Seel Building Design: Design Daa The Seel Consrucion Insiue and The Briish Consrucional Seelwork Associaion Limied
The Seel Consrucion Insiue develops and promoes he eecive use o seel in consrucion. I is an independen, membership based organisaion. SCI's research and developmen aciviies cover man aspecs o seel consrucion including mulisore consrucion, indusrial buildings, ligh seel raming ssems and modular consrucion, developmen o design guidance on he use o sainless seel, ire engineering, bridge and civil engineering, oshore engineering, environmenal sudies, value engineering, and developmen o srucural analsis ssems and inormaion echnolog. Membership is open o all organisaions and individuals ha are concerned wih he use o seel in consrucion. Members include designers, conracors, suppliers, abricaors, academics and governmen deparmens in he Unied Kingdom, elsewhere in Europe and in counries around he world. The SCI is inanced b subscripions rom is members, revenue rom research conracs and consulanc services, publicaion sales and course ees. The beneis o corporae membership include access o an independen specialis advisor service and ree issue o SCI publicaions as soon as he are produced. A Membership Inormaion Pack is available on reques rom he Membership Manager. The Seel Consrucion Insiue, Silwood Park, Asco, Berkshire, SL5 7QN. Telephone: +44 (0) 144 6655 Fax: +44 (0) 144 66570 Email: recepion@seel-sci.com World Wide Web sie: www.seel-sci.org The Briish Consrucional Seelwork Associaion Limied. The Briish Consrucional Seelwork Associaion Limied was ormed in 1906 and is he naional organisaion or he Consrucional Seelwork Indusr; is Member companies underake he design, abricaion and erecion o seelwork or all orms o consrucion in building and civil engineering. Associae Members are hose principal companies involved in he suppl o all or some Members o componens, maerials or producs. The principal objecives o he Associaion are o promoe he use o srucural seelwork; o assis speciiers and cliens; o ensure ha he capabiliies and aciviies o he indusr are widel undersood and o provide members wih proessional services in echnical, commercial, conracual, quali assurance, and healh and sae maers. The Associaion s aim is o inluence he rading environmen in which member companies have o operae in order o improve heir proiabili. The Briish Consrucional Seelwork Associaion Ld., 4 Whiehall Cour, London, SW1A ES. Telephone: +44 (00) 789 8566 Fax: +44 (00) 7976 164 Email: posroom@seelconsrucion.org World Wide Web sie: www.seelconsrucion.org
Publicaion P6 (Updaed Ocober 014) Seel Building Design: Design Daa In accordance wih Eurocodes and he UK Naional Annexes Joinl published b: The Seel Consrucion Insiue Silwood Park, Asco, Berkshire, SL5 7QN Telephone: 0144 6655 Fax: 0144 66570 The Briish Consrucional Seelwork Associaion Limied 4 Whiehall Cour, London, SW1A ES Telephone: 00 789 8566 Fax: 00 7976 164
The Seel Consrucion Insiue and The Briish Consrucional Seelwork Associaion Ld., 009, 011, 01, 014 Apar rom an air dealing or he purposes o research or privae sud or criicism or review, as permied under he Coprigh Designs and Paens Ac, 1988, his publicaion ma no be reproduced, sored, or ransmied, in an orm or b an means, wihou he prior permission in wriing o he publishers, or in he case o reprographic reproducion onl in accordance wih he erms o he licences issued b he UK Coprigh Licensing Agenc, or in accordance wih he erms o licences issued b he appropriae Reproducion Righs Organisaion ouside he UK. Enquiries concerning reproducion ouside he erms saed here should be sen o he publishers, a he addresses given on he ile page. Alhough care has been aken o ensure, o he bes o our knowledge, ha all daa and inormaion conained herein are accurae o he exen ha he relae o eiher maers o ac or acceped pracice or maers o opinion a he ime o publicaion, The Seel Consrucion Insiue and The Briish Consrucional Seelwork Associaion Limied assume no responsibili or an errors in or misinerpreaions o such daa and/or inormaion or an loss or damage arising rom or relaed o heir use. Publicaions supplied o he Members o SCI and BCSA a a discoun are no or resale b hem. Publicaion Number: SCI P6 ISBN 978-1-8594-186-4 Briish Librar Caaloguing-in-Publicaion Daa. A caalogue record or his book is available rom he Briish Librar. ii
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FOREWORD This publicaion presens design daa derived in accordance wih he ollowing Pars o Eurocode and heir Naional Annexes: BS EN 199-1-1:005: Design o seel srucures. Par 1-1: General rules and rules or buildings. BS EN 199-1-5:006: Design o seel srucures. Par 1-5: Plaed srucural elemens. BS EN 199-1-8:005: Design o seel srucures. Par 1-8: Design o joins. Where hese Pars do no give all he necessar expressions or he evaluaion o daa, reerence is made o oher published sources. The resisances in his publicaion have been calculaed using he parial acors or resisance given in he UK Naional Annexes or he Eurocodes (NA o BS EN 199-1-1:005 as published in December 008, NA o BS EN 199-1-5:006 as published in Ma 008 and NA o BS EN 199-1-8:005 as published in November 008). The parial acors are lised in Secion 5.1. The oher parameers given in he Naional Annex ha have been used when calculaing member resisances are given in he relevan secion o his publicaion. The ollowing srucural secions are covered in his publicaion: Universal beams, universal columns, joiss, bearing piles, parallel lange channels and srucural ees cu rom universal beams and universal columns o BS 4-1 Universal beams and universal columns produced b Taa Seel bu no included in BS 4-1 Asmmeric Slimlor beams (ASB) produced b Taa Seel Equal and unequal angles o BS EN 10056-1 Ho-inished srucural hollow secions o BS EN 1010- Cold-ormed srucural hollow secions o BS EN 1019- Secion ranges lised cover secions ha are readil available a he ime o prining. The preparaion and ediorial work or his Ediion was carried ou b Miss E Nune Moreno and Mr E Yandio, boh o he SCI, wih echnical