recommendations for the design and detailing fo ductile prestressed concrete frames for seismic...

7/27/2019 Recommendations for the Design and Detailing Fo Ductile Prestressed Concrete Frames for Seismic Loading

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8 9R E C O M M E N D A T I O N S F O R T H E D E S I G N A N D D E T A I L I N G O F

D U C T I L E P R E S T R E S S E D C O N C R E T E F R A M E S F O R S E I S M I C L O A D I N GP r e p a r e d by

T H E S E I S M I C C O M M I T T E E O F T H E N . Z . P R E S T R E S S E D C O N C R E T E I N S T I T U T E

M e m b e r sG . K . T o m ! i n s o nD r . R . A H . D o n a i dL G . C o r m a c k ( C o n v e n o r )

T E X T1.0 SCOPE

This document include s recent rese archinformation and suggests minimum requirementsfor the desig n of prestre ssed and parti allyprest resse d concrete frames to resist seismicforces . They are based on ACI 318 -7 1 3 w h e r eappr opri ate and shall be read in conjunct ionwith NZS 4 203^, and are supplementary toN2S R 32^-. The recomme ndat ions are not to beread as a code of practice.

2.0 GE NERAL REQUIRE MENTSThe philosophy of design shall be asrequir ed by NZS 4203^ which is summarised asfollows:A prestressed concrete ductile momentresist ing frame of more than two storeys shall

be capa ble of dissipa ting seismic energy ina flexural mode by the formation of plastichinge s in beams of adequat e ducti lity. Forframes of mor e than two storeys the f lexuralstrength of columns shall be such thatmechanis ms of collapse involving plastichinge s forming simultan eously at the upperand lower regions of the columns of one storeycannot occur. All forms of britt le failureshall be prevented. Consideration shall begiven to the probab le increa se of mate rialstrengths to above their design values.

C o r r e s p o n d i n g M e m b e r sP r o f e s s o r R . Pa rkR P a t t o n

C O M M E N T A R Y C L A U S E SCI.0 NZSR 3 2 1 conta ins no provis ions forthe seismic design of prestr essed concr etestruc tures . These recomm endati ons for thedetailing of ducti le prestressed andpartially prestressed concrete frames forseismic loading are intended to supplementNZSR 32. The recomm endat ions are based onrecent research evidence and tend to followAmerica n practice used for reinforc ed concrete where appropriat e. The design principlesand loadings of NZS 4 2 03 2 should also becomplied with.C2.0 The object is to design structu rescapable of behaving in a ductil e mann er wh enresponding to a major eart hquak e. Ducti lebehavi our is best obtained by ensuring thatthe beams reach flexural capacity beforealterna tive mere britt le failure states arereached, and that the beam plastic hingesare capabl e of under going significan tinelastic rotation under cyclic loadingwithout appreciable reduction in flexuralstrengt h. In gene ral, column sideswaymechanisms involving plastic hinges in thecolumns of one storey only are undesirablebecau se of the high ductilit y demand on theplastic hinges in the colum ns. Hence theflexural strength of columns should besuch that mech anis ms of collaps e involvingplasti c hinges existi ng simultaneou sly inthe upper and lower regions of the columnsof one storey cannot occur. For one andtwo storey frames the ductil ity demand onthe column hinges may be not so high andcolumn sidesway mechanisms may be permittedfor such frames if it can be shown that theductil ity demand can be met. It must alsobe ensured that all brittle forms of failure,such as due to shear, are preven ted. Thestrength of mat eria ls in member s wi llgeneral ly be higher than the value s specifie din desi gn and wil l resu lt in the actua lstrengths of the membe rs being great er thancalculated, using the specified materialstrengths. This enhanced member capacity,if unaccou nted for, may have the effect ofinducing alternative undes irable modes offailu re. For exampl e, enhanced beamflexural str ength may result in a failurein shear rather than yielding in flexure.A capacit y design approac h should be adoptedwhereby the probable overstrength of materi alsat plastic hinge zones is taken into accountin determin ing leve ls of strength requiredto avoid britt le failure states . For pre -stressing steel the actual stress -strai ncurves for the prestr essing steel shouldbe used in the flexur al strength comp utat ions .Note that the pres tres s losses caused by

B U L L E T I N O F T H E N E W Z E A L A N D N A T I O N A L S O C I E T Y FO R E A R T H Q U A K E E N G I N E E R I N G , V O L . 9 N 0 . 2 . J U N E 1 9 76


