Wind Moment Design for Unbraced Frames - 1991

8/6/2019 Wind Moment Design for Unbraced Frames - 1991

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W i n d M o m e n t D e s i g nto r U n b r a c e d F r a m e s

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- ~~.-' ''~j;'. I !! :1 d e u ts c h e r Z u s a m m e n fa s s u n g: ! ..1 lC r e s u m e fran~ais

2 : iI ! -'I ' n r e s u m e n e s p a n o l"Institut de la Construction Metallique Institut fur Stahlbau

TheSteel ConstructionInstitute

Istituto di Costruzioni in Acciaio Instituto de laConstrucci6n Metalica :I


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S CI P UB LIC AT IO N 0 82

W i n d M o m e n t D e s i g n f o rU n b r a c e d F r a m e so Ande r son S S C , P h D , C E n g , F IS tr uc tES J Read ing S S c , M S cK K a via n po u r SSe , M S c , P hD

IS BN : 1 870004 52 3 T he S te el C o nstru ctio n In stitu te 1 99 1

Th e S t e el Co n s tr u ct io n I n st it ut eS ilw o od P a rkAs co tB erk sh ire S L5 7 Q NT e le p ho n e: 0 3 44 2 3 34 5F a x: 0 34 4 2 29 44

O f fic e s a ls o a t:U n it 8 2 0B i rc hwo o d Bo v le v a rdB i rc hwo o d , Wa r r in g to nC he sh ire W A 3 7 Q Z

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FOREWORD..)

This publication is one of tw o com ple men tary guides on the design of un braced fram es by thew ind-moment m ethod. It is to be used in con junction w ith BS 5950: Part I and therecom mendations are the refo re given in the style o f a design code . The reason s fo r there co mm en datio ns are e xplain ed by comm en tary give n w ithin the te xt.The publication is based on studies un dertaken at the U niversity of W arw ick under theguidan ce of an A dviso ry G ro up o f e xpe rie nce d ste elw ork de sign ers:D rGWOwensMrlDuncanMrDFri endM r P W H ain sw orthD r R H en de rso nMr A R MortlockM r A H Pillinger

T he S te el C o ns tr uc tio n In stitu teK en ch in gto n L ittle p lcFormerly. B ritish S te el plcIDCLimitedO ve A rup an d P artn ersFormerly. B ritish S te el plcT etb ur y S te e l L im ite d

M r R eading 's w ork leading to this publication has be en fun de d by the D epartm en t of theE nviron me nt an d B ritish S te el plc,A ssistan ce from D r D B M oore , B uildin g R esearch Establishm en t, an d Mr A A N ajafi K oopae e,U niv ersity o f W arw ick , are also a ck no wle dg ed .

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C O N T E N T SP a g e

F O R E W O R D i iS U M M A R Y i vN O T A T I O N v1 . I N T R O D U C T I O N2 . B A S I S O F R E C O M M E N D A T IO N S 43 . R A N G E O F A P P L IC A T I O N 7

3 . 1 F ra m e la yo u t 73 . 2 F r a m e d im e n s i o n s 83 . 3 S t ru c t u r a l s e c ti o n s 93 . 4 B e a m - to - c o lu m n c o n n e c t i o n s 93 . 5 C o lu m n b a s e s 1 13 . 6 L o a d i n g 1 1

4 . D E S IG N F O R U L T IM A T E L IM I T S T A T E 1 24 . 1 G l o b a l a n a ly s i s 1 24 . 2 D e s ig n o f b e a m s 1 34 . 3 D e s ig n o f c o lu m n s 1 34 . 4 D e s ig n o f c o n n e c t i o n s 1 5

5 . D E S I G N F O R S E R V IC E A B IL IT Y L IM I T S T A T E 1 65 . 1 G e n e r a l 1 65 . 2 R e c o m m e n d a t i o n s 1 6

R E R E R E N C E S 1 8A P P E N D IX A P O R T A L M E T H O D O F A N A L Y S I S 2 0A P P E N D I X B D E S I G N E X A M P L E 2 3

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SUMMARY

Win d-momen t d esig n is a simplifie d m e th od fo r u nb ra ce d ste el frame s. U n de r g ra vity lo adth e c on n ec tio n s a re a ss umed p in n ed , wh ils t u n de r h or iz on ta l lo ad p oin ts o f c on tr at le xu rea re a ssume d a t th e m id -le ng th o f m emb ers. T he frame is th ere by re nd ere d static allyd ete rm in at e, a vo id in g ite ra tio n b etwe en g lo ba l a n aly sis a n d membe r d esig n .T his p ub lic atio n p ro vid es d esig n ru le s fo r th e w in d momen t m e th od whic h a re c on siste nt w ithBS 5950: Part 1: 1990. R ecomm en datio ns are give n fo r th e sco pe o f the m eth od , an d awo rk ed e xample is in c lu de d.Bemessung von verschieblichen Rahmen fur WindlastenZusammenfassungD ie B em es su ng fu r Mome nte a us W in dla sten stellt e in e ve re in fa ch se M e th od e/ilrversch ieb ltch e S tah lra hm en d ar. U nter Y ertika llasten w erd en d ie V erbind un gen a ls g elen kiga ngen om men , w ahrend u nter H orizo ntalb ela stu ng W en dep unkte in d en S ta bm itten an gen om menw erden . D er R ahm en ist dadurch sta tisch bestim mt, eine iltera tion zw tscnenT ra gw erk sb erec hn un g u nd B aia etln ac hw eis w ird v erm ie den .D ie se V ero ffe ntlic hu ng lie /e rt B em essu ng sve rfa hren fu rw tn dla ste n in Uberesinstimmung m itBS 5950, T1 , 1990 . Em p/eh lungen/ilr d ie angew andte m ethode w erden gegeben und ein Beispiell st be igej ilg t."Wind Moment Design"ResumeLe "w ind m om ent design" est une m ethode sim ple de dim ensionnem ent des cadres m etalliquesnon con tr even te s .S ow les ch arg es g ra sita tio nn elle s, le s a sse mb la ge s sons c on sid ere s c omm e d es a rtic ula tio nstan dis qu e, so us les ch arg es ho rizo nta les, d es p oin ts d'inflexion son t sup poses am i-lo ng ue ur d es elem en ts.Le cadre est, de cette m aniere, rendu sta tiquem ent determ ine; ce qui evite tou tein teraction en tre I' an alyse g lo bale et le d im en sion nem ent d es elem ents.C ette publication fourn it des reg les de dim ensionnem ent, pour la m ethode due "w ind m om entdesign", qu i sont en accord avec la BS 5950 Partie 1: 1990. D es recom mandations sontdonnees concernant le cham p d ' a pplica tion de la m ethode. U n exem ple illustre ['utilisationd e la m eth od e.

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D ise DO Para M orn en tos D ebidos A I V ie nto En Porticos S in C on travien tos.ResumenE l dtseio de m om entos debidos al viento es un m etoda sim pli/icado para porticos de acero sinc on tra ve nte ar. B ajo c ar ga s g ra vita to ria s la s u nio ne s se su po ne n a rtic ula da s, m ie ntra s q uea nte c arg as h ortzo nta le s se a dm ite la e xiste ncia d e p un to s d e in fle xiO n e n L a m itad de lasbarras. De esta fo rm a el portico s e e stud ia como tsostasico, e vi ta ndo la s iteraciones entreanal is is g lobal y d is eii o d e piezas.E sta p ub lic ac id n sumin istra reg la s p ara d ise iia r d e a cu erdo co n e l m eto do c ita do , q ue esc on gru en te co n la B S 5950: Parte 1:1990. Se inc luyen recomendac iones sobre lo s l tmues dea plic ab ilid ad a s( c omo u n e jemplo d esa rro lla do .

NOTATIONAg g ro ss c ro ss- se ctio n al a re aF a pp lie d a xia l c omp re ss io nh s to re y h e ig htH horizo ntal fo rce pe r bayL distance betw ee n le ve ls at w hich bo th axes o f the co lum n section a re r es tr ain ed; b e am

spanLE e f fec ti ve l engthm e qu iv ale nt u nifo rm mome nt fac to rM in te rn al momen tM b b uc klin g r esis ta nc e momen tM bs b uc klin g re sistan ce m om e nt fu r c olu mn s in sim ple m ulti-sto re y c on stru ctio nMx applied e nd m om en t about the m ajo r axisM y applie d e nd m om en t about the m in or axisPc c omp re ss iv e s tr e ng thPy d e sig n s tr e ng thPc c omp re ss io n r e sis ta n cery radius o f gyration about the m in or axisS shear fo rce in co lumnV she ar fo rce in be am~ horizon tal loadZy e lastic se ctio n m odulus about the m in or axisA r . T equivalen t slende rn ess

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1. INTRODUCTIONW here a stee l fram e is un braced, an established techn ique is to re ly o n the ro tation alstiffn ess of the con nection s to provide resistan ce to w in d, even though such restrain t isign ored un der the action o f gravity lo ads. T his approach is te rm ed the "w in d-m om en t" or"win d -c on n ec tio n " m e th od .In its usual fo rm the m etho d assum es:(i) un der grav ity load, the connections act as pin s (F igure l(a(ii) un de r w in d lo ad, th e co nn ectio ns be hav e as rigid jo in ts, w ith po in ts o f co ntrafle xureat the m id-he ight o f co lum ns an d m id-len gth of be am s (Figure l(b.

r- II , ,. "'V'XYX'Y"" .xtn

--.r-----~~------Ia ."

(a) FRAME UNDER GRAVITY LOAD Cb)FRAME UNDER WINDILOADFigure 1 Frame Idealisation for wind-moment method

Mem be rs an d co nn ectio ns are pro po rtio ne d in itially to w ithstan d gravity lo ad. T he in te rn alfo rces an d m om en ts due to gravity load and w ind (F igure 2 (a) and Figure 2 (b are thencom bin ed in appropriate load cases. T he design for stren gth is com ple ted by am en din g thein itial se ctio n size s an d o the r de ta ils fo r th e m em be rs an d co nn ectio ns, to w ith sta nd th ec omb in e d e ff ec ts .N o calculation is m ade for second-order m om en ts due to the "p-~" effect. It is assumedthat these can be acco un ted fo r by usin g effective co lum n len gths greate r than the truelen gths, fo r axes about w hich sw ay can o ccur.F or se rv ice ab ility , sw ay d efle ctio ns are calcu late d a ssumin g co nn ectio ns are rig id .The advan tage of the m ethod is its sim plic ity. A s the fram e is ren dered staticallyde te rm in ate , in te rn al m om en ts an d forces are n ot depe nden t on the re lative stiffn esses ofthe m em be rs. The need to repeat the an alysis to correspon d to chan ged section sizes isthe reby avoided. C on sequen tly, the m etho d has been used exten sive ly, a lthough it has n otb ee n v erifie d as a g en erally -ap plicab le ap pro ach . The S te el D es ig ne rs ' M a nual(1 )w arned that it m ust on ly be used on the basis of the "sim ple" design m ethod given inB S 449(2 ) . The w in d-m om en t approach has also been used w ith o ther co des, n otab lyth e A ISC a llow ab le s tre ss sp ec ific atio n s" , in which it is d esig nate d "T yp e 2 C on stru ctio n" .

