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HB 48—1999

STEEL STRUCTURES DESIGN HANDBOOK

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National Library of AustraliaCataloguing in Publication DataSteel Structures Design HandbookStandards Australia1 The Crescent, Homebush NSWISBN 0 7337 2754 9Copyright – Standards AustraliaFirst published 1993Second edition 1999

Copyright STANDARDS AUSTRALIA

Users of Standards Australia publications are reminded that copyright subsists in all Standards Australia publications and software.Except where the copyright Act allows and except where provided for below no publications or software produced by StandardsAustralia may be reproduced, stored in a retrieval system in any form or transmitted in any means without prior permission inwriting from Standards Australia. Permission may be conditional on an appropriate royalty payment. Requests for permission andinformation on commercial software royalties should be directed to the Head Office of Standards Australia.

Standards Australia will permit up to 10 percent of the technical content pages of this Handbook to be copied for use exclusively in-house by purchasers of the Handbook without payment of a royalty or advice to Standards Australia.

Standards Australia will also permit the inclusion of its copyright material in computer software programs for no royalty payment provided such programs are used exclusively in-house by the creators of the programs.

The use of material in print form or in computer software programs to be used commercially, with or without payment, or incommercial contracts is subject to the payment of a royalty. This policy may be varied by Standards Australia at any time.

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STEEL STRUCTURES DESIGN HANDBOOK

Edited by:

L. PhamP. BoxhallD. Mansell

PublishersStandards Australia

1 The Crescent, HomebushNSW Australia 2140

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The first edition of this Handbook was prepared by a consortium of design,construction and research engineers.

This Edition has been reviewed by the Institution of Engineers Australia’s National Committeeon Structural Engineering.

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CONTENTSPage

Preface viiNotation ixIndex xiii

Part I Simplified Design Rules

Chapter1 Scope and General 22 Materials 43 Design 64 Methods of Structural Analysis 145 Members Subject to Bending 216 Members Subject to Axial Compression 417 Members Subject to Axial Tension 508 Members Subject to Combined Action 519 Connections 52

10 Brittle Fracture 6411 Fatigue 65

AppendixA Alternative Method for Moment Amplification 67B Alternative Method for Members Subject to Combined Actions 73

Part II Design Aids

Connection Capacity, Bolts D1Connection Capacity, Welds D2Universal Section Capacities D3-D4Welded Section Capacities D5-D6Design Moment Capacity of Universal Sections for Given Effective Length

D7-D16

Design Moment Capacity of Welded Sections for Given Effective Length

D17-D24

(continued overleaf)

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Part III Worked Examples

Introduction

1 Example 1Design of Elements of a Braced Frame• Problem 1.1

Design of a Simply-Supported BeamE1/2

• Problem 1.2Design of a Simply-Supported Beam with AxialCompression

E1/4

• Problem 1.3Design of a Column with Biaxial Bending

E1/6

2 Example 2Design of Elements of a Portal Frame• Problem 2.1

Design of a Member Under Combined Compression andBending

E2/1

• Problem 2.2Design of the Rafter and a Column Under Tension

E2/4

• Problem 2.3Design of a Haunch

E2/5

3 Example 3Design of a Roof Truss• Problem 3.1

Design of a Web MemberE3/1

• Problem 3.2Design of a Bottom Chord

E3/2

• Problem 3.3Design of a Top Chord

E3/3

4 Example 4Design of a Transporter Support Beam• Problem 4.1

Bearing Capacity Under Wheel LoadE4/2

• Problem 4.2Bending Strength of a Cantilevered Beam

E4/3

• Problem 4.3Design of Web Stiffeners at Beam Support

E4/4

• Problem 4.4Assessment of Fatigue Life

E4/6

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PREFACE

This second edition of the Handbook is an update of the 1993 edition to incorporate:• The amendments to the Steel Structures Standard embodied in AS 4100—1998• The replacement of BHP Grade 250 steel sections with 300PLUS sections• Changes to the available range of sizes of BHP steel sections.

As a consequence of 300PLUS becoming the standard grade for hot-rolled steelsections, most rules, tables, design aids and examples relating to sections of grade 250have been replaced with ones corresponding to grade 300. Designers requiringinformation relating to grade 250 should consult the 1993 edition.

The preface to the 1993 edition outlines the essential features of the Handbook and isreproduced below. It is unchanged apart from an updating of the recommendedpublications in the final paragraph.

Preface to the 1993 edition

The first Australian Limit States Design Standard for Steel Structures, AS 4100—1990,incorporates material which permits a more advanced approach to some designproblems than is found in most other Standards. It is written in such a way that, in someinstances, designers may choose to use simpler options with some penalty in the designcapacity of the members in the sense that their design would be more conservative.Incorporating various tiers of design in one Standard may make the total document lessconvenient than it could be for those designers who wish to do most of their work in thelower tier mode.

To overcome this drawback, this Handbook offers a lower tier design method on itsown, providing rules and procedures which will result in designs fulfilling therequirements of AS 4100. The reader will find the appropriate cross-referencing toAS 4100 which may be needed in some circumstances.

The use of AS 4100 may enable the designer to justify a greater capacity in a givenmember than can be demonstrated by the use of this Handbook. There is therefore aprice to be paid for the simplicity of the rules contained herein. In most instances,however, the effect on the combined cost of design and materials will be marginal.

The Handbook contains three parts and each member of the consortium of engineerswho wrote it participated as author of the design rules, or author of the workedexamples, or as editorial adviser representative of future users. Therefore, theconsortium includes research engineers from CSIRO and the universities, and designersfrom large and small practices, and from the construction and fabrication industries. It isbelieved that the outcome is a book which is technically sound, and well-suited to useby a designer who wishes to make decisions with minimal design aids and only a hand-held calculator. The users of this Handbook are assumed to be qualified to undertakestructural design.

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Part I of the book provides advice and rules in a structure similar to that of the firsteleven sections of AS 4100. The chapter and paragraph numbers, titles, and notation,are kept as close to those of AS 4100 as possible so that designers can move readilyfrom one document to the other in order to use the tier of their choice.

Chapter 1 sets out the scope and the limitations for the use of this Handbook andChapter 2 lists the relevant standards with which the materials should comply.

Chapter 3 describes the difference between Working Stress and Limit States Design anddescribes the classes of Limit States which should be anticipated. It also setsserviceability limits. Chapter 4 defines the methods of analysis for the purposes ofobtaining design effects and displacements, the forms of construction, the assumptionsfor analysis and the limitations to the use of plastic analysis in this Handbook.

Chapters 5 to 8 provide rules and procedures for calculating the strength of memberssubjected to flexural, compressive, tensile and combined actions. Chapter 9 recognizesthe fact that a large part of Australian structural practice uses a very limited and discreterange of fasteners. It therefore also contains simple tables of bolt and weld capacities,and of the relevant geometric data on hole sizes and edge distances.

Chapter 10 identifies circumstances under which brittle fracture is not likely to be aproblem. Chapter 11 presents a simplified approach to design against fatigue. Advice isgiven only on situations where the stress range is constant and material is thin. The formof expression of the S-N curves is simplified by changing the definition of the detailcategory to reduce the number of ‘variables’ in the equations. The structure ofChapter 11 is such that the designer will often be able quickly to exempt the detail fromfatigue analysis with little or no computation. A more fundamental change inphilosophy is that the Handbook enables the designer to calculate the life of the detailwhen it is fatigue-prone.

Part II is a set of design aids in the form of tables and charts derived from thedimensions of standard sections and from the rules in the Chapters of this Handbook.They speed up the design process and reduce the opportunity for computational error.

Part III consists of worked examples of the application of the rules in Part I. Theexamples are chosen to demonstrate realistic situations and have been worked out bydesigners in active commercial practice.

Users of the Handbook are expected to have a copy of the tables of section properties(published by BHP under the title Hot Rolled and Structural Steel Products 1998), andwould find their work expedited even further by having access to Design CapacityTables for Structural Steel, 2nd ed, Vol 1: Open Sections published in 1994 by theAustralian Institute of Steel Construction (AISC) and DuraGal Design Capacity Tablesfor Steel Hollow Sections produced in 1996 by Tubemakers Structural and PipelineProducts (now BHP Structural and Pipeline Products). For reference to higher tiermethods, designers should use this Handbook together with AS 4100.

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NOTATION

Ac = minor diameter area of a bolt, as defined in AS 1275Ag = gross area of a cross-sectionAn = net area of a cross-section; or

= sum of the net areas of the flanges and the gross area of the webAo = plain shank area of a boltA

s = tensile stress area of a bolt as defined in AS 1275; or

= area of a stiffener or stiffeners in contact with a flange; or= area of an intermediate web stiffener

Aw = gross sectional area of a webae = minimum distance from the edge of a hole to the edge of a ply

measured in the direction of the component of a force plus half thebolt diameter

b = width; or= clear width of an element outstand from the face of a supporting

plate element; or= clear width of a supported element between faces of supporting

plate elementsbb, bbf = bearing widths defined in Para. 2.2.3bes = stiffener outstand from the face of a webbf = width of an RHS Sectionbs = stiff bearing lengthbw = depth of an RHS Sectioncm = factor for unequal momentsd = depth of a section; or

= depth of preparation for incomplete penetration butt weld; or= maximum cross-sectional dimension of a member

df = diameter of a fastener (bolt or pin)dh = hole diameterdo = overall section depth including out-of-square dimensions; or

= overall section depth of a segment; or= outside diameter of a circular hollow section

dp = clear transverse dimension of a web paneldv = coped web depthd1 = depth of a webd3, d4 = depths of preparation for incomplete penetration butt weldsE = young’s modulus of elasticity, 200 × 103 MPaF* = total design load on a member between supportsfu = tensile strength used in designfuf = minimum tensile strength of a boltfup = tensile strength of a plyfuw = nominal tensile strength of weld metalfy = yield stress used in designfys = yield stress of a stiffener used in designf3 = detail category fatigue strength at constant amplitude fatigue limitf* = design stress rangeG = shear modulus of elasticity, 80 × 103 MPa; or

= nominal dead loadGR = part of the dead load tending to resist instability

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H* = design horizontal forceh = height to the eave of a portal framehs = storey heightI = second moment of area of a cross-sectionIc = I of a columnIr = I of a rafterIs = I of a pair of stiffeners or a single stiffener about centreline of webIw = warping constant for a cross-sectionIy = I about the cross-section minor principal y-axisJ = torsion constant for a cross-sectionk = modifying factorke = member effective length factorkf = form factor for members subject to axial compressionkh = factor for different hole types

= load height effective length factor= factor for pin rotation= effective length factor for restraint against lateral rotation; or= effective length factor for a restraining member; or

kl = load height factorkr = lateral rotation restraint factor

= reduction factor to account for the length of a bolted or welded lapsplice connection

kss = factor for type of shear stress distributionkt = twist restraint effective length factor; or

= correction factor for distribution of forces in a tension memberl = span; or

= member length; or= segment or sub-segment length

lb = length between points of effective bracing or restraintlc = distance between adjacent column centresle = effective length of a compression member = kel; or

= effective length of a laterally unrestrained memberle/r = geometrical slenderness ratiolh = slotted hole lengthlj = length of a bolted lap splice connectionlw = greatest internal dimension of an opening in a web; or

= length of a fillet weld in a welded lap splice connectionMb = nominal member moment capacityMbx, Mby = Mb about major principal x-axis, and minor principal y-axis,

respectivelyMo = nominal out-of-plane member moment capacity; or

= reference elastic buckling moment for a member subject tobending

Mox = enhanced nominal out-of-plane member moment capacity aboutmajor principal x-axis

Mrbx, Mrby = reduced nominal capacity in bending of member about major x-axis and minor y-axis, respectively

Mrsx = Ms about major principal x-axis reduced by axial forceMrsy = Ms about minor principal y-axis reduced by axial forceMs = nominal section moment capacity

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Msx = Ms about major principal x-axisMsy = Ms about minor principal y-axisMtx = lesser of Mrsx and Mox

M* = design bending moment (amplified from first order analysis)M*

m = maximum calculated design bending moment along the length of amember or in a segment using first order analysis

M*x = design bending moment about major principal x-axis

M*y = design bending moment about minor principal y-axis

Nc = nominal member capacity in compressionNomb = elastic flexural buckling load for a braced member (= π2 EI/(kel)

2)Ns = nominal section capacity of a compression member; or

= nominal section capacity for axial loadNt = nominal member capacity in tensionNtf = nominal tension capacity of a boltnti = minimum bolt tension at installation; or

tension induced in a bolt during installationN* = design axial force, tensile or compressiveNtf

* = design tensile force on a boltnei = number of effective interfacesni = number of stress cyclesnn = number of shear planes with threads intercepting the shear plane

= for bolted connectionsnx = number of shear planes without threads intercepting the shear

plane for bolted connectionsnmax = maximum number of stress cyclesPc = the average of the computed first order compression forces in the

columns of a portal framePr = the average of the computed first order compression forces in the

rafters of a portal frameQ = nominal live loadQ* = design transverse force; or

= design live loadr = radius of gyrationR = nominal total design resistanceRbb = nominal bearing buckling capacityRby = nominal bearing yield capacityRsb = nominal buckling capacity of a stiffened webRsy = nominal yield capacity of a stiffened webR

u = nominal capacityR* = design bearing force; or

= design reactionry = radius of gyration about minor principal y-axisS* = design actions = length of rafter from eave to ridget = thickness; or

= thickness of thinner part joined; or= wall thickness of a circular hollow section; or= thickness of an angle section

tf = thickness of a flange; or= thickness of the critical flange

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tp = thickness of a ply; or= thickness of thinner ply connected; or= thickness of a plate

ts = thickness of a stiffenertt, tt1, tt2 = design throat thickness of a weldtw = thickness of a webVb = nominal bearing capacity of a ply or a pin; or

= nominal shear buckling capacity of a webVf = nominal shear capacity of a bolt or pin—strength limit stateVsf = nominal shear capacity of a bolt—serviceability limit stateV* = design shear force; or

= design horizontal storey shear force at lower column end; or= design transverse shear force

V*b = design bearing force on a ply at a bolt or pin location

V*f = design shear force on a bolt or a pin—strength limit state

V*sf = design shear force on a bolt—serviceability limit state

Vx1, Vx2, Vx3 = design shear capacity for uncoped and coped beam websWu = wind load for the strength limit stateWs = wind load for the serviceability limit stateZe = effective section modulusZmin = elastic section modulus for an angle about relevant axis normal to

leg and perpendicular to load

αb = compression member section constant, as defined in Para. 6.3.3αc = compression member slenderness reduction factorαm = moment modification factor for bendingαs = slenderness reduction factorαv = shear buckling coefficient for a webβe = modifying factor to account for conditions at the far ends of beam

membersβm = ratio of smaller to larger bending moment at the ends of a memberγ, γ

1, γ

2= ratios of compression member stiffness to end restraint stiffness

used in Para. 4.6.3.3∆s1 = 1st order sway displacement ∆s of top relative to the bottom

storey height∆s2 = 2nd order sway displacement ∆sδb = moment amplification factor for a braced memberδm = moment amplification factor, taken as the greater of δb and δsδs = moment amplification factor for a sway memberλc = elastic buckling load factorµ = slip factorφ = capacity factorψc = live load combination factor used in assessing the design load for

strength limit stateψs = short-term live load factor used in assessing the design load for

serviceability limit state

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INDEX

Action

combined Chapter 8

design 3.1

nominal 3.1 other 3.2.2

Amplification 4.4.2, Appendix A

Analysis

assumptions for 4.3

elastic 4.4

plastic 4.5

Angle

bending 5.1.7

compression 6.6

Area

effective 6.2

gross 6.2, 7

net Chapter 7

Beam Chapter 5

Bearing

web 5.2.3

bolt 9.2.3

Bending Chapter 5

biaxial Chapter 8

Bolt 9.2

Braced member 4.4.2, A1

Bracing 5.1.6

Brittle fracture Chapter 10

Capacity factor Table 3.1

Column Chapter 6

Combined actions Chapter 8, App B

Compression member Chapter 6

form factor 6.2

section constant Table 6.2

slenderness reduction factor Table 6.3

effective length 6.5

Connection Chapter 9

minimum design action 9.1

shear 9.4

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Corrosion 3.5.5

Critical flange Fig. 5.1

Deflection 3.5.2, Table 3.2

Design Chapter 3

Detail category Table 11

Eccentricity 4.3.2

Edge distance 9.2.2

Effective length

bending 5.1.5

compression 6.5

Elastic analysis 4.4.1

Fatigue Chapter 11

Form of construction 4.2

rigid 4.2.1

simple 4.2.1, 4.3.2

Frame 4.4.2

Hole 9.2.1

Hollow section

circular 5.2.2, Table 6.2

rectangular 5.1.4.2, Table 5.1, Table 6.2

Lateral buckling 5.1.5

Limit state Chapter 3

serviceability 3.5, 5, 9.2.4

stability 3.3

strength 3.4, 5, 6, 7, 8, 9, 9.2.3, 9.4

Limitation 1.2, 5.1.1

Load 3.2.1

arrangement of live 4.3.3

bearing stiffeners 5.2.4

combinations 3.3

design 3.2.1

Load height 5.1.5

Materials Chapter 2

Member 4, 5, 6, 7, 8

bending Chapter 5

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braced 4.4.2

compression 4.4.2, 4.4.3, 6

parallel restrained 5.1.6

sway 4.4.2

tension Chapter 7

Moment amplification 4.4.2, Appendix A

Moment connection 4.5.1

Moment capacity

member 5.1.2, 5.1.4

section 5.1.3

slenderness reduction factor 5.1.2, 5.1.4.1, 5.1.4.2

moment modification factor 5.1.2, Fig. A1

Pitch 9.2.2

Plastic analysis 4.1, 4.5

Restrained cross-section 5.1.5

fully lateral 5.1.4.1

Restrained member, parallel 5.1.6

Restraint

compression member 6.5.1

full lateral 5.1.4.1, 5.1.6

immediate lateral 5.1.5

lateral deflection 5.1.5, 6.5.1

lateral rotation 5.1.5

partial 5.1.5

torsional end 5.1.5, 5.2.4

twist rotation 5.1.5, 5.1.6

Second-order effect 1.1, 4.4

Section

angle 5.1.7

capacity 5.1.3

circular hollow 5.1.1

compact 5.1.1

non-compact 5.1.1

rectangular hollow 5.1.4., 5.1.4.2

Section modulus 5.1.3

Shear capacity

bolt 9.2.3, 9.2.5

web 5.2.2

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Shear connection capacity 9.4

single angle cleat Table 9.4.1

double angle cleat Table 9.4.2

flexible end plates Table 9.4.3

bearing pad Table 9.4.4

angle seat Table 9.4.5

web side plate Table 9.4.6Shear stress distribution Fig. 5.6Slenderness compression member 6.4, 6.5

flexural member 5.1.4, 5.1.5, 5.1.6

plate or section element Table 5.1, Table 6.1

web 5.2

Slenderness reduction factor 5.1.4.1, 5.1.4.2

compression member 6.4, Table 6.3Slip 9.2.4, 3.5.4, Table 3.1Slip factor 9.2.4Steel

grade Chapter 2

strength Table 2.1

type Table 2.1

Stiffener 5.2.4

Stress cycle Chapter 11

Stress range Chapter 11

Sway 4.4

Temperature (design service) Chapter 10

Tensile strength 2.2, 9.2.1, 9.3.2

Tension Chapter 7

Tension (minimum bolt) 9.2.5

Tension capacity

bolt 9.2.3

section Chapter 7

Tension member Chapter 7

Tensioning (snug tight) 9.2.1

Thickness

design throat of weld 9.3.2

effect on yield stress Table 2.1

Triangulated structure 4.4.1, 6.5.2, 6.6

Unrestrained cross-section 5.1.5

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Web

design 5.2

transversely stiffened 5.2.1

unstiffened 5.2.1

Weld

butt 9.3.1

category Table 3.1

fillet 9.3.2

GP (general purpose) Table 3.1

incomplete penetration Table 9.3.1

SP (special purpose) Table 3.1

size 9.3.1, 9.3.2

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PART I

SIMPLIFIED DESIGN RULES

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1 SCOPE AND GENERAL

1.1 SCOPE

AS 4100 Ref.