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90friction, etc. do not need to be consideredfor the ultimate load case as they willhave negligible effect. The major d i f f e r e n c ebetween the nonlinear response of p r e s t r e s s e dconcrete structures and reinforced concretestructures to seismic ground motions isthat the narrower load-deflection hystere sisloops of prestr essed concrete mean thatless energy is dissipated than for reinforcedconcrete when responding to inelastic loadingcycles. Because of this, a greater lateraldisplacement response may be expected fora prestr essed concr ete structure than for areinforced concrete structure of the samestrength when subjected to severe earthquakemotions^ . This factor is recognised inNZS 4203 2 which requires a 20% greatermaterials factor for prestressed concretethan for reinforced concrete, resulting ina 20% greater design horizontal seismicforce for a prestressed concrete frame thanfor an equivalent reinforced concrete frame.Even with this greate r mate rial s factorhowever, resulting in higher member strengthsthan for an equivalent reinforced concre teframe, there is no guarantee that largerlateral displacements will not occur in aprestressed concrete frame and the importance of this with respect to possible damageto nonst ruct ural elements should be considered by the designer. An alternative tofully prestressed members is to usepartially prestressed members, the non-prestressed steel in the plastic hingezones helping to dissipate energy and toprovide additional compressive resistanceduring major seismic ground motions. Theappropriate materials factor for such a"mixed" structure will need attention bythe designer. In general it appearsreasonable to adopt an intermediate figuredepending on the relative amount of prestressed or non-prestressed steel in the plastichinge zones.

3.0 MATERIALSW i r e s and strands for tendons inprest ressed con crete shall conform with theprovisions of NZS 1417 or BS 3617 respectively or shall be of equivalent quality.The specified concrete compressivecylinder strength shall not exceed 55 MPa(8000 psi) unless special transversereinforcement is provided.

4.0 DESIGN OF FLEXURAL MEMBERS4. 1 The content of flexura l steel (prestressed plus nonprestress ed) shall be such thata/h is not greater than 0.2 at the flexuralstrength of sections in the plastic hingezones, where 'a 1 is the depth of theequivalent rectangular concrete compressivestress block at the flexural strength and1 h 1 is the overall depth of the m e m b e r .4. 2 The flexural strength of the sectionshall be greater than the cracking moment

C3.0 It is of particular importance thatthe prestr essin g steel complies with thespecified requirements for p e r c e n t a g eelongation at rupture to ensure that it isadequately ductile. The actual stress-strain curve of the prestressing steel shouldbe available for flexural strength calculations . It is desirable that the concretestrength does not exceed 55 MPa (8000 psi)to ensure that the concrete is not overlybrittle. This is becaus e tests indica tethat the higher the concrete strength thesteeper the falling branch of the concretestress-strain curve and the smaller theextreme fibre concrete compressiv e st rainwhen the member reaches ultimate momentcapacity- This however is not the caseif special transverse reinforcement isprovided to confine the concrete, in w h i c hcase this upper limit of compressivestrength may be waived.C4.1 The object is to ensure ductilebehaviour in plastic hinge zones. Therequirement comes from an examination oftheoretical moment-curva ture curves^, andfrom a comparison of provisions for reinforced concrete. For rectangular sectionswith the prestressing steel concentratednear the extreme tension fibre it wasobserved previously^ that the normal ACI318-71 3 and MZR 32 :196s 1 requirement forpreventing over-reinforced members , namely


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91whe n allowa nce is mad e for likely vari ationsin prestr ess and the streng th of mat eri als .In the absence of special studies, it maybe assumed that the max imu m concrete tensil estress prior to cracking is 1.0/fMPa providedallow ance is mad e for a vari atio n of 1 0 % inthe calculated level of prestress at thesection under consideration.4.3 The maxim um desig n shear force shallnot be less than:

A f*D S

was inadeq uate for prestre ssed membe rs inseismic resistant structures where theductility demands could be more significant .It is considered that for seismic designfor prest ressi ng steel concen trated n earthe extreme tension fibre the requirementshould beM + M _ .

v u = - u A _ u B + vd g ... (1) A fp S _ P j Sbd f' 0.2

where and M u B are the ultimate momentcapacities of opposite sense at the ends ofthe beam taking into account the probableoverstrength of mat eria ls, 1 is the clearspa n of the bea m, and v^g is the sheardue to the design gravity loads acting onthe beam treated as a simply supportedspan. In plastic hinge zones, web reinforcement shall be provided to carry all thedesign shear force and should take the formof closed stirrups of size not less than10mm (3/8 in) in dia met er place d at spacingnot exceedi ng 100 mm (4 in) or d/ 4, whered is the effective depth of the member whichfor prestressed concrete need not be taken asless than 0.8 of the over all depth. Inplastic hinge zones the transverse steel shallalso be capable of providing adequate confinement to the conc rete . Else wher e in themem ber the spacing of web reinfo rceme ntshall not exceed d/2 . Long itud inal steelshal l be pre sen t at eac h co rne r of the-stirrups .4.4 The spacing of closed stirrups surround ing nonprestressed compression bars inplastic hinge zones shall not exceed 6comp ressi on steel bar dia met ers , 100mm (4 in)or d/ 4, whic heve r is leas t. The stirrupsshall be so arrang ed that every compre ssionbar shall have lateral support at notgreater than the above spacing providedeither by the corner of a stirrup havingan included angle of not more than 135 orby the equivalent welded steel arrangement.This does not apply to second (i.e. internal)layers of bars.

