Seismic Response of Composite Frames I

8/9/2019 Seismic Response of Composite Frames I

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E L S E V I E R0141-0296 95)00211-1

Engineering Structures Vol . 18 , No . 9 , pp . 696 -7 06 , 1996C o p y r i g h t 1 9 9 6 E l s e v i e r S c i e n c e L t d

Pr in t ed i n Grea t Br i t a in . A l l r i gh t s reserved0 1 4 1 - 0 2 9 6 / 9 6 1 5 . 0 0 + 0 . 0 0

S e is m i c r e s p o n s e o f c o m p o s i t e

f l a m e s I R e s p o n s e c ri te r ia a n di n p u t m o t i o nB M B r o d e r ic k

Dep artm ent of Civil, Structural and Environm ental Engineering, Trini~ College, Dublin,I re land

A S E l n a s h a i

Engineering Seismology and Earthquake Enginering Section Imperial College London UK(Received O ctober 1994; revised version accepted October 1995)

To fac i l i ta te the evalua t ion of the se ismic response of a c lass ofcompos i t e f rames th rough the app l i ca t ion o f non l inea r dynamicanalysis techniques, response cr i te r ia which ref lec t the acceptablel imi ts of s t ruc tura l response are def ined. These reponse cr i te r iare la t e to the b ehav iour o f t he f rames a t loca l me mb er ) and g loba lstorey) levels . To ensure tha t the ident i f ied f rame behaviour i s suf-

f ic ient ly genera l in na ture , the response analyses are performedusing a diverse range of ear thquake loads. To this end, s ix recordedaccelerograms are se lec ted on the basis of the i r peak ground accel -e ra t ion- to -ve loc i ty a / v ) rat ios. Ea ch record is scaled to po ssess aspec t rum in t ens i ty equa l to tha t o f the E urocode 8 des ign spec t rum,prese rv ing the impor t an t ve loc i ty cha rac te r i s t i c s o f t he g roundmot ion , w hi l e r em a in ing com pa t ib l e wi th p rov i s ions o f t he des igncode . In a com pa nion paper, these response cr i te r ia and ear th-quake loads are appl ied in the evalua t ion of behaviour fac tors formo me nt - re s i s t ing comp os i t e f rames . Cop yr igh t 1996 E l sevie rScience Ltd.

Ke y wo r d s : c o m p o s i t e b e a m s a nd c o l u m n s , r o t a ti o n d u c t il it y,ea r thquake acce le rograms

I n t r o d u c t i o n

In compos i te cons t ruct ion , the proper t i es of s teel and con-crete may be combined to offer eff ic ien t so lu t ions to thedes ign of engineer ing s t ructures . For bui ld ing sy s tems ,com po s i t e f r am es co m m o n l y fo rm t h e m os t econ om i ca l s o l-u t ion to the d iverse requi rements of s t i ffness , s t rength andinsula t ion . For s t ructures requi red to res i s t ear thquakeloads , th i s economy i s especia l ly re levant . Moreover, thei nhe ren t duc t i l i t y pos s es s ed b y co m pos i t e m em bers a l l owsa greater l evel of energ y d i ss ipat ion to be achieved , fur therincreas ing thei r appl icabi l i ty to ear thquake res i s tan t s t ruc-tures . These features are mos t s igni f icant in the case ofmoment -res i s t ing f rames , where l a tera l res i s tance i s pr im-ar i ly provided by the f l exural res i s tance of the beam andcolumn members . Whi le such s t ructures present d i ff i cu l t i esin des ign analys i s , p r incipal ly wi th respect to the s tab i l i tyof co lumn mem bers , i t is here that the enhanced d uct i l itys upp l y p rov i ded by p rop e r l y d es i g n ed com p o s i t e m em bers

i s mos t re levant . A s these duct i l i ty capaci t i es are a funct ionof the inelas t i c response character i s t i cs of the indiv idual

m em bers , t hey canno t b e p ro p e r l y a s s es s ed by s i m p l i f i edtechniques . Ins tead , use i s mad e of des ign force reduct ionfactors express ed as behaviour factors , q , in the st ructuralEurocodes) which seek to quant i fy the ex ten t to which theglobal duct i l i ty o f the s t ructure ma y be incorporated in toconvent ional des ign procedures . The val id i ty of th i sapproach i s based on the assumpt ion that accurate andrel iab le behaviour factors are provided for ind iv idual s t ruc-tura l forms and des ign deta i l s . However, the response ofs t ructures subjected to ear thquake loading d i sp lays a h ighdegree of var iab i l i ty resu l t ing f rom the in teract ion of thecharacter i s t i cs of the impose d ground m ot ions and theproper t i es of the par t i cu lar s t ructure under cons iderat ion .

In the fo l lowing, the procedures employed and the resu l t sobta ined in re la t ion to a ser ies of dynam ic analyses of thes e i s m i c r e s p o n s e o f p l ane com p o s i t e f r am es a re d es c ri bed .These analyses , the resu l t s f rom which are presented in a

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com pan i on pape r ~, em p l o y an ad v an ced nu m er i ca l i n te r -g ra t ion s chem e w h i ch s eeks t o r ed uce s om e o f t he i nco n -s i s tencies and inaccuracies inherent in nonl inear dynamicanalys i s . In to ta l , 20 compos i te f rames vary ing in d imen-s i on and m em ber t ype a re ana l y s ed u s i ng s i x d i f f e ren tground mot ion records . To ensure that the ident i f i edresponse and behaviour i s representa t ive of typ ical pract ical

s t ructures , each compos i te f rame i s des igned accord ing tothe requi rements o f the s t ructural Eurocod es . By l imi t ingthe range of the f rames to those which fu l f il Eurocoderequi rements , the var iab i l i ty in s t ructural response whichar i ses due to the d i fferences between indiv idual des ignswi l l be somewhat reduced . I t i s then hoped that the degreeof var ia t ion between each of the s t ructures analysed wi l lbe suff ic ien t to cover the major i ty of the reponse featureswhich ar i se in real i s t i c compos i te f rames . Thus , a compre-hens i ve a s s es s m en t o f t he d em ands i m p o s ed upon m om en t -res i s t ing compos i te f rames and the effect s of se i smic load-ing on thei r capaci t i es may be assessed . The f rames inves t i -ga t ed a re com pos ed o f e i t he r s t ee l o r pa r t i a l l y -encas edcom pos i t e co l um ns connec t ed t o co m po s i t e b eam s bymoment -res i s t ing connect ions . For each f rame, the s t ruc-tura l behaviour factors as def ined in the companion paperare ident i f i ed by obta in ing the ground mot ion in tens i t i essuff ic ien t to cause y ie ld and fa i lure . In th i s regard , the fa i l -ure l imi t s ta te i s represented by the a t t a inment of one of anum ber o f r e s pons e c r i te r i a co r re s pond in g t o a s e t o f con -d i t ions a t e i ther ind iv idual member or s torey level s .