This Handbook gives simplified rules and procedures for the design of alimited range of steel structures. The exclusions are given in Para. 1.2; otherlimitations to the use of the Handbook are given at the appropriate sections.The rules are based on and comply with Australian Standard AS 4100—1998.

1.1

The Handbook is not a comprehensive textbook; nor is it a commentary on AS 4100 except to the extentneeded to facilitate the use of the Standard itself. Because it is a Handbook and not a Standard, themandatory ‘shall’ is not used unless the rule is quoted verbatim from AS 4100, in which case it isidentified by an asterisk in the AS 4100 Reference marking. Only AS 4100 has the authority to assertmandatory requirements for design. If a designer chooses to act beyond the advice offered here, it isnecessary to ensure that such action is not beyond the mandatory limits set out in AS 4100. Any part ofAS 4100 may be used and the outcome substituted safely in a procedure based on this Handbook. While adesign determined with this Handbook complies with AS 4100, the reverse is not necessarily so.

The rules in this Handbook are intended to be self-sufficient for application in the design of a wide rangeof common structures which do not need or justify the refined methods of a higher tier design. Suchapplications are found in domestic structures, in low-rise buildings, in fully braced situations and inindustrial structures where the designer is confident that second-order effects can be ignored.

The main objective of this Handbook is simplicity, which is achieved by restricting the ranges of cross-sections and of materials to which the rules apply; members and materials produced in accordance withAustralian Standards mostly fall inside these restrictions, and specific exclusions, such as members withslender elements, are set down clearly in the rules.

Simplicity is bought at a price. Correspondingly, the effort incurred in using the higher tiers of AS 4100must be expected to offer some gain and, therefore, designs prepared by using this Handbook willfrequently be able to be refined by using AS 4100.

Throughout the Handbook, the rules are given in boxes in the text in order to make them easy tofind and read. The appropriate cross-referencing to AS 4100 is given in a marginal box adjacent tothe rule, and commentary is provided immediately under the text of the rule. This pagedemonstrates such a format. The rules given in the boxes either comply with or are conservativewith respect to AS 4100. However, it should be noted that some of the simple approximationsprovided in the commentary are intended for preliminary design only, and are not alwaysconservative.

A lower tier design method differs from a higher tier one in the way in which it assures the reliability ofthe structure being designed. Higher tier methods are designed to use more sophisticated models ofstructural behaviour so that the outcome is a structure which can be more severely loaded but still haveacceptable reliability. In Chapter 4, a more detailed commentary is given on restricting lower tier methodsto structures for which second-order analysis is not necessary.

An example of the limitations of a lower tier approach is to be found in the way this Handbook handlesyield stress. Advice is given in some rules for a specific yield stress of 300 MPa only. By contrast,AS 4100 gives the engineers the flexibility of selecting a value of yield stress to use in an algebraicexpression. A second example is the limitations of the advice on fracture-sensitive structures.

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1.2 EXCLUSIONS

AS 4100 Ref.

This Handbook is not intended for use outside the limits given in thetext, nor is it intended for:

(a) Lattice towers fabricated from angle sections*

(b) Cranes and crane beams†

(c) Buildings for which analysis for earthquake forces is required byAS 1170.4‡

(d) Vehicular bridges

(e) Arches

(f) Tall, wide, multistorey frames more than 10 storeys high and5 bays wide

(g) Structures fabricated from unidentified materials§

(h) Non-standard fabricated sections

(i) Fasteners other than those specified in Para. 2.3 of this Handbook

(j) Other structures and materials listed in Clause 1.1.1 of AS 4100,viz.

• Steel elements less than 3 mm thick, with the exception ofsections complying with AS 1163

• Steel members for which the design yield stress exceeds450 MPa

• Cold-formed members, other than those complying withAS 1163, which must be designed in accordance withAS/NZS 4600

• Composite steel-concrete members, which must be designedin accordance with AS 2327.

* Refer to AS 3995

† Refer to AS 1418.1 and AS 3500 respectively

‡ Refer to AS 1170.4

§ Refer to Clause 2.2.3 of AS 4100

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2 MATERIALS

2.1 AUSTRALIAN STANDARDS FOR STEEL

AS 4100 Ref.

Before fabrication, all structural steel coming within the scope ofthis Handbook is required to comply with the following AustralianStandards:

2.2.1

AS 1163 Structural steel hollow sections

AS/NZS 3678 Structural steel—Hot-rolled plates, floor plates andslabs

AS/NZS 3679 Structural steelPart 1: Hot-rolled bars and sectionsPart 2: Welded I sections

2.2 YIELD STRESS AND TENSILE STRENGTH OFSTEEL

AS 4100 Ref.

The yield stress fy and tensile strength fu used in design may beobtained from Table 2.1.

2.1

2.3 STEEL BOLTS, NUTS AND WASHERS

AS 4100 Ref.

Steel bolts, nuts and washers complying with AS/NZS 1111 ISOmetric hexagon commercial bolts and screws and AS/NZS 1112ISO metric hexagon nuts, including thin nuts, slotted nuts and castlenuts, and AS/NZS 1252, High strength steel bolts with associatednuts and washers for structural engineering, are suitable forconstruction based on this Handbook.

2.3.1

2.4 WELDS

AS 4100 Ref.

Welds complying with AS/NZS 1554.1 Structural Steel welding,Part 1: Welding of steel structures are suitable for constructionbased on this Handbook.

2.3.3

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Table 2.1 Strengths of steel complying with AS 1163,AS/NZS 3678 and AS/NZS 3679.1

FormSteelgrade

Thicknessof

material (t)

Yieldstress

fy

Tensilestrength

fu

SteelStandard

(mm) (MPa) (MPa)

Rolledsections

300 or300 LO or300 L15

t ≤ 1111 < t ≤ 17

17 ≤ t

320300280

440440440

350 or350 LO or350 L15

t ≤ 1111 < t ≤ 40

40 ≤ t

360340330

480480480

AS/NZS 3679.1Structural Steel—Part 1: Hot-rolledbars and sections

250 only 12 < t ≤ 5050 < t ≤ 8080 < t ≤150

250240230

410410410

250 L15 only 12 < t ≤ 5050 < t ≤ 150

250240

410410

Plate 300 or300 L15

8 < t ≤ 1212 < t ≤ 2020 < t ≤ 150

310300280

430430430

350 or350 L15

t ≤ 1212 < t ≤ 2020 < t ≤ 8080 < t ≤ 150

360350340330

450450450450

400 or400 L15

t ≤ 1212 < t ≤ 2020 < t ≤ 50

400380360

480480480

AS/NZS 3678Structural steel—Hot-rolled plates,floor plates andslabs

Hollowsections

C250 orC250 LO

AllAll

250 320

C350 orC350 LO

AllAll

350 430

C450 orC450LO

AllAll

450 500

AS 1163Structural steelhollow sections

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3 DESIGN

3.1 LIMIT STATES DESIGN PRINCIPLES

AS 4100 Ref.

Limit states design requires that structures, including all members andconnections, be designed so that the relevant design resistances are notless than the design actions arising from the design loadings for alllimit states.

3.1

The aim of structural design is to provide a structure which is stable, has adequate strength, is serviceableand durable, and which satisfies other objectives such as economy and ease of construction. This aim isachieved by using the ‘Limit States Design’ method to ensure that the limit states of stability, strength andserviceability are satisfied; a structure is considered to be unacceptable if it does not satisfy each of theselimit states. Conditions for which limit states have been selected take into account the statistical variationswhich occur in both member behaviour and material properties as well as the variations in the loads andactions applied to the structure and the imperfections of modelling of behaviour.

A structure is stable if it does not overturn, tilt or slide throughout its intended life. A structure hasadequate strength and is serviceable if the probabilities of structural failure and of loss of serviceabilitythroughout its intended life are acceptably low. A structure is durable if it withstands the expected wearand deterioration throughout its intended life without the need for undue maintenance.

For strength limit states, the design actions S*, such as bending moments, shear or axial forces, areobtained from the strength combination of dead, live, wind and other loads as specified in AS 1170.1,AS 1170.2, AS 1170.3 and AS 1170.4. The nominal loads provided in these Standards are multiplied bythe appropriate load factors to obtain the design loads (the load factors are generally greater than 1.0).The total design capacity is φRu and is determined in accordance with Para. 3.4.

For serviceability limit states, the design action, such as deflection, sway or bolt slip, is obtained from ananalysis of the structure or the member using the loads and load combinations for the appropriateserviceability limit states. (The load factors for serviceability are generally equal to or less than 1.0.) Thecomputation may be carried out without amplification for second order effects (see Section 4). The totaldesign resistances in this case are the serviceability limits such as those given in Table 3.2.

For stability limit states, the design criteria incorporating the required load combination are specified inAS 1170.1. The total design actions S* are obtained from the components of the loads tending to causeinstability. The total design resistance φR is calculated as 0.8 times the part of the dead load tending toresist instability plus the design capacity φRu of any element contributing toward resisting instability.

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3.2 LOADS AND ACTIONS

3.2.1 Loads

AS 4100 Ref.

The design of a structure should account for all potential loads arisingfrom its operation. These may include construction loads, theappropriate dead, live, wind, earthquake and snow loads specified inAS 1170, crane loads in AS 1418, lift loads in AS 1735 and platform,walkway, stairway and ladder loads in AS 1657. The design loadcombinations are those specified in AS 1170.1 for the appropriatelimit state.

3.2.1

3.2.2 Other actions

AS 4100 Ref.

There are other actions which may need to be considered becausethey may significantly affect the stability, strength or serviceability ofthe structure, including the following:

(a) Foundation movements

(b) Temperature changes and gradients

(c) Axial shortening

(d) Dynamic effects

3.2.13.2.2

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3.3 LOAD COMBINATIONS

AS 4100 Ref.

Load combinations can be obtained from AS 1170.1. For the casesinvolving dead, G, live, Q, and wind loadings, Wu, Ws, therequirements can be expressed by the following:

Load Combinations for Strength Limit State

(a) 1.25G + 1.5Q

(b) 1.25G + Wu + ψCq

(c) 0.8G + 1.5Q(d) 0.8G + Wu

where ψc = 0.0 for non-trafficable roofs

ψc = 0.6 for storage structures

ψc = 0.4 for all other situations

Load Combinations for Serviceability Limit State

(a) Ws(b) Q

(c) G + ψsQ

ψs = 1.0 for storage structures

ψs = 0.7 for all other structures

Design Criteria for Stability Limit State

(a) 1.25G + 1.5Q < 0.8GR + φRu

(b) 1.25G + ψcQ + Wu < 0.8GR + φRu

GR is the part of the dead load tending to resist instability. G, Q, Wuare parts of the dead, live and wind loads that tend to causeinstability.

For the serviceability limit state, the serviceability loads should be appropriate for the serviceabilitycondition. For steel structures, there should not be any long-term structural serviceability problem. Theserviceability loads and load combinations suggested here are the normal load combinations to bechecked for steel structures, but do not cover all the possibilities given in AS 1170.1 (e.g. long-termeffects such as creep). This should serve to remind designers that the load combinations need to beselected depending on the circumstances.

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3.4 STRENGTH LIMIT STATE

AS 4100 Ref.

The structure and its components are designed for the strength limitstate by ensuring that all members and connections are proportionedso that the design capacity φRu is not less than the design action S*

S* ≤ φRu

Specific values of φRu are given in Sections 5 to 9, as appropriate. Asummary of the φ values is found in Table 3.1.

3.4

DESIGN ACTIONS

The design actions S* are the actions such as axial force, shear force and bending moment which areproduced by the design loads. Separate design actions are calculated for each of the limit states.

DESIGN CAPACITIESThe design capacity φRu is obtained from the nominal capacity of the structure or member Ru modified

by a capacity factor φ. The capacity factor φ is always less than unity and reflects the variability anduncertainty of material properties and member behaviour. Significant variation in the value of thecapacity factors is therefore to be expected. In this Handbook the capacity factor is incorporatednumerically in the design rules as printed.

It is important to recognise that the limit states design method has some very significant differences fromthe allowable stress method of design which was used in AS 1250. In the allowable stress method, anelastic analysis is used to determine the design actions under so-called working load conditions, thesebeing roughly comparable to the serviceability loads of the limit state design method. The design actionsare then used with allowable stresses which have been set to provide a margin of safety which is intendedto take account of both overloading and uncertainties of member behaviour and material variations.

This approach is in direct contrast to the limit states design method where load factors are applied to loadsto allow for overloading and load variability; a separate allowance is made to the member behaviourthrough the use of a capacity reduction factor.

It is of utmost importance that the distinction between the two methods is recognised and that the loads,load combinations and design capacities are appropriate to the method used.

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Table 3.1 Capacity factors (φ) for strength limit states(These capacity factors have been incorporated in the design capacity

formulae in this Handbook, and are provided here for information only.)

Design capacity forCapacity factor

φφφφRelevant section

of AS 4100

Structural members and connectioncomponents other than a bolt, pin orweld

0.90 5 to 9

Bolted and pinned connections— ply in bearing— friction-grip with slip— all other conditions

0.900.700.80

9.3 to 9.5

3.5.5

Welded connections— complete penetration butt weld— longitudinal fillet weld in RHS (t < 3 mm)— all other welds

SP*0.900.70

0.80

GP*0.60

-

0.60

9.7.1.39.7.2.7

9.7.3.10

* SP — special purpose weld

GP — general purpose weld

Refer to AS/NZS 1554.1 for definition of SP and GP and for other requirements.

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3.5 SERVICEABILITY LIMIT STATE

3.5.1 General

AS 4100 Ref.

The serviceability limit states to be considered are deflection,vibration, bolt slip and corrosion. The loads and actions are to bedetermined in accordance with Para. 3.2.

3.5.1

3.5.2 Deflection limits

AS 4100 Ref.

Deflections may be determined by the elastic analysis method. Thedeflection limits are the responsibility of the designer and need to beappropriate to the structure and its intended use, the nature of theloading, and the elements supported by it. Guidance on somedeflection limits can be gained from Table 3.2. These may be mid-span deflections for beams, sway deflections for columns, or therelative horizontal deflection between adjacent frames at the eaveslevel of industrial buildings.

App. B

Deflection limits of Table 3.2 are not mandatory in accordance with AS 4100. The footnotes toTable 3.2 give some guide as to the levels of deflection at which different forms of serviceability failuremight occur. In some instances more conservative values may need to be adopted.

For guidance on the deflection limit below which moment amplification may be ignored, refer tocomments in Para. 4.4.2.

3.5.3 Vibration of beams

AS 4100 Ref.

Beams which support floors or machinery shall be checked to ensurethat the vibrations induced by machinery, or vehicular or pedestriantraffic, do not adversely affect the serviceability of the structure.

Where there is a likelihood of a structure being subjected tovibration from causes such as wind forces or machinery, measuresshall be taken to prevent discomfort or alarm, damage to thestructure, or interference with its proper function.

3.5.4*

AS 2670.2 gives guidance for the evaluation of human exposure to whole-body vibrations of the typelikely to be transmitted by structures.

An asterisk (*) on the AS 4100 reference indicates that the paragraph is a direct quotation from AS 4100.

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3.5.4 Slip in bolted connections

AS 4100 Ref.

Chapter 9 assumes that where slip in a bolted connection under theserviceability design loads is to be prevented, the selected fasteners areof grade 8.8/TF.

3.5.5

3.5.5 Corrosion protection

AS 4100 Ref.