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(a) GRA VITY LOAD (b) WIND LOADt t

Figure 2 In t9 rn ai m om en ts a nd fo re ss a cc ord in g to w in d-m om 9n t m etn odThe ju stific atio n o f th e m e th od h as b ee n p artly d ue to th e fa ct th at b uild in gs d esig ne d o nth is b asis h av e p ro ve d sa tisfa cto ry in u se . In re ce nt y ea rs, th e m eth od h as b ee n re ga rd eda s a fo nn o f sem i-rig id d esig n a nd a na ly tlc alju stific atio n h as b ee n c arrie d o ut o n th isba si s. Ne th e rco t( 4) and Ge rs tl e(5 )s ummari se a ll e xcep t t he mos t r ec e nt s tud ie s( 6.7 .8 ).T he c on c lu sio n s a re a s fo llows:BeamsThe se m emb ers te nd to b e o ve rd esig ne d fo r th e fo llow in g re aso n. B eam d esig n is u su allyg ov ern ed b y th e sa gg in g in te rn al m ome nt d ue to g ra vity lo ad . T he sem i-rig id n atu re o f th ec on n ec tio n s c au se s h oggin g s uppo rt momen ts to arise '(Figure 3). A s the usual fo rm of them etho d assum es ze ro m om en ts (F igu re 2 (a , n o ad van tag e is tak en o f the re du ctio n ins agg ing momen t.

GRAVITY LOAD

Figure 3 I nt9 rn ai m oments dU9 to s 9m i- rig id c on n9Ctio ns

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ColumnsThese m em be rs ten d to be un de rdesign ed, due to the detrim en tal e ffe ct on such m em be rs ofthe hoggin g m om en ts de ve lope d in the be am s. T he se m om en ts particularly affe ct e xte rn alco lum ns an d o the r m em be rs subje ct to un balance d loadin g. H ow ever, as colum ns are alsodesigned to suppo rt axial lo ad, the un de rde sign o f the colum ns is n ot as sign ifican t as theo ve rde sig n o f th e b eams.ConnectionsT he be am -to-co lum n co nn ectio ns w ill ge ne rally be un de rde sign ed. T his is be cause thein te rn al m om en t fo r at least on e end of a beam will be greater than that predicted by them etho d. In additio n to the hoggin g m om en ts due to g ra vity lo ad s (se e a bo ve ), se co n d-o rd erm om en ts arise due to the p-~ e ffect. A s be am s are usually gove rn ed by m id-span m om en t,w hilst con nection s are size d on ly for e nd m om en t, the con ne ction s w ill ge ne rally be on ly" pa rt ia l- st re n gt h" w it h r e sp e ct to th e b eam s.Sway detlectionsT he se are larger than those pre dicte d assum in g rigid jo in ts. T his is be cause of thesem i-r ig id a nd p ar tia l-str en gth n atu re o f th e c on n ec tio n s.Frame stabilityThe on se t o f fram e in stability w ill be above the design load leve l in low an d m edium -risefram es. F or re pe ate d variatio ns o f lo adin g e xpe cte d durin g the life tim e of the structure ,such as re ve rsals of w in d load, the fram e w ill shake do wn (8) w ith co nn ectio ns the n be havin gelastically.S ome ju stific atio n fo r th e m e tho d is also giv en b y rig id-pla stic th eo ry (9 ). A cco rd in g toth is, th e c olla pse c on ditio n h as th e fo llow in g c ha ra cte ris tic s:(i) a m echan ism of plastic hinges has fo rm ed(ii) the in tern al m om ents an d force s are in e qu ilib riu m w ith th e ap plie d lo ads(iii) n ow he re doe s the in te rn al m om en t e xce ed the plastic m om en t o f re sistan ce .P ro vide d that the se con d an d third co nditio ns are satisfie d, the L ow er-B oun d T he ore m(9)states that the applie d loads are e ithe r le ss than or equal to the loads w hich co llapse thefram e. The se con ditions are m et by the w in d-m om ent m ethod, w hich will t he r ef or e p ro vid esa fe de sig ns, pro vid ed th at th e frame a lso sa tisfie s th e assumptio ns o f rig id -p la stictheory:(i) the e ffect o f defle ction s on equilibrium can be ne glected(ii) collapse does n ot occur as a result o f an y fo rm of bucklin g.T he se assump tio ns the re fo re in dica te th ose a sp ects o f de sig n th at re qu ire p artic ularatte ntio n if the w in d-m om en t m etho d is to pro vide fram es o f ade quate stre ngth.Fo r con tin ued use , the m ethod m ust also be re late d to lim it state de sign codes; in th eU nite d K in gdo m to B S 5950: P art 1(10). T his p re se nt p ub lic atio n d escrib es h ow th ew ind- m om en t approach can be used in a m anne r con sisten t w ith B S 5 95 0. There comm e nd atio ns h av e b ee n d eve lo pe d in c on ju nctio n w ith a n an alytic al stu dy o f ty pic alfram es design ed by the m ethod. The scope of the re com men dation s is the refo re provided bythat of the study.

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2. BASIS OF RECOMMENDATIONS

The recom me ndation s have been used to design a ran ge of m ulti-sto rey an d sin gle sto reyplan e fram es, w ho se b ehav io ur w as the n de te rm in ed b y "e xact" co mpute r an aly sis(7 .8 ). T here sults of the an alyses have be en used to che ck the stre ngth o f the fram es fo r th e U ltim ateL im it S tate (U LS ) an d th eir sw ay stiffn ess fo r the S erv ice ability L im it S tate (S LS ).T h e fram es co nside re d w ere w ith in the ran ge s give n in T able 1, a lth ou gh n o t a ll p os sib lecom bin ation s w ere exam in ed. T he greatest g ravity load w as co mbin ed w ith the least w in dlo ad an d v ice -v ersa, by cho osin g ap pro priate lo ad valu es a n d colum n leng ths. Bo th wide andn arrow bay w idths w ere co nsidered , so that n ot on ly just the extrem e co mbin ation s ofloadw ere stud ie d. G reate r variation s of param ete rs w ere exam in ed in fram es up to fo ur sto reysthan fo r the highe r fram es, due to len gthy com putatio n tim e fo r the la tte r; fo r exam ple , inthe highe st fram es the m axim um num ber of bays was restric ted to tw o. S om e cases we re alsoe xc lu de d as im practicab le if d esig ne d as u nb race d fra me s.T able 1 R ang e of stud y

Minimum MaximumNumber of storeysNumber of baysBay widthStorey height (bottom storey)Storey height (elsewhere)Dead load on floorsImposed load on floorsDead load on roofImposed load on roofBasic wind speed

214.5m4.5m3.5m3.50 kN/m24.00 kN/m23.75 kN/m21.50 kN/m237 m/s

849.0m6.0m5.0m5.00kN/m27.50 kN/m23.75 kN/m21.50 kN/m252 m/s

T h e a na ly se s w e re performed b y a com pu te r p ro gram d ev elo pe d o rig in ally fo r rig id -jo in te dfram e s(1 1), b ut w hich n ow tak es acco un t o f th e semi-rig id n atu re o f p racticalcoonecnons" , T he an aly sis trace s the lo ad-de fle ctio n be havio ur o f a fram e u p toc olla ps e, a llow in g fo r in -p la ne s ec on d -o rd er (P-A) effects a n d the d ev elo pm e n t o f p la stichinges.T h e pro gram has been show n to be accurate by co mparison w ith results from o ther in depen de ntcomp ute r p ro gram s from v ario us re se arch ce ntre s (F ig ure 4 )(8 ).T h e b ehav io ur o f be am -to -co lum n co nn ectio ns is re pre se nte d by m om en t-ro tatio n (M -q re la tio nships (F igure 5). Fo r the study , the re latio nsh ip s w ere m ain ly pre dic te d by th em ethod of Eurocode 3 (1 2)(F ig ure 6 ) w hich te nd s to u nd ere stim ate stiffn ess at U LS .S om e u se w as also m ade o f an e mpirical po ly no mial e xpre ssio n(13) (F igure 7). T he fram esw ere also an aly se d as rig id -jo in te d stru ctu re s w ith fu ll-stre ng th co nn ectio ns, as an u pp erb o u n d o n co nn ectio n b ehavio ur. T he use o f vario us re pre se nta tio ns o f co nn ectio n be havio uren abled the study to de mon strate that the co nclusion s are n ot un duly sen sitive tov ar ia tio n s in the M-q>rela t ions.In th e m ajo rity o f th e studie s, the bases of the fram es w ere co nsidered as rigid, but insom e of the an alyses the stiffn ess o f a n om in ally rigid base w as taken as equal to thestiffn ess o f th e co lumn in a cc ord an ce w ith BS 5950: Part 1(10).

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-c 1.6. . .o()J 2 1 . 1 .uIIIo. . . . J 1 .2 ir,A q

". , , , . "7 " . ,0.8 35m1.0

0.6 -- Warwick (ref.B)--+-- Milan---o---Aachen

o 50 100 Overall sway (rnrn)F ig ur e 4 Compa ris on o f a naly se s

Extended end plate, . . . . , .[p300.>0:~EQ) /0~250

Top and seat angles2 00 /[JP150

Header plate

1 0 0 /[]o50

0.002 0.001. 0.006 0.008 0.010 0.012 0.011. 0.016 0.Q18Rotation (radians)

F ig ure 5 Moment -r ot ati on c harac te ri sti cs f or bo lte d c onnec ti on s

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F ram es w ere an alyse d un de r three lo ad co mbin atio ns, n am ely de ad an d im po se d lo ad; de ad,im pose d an d w in d load; de ad an d w in d load. T he appropriate partial safe ty facto rs fromBS 5950: Part 1(10) w ere in co rp or ate d to giv e d esig n v alu es.

EC DEo:! E

EC DEo:! E

Rotation Rotation

Figu re 8 M - < p relationship to m ethod of E C3 F ig ure 7 Po lynomia l .M -


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3. RANGE OF APPLICATION3.1 Frame layoutThe re com me ndation s apply to ste elw ork. w hich can be ide alised as a se rie s of un brace d plan efram es. T he ran ge o f applicatio n is re stricte d to m ulti-sto re y plan e fram es in w hich:

the fram e con sists prin cipally o f ho rizon tal beam s and vertical co lum ns (Figure 8) the fram e does no t exceed eight sto reys the number o f bays does no t exceed four the w idth of each bay is con stan t ove r the he ight of the fram e, except that co lum nsm ay te rm in ate at the top floo r, to give an ope n-plan top sto re y (Figure 9) fram es are e ffective ly braced again st out-o f-plan e sway at roo fleve l and at eachf lo o r le v e l beam grids m ay com prise on ly prim ary beam s (F igure 10), o r arrangem en ts o f prim aryand secondary beam s as shown in Figure s 1 I (a) and 11(b) floo ring and roofm g should span in the direction s shown in Figure s 10 and 11.

Commen ta r yA study o f Ackroyd(6) concluded tha t the m ethod shou ld no t be app lied to f ram eshaving m ore than n ine storeys . The study on w hich the above recom menda tions are based w asrestr icted to eigh t storeys. In add ition to Ackroyd 's conclusion , th is lim it w as chosenfo r th e f ollo win g re aso ns:( i) the com para tive rarity o f un braced construc tion in ta ller struc tures( ii) lack o f experim en ta l ev idence on the behaviour o f jo in ts connec ting sec tions o f large

size( iii) u nw illin gn ess to a cce pt a n a pp ro xim ate m eth od fo r ta lle r stru ctu re s.j

T he arrangem en t o f beam s in F igure 11b ) re du ces th e g ra vity lo ad ca rrie d by th e b ea m sform ing part o f the p lane fram e. T his leads to sm aller beam sec tions in the p lane fram e,com pared to the grids show n in F igure 10 and Figure 11a). A ll three arrangem en ts havebeen considered in the study w hich form s the basis of the recom menda tions. G rids w hich dono t con form to one of these arrangem en ts are ou ts ide the scope. T his is because the irpossib le e ffect on the stiffness and streng th o f beam s re la tive to co lum ns has no t beenstudied.