M e m b e r r o t a t i o n c a p a c i t yThe response of a s t ructure to ear thquake loading involvess t ructural deform at ions in excess of those norm al ly a l low-able under gravi ty loading . For s t ructures des igned to d i ss i -pate input se i smic energy through i r recoverable inelas t i c

s t ra ins , these deformat ions can involve large excurs ionsin to the p las t i c range of the cons t i tuent s t ructural mater ia l s .Whi le s imi lar inelas t i c behav iour i s encountered in the p las -t i c des ign of s t ructures to res i s t g ravi ty and o ther pr imaryloads , i t s ex ten t i s l imi ted to that requi red to a l low the red i s -t r ibu t ion of in ternal s t ress resu l tan t s . The level of inelas t i cdeformat ion involved in the se i smic response of s t ructures ,m ay, however, be m uch g rea te r. In th e capac i t y d es i gnapproach , cer ta in areas of a s t ructure are preselected to bethose in which the inelas t ic resp onse of the s t ructure wi l lbe accom m o d a t ed t h rough t he fo rm a t i on and s t ab l e ro t a ti onof p las t i c h inges , whi le the rem ain ing par t s o f the s t ructureare des igned to po ssess suff ic ien t s t rength to preclude y ie ld-i ng . In m om en t - r e s i s t i n g f r am es , p l a s t i c h i n g es m ay beal lowed to form in the beams and a t the base of the groundf loor co lum ns , imply in g that the local ro ta t ion duct i l ity sup-p l y p rov i ded by t hes e m em bers s hou l d a t l eas t equa l t hedem and i m pos ed upon t h em b y t he s e i s m i c ac t i ons .

F o r t he pu rpos es o f a s s es s i n g s e i s m i c p e r fo rm ance , t h educt i l i ty supply of ind iv idual members i s mos t readi lyexpressed as the ro ta t ion achievable by p las t i c h ingeswi th in the m em ber pr ior to the occurrence of cr i ter ia defin-ing fa i lure or excess iv e loss of res i s tance. T his pr incip le i si l l u s t r a t ed by t he m o m en t - ro t a t i on cu rv es o fFigure 1which sh ow the qual i t a tive behavio ur of non-duct i l e , mod-erate ly duct i l e and h ighly duct i l e members . Wi th referenceto Figure 1 ro t a ti on cap ac i t y m ay b e exp res s ed i n t e rm s o f

the rotat ional duct i l i ty as

O ~ Op I ).o= l=0y

~

Mp

/ i~ . ~ response~ \ non-ductileresponse

e l a s t i c p l a s t i c

Ou ~ highly-ductile~ *--Oy - 4 0p = , respon se ~

d u c t i l e / I

I s e i s m i c

R o t a t i o n

Figure M o m e n t r o t a t i o n r e s p o n s e o f d u c t i l e a n d n o n d u ct i l e m e m b e r s

in which Ou is the ul t ima te rotat ion co rresp ond ing to a l imit-ing cri terion, Oy is the rotat io n at y ield a nd Op is the rotat io nwhich occurs in the p las t i c h inge, namely

Op = Ou - Oy. (2)

In com pos i t e m em bers , t he p rov i s i on o f l a rge ro t a t i onduct i l i t i es , which mus t be accommodated wi th in p las t i ch inges of f in i te l ength , requi res that the component s t ruc-tura l mater ia l s be capable of accommodat ing large s t ra inswi thout d i sp lay ing s igni f icant ins tab i l i ty or loss of res i s t -ance. For the concrete components , th i s impl ies that crush-ing and spal l ing due to excess ive compress ive s t ra ins beavoided by ensur ing that adequate conf inement i s provided ,or by p lacing res t r i c t ions on the p las t i c neural ax i s depthof the section . For the s teel com ponen ts , which ma y usual ly

be cons i d e red t o cons i s t o f an a s s em b l y o f p l a te e l em en t s ,duct i l i ty i s enhanced by l imi t ing p la te s lenderness so thatthe adverse effect s of local buckl ing are avoided . Such localf lange and web buckl ing may al so render a s t ructural mem-ber more suscept ib le to l a tera l buckl ing and , under the cyc-l i c loading condi t ions of se i smic response, low-cyclefa t igue. The ro ta t ion capaci ty of an indiv idual memberdepends , amongs t o thers , on the cr i t i ca l s t ra in a t whichlocal ins tab il i ty wi l l occur, the l ength of mem ber ove rwhich th i s s t rain occurs , the in teract ion of the connectedelements of the cross -sect ion and the level of ax ia l loading .

The ro ta t ion capaci ty o f bare s teel mem bers , such as arecom m o n l y em p l oyed as co l u m ns i n com pos i t e f r am es ,which can sus ta in s t ra ins in to the s t ra in-hardening range(p las t i c or Class 1 sect ions in Euro code 3) may be con-servat ively determined by cons ider ing only the p las t i cro t a ti on o f the m e m b er2. As i l lustrated inFigure 2 this pro-cedure i s based on the assumpt ion that due to the format ionof s lip p lanes in the s teel , a dyn am ic jum p to the s t ra in-hardening poin t occurs upon y ie ld . Al though not a l lowingfor the var ia t ion in s t ra ins across the sect ion and the inf lu-ence of ax ia l forces , th i s assumpt ion a l lows the ro ta t ioncapaci ty to be evaluated wi thout determining the cr i t i ca lbuckl ing s t ra in . Where greater ro ta t ion duct i l i ty capaci t i esare required, higher cri t ical s t rains need to be sustained,i m p l y i n g t he app l i ca ti on o f m ore com pac t , and hence l e sseconomical , s t eel sect ions .

Greater ro ta t ion capaci t i es may a l so be achieved throught he u s e o f co m pos i t e s t ee l co l um ns where t he m u t u a l bene -f i t s provided by the s teel and concrete components ensurethat local ins tab i l i ty occurs only a t h igh s t ra ins . In pat t i -


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L

( a ) L o a d i n g

, , - - - - - C L ~

Figuro2 Rotat ion of s teel beam under m om ent gradient . [For

( b ) B e n d i n g M o m e n t s

( c ) C u r v a t u r e D i a g r a m

d e f i n i t i o n o f v a r i a b l e s s e eFigure 5 b)]

cu l a r, by em p l oy i ng p a r t i a l l y -en cas ed com p os i t e m em b erswi th the cross -sect ion shown inFigure 3 the t radi t ionalbene f i t s o ff e red by co m pos i t e co l u m ns i n t e rm s o f g l oba ls tab i l i ty and f i re insu la t ion may be re ta ined , whi le a t thesame t ime achieving increased ro ta t ion capaci t i es wi thoutresor t ing to uneconomical sect ion deta i l s . Fur thermore, theinclus ion of addi t ional re inforcement , such as the t ransversel inks shown in Figure 3b wil l ensure h igher ro ta t ioncapaci t i es even wi th h igh f lange and web s lendernesses .