Where steelwork in a structure is to be exposed to a corrosiveenvironment, the steelwork needs to be given protection againstcorrosion. Refer to AS 4100 Appendix C and AS/NZS 2312, Guide tothe protection of iron and steel against exterior atmosphericcorrosion.

3.5.6App. C

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Table 3.2 Suggested deflection limits from Appendix B of AS 4100

Type of member Deflection to be considered Deflection limit

500

l

Beam supportingmasonry partitions

Deflection which occurs afterthe attachment of partitions

where provision is made tominimize the effect ofmovement, otherwise

1000

l

All beams Total deflection250

l

Building clad in flexiblesheeting without gantrycranes and withoutinternal partitions againstexternal walls

Relative horizontal deflectionbetween adjacent frames ateaves level of industrialbuilding due to wind load

hs

150

Building with masonrywalls supported bysteelwork

Relative horizontal deflectionbetween adjacent frames ateaves level of industrialbuilding due to wind load

hs

240

Notes1 l/250 limit for all beams may not safeguard against ponding or dynamic response of floors or

problems caused by end rotation on simply supported beams.2 l = span of beam — for cantilevers the value of l to be used in Table 3.2 is twice the cantilever

span.3 hs = storey height.

4 The following behaviour might be expected at the indicated level of deflection:

Typical behaviour DeflectionCracking of brickwork l/1000 not visibleCracking of brittle partition wall hs/500 not visible

General architectural damage, cracking ofreinforced walls

l/300, hs/300 visible

Damage to ceiling and flooring, claddingleakage

Damage to lightweight partitions,display windows, finishes

l/200 to l/300hs/200 to hs/300

visible

Impaired operations of movable components-doors, windows sliding partitions

l/100 to l/200hs/100 to hs/200

visible

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4 METHODS OF STRUCTURAL ANALYSIS

4.1 METHODS OF DETERMINING DESIGN ACTIONS

AS 4100 Ref.

The design actions in a structure and its members and connectionscaused by the design loads may be determined by structural analysisusing the assumptions of Paragraphs 4.2 and 4.3 and one of themethods of

(a) Elastic analysis, in accordance with Para. 4.4 (for strength andserviceability limit states),

(b) Plastic analysis, in accordance with Para. 4.5 (for strength limitstate).

4.1

4.2 FORMS OF CONSTRUCTION ASSUMED FOR ANALYSIS

4.2.1 GeneralAS 4100 Ref.

Structures may be analysed by assuming that both shear and momentare transferred across a connection (rigid construction) or only shearis transferred across a connection (simple construction).

4.2

For design under the simplified conditions applicable to this Handbook, semi-rigid construction is notappropriate.

4.2.2 Design of connections

AS 4100 Ref.

The design of connections should be consistent with the assumptionsmade for structural analysis in Para 4.2.1. Connections in rigidconstruction need to be at least as stiff as the more flexible of the twomembers being connected and to be designed for the maximumexpected loads at the connection.

Connections in simple construction should be capable of transferringthe shear forces acting at an eccentricity appropriate to theconnection detailing. The connection should be capable of deformingto provide the required rotation at the connection, without developinga significant restraining bending moment.

4.2.59.1.2

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4.3 ASSUMPTIONS FOR ANALYSIS

4.3.1 Arrangements of live loads for buildings

AS 4100 Ref.

For building structures, the arrangements of live loads considered inthe analysis shall include at least the following:

(a) Where the loading pattern is fixed, the arrangement concerned.

(b) Where the nominal live load (Q) is variable and not greaterthan three-quarters of the nominal dead load (G), the design

live load (Q*) on all spans.

(c) Where the nominal live load (Q) is variable and exceeds three-quarters of the nominal dead load (G), arrangements for thefloor under consideration consisting of

(i) the design live load (Q*) on alternate spans;

(ii) the design live load (Q*) on two adjacent spans; and

(iii) the design live load (Q*) on all spans.

4.3.3*

The term ‘nominal’ refers to the unfactored values of the loads as given in AS 1170.1The arrangement under (c) above assumes approximately equal spans for beams.

.4.3.2 Simple construction

AS 4100 Ref.

Bending members may be assumed to have their ends connected forshear only and to be free to rotate. In triangulated structures, axialforces may be determined by assuming that all members are pinconnected.

A beam reaction or a similar load on a column shall be taken as actingat a minimum distance of 100 mm from the face of the columntowards the span or at the centre of bearing, whichever gives thegreater eccentricity, except that for a column cap, the load shall betaken as acting at the face of the column, or the edge of the packing ifused, towards the span.

For a continuous column, the design bending moment (M*) due toeccentricity of loading at any one floor or horizontal fame level shallbe taken as:

(a) Ineffective at the floor or frame levels above and below that floor;and

(b) Divided between the column lengths above and below that floor orframe level in proportion to the values of I/l of the column lengths.

4.3.4*

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4.4 ELASTIC ANALYSIS

4.4.1 General

AS 4100 Ref.

The method of elastic analysis can be used generally. In a first orderanalysis, the effects of changes in the geometry on the distribution andmagnitude of design actions are not taken into account; the changes inthe effective stiffness of members due to axial force are neglected. Theeffects of these changes on the first order bending moments are allowedfor by using one of the methods of moment amplification of 4.4.2 orAppendix A, as appropriate. When the moment amplification factor isgreater than 1.4, then a second order analysis is required by AS 4100.

4.4.2.1

For design under the simplified conditions applicable to this Handbook, the determination of designactions may be made by the use of a first order analysis for both the general frame analysis and formember design.

The types of structural systems for which first order frame analysis may be used to determine designaction S* without any corrections for second order effects, include:

(a) triangulated frames in which the member forces are predominantly axial, i.e. where lateralforces acting on the compression chord are negligible.

(b) structures in which there are negligible axial compressive forces.

Structural systems for which a first order frame analysis may need to be modified to account for secondorder effects in order to obtain design actions S* include:

(a) braced rigidly-jointed frames in which sway is negligible but with:

(i) high axial force; and(ii) moments due to lateral loads on members. (Refer Figure 4.1)

(b) unbraced rigidly-jointed frames with:

(ii) high axial forces; and(ii) moments due to sway-displacement. (Refer Fig. 4.2)

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H*

N* N*

Deflections Bending moments

Amplified deflections

(a) First order behaviour

Amplified bending moments

(b) Second order behaviour

H*

N* N*

Note: The symbols used in the above illustrations are defined solely by their use in thesefigures.

FIGURE 4.1 BRACED SYSTEMS

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H*

N* N*

Deflections Bending moments

H*N* N*

Amplified deflections

(a) First order behaviour

Amplified bending moments

(b) Second order behaviour

∆s1

Vs*

h s

Vs*

Vs* = H* /2

Vs* . hs + N*. ∆s2

Vs* . hs

Vs* Vs*

∆s2

Vs* . hs

Note: The symbols used in the above illustrations are defined solely by their use in thesefigures.

FIGURE 4.2 UNBRACED SYSTEM WITH SWAY

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4.4.2 Moment amplification

AS 4100 Ref.

For a member with a design axial compressive force N* and a calculated

design bending moment M*m as determined by the first order analysis,the design bending moment M* may be taken as:

M Mm* *.= 1 1

without any further analysis for amplification provided that thefollowing conditions apply:

(i) For both braced and sway members of grade 300 steel,

3009.0/

27/

*≤≤

s

eNN

rl

where le/r is the member slenderness about the same axis as that aboutwhich the design bending moment is applied and Ns is the nominalcompressive axial section capacity of the member (see Para. 6.2). Forsteel grades other than 300 the above limit is changed by a factor equalto yf/300 .

(ii) For sway members in rectangular frames only

∆s

s

h

vh

F

F≤ ∑

∑0 1.

where ∆s is the horizontal displacement of the top relative to the bottom

of member, hs is the height of the member, and ∑∑

F

Fh

v is the ratio of the

total horizontal loads to the vertical loads above the storey.

If the above limits are not satisfied, a moment amplification analysis inaccordance with AS 4100 is recommended and is explained inAppendix A.

4.4.2.2

Moment amplification can be effectively neglected (M Mm* *.≤1 01 ) if the limits corresponding to the

conditions above are:

s

eNN

rl9.0/

9/

*≤ and

∆s

s

h

vh

F

F≤ ∑

∑0 01.

For preliminary design, moment amplification in a portal frame may be neglected. For a more carefulassessment refer to Appendix A (Para. A3).

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4.5 PLASTIC ANALYSIS

4.5.1 Limitation

AS 4100 Ref.

(a) For the use of this Handbook, plastic analysis may be applied tothe design of beams and portal frames only if the axial forces inthe members are less than 5% of their design axial capacities.

(b) Plastic analysis may be used only for members of hot-formed,doubly symmetric, compact I section with minimum specifiedyield stress not exceeding 450 MPa and complying withAS/NZS 3678 or AS/NZS 3679.1.

(c) All moment connections are limited to full strength momentconnections.

4.5.2

4.5.2 Analysis

AS 4100 Ref.

(a) Design actions may be determined using a rigid plasticanalysis.

(b) The moment capacity of a connection may not be less than thatof the members being connected.

4.5.3

For the type of simplified design applicable to this Handbook, it is preferable to have the hinges inmembers for maximum rotation capacity rather than in the connections.

When plastic design is used, it is essential to ensure the members are fully restrained (as defined in 5.1.5).

In addition, for plastic design of beams, the shear connections at the ends of a beam require adequaterotational capacity so that a plastic hinge can form elsewhere in the beam. This requirement is to beachieved without reducing the connection shear capacity.

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5 MEMBERS SUBJECT TO BENDING

The procedure for checking of members subject to bending is as follows:

(a) Establish the bending moment diagram, the conditions of supports and lateral restraints (seePara. 5.1.5).

(b) For long span beams (say span exceeding 25 times beam depth), first check the serviceabilitylimit of deflection; although the deflection limits are not mandatory according to AS 4100, itwill often be the controlling factor for long span beams.

(c) For other beams, first check the strength limit states:

(i) Member bending capacity• Calculate the section capacity (Para. 5.1.3, Design aids D3-D6) to provide a basic load

capacity irrespective of length.• Calculate the member capacity (Para 5.1.4, Design aids D7-D24), which allows for

member length.• Check the adequacy of the restraining elements (Para 5.1.6).

(ii) Shear capacity (Para 5.2.2, Design aids D3-D6).

(iii) Check the bearing condition at the support (Para 5.2.3) and if necessary provide loadbearing stiffeners (Para 5.2.4, Design aids D3-D6).

5.1 DESIGN FOR BENDING MOMENT

5.1.1 General

(a) Classification of sections

AS 4100 Ref.

Steel sections are classified on the basis of the maximum width-thickness ratios of their compressive elements as specified inTable 5.1

5.2.2

Section in bending with:• maximum (b/t) less than the plastic limit are COMPACT sections• maximum(b/t) less than the yield limit but more than the plastic

limit are NON-COMPACT sections• maximum(b/t) more than the yield limit are SLENDER sections

5.2.35.2.4

5.2.5

Limiting b/t is necessary to avoid local buckling problems which depend on stress levels, plate geometryand boundary conditions.

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(b) Limitations

AS 4100 Ref.

The rules in this section are applicable only for

• SECTION TYPES: Compact or non-compact sections with singleor double symmetry such as Australian standard universal andwelded beams and columns, channels, rectangular and circularhollow sections or angles.

5

• DESIGN METHODS: Elastic design method generally andplastic design for beams and for beam-columns where the axialload is limited to 5% of the design axial capacity. The type ofsections suitable for plastic design requires the width-thicknessratios of both the flange and web components be within theplastic limit of Table 5.1.

4.5.25.10.6

Table 5.1 Limiting width-thickness ratios for elements in flexural compression

(b/t)lim

Plastic limit Yield limitDescription of element

300 350 400 300 350 400

Flanges of universal sections,tee sections and channels(major axis bending)

8 7.5 14 13

Flanges of welded sections(major axis bending)

7 6 12 11

Flanges of universal sectionsand channels(minor axis bending)

8 7.5 22 21

Flanges of welded sections(minor axis bending)

7 6 20 17

Flanges of RHS 25 Grade 450:22

34 Grade 450:30

Angles 8 7.5 22 21

Stems of tees 8 7.5 22 21

Webs 74 69 65 105 97 91

Circular hollow sections(b = do)

Grade 250:42

30 Grade 250:120

85

Table 5.1 is an interpretation of Table 5.2 of AS 4100 as applicable to commonly used types of sectionsusing the grade designation as the yield stress.

If a section is compact, the effective section properties are the same as the gross section properties. If thesection is non-compact or slender, the effective section properties are less than the gross sectionproperties. Note that the minimum radius of gyration ry is based on GROSS section geometry.

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5.1.2 Design requirements

AS 4100 Ref.

When a member is subject to a design bending moment M* about thesection principal axis it is recommended that:

( )sMsbMM α9.09.0* =≤

i.e. eZyfsM α9.0* ≤

whereMb = the nominal capacity of the member in bending

Ms = the nominal capacity of the section in bending about therelevant principal axis as specified in 5.1.3

αs = slenderness reduction factor (as specified in 5.1.4and 5.1.5) which never exceeds 1.0.

5.15.25.6

This is a simplified form of Equation 5.6.1.1(1) of AS 4100 with αm = 1.0, which is conservative for allsituations. Further increase in the design moment capacity for a member lightly restrained is possible byintroducing a factor αm calculated as follows:

α mmM

M M M=

+ +≤1 7

2 52

23

24

2

.

( ) ( ) ( ).

*

* * *

whereMm

* = maximum design bending moment in the segment

M2*,M4

* = design bending moments at the quarter points of the segment

M3* = design bending moment at the midpoint of the segment

Note that (ααααs ααααm) must never exceed 1.0.

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5.1.3 Nominal section capacity

AS 4100 Ref.

The nominal capacity of a section in bending is given by

Ms = fy Ze

where

Ze is the effective section modulus and is given in BHP StructuralProducts Handbook or similar

5.2.35.2.4

Deduction for holes in the computation of the effective sectionmodulus is required by AS 4100 when the hole area exceeds thefollowing percentages of either of the flange areas:

5.2.6

Grade 250 300 350 400

% of hole areas 25 15 11 2

For standard types of sections, refer to the supplier's catalogues for section classification and properties,

e.g.

BHP Hot Rolled and Structural Steel Products 1998 edition;BHP Structural and Pipeline Products – DuraGal design capacity tables:

For steel hollow sections, June 1996.For structural steel angles, channels and flats, July 1997.

For fabricated sections, refer to AS 4100 for the computation of Ze.

5.1.4 Nominal member capacity

AS 4100 Ref.

The nominal capacity of a member in bending is given by

Mb = αs Ms

Where αs is a slenderness reduction factor and is given inPara. 5.1.4.1 and Para. 5.1.4.2. and never exceeds 1.0.

5.6.1

Refer to comments on Para. 5.1.2.

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5.1.4.1 Slenderness reduction factor for members with full lateral restraints

AS 4100 Ref.The slenderness reduction factor αs has the value of 1.0 for: 5.1

• A member bending about its minor principal axis 5.3

• A member with the compression flange continuously restrainedagainst lateral movement

• A member with an effective length le which does not exceed thelimit described below (for determination of le see 5.1.5).

5.3.2.4

Type of section Limiting slenderness ratio(le/ry)

I section, 300 grade 27

Channel section, 300 grade 18

Rectangular hollow section,350 grade

w

f

b

b214

Rectangular hollow section,450 grade

w

f

b

b214

w

f

b

b is the ratio of width to depth of the rectangular hollow section.

For the design of restraining elements refer to Para. 5.1.6.

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5.1.4.2 Slenderness reduction factor for members without full lateral restraints

AS 4100 Ref.

The slenderness reduction factor for members without full lateralrestraint, αs, is given by:

αs

−

+

=

oMsM

oMsM

32

6.0

with

Mo

+=

2

2

2

2

el

wEIGJ

el

yEI ππ

For rectangular hollow sections Iw = 0.

5.6.1.1(a)

The design moment capacities for beams without full lateral restraints are provided in the Design aids D7-D24.

For preliminary design of beams, the following simple approximations for αS may be useful (but notalways conservative):

For I sections—assume αS is 1.0 up to le/ry = 25, then varies linearly to 0.5 at le/ry = 120.

For channel sections—assume αS is 1.0 up to le/ry = 18, then varies linearly to 0.5 at le/ry = 130.

For rectangular hollow sections—assume αS is 1.0 up to le/ry = 50, then varies linearly to 0.75 at le/ry = 500.

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5.1.5 Effective length le of beams for lateral buckling

AS 4100 Ref.

In the design of beams, one of the most important steps is theassessment of the relevant restraints and their location. The primerequirement is that the overall stability of the member must bemaintained, i.e. the rigid body rotation of the cross-section must beprevented for at least one cross-section along the beam or cantileverlength.

Critical flange The critical flange at any cross-section is the flangewhich, in the absence of any restraint at that section, would deflectmost during buckling. The critical flange at any section of a segmentrestrained at both ends is the compression flange.

The member effective length for lateral buckling depends on the typeof the rotational and lateral restraints on the member.

xy

z

Lateral restraint is the restraint of movement of the critical flange inthe direction of the x axis.

Twist restraint is the restraint of rotation of the section about the z axis.

Lateral rotational restraint is the restraint of rotation of the criticalflange about the y axis (see Fig. 5.1(c)).

A section is fully restrained if either—

(a) the critical flange is laterally restrained and the section is fully orpartially restrained against twisting; or

(b) the non-critical flange is laterally restrained and the section is fullyrestrained against twisting (see Fig. 5.1(a)).

A section is partially restrained if the non-critical flange is laterallyrestrained and the section is partially restrained against twisting (seeFig. 5.1(b)).

5.45.6.3

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5.1.5 Effective length le of beams for lateral buckling (continued)

AS 4100 Ref.

