kN/mExternal column FEd = 760.5 kNBracing FEd = 79.8 kN (tension)

Internal column (unbraced frame) FEd = 1521.0 kNInternal column (braced frame) FEd = 1616.0 kN

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

Serviceability load combinations, as defined by Equations D4.16 toD4.19, are shown in Figures 4.8 to 4.11, respectively.

Figure 4.8: SLS loading arising from Equation D4.16

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

Roof SLS UDL qEd = 7.1 kN/mFloor SLS UDL qEd = 30.0 kN/mLateral SLS load at roof level HEd = 14.6 kNLateral SLS load at levels 1, 2 and 3 HEd = 29.2 kN

17

EHF = 4.1 kNWind = 43.7 kN qEd = 15.3 kN/m

EHF = 5.7 kNWind = 87.5 kN

EHF = 5.7 kNWind = 87.5 kN

EHF = 5.7 kNWind = 87.5 kN

qEd = 21.0 kN/m

qEd = 21.0 kN/m

qEd = 21.0 kN/m

External column FEd

Internal column FEd

Bracing FEd

EHF = 10.7 kNWind = 0.0 kN qEd = 39.8 kN/m

EHF = 19.2 kNWind = 0.0 kN

EHF = 19.2 kNWind = 0.0 kN

EHF = 19.2 kNWind = 0.0 kN

qEd = 71.3 kN/m

qEd = 71.3 kN/m

qEd = 71.3 kN/m

External column FEd

Internal column FEd

Bracing FEd

Wind = 14.6 kN qEd = 7.1 kN/m

Wind = 29.2 kN

Wind = 29.2 kN

Wind = 29.2 kN

qEd = 30.0 kN/m

qEd = 30.0 kN/m

qEd = 30.0 kN/m

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

18

Figure 4.9: SLS loading arising from Equation D4.17

Summary of SLS loading:1.00Qk “+” 0.7Qk

Roof SLS UDL qEd = 2.5 kN/mFloor SLS UDL qEd = 21.0 kN/mLateral SLS load at roof level HEd = 29.2 kNLateral SLS load at levels 1, 2 and 3 HEd = 58.3 kN

Figure 4.10: SLS loading arising from Equation D4.18

Summary of SLS loading:1.00Qk

Roof SLS UDL qEd = 9.0 kN/mFloor SLS UDL qEd = 30.0 kN/mLateral SLS load at roof level HEd = 0.0 kNLateral SLS load at levels 1, 2 and 3 HEd = 0.0 kN

Figure 4.11: SLS loading arising from Equation D4.19

Summary of SLS loading:1.00Wk

Roof SLS UDL qEd = -3.8 kN/mFloor SLS UDL qEd = 0.0 kN/mLateral SLS load at roof level HEd = 29.2 kNLateral SLS load at levels 1, 2 and 3 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 forhorizontal deflections of the frame at levels 1, 2 and 3 but at rooflevel Equation D4.19 (1.00Wk “+” EHF) governs.

For checking against overturning (EQU), only Equation 6.10 maybe applied, resulting in the load combination given by EquationD4.6, illustrated for the example frame in Figure 4.12. Note thatloads, together with the overturning and restoring moments, areshown per frame in Figure 4.12.

Figure 4.12: Loading per frame for EQU overturning check

Equilibrium assessment:0.9Gk “+” 1.5Wk “+” EHFOverturning moment per frame M = 893.7 kNm