_ . . . . _ . . . . . . -- _ . . . . . . - - -'-Figure 8 F rame o f hor iz on ta l

b eam s a nd ve rtic alcolumnsFigure 9 O pen - pla n top storey

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H - - - - - - - - - H---------H - Plane frame

t- - - - - - - - - - - - - - - - - - - HF ig ur e 1 0 G rid o f p rim ary b eams

. . . , . . . - - - - - : - - - - - - - I - ; i

t----.....;_----H - Planerame-171---------Ht- -H - - - - - - - - - - - - - -

H-----'----- H--------------- H(a) (b)

Figure 11 G rid s o f p rim ary a nd se con da ry b eams

3.2 Frame dimensionsThe range of application is limited to the relative dimensions given inTable 2, and to theactual dimensions inTable 3.Table 2 Re la t ive d imens ions

Minimum MaximumBay width: storey height(bottom storey)Bay width: storey height(above bottom storey)Greatest bay width:smallest bay widthClear span: storey height(open-plan top storey)

0.75 2.00

0.90 2.50

1.00 2.00

1.80 5.00

Table 3 Ma xim um c olum n h eig htBottom storeyOther storeys

8.0m5.0m

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Commen ta r yT he re la tive d im ensions are based on the ac tua l dim ensions g iven in T ab le 1.T he actua l he igh t o f a co lum n shou ld be lim ited because sway s ti ff ne ss i s i nv e rs el yproportiona l to the square o f the m em ber 's leng th .T he lim its a re n ot un du ly restrictiv e in pra ctice .3.3 Structural sectionsS ection s m ay be in e ithe r G rade 43 or G rade 50 ste el, o r in ste el havin g sim ilar structuralprope rtie s. The sam e grade of stee l should be used fo r all section s in a fram e. Inaddition:

ho t-ro lled 1- o r H-section s should be u se d fo r h oriz on tal m em be rs Un ive rsal C olum ns (o r sim ilar section s) should be used fo r ve rtical m em bers section s should be o rien tated such that loads in th e plan e o f the fram e tend to cause

be ndin g abo ut the m ajo r axis.Commen ta r yThe m ethod does no t prov ide an exact ca lcula tion o f co lum n end m om ents. U niversa l C olum nso r sim ila r se ctio ns w ith su bsta ntia l b uc kling re sis ta nce m om en t sh ou ld th erefo re b e u sedfo r th ese m em be rs.C olum n sections shou ld be orien ta ted as recom m ended because the study d id no t exam inestructures in w hich the beam s fram e in to the colum n w eb . There is no t yet an accep tedm eth od fo r p red ic tin g th e b eh avio ur o f su ch c on ne ction s.T he recom m ended orien ta tion o f the beam sec tions is usual practice . It is necessary toadhere to th is to provide stiffness in the p lane o f the fram e.

3.4 Beam-to-columnconnectionsExte nde d e nd-plate (F igure 12 (a or flush en d-plate (Figure 12 (b con ne ction s should beuse d. E xte nde d e nd-plate co nn ectio ns sho uld have tw o ro ws of bo lts dispo se d symm etricallyabout each flan ge . V arious fo rm s of stiffe nin g m ay be used to in cre ase the re sistan ce o f aconnect ion:(i) patch plate s (Figure 13), to in crease the re sistance o f the co lum n w eb to shear(ii) backin g plate s (F igure 1 4), to in cre ase the re sistan ce o f the co lum n flan ge to te nsile

fo rce from the be am flan ge(iii) stiffe ne rs be tw ee n the co lum n flan ge s (F igure 1 5), to in cre ase the re sistan ce o f theco lum n to te nsile an d/o r com pre ssive fo rce s fro m the be am flan ge s.E nd plates should be in G rade 43 ste el or ste el o f sim ilar structural prope rties. B oltsshould b e G rade 8 .8 o r sim ilar. .Commen ta r yT he fo rm s o f c onn ec tio n (F ig ure 12) and m ateria ls are those used in the study .IC onnections w ith m ore than one bo lt rO w outside the top or bo ttom beam flange correspond toh igh w ind m om en ts , as do connec tions w ith stiffeners to the co lum n flanges. Fram es w hichinc lude such connec tions are no t excluded from the scope o f the m ethod . H ow ever, ife xten siv e u se is m ad e o f th ese co nn ectio ns, the fra me is b est d esig ne d a s rig id -jo in te db ec au se th e se rv ic ea bility lim it o n sway is like ly to c on tro l th e d esig n.

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- 1--- f--

- 1-- 1- 1--

.__.-

-- f-- --- f---- f---- f--

(a) EXTENDED END PLA TE (b) FLUSH END PLATE

Flgure12 End p la te c onnectio ns

J

- -

Figure 13 Web s treng thenedby p atc h p lateFigure 14

-- --- r-

-- I---- f--

Figure 15 Connection with stiffened column flanges

10

-- . . . . . -

Con ne ctio n w ith c olumn fla ng ere in fo rc ed b y b ac kin g p la te


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3.5 Column basesCo lumns s ho uld be rig idly co nn ecte d to fo un datio ns, by base s de sign ed in acco rdan ce w ithu su al p ra ctic e fo r th is ty pe o f c on stru ctio n.CommentaryT he stu dy o n w hic h th e re comm en da tio ns are b ased to ok ac co un t o f th e in ev ita ble fle xib ilityo f nom inally -rig id bases , in accordance w ith B S 5950: P art 1:C l au se 5 .1 .2 .4 .C olu mn s w ith p inn ed b ase s req uire large e ffec tive len gths (ou ts ide the sc ope o f th estan da rd co nd ition s o f re strain t in B S 5 95 0: T ab le 2 4) i/they are to be designed sa fe ly.Such m em bers can a lso cause large sway d efle ctio n in th e b otto m sto re y o f th e stru cture.F ra me s w ith p in ned ba ses a re th erefo re ex clu ded fro m th e rec omm en datio ns g ive n he re in .

3.6 LoadingT he ran ge o f applicatio n is re stricte d to the follo win g value s o f lo adin g:

the to tal un facto red dead and im pose d load on an y floo r should n ot e xce ed 12 .5kN/m2w in d lo ad s sh ou ld be based on a basic w ind speed of at least 37 m lsthe w ind load should n ot be such that it con tro ls th e design of an y beam .

CommentaryT he tendancy to underdesign co lum ns and connections, because of neglect o f end m om en ts dueto g ra vity lo ad (F ig ur e 3), is increased i/the w ind load is low . The restr ictions onm axim um gravity load and m in im um w ind speed inh ibit th is tendency .If the w ind load is so h igh tha t it begins to govern the design of the beam s, the fram e isb est de sig ned a s rigid -jo in ted .for th e re aso n g ive n in Se ctio n 3.4.

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4. DESIGN FOR ULTIMATE LIMIT STATER eferen ce s in the recom me ndation s are to BS 5950: Part 1: 1990(10).

4.1 Global analysis4.1.1 Load combinationsThe fo llo win g lo ad co mbin atio ns sho uld be use d in de sign :(i) 1 .4 (Dead load) plus 1 .6 (Im posed load) plus no tional ho rizon tal fo rces(ii) 1.2 (D ead load plus im posed load plus w in d load)(iii) 1.4 (D ead lo ad plus w in d lo ad).T he n otio nal ho rizo ntal fo rce s sho uld be take n as 0 . 5% o f the facto re d de ad plus im po se dlo ad (C la us es 5 .6 .3 , 5 .1 .2 .3 ).P atte rn lo ad in g sh ou ld b e c on sid ere d, in a dd itio n to full g ra vit y lo a d.CommentaryF or m u lti-b ay fr am es , p atte rn g ra vity lo ad in g may b e critica l in th e d esig n o f in tern alco lumns .T h e lo a d c omb in at io n 1.4 (D ead load plus w ind load) w ill usua lly govern the design of thec on n ec tio n s a s m om en t- re sis ti ng c omp o ne nts .4.1.2 Internal moments and forces due to gravity loadA llow an ce sho uld be m ade fo r the partial-fix ity o f th e connection s be tw een a beam and aco lum n by an end restrain t m om en t equal to 1 0% of the m axim um saggin g m om en t in th e b eam,assumin g this to b e sim ply su ppo rte d.Each co lum n has to be design ed to re sist the alge braic sum o f the re strain t m om en ts fro mthe beam s at the sam e level on each side o f the co lum n, in addition to m om en ts due toeccen tricity o f con ne ction s (C lause 4 .7 .6). The n et m om en t applied at an yon e leve l shouldbe divided be tw ee n the co lum n le ngths above an d be low that leve l in acco rdan ce w ith C lause4.7.7.The mom en ts applie d to the co lum n due to partial-fix ity an d e cce ntricity sho uld be assum edto have no e ffect at the levels above and below the leve l at which they are applied.CommentaryThe assum ption o f an end restra in t m om en t equa l to 10% of the f ree m om ent is perm itted byB S 5950: P art 1fo r fra mes b ra ced a ga in st sidesway,Its exten sion to th e w ind -m om en t m etho d p artia lly o ffse ts the tenden cy of the m etho d tou nd er de sig n c olu m ns a nd c on ne ctio ns .

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4.1.3 Internal moments and forces due to horizontal loadT he an alysis should be by the "po rtal m etho d" o r an othe r e satablishe d m etho dn '.F or the po rtal m etho d, the fo llow in g assum ptio ns are m ade :(i) ho rizon tal loads are applied at floo r levels(ii) the re is a po in t o f con trafle xure at the m id-he ight o f each co lum n(iii) the re is a po in t o f con trafle xure at the m id-le ngth of each beam(iv) e ach bay acts as a sim ple portal an d the to tal ho rizon tal load is divide d betw ee n thebays in pro po rtion to the ir span s.A lge braic fo rm ulae base d on the se assum ptio ns are give n in A ppe ndix A.CommentaryH orizo nta l de sig n loa ds a rise d ue to :(i) p rac tica l im pe rfec tio ns su ch a s la ck o f ve rtica lity w hic h a re rep re se nted by notionalho r iz onta l f o rce s(ii) w in d lo ad .T he assum ed poin ts of con tro flexure for a sing le bay fram e are show n in Figure 1b). Theresulting bend ing m om ent d iagram is show n in F igure 2(b ).

4.2 Design of beamsS ectio ns sho uld be C lass I, P lastic (C lause 3.5).The m om ent capacity should be lim ited to 90% of the plastic m om ent of re sistan ce .CommentaryAs the w ind-m om en t m ethod can be justified in part as a m ethod o f p lastic design ,c ro ss-se ctio ns m ust b e a ble to f orm p la stic hin ges an d p artic ip ate in c ollap se m ech anism s.T o p re ve nt p re m atu re fa ilu re by loc al b uck ling , sec tio ns m ust the re fore be C lass 1,Plast ic.T he m om ent capacity is restr icted to 90% of the p lastic m om en t to prov ide restra in t to thec olum ns in ac co rd an ce w ith C lau se 4.7.2.