The general procedure for determining effective length le for lateralbuckling is as follows:

Classify the type of restraints for each end of the beam segments underconsideration as fully restrained, partially restrained or laterallyrestrained as shown in Figure 5.1(a) and (b).

Effective length le for lateral buckling is given by:

le = kt kl kr l

Twist restraint factor kt is to be taken as 1.0 unless the segment has oneor both ends partially restrained, in which case kt is greater than 1.0.

For universal beams or columns with span/depth ratios greater than 6,it is conservative to assume:

For one end partially restrained kt = 1.1

For both ends partially restrained kt = 1.2

Load height factor kl is to be taken as 1.0 unless the load is on the topflange and free to move laterally and

One end unrestrained kl = 2.0

Both ends restrained kl = 1.4

Lateral rotation restraint factors kr are to be taken as 1.0 unless it is asegment with each end fully or partially restrained and:

One end with lateral rotation restraint k = 0.85

Both ends with lateral rotation restraint kr = 0.70

5.45.6.3

For beams and cantilevers with restraints at both ends, the effective length for lateral buckling is given inFig. 5.2 for cases in which the loads are applied at the shear centres of the sections.

Fig. 5.3 gives further examples of types of restraints occurring in practice. These examples have beenobtained from Steel Designers Handbook by Gorenc and Tinyou.

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Web stiffener

C

C

x

z

x

z

Rotationallyrestrainedflange

Rotationallyunrestrainedflange

Buckling shape of flange

Buckling shape of flange

Flexible

Web stiffener

Stiff

Web stiffener

Flexible

C

C

C

Flexible

C

Flybrace

StiffC

Flybrace

FlexibleC

Flybrace

LEGEND= Pin connection= Moment connection= Critical flangeC

(a) Fully restrained cross sections

(b) Partially restrained cross sections

(c) Rotationally restrained and unrestrained flanges

FIGURE 5.1 DEFINITIONS OF FULLY, PARTIALLY AND ROTATIONALLYRESTRAINED CROSS-SECTIONS

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(a) Continuous lateral restraint le = 0

or

(b) Fully restrained ends without intermediate restraints le = l

(c) Partially restrained ends without intermediate restraints le = 1.2 l

A

B C

D

l1 lr l2

(d) Intermediate lateral restraints

Segment AB le = l1 Segment BC le = lr Segment CD le = 1.1 l2

Restraining beam

l

( >6) ld

( >6) l2d

l

FIGURE 5.2 ILLUSTRATIONS OF EFFECTIVE LENGTHSFOR LATERAL BUCKLING

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Load bearing stiffenersto AS 4100, clause 5.14

FIGURE 5.3(a) EXAMPLES OF CONNECTIONS WHICH MAY BE CONSIDEREDTO BE FULLY RESTRAINED WITHOUT LATERAL ROTATIONAL RESTRAINT

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Beamsupportedunder

Beamsupportedover

Continuous undersupporting beam

Continuous oversupporting beamcolumn or wall

FIGURE 5.3(b) EXAMPLES OF CONNECTIONS WHICH MAY BE CONSIDEREDTO BE PARTIALLY RESTRAINED WITHOUT LATERAL ROTATIONAL RESTRAINT

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Masonry orconcrete wall

FIGURE 5.3(c) EXAMPLES OF CONNECTIONS WHICH MAY BE CONSIDEREDTO BE LATERALLY ROTATIONALLY RESTRAINED

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5.1.6 Design of restraining elements

AS 4100 Ref.

Restraint against lateral deflection The lateral restraint at any sectionis to be designed to have a capacity to transfer a transverse force actingin either direction at the critical flange equal to 0.025 times themaximum force in the critical flange.

Restraint against twist rotation A torsional restraint at a cross-sectionmay be deemed to provide effective restraint against twist rotation if itis designed to transfer a transverse force equal to 0.025 times themaximum force in the critical flange from any unrestrained flange tothe lateral restraint.

Parallel restrained member When a series of parallel members isrestrained by a line of restraints, each restraining element is to bedesigned to transfer a transverse force equal to the sum of 0.025 timesthe flange force from the connected member and 0.0125 times the sumof the flange forces in the connected members beyond, except that nomore than seven members need be considered.

Restraint against lateral rotation A restraint at a cross-section whichis considered to be fully or partially restrained may be deemed toprovide restraint against lateral rotation out of the plane of bending,providing its flexural stiffness in the plane of rotation is comparablewith the corresponding stiffness of the restrained member.

5.4.3*

For restraint against lateral buckling, the design force needs to be equal to 2.5% of the flange force causedby M*.

The rule for parallel restrained members may be interpreted to mean that each restraining element is to bedesigned for 10% of the flange force in one of the connected members. Provision should be made foranchoring the restraining system effectively.

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5.1.7 Angles as simple beams

AS 4100 Ref.

Angles subject to bending in a principal plane are to be assessed as inPara. 5.1.4.2. Angles subject to bending in a non-principal plane are tobe assessed using a rational analysis with the calculated principal axisbending moment satisfying the requirements for biaxial bending ofChapter 8.

5.7

For grade 300 angles which are subject to a design moment M* about an axis n-n normal to one leg, andwhich are—

(a) torsionally restrained at supports, and(b) under continuous lateral restraint (see Fig. 5.4(a)),

the following approximation may be useful (but not always conservative) for preliminary design:

M* ≤ 0.9 β fy Zmin

where Zmin is the minimum elastic section modulus about the relevant axis normal to the leg, andβ = 1.2 for equal anglesβ = 1.1 for unequal angles with the vertical leg (long or short) downβ = 1.0 for unequal angles with the vertical leg (long or short) up.

For angles without lateral restraint which are subject to a design moment M* about an axis n-n normal toone leg (see Fig. 5.4(b)), designers are referred to AISC Design Capacity Tables for Structural Steel, 2nd

Edition, Volume 1: Open Sections (including Addendum No. 1). It is not possible to propose a simplerule of thumb similar to that given above for angles with continuous lateral restraint; the maximum designmoment will usually reduce with increasing span, and shear/torsion may control the design up to evenmoderate spans. The moment capacity is most reduced for the case of an unequal angle with the long legup.

(a) With lateral restraints (b) Without lateral restraints

n n n n

W W

FIGURE 5.4 REPRESENTATION OF ANGLE SITUATIONS

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5.2 DESIGN OF WEBS

5.2.1 Limitations

AS 4100 Ref.

The recommendations in this Section are applicable to webs with d/tvalues less than the plastic limit given for webs in flexuralcompression in Table 5.1. The webs are unstiffened with respect totheir resistance to shear forces and bending but may have load bearingstiffeners for concentrated loads and reactions.

5.10.1

For webs exceeding these limits, stiffeners should be used or if the web is unstiffened, the shear

capacity of 5.2.2 should be reduced by a factor αv =ywp ftd

250

)/(

64002

(rule 5.11.5.1 of AS 4100)

(As this Handbook does not provide advice concerning stiffeners, dp = d1)

5.2.2 Shear capacityAS 4100 Ref.

• For sections with webs V* ≤ 0.9 kss (0.6 fy Aw ) 5.11.15.11.2

• For circular hollow sections V* ≤ 0.9 (0.36 fy Ae) 5.11.35.11.4

wherekss = a factor for type of shear stress distribution (see Fig. 5.5)Aw = dv tw

For I sections, dv is the clear depth between flanges.

For a coped section dv (see Fig. 5.5) should be greater than d1/2, and the length of cope should be kept to

d1/2 for single coped and d1/4 for double coped sections to avoid the problem of shear and bendinginteraction. For coping lengths longer than these limits, the effects of shear and bending momentinteraction should be considered (see Clause 5.12 of AS 4100).

Design shear capacities for universal sections are given in Design aids D3-D4.Design shear capacities for welded sections are given in Design aids D5-D6.

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UNCOPED COPED DOUBLE COPEDd v

= d

1

d v d v

(a) Cope details

kss = 1.0 kss = 0.89 kss = 0.81

(b) Shear stress distribution

d v

d v d v

FIGURE 5.5 FACTOR FOR SHEAR STRESS DISTRIBUTION

bb

bbf

bs

1:2.5

1:2.5bs

bbf

bb1:1

1:1

N.B.For RHS, the outside radius ofsection applies here instead ofthe flange thickness.(Refer Fig. 5.13.1.3 of AS 4100)

tf

FIGURE 5.6 DISPERSION OF FORCES THROUGH FLANGES AND WEBS

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5.2.3 Bearing

Design requirements

AS 4100 Ref.

A web subject to a bearing force R* needs to be reinforced with loadbearing stiffeners if :

R* > 0.9 times the lesser of Rby and Rbb 5.13.2where

Rby = the nominal yield capacity in bearing 5.13.3

= 1.25 bbf tw fy for sections other than square and

rectangular hollow sections

bbf = 5tf +bs 5.13.1

andRbb = the nominal buckling capacity in bearing

buckling= axial compressive capacity of a member (with

�b = 0.5 and kf = 1.0) of area twbb and

slenderness ratio 2.5d1/tw where bb is the load

dispersion length at mid depth of the web

5.13.4

bb = 5tf + bs + d1

for interior force

= 2.5tf + bs + d1/2 for end force

See Fig. 5.6 for illustration of bbf and bb.

AS 4100 provides a method for the calculation of Rby for the case of square and rectangular hollowsections. The simple expression for Rby given above is only applicable if the web is in direct compressionsuch as in an I section. In square and rectangular hollow sections with an external radius, the web is undercombined bending and compression; the use of the simple expression could be up to 40% unconservative,and the procedure in AS 4100 is thus recommended if the bearing load is very high.

Tabulated values of (Rby/bbf) and (Rbb/bb) are given in Design aids D3-D6 in Part II.

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5.2.4 Load bearing stiffeners

Design requirements

AS 4100 Ref.

If load bearing stiffeners are needed, they should be provided in pairs(one on each side of the web) at the mid-point of the stiff bearinglength, such that both:

5.10.25.14.15.14.25.14.3

(a) bes

≤14 ts (for 300 grade) or bes≤12t

s (for 400 grade)

where

bes is the stiffener outstand from the face of the web and ts is the

thickness of this stiffener

and

(b) R* ≤ 0.9 times the lesser of Rsy and Rsb

where

Rsy = the nominal yield capacity in bearing (stiffened

web)= R

by + As fys

Rby is calculated in 5.2.3 and As is the area of the stiffeners in

contact with the flange

Rsb = nominal buckling capacity of the stiffened web

= axial compressive capacity of a member(with �b = 0.5 and kf = 1.0) of area taken as the area of the

stiffener together with a length of web on each side of thecentre-line equal to 16 tw (for 300 grade) or 14 tw (for 400

grade). The effective length of this member shall be equal to theclear depth between flanges.

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5.2.4 Load bearing stiffeners (continued)

Design for torsional end restraints

AS 4100 Ref.

When load bearing stiffeners are the sole means of providing torsionalend restraint at supports, they should be proportioned to have at leastthe following second moment of area Is about the centre-line of theweb

*

*3

250F

RtdI f

s ≥

where

F* = total design load on the member between supports

5.14.5

This rule is a conservative approximation to rule 5.14.5 of AS 4100.

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6 MEMBERS SUBJECT TO AXIAL COMPRESSION

The procedure for checking a member subject to compression is as follows:

(a) Estimate the kf value for the section using the BHP Handbook or similar; for fabricated sections use

Clause 6.2 of AS 4100.

(b) Estimate the design section capacity, i.e. the short column capacity Ns = 0.9 kf An fy (=�Ns which istabulated in Design aids D3-D6).

(c) Select the member section constant �b, to allow for residual stresses and section type, fromTable 6.2.

(d) Estimate the member effective length factor ke (from Para. 6.5).

(e) Estimate the slenderness ratio (ke l/r) for the relevant buckling axis.

(f) Obtain the member slenderness reduction factor �c from Table 6.3.

(g) The axial load nominal design capacity is �cNs.

Note that all columns in simple construction should be designed for a nominal load eccentricity(see Para. 4.3.2) and, therefore, have to be checked for combined axial compression and bending.

6.1 GENERAL

AS 4100 Ref.

For a concentrically loaded member subject to a design axial

compressive force N*, it is recommended that:

N* ≤ 0.9 Nc ( = 0.9 �cNs)

i.e. N* ≤ 0.9 �c kf An fy

6.16.2.1

where

Nc = the nominal capacity of the member in axialcompression

Ns = the nominal capacity of the section in axialcompression as specified in Para. 6.2

�c = a member slenderness reduction factor as specified inPara. 6.4

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6.2 NOMINAL SECTION CAPACITY

AS 4100 Ref.

The nominal capacity of a section in axial compression is given by

Ns = Ae fy

where

6.2

Ae = kf An = effective area of the cross-section

kf = form factor and is given in BHP Structural ProductsHandbook or similar

For a section with maximum (b/t) more than the yield limit of Table 6.1, the effective area should becalculated from the gross area by summing the effective areas of the individual elements, where effectivewidths are given by be = b((b/t)lim/(b/t)actual). Refer to AS 4100 for further details.

6.3 NOMINAL MEMBER CAPACITY

AS 4100 Ref.

The nominal capacity of a member in axial compression is given byNc = �cNs

where

6.3.3

�c = a member slenderness reduction factor as specifiedin Para. 6.4

6.4 MEMBER SLENDERNESS REDUCTION FACTOR �c

AS 4100 Ref.

The member slenderness reduction factor �c may be determined

from the slenderness ratio le/r and the member section constant �busing Table 6.3.

• The slenderness ratio le/r is the ratio of the effective length tothe radius of gyration about the relevant axis. The effectivelength le is determined from the actual length l and the effectivelength factor ke:

le = ke l

where ke is specified in 6.5

• The member section constant �b is specified in Table 6.2.

6.3

The member section constant αb reflects the section type and the residual stress distribution andmagnitude.

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Table 6.1 Limiting width-thickness ratios for elements with axial compression

Description of element (b/t)lim

Yield limit

250 300 350 400 450

Flanges of universal sectionsand channels

— 14.5 13.5 — —

Flanges of welded sections — 13 — 11 —

RHS — — 34 — 30

Angles — 14.5 13.5 — —

Tees — 14.5 13.5 — —

Webs of universal sections — 41 38 — —

Webs of welded sections — 32 — 27.5 —

Circular hollow sections (b = do) 82 — 58.5 — —

Table 6.2 Values of member section constant ����b

Section description����b

for kf = 1.0����b

for kf < 1.0

Hot-rolled UB and UC sections with• flange thickness up to 40 mm• flange thickness over 40 mm

01.0

01.0

Hot-rolled channelsHot-rolled angles

0.50.5

1.01.0

RHS and CHS• cold-formed non-stress-relieved• cold-formed stress-relieved• hot-formed

-0.5-1.0-1.0

-0.5-0.5-0.5

Welded H and I sections• from flame-cut plates• from rolled plates

— flange thickness up to 40 mm— flange thickness up to 40 mm

0

0.51.0

1.0

0.51.0

Tees flame-cut from universal sections 0.5 1.0

Welded box sections 0 0

Other sections 0.5 1.0

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Table 6.3 Values of member slenderness reduction factor, ����c, for kf = 1.0

le/r Compression member section constant (����b) le/r

grade 300 -1.00 -0.50 0.00 0.50 1.00 grade 400

10 1.000 1.0 00 1.000 1.000 1.000 8.5

20 0.999 0.985 0.972 0.958 0.943 17

30 0.987 0.961 0.933 0.902 0.868 26

40 0.963 0.928 0.889 0.844 0.791 34.5

50 0.928 0.886 0.837 0.779 0.713 43

60 0.882 0.833 0.775 0.709 0.637 52

70 0.825 0.768 0.704 0.635 0.566 60.5

80 0.754 0.692 0.627 0.562 0.501 69

90 0.672 0.611 0.550 0.494 0.442 78

100 0.587 0.532 0.480 0.433 0.391 86.5

110 0.507 0.460 0.418 0.380 0.347 95

120 0.436 0.399 0.365 0.335 0.308 104

130 0.376 0.347 0.320 0.296 0.275 112.5

140 0.327 0.304 0.283 0.263 0.246 121

150 0.286 0.267 0.251 0.235 0.221 130

160 0.252 0.237 0.224 0.211 0.200 138.5

170 0.223 0.211 0.201 0.191 0.181 147

180 0.199 0.190 0.181 0.173 0.165 155.5

190 0.179 0.171 0.164 0.157 0.151 164.5

200 0.161 0.155 0.149 0.143 0.138 173

210 0.146 0.141 0.136 0.131 0.127 181.5

220 0.133 0.129 0.125 0.121 0.117 190.5

230 0.122 0.118 0.115 0.111 0.108 199

240 0.112 0.109 0.106 0.103 0.100 207.5

250 0.103 0.101 0.098 0.096 0.093 216.5

260 0.096 0.093 0.091 0.089 0.087 225

270 0.089 0.087 0.085 0.083 0.081 233.5

280 0.082 0.081 0.079 0.077 0.076 242.5

290 0.077 0.075 0.074 0.072 0.071 251

300 0.072 0.071 0.069 0.068 0.067 259.5

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6.5 MEMBER EFFECTIVE LENGTH FACTOR ke

6.5.1 General

AS 4100 Ref.

The member effective length factor ke depends on the rotationalrestraints and the translational restraints at the ends of the member. Itmay be determined by the simple method in Para. 6.5.2 or by the morerefined method in Para. 6.5.3.

4.6.3

The member effective length in compression varies with the condition to be checked.

For out-of-plane buckling, the effective length is the distance between lateral restraints.