assisance rom Mr A S Malik o he SCI and Mr C M King, ormerl o he SCI. The projec was coordinaed b Mr D G Brown, also o he SCI. The work leading o his publicaion has been joinl unded b Taa Seel, SCI and BCSA and heir suppor is graeull acknowledged. Reprin - Ma 011 Several correcions have been made, including clariicaion in he explanaor noes. Raios used or he classiicaion o ees and cold ormed secions have been correced. The onl changes o abulaed member resisances are he shear resisances o parallel lange channels. A ew minor ormaing errors have been correced in he design ables. Revision 01 In his revision, addiional bending resisances are presened or values o C 1 ha correspond o common design siuaions. More explanaion is given in noe 8. The secion range or ho inished hollow secions has been modiied. The calculaed bol bearing resisances are based on he geomer quoed in he ables, no he nominal values. All reerences o he seel manuacurer reer o Taa Seel. iv
Revision Ocober 014 In his revision, he secion range or ho inished hollow secions has been exended o include S40 secions supplied b Taa Seel. v
CONTENTS vi Page No (Whie pages) 1 EXPLANATORY NOTES 1 1.1 GENERAL 1 1.1.1 Maerial, secion dimensions and olerances 1 1.1. Dimensional unis 1.1. Proper unis 1.1.4 Mass and orce unis 1.1.5 Axis convenion DIMENSIONS OF SECTIONS.1 Masses. Raios or local buckling. Dimensions or deailing..1 UB secions, UC secions and bearing piles.. Joiss.. Parallel lange channels 4 SECTION PROPERTIES 5.1 General 5. Secions oher han hollow secions 5..1 Second momen o area (I) 5.. Radius o graion (i) 5.. Elasic secion modulus (W el) 5..4 Plasic secion modulus (W pl) 5..5 Buckling parameer (U) and orsional index (X) 5..6 Warping consan (I w) and orsional consan (I T) 6..7 Equivalen slenderness coeicien ( ) and monosmmer index ( ) 8. Hollow secions 10..1 Common properies 10.. Plasic secion modulus o hollow secions (W pl) 10.. Torsional consan (I T) 10..4 Torsional secion modulus (W ) 10 4 EFFECTIVE SECTION PROPERTIES 1 4.1 General 1 4. Eecive secion properies o members subjec o compression 1 4. Eecive secion properies o members subjec o pure bending 1 5 INTRODUCTION TO RESISTANCE TABLES 14 5.1 General 14 5. Yield srengh 14 6 COMPRESSION TABLES 15 6.1 Compression members: UB and UC secions 15 6. Compression members: hollow secions 17 6. Compression members: parallel lange channels 19 6.4 Compression members: single angles 1
7 TENSION TABLES 4 7.1 Tension members: Single angles 4 8 BENDING TABLES 5 8.1 Bending: UB secions, UC secions, joiss and parallel lange channels 5 8.1.1 Design resisance o cross secion 5 8.1. Design laeral orsional buckling resisance momen 5 8. Bending: Hollow secions 7 8..1 Circular and square hollow secions 7 8.. Recangular hollow secions 8 8.. Ellipical hollow secions 9 9 RESISTANCE TO TRANSVERSE FORCES TABLES (WEB BEARING AND BUCKLING) 0 9.1 UB secions, UC secions, joiss and parallel lange channels 0 9. Square and recangular hollow secions 1 10 AXIAL FORCE & BENDING TABLES 5 10.1 Axial orce and bending: UB secions, UC secions, joiss and parallel lange channels 5 10.1.1 Cross secion resisance check 5 10.1. Member buckling check 7 10. Axial orce and bending: hollow secions 8 10..1 Cross secion resisance check 8 10.. Member buckling check 40 11 BOLTS AND WELDS 4 11.1 Bol resisances 4 11. Welds 45 1 SECTION DESIGNATIONS AND STEEL GRADES 47 1.1 Open Secions 47 1. Hollow Secions 48 1 REFERENCES 50 vii
B.1 TABLES OF DIMENSIONS AND GROSS SECTION PROPERTIES (Yellow pages) Universal beams B- Universal columns B-8 Joiss B-10 Universal bearing piles B-1 Ho-inished circular hollow secions B-14 Ho-inished square hollow secions B-18 Ho-inished recangular hollow secions B- Ho-inished ellipical hollow secions B-9 Cold-ormed circular hollow secions B-0 Cold-ormed square hollow secions B- Cold-ormed recangular hollow secions B-6 ASB (Asmmeric beams) B-40 Parallel lange channels B-4 Two parallel lange channels laced B-44 Two parallel lange channels back o back B-45 Equal angles B-47 Unequal angles B-48 Equal angles back o back B-50 Unequal angles long leg back o back B-51 Srucural ees cu rom universal beams B-5 Srucural ees cu rom universal columns B-56 viii
B. TABLES OF EFFECTIVE SECTION PROPERTIES (Blue pages) Universal beams subjec o compression B-6 Ho-inished square hollow secions subjec o compression B-65 Cold-ormed square hollow secions subjec o compression B-66 Ho-inished recangular hollow secions subjec o compression B-67 Cold-ormed recangular hollow secions subjec o compression B-69 Equal angles subjec o compression B-70 Unequal angles subjec o compression B-71 Ho-inished square hollow secions subjec o bending abou - axis B-7 Cold-ormed square hollow secions subjec o bending abou - axis B-74 Ho-inished recangular hollow secions subjec bending abou - axis B-75 Cold-ormed recangular hollow secions subjec bending abou - axis B-77 ix
Seel Grade S75 S55 C,D MEMBER RESISTANCE TABLES (Pink pages) (Green pages) Compression Universal beams C- D- Universal columns C-11 D-11 Ho-inished circular hollow secions * D-14 Ho-inished square hollow secions * D-18 Ho-inished recangular hollow secions * D- Ho-inished ellipical hollow secions * D-7 Cold-ormed circular hollow secions * D-9 Cold-ormed square hollow secions * D-4 Cold-ormed recangular hollow secions * D-45 Parallel lange channels - subjec o concenric axial C-5 D-5 compression Parallel lange channels - conneced hrough web C-55 D-55 Equal angles C-57 D-57 Unequal angles - Shor leg aached C-59 D-59 Unequal angles - Long leg aached C-61 D-61 Tension: Equal angles C-6 D-6 Unequal angles - Shor leg aached C-66 D-66 Unequal angles - Long leg aached C-69 D-69 Bending Universal beams C-7 D-7 Universal columns C-9 D-9 Joiss C-100 D-100 Ho-inished circular hollow secions * D-10 Ho-inished square hollow secions * D-108 Ho-inished recangular hollow secions * D-11 Ho-inished ellipical hollow secions * D-119 Cold-ormed circular hollow secions * D-10 Cold-ormed square hollow secions * D-1 Cold-ormed recangular hollow secions * D-16 Parallel lange channels C-10 D-10 * Tables or hese srucural secions in S75 have no been prepared. See noes on pages C-14 and C-10. x