By avai l ing fu l ly of the cont r ibut ion to s t i ffness ands t r eng t h p rov i ded by f l oor s l abs , co m p os i t e b eam s o ffe r aneconom i ca l m eans o f p ro v i d in g f l exu ral r e s is t ance . H ow-ever, despi te thei r f requent appl icat ion to the res i s tance ofwind forces in t a l l s t ructures , the corresponding cont r i -but ion to l a tera l s t i ffness offered by compos i te beams hasnot received much a t ten t ion in ear thquake res i s tan t s t ruc-tures 3. Wh i le a cons iderable body of research ex is t s on thero t a t i on capac i t y p rov i ded b y co m po s i t e beam s o f va r i ousdimen s ions 4 s , there i s mu ch less info rmat ion on the l evelo f duc ti l it y dem and i m pos ed on t hes e m em b ers d u r i ng t he irrespon se to ear thquake loading . R oeder 3 repor t s that thereappears to be a d i s t rus t of the duct i l i ty capaci ty of thesem em bers i n t he cyc l ic l o ad i n g con d i ti o n s i m pos ed by ea r th -

quake ground mot ion , ar i s ing due to the predominant ly one-d i rect ion res i s tance which they provide. Al though the hys-

Vertical einforcing Transverse S p o t - We l deinforcement H o o p s '

/

a) Conventional Sectionwith Reinforcing Hoops

b) Section w ith TransverseBars or Im proved Ductil ity

Figure 3 P a r t ia l ly e n c a s e d b e a m - c o l u m n s e t i o n s

t eres i s loops of these mem bers are s tab le , they d i sp lay ap inched appearance, reducing thei r ab i l i ty to d i ss ipate se i s -m i c ene rgy. I t i s com m on , t he re fo re , fo r com pos i t e ac t i onin beams to be neglected when evaluat ing se i smic res i s t -ance ; an a s s um pt i on wh i ch a l t hough p rov i d i ng a cons e rva -t ive es t imate of l a tera l s t i ffness and s t rength wi l l haveadverse effect s upon the y ie ld mechanism of the s t ructure .The widespread appl icat ion of par t i a l in teract ion shear con-nect ions have increased doubts about the duct i l i ty supply ofcom po s i t e beam s , a s no i nves t ig a t i ons have been pe r fo rm edconcern ing the s igni f icance under cycl ic ear thquake loadsof secondary effect s , such as the deformat ion of s teeldecking and shear conn ectors 3. Despi te these concerns , theat t ract ive s t rength and s t i ffness character i s ti cs of comp os i tebeam s are universal ly ackno wledg ed 6 . In addi t ion , s tudies ,a l b ei t under m ono t on i c l oad i ng , have s ho wn t ha t co m po s i t ebeams may be des igned to possess s igni f icant ro ta t ion duc-t i li ty, espe cia l ly in pos i t ive mo me nt reg ions 4 7 . In the fo l -lowing, i t i s assumed that fu l l in teract ion between the s teeljo i s t and concrete s lab i s provided .

R e s p o n s e c r it e r i a f o r c o m p o s i t e f r a m e s

To as s es s t he s e i s m i c pe r fo rm ance o f com pos i t e f r am esfrom the resu l t s of dynamic analyses , a se t of cr i t er ia corre-sponding to the condi t ions a t which s t ructural fa i lure occursare def ined . These cr i t er ia are invoked whenever the res i s t -ance o r duc t i l i t y dem an d s i m pos ed du r i ng an ea r t hquakeexceed the cap abi l i t i es of the s t ructure under con s iderat ion .In pract ice , the a t t a inment of such cr i t eria should im ply thecol lapse , in whole or in par t , o f the s t ructure . H owe ver,before th i s condi t ion i s reached , the proper t i es and behav-iour of the s t ructure wi l l be dras t ical ly a l t ered f rom i t s pre-ear thquake condi t ion . G iven the com plex nature of bui ld ings t ructures , i t i s no t poss ib le to accurate ly capture th i sdeter iora t ion in convent ional analyses . Therefore , the cr i -

t er ia chosen to def ine s t ructural fa i lure should ref lect no tonly the l imi t s of re l i ab le s t ructural response, bu t a l so thel imi ta t ions of the analy t ical too l s employed.

The appl icat ion of such cr i t er ia wi l l ensure that a con-


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servat ive es t imate of s t ructural fa i lure wi l l be achieved . Int h i s i n s t ance , t he dynam i c an a l y s i s p ro g ram em p l oyed ,ADAPTIC, i s ab le to accurate ly t race s t ructural responsewel l in to the inelas t i c range of mater ia l response, evenwhen g ro s s de fo rm a t i o n o f i nd i v idua l m em be rs o r t he s t ruc -ture as a whole has occurred . In essence, as the l imi t s towh i ch t he p rog ram can be r e l i ed upon t o accu ra t e l y com -

pute s t ructural response co incide wi th the condi t ions a twh i ch m uch pe rm anen t d am age wi l l occu r, t he f a i l u re c r i -t er ia der ived therefrom rela te to a damage l imi t s ta te . Thus ,the l imi t s of response ident i f i ed f rom the evaluat ion of ana-ly t ical resu l t s wi th respect to these cr i t er ia may be con-servat ively and re l i ab ly appl ied to fu ture des igns . H ereaf ter,the fo l lowin g sect ions deta i l the def in i t ions of fa i lureem p l oyed i n t he l a t e r des c r i bed a s s es s m en t s o f t he pe r fo rm -ance of compos i te f rames . These fa i lure cr i t er ia arearranged in tw o groups : those re la t ing to fa i lure on a g lobalor ind iv idual s torey level and those def in ing the l imi t s ofresponse for ind iv idual members . In to ta l , seven separatefa i lure cr i t er ia are employed. As descr ibed , the def in i t ionsof these cr i t er ia are based upon the combined resu l t s ofexper imental and numerical s tudies , in addi t ion to com-m on l y app l i ed des i g n g u i d an ce . Wh ere neces s a ry t hes edef in i t ions are supplem ented by engineer ing judgem ent ,appl ied conservat ively.

Storey response cri teriaInterstorey drift. To l imi t the s t ructural and non-s t ruc-

tura l damage incurred dur ing a se i smic event , an upperl imi t i s p laced on the maximum al lowable in ters torey dr i f t .The m os t conven ient me thod o f def in ing th is cr i t er ion i s interm s of the inters torey drift index, A~, defined as

whi le that of equat ion (4) imposes a s imi lar l imi t on defor-mat ion in t erms of a s t ructure ' s res i s tance and gravi ty load-ing . To ensure that the s t rength demands imposed on as t ructure are not excess ive , the format ion of p las t i c h ingesi s al so moni tored . Th e forma t ion of a co lumn h inging co l -l ap s e m echan i s m i m p l i ed by t h e s i m u l t aneo us ex i s t ence o fp las t i c h inges a t the upper and lower ends of each co lumn

cons t i tu tes a s ta te of fa i lure . In th i s regard , the occurrenceof a p las t i c h inge i s ident i f i ed by the exceedance of theyie ld s t ra in in both tens ion an d com press ion f langes of theco l u m n . Th e fo rm a t i on o f o t he r m echan i s m s wh i ch do no tlead to s torey ins tab i l i ty are not t aken as imply ing theoccurrence of a fa i lure condi t ion .