If the interaction effect is computed using Appendix B, then the following should be noted:For in-plane buckling, the effective length for checking the member as a column (i.e. without bending) isthe effective length as determined using Para. 6.5.2 and 6.5.3, but the effective length for checking themember under combined action is the actual length of the member as given in Appendix B.

out of plane restraint

1

2

l

l

l

FIGURE 6.1 FREESTANDING COLUMN WITH LATERAL BRACING

Referring to Figure 6.1 above note that:(a) for out-of-plane buckling le = max (l1, 0.85l2)

(b) for in-plane buckling(i) as axial compression member le = 2.2l

(ii) under combined action le = l

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6.5.2 Simple method

AS 4100 Ref.

The factor ke may be determined in accordance with Figure 6.2 forbraced members in frames, or for sway members in rectangular frameswith regular loading and negligible axial force in the beams. Theeffective length le of a member in a triangulated structure may be takenas not less than its length l from centre to centre of intersections withother members.

4.6.3

6.5.3 is generally applicable to members in frames where the idealised conditions of end restraints givenin 6.5.2 are not realisable.

Braced member—one for which the transverse displacement of one end of the member relative to theother is effectively prevented. This situation applies in triangulated frames or trusses or to frames wherein-plane stiffness is provided by diagonal bracing, or by shear walls, or by floor slabs or roof deckssecured horizontally to walls or to bracing systems parallel to the plane of buckling of the member.

Sway member—one for which the transverse displacement of one end of the member relative to the otheris not effectively prevented. Such members occur in structures which depend on flexural action to limitthe sway.

BRACED MEMBER SWAY MEMBER

BUCKLEDSHAPE

Effective lengthfactor (ke)

Symbols for endrestraint conditions

= Rotation fixed, Translation fixed

= Rotation free, Translation fixed

= Rotation fixed, Translation free

= Rotation free, Translation free

0.70 0.85 1.00 1.20 2.20 2.20

FIGURE 6.2 EFFECTIVE LENGTH FACTORS FOR MEMBERS FORIDEALIZED CONDITIONS OF END RESTRAINT

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6.5.3 Refined method

AS 4100 Ref.

For a compression member that forms part of a rigidly jointed structure,the member effective length factor ke may be obtained fromFigure 6.3(a) for a braced member and from Figure 6.3(b) for a swaymember. In Figure 6.3(a), the translational restraint is assumed to beinfinite and in Figure 6.3(b) it is assumed to be zero. �1 and �2 are the

ratios of the compression member stiffnesses to the end restraintstiffnesses and are determined, if there is negligible axial force in thebeams, by:

( )( ) be

c

lI

lI

/

/

βγ

∑∑

=

except that for a compression member whose base is:

4.6.3.3

(a) rigidly connected to a footing, the � value is not to be taken as lessthan 0.6.

(b) not rigidly connected to a footing, the � value is not to be taken asless than 10.

The quantity clI )/(∑ is calculated from the sum of the stiffnesses in theplane of bending of all the compression members rigidly connected atthe end of the member under consideration, including the member itself.

The quantity be lI )/(β∑ is calculated from the sum of the stiffnesses inthe plane of the bending for all the beams rigidly connected to the end ofthe member under consideration. The contributions of any beams pin-connected to the member are neglected.

The modifying factor eβ , which accounts for the condition at the farends of the beams, is determined from Table 6.4.

Table 6.4 Modifying factor ����e for joint stiffness

Fixity condition at far end ofbeam

Beam restraininga braced member

Beam restraininga sway member

Pinned 1.5 0.5

Rigidly connected to a column 1.0 1.0

Fixed 2.0 0.67

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48

8

50106

43

2

1.5

1.2

1.0

0.5

0100 0.5 1.0 1.2 1.5 8506432

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.55

ke

ST

IFF

NE

SS

RA

TIO

AT

EN

D 1

, γ1

STIFFNESS RATIO AT END 2, γ2

8

50106

43

2

1.5

1.2

1.0

0.5

0

ST

IFF

NE

SS

RA

TIO

AT

EN

D 1

, γ1

100 0.5 1.0 1.2 1.5 8506432

STIFFNESS RATIO AT END 2, γ2

ke

2.5

2.0

1.8

1.6

1.5

1.3

1.25

1.20

1.15

1.10

1.05

1.4

4

3

(a) For braced members (b) For sway members

FIGURE 6.3 EFFECTIVE LENGTH FACTORS

Accessed by UNSW - LIBRARY on 05 Oct 2002

49

6.6 ECCENTRICALLY LOADED DOUBLE BOLTED OR WELDEDSINGLE ANGLES

AS 4100 Ref.

AS 4100 requires that eccentrically loaded, double bolted or welded,single angles be treated as a combined action problem.

Clause 8.4.6 of AS 4100 is applicable only to single angle webcompression members in trusses.

8.4.6

For the general problem of angles as compression members loaded through the leg, the approach ofClause 8.4.6 of AS 4100, if used, is conservative and can be approximated by the following simplifiedmethod:

Single angle web compression members in trusses, which are connected with at least two bolts or weldedat their ends and loaded through one leg (see Fig. 6.4), may be designed as axially loaded members inaccordance with Para. 6.1, but with slenderness ratios modified to account for end eccentricities andfixities as follows:

Angles on the same side (l/r)e = 0.45(l/ry)+130

Angles on opposite sides (l/r)e = 0.30(l/ry)+250

where l is the member length and ry is the radius of gyration about the minor principal axis.

For the design of lattice tower members, refer to AS 3995—1994.

Webtensionmember

Webcompression

member

Webtensionmember

Webcompression

member

Chord Chord

(a) Angles on same side (b) Angles on opposite sides

FIGURE 6.4 SINGLE ANGLES LOADED THROUGH ONE LEG

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7 MEMBERS SUBJECT TO AXIAL TENSION

AS 4100 Ref.

For a member subject to an axial tension force N*, it is recommendedthat :

N* ≤0.9 Nt

7.17.27.3

whereNt = nominal capacity of the member in tension

= the lesser of Ag fy (section capacity) and 0.85kt An fuwhere

An = net area of the cross-sectionAg = gross area of the cross-section

kt = a factor for eccentricity of loading= 1.00 where there is uniform force distribution= 0.90 for tee sections connected by flange= 0.85 for:

• channel sections connected by web• equal angles connected by leg• unequal angles connected by long leg• I sections or channels connected by both flanges only

= 0.75 for unequal angles connected by short leg

For any eccentric connections other than the above, it is suggested that kt = 0.75.

For threaded rods kt = 1.0 and An = tensile stress area of the equivalent threaded fastener (refer to

Para. 9.2.5 for tensile stress area).

For holding down bolts, fy and fu of the material used for the bolt may not be the same as that for bolts to

AS/NZS 1111 and therefore can be designed to this Chapter instead of Chapter 9.

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8 MEMBERS SUBJECT TO COMBINED ACTION

AS 4100 Ref.

The interaction equation for a section subject to an axial load, N*, amajor axis bending moment, *

xM , and a minor axis moment *yM :

0.19.09.09.0

* **

≤++yb

y

bx

x

M

M

M

M

N

N

8

where

N = Nt or Nc = the nominal axial tension or compression

capacity, respectively, of the member (for acompression member it is the lesser of the capacitiesfor either principal axis).

Mbx = nominal capacity of the member in bending about thex-axis

Mby = nominal capacity of the member in bending about they-axis

This is a simplified procedure which avoids the need for checking section and member capacityseparately. Considerably less conservative results can be obtained by using the more complex checkingprocedure of AS 4100 which is explained in Appendix B.

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9 CONNECTIONS

9.1 MINIMUM DESIGN ACTIONS ON CONNECTIONS

AS 4100 Ref.

Connections are to be designed to transmit the greater of: 9.1.4

(a) the design action in the member(b) the minimum design actions specified below:

Type of connection Minimum design action

In rigid construction 0.5 (member design momentcapacity)

In simple construction 40 kN shear force

Axially loaded member 0.3 (member design capacity)

Full contact bearing splices incompression

0.15 (member design capacity)

Other splices 0.3 (member design capacity)

Threaded rods member design capacity

For rigid construction, the connection is assumed to have sufficient stiffness to hold the original anglesbetween the members unchanged.

For simple construction, the connections at the ends of members are assumed not to develop bendingmoments.

In addition, for plastic design of beams, the shear connections at the ends of a beam require adequaterotational capacity so that a plastic hinge can form elsewhere in the beam. This requirement must beachieved without reducing the connection shear capacity.

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9.2 DESIGN OF BOLTS

9.2.1 Bolts and bolting categories

AS 4100 Ref.

Boltingcategory

Bolt standard Bolt gradeMethod oftensioning

fuf(MPa)

9.3.1

4.6/S AS/NZS 1111 4.6 Snug tight 400

8.8/S AS/NZS 1252 8.8 Snug tight 830

8.8/TB AS/NZS 1252 8.8 Full tensioning 830

8.8/TF AS/NZS 1252 8.8 Full tensioning 830

Refer to Chapter 7 for the design of holding-down bolts.

9.2.2 Detailing requirements

(a) Pitch and edge distance

AS 4100 Ref.

• Minimum pitch 2.5df 9.6

• Maximum pitch lesser of (15tp, 200 mm)

• Minimum edgedistance

Sheared or hand flame-cut edge 1.75df

Rolled plate, flat bar or section:machine flame-cut, sawn orplaned edge

1.50df

Rolled edge of rolled flat bar orsection

1.25df

(b) Hole type

AS 4100 Ref.

• Standard (kh = 1.0) dh < df + 2 mm df ≤ 24 mm 14.3.5.29.3.3.1

dh < df + 3 mm df > 24 mm

• Oversize (kh = 0.85) dh ≤ max (1.25df, df + 8 mm)*

• Short slot (kh = 0.85) lh ≤ max (1.33df, df + 10 mm)*

• Long slot (kh = 0.70) lh < 2.5df

* These are the requirements for oversize and short slotted holes as presented in AS 4100, 14.3.5.2 (a)(i) and (ii). However, in the now withdrawn High-strength Structural Bolting Code (AS 1511), theserequirements were based on the minimum, not the maximum, of the two values.

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9.2.3 Strength requirements

AS 4100 Ref.

Condition Design requirements

Bolts in tension ufstftf fANN 8.08.0* =≤ 9.3.2.2

Bolts in shear ff VV 8.0* ≤ = )()62.0)(8.0( oxcnufr AnAnfk + 9.3.2.1

Bolts in bearing *bV � 0.9Vb 9.3.2.4

= lesser of 0.9ae tp fup

and ( . )( . )0 9 3 2 df tp fup

Bolts in combinedtension and shear

0.18.0

*

8.0

* 22

≤

+

tf

tf

f

f

N

N

V

V9.3.2.3

For common bolt sizes, designers may use the design aids given in D1.

kr = length factor for lap connection= 1.0 for lj < 300 mm

= 1.075 – lj/4000 for 300 mm ≤ lj ≤1300 mm

= 0.75 for lj > 1300 mm

nn = No. of shear planes with threads includednx = No. of shear planes with threads excludedae = edge distance which is the distance from the nearer edge of a hole and the physical edge of a

plate or rolled section, plus half the fastener diameter dftp = ply thicknessfup = tensile strength of ply materialfuf = minimum tensile strength of the boltAc = bolt minor area (see Para. 9.2.5)Ao = nominal shank area (see Para. 9.2.5)As = tensile stress area (see Para. 9.2.5)df = diameter of the boltdh = diameter of the holelh = hole length

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9.2.4 Serviceability requirements (bolts in friction grip only)

AS 4100 Ref.

Condition Design requirements 9.3.3

Shearsfsf VV 7.0* ≤ = (0.7) µ kh nei Nti

Combined shear and tension 0.17.0

*

7.0

*≤

+

ti

tf

sf

sf

N

N

V

V

µ = slip factor (0.35 for ‘as rolled’ surfaces)kh = hole factor (refer to Para. 9.2.2 (b))dh = hole diameterdf = bolt diameterlh = hole length of slotted holenei = number of effective interfacesNti = minimum bolt tension at installation (see Para. 9.2.5)

If the surface coating is such that the slip factor µ would normally be more than 0.35 and if the load isshared by more than two bolts in a line, designers are advised to exercise caution by reducing the slipfactor by 25%. (This recommendation goes beyond the requirements of AS 4100.)

9.2.5 Bolt properties for design

AS 4100 Ref.

Size M12 M16 M20 M24 M30 M36

Tensile stress area

(mm2)

As 84 157 245 353 561 817 9.3.2.2

Shear area(thread included)

(mm2)

Ac76.2(80)

144(150)

225(235)

324(338)

519(539)

759(787) 9.3.2.1

Shear area(thread excluded)

(mm2)

Ao 113 201 314 452 707 1017

Min. tension atinstallation

(8.8/TF only)(kN)

Nti — 95 145 210 335 490 15.2.5

The figures in brackets in the table above are those given in AS 1275—1985, which are approximately5% larger than those in AS 1275—1972. The more conservative values have been adopted in thisHandbook.

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9.3 DESIGN OF WELDS

9.3.1 Butt welds

AS 4100 Ref.

Complete penetration butt welds: no analysis is required for SPwelds. The design capacity is equal to the design capacity of theweaker part for SP welds and 2/3 of the design capacity of the weakerpart for GP welds.

9.7.2

Incomplete penetration butt welds: the design capacity is calculatedas for fillet welds using the following design throat thickness tt forangle of preparation less than or equal to 60° (see Fig. 9.3):

Single-V butt tt = (d – 3) mmDouble-V butt tt = (d3 + d4 – 6) mm

except for submerged arc welds where the design throat thickness canbe taken to the full depth of penetration.

Refer to AS/NZS 1554.1 for definitions of SP, GP and other requirements such as prequalification.

9.3.2 Fillet welds

AS 4100 Ref.

The design capacity of a fillet weld per unit length is 9.7.3.10

0.36 fuw tt kr for GP welds0.48 fuw tt kr for SP welds

where

fuw = nominal tensile strength of the weld metal= 410 MPa for E41xx/W40x electrodes= 480 MPa for E48xx/W50x electrodes

tt = design throat thickness (see Fig. 9.3)kr = a reduction factor for lap connections

= 1.0 for lw < 1.7 m

= 1.1 – 0.06lw for 1.7 m < lw < 8.0 m

= 0.62 for lw > 8.0 mlw = weld length

Design capacities of fillet welds of common sizes are tabulated in Design aid D2.

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s

Leg

3mm

t t

dd

3mm

t t3m

m

dt t

θ < 60°

D 2

D1

= D1 + 0.85D2

(d) Deep penetration weld

DTT

s

Leg

Gap

s

App

aren

tsi

zeLeg

(c) Fillet weld with gap

DTT

sLeg

(a) Equal leg fillet weld

Q

θ

90°R P

Q

θ90°R P

Reinforcement

s1

Leg

DTT

Leg

(b) Unequal leg fillet weld

Q

θ 90°R P

Reinforcement

Design throat thickness for deep penetrationwelds made by fully automatic processes

(e) Incomplete penetration single V butt weld

(f) Incomplete penetration double V butt weld

s 2

FIGURE 9.3 NOTATION FOR WELDS

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9.4 SIMPLE SHEAR CONNECTIONS

AS 4100 Ref.

The shear capacity and the detailing requirements of a range of simpleconnections are given in Tables 9.4.1 to 9.4.6. For greater detail,reference should be made to the Australian Institute of SteelConstruction publication Standardized Structural Connections—4thedition, due 2000.

Tables 9.4.1 to 9.4.6 are the original ones prepared for the 1993 edition and are based on a plate andsection grade of 250. Thus some connection capacity values, those based on plate failure rather than boltor weld failure, will be conservative if plate or sections of higher grade are used.

Table 9.4.1 Single Angle Cleat Connection Capacity

Single angle cleat connections (kN)9 8 7 6 5 4 3 2Member

Bolts Bolts Bolts Bolts Bolts Bolts Bolts Bolts

760UB 531 472 413 354

690UB 472 413 354 284

610UB 413 354 284 207

530UB 354 284 207 136

460UB 284 207 136

410UB 207 136 73

360UB 136 73

310UB 136 73

250UB 73*

* Double web cope not recommended

ANGLES: USE 100 × 100 × 6 ANGLE, LENGTH = 70 × No. ROWS BOLTS.BOLTS: USE M20 8.8\S

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Table 9.4.2 Double Angle Cleat Connection Capacity

Double angle cleat connections (kN)

9 8 7 6 5 4 3 2Member

Bolts Bolts Bolts Bolts Bolts Bolts Bolts Bolts

760UB244-197 1061 943 826 708

760UB173 1061* 943 826 708

760UB147 1061* 905 826 708

690UB140 943* 772 708 568

690UB125 943* 750 708 554

610UB125 808* 671 563 411

610UB113 755* 625 530 386

610UB101 710* 585 502 366

530UB92 593* 481 352 230

530UB82 551* 445 330 216

460UB82 469* 342 224

460UB78 430* 314 205

460UB67 401* 293 192

410UB60 269* 176 96

410UB54 262* 172 93

360UB57 175 97

360UB51 157 89

360UB45 144 82

310UB46 155* 82

310UB40 138* 75

250UB37 78**

250UB31 75**

* Double web cope not recommended** Double or single web cope not recommended

ANGLES: USE 100 × 100 × 6 ANGLE, LENGTH = 70 × No. ROWS BOLTSBOLTS: USE M20 8.8\S

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Table 9.4.3 Flexible End Plate Connection Capacity

Flexible end plate connections (kN)

9 8 7 6 5 4 3 2Member

Bolts Bolts Bolts Bolts Bolts Bolts Bolts Bolts

760UB244-197 1122 1095 958 821

760UB173 1016 1016 946 811

760UB147 1066* 905 853 731

690UB140 918* 772 703 586

690UB125 894* 750 690 575

610UB125 808* 671 585 486

610UB113 755* 625 550 440

610UB101 710* 625* 521 417

530UB92 583* 481 401 301

530UB82 551* 445 375 282

460UB82 485* 383 292

460UB78 442* 348 268

460UB67 409* 321 250

410UB60 307 230 153

410UB54 298* 224 149

360UB57 234* 156

360UB51 215* 143

360UB45 202* 135

310UB46 198* 117

310UB40 179* 120*

250UB37 126**

250UB31 120**

* Double web cope not recommended** Double or single web cope not recommended

END PLATE: WIDTH = 150 mm, THICKNESS = 8 mm, LENGTH = 70 × No. ROWS BOLTSBOLTS: USE M20, 8.8\SALL WELDS: USE 6E48 FILLET WELDS — FULL LENGTH OF PLATE

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Table 9.4.4 Bearing Pad Connection Capacity

Bearing pad connections (kN) Bearing pad connections (kN)Member

End plate Bearing pad CAP.Member

End plate Bearing pad CAP.