Seel Grade S75 S55 C,D MEMBER RESISTANCE TABLES (Pink pages) (Green pages) Web bearing and buckling Universal beams C-14 D-14 Universal columns C-14 D-14 Joiss C-146 D-146 Ho-inished square hollow secions * D-147 Ho-inished recangular hollow secions * D-151 Cold-ormed square hollow secions * D-158 Cold-ormed recangular hollow secions * D-161 Parallel lange channels C-165 D-165 Axial orce and bending Universal beams C-168 D-168 Universal columns C-196 D-196 Joiss C-06 D-06 Ho-inished circular hollow secions * D-10 Ho-inished square hollow secions * D-8 Ho-inished recangular hollow secions * D-44 Ho-inished ellipical hollow secions * D-08 Cold-ormed circular hollow secions * D-1 Cold-ormed square hollow secions * D-4 Cold-ormed recangular hollow secions * D-6 Parallel lange channels C-76 D-76 Bol resisances Non preloaded bols hexagon head C-80 D-80 Non preloaded bols counersunk C-8 D-8 Preloaded bols a serviceabili limi sae (Caegor B) Preloaded bols in ension (Caegor E) C-86 C-86 D-86 D-86 Preloaded bols a ulimae limi sae (Caegor C) C-88 D-88 Preloaded bols a serviceabili limi sae counersunk C-90 D-90 (Caegor B) Preloaded bols a ulimae limi sae counersunk (Caegor C) C-9 D-9 Fille Welds Design weld resisances C-94 D-94 * Tables or hese srucural secions in S75 have no been prepared. See noes on pages C-147 and C-10. xi
1 EXPLANATORY NOTES 1.1 GENERAL This publicaion presens design daa in abular ormas as assisance o engineers who are designing buildings in accordance wih BS EN 199-1-1: 005 [1], BS EN 199-1-5: 006 [1] and BS EN 199-1-8: 005 [1], and heir respecive Naional Annexes. Where hese Pars do no give all he necessar expressions or he evaluaion o daa, reerence is made o oher published sources. The smbols used are generall he same as hose in hese sandards or he reerred produc sandards. Where a smbol does no appear in he sandards, a smbol has been chosen ollowing he designaion convenion as closel as possible. 1.1.1 Maerial, secion dimensions and olerances The srucural secions reerred o in his design guide are o weldable srucural seels conorming o he relevan Briish Sandards given in he able below: Table 1.1 Srucural seel producs Produc Technical deliver requiremens Dimensions Tolerances Non allo seels Fine grain seels Universal beams, Universal columns, and universal bearing piles BS 4-1 [] BS EN 1004 [4] BS 4-1 Joiss BS 4-1 BS EN 1004 [5] BS EN 1005- [] BS EN 1005- [] Parallel lange channels BS EN 1005-4 [] BS 4-1 BS EN 1079 [6] Angles BS EN 10056-1 [7] BS EN 10056- [7] Srucural ees cu rom universal beams and universal columns BS 4-1 ASB (asmmeric beams) Slimlor beam Generall BS EN 1005, bu see noe b) See noe a) Generall BS EN 1004 [4], bu also see noe b) Ho inished srucural hollow secions BS EN 1010-1 [8] BS EN 1010- [8] BS EN 1010- [8] Cold ormed hollow secions BS EN 1019-1 [9] BS EN 1019- [9] BS EN 1019- [9] Noes: For ull deails o he Briish Sandards, see he reerence lis a he end o he Explanaor Noes. a) See Taa Seel publicaion, Advance Secions: CE marked srucural secions [11]. b) For urher deails, consul Taa Seel. Noe ha EN 199 reers o he produc sandards b heir CEN designaion, e.g. EN 1005-. The CEN sandards are published in he UK b BSI wih heir preix o he designaion, e.g. BS EN 1005-. 1
1.1. Dimensional unis The dimensions o secions are given in millimeres (mm). 1.1. Proper unis Generall, he cenimere (cm) is used or he calculaed properies bu or surace areas and or he warping consan (I w), he mere (m) and he decimere (dm) respecivel are used. Noe: 1 dm = 0.1 m = 100 mm 1 dm 6 = 1 10-6 m 6 = 1 10 1 mm 6 1.1.4 Mass and orce unis The unis used are he kilogram (kg), he Newon (N) and he mere per second squared (m/s ), so ha 1 N = 1 kg 1 m/s. For convenience, a sandard value o he acceleraion due o gravi has been acceped as 9.80665 m/s. Thus, he orce exered b 1 kg under he acion o gravi is 9.80665 N and he orce exered b 1 onne (1000 kg) is 9.80665 kilonewons (kn). 1.1.5 Axis convenion The axis ssem used in BS EN 199 is: x along he member major axis, or axis perpendicular o web minor axis, or axis parallel o web This ssem is convenien or srucural analsis using compuer programs. However, i is dieren rom he axis ssem previousl used in UK sandards such as BS 5950.
DIMENSIONS OF SECTIONS.1 Masses The masses per mere have been calculaed assuming ha he densi o seel is 7850 kg/m. In all cases, including compound secions, he abulaed masses are or he seel secion alone and no allowance has been made or connecing maerial or iings.. Raios or local buckling The raios o he lange ousand o hickness (c / ) and he web deph o hickness (c w / w) are given or I, H and channel secions. 1 c b w r or I and H secions c b w r or channels cw d h r or I, H and channel secions For circular hollow secions he raios o he ouside diameer o hickness (d / ) are given. For square and recangular hollow secions he raios (c / ) and (c w / ) are given c b and c h w For square hollow secions c and c w are equal. Noe ha hese relaionships or c and c w are applicable o boh ho-inished and cold-ormed secions. The dimensions c and c w are no precisel deined in EN 199-1-1 and he inernal proile o he corners is no speciied in eiher EN 1010- or EN 1019-. The above expressions give conservaive values o he raio or boh ho-inished and cold-ormed secions.. Dimensions or deailing The dimensions C, N and n have he meanings given in he igures a he heads o he ables and have been calculaed according o he ormulae below. The ormulae or N and C make allowance or rolling olerances, whereas he ormulae or n make no such allowance...1 UB secions, UC secions and bearing piles N = (b w) / + 10 mm n = (h d) / C = w / + mm.. Joiss N = (b w) / + 6 mm n = (h d) / C = w / + mm (rounded o he neares mm above) (rounded o he neares mm above) (rounded o he neares mm) (rounded o he neares mm above) (rounded o he neares mm above) (rounded o he neares mm) Noe: Flanges o BS 4-1 joiss have an 8 o aper.