Restoring moment per frame M = 11330 kNm

Wind = 29.2 kN qEd = 2.5 kN/m

Wind = 58.3 kN

Wind = 58.3 kN

Wind = 58.3 kN

qEd = 21.0 kN/m

qEd = 21.0 kN/m

qEd = 21.0 kN/m

Wind = 29.2 kN qEd = -3.8 kN/m

Wind = 58.3 kN

Wind = 58.3 kN

Wind = 58.3 kN

qEd = 0.0 kN/m

qEd = 0.0 kN/m

qEd = 0.0 kN/m

EHF = 1.2 kNWind = 14.6 kN qEd = 13.2 kN/m

EHF = 1.7 kNWind = 29.2 kN

EHF = 1.7 kNWind = 29.2 kN

EHF = 1.7 kNWind = 29.2 kN

qEd = 18.9 kN/m

qEd = 18.9 kN/m

qEd = 18.9 kN/m

Wind = 0.0 kN qEd = 9.0 kN/m

Wind = 0.0 kN

Wind = 0.0 kN

Wind = 0.0 kN

qEd = 30.0 kN/m

qEd = 30.0 kN/m

qEd = 30.0 kN/m

Page 20: Eurocode Load Combinations for Steel Structures 2010

EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

5.1 General

Although industrial buildings can be designed to supportmezzanine floors and cranes, they are primarily loaded by theirself weight, service loads, imposed loads or snow loads and windloads. Service loads tend to be ‘project specific’ but a nominalvalue of around 0.05 kN/m2 should always be considered instructural design to allow for loads from nominal lighting. Thisvalue will increase if more substantial services such as sprinklersystems or air-conditioning are incorporated. The self weights offalse ceilings over intermediate floors are often also treated asservice loads. Snow loads and wind loads are site specific and areinfluenced by the geometry of the structure and its orientation.Snow loads are determined by reference to EN 1991-1-3 and itsUK National Annex. Wind loads are determined by reference toEN 1991-1-4 and its UK National Annex, but designers might alsolike to refer to Reference [5].

Clause 3.3.2 (1) of EN 1991-1-1 states that on roofs, imposedloads and snow loads or wind loads should not be applied togethersimultaneously. This implies (1) that snow load and imposed loadshould not appear together in any given load combination, and (2)that imposed load and wind load should not appear together in anygiven load combination. The basis for this clause is that it would beunreasonable to consider that maintenance would be undertakenin severe weather conditions. The first implication is in line withcurrent practice in the UK, where, for roofs that are not accessibleexcept for normal maintenance and repair, the loading wouldtypically be taken as the larger of an imposed load of 0.6 kN/m2 orthe snow load (i.e. the imposed loads and snow loads are notapplied simultaneously). The same value of 0.6 kN/m2 is alsorecommended for roof slopes less than 30º in Table NA.7 of the UKNational Annex to EN 1991-1-1. The second implication is that forcases where the snow load is less than 0.6 kN/m2, then it is onlythis lesser value that would be applied in combination with the windload, which, coupled with the fact that the combination factor forsnow loading (ψ0 = 0.5) is lower than that for imposed loading (ψ0= 0.7), may result in significantly lower roof loading (in combinationwith wind) than is used in current UK practice. It is recommendedin this guide that imposed loads and wind loads continue to beconsidered in combination for the design of portal frames in theUK. Given the different combination factors for snow and imposedloading, the snow load would have to be greater than 1.4 times theimposed load (i.e. greater than 0.84 kN/m2) to be critical in thewind (leading) plus imposed or snow load combination. Where theimposed load or snow load is the leading variable action, the snowload simply needs to exceed the imposed load to become critical.

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

Table 5.1: ψ factors relevant to portal frame structures

ψ0 ψ1 ψ2

Imposed loads on roofs 0.7 0.0 0.0

Snow loads at altitude less than or equal to 1000 m 0.5 0.2 0.0

Wind loads 0.5 0.2 0.0

Crane loads 1.0 0.9 Gkc/(Gkc+Qkc)

5.1.1 EN 1991-1-3: 2003 - Snow loadingIn Section 2 of EN 1991-1-3, ‘Classification of actions’, snow loadsare classified as variable fixed actions unless otherwise specified inthe code. In this section it also states that exceptional snow loadsand exceptional snow drifts may be treated as accidental actions,depending on geographical locations. The UK National Annexconfirms this in clauses NA.2.4 and NA.2.5 and also states thatAnnex B should be used to determine the drifted snow load case.This approach is consistent with current UK practice for designersusing BS 6399-3 and BRE Digest 439 [9] to determine uniformsnow loads and the loads caused by the build up of drifted snow.