760UB244 140×800×25 140×650×25 1144 310UB46 90×320×20 90×200×20 290

760UB220 1144 310UB40 260

760UB197 1144 250UB37 90×270×20 90×150×20 230

760UB173 1144 250UB31 215

760UB147 1144 200UB30 90×220×20 183

690UB140 140×700×25 1082 200UB25 167

690UB125 1082 310UC283 90×360×25 90×300×25 579

610UB125 140×630×25 140×600×25 962 310UC240 579

610UB113 955 310UC198 579

610UB101 140×550×25 896 310UC158 579

530UB92 90×550×25 90×500×25 763 310UC137 579

530UB82 90×450×25 708 310UC118 525

460UB82 90×480×25 90×400×25 640 310UC97 428

460UB74 90×470×20 90×400×20 583 250UC89 90×280×20 90×250×20 352

460UB67 90×350×20 540 250UC73 90×200×20 308

410UB60 90×420×20 90×300×20 445 200UC60 90×230×20 273

410UB54 429 200UC52 232

360UB57 90×380×20 400 200UC46 90×150×20 209

360UB51 90×250×20 364 150UC37 90×180×20 185

360UB45 339 150UC30 145

150UC23 131

PLATES: USE DIMENSIONS AS GIVEN IN TABLEBOLTS: USE M20, 8.8\SWELDS: USE 6 mm E48 FILLET WELDS — FULL LENGTH OF PLATES , OR

USE 8 mm E48 FILLET WELDS — FULL LENGTH OF PLATES (310UC ONLY)

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Table 9.4.5 Angle Seat Connection Capacity

Angle seat connections (kN) Angle seat connections (kN)

Member Boltedseat

6E48Welded

seat

8E48Welded

seat

Member Boltedseat

6E48Welded

seat

8E48Welded

seat760UB244 - - 386 310UB46 151 151 151760UB220 - 287 386 310UB40 135 135 135

760UB197 357 287 386 250UB37 357 287 386760UB173 357 287 386 250UB31 357 287 386

760UB147 342 287 342 200UB30 357 287 386

690UB140 331 287 331 200UB25 357 287 386

690UB125 308 287 308 310UC283 357 287 385

610UB125 318 287 318 310UC240 329 287 329610UB113 287 287 287 310UC198 260 260 260610UB101 259 287 259 310UC158 NR NR NR

530UB92 225 252 255 310UC137 NR NR NR530UB82 228 228 228 310UC118 NR NR NR

460UB82 237 237 237 310UC97 NR NR NR

460UB74 213 213 213 250UC89 NR NR NR460UB67 192 192 192 250UC73 NR NR NR

410UB60 180 180 180 200UC60 NR NR NR410UB54 168 168 168 200UC52 NR NR NR

360UB57 183 183 183 200UC46 NR NR NR

360UB51 165 165 165 150UC37 NR NR NR360UB45 151 151 151 150UC30 NR NR NR

150UC23 NR NR NR

ANGLE SEAT: USE 150 × 90 × 12 ANGLE, LENGTH = 180 mm, SHORT LEG IS USED AS SEAT(MAY BE BOLTED OR WELDED AS GIVEN)

RESTRAININGCLEAT: USE 100 × 75 × 6 ANGLE, LENGTH = 140 mmBOLTS: USE M20, 8.8\SWELDS: USE 6 mm E48 FILLET WELDS—FULL LENGTH OF SEAT LEG (2 × 150 mm), OR

USE 8 mm E48 FILLET WELDS—FULL LENGTH OF SEAT LEG (2 × 150 mm)(AS GIVEN IN TABLE)

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Table 9.4.6 Web Side Plate Connection Capacity

Web side plate connections (kN)

9 8 7 6 5 4 3 2Member

Bolts Bolts Bolts Bolts Bolts Bolts Bolts Bolts

760UB 726* 632 538 444

690UB 632* 538 444 351

610UB 538* 444 351 260

530UB 444* 351 260 173

460UB 351* 260 173

410UB 260* 173 96

360UB 173 96

310UB 173* 85

250UB 85*

* Double web cope not recommended

SIDE PLATE: WIDTH = 90 mm, THICKNESS = 10 mm, LENGTH = 70 × No. ROWS BOLTSBOLTS: USE M20, 8.8\SWELDS: USE 6E48 FILLET WELDS — FULL LENGTH OF PLATE

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10 BRITTLE FRACTURE

AS 4100 Ref.

Brittle fracture is unlikely if all of the following conditions apply:

• Thickness does not exceed 70 mm

• Not exposed to sub zero temperature

• Fabrication does not result in a bending radius of less than 50 timesthe plate thickness

10.4

This Handbook highlights the conditions under which brittle fracture is not a problem; otherwise refer toAS 4100 for detailed consideration.

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11 FATIGUE

11.1 LIMITATIONS

AS 4100 Ref.

The advice in this Section is applicable to conditions where all cyclicloadings can be assumed to be equal to the most severe and wheremetal thickness does not exceed 25 mm.

11

This Handbook highlights the conditions under which fatigue is not a problem; otherwise refer toAS 4100 for detailed consideration.

11.2 METHOD OF ASSESSMENTAS 4100 Ref.

(a) Number of stress cycles: estimate the number of stress cycles ni for

the expected life of the detail. If ni < 104 (i.e. one application every

day for 25 years), no further assessment is required.

11.1.611.411.511.7

(b) Stress range: estimate the stress range f*, i.e. the algebraicdifference between two extremes of stress. The stresses arecalculated taking into account all cyclic design actions butexcluding stress concentrations due to the geometry of the detail.The loading is to be the actual cyclic service loading includingdynamic effects.

No further assessment is required if:

(i) f* < 26 MPa or

(ii) ni <

3

6

*27

105

×

f ( )

=

3

11

*10

f

(c) Detail category: select the appropriate detail category in accordancewith Table 11, to obtain the constant stress range fatigue limit f3.

(i) if f* < f3 no further assessment is required.

(ii) if f* > f3 the number of cycles the detail can survive is

ni max =

3

36

*105

×

f

f

If the structural system is such that failures of the detail lead to the collapse of the structure, AS 4100requires that the expected life should be increased by a factor of at least 3.0. To avoid this penalty it isnecessary to modify the structural system to one that is fail-safe (i.e. with alternative load paths).

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Table 11 Detail Category

Type of detail f3 (MPa)

• Bolts and threaded rods in tension• Joints with partial penetration butt welds or fillet welds (stress

range on the weld throat)• Cover plates in beams and plate girders

27

• Beams subjected to bending with stiffeners fillet-welded toflanges and webs

• Tapered built-up members connected by full penetration butt-welds perpendicular to the direction of applied stress

• Stud-welded base metal• Base metal having fillet welded attachments

52

• Prismatic members connected by full penetration butt-weldsperpendicular to the direction of applied stress

• Bolt in shear 8.8/TB• Any continuous longitudinal butt or fillet weld other than those

with an f3 value of 92 MPa

66

• Manual flame-cut base metal, automatic flame-cut base metal withdrag line

• Built-up members connected by continuous full penetration butt-welds or continuous fillet welds parallel to the direction of appliedstress (no unrepaired stop-start positions and welded from bothsides)

92

• Automatic flame-cut or shear edge base metal• Material for bolted connection using 8.8/TF procedure

103

• Rolled and extruded products 118

This Table is based on AS 4100 but has been simplified greatly to be used for preliminary fatigueassessment. For detailed fatigue assessment refer to AS 4100.

For bolts subject to fluctuating stresses in tension it is common practice to fully tension the bolt toalleviate fatigue problems.

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APPENDIX A

ALTERNATIVE METHOD FOR MOMENT AMPLIFICATION

A1 Moment amplification for a braced member

AS 4100 Ref.

For a braced member with a design axial compressive force N* and a

calculated design bending moment M *m as determined by the first order

analysis, the design bending moment M* is calculated as follows:

M* = �bM*m

where �b is a moment amplification factor for a braced membercalculated as follows:

�b = 1 *

1

≥

−

omb

m

N

N

c

and Nomb is the elastic buckling load for the braced member bucklingabout the same axis as that about which the design bending momentM* is applied.

For a braced member subject to end bending moments only, the factorcm is calculated as follows:

cm = 0.6 – 0.4�m ≤ 1.0

where �m is the ratio of the smaller to the larger bending moment atthe ends of the member, taken as positive when the member is bent inreverse curvature.

For a braced member with a transverse load applied to it, �m is takenas –1.0 or approximated by the value obtained by matching thedistribution of bending moment with one shown in Fig. A1.

4.4.2.2

Nomb = π2EI/l2e where le and EI are the effective length and rigidity of the member about the same axis asthe applied bending moment M*. See Chapter 6, Fig. 6.1 and Fig. 6.2 for braced members.

For most practical designs the factor N*/Nomb is usually small so that the amplification factor should alsobe small. A limiting value of δb not greater than 1.4 has been set before it is necessary to proceed to a fullsecond order analysis.

Values of le/r for δb = 1.0 and δb = 1.1 are plotted in Fig. A2 as a function of βm and the applied axialload N*/0.9Ns.

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Moment distribution βm Moment distribution

M*-1.0

+0.2

+0.6

-0.5

+0.2

+0.2

+0.5

+1.0

+0.4

0.0

+0.5

-1.0

M*

M*

M*

M*

M*

M*

M*

M*/2

M*

M*/2

M*

M*

M*

M*

M*

M*

M*

M*

M*/2

M*

M*

M*M*/2

M*

M*

M*/2

M*/2

M*/2

M*/2

M*

M*/2

M*

M*

M*

M*/2

M*/2

M*/2

M*

M*/2

M*

M*/2

M*

M*

M*

M*/2

Moment distribution Moment distribution

M*

M*

M*

M*

+0.1

+0.7

-0.5

+0.2

-0.4

-0.1

+0.3

+0.4

-0.1

+1.0

-0.5

ββM*

βm βm βm

FIGURE A1 EXTRACTS FROM AS 4100 FIGURE 4.4.2.2 FOR VALUES OF βm FORVARIOUS DISTRIBUTIONS OF BENDING MOMENT

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69

180

140

120

100

80

60

40

20

160

0–1.0 0 +1.0

N*

φNsp =

δb = 1.1

δb = 1.0

( le/r)

βm

p = 0.25

p = 0.5

p = 1.0

FIGURE A2 LIMITING VALUES OF rle / FOR MOMENT AMPLIFICATION

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A2 Moment amplification for a sway member

AS 4100 Ref.

For a sway member with a design axial compressive force N* and a

calculated design bending moment M *m as determined by the first order

analysis, the design bending moment M* is calculated as follows:

M* = �mM *m

The moment amplification factor �m is taken as the greater of—

4.4.2.3

�b = the moment amplification factor for a braced memberdetermined in accordance with A1, or

�s = the moment amplification factor for a sway member

For all sway columns in a storey of a rectangular frame, �s iscalculated from:

�s =

Σ

Σ−∆

*

* 1

1

V

N

hs

s

where ∆s is the translational displacement of the top relative to thebottom in the storey of height hs, caused by the design horizontalstorey shears V* at the column ends, N* is the design axial force in acolumn of the storey, and the summations include all the columns ofthe storey.

The term *

*

V

N

Σ

Σ can also be considered as the ratio of the total vertical loads to the total horizontal loads

above the storey.

The limiting value for �m is set at 1.4 for rectangular frames but for most practical designs the

amplification factor should be considerably less. If �m is greater than 1.4 then it is necessary to perform asecond order analysis.

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A3 Moment amplification for pitched-roof portal frames

AS 4100 Ref.

The moment amplification factor � for a steel pitched-roof portalframe is obtained from the frame elastic buckling load factor λcusing:

)/1(1

1

cλδ

−=

where �cis the ratio of the elastic buckling load set of the frame to

the design load set (with load factors) for the frame.

4.4.2.3

• For sway buckling mode

]3.0[

3

sPhPs

EI

rc

rc +

=λ for pinned based frames

)/2()/5(

)10(522

ccrrc

IhRPIsP

RE

++=λ for fixed based frames

whereIc , Ir = the second moments of area of the column and

rafter, respectivelyPc , Pr = the averages of the computed first-order

compression forces in the columns and rafters,respectively

s = the length of the rafterh = the height to the eavesR = (Ic/h) / (Ir/s)

λ

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A3 Moment amplification for pitched-roof portal frames (continued)

AS 4100 Ref.

• For symmetrical buckling mode

re

rc

Psk

EI2

2

)2(

πλ =

in which the effective length factor ke is obtained from the braced

member effective length chart of Figure 6.3 by using:

4.4.2.3

hI

sI

c

r

/5.1

2/21 == γγ for pinned based frames

hI

sI

c

r

/2

2/21 == γγ for fixed based frames

The above buckling formulae have been obtained from J.M. Davies In-plane Stability of Portal Frames,The Structural Engineer Vol. 68, No. 8, April 1990. For multi-bay formulae, refer to J.M. Davies TheStability of Multi-bay Portal Frames, The Structural Engineer Vol. 69, No. 12, June 1991.

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APPENDIX B

ALTERNATIVE METHOD FOR MEMBERSSUBJECT TO COMBINED ACTIONS

The checking of a member subject to combined axial and bending actions may be carried out as follows:

(a) Establish design section capacities under separate axial and bending actions using Chapters 5, 6and 7 as appropriate.

(b) Use interaction equations in B2 to check design section capacity under combined actions.

(c) Establish the effective lengths for in-plane and out-of-plane actions for the member.

(d) If the member is subject to compression, first check it as a compression member in accordancewith Chapter 6.

(e) Establish the design member capacity under separate axial and bending action using Chapters 5, 6and 7 as appropriate. For in-plane action use the actual member length for the effective length incompression.

(f) Use interaction equations in Para. B3 to check the design member capacity under combined actions.

Note that all members under combined axial compression and bending are to be checked separatelyfor axial compression without bending as given in Chapter 6, and then for the combined actions asgiven in Chapter 8 because different effective lengths have to be used in each case.

Section capacity requirements often control the design of highly restrained members while membercapacity requirements often control the design of members without full lateral restraint.

B1 GENERAL

AS 4100 Ref.

For a member subject to combined axial and bending actions, it isrecommended that the requirements for section capacity undercombined action be checked in accordance with Para. B2 and membercapacity under combined action be checked in accordance withPara. B3.

Eccentrically loaded angles may be designed using Para. 6.6.

8.1

Note that the applied bending moments Mx* and My* used in the interaction equations of thisSection are amplified bending moments. They are obtained by modifying the first order designbending moments with the appropriate moment amplification factors determined in accordancewith Para. 4.4.2 or Appendix A.

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B2 SECTION CAPACITY UNDER COMBINED ACTIONS

B2.1 Section under uniaxial bending and axial force (tension or compression)

AS 4100 Ref.

The interaction equation for a section subject to a bending momentM*about a principal axis and an axial force N* is:

8.3.28.3.3

0.19.0

*

9.0

*≤

+

ss kM

M

N

N

where

k = 1.18 for doubly symmetric compact I-sections andrectangular and square hollow sections with kf = 1.0

= 1.00 for other sectionsMs = nominal capacity of the section in bending without

axial force

Ns = nominal capacity of the section in tension orcompression without bending

The effect of axial force can be ignored for doubly symmetric compactI-sections and rectangular and square hollow sections with kf = 1.0, if

15.09.0

*≤

sN

N for bending about the majorprincipal axis

40.09.0

*≤

sN

N for bending about the minorprincipal axis

The checking of section capacity is necessary for the combined action of uniaxial bending and axialtension because in Para. B3.1, the member capacity is enhanced with the presence of axial tension.

The nominal capacity of a section in bending Ms = Ze fy as is specified in Para. 5.1.3.

The nominal capacity of a section in tension Ns is the lesser of (Ag fy) and (0.85 kt An fu) as is specified inChapter 7.

The nominal capacity of a section in compression Ns = Ae fy as is specified in Para. 6.2.

For doubly symmetric compact I sections and rectangular and square hollow sections with kf < 1.0,

AS 4100 allows values of k between 1.0 and 1.18.

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B2.2 Section under biaxial bending and axial force (tension or compression)

AS 4100 Ref.

The interaction equation for a section subject to an axial load N*, a

major axis bending moment Mx* and a minor axis moment M y

* is:

8.3.4

0.19.0

*

9.0

*

9.0

*≤

++

sy

y

sx

x

s M

M

M

M

N

N

where

Ns = nominal capacity of the section under axial loadMsx = nominal capacity of the section in bending about x-

axisMsy = nominal capacity of the section bending about y-axis

The checking of section capacity for combined biaxial bending and axial force is necessary because amore generous allowance has been given to the member combined action capacity in Para. B3.2 andPara. B3.4.

The nominal capacity of a section in tension Ns is the lesser of (Ag fy) and (0.85 kt An fu) as specified in

Chapter 7.

The nominal capacity of a section in compression Ns = Ae fy as specified in Para. 6.2.

The nominal capacity of a section in bending about x axis Msx = Zex fy and about y axis is Msy = Zey fywhere Zex and Zey are the effective section moduli about x and y axes respectively.