.. Parallel lange channels N = (b w) + 6 mm (rounded up o he neares mm above) n = (h d) / (aken o he nex higher muliple o mm) C = w + mm (rounded up o he neares mm) 4
SECTION PROPERTIES.1 General All secion properies have been accurael calculaed and rounded o hree signiican igures. The have been calculaed rom he meric dimensions given in he appropriae sandards (see Secion 1.1). For angles, BS EN 10056-1 assumes ha he oe radius equals hal he roo radius.. Secions oher han hollow secions..1 Second momen o area (I) The second momen o area has been calculaed aking ino accoun all apers, radii and illes o he secions. Values are given abou boh he - and - axes... Radius o graion (i) The radius o graion is a parameer used in he calculaion o buckling resisance and is derived as ollows: i = [I / A] 1/ I A is he second momen o area abou he relevan axis is he area o he cross secion... Elasic secion modulus (Wel) The elasic secion modulus is used o calculae he elasic design resisance or bending or o calculae he sress a he exreme ibre o he secion due o a momen. I is derived as ollows: W el, = I / W el, = I /, are he disances o he exreme ibres o he secion rom he elasic - and - axes, respecivel. For parallel lange channels, he elasic secion modulus abou he minor (-) axis is given or he exreme ibre a he oe o he secion onl. For angles, he elasic secion moduli abou boh axes are given or he exreme ibres a he oes o he secion onl. For elasic secion moduli abou he principal axes u-u and v-v, see AD40 [16]. For asmmeric beams, he elasic secion moduli abou he - axis are given or boh op and boom exreme ibres, and abou he - axis or he exreme ibre...4 Plasic secion modulus (Wpl) The plasic secion moduli abou boh - and - axes are abulaed or all secions excep angle secions...5 Buckling parameer (U) and orsional index (X) UB secions, UC secions, joiss and parallel lange channels The buckling parameer (U) and orsional index (X) have been calculaed using expressions in Access Seel documen SN00 Deerminaion o non-dimensional slenderness o I and H secions []. 5
Wpl, U A X g E A I T 0.5 0G I I w I I w 0.5 W pl, is he plasic modulus abou he major axis g = I I E G I 1 I is he second momen o area abou he major axis is he second momen o area abou he minor axis = 10 000 N/mm is he modulus o elasici is he shear modulus where G is Poisson s raio (= 0.) A I w I T is he cross secional area is he warping consan is he orsional consan. Tee secions and ASB secions E 1 The buckling parameer (U) and he orsional index (X) have been calculaed using he ollowing expressions: U = [(4 W pl, g / (A h )] 1/4 X = 0.566 h [A/ I T] 1/ W pl, is he plasic modulus abou he major axis g = I I A h I T I 1 I is he second momen o area abou he major axis is he second momen o area abou he minor axis is he cross secional area is he disance beween shear cenres o langes (or T secions, h is he disance beween he shear cenre o he lange and he oe o he web) is he orsional consan...6 Warping consan (Iw) and orsional consan (IT) Rolled I secions The warping consan and S Venan orsional consan or rolled I secions have been calculaed using he ormulae given in he SCI publicaion P057 Design o members subjec o combined bending and orsion [1]. In Eurocode erminolog, hese ormulae are as ollows: I w = I h s 4 6
I is he second momen o area abou he minor axis h s is he disance beween shear cenres o langes (i.e. h s = h ) b 1 4 4 I T = h w 1D1 0. 40 1 = 0.04 + 0.04 w + 0.155 D 1 = r r 0.5 w b h w r Tee secions r is he widh o he secion is he deph o he secion is he lange hickness is he web hickness is he roo radius. w r 0.0865 r w w 0.075 For Tee secions cu rom UB and UC secions, he warping consan (I w) and orsional consan (I T) have been derived as given below. I w = 1 144 1 b b 1 1 6 h 4 4 4 I T = w h w 1D1 0.1 0. 105 w r w r w 1 = 0.04 + 0.04 0.155 0.0865 0.075 D 1 is as deined above Noe: These ormulae do no appl o ee secions cu rom joiss, which have apered langes. For such secions, expressions are given in SCI Publicaion 057 [1]. Parallel lange channels For parallel lange channels, he warping consan (I w) and orsional consan (I T) have been calculaed as ollows: ( h ) I w = 4 1 I A c w ( h ) 4I 4 4 I T = b h D 0. c w 4 A 1 is he disance rom he back o he web o he cenroidal axis w α = 0.0908 0.61 w r 0.11 [ w w 0.075 D = r r r ] r w 0.0945 w 7
Noe: The ormula or he orsional consan (I T) is applicable o parallel lange channels onl and does no appl o apered lange channels. Angles For angles, he orsional consan (I T) is calculaed as ollows: 1 b 1 h D 4 4 I T = α = 0.0768 +0.0479 r D = r r ASB secions 0.1 For ASB secions he warping consan (I w) and orsional consan (I T) are as given in Taa brochure, Advance secions [11]...7 Equivalen slenderness coeicien ( ) and monosmmer index ( ) Angles The buckling resisance momens or angles have no been included in he bending resisance ables o his publicaion as angles are predominanl used in compression and ension onl. Where he designer wishes o use an angle secion in bending, BS EN 199-1-1, 6.. enables he buckling resisance momen or angles o be deermined. The procedure is quie involved. As an alernaive o he procedure in BS EN 199-1-1, supplemenar secion properies have been included or angle secions in his publicaion which enable he designer o adop a much simpliied mehod or deermining he buckling resisance momen. The mehod is based on ha given in BS 5950-1:000 Annex B..9 and makes use o he equivalen slenderness coeicien and he monosmmer index. The equivalen slenderness coeicien ( a) is abulaed or boh equal and unequal angles. Two values o he equivalen slenderness coeicien are given or each unequal angle. The larger value is based on he major axis elasic secion modulus (W el,u) o he oe o he shor leg and he lower value is based on he major axis elasic secion modulus o he oe o he long leg. The equivalen slenderness coeicien ( a) is calculaed as ollows: W el,u g a AI T W el,u is he elasic secion modulus abou he major axis u-u g = I 1 I v u I v I u A I T is he second momen o area abou he minor axis is he second momen o area abou he major axis is he area o he cross secion is he orsional consan. 8