4.3 Design of columns4.3.1 E ffec tiv e len gth s fo r c om p res sio n reS is tan ce, P cF or in -plan e be havio ur (be ndin g abo ut m ajo r axis):

(2)F or o ut-o f-p lan e b eha vio ur (b en din g ab ou t m in or a xis):

(3)Commentary ,T he e ffec tive len gth fac to rs a re n om in al v alu es w hich , in c onju nctio n w ith th e oth err ec omm e nd atio ns, w er e fo un d in th e s tu die s(7 ,8 ) to r esu lt in a de qu ate c olu m nsec tio ns. T he va lu e fo r o ut-o f-p lan e b eh avio ur is b ased o n the fra me b ein g e ffec tive lyh eld a ga in st o ut-o f-p la ne s wa y.

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4.3.2 Equivalent slenderness for buckling resistance moment, MbThe slende rn ess ALT should be taken a s A . LT = O.S (Llry)CommentaryT his is consisten t w ith the provisions in C lause 4.7.7 fo r sim ple d esig n.

(4)

4.3.3 Design momentsU nder each load co mbin atio n (se e S ectio n 4 .1 .1 ). the co lum n en d m om en t sho uld be take n asthe sum of: n et (i.e . o ut-o f-b alan ce ) m ome nt d ue to g ra vity lo ad s a nd e cc en tricity o f c on n ectio ns(C au se 4 .7 .6 )

n et (i,e . o ut-o f-b alan ce ) m ome nt d ue to re stra in t m om en ts fro m th e b eam s arisin g un de rg rav ity lo ad s (C au se 2 .1 .2 .4 )m om en t due to h oriz on tal lo ad (l.e , n otio n al h oriz on ta l fo rce s o r w in d).

Commen tr yT he calculation of these m om ents is explained in Section 4.1.As the horizonta l load may reverse, th e total m om ent should be calcu lated by a dd itio n o fthe n um erical m agnitudes of th e com pon ent m om ents.4.3.4 Class of sectionS ectio ns sh ould b e C lass 1. Plastic.CommentaryS ee c ommen ta ry to S ec tio n 4 .2 .4.3.5 Overall buckling checkThe fo llow in g r ela tio n sh ip s ho uld be satisfied:

!!:t_Z S 1.0Py y (5)

whereFc = the applie d axial load in the m em be rPc = th e c om p re ss io n r es is ta nc eMx = the applie d m om en t abo ut the m ajo r ax isMbs = th e b uck lin g re sistan ce m om en t fo r sim ple d esig nMy = the applie d m om en t about the m in or axisPy = th e d e sig n s tr en g thZy = the e lastic se ctio n m odu lu s ab ou t th e m in or ax is

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CommentaryT h is r ela tio n sh ip is c on sis te nt w ith C la u se 4.7.7 and 4.8.3.3.1. As th e en d m om en ts areno t ca lcu la t ed by e xa ct a na ly sis, th e e qu iv ale nt u nifo rm m ome ntfa cto r, m , s ho uld b e ta ke nas 1.0.

4.4 Design of connections4.4.1 T yp e o f c on nec tio nT he re comm e nd atio ns are ap plicab le to fra me s w ith e xte nd ed e nd -p late an d flu sh e nd -p lateco nn ectio ns (se e S e ctio n 3 .4 ).4.4.2 D es ign m o m en ts an d fo rc esU nder each load co mbin ation (see S ection 4.1.1 above), the m om en t at the con nection shouldbe taken as the sum of:

end restrain t m om en t arising from partia l fixity in con junction w ith gravity load onthe be am s (se e S ectio n 4 .1 .2 ab ove ). m om en t due to horizon tal load (ie . no tional horizon tal fo rces or w ind).

T he ve rtical sh ear fo rce at the co nn ectio n sho uld be taken as the sum of: the beam end shear due to g ra vity lo ad the shear force in the beam due to ho rizo ntal lo ad o n the fram e.

CommentaryT he c alc ula tio n o f th e c om p on en t m ome nts is e xp la in ed in S ec tio n 4.1. T he sh ea r f orces inth e b eam a re c alc ula te d Oy equil ibrium.In a cc or da nc e w ith u su al p ra ctic e in sim p le d es ig n, th e c on ne ctio ns th em se lv es a re n otd es ig n ed fo r b en d in g momen t a ris in g fr om e cc en tr ic ity ( Cla u se 2 .1 .2 .4 ( b)6).IA s th e h orizo nta l lo ad m ay reverse, th e to ta l va lu es o f m om en t a nd sh ea r sh ou ld b ecalculated by add it ion o f nume ri ca l magn it ude s.4.4.3 D es ig n c r it er iaT he co nn ectio ns sh ou ld p osse ss ro ta tio n cap acity ap pro pria te to p lastic d esig n o f fra me sw it h p ar ti al -s tr en g th c o nn e ct io n s.CommentaryA s b eam s a re u su ally g ov er ne d Oy m id -sp an m ome nt w hils t c on ne ctio ns a re siz ed fo r e ndm ome nt, th e c on ne ctio ns w ill g en era lly b e o nly p artia l-str en gth w ith r esp ect to th e b eam s.A s th e w in d-m om en t m eth od ca n b e ju stified in p art a s a m eth od o f p la stic d esig n,c on ne ctio ns m u st b e a ble to f orm p la stic h in ge s a nd p ar tic ip ate in c olla ps e m ec ha nis ms .In fo rma tio n o n r ota tio n c ap a city is a va ila b le in th e SC I P ublic atio n (1 4)o n Conne ctio nsfo r W in d-M om en t F ram es.4.4.4 D e ta ile d d es ig nR efe re nce sho uld b e m ade to the S CI P ub licatio n(141.

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5. DESIGN FOR SERVICEABILITY LIMIT STATE5.1 GeneralThe sign ifican ce of sw ay deflection s in the design o f un braced fram es is in fluen ced by theratio of gravity lo ad to w in d lo ad(15). E ven though the de sign o f so me fram es w ill begovern ed by lim itation o f sw ay, fo r o thers a de sign m ade for the u ltim ate lim it state w illb e a de qu ate ly s tiff.D e sig n co de s(1 o.1 2)g iv e re comme nd ed lim its o n d efle ctio ns, b ut th ese are n ot p erfo rm an cec rite ria ; rath er, th e lim its a re in te nd ed fo r c om pariso n w ith th e re su lts o f ca lcu latio ns,u sually o n b are fram es. T he justificatio n fo r the se lim its re sts o n the satisfacto ryp erfo rm an ce o f stru ctu re s in p ractice .A n aly sis ac co un tin g fo r c on n ectio n fle xib ility sh ow s th at s way d efle ctio ns in w in d-m om e ntfram es are sig nifican tly larg er th an tho se pre dicte d assum in g rigid jo in ts, an d y et, as faras is kn ow n, structu re s in co rpo ratin g such fram es d o n ot e xh ib it d istre ss in p ractice .T he in cre ase in de fle ctio n giv en b y su ch an aly se s is de pe nde nt o n th e m om en t-ro ta tio n(M - c p ) re latio nship s o f th e co nn ectio ns. T he calculate d in cre ase in d efle ctio n is large rif the M - c p re la tio nsh ip is re pre se nte d b y an e lastic-p la stic ap pro xim atio n (F ig ure 6 ).A le sse r incre ase is calcu lated if M - c p is represen te d by a n on -lin ear curve w itho ut aplate au (F ig ure 7). In shape th e latte r co nfo rm s m ore clo se ly to th e e xp erim en talb eh av io ur o f c on n ectio ns (F ig ure 5). .E ve n w ith an e lastic-p lastic ap pro xim atio n, s tu die s(7 ) sh ow th at w in d-m ome nt fram e s su bje ctto on ly light w in d load will no t deflec t m ore than the com mon lim it of 1/300th o f th ehe ight. M an y such fram es w ill deflec t less than l/S 00th of the he ight.

F or fram es w ith h igh w in d lo ad, in w hich de fle ctio ns are critical, the n on -lin earre pre se nta tio n o f co nn ectio n be havio ur gav e in cre ase in o ve rall de fle ctio n w hich v arie dfrom fram e to fram e. The m axim um increases in deflec tion w ere in th e r ang e S0 -6 0%(8 .1 6 ).H ow eve r, it is n ot possib le from these stud ies to pre dict the increase in de fle ctio n fo r ag iv en fram e. Particu lar care sho uld be take n if sw ay d efle ctio ns a re s pe cifie d fo rs atis fa cto ry fittin g o f c la dd in g , e tc . In th e se c as es , the e ffe ct o f c on n ec tio nfle xib ility c an b e a sse sse d b y u sin g a " fix ity fac to r"(1 7), t o m od ify b eam stiffn ess b efo rean aly sin g th e fram e .The re co mm en datio ns give n b elo w are fo r fram es inwhich su ch an aly se s a re co nsid ere dunnecessary.

5.2 Recommendations5.2.1 Initial analysisThe de sig n m ad e fo r th e ultim ate lim it sta te sho uld be a na ly se d a s a n e la stic r ig id -jo in te dfram e to d ete rm in e sw ay de fle ctio ns. S im ple grap hical pro ce du re s g iv e sufficie nta cc ur ac y(1 8). T h e c alc ula te d d efle ctio n s s ho uld be in creased by S O% (i.e . m ultiplied by afa cto r o f 1.S) a s an ap pro xim ate allo wa nce fo r co nn ectio n fle xib ility . Ift he i n cr ea se dv alu es a re a cc ep ta ble , the d es ig n is c om p le te .

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Commen ta ryTh e correction for con nection flexib ility is based on the stu dies on fra mes w ith h ig h w in dlo ad , u sin g a n on -lin ea r r ep re se nta tio n o f c on ne ctio n b eh av io u~ 8. 18). In view o f thea pp ro xim a te n atu re o f th e c or re ctio n, it is a pp ro pr ia te to reco mm end th e roun ded value o f50%.5.2.2 R e de s ig n fo r s tiffn e s sIfthe deflections are unacceptable, then the design should be revised to provideadditional stiffness: connection details should be changed to provide greater stiffness so that they may betaken as rigid(19);the deflections calculated in Section 5.2.1 above are nowapplicable, without increase for connection flexibility member sections should be increased; methods are available which enable this to bedone in a beneficial manner without necessarily re-analysing the complete frarne(20).

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REFERENCES

1. CONSTRUCfIONAL STEEL RESEARCH AND DEVELOPMENT ORGANISATIONSteel designers' manualCrosby Lockwood Staples, 1972

2. BRITISH STANDARDS INSTITUTIONBS 449: Use of structural steel in buildingBSI,1969

3. AMERICAN INSTITUTE OF STEEL CONSTRUCfIONManual of steel constructionAISC, Chicago, 1980

4. NETHERCOT, D.A.Joint action and the design of steel framesThe Structural Engineer Vol. 63A, No. 12, December 1985, pp. 371-379

5. GERSTLE, K.H.Flexibly connected steel framesSteel framed structures: Stability and strength (ed. R Narayanan), Elsevier, 1985,pp. 205 - 239

6. ACKROYD, M.Design of flexibly connected unbraced steel building framesJournal of Constructional Steel Research Vol. 8, 1987, pp. 261-286

7. READING, s.rInvestigation of the wind connection methodMSc thesis, University of Warwick, 19898. KAVIANPOUR, K.Design and analysis of unbraced steel framesPh.D thesis, University of Warwick, 19909. NEAL, B.G.T h e plastic methods of structural analysis

Chapman and Hall, 197710. BRITISH STANDARDS INSTITUTIONBS 5950: Structural use of steelwork in building

Part 1: Code of practice for design in simple and continuous constructionBSI,199O

11. MAJID, K.I. a n d ANDERSON, D.T h e computer analysis of large multi-storey framed structuresThe Structural Engineer Vol. 46, No. 11, November 1968, pp. 357-365

12. COMMISSION OF THE EUROPEAN COMMUNITIESEurocode No.3: Design of steel structuresPart 1: General rules and rules for buildings(Edited Draft, April 1990)

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13. FRYE, M.J. and MORRIS, G.A.Analysis of flexibly connected steel framesCanadian Journal of Civil Engineering, Vol. 2 1975, pp. 280-29114. SCI/BCSA CONNECI'IONS GROUP

Publication on Moment Connections - to b e published15. ANDERSON, D. and LOK, T.S.