For doubly symmetric compact I sections with kf = 1.0 less conservative results can be obtained by usingthe alternative equations of Clause 8.3.4 of AS 4100 (as given in Fig. B1).

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B3 MEMBER CAPACITY UNDER COMBINED ACTIONS

B3.1 Member under axial tension and uniaxial bending

AS 4100 Ref.

The interaction equation for a member subject to an axial tensile loadN* and a principal axis bending moment M* is:

8.4.4.2

0.19.0

*

9.0

*≤

−

tb N

N

M

M

where

Mb = nominal capacity of the member in bending

Nt = nominal capacity of the member in tension

The enhancement in bending capacity in the presence of axial tension (evident in the minus sign above) isavailable only for beams where bending capacities have been reduced because of lateral bucklingproblems.

Mb = αs Ms as specified in Para. 5.1.

Nt is the lesser of (Ag fy) and (0.85 kt An fu) as specified in Chapter 7.

B3.2 Member under axial tension and biaxial bending

AS 4100 Ref.

The interaction equation for a member subject to an axial tensile loadN*, a major axis bending moment Mx* and a minor axis bending

moment My* is

8.4.5.2

0.19.0

*

9.0

* 4.14.1

≤

+

ry

y

tx

x

M

M

M

M

where

Mtx = the lesser of

−

tsx

N

NM

9.0

*1 and

+

tbx

N

NM

9.0

*1

Mry =

−

tsy

N

NM

9.0

*1

This Para. is applicable to members bent about a non-principal axis or bent about both principal axes.

Nt is the lesser of (Ag fy) and (0.85 kt An fu) as specified in Chapter 7.

Mbx = αs Ms is the nominal capacity of the member in bending about its major principal axis.

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B3.3 Member under axial compression and uniaxial bending

AS 4100 Ref.

The interaction equation for a member subject to an axial compressive

load N* and a principal axis bending moment M* is:

8.4.4.1

0.19.0

*

9.0

*≤

+

bc M

M

N

N

where

Mb = nominal capacity in bending of the member

Nc = nominal capacity in compression of the member

M* = applied moment with moment amplification asdetermined in Para. 4.4.2 or Appendix A asapplicable

For bending about the minor principal axis or for bending about the major principal axis without lateralbuckling problems (αs = 1.0), the rule should be checked for in-plane action, i.e. with Nc as thecompressive capacity for buckling about the same axis as the applied moment using ke = 1.0 for bothbraced or sway members. The member will need to be checked as a compression member inaccordance with Para. 6.1 using the effective length le as given in Para. 6.5.

For bending about the major principal axis with lateral buckling problems (αs < 1.0), the rule should bechecked twice, once for the in plane action (as above) and once for the out-of plane action, i.e.

(a) In-plane actionNc = Ncx = the compressive capacity for buckling about the major principal axis using ke =1.0

Mb = Msx = the section capacity in bending about the major principal axis

(b) Out-of-plane actionNc = Ncy = the compressive capacity for buckling about the minor principal axis using ke = 1.0

Mb = αsMsx = the member capacity in bending about the major principal axis (lateral buckling

included)

For doubly symmetric I sections with kf = 1.0 less conservative solutions can be obtained using thealternatives given in Clauses 8.4.2.2 and 8.4.4.1 of AS 4100.

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B3.4 Member under axial compression and biaxial bending

AS 4100 Ref.

The interaction equation for a member subject to an axial compressive

load N*, a major axis bending moment Mx* and a minor axis moment

M y* is:

8.4.5.1

0.19.09.0

4.1*4.1*

≤

+

rby

y

rbx

x

M

M

M

M

where

Mx* , M y

* = applied moments with moment amplificationsdetermined in Para. 4.4.2 or Appendix A asapplicable

Mrbx , Mrby = reduced nominal capacity in bending of themember about the major and minor axis

Mrbx =

−

cbx

N

NM

9.0

*1

Mrby =

−

cby

N

NM

9.0

*1

For the major axis bending, Mrbx is the lesser value of the in-plane and out-of-plane capacitiesdetermined as follows:

• for in-plane capacities: Nc is the member compressive capacity for buckling about the majorprincipal axis using ke = 1.0 for both braced or sway members and Mbx = Msx = nominal capacity ofsection in bending about the major principal axis. The member will need to be checked as acompression member in accordance with Para. 6.1 using the effective length le as given inPara. 6.5.

• for out-of-plane capacities: Nc is the member compressive capacity for buckling about the minor

principal axis and Mbx = αs Msx = nominal capacity in bending of the member about the majorprincipal axis.

For the minor axis bending Mrby is the minor principal axis in-plane member moment capacity and Nc isthe compressive capacity for buckling about the minor principal axis using ke = 1.0 for both braced andsway members and Mby = Msy = nominal capacity of section in bending about the minor principal axis.

The interaction equation is plotted in Fig. B2.

Fig. B3 illustrates in-plane and out-of-plane behaviour of a member under axial compression andbending.

Fig. B4 summarizes all interaction equations for combined actions. These equations are exactly the sameas those given in AS 4100 but cast in a different form.

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79

1.0

0.8

0.6

0.4

0.2

0.00.0 0.2 0.4 0.6 0.8 1.0

p = 0.0

p = 0.6

p = 0.9

p = 0.3

p = 0.0

p = 0.6

p = 0.9

p = 0.3

MX*

0.9MSX

Paragraph B.2.2 aboveClause 8.3.4 of AS4100

p =N*

0.9Ns

MY*

0.9MSY

FIGURE B1 SECTION INTERACTION DIAGRAMS FOR COMBINED AXIALCOMPRESSION AND BIAXIAL BENDING FOR DOUBLY SYMMETRIC

COMPACT � SECTIONS

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1.0

0.8

0.6

0.4

0.2

0.01.00.80.60.40.20.0

p = 0.0

p = 0.1

p = 0.2

p = 0.3

p = 0.5

Mx*

0.9Mbx

My*

0.9Mby

N*0.9Nc

p =

p = 0.4

FIGURE B2 MEMBER INTERACTION EQUATIONS FOR COMBINED AXIALCOMPRESSION AND BIAXIAL BENDING

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81

Z

P

M

Y

X

M

P

Z

P

M

Y

X

M

P

Z

P

MX

Y

XP

Lateralrestraints

MY

MX

MY

(a) In-plane behaviour (Column deflects in YZ plane only.)

(b) Flexural-torsional buckling (Column deflects in YZ plane, then buckles by deflecting in XZ plane and twisting about Z.)

(a) Biaxial bending (Column deflects in YZ and XZ planes and twists about Z.)

l l

FIGURE B3 BEAM-COLUMN BEHAVIOUR

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FIGURE B4 SUMMARY OF INTERACTION EQUATIONS FOR COMBINED ACTIONS

Type of combined action Section capacity Member capacityUniaxial bending and tension

skM

M

9.0

* +

tN

N

9.0

* ≤ 1.0

bM

M

9.0

* –

tN

N

9.0

* ≤ 1.0

Uniaxial bending and compression

skM

M

9.0

* +

sN

N

9.0

* ≤ 1.0

bM

M

9.0

* +

cN

N

9.0

* ≤ 1.0

Biaxial bending and tension

tN

N

9.0

* +

sxM.xM

90

* +

syM

yM

9.0

* ≤ 1.0

txMxM

9.0

* 1.4

+

ryM

yM

9.0

* 1.4

≤ 1.0

Biaxial bending and compression

sN

N

9.0

*+

sxMxM

9.0

* +

syM

yM

9.0

* ≤ 1.0

rbxMxM

9.0

* 1.4

+

rbyM

yM

9.0

* 1.4

≤ 1.0

• M*, M*x, M*y are amplified applied bending moments

• N* = the applied axial force• Nt = the lesser of (Ag fy) and (0.85 kt An fu)

• Mb = �s Ms; Mbx = �s Msx• Ms = Ze fy; Msx = Zex fy; Msy = Zey fy

• Ns = kf An fy

• k = 1.18 for compact I sections.= 1.0 for all other sections.

• kt = correction factor for distribution of forces in a tension member• kf = form factor for members subject to axial compression

• Nc = �c Ns (see Note under Para. B3.3).

82

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• Ncx = the compression capacity for buckling about the x-axis• Ncy = the compression capacity for buckling about the y-axis

• Mrbx = the lesser of Msx

−

cxN

N

9.0

*1 and Mbx

−

cyN

N

9.0

*1

• Mrby = Msy

−

cyN

N

9.0

*1

• Mtx = the lesser of Msx

−

tN

N

9.0

*1 and Mbx

+

tN

N

9.0

*1

• Mry = Msy

−

tN

N

9.0

*1

83

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PART II

DESIGN AIDS

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CONNECTION DESIGN DATAD1

BOLTSDESIGN CAPACITY (kN)

Bolt sizeLoading condition Bolt grade

M12 M16 M20 M24 M30 M36

Bolt in Tension 4.6 27 50 78 113 179 260

8.8 - 104 163 234 371 540

Bolt in Shear, with 4.6 14 27 43 62 100 145

Threads Included# 8.8 - 56 89 128 207 302

Bolt in Shear, with 4.6 22 40 62 90 140 202

Threads Excluded# 8.8 - 83 129 186 291 419

Friction Grip* 8.8/TF - 23 36 52 82 -

Bolt sizeLoading condition Plate thickness

(mm) 12 16 20 24 30 36

Bolt Bearing 6 - 113 142 170 213 -

for 250 steel plate 8 - 151 189 227 283 -

10 - 189 236 283 254 -

Edge distance(mm)Loading condition Plate thickness

(mm)35 40 45

6 77 89 100

Plate Tear out 8 103 118 133

for 250 steel plateo 10 129 148 166

12 155 177 199

# capacity per interface* serviceability design capacity per interface for standard holes (kh = 1.0)° independent of bolt size

D2FILLET WELDS

Design capacity per unit length (kN/mm)

Weld size (mm)Weld type Weld quality

5 6 8 10 12

E41/W40 GP 0.53 0.62 0.83 1.04 1.25

SP 0.70 0.83 1.11 1.39 1.67

E48/W50 GP 0.61 0.74 0.98 1.22 1.47

SP 0.81 0.98 1.30 1.63 1.96

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D3UNIVERSAL SECTION CAPACITIES—GRADE 300

Axial Moment Shear Bearing���� Ns ���� Msx ���� Msy ���� Vx1 ���� Vx2 ���� Vx3 ���� Rbb/bb ���� Rby/bbfDesignation

kN kNm kNm kN kN kN KN/mm KN/mm610UB125 3830 927 130 1103 905 753 1.07 4.02610UB113 3384 829 114 1038 847 701 0.92 3.78610UB101 3117 783 104 1048 851 700 0.81 3.82

530UB92 2957 640 92 885 710 575 0.90 3.67530UB82 2557 559 78 833 664 535 0.77 3.46

460UB82 2775 497 79 732 577 457 1.06 3.56460UB75 2437 448 62 673 528 417 0.86 3.28460UB67 2136 400 55 629 492 385 0.73 3.06

410UB60 1935 324 47 514 394 301 0.70 2.81410UB54 1812 305 56 500 382 290 0.65 2.74

360UB57 1947 273 45 460 346 256 0.91 2.88360UB51 1682 242 38 420 314 231 0.72 2.63360UB45 1532 222 47 397 294 214 0.63 2.48

310UB46 1587 197 38 329 237 166 0.74 2.41310UB40 1428 182 25 299 215 149 0.59 2.20310UB32 1075 134 33 268 190 129 0.46 1.98

250UB37 1368 140 33 259 177 NR 0.86 2.30250UB31 1155 114 26 247 167 NR 0.77 2.20250UB26 894 92 18 200 135 NR 0.48 1.80

200UB30 1100 91 25 205 128 NR 1.06 2.27200UB25 930 75 20 188 116 NR 0.90 2.09200UB22 827 65 17 162 100 NR 0.65 1.80200UB18 661 52 10 143 87 NR 0.52 1.62

180UB22 812 56 12 165 96 NR 1.12 2.16180UB18 662 45 9 137 78 NR 0.79 1.80180UB16 588 40 8 124 70 NR 0.63 1.62

150UB18 662 39 8 141 74 NR 1.24 2.16150UB14 513 29 6 118 60 NR 0.91 1.80

310UC158 5065 675 305 705 536 406 3.47 5.30310UC137 4410 580 262 619 466 346 2.90 4.66310UC118 3780 494 222 534 397 289 2.32 4.02310UC97 3348 421 187 474 347 247 1.76 3.56

250UC90 2873 310 143 408 287 NR 2.24 3.78250UC73 2516 266 123 334 231 NR 1.62 3.10

200UC60 2057 177 81 291 187 NR 2.08 3.35200UC52 1798 154 70 250 158 NR 1.66 2.88200UC46 1593 133 60 228 143 NR 1.43 2.63

150UC37 1277 84 37 195 107 NR 1.90 2.92150UC30 1112 72 32 159 85 NR 1.42 2.38150UC23 858 51 21 147 75 NR 1.26 2.20

100UC15 544 21 10 72 NR NR 1.19 1.80

� Vx1 = design shear capacity for uncoped web.

� Vx2 = design shear capacity for single coped web. (standard cope = 65 mm)� Vx3 = design shear capacity for double coped web. (standard cope = 65 mm)

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D4UNIVERSAL SECTION CAPACITIES—GRADE 350

Axial Moment Shear Bearing

���� Ns ���� Msx ���� Msy ���� Vx1 ���� Vx2 ���� Vx3 ���� Rbb/bb ���� Rby/bbfDesignation

kN kNm kNm kN kN kN KN/mm KN/mm610UB125 4485 1126 158 1250 1026 853 1.11 4.55610UB113 3953 1007 138 1176 960 795 0.95 4.28610UB101 3449 887 118 1179 958 788 0.83 4.29

530UB92 3275 725 105 995 798 647 0.93 4.13530UB82 2827 633 88 937 747 602 0.79 3.89

460UB82 3072 563 89 824 649 514 1.1 4.01460UB75 2698 508 70 757 594 469 0.89 3.69460UB67 2366 453 62 707 553 434 0.74 3.44

410UB60 2146 367 53 578 443 339 0.72 3.16410UB54 1996 340 63 563 430 327 0.67 3.08

360UB57 2158 309 51 518 389 288 0.94 3.24360UB51 1867 274 43 473 353 260 0.75 2.96360UB45 1688 247 53 447 331 241 0.65 2.79

310UB46 1764 223 42 370 267 187 0.76 2.71310UB40 1580 204 28 337 241 167 0.6 2.47310UB32 1187 150 38 302 214 145 0.47 2.23

250UB37 1539 157 38 291 199 NR 0.9 2.59250UB31 1288 127 29 277 188 NR 0.8 2.47250UB26 987 103 20 226 151 NR 0.5 2.03

200UB30 1238 102 28 230 144 NR 1.12 2.55200UB25 1047 83 22 212 131 NR 0.94 2.35200UB22 930 73 19 183 112 NR 0.67 2.03200UB18 729 58 11 161 98 NR 0.54 1.82

180UB22 914 63 13 185 108 NR 1.2 2.43180UB18 745 51 11 155 88 NR 0.83 2.03180UB16 661 45 9 139 79 NR 0.66 1.82

150UB18 745 44 9 159 84 NR 1.35 2.43150UB14 577 33 6 132 67 NR 0.97 2.03

310UC158 6151 820 370 798 608 460 3.84 6.01310UC137 5355 704 318 702 528 392 3.19 5.28310UC118 4590 597 270 605 450 327 2.53 4.55310UC97 3794 474 212 533 390 277 1.88 4.01

250UC90 3488 376 174 459 323 NR 2.44 4.25250UC73 2852 299 139 376 260 NR 1.73 3.48

200UC60 2332 201 91 327 210 NR 2.28 3.77200UC52 2038 174 80 281 178 NR 1.8 3.24200UC46 1805 150 68 257 160 NR 1.54 2.96

150UC37 1447 95 42 219 120 NR 2.1 3.28150UC30 1251 80 36 178 95 NR 1.55 2.67150UC23 966 56 24 165 85 NR 1.37 2.47

100UC15 612 24 11 81 NR NR 1.31 2.03

� Vx1 = design shear capacity for uncoped web.� Vx2 = design shear capacity for single coped web. (standard cope = 65 mm)� Vx3 = design shear capacity for double coped web. (standard cope = 65 mm)

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D5WELDED SECTION CAPACITIES—GRADE 300

Axial Moment Shear Bearing

���� Ns ���� Msx ���� Msy ���� Vx1 ���� Vx2 ���� Vx3 ���� Rbb/bb ���� Rby/bbfDesignation

kN kNm kNm kN kN kN KN/mm KN/mm1200WB455 12140 7106 1260 2903 2526 2246 0.78 5.401200WB423 11124 6502 1134 2903 2517 2230 0.78 5.401200WB392 10123 5897 1008 2903 2508 2213 0.78 5.401200WB342 8507 4990 645 2903 2508 2213 0.78 5.401200WB317 7698 4511 564 2903 2498 2196 0.78 5.401200WB278 6468 3780 386 2903 2491 2184 0.78 5.401200WB249 5528 3251 239 2903 2491 2184 0.78 5.40

1000WB322 8524 4133 645 2488 2138 1877 1.02 5.401000WB296 7716 3730 564 2488 2129 1860 1.02 5.401000WB258 6475 3100 386 2488 2122 1848 1.02 5.401000WB215 5460 2584 244 2488 2111 1827 1.02 5.40

900WB282 7590 3427 645 1728 1479 1292 0.57 4.18900WB257 6782 3074 564 1728 1471 1279 0.57 4.18900WB218 5548 2510 386 1728 1466 1269 0.57 4.18900WB175 4456 2025 243 1728 1457 1253 0.57 4.18

800WB192 5024 2016 318 1272 1077 930 0.43 3.49800WB168 4266 1709 238 1272 1073 922 0.43 3.49800WB146 3817 1534 204 1272 1065 908 0.43 3.49800WB122 3007 1215 134 1272 1059 898 0.43 3.49

700WB173 4674 1610 267 1105 928 795 0.54 3.49700WB150 3942 1353 197 1105 924 786 0.54 3.49700WB130 3550 1212 169 1105 916 773 0.54 3.49700WB115 3008 1023 134 1105 910 762 0.54 3.49

500WC440 14112 2621 1263 2419 2019 1715 9.42 12.60500WC414 13306 2545 1263 1935 1615 1372 7.27 10.10500WC383 12298 2301 1137 1935 1598 1340 7.27 10.10500WC340 10886 2263 1008 1701 1403 1176 5.18 7.88500WC290 9324 1908 859 1458 1191 987 3.97 6.75500WC267 8568 1688 748 1458 1182 971 3.97 6.75500WC228 7830 1407 594 1458 1168 945 3.97 6.75

400WC361 11592 1880 809 2117 1749 1470 9.59 12.60400WC328 10534 1789 806 1482 1225 1029 6.36 8.82400WC303 9727 1618 726 1482 1209 1001 6.36 8.82400WC270 8669 1426 645 1323 1066 870 5.55 7.88400WC212 6804 1099 504 1134 894 709 4.43 6.75400WC181 6210 921 408 1134 879 682 4.43 6.75400WC144 4968 699 302 907 694 529 3.23 5.40

350WC280 8996 1245 617 1164 942 772 6.61 8.82350WC258 8291 1121 557 1164 927 744 6.61 8.82350WC230 7384 985 494 1040 814 640 5.81 7.88350WC197 6325 844 433 891 686 528 4.74 6.75

φ Vx1 = design shear capacity for uncoped web.