The monosmmer index ( a) is calculaed as ollows: a v 0 u i and v i v 0 Tee secions v i u i I v u i da 1 are he coordinaes o an elemen o he cross secion is he coordinae o he shear cenre along he v-v axis, relaive o he cenroid is he hickness o he angle. The monosmmer index is abulaed or Tee secions cu rom UBs and UCs. I has been calculaed as: 0 0 b 0 = c - / 1 b 0 w 4 I 4 c h c c is he widh o he lange ousand ( = (b w r)/ ) b w h is he lange widh is he lange hickness is he web hickness is he deph o he secion. The above expression is based on BS 5950-1, Annex B..8.. ASB secions 9 4 1 h The monosmmer index is abulaed or ASB secions. I has been calculaed using he equaion in BS 5950-1, Annex B..4.1, re-expressed in BS EN 199-1-1 nomenclaure: 1 hs I c I h c c I I h h s = c h d c = h c c / d = h / I c = b c c / 1 I = b / 1 h c h b c b c 4 4 I h I h b h b h d d c c c is he disance rom he cenre o he compression lange o he cenroid o he secion is he disance rom he cenre o he ension lange o he cenroid o he secion is he widh o he compression lange is he widh o he ension lange is he hickness o he compression lange c c I 4 c
is he hickness o he ension lange. For ASB secions c = and his is shown as in he ables.. Hollow secions Secion properies are given or boh ho-inished and cold-ormed hollow secions (bu no or coldormed ellipical hollow secions). For he same overall dimensions and wall hickness, he secion properies or square and recangular ho-inished and cold-ormed secions are dieren because he corner radii are dieren...1 Common properies For general commen on second momen o area, radius o graion, elasic and plasic modulus, see Secions..1,..,.. and..4. For ho-inished square and recangular hollow secions, he secion properies have been calculaed using corner radii o 1.5 exernall and 1.0 inernall, as speciied b BS EN 1010- [8]. For cold-ormed square and recangular hollow secions, he secion properies have been calculaed using he exernal corner radii o i 6 mm,.5 i 6 mm < 10 mm and i > 10 mm, as speciied b BS EN 1019- [9]. The inernal corner radii used are 1.0 i 6 mm, 1.5 i 6 mm < 10 mm and i > 10 mm, as speciied b BS EN 1019- [9]... Plasic secion modulus o hollow secions (Wpl) The plasic secion moduli (W pl) abou boh principal axes are given in he ables... Torsional consan (IT) For circular hollow secions: I T = I For square, recangular and ellipical hollow secions: I T = I p A p R c 4 A p p p is he second momen o area o a CHS is he hickness o he secion is he mean perimeer lengh For square and recangular hollow secions: p = [(b ) + (h )] R c (4 - ) For ellipical hollow secions: p = h b is he area enclosed b he mean perimeer π h b 1 0.5 h b For square and recangular hollow secions: A p = (b ) (h ) R c (4 - ) For ellipical hollow secions: A p = is he average o he inernal and exernal corner radii π h b 4..4 Torsional secion modulus (W) W = W el or circular hollow secions 10
I T W = A p p or square, recangular and ellipical hollow secions W el is he elasic modulus and I T,, A p and p are as deined in Secion... 11
4 EFFECTIVE SECTION PROPERTIES 4.1 General In BS EN 199-1-1:005, eecive secion properies are required or he design o members wih Class 4 cross secions. In his publicaion, eecive secion properies are given or secions subjec o compression onl and bending onl. Eecive secion properies depend on he grade o seel used and are given or rolled I secions and angles in S75 and S55. Channels are no Class 4 and hereore no eecive secion properies are provided. For ho-inished hollow secions, eecive secion properies are given or S55 and S40. For cold-ormed hollow secions, eecive secion properies are onl given or S55. 4. Eecive secion properies o members subjec o compression The eecive cross secion properies o Class 4 cross secions are based on he eecive widhs o he compression pars. The eecive cross secional area A e o Class 4 secions in compression is calculaed in accordance wih BS EN 199-1-1, 6...5 and BS EN 199 1 5:006, 4. and 4.4. The eecive secion properies ables lis he secions ha can be Class 4 and he ideniier W, F or W, F indicaes wheher he secion is Class 4 due o he web, he lange or boh. In recangular hollow secions subjec o bending abou he major axis, he langes are he shor sides and he webs are he long sides. The eecive area o he secion is calculaed rom: For UB, UC and joiss: A e A 4 1 c w 1 w c w For recangular hollow secions and square hollow secions: A 1 c w w w e A 1 c For parallel lange channels: A e A 1 c w 1 w c w For equal angles: A A 1 h For unequal angles: A A 1 h b For circular hollow secions: e e Eecive areas are no abulaed or circular hollow secions in his publicaion. BS EN 199-1-1 6...5(5) reers he reader o BS EN 199-1-6. For ellipical hollow secions: Eecive areas are no abulaed in his publicaion, bu ma be calculaed rom: [14] A e 90 A De 5 0.5 D e is he equivalen diameer = h b Expressions or he reducion acors, w and are given in BS EN 199-1-5, 4.4. The raio o eecive area o gross area (A e / A) is also given in he ables o provide a guide as o how much o he secion is eecive. Noe ha alhough BS EN 199-1-1 classiies some secions as Class 4, heir eecive area according o BS EN 199-1-5 is equal o he gross area. 1
4. Eecive secion properies o members subjec o pure bending The eecive cross secion properies o Class 4 cross secions are based on he eecive widhs o he compression pars. The eecive cross secional properies or Class 4 secions in bending have been calculaed in accordance wih BS EN 199-1-1, 6...5 and BS EN 199 1 5:006, 4. and 4.4. Cross secion properies are given or he eecive second momen o area I e and he eecive elasic secion modulus W el,e. The ideniier W or F indicaes wheher he web or he lange conrols he secion Class 4 classiicaion. Equaions or he eecive secion properies are no shown here because he process or deermining hese properies requires ieraion. Also he equaions are dependen on he classiicaion saus o each componen par. For he range o secions covered b his publicaion, onl a selecion o he hollow secions become Class 4 when subjec o bending alone. For cross secions wih a Class web and Class 1 or langes, an eecive plasic modulus W pl,e can be calculaed, ollowing he recommendaions given in BS EN 199-1-1, 6...4 (1). This clause is applicable o open secions (UB, UC, joiss and channels) and hollow secions. For he range o secions covered b his publicaion, onl a limied number o he hollow secions can be used wih an eecive plasic modulus W pl,e, when subjec o bending alone. 1