5.1.2 EN 1991-1-4: 2003 - Wind loadingWind actions are defined as variable fixed actions. The processfor determining wind pressures is based on a 10-minute meanwind velocity and a new map has been provided in the UK NationalAnnex. Designers who have been working with BS 6399-2 will findthe approach for determining wind pressures very similar althoughsome terminology has changed. The publication “Designers’Guide to EN 1991-1-4 Eurocode 1: Actions on structures, generalactions part 1-4. Wind actions” [2] is very important in explainingthe limitations of the new European Standard.

Although wind pressures vary depending on site location, altitude,orientation etc, the pressure and force coefficients depend only onthe external shape of the structure. By looking at the overallpressure coefficients, irrespective of the actual site windpressures, it is possible to determine the critical load cases. Themajority of portal frames have roof pitches of 5°, 6° or 10°. Figures5.1c, 5.1d and 5.1e have been produced for portal frames withthese roof pitches and present overall pressure coefficients.Figures 5.1a and 5.1b have been included to show theintermediate steps required to arrive at the figures in 5.1c. Similarintermediate steps have not been included for Figures 5.1d and5.1e, although some extended expressions have been shown.

External pressure coefficients for the walls have been extractedfrom Table 7.1 of EN 1991-1-4 assuming an h/d ratio ≤ 0.25. Table7.4a 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, tocomply with the requirements of Clauses 5.3 and 7.2.2 of EN1991-1-4 two addition factors must be applied to the external forcecoefficients: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

55.. IInndduussttrriiaall bbuuiillddiinnggss

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

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

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

20

Longitudinal Wind 1

-0.6-0.6

-0.8 -0.8

Transverse Wind 1

-0.40.3-0.6-1.2

0.7 -0.3

Transverse Wind 2

-0.40.30.0

0.7 -0.3

Longitudinal Wind 1

-0.6-0.6

-0.8 -0.8

Transverse Wind 1

-0.34-0.255-0.51-1.02

0.595 -0.255

-0.34-0.2550.0

0.595 -0.255

Transverse Wind 2

Figure 5.1a: External Pressure Coefficients – Portal framewith 5° roof pitch

The above coefficients are now modified by the 0.85 and cscdfactors to give:

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

KeyOverall coefficients shown thus:Pressure shown as positive valuesSuction shown as negative values

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

21

Longitudinal Wind 1

-0.6

-0.8

-0.6

-0.8-0.8

-1.0 Internalpressure 0.2

-0.8-1.0

Transverse Wind 1

-0.340.255-1.02 -0.51

0.595 Internalpressure 0.2

-0.255

Transverse Wind 1a

-0.34

-0.04

0.255

0.045

-1.02

-0.72

-0.51

-0.21

0.5950.895 Internal

suction -0.3

-0.30.0

Transverse Wind 2

-0.34

-0.14

-0.255

-0.055

0.0

0.20.595

0.395 Internalpressure 0.2

-0.3-0.5

Transverse Wind 2a

-0.34-0.2550.0

0.595 Internal suction -0.3

-0.3

Longitudinal Wind 1

-0.6

-0.8

-0.6

-0.8-0.8

-1.0 Internalpressure 0.2

-0.8-1.0

Transverse Wind 1

-0.41 x 0.85

-0.589

-0.36 x 0.85

-0.506

-1.16 x 0.85

-1.186

-0.58 x 0.85

-0.693

0.7 x 0.850.395 Internal

pressure 0.2

-0.3 x 0.85-0.455

Transverse Wind 1a

-0.389

-0.089

-0.306

-0.006

-0.986

-0.686

-0.493

-0.193

0.5950.895 Internal

suction -0.3

-0.2550.045

Transverse Wind 2

-0.41 x 0.85

-0.489

-0.36 x 0.85

-0.506

0.02 x 0.85

-0.1830.595

0.395 Internalpressure 0.2

-0.255-0.455

Transverse Wind 2a

-0.389

-0.089

-0.306

-0.006

0.017

0.3170.595

0.895 Internal suction -0.3

-0.2550.045

KeyOverall coefficients shown thus:Pressure shown as positive valuesSuction shown as negative values

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

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

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

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

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 2acauses maximum sidesway.