φ Vx2 = design shear capacity for single coped web. (standard cope = 65 mm)

φ Vx3 = design shear capacity for double coped web. (standard cope = 65 mm)

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D6WELDED SECTION CAPACITIES—GRADE 400

Axial Moment Shear Bearing

φφφφ Ns φφφφ Msx φφφφ Msy φφφφ Vx1 φφφφ Vx2 φφφφ Vx3 φφφφ Rbb/bb φφφφ Rby/bbfDesignation

kN kNm kNm kN kN kN KN/mm KN/mm1200WB455 15308 9040 1620 3677 3200 2846 0.81 6.841200WB423 14006 8262 1458 3677 3188 2824 0.81 6.841200WB392 12724 7484 1264 3677 3176 2803 0.81 6.841200WB342 10641 6318 829 3677 3176 2803 0.81 6.841200WB317 9610 5702 723 3677 3165 2782 0.81 6.841200WB278 8017 4795 496 3677 3156 2766 0.81 6.841200WB249 6820 4082 307 3677 3156 2766 0.81 6.84

1000WB322 10654 5314 829 3152 2709 2377 1.06 6.841000WB296 9626 4795 726 3152 2697 2356 1.06 6.841000WB258 8037 3985 496 3152 2688 2340 1.06 6.841000WB215 6597 3273 303 3152 2674 2314 1.06 6.84

900WB282 9584 4309 829 2229 1908 1667 0.58 5.40900WB257 8539 3856 723 2229 1899 1650 0.58 5.40900WB218 6954 3140 496 2229 1892 1638 0.58 5.40900WB175 5461 2483 302 2229 1880 1617 0.58 5.40

800WB192 6340 2505 408 1642 1390 1200 0.44 4.50800WB168 5367 2119 307 1642 1384 1190 0.44 4.50800WB146 4707 1867 259 1642 1375 1172 0.44 4.50800WB122 3681 1471 166 1642 1367 1158 0.44 4.50

700WB173 5888 2070 343 1426 1198 1025 0.56 4.50700WB150 4945 1740 253 1426 1192 1015 0.56 4.50700WB130 4366 1529 214 1426 1182 997 0.56 4.50700WB115 3680 1289 166 1426 1175 983 0.56 4.50

500WC440 18144 3370 1623 3110 2595 2204 11.90 16.20500WC414 17107 3272 1623 2488 2076 1764 9.10 13.00500WC383 15811 2958 1461 2488 2054 1723 9.10 13.00500WC340 13997 2861 1270 2187 1804 1512 6.35 10.10500WC290 11988 2401 1072 1847 1509 1250 4.68 8.55500WC267 11016 2119 927 1847 1498 1230 4.68 8.55500WC228 9561 1662 718 1847 1479 1197 4.68 8.55

400WC361 14904 2417 1040 2722 2249 1890 12.10 16.20400WC328 13543 2300 1037 1905 1574 1323 7.97 11.30400WC303 12506 2080 933 1905 1555 1287 7.97 11.30400WC270 11146 1834 829 1701 1371 1118 6.91 10.10400WC212 8748 1383 632 1436 1132 898 5.36 8.55400WC181 7866 1139 499 1436 1114 864 5.36 8.55400WC144 6066 824 366 1149 880 670 3.82 6.84

350WC280 11567 1601 794 1497 1211 992 8.34 11.30350WC258 10660 1442 716 1497 1192 957 8.34 11.30350WC230 9493 1267 635 1337 1047 823 7.30 10.10350WC197 8132 1085 557 1129 869 668 5.82 8.55

φVx1 = design shear capacity for uncoped web.

φVx2 = design shear capacity for single coped web. (standard cope = 65 mm)

φVx3 = design shear capacity for double coped web. (standard cope = 65 mm)

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UNIVERSAL BEAMS—GRADE 300

0

100

200

300

400

500

600

700

800

900

1000

0 1 2 3 4 5 6 7 8 9 10

l e (m)

φ φφφ

610UB125

610UB113

610UB101

530UB92

530UB82

460UB75

460UB67

410UB60

410UB54

460UB82

Section Ix Iy

X106mm

4X10

6mm

4

610 UB 125 986 39.3610 UB 113 875 34.3610 UB 101 761 29.3

530 UB 92 554 23.8530 UB 82 477 20.1

460 UB 82 372 18.6460 UB 75 335 16.6460 UB 67 296 14.5

410 UB 60 216 12.1410 UB 54 188 10.3

D7

Y

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UNIVERSAL BEAMS—GRADE 300

0

50

100

150

200

250

300

0 1 2 3 4 5 6 7 8 9 10

l e (m)

φ φφφ

360UB57

360UB51

360UB45

310UB40

310UB32

250UB37

250UB31

250UB26

310UB46

310UB46

360UB45

D8

Y

Y

XX

Section Ix Iy X10

6mm

4X10

6mm

4

360 UB 57 161 11.0360 UB 51 142 9.60360 UB 45 121 8.10

310 UB 46 100 9.01310 UB 40 86.4 7.65310 UB 32 63.2 4.42

250 UB 37 55.7 5.66250 UB 31 44.5 4.47250 UB 26 35.4 2.55

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UNIVERSAL BEAMS—GRADE 300

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10

l e (m)

φ φφφ

200UB30

200UB25

200UB22

200UB18

180UB22

180UB18

180UB16

150UB18

150UB14

180UB16

D9

Y

Y

XX

Section Ix Iy

X106mm

4X10

6mm

4

200 UB 30 29.1 3.86200 UB 25 23.6 3.06200 UB 22 21.0 2.75200 UB 18 15.8 1.14

180 UB 22 15.3 1.22180 UB 18 12.1 0.975180 UB 16 10.6 0.853

150 UB 18 9.05 0.672150 UB 14 6.66 0.495

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UNIVERSAL BEAMS—GRADE 350

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0 1 2 3 4 5 6 7 8 9 10

l e (m)

φ φφφ

610UB125

610UB113

610UB101

530UB92

530UB82

460UB75

460UB67

410UB60

410UB54

460UB82

D10

Y

Y

XX

Section Ix Iy X10

6mm

4 X10

6mm

4

610 UB 125 986 39.3610 UB 113 875 34.3610 UB 101 761 29.3

530 UB 92 554 23.8530 UB 82 477 20.1

460 UB 82 372 18.6460 UB 75 335 16.6460 UB 67 296 14.5

410 UB 60 216 12.1410 UB 54 188 10.3

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UNIVERSAL BEAMS—GRADE 350

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8 9 10

l e (m)

φ φφφ

360UB57

360UB51

360UB45

310UB40

310UB32

250UB37

250UB31

250UB26

310UB46

310UB46360UB45

D11

Y

Y

XX

Section Ix Iy X10

6mm

4 X10

6mm

4

360 UB 57 161 11.0360 UB 51 142 9.60360 UB 45 121 8.10

310 UB 46 100 9.01310 UB 40 86.4 7.65310 UB 32 63.2 4.42

250 UB 37 55.7 5.66250 UB 31 44.5 4.47250 UB 26 35.4 2.55

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0

10

20

30

40

50

60

70

80

90

100

110

0 1 2 3 4 5 6 7 8 9 10

l e(m)

φ φφφ

200UB30

200UB25

200UB22

200UB18

180UB22

180UB18

180UB16

150UB18

150UB14

180UB16

D12

Section Ix Iy X10

6mm

4 X10

6mm

4

200 UB 30 29.1 3.86200 UB 25 23.6 3.06200 UB 22 21.0 2.75200 UB 18 15.8 1.14

180 UB 22 15.3 1.22180 UB 18 12.1 0.975180 UB 16 10.6 0.853

150 UB 18 9.05 0.672150 UB 14 6.66 0.495

Y

Y

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UNIVERSAL COLUMNS—GRADE 300

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10

l e (m)

φ φφφ

310UC158

310UC137

310UC118

310UC97

250UC90

250UC73

D13

Y

Y

XX

Section Ix Iy X10

6mm

4 X10

6mm

4

310 UC 158 388 125310 UC 137 329 107310 UC 118 277 90.2310 UC 97 223 72.9

250 UC 90 143 48.4250 UC 73 114 38.8

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UNIVERSAL COLUMNS—GRADE 300

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

0 1 2 3 4 5 6 7 8 9 10

l e (m)

φ φφφ

200UC60

200UC52

200UC46

150UC37

150UC30

150UC23

100UC15

D14

Y

Y

XX

Section Ix Iy X10

6mm

4X10

6mm

4

200 UC 60 61.3 20.4200 UC 52 52.8 17.7200 UC 46 45.9 15.3

150 UC 37 22.2 7.01150 UC 30 17.6 5.62150 UC 23 12.6 3.98

100 UC 15 3.18 1.14

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UNIVERSAL COLUMNS—GRADE 350

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6 7 8 9 10

l e (m)

φ φφφ

310UC158

310UC137

310UC118

310UC97

250UC90

250UC73

D15

Section Ix Iy X10

6mm

4 X10

6mm

4

310 UC 158 388 125310 UC 137 329 107310 UC 118 277 90.2310 UC 97 223 72.9

250 UC 90 143 48.4250 UC 73 114 38.8

Y

Y

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UNIVERSAL COLUMNS—GRADE 350

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

210

0 1 2 3 4 5 6 7 8 9 10

l e (m)

φ φφφ

200UC60

200UC52

200UC46

150UC37

150UC30

150UC23

100UC15

D16

Section Ix Iy X10

6mm

4 X10

6mm

4

200 UC 60 61.3 20.4200 UC 52 52.8 17.7200 UC 46 45.9 15.3

150 UC 37 22.2 7.01150 UC 30 17.6 5.62150 UC 23 12.6 3.98

100 UC 15 3.18 1.14

Y

Y

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WELDED BEAMS—GRADE 300

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

l e (m)

φ φφφ

D17

1200WB455

1200WB423

1200WB392

1200WB342

1200WB317

1000WB322

1000WB296

900WB282

1000WB258

900WB257

900WB218

800WB192

700WB173

700WB150

Section Ix Iy X10

6mm

4 X10

6mm

4

1200 WB 455 15300 8341200 WB 423 13900 7501200 WB 392 12500 6671200 WB 342 10400 3421200 WB 317 9250 299

1000 WB 322 7480 3421000 WB 296 6650 2991000 WB 258 5430 179

900 WB 282 5730 341900 WB 257 5050 299900 WB 218 4060 179

800 WB 192 2970 126

700 WB 173 2060 97.1700 WB 150 1710 65.2

Y

Y

XX

900WB257

1000WB258

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WELDED BEAMS—GRADE 300

0

500

1000

1500

2000

2500

3000

3500

4000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

l e (m)

φ φφφD18

1200WB278

1200WB249

1000WB215

900WB175

800WB168

700WB115

700WB130

800WB122

800WB146

Y

Y

XX

Section Ix Iy X10

6mm

4 X10

6mm

4

1200 WB 278 7610 1791200 WB 249 6380 87.0

1000 WB 215 4060 90.3

900 WB 175 2960 90.1

800 WB 168 2480 86.7 800 WB 146 2040 69.4 800 WB 122 1570 41.7

700 WB 130 1400 52.1 700 WB 115 1150 41.7

700WB130

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WELDED BEAMS—GRADE 400

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

l e (m)

φ φφφ

D19

Y

Y

XX

1200 WB 455

1200 WB 423

1200 WB 392

1200 WB 342

1200 WB 317

1000 WB 322

1000 WB 296

900 WB 282

1000 WB 258

900 WB 257

900 WB 218

800 WB 192

700 WB 173

700 WB 150

Section Ix Iy X10

6mm

4 X10

6mm

4

1200 WB 455 15300 8341200 WB 423 13900 7501200 WB 392 12500 6671200 WB 342 10400 3421200 WB 317 9250 299

1000 WB 322 7480 3421000 WB 296 6650 2991000 WB 258 5430 179

900 WB 282 5730 341 900 WB 257 5050 299 900 WB 218 4060 179

800 WB 192 2970 126

700 WB 173 2060 97.1 700 WB 150 1710 65.2

900WB257

1000WB258

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WELDED BEAMS—GRADE 400

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

l e (m)

φ φφφ

D20

1200 WB 278

1200 WB 249

1000 WB 215

900 WB 175

800 WB 168

800 WB 146

700 WB 130

800 WB 122

700 WB 115

Y

Y

XX

Section Ix Iy X10

6mm

4X10

6mm

4

1200 WB 278 7610 1791200 WB 249 6380 87.0

1000 WB 215 4060 90.3

900 WB 175 2960 90.1

800 WB 168 2480 86.7 800 WB 146 2040 69.4 800 WB 122 1570 41.7

700 WB 130 1400 52.1 700 WB 115 1150 41.7

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WELDED COLUMNS—GRADE 300

0

500

1000

1500

2000

2500

3000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

l e (m)

φ φφφ

D21

500 WC 440

500 WC 414

500 WC 383

500 WC 340

400 WC 361

400 WC 328

500 WC 267

500 WC 228

350 WC 258

Y

Y

XX

Section Ix Iy X10

6mm

4X10

6mm

4

500 WC 440 2150 835500 WC 414 2110 834500 WC 383 1890 751500 WC 340 2050 667500 WC 267 1560 521500 WC 228 1260 417

400 WC 361 1360 429400 WC 328 1320 427

350 WC 258 661 258

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WELDED COLUMNS—GRADE 300

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

l e (m)

φ φφφ

D22

Section Ix Iy X10

6mm

4 X10

6mm

4

500 WC 290 1750 584

400 WC 303 1180 385400 WC 270 1030 342400 WC 212 776 267400 WC 181 620 214400 WC 144 486 171

350 WC 280 747 286350 WC 230 573 229350 WC 197 486 200

Y

Y

XX

500 WC 290

400 WC 303

400 WC 270

350 WC 280

400 WC 212

350 WC 230

400 WC 181

350 WC 197

400 WC 144

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WELDED COLUMNS—GRADE 400

0

500

1000

1500

2000

2500

3000

3500

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

l e (m)

φ φφφD23

500 WC 440

500 WC 414

500 WC 383

500 WC 340

400 WC 361

400 WC 328

500 WC 267

500 WC 228

350 WC 258

Section Ix Iy X10

6mm

4X10

6mm

4

500 WC 440 2150 835500 WC 414 2110 834500 WC 383 1890 751500 WC 340 2050 667500 WC 267 1560 521500 WC 228 1260 417

400 WC 361 1360 429400 WC 328 1320 427

350 WC 258 661 258

Y

Y

XX

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WELDED COLUMNS—GRADE 400

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

l e (m)

φ φφφ

D24

500 WC 290

400 WC 303

400 WC 270

350 WC 280

400 WC 212

350 WC 230

400 WC 181

350 WC 197

400 WC 144

Section Ix Iy X10

6mm

4X10

6mm

4

500 WC 290 1750 584

400 WC 303 1180 385400 WC 270 1030 342400 WC 212 776 267400 WC 181 620 214400 WC 144 486 171

350 WC 280 747 286350 WC 230 573 229350 WC 197 486 200

Y

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PART III

WORKED EXAMPLES

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INTRODUCTION TO THE WORKED EXAMPLES

This part of the Handbook offers a series of sample computations to demonstrate theapplication of the simplified design rules and design aids found in Part I and Part II.The examples have been derived from actual designs, but have been simplified todemonstrate particular aspects of design problems rather than to provide solutions tocomplete design tasks.

All examples follow a common format, which includes:

(i) a statement of the problem, including the geometry of the structure, and its loading,

(ii) proposed solutions

(iii) commentary on the solutions offered (in selected instances)

The alternative solutions make varying use of the design aids and demonstrate different‘tiers’ of design methodology in some instances.

References to the appropriate paragraph of the Handbook are given in the right-handmargin.

All problems are solved using only this Handbook, a booklet of section properties, and arudimentary hand-held calculator. Most of the computations are strength checks, thisbeing the area on which the Handbook has concentrated. The loads are calculated withthe appropriate load factors. In some instances, a serviceability Limit State is alsochecked as a reminder that, in Limit States Design, both types of Limit States must bedesigned for.

The computations have been carried out with a degree of accuracy appropriate to alower tier design.

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