Degradation of lateral resistance.During the largeampl i tude d i sp lacement osci l l a t ions produced by thes t rong-mot ion per iod of the ear thquake, the l evel of l a tera lres i s tance provided by each s t ructure wi l l increase to am ax i m um l ev e l de t e rm i n ed by t h e ben d i n g r e s i s t ances o fi t s s t ructural members . After th i s poin t , second-ordere ff ec t s and t h e l o s s o f s t r eng t h d i s p l ayed by co m pres s i onconcrete a t h igh s t ra ins wi l l cause a decrease in l a tera lres i s tance. Whi le such a decrease does not imply fa i lure ini t sel f , par t i cu lar ly as the l evel of res i s tance d i sp layed a t th i ss tage wi l l be in excess of i t s des ign value , a progress ivereduct ion in res i s tance i s d i sp layed thereaf ter, imply ing anuns tab le and unrel iab le response. Thus , for each hal f -cycleof d i sp lacement response, the l a tera l res i s tance provided ineach s t o rey i s m on i t o red t o de t e rm i ne t he m ax i m u m va l ueoccurr ing . The con di t ion that subsequent v alues of res is t -an ce m us t no t d ec reas e be l ow 90 o f t h is m a x i m u m i s t henemployed as a fa i lure cr i t er ion .

~ i ~ i _ lA i _ ~< 0 . 0 3 , (3 )h/

where 8 i i s the ins tan taneous d i sp lacement a t f loor l evel iand h i is the height of the s torey under cons iderat ion . A sindicated in equat ion (3) a l imi t of 3 i s p laced on Ai; avalue which i s in tended to l imi t p-A effect s as wel l asres t r i c t ing the amo unt of dama ge incurred , whi le a l soref lect ing the ab i l i ty of sway f rames to undergo re la t ivelylarge g lobal deformat ions .

Storey stabil i ty.Eurocode 8 requi res that the s tab i l i tyindex , def ined in equat ion (4) be evaluated for each s toreyof the s t ructure;

t o t d r

0 = V,o~h (4)

where , for the s torey under cons iderat ion ,t o t i s to ta l g rav-i ty load, dr is the desig n in terstore y drift , Vtot is the totalse i smic des ign shear and h i s the height . In addi t ion to theabove res t r i c t ion on in ters torey dr i f t , as a fur ther check onthe s tab i l i ty, the s tab i l i ty index of each s torey i s m oni toredt h roughou t i t s r e s po n s e an d co m pared wi t h t he l i m i t p re -s c r i bed by Eu rocode 8 , nam el y,

0 ~< 0 . 3 . 5 )

Col lapse mechanism format ion .The cond i t i on o f eq u -at ion (3) l imi t s the a l lowable deformat ion in each s torey,

Local response cri teria

Steel columns. A num b er o f m ode l s bas ed o n p l a t e buck -l ing theory have been proposed for the predic t ion of thero t a t i on capac i t y o f s t ee l m em bers2,8-~. To ensure thesecapaci t i es are suff ic ien t to meet the l evel of demand exper i -enced in the d i ss ipat ive zones of ear thquake res i s tan tf rames , i t i s o f pr im ary impor tance that a cr i t ica l me mb eri s capable of a t t a in ing a l evel of s t ra in in i t s compress ionf lange in excess o f that a t which s t ra in-hardening occurs .In th is regard , the present p rovis ions of the s t ructural des igncodes in p lacing l imi t s on sect ional s lendernesses are suf-f ic ien t for the l evel of duct i l i ty requi red in convent ionaldes ign processes . In se i smic des ign , however, h igherro ta t ion duct i l i ty demands may requi re that cr i t i ca l buck-l ing s t ra ins be far in excess of that a t which s t ra in hardeningcom m ences , i m p l y i ng t h a t t he p rov i s i on o f s m a l l e rb / tra t ios may be necessary. Inelas t i c p la te buckl ing theory,which re l i es upon the appl icat ion of modi f ied mater ia lproper t i es to e las t i c re la t ionships , cannot be re l i ed upon topredict these high cri t ical s t rains.

To ove rcom e t h i s d i f f i cu l t y, a m ore r i go rous app roachto the evaluat ion of the ro ta t ion duct i l i ty capaci ty of s teelm em bers was u n d er t aken by K a t o ~~,~2 whic h acco unted forthe change f rom elas t i c to inelas t i c mater ia l p roper t i esalong the length of the member, a l lowed for the y ie ld p la-teau in the s t ress -s t ra in response and employed a cr i t i ca lbuckl ing s t ra in , ra ther than the p las t i c h inge length , as a

l imi t ing condi t ion . To faci l i t a te the numerical and der i -v a t i ona l p rocedu re , Ka t o em p l oyed a s i m p l i f i ed m ode l o fan I -sect ion cons i s t ing of two f langes which possessed thes am e co m bi ned a rea and m om en t o f i ne r t i a a s t h e ac t ua l


5/11

7 0 0 S e i s m i c r e s p o n s e o f c o m p o s i t e f r a m e s I : B. M . B r o d e r i c k a n d A . S . E l n a s h a i

s e c t i o n Figure4a) .M a t e r i a l b e h a v i o u r w a s r e p r e s e n t e di n i t i a l l y b y a r i g i d - p l a s t i c - s t r a i n h a r d e n i n g m o d e lFigure 4b)a n d l a t e r b y a q u a d r i l i n e a r m o d e l ~L,2

T h e s e m o d e l s a r e u s ed t o tr a c e th e m o m e n t - c u r v a t u r er e s p o n s e c o r r e s p o n d i n g t o e l a s t i c , p l a s t i c - f l o w a n d s t r a i nh a r d e n i n g s t a t e s i n b o t h t h e t e n s i o n a n d c o m p r e s s i o nf langes . Doub le in tegra t ion o f the r e su l t ing curva ture d is t r i -

b u t i o n p r o v i d e s t h e s t r u c t u r a l r o t a t i o n s a n d d i s p l a c e m e n t s .I f the ax ia l load i s expressed in te rms of the s t r e ss r a t io p= O-o/O-y, wh ere O o is th e appl ied axia l s tress and cry is they ie ld s t r ess , then for ( s - 1 ) /2 < p , (wh ere s = o- JO-y r ep-re sen ts the norma l ized c r i t ica l s t r e ss ) , the tens ion f langew i l l b e r e s p o n d i n g e l a s t i c a l l y w h e n t h e c o m p r e s s i o n f l a n g ereaches o ~ , whi le fo r ( s - 1 ) / 2 / > p > 0 , the tens ion f langeyie lds p r io r to f a i lu re . These va r ia t ions in ax ia l load g iver i se to th ree express ions fo r ro ta t iona l duc t i l i ty a s fo r ( s-1 / 2 < p

s - 1 [ E l/J,o - 4 ( 1 - - p ~ -( s - p ) 2 ~ ~ ( 2 s - 3 p + l ) ( s - l )

h E ~ t ) ]+ 3 h ~ - ( s - 2 p + 1

( 6 )

f o r ( s - 1 ) / 2 > / p > 0

/x o - 2 ( 1 - p ) ( s - p )2 E~t~ [ ( 2 s - 2 p - - - 1 ) 2 ( 2 s - p + l )

h ~ , 2+ 2 p 2 ( p +3 ) ] 3 h _ ~ ( s 2 p s + l J, ( 7 )

whi le fo r p = 0

r E ] + 3 , S s 2 _ l) ]8 )The de te rm ina t ion of the c r i t ica l b uck l ing s t r e ss O e r,

r e q u ir e d f o r t he e v a l u a ti o n o f e q u a t io n s ( 6 ) - ( 8 ) c o u l d b ed e t e r m i n e d f r o m c o n v e n t i o n a l l o c a l b u c k l i n g t h e o r y 9 : .H o w e v e r , a s t h i s w o u l d r e q u i r e a n a c c u r a t e e v a l u a t i o n o fbo th the ine la s t ic ma te r ia l p rope r t ie s , p la te s t i f fnesses andt h e a m o u n t o f r e s t ra i n t p r o v i d e d t o t h e fl a n g e o u t s t a n d b yt h e w e b , K a t o i n s t e a d c o n d u c t e d a s e r i e s o f s t u b c o l u m nt e s ts f r o m w h i c h e x p r e s s i o n s f o r t h e c ri t ic a l s t r e ss w e r ede r ived by l inea r r egress ion . For mi l id s tee l , th i sexp ress ion is ~2

1 0 .651 0 .0553= 0 .6 89 + + - - _+ 0 .0 30 3 ( 9)

S O{f O~w

Ocl . . . . .