Design studies on unbraced, multi-storey steel framesThe Structural Engineer Vol. 61B, No.2, June 1983, pp. 29-34

16. ANDERSON, D. and NAJAFI KOOPAEE, A.A.Sway deflection in frames designed by wind-moment methodUniversity of Warwick, Civil Engineering Research Report, 199117. CUNNINGHAM, R.Some aspects of semi-rigid connections in structural steelwork

The Structural Engineer Vol. 68, No.5, 1990, pp. 85-9218. WOOD, R.H. and ROBERTS, E.H.A graphical method of predicting sidesway in the design of multistorey buildings

Proceedings of the Institution of Civil Engineers, Part 2, Vol. 59, June 1975,pp.353-372

19. OWENS, G.W. and CHEAL, B.D.Structural steelwork connectionsButterworths, 1989

20. ANDERSON, D.Design of multi-storey steel frames to sway deflection limitationsSteel framed structures: Stability and strength (ed. R Narayanan), Elsevier, 1985,pp.55-80

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Appendix A PORTAL METHOD OF ANALYSISIn t roduct ionD etailed explan atio n is given be lo w fo r the applicatio n o f the po rtal m etho d to part o f am ulti-sto re y tw o b ay fra me (F ig ure A .Ia).

D is tributio n o f h o rizo n tal lo adE ach b ay is assu me d to act as a sin gle po rtal an d the total h oriz on tal lo ad is d iv id edb etw ee n the bays in p ro po rtio n to the ir span s. Thus fo r the tw o separate bays show n inF ig ure A .I b:

(A . I )

C alc ulatio n o f in tern al fo rc es in c olum n sT his w ill be dem on strate d for the sin gle po rtal bay show n in F igure A .2 a.F igure A .2 b show s the forces actin g on the po rtion o f the bay above the poin ts ofcon traflexure at A and D . The ho rizon ta l fo rce ~ , is assumed to b e d iv id e d e qua ll ybe tw een the tw o colum ns. Thus:

(A2)The v e rt ic al f or ce s F} ca n b e fo un d b y tak in g m om en ts ab out the p oin t o f co ntrafle xu reat e ithe r A o r 0:

w h ic h g iv es :(A3)

Figure A .2 c show s the fo rce s acting on the po rtion A BC DEG of the bay. It fo llow s from thea ssump tio n ab ov e th at:(A4)

Takin g m om en ts about the poin t o f con traflexure at e ithe r C or G :

S ub stitu tin g fo r S } a nd F } and r e -a rr a nging :(AS)

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-

" AY ,

H2,1 -r---------.1 -W2- H',2 -1------1

H , , 3 -1------1

. I . ArII ll2(a) TWO SAY FRAME (b) TWO SINGLE PORTALS

Figure A.1 D is tr ib u tio n o f h or iz on ta l lo ad

H I-

(a) c

0B E

G

AY

(a)

Shear force VIM , 1 ~MIM'y-VM'I . L 1

A

H2-

l L . 1 (b)M, M2

(b) H ' - l 5 1 _ 1 ~ h ' / 2,- A Shear force V2~ F, t F,t F, ~ FI Figure A.3 I nt ernal momen ts

SI- A 5 ' - 3e) B hl2H2- E h2/2S2- C S2~ G I

~ F2 t F2Figure A.2 In te rn al fo rc es in c olumns

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C a lc ulatio n o f in te rn al m o m e ntsIt is clear from Figure A .2 b that the in ternal m om en t at the head of each co lum n is givenby:

S u bs titu tin g fo r S I :

For equilibrium . the m om en t at each end of the roo f beam is also equal to MI' Theben din g m om en t diagram is show n in Figure A .3a.Referring to Figure A .2 c. the in te rn al m om ent in each uppe r colum n at B and E is alsoMI' The correspondin g m om en t in the low er co lum ns is given by:

M2 = S2h212S u bs titu tin g fo r S 2 :

M2 = (H I + H2)h214For equilibrium at B and E , the in tern al m om en t at each end of the beam B E equals(MI +M2), as show n in Figure A .3b.

C alc ulatio n o f s hear fo rc es In beam sA s a po in t of con trafle xure is assum ed at the m id-le ngth of each be am (Figure A .3), theshear fo rce in the roo f beam is given by:

Su bs tit ut in g f or MI:

S im ilar ly, the sh ear fo rce V2 in beam BE is given by

Su bs tit ut in g f or M I and M2 :

Fo rc es an d m o m en ts In an In tern al c olum nThe se are obtain ed by sum min g the values calculated for adjacen t bays on eithe r side o f thecolumn.It is found that the ve rtical fo rce s in an in te rn al colum n are ze ro .

22

(A6)

(A7)

(AS)

(A9)


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Appendix B DESIGN EXAMPLEC alculation s are give n to de mon strate the de sign rule s as fo llo ws:Ca lc ula tio n s he e t 1 F ram in g an d lo ads

C alculation she ets 7 - 15

G lo b al a n al ys isB eam d esig n (in clu din g S L S ca lc ula tio n fo r d efle ctio n)C o lumn d esig n

C alculation she ets 2 - 4C alculation she ets 5 - 6

Ca lc ula tio n s he e t 16 L oa din g o n c on n ec tio n sCa lc ula tio n s he e ts 17 - 19 SLS - sway due to w indThe design of con ne ction s an d base de tails is outside the scope of this docum en t.R efe re nce m ay be made to Ow en s an d C he al(1 9).

23


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Commentary to calculation sheet

T he plane fram efor w hich ca lcu la tions are gtvenform s part o f a steel struc ture w hichco nfo rm s to the fra me la yo ut sp ecifie d in S ec tio n 3.1 o f th is p ub lic atio n. In p artic ula r:the plane fram e is e ffectively braced against out-of-p lane sw ay a t roo f level and eachflo or le ve l.in th is exam ple , the beam grid com prises on ly prim ary beam s, w ith flooring androo fin g sp an nin g a s sh ow n in F ig ure 10.

Thefram e d im ensions con form to the range o f app lica tion spec ified in Sec tion 3.2:bay w id th: s torey heigh t 6 1.2" 5 =( bo tt om s to re y )bay w id th: s torey heigh t 6 1.54 =( ab ov e b otto m s to re y)greatest bay w id th : sm allest bay w idth 6 1.0(5 =sto re y h eig ht (b otto m s to re y) = 5m < 6ms to re y h eig ht ( oth er s to re ys ) = 4m < 5m

T he lo ads g iv en are u nfa cto re d va lu es.

Horizontal windforces are based on S2factor vary ing w ith he ight. A llow ance is m ade inthe force at roo f leve l for a parapet above .T he load ing con form s to the range o f app lica tion spec ified in Section 3.6:

the to tal u rfa ctored floo r le ve l = 4.50 + 5.00 = 9.50 < 1 2.5 0 k Nlm 2w ind forces are based on a basic w ind speed


34/70

~t~:1ConstructionInstituteSilwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944CALCULATION SHEET

Jo b N o . PUB 7820 I S h e e t (Jo b T it le Oes~qn Example

o f (9 I R e v .

4 0

D a t e June 90D a t e Sept 90

Su b j e c t Framin.qand LoadeSCI M ad e b y 01)

C h ec ke d b y OlltlfR .fU rtlG f}D l(J f}DS

C l i e n t

16.6 kN ~ _----.....-----""T"'"----""T"'"----...,-,..-

170 kN ~ I-----.J-----.J------I-------l -I-

142 kN" ~-----'-----+----+--------I-I-130 kN ..... I-----.J-----.J------I-------l -~

frames at 6.0 m centres longitudinally

4 0

- [ ~ ~ - 6 - . 0 - - ~ ~ * [_ - 6 ~ . - 0 - - ~ ~ ~ 1 . ~ - - - 6 - . 0 ~ - - ~ . 1 ~ ~_ ~ 6 ~ ' 0 ~ _ ~ . - r - ~

4 0

50

R.oofDead loadImposed loadfloore.Dead loadImposed load

If.OO {((1m2i . s c {((1m2

If.SO {((1m2S.OO {((1m2

27.0 {((1m30.0 {((1m

25


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T he ana lysis fo r in ternal m om ents a nd forces due to w ind is m ad e w ith urifa cto red loa ds,to p erm it th e resu lts to b efa cto red fo r th e req uired lo ad co mb in atio ns: 1.2 (D ead lo ad p lus im posed lo ad p lus w in d load ) 1.4 (D ead lo ad p lus w ind loa d).

A na lysis is by t he '' po r ta l' ' m e th od .

To ta l w ind shear is d iv ided betw een the bays in proportion to their spans. For anin tern al co lu mn , th e sh ea r is o bta in ed by su mm in g th e co ntrib utio ns to th e c olu mn fro mad jacent ba ys. T he in terna l m om ent is ob ta ined by mu ltip ly in g th e s he ar by half th esto rey h eig ht (th e assum ed d istan ce fro m the p oin t o f con tra flexure to the en d of th ecolumn) .Th e axia l fo rce in an externa l co lum n is obta in ed by takin g m om ents a bou t th e p oin t o fcon tra flexure .for th e p ortio n of th e fram e abo ve the level bein g co nsidered . F orces a recom pressive in the leew ard co lum n, tensile in the w ind ward colum n. T he axia l fo rce inan in terna l co lum n, due to w ind , is zero .

2 6


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TheSteel ConstructionInstituteSilwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944CALCULATION SHEET

Job No. PU87820 Sheet 2 of 19 Rev.Job TitleSubject (Jind anah 8i8:CDlumnBClient SCI Made by Dii Date June 90

Checked by Dl/fI Date Sept 90lJlN D fJN FUYSIS

416 kNm 830kNm

STfJREY T fJm e MIND SHEAR f(JRCf IN BENDING 1tI(JItIENT IN C(jlfJ ItINSH EAR (kN) C (J lf JI tIN ( kN ) (kNm)

EXTERNAL INTERNAL EXTERNAL INTERNALfI 16.6 2.08 fl. 15 2.08 x 2. 0 = fI.16 'US x 2. 0 = 8.303 33.6 fI.20 8.flO fI.20 x 2.0 = 8.flO 8.flO x 2. 0 = 16.82 t.e 5.98 12.0 5.98 x 2.0 = 12.0 12.0 x 2. 0 = 2f1.0I 60.8 7.60 15.2 7.60 x 2.5 = 19.0 15.2 x 2.5 = 38.0

smREY 1tI(J ItIE IV TS AB (J {ff P (J IN T (J f C (J NT RA flfX lJ RE A T ItIID -H EIGHT r : (kN)fI 2' 1 foq = 16.6 x 2.0 1.383 2f1 fo3 = 16.6 x 6. 0 + 17.0 x 2.0 5.572 2f1 fo2 = 16.6 x 10.0 + 17.0 x 6. 0 + IfI.2 x 2. 0 12.'1I 2'1 fo r = 16.6 x 1'1.5 + 17.0 x 10.5 + 1'1.2 x 6.5 + 13.0 x 2.5 22.7

N8 Oafues are UlYffJC rDRED

27


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Internal beam m om ents are in equilib rium w ith colum n end m om ents .