-0.54-0.455-1.22 -0.71

0.395 -0.455

-0.040.0450.3

0.895 0.0

-0.3

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

Figure 5.1e: Wind Pressure Coefficients – Portal frame with10° roof pitch

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

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

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

5.2 Portal frames

Combinations of actions for portal frames are considered in thisSection. Additional considerations for cranes are introduced inSection 5.3. The serviceability limit state is treated first since thisis likely to govern the design of this form of construction.

5.2.1 Serviceability limit state designFor the serviceability limit state, the UK National Annex to EN1993-1-1 states that deflections may be checked using thecharacteristic combination of loading and considering variableloads only, as discussed in Section 3.2.

Assuming that for steel portal frame structures the dead load canbe accurately determined and that the combined dead and serviceloads can be treated as one dead load:

Gksup = Dead load + Service loadGkinf = Dead loadQk = Imposed load (or uniform snow load if greater than

0.6 kN/m2)Wk = Wind load - three load cases as identified earlierAd = Load from snow build-up or drift (accidental load

condition)

6.14b 1.00Qk “+” 0.50Wk (pressure) “+” EHF0.70Qk “+” 1.00Wk (pressure) “+” EHF0.00Qk “+” 1.00Wk (suction) “+” EHF

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

Figure 5.2: Typical clear span portal frame

Dead load: Cladding 0.150 kN/m2

Purlins (0.046 × 1.25/1.8) 0.032 kN/m2

(1.25 factor to allow for purlin sleeves)Rafter (0.54 × 1.1 / 6.0) 0.099 kN/m2

(1.10 factor to allow for rafter haunches)Dead load on slope 0.281 kN/m2

Slope factor (6° slope) 1.0055Dead load on plan 0.283 kN/m2

22

Longitudinal Wind 1

-0.65

-0.85

-0.65

-0.85-0.8-1.0 Internal

pressure 0.2

-0.8-1.0

Transverse Wind 1

-0.45 x 0.85

-0.583

-0.6 x 0.85

-0.71

-1.00 x 0.85

-1.05

-0.5 x 0.85

-0.625

0.7 x 0.850.395 Internal

pressure 0.2

-0.3 x 0.85-0.455

Transverse Wind 1a

-0.383

-0.083

-0.51

-0.21

-0.85

-0.55

-0.425

-0.125

0.5950.895 Internal

suction -0.3

-0.2550.045

Transverse Wind 2

-0.383

-0.583

-0.51

-0.71

0.1 x 0.85

-0.1150.595

0.395 Internalpressure 0.2

-0.255-0.455

Transverse Wind 2a

-0.383

-0.083

-0.51

-0.21

0.085

0.3850.595

0.895 Internal suction -0.3

-0.2550.045

KeyOverall coefficients shown thus:Pressure shown as positive valuesSuction shown as negative values

-0.15

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EUROCODE LOAD COMBINATIONS FOR STEEL STRUCTURES

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

Gkinf = Dead= 0.283 kN/m2

Qk = Imposed load= 0.600 kN/m2

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

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

Applying the loads for the example to the set of serviceabilityequations yields the design loads as summarised in Table 5.2. Thevalues of the EHF will vary with the load combination and may,when HEd ≥ 0.15 VEd, be ignored. The bold figures identify thecritical load combinations.

Table 5.2: Load combinations for the serviceability limit state

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

Wk (suction) = -0.800

Equation 6.14b 0.600 0.250 0.000 0.8500.420 0.500 0.000 0.9200.000 -0.800 0.000 -0.800

The normal roof pitch for portal frame structures in the UK is in therange 5-15°. In this range it is unlikely that the roof will besubjected to wind pressure throughout the span. Hence, all threecombinations to Equation 6.14b must be considered.

Now consider the same example, but removing the load conditionof pressure on the roof – the load combinations of Table 5.2aemerge.