5 INTRODUCTION TO RESISTANCE TABLES Reerence 5.1 General The design resisances given in he ables have been calculaed using exac values o he secion properies calculaed rom he speciied dimensions. The values obained have hen been rounded o signiican igures. For open secions design resisance ables are given or seel grades S75 and S55. For hollow secions, resisance ables are given or grade S55 and S40 (ho inished) and grade S55 onl or cold-ormed secions. EN 199-1-1 unless oherwise noed The ollowing parial acors or resisance have been used hroughou he publicaion or he calculaion o he design resisances. The values are hose given in he relevan UK Naional Annexes o Eurocode : M0 = 1.0 or he resisance o cross secions M1 = 1.0 or he resisance o members M = 1.5 or bols M = 1.5 or welds M = 1.5 or slip resisance a ULS M,ser = 1.1 or slip resisance a SLS 5. Yield srengh The member resisance ables are based on he ollowing values o ield srengh...1 Table 5.1 Seel Grade S75 Yield srengh values Maximum Thickness less han or equal o (mm) 16 40 6 80 Yield srengh (N/mm ) 75 65 55 45 EN 1005- EN 1010-1 EN 1019-1 S55 16 40 6 80 55 45 5 5 S40 16 40 The above values are hose given in he produc sandards BS 1005-:004 or open secions, BS EN 1010-1:006 or ho-inished hollow secions and BS EN 1019-1:006 or coldormed hollow secions. The use o he values in he produc sandards is speciied in he Naional Annex o BS EN 199-1-1. 14
6 COMPRESSION TABLES 6.1 Compression members: UB and UC secions (a) Design resisance o he cross secion Nc,Rd The design resisance is given b: 6..4 6..4 () (i) For Class 1, or cross secions: N c, Rd A M0 (ii) For Class 4 cross secions: N c, Rd A e M0 A A e M0 is he gross area o he cross secion is he ield srengh is he eecive area o he cross secion in compression is he parial acor or resisance o cross secions ( M0= 1.0 as given in he Naional Annex) For Class 1, and cross secions he value o N c,rd is he same as he plasic resisance, N pl,rd given in he ables or axial orce and bending, and is hereore no given in he compression ables. For Class 4 secions he value o N c,rd can be calculaed using he eecive areas abulaed in secion B o his publicaion. The values are no shown in he ables. None o he universal columns are Class 4 under axial compression alone according o BS EN 199-1-1, bu some universal beams are Class 4 and hese secions are marked hus *. The secions concerned are UB where he widh o hickness raio or he web in compression is: Table 5. c / = d / w > 4 d w is he deph o sraigh porion o he web (i.e. he deph beween illes) is he hickness o he web = (5/ ) 0.5 is he ield srengh. (b) Design buckling resisance Design buckling resisances or wo modes o buckling are given in he ables: 6..1.1 Flexural buckling resisance, abou each o he wo principal axes: N b,,rd and N b,,rd Torsional buckling resisance, N b,t,rd No resisances are given or orsional-lexural buckling because his mode o buckling does no occur in doubl smmerical cross secions. 15
(i) Design lexural buckling resisance, N b,,rd and N b,,rd The design lexural buckling resisances N b,,rd and N b,,rd depend on he non-dimensional slenderness ( ), which in urn depends on: The buckling lenghs (L cr) given a he head o he able The properies o he cross secion. The non-dimensional slenderness has been calculaed as ollows: 6..1. For Class 1, or cross-secions: Lcr, or - axis buckling 9.9 i Lcr, or - axis buckling 9.9 i For Class 4 cross secions: Lcr, Ae 9.9 i A or - axis buckling Lcr, Ae 9.9 i A or - axis buckling L cr,, L cr, i, i are he buckling lenghs or he - and - axes respecivel are he radii o graion abou - and - axes respecivel. The abulaed buckling resisance is onl based on Class 4 cross secion properies i his value o orce is suicien o make he cross secion Class 4 under combined axial orce and bending. The value o n (= N Ed/N pl,rd) a which he cross secion becomes Class 4 is shown in he ables or axial orce and bending. Oherwise, he buckling resisance is based on Class cross secion properies. Tabulaed values based on he Class 4 cross secion properies are prined in ialic pe. An example is given below: 5 10 101 UB S75 For his secion, c/ = d/ w = 44.1 > 4 = 9.6 Hence, he cross secion is Class 4 under compression alone. The value o axial orce a which he secion becomes Class 4 is N Ed = 890 kn (see axial orce and bending able, where n = 0.845 and N pl,rd = 40 kn). For Lcr, = 4 m, N b,,rd = 70 kn The able shows 70 kn in ialic pe because he value is greaer han he value a which he cross secion becomes Class 4 For Lcr, = 14 m, N b,,rd = 860 kn The able shows 860 kn in normal pe because he value is less han he value a which cross secion becomes Class 4 (890 kn). 16
(ii) Design orsional buckling resisance, N b,t,rd The design orsional buckling resisance N b,t,rd depends on he non-dimensional slenderness ), which in urn depends on: ( T 6..1.4 The buckling lenghs (L cr) given a he head o he able The properies o he cross secion. The non-dimensional slenderness has been calculaed as ollows: A T or Class 1, or cross secions N cr, T Ae T or Class 4 cross secions N cr, T N cr,t is he elasic orsional buckling orce, given b i 1 0 GI T EI L cr w Access Seel documen SN001 [] i 0 = i i 0 0 is he disance rom he shear cenre o he cenroid o he gross cross secion along he - axis (ero or doubl smmeric secions). 6. Compression members: hollow secions (a) Design resisance o he cross secion Nc,Rd The design resisance is given b: (i) For Class 1, or cross secions: A N c, Rd M0 (ii) For Class 4 cross secions: N c, Rd A A e M0 A e M0 is he gross area o he cross secion is he ield srengh is he eecive area o he cross secion in compression is he parial acor or resisance o cross secions ( M0 = 1.0 as given in he Naional Annex). 6..4 6..4 () For Class 1, and cross secions, he value o N c,rd is he same as he plasic resisance, N pl,rd given in he ables or axial orce and bending, and is hereore no given in he compression ables. For Class 4 secions, he value o N c,rd can be calculaed using he eecive areas abulaed in Secion B o his publicaion. The values are no shown in he ables. 17