28


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TheSteel ConstructionInstituteSilwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944CALCULATION SHEET

Job No. PU8 7820 Sheet 3 of 19 Rev.Job TitleSubject M ind fJna l4 8i8: 8eam 8Client SC I Made by DfJ Date June 90

Checked by DlIYI Date Sepf 90

(J 'IVD A IVAlrs 'S (C lJ lV 17 lV lJ [D )

126 kNm

20'4km

31'OkNm

noo 8lNDING (t{(j(t{lNr IN lXflRNfU coum (kNm) 8lNDINGI(t{(j(t{lNr IN 8lfl(t{u o e c (kNm)(JPPlR C(jlfJ(t{N lDfJJERCDlfJ(t{NRoof tU6 0.0 + '1.16 = '1.163 if.f6 8.'10 '1.16 + 8.'10 = 12.62 8.'10 12.0 8.'10 + 12.0 = 20.'11 12.0 19.0 12.0 + 19.0 = 31.0

f(fj Oalues are Uf(ffJC rDRED

29


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S ee C la use 5.6.3 Swa y fram es a nd C la use 5.1.2.3 Notio na l h orizo nta l lo ad s. T hen otio na l h orizo nta l lo ad s re pre se nt in itia l sw ay im p erfe ctio n. T he v ery sm a ll c ha ng es inc olumn a xia l f o rc es d ue to in iti al s wa y impe rfe ctio ns a re n eg le cte d.

A na ly sis fo r in te rn al m om en ts is by th e " po rta l" me th od ,fo llow in g th e s ame p ro ce du rea s f or w in d a na ly sis .

30


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The Job No. p u n 7820 Sheet If of 19 Rev.Steel ConstructionInstitute Job Title-Silwood Park Ascot Berks SL5 7QN Subject Notional Horizontal forcesTelephone: (0344) 23345Fax: (0344) 22944 Client SCI Made by DA Date June 90CALCULATION SHEET Checked by DlIrt Date Sept 90

ND17lJNIU HDRIZlJNr~L fDRCESNotional borieonta! force = 0.005 ('.'1 Dead + '.6 Imposed)Roof H = 0.005 ('.'1 x 2q. + '.6 x 9) x 2q. = 5.76 MVfloDr H = 0.005 ('.II x 27 + '.6 x 30) x 2q. = '0.3 kf{

SrMY tome SHE~R IN BEND ING IYIDIYIENr IN CD ll Jl YINSHE~R (kN) CDllJ lYIN (kN) (kNm)

EXnRN~L INnRN~L EXnRN~L INnRN~Lif 5.76 0.72 ts 0.72 x 2 = f.ifif ts x 2 = 2.883 ts. f 2.0f if.Of 2.0f x 2 = if.02 o f x 2 = 8.032 26/1 3.30 6.60 3.30 x 2 = 6.60 6.60 x 2 = f3.2f 36.7 if.58 9. f6 if.58 x 2.5 = t t.s 9.f6 x 2.5 = 22.9

FWDR (j[NDING IYIDIYIENr IN EXnRN~L CDllJlYIN (kNm) BENDING IYIDIYIENr IN BE~IYIL E O E L (kNm)( JPPER CD ll Jl YIN W ~ER CDllJ lYINRoof - ts 0.0 + f.lflf = f.lflf3 ts if.02 '.lflf + if.02 = ss2 if.02 6.60 if.02 + 6.60 = fO.6f 6.60 I t t.s 6.60 + t t.S = f8. f

f{fj Oalues are f~C rDRED

31


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A llow anc e/or p artia l fix ity o/th e c on ne ction s in a cc ord anc e w ith C la use 2.1 .2 .4(b ).

Load factors g iven in Tab le 2.B eam end m om ent due to no tiona l horizon tal loads no t considered as m axim um m om ent dueto gravity load is a t m id -span and is m uch grea ter . In teraction 0/ sh ear an d m om entneed no t be considered as m axim um shear occurs a t ends o f beam s.

M om en t and shear capacities g iven in V ol. 1o f SC I Guide to B S5950: P art 1 ,p .133, 141respect ively.M o me nt ca pa city re stricte d to 0 .9 Mcx to p ro vid e d ir ec tio na l re stra in t to c olu m ns(Clause 4.7.2). T he roo f de ta ils are to be such tha t the beam is e ffec tively restra ineda ga in st la te ra l a nd la te ra l- to rs io na l b uc klin g.Vo l . 1o f SC I Guide to B S5950: P art 1g iv e s c la ss if ic a ti on , p .1 3 3.Account cou ld be taken o f end restra in t m om en t if d efle ctio n p ro ve d c ritic al.D eflec tio n lim it is sp an /360 (T ab le 5).

To ta l design m om en t a t end of beam is due to(i) w ind(U ) end restrain t m omen t due to g ra vity lo ad .B y inspec tion , th is is m uch less than m axim um m id-span m om en t due to dead p lus im posedloading.In th is exam ple, axia l fo rces in beam s due to w ind are sm all and are neg lec ted .

32


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Job No. PUB 7820 I Sheet S of 19 I Rev.~~:IonstructionInstitute ~Silwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944

Job Title De8(qn ExampleSubject RDDf BeamClient SCI Made by DEi Date June 90

Checked by DlJYl Date Sepf 90ALCULATION SHEET

RDD' BEfUy/U O L1I lake end restraint moment due to gravityload equal to 10% of ''freeIImoment.

60

Dead plus imposed loadingDesign load for UlS: M = (1.'1 x 2q. + 1.6 x 9) x 6

0.9 M l 0.9 x 288 x 61 1 1 = =-----8 8f = M = 288

o 2 2

= 288 kN= 19q . kNm= 1q.q.kN

fry 30S x 16S x Sq. U8 Grade q.30.9 ilia = 0.9 x 232 = 209 kNm > 19q. klVm DI(r ; = 39S kN > ts klV IDI(Section is Class 1Plastic D/(Design load for SlS: M = 9.0 x 6 = sq . klVDeflection at centre of beam (assuming simply supported)

5 x 5q. x 60003 Span= =.3 mm=--38q. x 20S x 11700 x 10 lf 950 (J/(Dead plus wind loadingDesign moment at end of beam due to wind = 1.q. x q..2 = 5.9 klVm8y inspection, this load combination not criticalDead plus imposed plus lJJindloadingDeSign moment at end of beam due to wind = 1.2 x q..2 = S .O kNmBy inspection, this load combination not critical

II1dopt 30S x 16S x Sq . U8 Grade q.3

33


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See C om m entary to C alcu la tion Sheet 5 .

1 11 1 .; M om ent capacity and classifica tion for proposed sec tion given on p .131 o f V ol. 1 of SC IG uide to B S5950: P art 1. T he floor deta ils are to be such tha t the beam is effectivelyr es tr ain ed a ga in st la te ra l a nd la te ra l- to rs io na l b uc klin g.

T he lo ad in g c onfo rm s to th e re quirem en t in S ec tion 3.6 th at w ind loa d sh ou ld n ot c on tro lthe design o f any beam .

34


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The .= Job No. P(j8 7820 1 Sheet 6 of 19 '1 Rev.Steel ConstructionInstitute Job Title Design Example-- ~ - - - - - - ~ ~ - - ~ - - - - - - - - - - - - - - - - - - ~ - - ~Silwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944

Subject floor 8eamClient SCI Made by DIl Date June 90

Checked by DlIYI Date Sept 90ALCULATION SHEET

fiD(JR B{f)ffIU O L7 I lake end restraint moment due to gravityload equal to 10% of "free IImoment.

6'0 ~

Dead plus imposed loadingDesign toad fDr (Ji8: bJ = (f.tl x 27 + f.6 x 30) x 6

0.9 t o e 0.9 x 5 f 5 x 6ffI= =-----8 8f.=bJ=515

u 2 2

= 5f5 kN

= 257 kNfry '106 x 178 x 7'1 (JB Grade '130.9 fflex = 0.9 x 'I f2 = 37 f kNm > 3'17 kNm (JI(Ie. = 661 kN > 257 kN DKSection is Class f Plastic (J/(Design load for 8i8: bJ = 30 x 6 = f 80 kNDeflection at centre of beam (assuming simply supported)

5 x f 80 x 60003 8pan= =.05 mm =--38'1 x 205 x 27300 x fO" 660 D/(Dead plus tnind IDadingDesign moment at end of beam due to wind = f.'I x 3 f.O = '13.'1 kNmBy inspection, this load combioatioo not criticalDead plus impDsed plus tnind IDadingDesign moment at end Df beam due to wind = f.2 x 3 f. = 37.2 kNmBy inspection, this Iood combinatior: not critical

If)dopt '106 x f78 x 7'1 (JB Grade '13

3 5


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V alu es o f end restra in t m om ent a pply to th e end s of bea ms, calcu la ted as 0.1 W L/8.F or mom en ts d ue to n otio na l lo ad s, se e C alc ula tio n S he et 4.F or m om ents due to w ind, see C alcu lation Sheet 2.

36


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The - - - = - Jo b N o. PUB 7820 I S h e e t 7 a t I R e v .Steel ConstructionInstitute - I - J _Ob_T_ i t _ l e _D_es_ i g.. _ I n _ _ x o _ m _ 1 , _ p l f 4 _ e --1Silwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944

Su b j e c t C D lu m n D e s ig nDa t e J u n e 90Da t e S e p t 90

C l i e n t SCI Mad e b y DilC he c k ed b y D l I Y IALCULATION SHEET

CDlUIY/f( DfSIGf(Splices abooe second sfDrey flDDrbeam.Design catcaiatione required fDr sfDreys 3 and f.Data fDr cakukitioo Df colamn momente:SIMEY BE llM RE lle liONS 10 % RES1R Il IN t ( t{O (t {EN1 ( t{O( t{ENfS D(JE r o HOR IZON tlll W ilD S

DEIlD I( t{POSED DEIlD I(t{POS{(J NOIION lll LDIWS M IND(kN) (kN) (kNm) (kNm)

EXlfRNll l IN fE RN lll E XtE RN lll IN lfR Nlll( kNm) (kNm) (kNm) (kNm)3 81 90 12.2 13.S '1 .02 8.03 8.'10 16.81 81 90 12.2 13.S I1 .S 22.9 19.0 38.0

f(fj 1)(1values are Uf({AC rDRfD, except fOr momente due to notionalborieootat loads.

37


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B eam re ac tio ns a re c alc ula te d/rom lo ad in gs g iv en o n C alc ula tio n S he et 1 .A cco unt is ta ken o fredu ctio n in im po sed lo ad ing , in a ccord an ce w ith B S 6399: Part 1 .