Table 5.2a: Load combinations for the serviceability limitstate (no uniform roof pressure)

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

Equation 6.14b 0.600 0.000 0.000 0.6000.000 -0.800 0.000 -0.800

The designer must be aware of the possible number of wind loadcases to be considered, the above matrix simply presents these asuniform suction or pressure on the roof. In reality the loadingpattern is more complex than this and the following procedure maybe 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)

3. Identify the wind case that results in the maximum eavesdisplacement (side sway). This is likely to be transverse windwith pressure on the windward slope and suction on theleeward slope.

4. Use the wind load cases identified in steps 2 and 3 of thisprocedure in equation 6.14b to identify maximumdisplacements.

5. If frame is unsymmetrical in any way the designer should applythe wind load in the direction to maximise the sway effect.

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

The relevant ψ factors are given in Table 5.1 above.

With the following loading,

Gksup = Dead load + Service load

Gkinf = Dead load

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

Wk = Wind load – 5 load cases, 2 of which can be discardedafter SLS analysis

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

if the typical load cases that were considered for the serviceabilitylimit state are now considered for ultimate limit state with thefollowing possible load combinations result:

6.10 1.35Gksup “+” 1.50Qk “+” 0.00Qk + EHF1.35Gksup “+” 1.50Qk “+” 0.75Wk (pressure) + EHF1.35Gksup “+” 1.05Qk “+” 1.50Wk (pressure) + EHF1.00Gkinf “+” 0.00Qk “+” 1.50Wk (suction) + EHF

6.10a 1.35Gksup “+” 1.05Qk “+” 0.00Wk + EHF1.35Gksup “+” 1.05Qk “+” 0.75Wk (pressure) + EHF1.00Gkinf “+” 0.00Qk “+” 0.75Wk (suction) + EHF

6.10b 1.25Gksup “+” 1.50Qk “+” 0.00Wk + EHF 1.25Gksup “+” 1.50Qk “+” 0.75Wk (pressure) + EHF1.25Gksup “+” 1.05Qk “+” 1.50Wk (pressure) + EHF1.00Gkinf “+” 0.00Qk “+” 1.50Wk (suction) + 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 isbeing considered in combination with wind, and that if the snow load wereto 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 combinationsshould be analysed with the relevant equivalent horizontal force, noting thatthe equivalent horizontal force is 0.5% of the vertical reaction at the columnbase and therefore includes the self weight of any cladding carried by thecolumn, as well as the effects of the wind. The above ultimate limit stateload combinations are implemented in the design example started earlier forthe serviceability limit state. Substituting the loadings for the example intothese equations yields the design loads as summarised in Table 5.3. Thebold figures identify the critical load combinations, assuming that thedesigner will opt for Equations 6.10a and 6.10b at ULS.

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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 = Imposed = 0.600 kN/m2

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

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

Table 5.3: ULS load combinations

Load Gksup = Qk = Wk (pressure) Ad = Design(kN/m2) 0.433 0.600 = +0.500 0.550 load

Gkinf = Wk (suction) (kN/m2)0.283 = -0.800

Equation 6.10 0.585 0.900 0.000 0.000 1.4850.585 0.900 0.375 0.000 1.8600.585 0.630 0.750 0.000 1.9650.283 0.000 -1.200 0.000 -0.917

Equation 6.10a 0.585 0.630 0.000 0.000 1.2150.585 0.630 0.375 0.000 1.5900.283 0.000 -0.600 0.000 -0.317

Equation 6.10b 0.541 0.900 0.000 0.000 1.4410.541 0.900 0.375 0.000 1.8160.541 0.630 0.750 0.000 1.9210.283 0.000 -1.200 0.000 -0.917

Equation 6.11b 0.433 0.000 0.100 0.550 1.083

BS5950-1: 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

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 mostonerous design combination is to be considered.

Portal frame designers will generally set out to provide the mosteconomic frame solution and, given the choice of 6.10 or 6.10aand 6.10b the design loads to be considered in 6.10 are moreonerous and therefore are likely to be ignored. It would appearthat there are more combinations to consider if we apply 6.10a and6.10b but, by observation, 6.10b combinations are more onerousthan those of 6.10a, other than for a high ratio of dead to imposedload (see Section 3.1) which is particularly unlikely for this form ofconstruction.