EstIII

Est

rcr

a ) E qu i v a l e n t S t e e l Se c t i on b ) R i g i d -Pl a s t i c S t r a i n Ha rde n i ng Mod e l

Figure 4 S e c t i o n a n d m a t e r i a l m o d e l s f o r t h e e v a l u a t i o n o f th er o t a t i o n c a p a c i t y o f s t e e l m e m b e r s 11

i n w h i c h a s = [E b-/b)2]/~ryrand aw = [E tw/d)2]/~rywep-re sen t the s lende rness o f the f lange and the web , r e spec t -i v e l y. T h e a b o v e r e l a t i o n s h i p s a r e f u r t h e r e m p l o y e d i n t h ed e r i v a t i o n o f e x p r e s s i o n s f o r t h e f l a n g e a n d w e b w i d t h - t o -th ickness r a t ios r equ i red to ach ieve a g iven leve l o fro ta t iona l duc t i l i ty capac i ty.

U n l i k e p r e d i c t i o n s b a s e d o n p l a t e t h e o r y, t h e s o l u ti o n f o r

t h e c r i t i c a l b u c k l i n g s t r e s s g i v e n b y e q u a t i o n ( 9 ) d o e s n o ti n c r e a s e a s y m p t o t i c a l l y w i t h d e c r e a s i n gb/t), ins tead tend-i n g t o w a r d s a m a x i m u m l e v e l d e p e n d e n t o n t h e r e s i s t a n c ep r o v i d e d b y t h e w e b . T h i s f e a t u r e i s m o s t p r o b a b l y a c o n s e -q u e n c e o f q u a l it y c o n t r o l m e a s u r e s i n th e s t e el p r o d u c t i o nprocess th rough which the u l t ima te s t r e ss /y ie ld s t r e ss r a t ioi s r e s t ri c t e d t o a m a x i m u m l e v el , t y p i c a l l y o f t he o r d e r o f1 .2 . K a to s m e thod th e re fore r e f lec ts the true beha viour o fs tee l s t ruc ture s a s found in p rac t ice , a t l ea s t a s f a r a s thee x p e r i m e n t a l s a m p l e i s c o n c e r n e d . T h e i m p l i c a t i o n s o fh i g h e r u l t i m a t e s t r e s s es o n t h e a c c u r a c y o f e q u a t i o n ( 9 )have no t been r epor ted , making i t d i f f icu l t to eva lua te i t ssens i t iv i ty in th is r e spec t .

Partially-encased composite beam-columns.In expe r-i m e n t s a n d d u r i n g a c t u a l e a r t h q u a k e s , c o m p o s i t e s t r u c t u r e sh a v e b e e n s e e n t o a c h i e v e s i g n i f i c a n t i m p r o v e m e n t s i nro ta t ion duc t i l i ty ove r tha t d i sp layed by equiva len t s tee ls t ruc ture s j3 . In pa r t icu la r, the in te rac t ion of the conc r e tea n d s t e e l c o m p o n e n t s a l l o w p r o p e r l y d e t a i l e d p a r t i a l l y -e n c a s e d c o m p o s i t e b e a m - c o l u m n s t o u n d e r g o m u l t i p l es tab le osc i l la t ions a t h igh ro ta t iona l duc t i l i t i e s by ensur ingt h a t c o n f i n e m e n t o f th e c o m p r e s s i o n c o n c r e t e a n d r e s i s ta n c et o l o c al a n d l a t e ra l b u c k l i n g o f t h e c o m p r e s s i o n e l e m e n t sof the s tee l sec t ion i s sus ta ined a t h igh leve ls o f curva tureand s t r a in ~4 :6 . In add i t ion to the r e in forcem ent de ta i l ingc h a r a c t e r i st i c s o f t h e s e m e m b e r s , t h e r e l e v a n t d i m e n s i o n s

a n d m a t e ri a l p r o p e r t i e s o f t h e v a r i o u s c o m p o n e n t s o f th e i rc r o s s - s e c t i o n s d e t e r m i n e t h e m a x i m u m r o t a t i o n s t h a t c a nb e r e l i a b ly a c h i e v e d . T h e e v a l u a t i o n o f m e m b e r u l t i m a t er o t a t i o n c a p a c i t i e s c a n n o t b e p e r f o r m e d b y t h e e x a m i n a t i o no f c r o s s - s e c ti o n s a l o n e , a s a l l o w a n c e m u s t b e m a d e f o r t h es p r e a d o f p l a s t ic i t y a l o n g t h e l e n g t h o f t h e m e m b e r a r i s i n gd u e t o c u r v a t u r e d i s t r i b u t i o n s w h i c h a r e d e p e n d e n t o nh i g h l y v a r i a b l e m o m e n t - c u r v a t u r e r e l a t i o n s h i p s .

To d e t e r m i n e t h e r o t at i o n d u c t i li t y c a p a c i t y o f m e m b e r sw i t h t h e c r o s s - s e c t i o n s s h o w n i nFigure3, a para lle l pro-c e d u r e t o t h a t e m p l o y e d b y K a t o f o r b a r e s t e e l m e m b e r s i sem plo yed ~5. The s impl i f ied mo de ls show n inFigure 5areu s e d t o d e t e rm i n e t h e m o m e n t s a n d c u r v a t u r e s a t e a c h c r i ti -c a l p o i n t in t h e m o n o t o n i c r e s p o n s e o f a c a n t i le v e r m e m b e r.U n d e r e a r t h q u a k e l o a d i n g , t h e c o l u m n s i n a f r a m e m a y b ec o n s i d e r e d t o b e h a v e a s a c o l le c t i o n o f c a n t i l e v e r e l e m e n t s ,

l tPartially Encased Composite Section Equivalent Three Element Model

Figure a ) E q u i v a l e n t m o d e l o f p a r t ia l l y e n c a se d c o m p o s i t es e c t i o n