38


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SfI

Silwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944

Subject I n t e r n a l C D lu m n

The -=:- -=:- Job No. PUB 7820 I Sheet 8 of 19 I Rev.Steel ConstructionInstitute _ - I - J _ O b _ T _ i t _ l e _ D _ e _ B. . . . .ig . . . . . n _ { " ' _ u _m . . . L ' l p _ . l e -- i

CALCULATION SHEETDate J u n e 9 0Date S e p t 9 0

S C I Made by D I lChecked by D U Y I

SM OfCOllJftlf{

(ltf{)

Client

( f'(r lR f '( IU CDlfJ lY l f'(SrtJR.EY WAD lf{G ( ltf{ )

D 72 D 72-H-1 2 7 1 2 7

3

6f17

ron WAD

o

3D81 D81-H-190 190

DEAD(ltf{)

1 f 1 7

3 312

If t lPOS{[J(ltf{)

2 3 f 1

R. {[J (JC1I0f { I f{If t lPOSEDWAD (ltf{)

R.D(Jc{DIft lP(JS{[JWAD (ltf{)

2D 81 D 81-H-190 190 S fl79 fllfl

1 0%23 211

1D81 D81-H-190 190

f'({j Daksee are fJf '( ffJC rDR lD

6 S 9 f 1

2 0%83 331

3 0%178 f116

39


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L oad/a cto rs g iven in Tab Le 2. Axia l fo rces due to dead and im posed loading are giveno n C a lc ula tio n S he et 8.Momen t is d ue to n otio na L h orizo nta L L oa ds a nd is a Lrea dy fa cto red (see C alcu la tio n S heet7).

S ec tio n is C la ss 1P la stic in b en din g (see V ol. 1o/SC I G uide to BS5950 : Part 1,p.137) .

C om pressio n resista nce a nd b ucklin g resista nce m om en t g iven in V ol. 10/ SC I Guide toB S5 95 0: P art 1,p .1 76 . B uck lin g resista nce m om en t is th at/o r "sim ple" d esig n(C la u se 4 .7 .7 ).S ee C la use 4.7.7 and 4.8.3.3.1. E quiva len t u niform m om en t/ac to r m = 1 .0 (C la u se4 .7 .7). As m = 1 .0 , there is no need/o r a sep arate loca l capa city check.F or pattern loa d, om it im posed loa d on on e beam a t th ird-floor level.

L oad /a ctors g iven in Ta ble 2. F rom " po rta l" a na ly sis (C a lc ula tio n S he et 2), n o a xia llo ad a rises in in tern al co lum n due to w in d.M om ent is due to w ind (see C alcu la tion Sheet 7).

203 x 203 x 46 UC G ra de 43 is n ot C la ss 1,Plastic.

40


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S u b j e c t Internal Golum n

The J o b N o . PUB 7820 I S h e e t 9 o f 19 I R e v .Steel ConstructionInstitute J - J _ O b _ T _ i t l e _ D _ e _ 8 i g . J J . , "jn__xo_m... .1'p _ l l e --iSilwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944 Made by O~ Date June 90lient SC ICALCULATION SHEET C h e c k e d by OllYl Date Sepf 90SfDRlY 3Dead plus imposed loading plus notional forcesDesign load for (JL8: Fe.= 1.q, x 312 + 1.6 x 211 = 77q, kNDesign moment for (JL8: I Y f x = 8.03 kNmL = q,.0 mLEy= 1.0L = q,.0 m: LEx= 1.SL = 6.0 mfry 203 x 203 x 52 (J(, Grade q,3Pc.y= 1100 kN> 77q, kNP ex = 1370 kN> 77q, kN1t16s = 150 klVm > 8.03 kNmt, 1 t I / C 77q, 8.03- +- =--+-- =.76 < 1.00Pc. 1t16s 1100 150

(JI(D I (D I (D I (

B y inspection, pattern imposed load wiff not be critical.Dead plus imposed plus wind loadingDesign load for (JL8: Fe.= 1.2 x 312 + 1.2 x 211Design moment for (JLS: I Y f x = 1.2 x 16.8 = 628 kN= 20.2 kNmFc. I Y f x 628 20.2- + - = - - + - = 0.71 < 1.00e, 1t16s 100 (SO D I (Dead plus wind loadingDeSign load for (JL8:Design moment for (JL8:

Fe.= 1.q, x 312f Y I / C = 1.q, x 16.8 = q,37 kN~ 23.5 kNm

F e . I Y f x q,37 23.5-+-=--+--=.55 < f.OOe . : 1100 150fJdopt 203 x 203 x 52 (J(, Grade q,3

D I (

41


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See Commentary to Calculation Sheet 9.

Compression resistance and buckling resistance moment given in Vol.1ojSCI Guide toBS5950: Part 1,p.175.

For pattern load, omit imposed load on one beam atfirst-floor level.

42


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Job No. PUB 7820 I S h e e t 10 o f 19 I R e v .heSteel ConstructionInstitute Job T i t le Oee.!9n ExampleSu b j e c t Internal Column

SrDRlY 1Dead plus imposed loading plus notional forcesDesign load fOr (J lB: F r . = 1.11x 6117 + 1.6 x II 16 = 1571 kNDesign moment fOr (J lB: I t I x = 22.9 kNml = 5.0 mlE !} = 1.0l = 5.0 m; lE x = 1.5l = 7.5 m

fry 25'1 x 25'1 x 89 (J e Grade '1 3Pe.!}= 1860 kN > 1571 kN (J(P ex > Pe.!} (J(I t I b s = 317 kNm > 22.9 kNm (J(Fe. I Y l x . 1571 22.9-+-=--. +--=0.92 < 1.00 (J(e. I t I b s 1860 317B y inspection, pattern impoeed load will not he criticalDead plus impo8ed plus (DindloadingDeSign load for (JlB : Fe.= 1.2 x 6'17 + 1.2 x '116DeSign moment for (Jl8: I Y f x = f.2 x 38.0Fe. I Y I x 1276 '15.6- +- =-- +-- =.8 3 < f.OOe. n: f860 3 f7

= f276 kN= '15.6 kNm(J(

Silwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944 Ma de b y 0 1 1 D a t e June 90l i e n t SCI

D a t e Sept 90ALCULATION SHEET C he ck ed b y OllYl

Dead plus wind loadingDeSign load for (J lB : Fe.= 1.'1 x 6'17DeSign moment for (JlS: I t I x = f.'I x 38.0Fe. I t I x 906 53 .2-+-=--+--=.6 5 < 1.00r. : 1860 317

= 906 kN~ 53.2 kNm

(J(

~dopf 25'1 x 25'1 x 89 (J e Grade '1 3

43


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B eam rea ctio ns are ca lcu la ted /ro m lo ad ing s g iven o n C alculatio n Sh eet 1 .Acco un t is ta ken ofred uctton in im po sed loa din g, in a ccord ance w ith B S 6399: Part 1.

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Silwood Park Ascot Berks SL5 7QNTe l e p hone : (0344) 23345Fax: (0344) 22944

Sub jec t External ColumnCl ien t Da t e June 90

Date Sept 90

The Job N o. p u n 7820 I Shee t 11 o f 19 I Rev .Steel ConstructionInstitute - = - I -J_Ob_T_it_le_D_e_8-" ' (qt. . . . ln_{~_a_m. . . . l . )p_j l4_e ---iCALCULATION SHEET

E X r E R . l V l i l C D l U l t / 1 V

SCI Made by DliC hecked by DUt !

SIfJRY W fW lf(G (k f() SM (J f IfJm e W flD REDUC1I(Jf( If(COl fJ lY l f ( I - -D-Ef I -fJ- - r- - IM , - 'P-O-S-ED-f IYIPOSEfJ

(kf() (kf() (kf() toeo (kf()REDUCEDIMPOSEfJtoeo (kf()

Ifo 72H-127

o3 75 2 7 2 7

3 H-o 81 10%3 159 117 12 10 52

190D 81H-190

20%5 2lf5 207 1 66

1D 81H-190

30%332 2 9 7

I V B Oa(ues are U I V F I iC r O R . E D

89 208

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See C omm entary to C alculation Sh eet 9. A dd itio na l c omm en ts g iv en b elo w.

S ee C la use 4.7.6. B eam reactions are given on C alculation Shee t 11 .A llo w an ce /o r p ar tia l fix ity 0/ connections. V alues are given on C alcula tion Sheet 7.See C Lau se 4.7.7. T he r atio 0/ c olu mn stifJ ne sse s a t th ird -flo or le ve l d oe s n ot e xc ee d1.5. 1/ th e r atio e xc ee ds 1.5 a t s ec on d-flo or le ve l, d is tr ib utio n in p ro po rtio n tostiffn ess w ill g ive le ss m om en t in colum n being de sig ned .M om ent d ue to n otio nal h orizon ta L L oa ds is given on C alc uL atio n Shee t 7.

203 x 203 x 46 U C is not C lass 1, Plastic.C om pre ssio n resistance and b uckling resistanc e m om en t given in V ol. 1o/SCI Guide toB S5950: P art 1,p.176.

Axial force due to w ind load ing given on C alcu la tion Sheet 2.

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The Job N o . P(jB 7820 1Shee t 12 o f 19 J Rev .Steel ConstructionInstitute - I -J_ob_T_it l_eD _ e _ B J J . i g _ l n _ _ x o _m . . . . . l ' l p _ j / e --lSilwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944

Subject E xte r n a l C o lu m nCl ien t S C I Made b y DA

Checked by D l 1 Y IDate J u n e 9 0Date S e p f 9 0ALCULATION SHEET

SmREy3Dead plus imposed loading plus notional forcesDesign load for ULS: F e . = 1.i1 x 1S9 + 1.6 x 10SI = 391 kN

= S1.S kNm= 38.790.2 kNmq.S.1 kNmq..0

q.9.1 kNm

D I (DI(D I (D I (

= q.1.0 kNm= 30.871.8 kNm

Design moment for ULS: ~~ssume section 200 deep.

100

~-.~~J100 I

Eccentricity moment (1.q. x 8 1 + 1.6 x 90) (0. 1 + O.1)10% restraint moment (t x 12.2 + 1.6 x 13.S)Divide equally between upper and lower column lengtnsNotional norizontal loadsTota! design moment t r l x =L = q..o mLEy = 1.0L = q..0 m, LEx = 1.SL = 6.0 mfry 203 x 203 x S2 UG Grade q.3Pc.y = 1100 kN> 391 kNP ex = 1370 kf'( > 391 kf'(tribe = 1SO kNm > q.9.1kNmt; t r l x 391 q.9.1- +- = -- +- = 0.68 < 1.00r. tribe 1100 1S0Dead plus imposed plus wind loadingDeSign load for ULS: F e = 1.2(1S9 + 10S + S.6)DeSign moment for ULS: / Y f xEccentricity moment (1.2 x 81 + 1.2 x 90) (0. 1 + O.1)10% restraint moment (1.2 x 12.2 + 1.2 x 13.S)

I

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Io '! ' ,"I iiIIII;!i'

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~~:IonstructionInstituteSilwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944

C ALC U L A TIO N S HEET

Job No. PU8 7820 I S h e e t (3 o f (9 I R e v .Job T i t le De8(qn ExampleSu b j e c t External CDlumn

Mad e b y DfJ Da t e June 90l i e n t SC IDa t e Sept 90h e ck ed b y D I J Y I

SI O R , E Y 3 ( C D I V I f I V ( J E D )Divide equally between upper and lower column lengthsMind (f. 2 x 8.11)Iotal design moment I Y / I ( =

3S.9 kNmt o . rlf6.0 kNm

F e . ~ e z lf6.0-+-= - - +--= 0.60 < f.OOr, I Y / bl l f fOO f SODead plus wind loadingB y inspection, not critical

D I (

~dopt 203 x 203 x S2 UC Grade lf3

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S ee C omm en ta ry to S he et 12 o f Calcu la t ions .