As shown in Figures 5.1, positive pressure on the whole roof doesnot occur for normal portal frame roof pitches. If this pressure isremoved from the example, the design loads in Table 5.3a result.

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

Load Gksup = Qk = Wk (suction) Ad = Design(kN/m2) 0.433 0.600 = - 0.800 0.55 load

Gkinf = (kN/m2)0.283

Equation 6.10b 0.541 0.630 0.750 0.000 1.9210.283 0.000 -1.200 0.000 -0.917

Equation 6.11b 0.433 0.000 0.000 0.550 0.983

5.3 Portal frames with cranes

The inclusion of one additional imposed load type increases thenumber of possible load combinations since each imposed loadtype has to be considered as the leading or main accompanyingvariable action in turn. The introduction of a crane also increasesthe horizontal loads (both transverse and longitudinally) to becarried by the structure as the crane will generate horizontal surgeloads as it lifts and moves loads around. The crane’s load Qkcconsidered below may therefore have both vertical and horizontalcomponents. The vertical loads are modified by dynamic factorstaken from Table 2.2 of EN 1991-3:2006.

5.3.1 Serviceability limit state designGksup = Dead load + Service load

Gkinf = Dead load

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

Qkc = Crane load (vertical load (including crane self weight) and horizontal surge load)

Wk = Wind load (generally suction) - three load cases

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

Other combinations are possible, but those that are most likely toprovide the critical design condition are as follows:

6.14b 1.00Qk “+” 1.00Qkc “+” 0.50Wk (pressure)0.70Qk “+” 1.00Qkc “+” 0.50Wk (pressure)0.70Qk “+” 1.00Qkc “+” 1.00Wk (pressure) 0.00Qk “+” 0.00Qkc “+” 1.00Wk (suction)

5.3.2 SLS design example for a single span portal withoverhead crane

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

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TYPICAL WELDING PROCEDURE SPECIFICATIONS FOR STRUCTURAL STEELWORK

magnitude of the horizontal load is dependent on factors particularto each project.

Assume that the crane is supported centrally on bogies with a3.6m wheel base. If one wheel is positioned directly on the lineof the portal, the second wheel is 3.6m into the span and hencethe maximum reaction to the portal is 1+2.4/6.0 = 1.4 times thewheel 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.

Figure 5.3: Typical clear span portal frame with travellingoverhead crane

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

Gkinf = Dead = 0.283 kN/m2

Qk = Imposed load= 0.600 kN/m2

Qkc = Max / min crane wheel loads= 56.0 / 17.5 kN

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

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

Substituting the loadings for the example into these equationsyields the design loads as summarised in Table 5.4. The bold andshaded figures identify the critical load combinations.

Table 5.4: SLS load combinations

Load Qk = Wk (pressure) Ad = Design Qkc =(kN/m2) 0.600 = +0.500 0.550 load 56.0/

Wk (suction) (kN/m2) 17.5kN= -0.800

Equation 6.14b 0.600 0.250 0.000 0.850 56.0 /17.50.420 0.250 0.000 0.670 56.0 /17.50.420 0.500 0.000 0.920 56.0 /17.50.000 -0.800 0.000 -0.800 0.000

5.3.3 Ultimate limit state (STR)The number of load combinations again increases because of theaddition of the load from the crane. The individual load cases areas follows:

Gksup = Dead load + Service load

Gkinf = Dead load

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

Qkc = Crane load (vertical load on columns with horizontalsurge loads)

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

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

When each load combination is considered with respect toEquations 6.10, 6.10a, 6.10b and the accidental condition thefollowing combinations result:[For the accidental combinations, ψ2 = ratio of the permanentcrane action and the total crane action = 50/125 = 0.40 (ClauseA.2.3 from EN 1991-3 Annex A)].