6/11

Seismic response o f compo site fra mes I: B. M. Broderick and A. S. Elnashai

O s c

Figure5 ( b ) T r i l in e a r s t e e l m a t e r i a l m o d e l

sh

te i True Response

E c l E c E c 2 E c 3

Figure 5 ( c ) M u l t i - l i n e a r c o n c r e t e m a t e r i a l m o d e l

al lowing a curvature d i s t r ibu t ion to be der ived f rom anas s um ed bend i ng m om en t d i s t r i bu t i on( F i g u r e 6 ) .Ul t i m a t ero ta t ions may then be determined f rom the curvature d i s t r i -but ion per ta in ing upon the a t t a inment o f the cr i t ica l f l angebuckl ing s t ra in . These cr i t i ca l s t ra ins are determined f rom

an analy t ical model b ased on p la te buckl ing theo ry and cal i -bra ted agains t exper imental resu l t s .F i g u r e 7 presents ades ign char t , der ived f ro m the resu l t s of th i s model , whichal lows the cr i t i ca l s t ra in to be determined f rom the f l anges lenderness and t ransverse l ink spacing . InTa b l e 1 , thero ta t ion duct i l i ty capaci t i es obta ined wi th th i s method arecompared wi th those ident i f i ed in exper imental s tudies oncant i l ever m em bers where 2~y and Au refer to the y ie ld andul t imate t ip d i sp lacement , respect ively. I t can be observedthat reasonable agreement i s achieved cons ider ing the accu-racy to which the u l t imate ro ta t ion can be def ined and that

:~ I ~ ~ - - - - - - : - -- k - : . . . . . . . . . . . . . . . . . . . i i i ~ _ i i f L. . . . . . .

~1 1 ~ : i / I I I /

V~ $t ~ , Cu~rature" = i /Moment-Curvature Characteris t ic

F L , 'C ompos i t e C a n t i l e ve r M e mb e r

B e nd ing M om e n t D ia g ra m i

I J~t' Y L 5

/ . . . . . o i

- L 1

Curva ture Dis tr ibution

Figure 6 D e t e r m i n a t i o n o f m e m b e r c u r v a t u r e d i s t ri b u t io n f r o mb e n d i n g m o m e n t d i s t r i b u t io n a n d s e c t io n a l m o m e n t - c u r v a t u r ec h a r a c t e r i s t i c

7 1

3 0 . .

:

z 1

O . t i ~ i :

o

iiiiiiLIIII_ ill iiiii

0.4

......... i .. i .i ........

0.8 1.2 1.6s/b

~ : ~ t ~ sE = 2 1 0 , 0 0 0 N / r n m 2

y i e l d s t r e s s = 2 7 5 N / m m 2

. . . . . . . . F la n g e B u ck li ng S tr a i no r m a l l z e a L . r a l c a l ~ t r a l n -

Y i e l d S t r a i n

Fi g u r e 7 Design chart for the evaluation of critical strain fromtransverse l ink spacing (s/b) and flange slen derness (b/t )

the method i s suff ic ien t ly conservat ive to be appl ied infu ture des igns . Moreover, i t p rovides a ra t ional method

through which a fa i lure cr i t er ion for these members can beevaluated in t erms of ro ta t ion duct i l i ty.

C o m p o s i t e b e a m s .The ro t a t i on capac i t y o f co m pos i t ebeams i s l imi ted by a var ie ty of poss ib le fa i lure modes .During i t s response to an ear thquake, a compos i te beamwi l l be requi red to res i s t l arge imposed end moments ,whose d i rect ion wi l l be reversed wi th each osci l l a t ion ofthe s tructure. M oreover, the ex ten t of the negat ive mom entregion near each suppor t wi l l vary cont inuous ly, wi thconsequen t impl icat ions for ro ta t ion duct i li ty supply. He re-af ter, the main parameters affect ing the ro ta t ion capaci tyo f com p o s i t e beam s i n bo t h pos i t i ve and nega t i v e m om en tregions are ident ified. Full interact ion between the steel andconcrete components i s assumed and the cont r ibut ion ofpermanent formwork or sheet ing i s neglected .

Ear ly inves t igat ions ]7 in to the beh aviour of s im ply-sup -por ted compos i te beams indicated that they could bes t rength-sof ten ing , or ' load-shedding ' , in character due tothe presence of excess ive compress ive s t ra ins in the s labconcrete . Fur ther s tudies ind icated that th i s behaviour couldbe cont ro l led by l imi t ing the depth of the p las t i c neut ra lax i s of the compo s i te sect ion so that s tra in hardening occu rsin the t ens ion f lange of the jo i s t p r ior to the a t t a inment ofthe nom inal c rushin g strain in the concrete ~8. Ex perim entaland analy t ical s tudies 7 have been used to der ive des ignexpress ions which ensure that ro ta t ion capaci t i es are suf-

f ic ien t for p las t i c des ign method s , how ever, these capaci t i esmay s t i l l be exceeded in se i smic response s i tuat ions . How-ever, s l ab fa i lure i s no t of ten encountered in pos t -ear th-quake reconnaissance, sugges t ing that o ther factors cont r ib-


7/11

7 2 S e i s m i c r e s p o n s e o f c o m p o s i t e f r a m e s I : B . M . B r o d e r i c k a n d A . S . E l n a s h a i

Table 1 E x p e r i m e n t a l a n d a n a l y t i c a l r o t a t i o n d u c t i l i t ycapacit ies

Te s t El My Ay Mo Au /z,jN m m 2) k N m ) m m ) k N m ) m m )

IC02 -Exp . 2.62 x 1012 61.1 11.2 89.8 66 4.9-An al. 2.85 1012 80.8 13.6 90.4 73.2 4.4

ICA 2-E xp. 2.61 1012 71.1 11.0 90.0 75 5.8-An al. 3.07 1012 81.4 10.7 89.5 73.6 5.9

ICB 2-E xp. 2.93 x 1012 78.4 10.8 118.7 60 5.5-An al. 4.35 x 1012 113.3 10.5 119.3 51.5 4.9

ute to the duct i l i ty supply. P r imary amongs t these i s theeffect ive breath of the s lab which cont r ibutes to the bendingres i s tance of the beam. W hi le des ign code v alues for effec-t ive breadth are based on e las t i c shear l ag theory, exper-imental s tudies have shown that l arger effect ive breadthsmay be assumed at the u l t imate l imi t s ta te . This d i fferencehas impl icat ions for capaci ty des ign , where i t i s requi redthat co lumn y ie ld s t rengths be greater than the u l t imatebeam bending res i s tances .

The behav i ou r o f com pos i t e b eam s under nega t i vemoment i s s imi lar to that of s teel members in that ro ta t ionduct i l i ty i s l imi ted by local ins tab i l i ty in the e lements ofthe s teel sect ion . However, the des ign guidel ines for s teelm em bers canno t be app l i ed d i r ect l y t o com p os i t e beam s asaddi t ional features of thei r respon se m us t a l so b e included 5.Pr incipal amongs t these i s the compress ive ax ia l forceimposed on the s teel sect ion which balances the t ens ion inthe re inforcing bars and var ies accord ing to the momentgradient . Due to the increased bending res i s tance of them em ber, webs i n co m pos i t e beam s a re expos ed t o p ro -

por t ionate ly h igher shear forces than in thei r s teel equiva-len t s . In addi t ion , the presence of a net compress ive ax ia lforce on the s teel jo i s t im pl ies that a greater depth o f theweb wi l l be in compress ion , increas ing i t s suscept ib i l i ty toweb buck l i ng . Th i s p l aces even g rea t e r i m p or t an ce o n t h ein teract ion of the var ious fa i lure mode s which can affectt he m em ber i n nega t i ve m om en t r eg i o n s ; nam el y, l oca lf lange and web buckl ing and la tera l buckl ing of the com-press ion f lange. Exp er imen tal inves t igat ions 19 have shownthat for s tocky sect ions f l ange buckl ing wi l l usual ly preced eweb buckl ing , b u t that s igni f icant loss of res i s tance i s on lyexper ienced af ter the occurrence of web buckl ing .