Secions ha are Class 4 under axial compression are marked hus *. The secions concerned are: Square hollow secions, where c / > 4 and c = h Recangular hollow secions, where c w / > 4 and c w = h Circular hollow secions, where d/ > 90 Table 5. h is he overall deph o he cross secion is he hickness o he wall = (5/ ) 0.5 is he ield srengh. Ellipical hollow secions, where D e > 90 (See Reerence 15) where D e is deined in Secion 4.. (b) Design buckling resisance Design buckling resisances or lexural buckling are given in he ables. 6..1.1 The design lexural buckling resisances N b,,rd and N b,,rd depend on he non-dimensional slenderness ( ), which in urn depends on: The buckling lenghs (L cr) given a he head o he able The properies o he cross secion. The non-dimensional slenderness has been calculaed as ollows: 6..1. For Class 1, or cross secions: Lcr, or - axis buckling 9.9 i Lcr, or - axis buckling 9.9 i For Class 4 cross secions: Lcr, Ae 9.9 i A or - axis buckling Lcr, Ae 9.9 i A or - axis buckling L cr,, L cr, i, i are he buckling lenghs or he - and - axes respecivel. are he radii o graion abou he - and - axes respecivel. 18
The abulaed buckling resisance is onl based on Class 4 cross secion properies when he value o he orce is suicien o make he cross secion Class 4 under combined axial orce and bending. The value o n ( = N Ed / N pl,rd) a which he cross secion becomes Class 4 is shown in he ables or axial orce and bending. Oherwise, he buckling resisance is based on Class cross secion properies. Tabulaed values based on he Class 4 cross secion properies are prined in ialic pe. For Class 4 circular hollow secions, BS EN 199-1-1 reers he user o BS EN 199-1-6. Resisance values or hese secions have no been calculaed and he smbol $ is shown insead. For Class 4 ellipical hollow secions, he design buckling resisance has been aken as he greaer o: 1. The design buckling resisance based on an eecive area (see Secion 4.) and. The design buckling resisance based on he gross area, bu reducing he design srengh such ha he secion remains Class. The reduced design srengh,reduced is given b 5 90,reduced = De D e is deined in Secion 4.. 6. Compression members: parallel lange channels (a) Design resisance o he cross secion Nc,Rd The design resisance is given b: A N c, Rd A M0 M0 is he gross area o he cross secion is he ield srengh is he parial acor or resisance o cross secions ( M0 = 1.0 as given in he Naional Annex). The value o N c,rd is he same as he plasic resisance, N pl,rd given in he ables or axial orce and bending, and is hereore no given in he compression ables. (b) Design buckling resisance Design buckling resisance values are given or he ollowing cases: Single channel subjec o concenric axial orce Single channel conneced onl hrough is web, b wo or more bols arranged smmericall in a single row across he web. 6..4 6..4() 6..1 1. Single channel subjec o concenric axial orce Design buckling resisances or wo modes o buckling are given in he ables: Flexural buckling resisance abou he wo principal axes: N b,,rd and N b,,rd Torsional or orsional-lexural buckling resisance, whichever is less, N b,t,rd (i) Design lexural buckling resisance, N b,,rd and N b,,rd The design lexural buckling resisances N b,,rd and N b,,rd depend on he non-dimensional slenderness ( ) which in urn depends on: 19
The buckling lenghs (L cr) given a he head o he able The properies o he cross secion. The non-dimensional slenderness, which has been calculaed as ollows: Lcr, or - axis buckling 9.9 i Lcr, or - axis buckling 9.9 i L cr,, L cr, are he buckling lenghs or he - and - axes respecivel. 6..1. (ii) Design orsional and orsional-lexural buckling resisance, N b,t,rd 6..1.4 The resisance ables give he lesser o he orsional and he orsional-lexural buckling resisances. These resisances depend on he non-dimensional slenderness ( T ), which in urn depends on: The buckling lenghs (L cr) given a he head o he able The properies o he cross secion The non-dimensional slenderness, which has been calculaed as ollows: max A T ; N cr, T A N cr, TF N cr,t is he elasic orsional buckling orce, = i 0 = 0 i i 0 i 1 0 GI T EI L is he disance along he - axis rom he shear cenre o he cenroid o he gross cross secion. N cr,tf is he elasic orsional-lexural buckling orce, = A TF 1 E T E T 4 TF = E = T L e E / i = N cr,t / A = 1 ( 0/i 0) L e is he unresrained lengh considering buckling abou he - axis. E T cr w. Single channel conneced onl hrough is web, b wo or more bols arranged smmericall in a single row across he web Design buckling resisances or wo modes o buckling are given in he ables: Flexural buckling resisance abou each o he wo principal axes: N b,,rd and N b,,rd Torsional or orsional-lexural buckling resisance, whichever is less, N b,t,rd 6..1 0
(i) Design lexural buckling resisance, N b,,rd and N b,,rd The design lexural buckling resisances N b,,rd and N b,,rd depend on he non-dimensional slenderness ( ), which in urn depends on: The ssem lengh (L) given a he head o he ables. L is he disance beween inersecions o he cenroidal axes o he channel and he members o which i is conneced. The properies o he cross secion. The non-dimensional slenderness, which has been calculaed as ollows: L or - axis buckling 9.9 i e, 0.5 0. 7 where L 9.9 i or - axis buckling (Based on a similar raionale given in Annex BB.1. or angles) L cr,, L cr, i, i = (5/ ) 0.5. are he lenghs beween inersecions are he radii o graion abou he - and - axes. Annex BB.1. (ii) Design orsional and orsional-lexural buckling resisance, N b,t,rd The orsional and orsional-lexural buckling resisance has been calculaed as given above or single channels subjec o concenric orce. 6..1.4 6.4 Compression members: single angles (a) Design buckling resisance Design buckling resisances or modes o buckling, noed as F and T, are given in he ables: F: Flexural buckling resisance (aking orsional-lexural buckling eecs ino accoun), N b,,rd and N b,,rd T: Torsional buckling resisance, N b,t,rd. 6..1.1 (i) Design lexural buckling resisance, N b,,rd, N b,,rd The ables give he lesser o he design lexural buckling resisance and he orsional lexural buckling resisance. The design lexural buckling resisances N b,,rd and N b,,rd depend on he non-dimensional slenderness ( ), which in urn depends on: e The ssem lengh (L) given a he head o he ables. L is he disance beween inersecions o he cenroidal axes (or seing ou line o he bols) o he angle and he members o which i is conneced. The properies o he cross secion. The non-dimensional slenderness, which has been calculaed as ollows: 1