6.101.35Gksup “+” 1.50Qk “+” 1.50Qkc “+” 0.00Wk (suction) “+” EHF1.35Gksup “+” 1.50Qk “+” 1.50Qkc “+” 0.75Wk (pressure) “+” EHF1.35Gksup “+” 1.05Qk “+” 1.50Qkc “+” 0.75Wk (pressure) “+” EHF1.35Gksup “+” 1.05Qk “+” 1.50Qkc “+” 1.50Wk (pressure) “+” EHF1.00Gkinf “+” 0.00Qk “+” 0.00Qkc “+” 1.50Wk (suction) “+” EHF

6.10a1.35Gksup “+” 1.05Qk “+” 1.50Qkc “+” 0.00Wk (suction) “+” EHF1.35Gksup “+” 1.05Qk “+” 1.50Qkc “+” 0.75Wk (pressure) “+” EHF1.00Gkinf “+” 0.00Qk “+” 0.00Qkc “+” 0.75Wk (suction) “+” EHF

6.10b1.25Gksup “+” 1.50Qk “+” 1.50Qkc “+” 0.00Wk (suction) “+” EHF1.25Gksup “+” 1.05Qk “+” 1.50Qkc “+” 0.75Wk (pressure) “+” EHF1.25Gksup “+” 1.05Qk “+” 1.50Qkc “+” 1.50Wk (pressure) “+” EHF1.00Gkinf “+” 0.00Qk “+” 0.00Qkc “+” 1.50Wk (suction) “+” EHF

Accidental 6.11b Gksup “+” 1.00Ad “+” 0.00Qk “+” 0.40Qkc “+” 0.00Wk (pressure) “+” EHFGksup “+” 1.00Ad “+” 0.00Qk “+” 0.90Qkc “+” 0.00Wk (pressure) “+” EHFGksup “+” 1.00Ad “+” 0.00Qk “+” 0.40Qkc “+” 0.20Wk (pressure) “+” EHF

5.3.4 ULS design example for a single span portal withoverhead crane

Substituting the loadings for the example into these equationsyields the design loads as summarised in Table 5.5. The boldfigures identify the critical load combinations.

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Table 5.5: ULS load combinations

Load Gksup = Qk = Wk (pressure) Ad = Design Qkc =(kN/m2) 0.433 0.600 = +0.500 0.550 load 56.0/

Gkinf = Wk (suction) (kN/m2) 17.5kN0.283 = -0.800

Equation 6.10 0.585 0.900 0.000 0.000 1.485 84.0 / 26.250.585 0.900 0.375 0.000 1.860 84.0 / 26.250.585 0.630 0.375 0.000 1.590 84.0 / 26.250.585 0.630 0.750 0.000 1.965 84.0 / 26.250.283 0.000 -1.200 0.000 -0.917 0.00

Equation 6.10a 0.585 0.630 0.000 0.000 1.215 84.0 / 26.250.585 0.630 0.375 0.000 1.590 84.0 / 26.250.283 0.000 -0.600 0.000 -0.317 0.000

Equation 6.10b 0.541 0.900 0.000 0.000 1.441 84.0 / 26.250.541 0.630 0.375 0.000 1.546 84.0 / 26.250.541 0.630 0.750 0.000 1.921 84.0 / 26.250.283 0.000 -1.200 0.000 -0.917 0.00

Equation 6.11b 0.433 0.000 0.000 0.550 0.983 50.4 / 15.750.433 0.000 0.100 0.550 1.083 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.

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[1] Steel Building Design: Introduction to the Eurocodes, SCIPublication P361, The Steel Construction Institute, 2009.

[2] Steel Building Design: Concise Eurocodes, SCI PublicationP362, 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 andEire: Ground snow load map. The Structural Engineer (Vol;80, Issue: 12).

[5] Cook, N. (2007). Designers’ Guide to EN 1991-1-4 Eurocode1: Actions on structures, general actions - Part 1-4. Windactions. Thomas Telford Ltd.

[6] Wind loading on buildings, BRE, Digest 436, The BuildingResearch Establishment, 1999.

[7] Gulvanessian, H., Calgaro J.-A. and Holický, M. (2002).Designers’ Guide to EN 1990 Eurocode: Basis of StructuralDesign. 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. ECCSPublication No. 119. ECCS Technical Committee 8 – Stability.

[9] Roof loads due to local drifting of snow, BRE Digest 439, TheBuilding 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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