The s igni f icant d i fferences between the behaviour ofcom pos i t e beam s under pos i t i ve an d nega t i v e m om en trequi res that separate fa i lure cr i t er ia mus t be def ined inei ther case . Whereas the locat ions of the poin t s of con-t raf lexure in co lumns are eas i ly determined f rom the bend-ing moment d i s t r ibu t ion provided by f in i te e lement analy-ses , those occurr ing in beam elements under se i smicloading are l ess wel l def ined . Hence, whi le i t i s poss ib leto cont inuous ly reevaluate the ro ta t ion between poin t s ofres t ra in t and cont raf lexure in co lumn members , a l argenumber of f in i te e lements are requi red to accurate ly per-form the same exerci se for beams. I t i s no t pract ical there-fore to def ine the local fa i lure cr i t er ia for compos i te beamsin terms of ro ta t ion duct i l i t i es . In any case , as observed byK e m p5, compos i te beam yie ld ro ta t ions are of ten associa ted

wi th the occurren ce of y ie ld in the longi tudinal re inforce-ment . D epend ing on the des ign deta i l s of the indiv idualbeam under cons iderat ion , th i s condi t ion may be associa tedwi th a wide ra nge of com press ion s t ra ins in the s teel jo i s t .

Thus , the def in i tion of a unique ro ta t ion duct i li ty capaci tyi s more d i ff i cu lt in the case o f compo s i te beam s than in thecas e o f co l um ns .

The def in i tion of be am fai lure cr it er ia i s therefore res t r ic-t ed t o t he m ax i m um co m pres s i on s t r e s s es wh i ch can occu ri n e lem en t s o f t he m em ber p r i o r t o t he o ccu r rence o f l oca lins tab il i ty. In pos i t ive bend ing , the r i sk of t ens i le fa i lure i sm i n i m a l , hen ce on l y com pres s i on f a i l u re o f t he concre t es lab needs be cons idered . In a s imi lar fash ion , rupture oflongi tudinal re inforcemen t in negat ive mom ent reg ions isunl ikely to occur pr io r to the occurrence of local ins tab i li tyin the s teel jo i s t . Co mp ress ion fa i lure of the concrete s labi s assumed to occur wh eneve r the s t ra in a t the top of theme m ber exceeds 0 .0035. G iven the re la t ive s lab and jo i s td imens ions , the assum pt ion of fu l l in teract ion and the effec-t ive beam widths employed in th i s s tudy, the occurrence ofth i s fa i lure condi t ion i s mos t unl ikely. Composi te beamsare more vulnerable to excess ive compress ion s t ra ins in thes t ee l j o i s t. The m ax i m u m co m pres s i ve s t r e s s wh i ch eachf lange outs tand can suppor t pr ior to local buckl ing can be

d e t e rm i ned f ro m equa t i o n (9 ) . F o r each beam m em ber, t hel ower bound ob t a i n ed f rom t h i s equa t i o n i s em p l oyed asthe fa i lure condi t ion in negat ive bending .

e lec t ion and sca l ing of ear thquake groundmot ions

In dynam ic se i sm ic response analys i s , i f the s i t e of thes t ructure under cons iderat ion i s known, su i tab le ear thquakeground mot ions may be se lected f rom records ref lect ing theambient se i smological and geotechnical condi t ions . Other-wi s e , t he g ro u n d m o t i o n dep enden ce o f i m por t an t r e s pons epa ram et e r s m us t be cons i de red by em p l oy i ng a w i de r r ange

of ear thquake loads , each s caled to a com m on in tens i ty.

Pea k groun d accelera t ion to veloci ty a /v) ra t ioZhu et a l 2 def ine three categor ies of ear thquake groundm ot i ons as : ( a ) no rm al g round m o t i o n s exh i b it i ng s i g -n i f icant energy content over a broad range of f requencies ;(b ) g round m o t i ons p rodu c i ng acce l e rog ram s p o s s es s i ngmany large-ampl i tude, h igh-frequency osci l l a t ions ; and (c)records in which the s igni f icant response i s conta ined in afew long durat ion accelera t ion pulses . I t has been pro-posed 2 that the pea k gro und accelera t ion to pe ak gro undveloci ty ra t io a / v ) i s a s imple , yet meaningfu l means ofident i fy ing the character i s t i cs of ind iv idual accelerograms.

For ins tance, as the veloci ty character i s t i c i s ob ta ined f roman in tegrat ion of the ground accelera t ions , the peak groundveloci ty i s associa ted wi th the moderate to low frequencywav es of the accelerogram, l eading to the long durat ion


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S e i s mic r e s p o n s e o f c o m p o s i t e f r a m e s I : B . M . B ro d e r ic k a n d A . S . E ln a s h a i 7 3

acce l era t ion pu l s es o f t h e t ype ( c ) m o t i o n s p ro d uc i ng l owa/v ra t ios . S imi lar ly, due to the f requency-dependentat tenuat ion of se i smic waves , a t t enuat ion of veloci ty wi thdis tance i s s lowe r than the a t tenuat ion of accelera t ion , caus-ing accelerograms recorded near the ear thquake source topos s es s com para t i ve l y h i gha/v rat ios. In addit ion, the fi l -t er ing effect of the ground medium causes long durat ion

records to be associa ted wi th a h igha/v ra t io whi le s t ruc-tures on rock and f i rm so i l s wi l l exper ience re la t ivelyshor ter durat ion and h igher f requency base exci ta t ion .S awanad et al. 2~ perfo rme d a s ta t is t i cal s tudy on a se lect iono f J apanes e ea r t hqu ake r eco rd s f ro m wh i ch i t was co n -cluded that lowera/v ra t ios wi l l be exhib i ted by ear th-quakes w i t h l ower p red o m i nan t f r equenc i es , b road e rresponse spect ra , longer durat ions and increased magni -tudes , ep icent ra l d i s tances and predominant s i t e per iods .Thes e p a t t e rn s have been con f i rm ed fo r C a l i fo rn i an r ec -ords 2 and co l lect ions o f North Am erican and E uras ianacce l e rog ram s22.23, ind icatin g t hat a ra ng e o fa/v rat ios wil linclude each o f the s igni f icant se i smolog ical features l ikelyto affect s t ructural response.