For wo or more bols in sandard clearance holes in line along he angle a each end or an equivalen welded connecion, he slenderness has been aken as: For Class cross secions: e,.5 0. 7 0 where L 9.9 i EN 199-1-1 BB.1.( e,.5 0. 7 0 where L 9.9 i e, v.5 0. 7 0 where v v L v 9.9 i v For Class 4 cross secions: e,.5 0. 7 0 where L 9.9 i A e A e,.5 0. 7 0 where L 9.9 i A e A e, v.5 0. 7 0 where v Lv v 9.9 i L, L and L v are he ssem lenghs beween inersecions. These expressions ake accoun o he orsional lexural buckling eecs as well as he lexural buckling eecs. For he case o a single bol a each end, BS EN 199-1-1 reers he user o 6..9 o ake accoun o he eccenrici. (Noe: no values are given or his case). v A e A (ii) Design orsional buckling resisance, N b,t,rd The design orsional buckling resisance N b,t,rd depends on he non-dimensional slenderness ( T ), which in urn depends on: 6..1. The ssem lengh (L) given a he head o he able The properies o he cross secion The non-dimensional slenderness, which has been calculaed as ollows: A T or Class 1, or cross secions 6..1.4() N cr, T Ae T or Class 4 cross secions N cr, T
N cr,t is he elasic orsional buckling orce = E G is he shear modulus 1 E is he modulus o elasici is Poisson s raio (= 0.) I T AG I is he orsional consan I u I v A u0 v0 is he second momen o area abou he u-u axis I 0 I u I v u 0 v 0 is he second momen o area abou he v-v axis is he disance rom shear cenre o he v-v axis is he disance rom shear cenre o he u-u axis. I 0 T
7 TENSION TABLES EN 199-1-1 7.1 Tension members: Single angles For angles in ension conneced hrough one leg, BS EN 199-1-1, 6..(5) reers o BS EN 199-1-8,.10.. However he Eurocode does no cover he case o more han one bol in he direcion perpendicular o he applied load. Thereore he resisance has been calculaed using expressions rom BS 5950-1 or angles boled and welded hrough one leg. The resisance is independen o he number o bols along he angle and heir spacing. Tables onl give values or he cross-secional check; see AD51 [17] or more inormaion. 6.. The value o he design resisance o ension N,Rd has been calculaed as ollows: 6..() N, Rd A eq M0 A eq M0 is he equivalen ension area o he angle is he ield srengh is he parial acor or resisance o cross secions ( M0 = 1.0, as given in he Naional Annex). The equivalen ension area o he secion A eq is given b: For boled secions: Aeq Ae 0. 5a For welded secions: Aeq Ae 0. a A e = a e1 + a e bu A e 1. (a n1 + a n) a e1 = K e a n1 bu a e1 a 1 a e = K e a n bu a e a K e = 1. or grade S75 = 1.1 or grade S55 a n1 a 1 = a 1 n bols d 0 = h i he long leg is conneced = b i he shor leg is conneced n bols is he number o bols across he angle d 0 a n = a is he diameer o he hole a = A a 1 A is he gross area o a single angle. Noe: A block earing check (BS EN 199-1-8,.10.) is also required or ension members. However, block earing resisances have no been abulaed, as here are oo man variables in he possible bol arrangemens. 4
8 BENDING TABLES 8.1 Bending: UB secions, UC secions, joiss and parallel lange channels 8.1.1 Design resisance o cross secion 6..5 () The design resisances or bending abou he principal axes o he cross secion are given b: 6..8 () (i) For Class 1, cross secions: W M c,,rd pl, M0 W Mc,, Rd (ii) For Class cross secions wih a Class 1 or lange: W M c,,rd where pl,e, M0 W pl,e, is calculaed according o BS EN 199-1-5, 4.4. (iii) For oher Class cross secions: W Mc,,Rd el, M0 pl, W Mc,, Rd M0 el, M0 (iv) For Class 4 cross secions: W M c,,rd e, M0 W Mc,, Rd e, M0 Noes: None o he universal beams, universal columns, joiss or parallel lange channels in grade S75 or S55 are Class 4 under bending alone. Where he design shear orce is high (> 50% o he shear resisance), a reduced value o resisance or bending M v,,rd and M v,,rd should be calculaed. No values are abulaed in his publicaion. Values o he design shear resisance V c,rd are given in he ables o web bearing and buckling resisance (see secion 9.1). 6..8 () 8.1. Design laeral orsional buckling resisance momen 6.. The laeral orsional buckling resisance momen M b,rd is given in he ables or a range o values o he ollowing parameers: The lengh beween laeral resrains, L, given a he head o he ables The value o acor C 1 The laeral orsional buckling resisance momen, M b,rd, is given b: 6...1 () M b,rd W LT M1 5
W W pl, or Class 1, cross secions W W pl,e, or Class cross secions wih Class 1 or langes 6... (1) W W el, or oher Class cross secions W W e, or Class 4 cross secions LT is he reducion acor or laeral orsional buckling. I depends on he M cr W non-dimensional slenderness LT and he imperecion acor M corresponding o he appropriae buckling curve. is he elasic criical momen or laeral orsional buckling based on gross secion properies and akes ino accoun he ollowing: he momen disribuion he lengh beween laeral resrains. cr C 1 M cr = C 1 EI L I I w L GI EI is a acor ha akes ino accoun he shape o he bending momen diagram. Values o C 1 given in he ables include 1.0; 1.1; 1.5; 1.5; 1.77;.0 and.5. Access Seel documen SN00 Elasic criical momen or laeral orsional buckling [4] gives background inormaion relaed o his acor. To ake C 1 = 1,0 is conservaive. The C 1 values o 1.1, 1.5 and 1.77 correspond o common design siuaions, as shown below. Table 8.1 C 1 values or common design siuaions Loading Bending momen diagram C1 acor UDL, pin-ended beam 1.1 Cenral poin load, pin-ended beam 1.5 Triangular bending momen diagram, pin a one end 1.77 6
For linear bending momen diagrams, C 1 ma be deermined rom he ollowing able, based on, he raio o he end momens. Table 8. C 1 values based on he raio o he end momens End momen loading C1 +1.00 1.00 +0.75 1.17 +0.50 1.6 M M +0.5 1.56-1 +1 0.00-0.5 1.77.00-0.50.4-0.75.49-1.00.76 For oher shapes o bending momen diagram, he acor C 1 ma be deermined rom he raio: M C1 M cr cr or he acual bending momen diagram or a uniorm bending momen diagram M cr ma be deermined b using he soware LTBeam, reel available rom www.cicm.com The reducion acor LT is calculaed or he rolled secions case, using buckling curves b or c as appropriae and he values o LT,0 and given b he Naional Annex. The UK Naional Annex gives he ollowing values: 6... (1) LT,0 = 0.4 = 0.75 The reducion acor is modiied o ake accoun o he momen disribuion beween he laeral resrains o members using he modiicaion acor : LT LT, mod = 1 bu LT, mod 1 and LT, mod LT 6...() and he UK NA = 1 0.5 (1 k c)[1.0 ( LT 0.8) ] bu 1.0 k c = 1 C 1 8. Bending: Hollow secions 8..1 Circular and square hollow secions The design resisances or bending M c,rd and he design shear resisance V c,rd are abulaed or circular and square hollow secions in S55 and S40 seel. No values have been calculaed or S75 circular and square hollow secions. M c,rd has been calculaed as deailed in Secion 8.1 (a) above. 7