i.e. A f < 0.2f'bd.ps ps cThis means that the maximum possible tensileforce in the tendons at the flexuralstrength is 0.2f^bd and hence that the maximum possible depth of the rectangularstress block is0.2f M D d0.85f'bc

= 0.235d

But since d is approxim ately 0.8h therequirement may be written asa < 0.2h

For sectio ns with tendons at variou sposi tion s down the depth of the memb er itis difficult to set a limiting value for/ * p Sf p s/bdf^ because tendons at variouslevels result in sections with differentmome nt-c urv atur e chara cteris tics from the.case when all the tendons are placed nearthe extre me tension fibre. Rather thanstipulating different limiting A p s f p s / b d f ^values for vario us steel arrangem entsit is mor e conven ient to require thata/h < 0.2 for all secti ons. This ac hiev esthe same end result since the ultimatecurvature will always be at least equal tothat of the section with all tendons placednear the extreme tension fibre. Neve rthe less tendons should not be conce ntrat edonly in the mid- dept h of the beam sect ion.Ideally tendons or nonprestressed reinfo rcement should also exist at the top and bottomof the section if centrally placed tendonsare used. Secti ons with great er a/h ratiosmay need mor e confinin g steel tha n spec ifiedin Section 4.3 to reach the required ultimatecurvatur e. Equations relating content ofconfining steel to maximum concrete c ompre ssion strain are available elsewhere^.

It has not been made mandatory to havenonprestressed longitudinal bars present atthe plastic hinge sections because the webreinforceme nt which additionally providessome degree of concrete confinement, andthe small depth of compressed concrete,should result in ductile behaviour, evenat high concrete strains. Nonprest ressedsteel will improve the compression zonebehaviour and allow greater energy dissipation but such steel is only effec tive ifthe bond throughout the beam-colum n jointcore does not deteriorate and allow thebars to slip throu gh the joint cor e. Thetotal beam bar force to be transferred tothe joint core by bond when lateral loadingis applied to the frame is approximatelytwice the yield force of the bar and theresul ting bond stresse s can be very hi gh.


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If slip of steel occurs through the corethere will be a loss of compression steelbecause the bars will actually be in tensionin the compression zone and lead to areduction in the available curvature ductility. This points to the need for rel atively deep memb ers and/or relat ively smalldiameter longitudinal bars. For examplein the Canterbury tests 7 on beam-columnassemblies involving partially prestressedbea ms fram ing into a 406 mm (16 in) d eepcolumn, 2 8.6 mm dia mete r (1 1/8 in ) de for mednonpre stress ed mild steel beam bars eventu allyslipped through the joint core after severalcycles of loading where as 19.1 mm diam ete r(\ in) defo rmed mil d steel beam ba rs d idnot. Note that at sections subjected tomoment reversals prestressing tendons willexist at the top and bottom of the memberand these will act as compression steel inthe event of very large curvatu res bein genforced after crushing of the concreteduring catastro phic load ing.C4.2 The section should crack bef ore theflexural strength is reached, otherwi se abrittle failure may result. Allow ance hasbeen made for the case of a high mod ulu sof rupt ure (for exam ple 0.83/fc MPa orhigh er is occasion ally measured in tes ts)and the case of concrete cylinder strengthbeing greater than specified.C4.3 Shear failure caused by cyclic loa dsare generally non-ductile and mus t thereforebe avoided by a capacity desi gn ap pro ach .The design shear force is calc ulate d u singthe design gravity loads and the beam plastichinge mome nts. To ensure that the greatestprobable shear force is calculated, the beamplastic hinge capacities used are thosecomputed assuming a capacity redu ctio nfactor 0 of 1.0 and including an allowancefor probable overstrength mat eria ls. Forexample, in the Canterbury tests 7 themaximum moment capacities measured in p r e stressed concrete beams at the column faceswere up to 16% greater than the t heo reti calvalues calculated using 0 = 1 a nd t h emeasured concrete cylinder strength andthe measured steel stress-strain charac teristics. This strength increase was due tomaximum moment occurring at an extremefibre concrete strain of greater than 0.003and due to the extra confinement given tothe beam concrete by the proximity of thecolu mn. It should be noted that str engt hincrease may also result from the contribution of the floor slab and Fauschingereffect s in the nonpre stress ed steel. Acapacity reduction factor of 0 = 0.85 sh ouldbe used when calculating the capacity ofthe shear reinforcement. The stirrup spacingspecifie d in plastic hinge zo nes is suchthat the stirrups are close enough to actas confining steel for the concrete as wellas shear reinforcement . In plastic hing ezones the stirrups are to be closed and, toconfine the concrete effectively acrossthe width of the secti on, the max imu m u nsup ported width of stirrup measured betw eenperpendicular legs of the stirrup or supplement ary crossti es should be limit ed. 150mmbetween longitudinal bars supported by thecorners of ties is acceptab le. Concre tecover to the stirrups should be as smallas possible so as to avoid a large loss ofmom ent capacity if the cover concr ete isshed at high strain levels during seismicresp onse . Reversed loading effe cts are