S igni f icant ly, i t can be expected that ear thquake recordspos s es s i ng h i gha/v ra t ios wi l l be more cr i t i ca l for s t i ffers t ructures , whereas lowa/v records wi l l p lace greaterdemands on more f lex ib le s t ructures . This feature i simpl ic i t ly ref lected by the prescr ip t ion of d i fferen t des ignaccelera t ion spect ra for s t ructures located on var ious so i lt ypes . The Na t i ona l B u il d i ng C o d e o f C anada , however,exp res s es i t s des ign s p ec t r a i n t e rm s o f peak g ro u nd ve l o -ci ty, wi th a correct ion being appl ied in the accelera t ion-depende nt low per iod range ( T < 0 .5 s ) to account for therat io of expected peak ground accelera t ions and veloci t i es .Ground mot ions are c lass i f i ed in the fo l lowing ranges :

low : a/v < 0 .8 g /m s -~ (10a)norm al : 0.8 g /m s -~ ~


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7 0 4 S e i s m i c r e s p o n s e o f c o m p o s i t e f r a m e s I : B . M . B r o d e r i c k a n d A. S. E l n a s h a i

Table 2 G r o u n d m o t i o n r e c o r d s s e l e c t e d f o r d y n a m i c a n a l y s e s

G r o u n d m o t i o n r e c o r d s

R e c o r d l a b e l E a r t h q u a k e e v e n t D i r e c t io n E p i c e n t r a l d i s t a n c e S o i l t y p e M a g n i t u d e M L

F ru i l i F r iu l i E W 5 2 k m R o ck 6 . 46 M a y 1 9 7 6 )

G az l i G az l i E W 1 4 k m In t e rm e d ia t e 7 . 31 7 M ay 1 9 7 6 ) s t i ffn es s

L . P r i e t a E W L o m a P r i e t a S 8 0 W 9 7 k m S o f t 7 .11 7 O c t o b e r 1 9 7 9 )

E l C en t ro Im p er i a l Va l l ey S 0 0 E 8 k m S t i f f 6 . 61 8 M a y 1 9 4 0 )

S p i t a k S p i t a k Tr a n s . 2 7 k m I n t e r m e d i a t e 6 . 81 7 D e c e m b e r 1 9 8 8 ) s t if f n e s s

L . P r i e t a N S L o m a P r i e t a N 1 0 W 9 7 k m S o f t 7 .11 7 O c t o b e r 1 9 7 9 )

Table 3 C o r r e ct e d p r o p e r t ie s o f g r o u n d m o t i o n a c c e l e r o g ra m s

G r o u n d m o t i o n r e c o r d p r o p e r t i e s

R e c o rd P e a k g r o u n d P e a k g r o u n d a/v r a t io P e r io d o f m a x i m u macce l e ra t i o n g ) v e lo c i ty m sec 1 ) g m 1 sec 2 am p l i f i ca t i o n s )

Fru i l i 0 .159 0 .080 1 .99 0 .95G az l i 0 . 7 2 4 0 . 6 0 6 1 . 2 0 0 . 1 3L . P r i e t a E W 0 . 2 1 3 0 . 2 1 6 0 . 9 9 0 . 6 5E l C e n t ro 0 . 3 4 4 0 . 3 6 5 0 . 9 4 0 . 2 6S p i t ak 0 . 1 8 2 0 . 2 3 7 0 . 7 7 0 . 3 6L. P r ie ta NS 0 .250 0 .433 0 .58 1 .20

Table 4 S c a l i n g o f a c c e l e r o g r a m s to d e s i g n p e a k g r o u n d a c c e l e r a t i o n a n d E C 8 d e s i g n s p e c t r u m s p e c t r a l in t e n s i t y

S c a l i n g o f g r o u n d m o t i o n a c c e l e r a t i o n s

Record aglr~o [ a g d e s ig n ) / S I E Q S I E c 8 / S I E Q To ta l s ca l e ag{ . . . . . . . )g ) [ag{r,a)] m) =B) =Ax B) g )

= A )

F u i 0 .15 9 1.56 143.7 1.20 1.89 0.301G az l i 0 . 7 2 4 0 . 3 5 7 1 . 3 2 . 4 2 0 . 8 4 0 . 6 0 8L. P r ie ta EW 0 .213 1 .17 116 .3 1 .48 1 .74 0 .371El Ce n tro 0 .344 0 .73 100 .5 1 .72 1 .25 0 .430Sp i tak 0 .182 1 .37 95 .6 1 .80 2 .47 0 .500L. P r ie ta NS 0 .250 1 .00 192 .3 0 .90 0 .90 0 .225

M ea n , /~ 0 .312 1 .03 119 .9 1 .75 1 .52 0 .406S td . d ev. , ~ 0 . 1 9 4 0 . 4 0 3 9 .1 0 . 3 8 0 . 5 8 0 . 1 2 6COV = ~ / /~ 0 .62 0 .39 0 .33 0 .22 0 .38 0 .31

T h e p s e u d o - s p e c t r a l v e l o c i t y i s o b t a i n e d f r o m a c o m p a r i s o nw i t h r e s p e c t t o p e r i o d o f t h e a c c e l e r a t i o n r e s p o n s e s p e c -t rum, v iz ,

S , ( T , , / 3 ) . T ~S v ( T i , / 3 ) - 2 r r ( 1 2 )

wh ere Sa i s the spec t r a l acce le ra t ion . T hus Sv m ay be con-s i d e r e d t o b e a r e f l e c t i o n o f t h e a c c e l e r a t io n r e s p o n s e s p e c -t r u m a n d t h e s p e c t r u m i n t e n s i t y, S I , c o n s i d e r e d t o b e t h ea r e a u n d e r t h e p s u e d o - s p e c t r a l v e l o c i t y c h a r a c t e r i s t i c

b e t w e e n t h e l i m i t s i n d i c a te d . T h e e f f e c t o f s c a li n g t o e q u a lspec t r um in tens i t i te s i s to ensure tha t ea r thq uake r ecordsp o s s e s s e q u a l e n e rg y c o n t e n t s b e t w e e n t h e p e r i o d s 0 .1 a n d2 .5 s . I t ha s been dem ons t ra ted 26 tha t such a p roced ure s ig -

n i f ican t ly r educes r e sponse spec t r a l d i spe r s ion in the r ange0 . 5 - 3 . 0 s, p r o d u c i n g a m o r e c o n s i s t e n t l e v e l o f d i s p la c e -m e n t d u c t i l i t y d e m a n d .

A s t h e c o m p o s i t e f r a m e s b e i n g i n v e s t i g a t e d h e r e g e n e r -a l ly possess na tura l pe r io ds in the r ange 0 .7 -1 .2 s , basee x c i t a t i o n s c a l i n g t o a p e a k g r o u n d v e l o c i t y w o u l d b e m o s tappro pr ia te to ensure equa l load ing in tens i t ie s . Ho wev er,E u r o c o d e 8 d o e s n o t m a k e a n y a l l o w a n c e f o r s u c h a p r o -cedure , ins tead r equ i r ing tha t se i smic load ing be un ique lyde f ined in te rms o f a peak g rou nd acce le ra t ion . As a l l r ec -o r d s p o s s e s s a u n i c u ea v r a t io , s c a l i n g t h e g r o u n d m o t i o n s

t o a c o m m o n v e l o c i t y w i l l d e s t r o y t h e e q u i v a l e n c e b e t w e e nt h e r e c o r d s a n d t h e d e s i g n s p e c t r a . To o v e r c o m e t h i s d i f -f icu l ty, use i s mad e of the spec t rum in tens i ty. Inspec t ion ofe q u a t i o n s 11 ) a n d 1 2 ) i n d i c a te s t h e d e p e n d e n c e o f t h i s


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Seismic response of composite fra mes I: B. M. Broderick and A. S. Elnashai 7 5

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Seismic Response of Composite Frames I

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