T he r atio o f c olum n stiffn esse s a t firs t-flo or le ve l d oe s n ot e xc ee d 1 .5 .

I, Compre ssio n r esista nc e a nd b uc klin g re sis ta nc e m om en t g iv en in V ol. 1o f SC I G uide toB S5 95 0: P art 1,p.176.

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The ~ - Jo b N o . PUB 7820 1 S h e e t ('I o f (9 1R e v .Steel ConstructionInstitute =~ Jo b T it le Design Example-- ~ - - - - - - ~ - - - - ~ - - - - - - - - - - - - - - - - - - - - ~Silwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944

Su b j e c t E xte rn al C olu m nMa de b y D~

CALCULATION SHEETC h ec ke d b y DlIYI D a t e Sepf 90

D a t e June 90l i e n t SC I

SIfJR Y 1Dead plus imposed loading plus notional forcesDesign load fOr Ul8: F e . = 1. f x 332 + 1.6 x 208

I= 798 I


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=- Job No. PUB 7820 1Sheet (S of (9 1ev.heSteel ConstructionInstitute Job Title Design ExampleSubject External Columnilwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345

Fax: (0344) 22944 Made by 0 1 1 Date June 90Date Sept 90

3S.9 I d V m22.8S8.7 {(f'{mfJl(

Client SCICALCULATION SHEET

Checked by DlIYI8 roRlY 1(C{Jf(17f((JlIJ)Divide equally betioeen upper and lower column lengtn8Mind (1.2 x 19.0)Iotal de8ifJn moment IYIJ(

67S S8.7= -- +--= 0.87 < '.001200 190Dead plus wind loadingB y inspection, not criticalI1dopt 203 x 203 x 71 UC Grade '13

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Values 0/ b eam r ea ctio ns a nd e nd r es tr ain t m om en ts a re g iv en o n C a lc ula tio n S he et 7 .Fac to r ed va lu e s cf moment d u e to n o tio n al h o rtz on ta l fo rc es a re g iv en o n Ca lc u la tio nSheet 4 .

Va lu es o fb en din g m om en t d ue to w in d a re g iv en o n C a lc ula tio n S he et 3 .

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The - Job No. PUB 7820 I Sheet 16 of 19 I Rev.Steel ConstructionInstitute Job Title Des(qn Example~ - - - - - - ~ - - - - ~ - - - - - - - - - - - - - - - - - - - - ~Silwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944

Subject EonnecticneDate June 90Date Sept 90

SCI Made by DRChecked by DllYl

ClientCALCULATION SHEET

LOfUJINGON Bllihl- ,O-CDLlIhlN CONNlC ,IONSCalculations are given for connectione at 1st floor levelDead plus imposed loading plus notional forcesDeSign moment for lILS: hl = (1.11 x 12.2 + 1.6 x 13.5) + 18.1 = 56.8 kNm

18.1fv = (1/1 x 81 + 1.6 x 90) + -3-eSign shear for lILS: = 263 kN

Dead plus imposed plus wind loadingDeSign moment for lILS: hl = (1.2 x 12.2 + 1.2 x 13.5) + 1.2 x 31

= 68.0 kNmDeSign shear for lILS: 1.2 x 31fv=(1.2x81+1.2x90)+ =218kN3Dead plus lDindloadingDeSign moment for lILS: hl = 1/1 x 12.2 + 1.q. x 31.0

1.q. x 31fv = 1.q. x 81 + 3

= 60.5 kNmDeSign shear for lILS: = 128 kN

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Commen tary to ca lcu la tion sh eet

Sway de fl ec ti on s can be ca lcu la ted by a ny re co gn ise d m eth od . T ha t u se d in th e d esig ne xamp le is a sim plifie d p ro ce du re d ue to W o od a nd R ob erts d esc rib ed in R efere nc e 1 8(a nd a lso in R efe re nc e 2 0J.T he a ctu alfra me is re pla ce d b y a su bstitu te b eam-co lu mn fra me . T he b asis o f th es ub sti tu te fr ame is th a t:(i) fo r h orizo nta l lo ad in g o n th e a ctu al f ra me , th e ro ta tio ns o f a ll j oin ts a t a ny on e le vela re a p pr ox ima te ly e qu al , a n d(iiJ each beam restra ins a colum n at both ends.

T he to ta l stiffn ess K b o f a b eam in th e su bstitu te fra me is o bta in ed fro m a summ atio no ve r a ll th e b eams in th e a ctu alfra me a t th e le ve l b ein g c on sid ere d.

T he to ta l stiffn ess K c o f a c olum n in th e s ub stitu te fram e is o bta in ed by a summa t iono ve r a ll th e c olum ns in th e a ctu al f ram e a t th e le ve l b ein g c on sid ere d.

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The = Job No. PUB 7820 I Sheet 17 of 19 Rev.=Steel Construction Des(qn ExampleInstitute Job TitleSilwood Park Ascot Berks SL5 7QN Subject Sway deflectionsTelephone: (0344) 23345Fax: (0344) 22944 Client SCI Made by DA Date June 90CALCULATION SHEET Checked by DlfY{ Date Sept 90SEROICEIUJllI1Y uan: e ttm - StiJl}Y DUE ro MIND

3 0 5 x 1 6 5 x 5 4U B 1 6 6 k N _ . K b 4 I1 6 '6 k N _ . -.-C" ' ) C " ' )O u O u KC 4 Kb 3 J 4 0";:::> 4 0 6 x 1 7 8 x 7 4 U B N: :>1 7 0 kN_ ' XN 1 7 O kN - .C " ' )N C" ' ) L t lO L t l O x K o K b z J 4 0N x -do- N1 4 2 k N _. -.t 1 42 k N _ _..L t lu C" ' ) K cz K b l I 4 01 3 '0 kN _. . ";:::> -do~ o u 1 3 'O kN _ ..:: >-.tal X~ KC l 5 0" ' )1 : "0L tlCO ~ xX-'- -- -'- -- -'- _'--I 6 0 I 6 0 I 6 0 I 6 0 . 1II .. II .. ., ..

S u b s t i tu te fra m eS17ffNiSS IN S U B S tmm fRAMi

SItJREY 1 6 (emq) 4, (em) K 6 = 3r.f/l K 6 (em3)fI ((700 600 3 x fI x ((700/600 23f13 27300 600 3 x fI x 27300/600 I 5'162 27300 600 3 x fI x 27300/600 5f16( 27300 600 3 x 'I x 27300/600 5'16

S1'DR.EY E x t . I e (emq) Int '" (emq) II (em) K c = J:.tJII K c (em3)fI 5260 5260 flOO 5 x 526D1f100 65.83 5260 5260 flOO 5 x 5260/f lOO 65.82 7650 (f l300 flOO (2 x 7650 + 3 x ( fl 300 ) lf lDO (fl5( 7650 (f l300 500 (2 x 7650 + 3 x ( fl 30 0 )1500 '(6

I

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In the simplified method o/Wood and Roberts, the sway 0/ a storey is dependentpartlyon stiffness distribution coefficients calculated/or the substitute frame,To allow/or continuity 0/ columns in a multi-storey structure, it is recognised that eachfloor beam restrains column lengths above and below its own level. This is reflected intheform o/the distribution coefficients.

The stiffness distribution coefficients enable a non-dimensional sway index, c p , to bedeterminedfrom the chart given below. By definition:

where: !!Jh is the sway angle 0/ the storey being considered,F is the total wind shear on the column 0/ the substituteframe, andE is Young's modulus 0/ elasticity (205 kNlmm2).

Values of

(Reproduced by the kindpermission of Thomas Telford Limitedjrom "Agraphical method of predictingside-sway in design o/multi-storey buildings", Proc.ICE, Vol. 59, Part 2,1975).

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The Job No. PU87820 I Sheet 18 of 19 I Rev.Steel Construction De8~qn Examp leInstitute Job Title-Silwood Park Ascot Berks SL5 7QN Subject Sw ay d efle ctio nTelephone: (0344) 23345Fax: (0344) 22944 Client SC I Made by DA Date June 90CALCULATION SHEET Checked by Dl./I1 Date Sept 90

8(,JIW DUE 1'0 (,Jlf{D (C(Jf{rlf{UED 1817fff{[SS DIS rRI8fJ17(Jf{ C(J[ffICI[N1S

SfMfY K G + I(. fe , K , , + / < t fe be , = fe b =K G + 1(.+ K b , K ,,+ K ,+ /< t ,b65.8 + 0 65.8 + 65.8II 0.22 0.1965.8 + 0 + 2311 65.8 + 65.8 + 5116

65.8 + 65.8 6S.8 + te s3 0.(9 0.286S.8 + 6S.8 + Sfl6 6S.8 + IllS + 5116(liS + 6S.8 (liS + ((62 0.28 0.32IllS + 6S.8 + SII6 IllS + fl6 + SII611 6 + IllS fiK ed b ae e0.32 0fl6 + {liS + SII6

8(,J~ y oaac 17(Jf{S- ~ fh lf J ~Sf(JR.fY fe , le b lf J f ( leN) -=-- - ~ (mm )h 12f K " h

16.6 x 1100 x 1.39 III 0.22 0.19 1.39 (6.6 -- 2.312 x 20S00 x 6S.8 17S033.6 x 1100 x 1.f17 I3 0.19 0.28 (.117 33.6 - 11.9(2 x 20S00 x 6S.8 8(91/7.8 x 1/00 x 1.6S (2 0.28 0.32 1.6S 117.8 - 3 .S(2 x 20S00 x (liS "3060.8 x SOO x 1.311 II 0.32 0 1.3f1 60.8 - 7. 112 x 20S00 x 11 6 700

Iotal I- 17.89S SI

i

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Th e d e fl ec tio n s c a lc u la te d t re a ti ng th e fr ame a s r ig id -j oi nte d a re in c re a se d by 50% tomak e a n appr ox ima te a llowanc ej or c o nn e cti on f le xi bi lit y ( se e S e ct io n 5 .2 .1 ).The in cr eas ed de fl ec ti on s a r e accep tab l e.

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~!:IonstructionInstitute --SCI Made byDI}

Checked by DLItI

Job No. Pt18 7820 I Sheet 19 of 19 I Rev.Job Title Des~qn beample

Silwood Park Ascot Berks SL5 7QNTelephone: (0344) 23345Fax: (0344) 22944

Subject Sway deflectionDate June 90Date Sepf 90

ClientCALCULATION SHEET

86.)1 1 Y DUE m 6 .) /NO (GONrt flUEO lAUOtnl1f1GE fOR. GOflflEG tto flX/8/l/1YSIfJRfY R I G I D ~ d lilY/if C H f C K.5 -II II

if (/1750 (/1170 1/300 ( J K3 (/8(9 (/5f/6 (/300 ( J K2 1/( (30 1/753 (/300 ( J K, '/700 '/f/67 (/300 ( J I (

rota( (/955 (/637 (/300 ( J K

Wind Moment Design for Unbraced Frames - 1991

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Transcript of Wind Moment Design for Unbraced Frames - 1991