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93included by ignoring the shear carried bythe concrete shear resisting mechanism inplastic hinge zones. For the purpo ses ofSections 4.3 and 4.4 plastic hinge zonesmay be regarded as the end regions of thebeam extending over a dista nce of at leasttwic e the memb er dept h from the face of thecolumns, and where ver else in the membe rultima te moment capacity may be dev elope dduring inelastic lateral disp lacem ent ofthe frame.C4.4 The stirrups spacing should be closeenough to restrain buckling of co mpress ionsteel.

5.0 DESI GN OF COLU MNS5.1 The flexural strength of a column sectionshall be greate r than the maximum likelycracking moment as calculated in section 4.2except that the effect of axial load shallbe allowed for.5.2 Tran svers e reinf orcem ent in columns shallbe provi ded to ensure that the shear capacityof the mem ber is at least equ al to the shearforces applied at the formation of plastichinges in the struc ture, due to the combi nation of design lateral and gravity loadings,taking into account the probab le o verstren gthof the mat eri als . In the case of spaceframes, for the calculation of shear forces,the simultaneous development of plastichinges in the beams in both principal direct ionsof the frame due to earthquake loading actingin a gener al direction shall be considered.The transverse reinforcement for shear shallbe detailed as fcr flexural members and endregions of columns shall be regarded asplastic hinge zones when detailing shearreinforceme nt. For calculation of maximumdesign shear force refer to 4.3.5.3 The spacin g of hoo ps in the end regio nsof columns when nonprestressed longitudinalbars are present shall not exceed six longitudina l bar diamet ers, 100mm (4 in) or d/4,whic heve r is least. The hoops shall bearrang ed so that every compression bar shallhave latera l support provide d either by thecorner of a hoop having an included angleof not more than 135 or by the equival entwelded steel arrangements.5.4 Special trans verse reinfor cement shallbe provided in the end regions of columns ifthe desig n load on the column exceeds 0.1 P Cor if a/h is gre ate r than 0.2 at the f lexu ralstreng th or if column sidesway me chani smsare perm itte d in one or two storey frames,where P Q is the axial load strength of thecolumn without fle xure making allow ance forthe effect of prestress, 1 a' is the depthof the equi vale nt recta ngular concre te compressive stress block at the flexuralstrength and 1 h' is the overall depth of them e m b e r .

Where a spiral (circular) is used asspecial transverse reinforcement, the ratioof the vol ume of spiral reinforce ment tovolum e of conc rete core (measured to outsid eof spirals) shall not be less than

C5. 1 The inte ntio n is the same as thatstated in C4.2 for flexural mem ber s. Theeffect of axial load on the cracking momentis to be inclu ded.C5.2 The design shear force is calculatedusing a capacity design approa ch to determ inethe maximu m probable shear force using acapacity reduction factor 0 = 1 f or t h ememb er strengths and making al lowan ce foroverstrength materials, The column shearforc e is equa] to the sum. of th e col umnmoments at the top and bottom of the columndivided by the column heigh t. The maxi mumprobable shear force in the column will bewhen the top and bottom column moments area maximu m. In the limit this would be whenthe maximum probable ultimate moment capacities develop top and botto m in the colum n.Howev er, generally a beam sidesway m echan ismoccurs and the top and bottom column momentsto be used are the maximu m pro babl e m omen tsthere when plastic hinges form in the beams.Shear reinforceme nt is provi ded as forbeam s. For space frames the resu ltan tdesign shear force on the columns shouldbe calculated for the genera l case ofseismic loading acting simultane ously inthe directions of both princi pal ax es ofthe frame. For that loading case, thecolumn should be capable of carrying theresulta nt design shear force. For thepur pos es of Sect ions 5. 2, 5.3 and 5.4, theend regions of columns shall be regard edas the regions of the columns above andbelow beam-column connections over aminimum length from the faces of the connectio n at least equal to the grea test columncross sectional dimension, 4 50mm (18 in)and one-sixth of the clear height of thecolumn.C5.3 Buckling of non-prestress ed columnbars is to be r estrai ned.

2 in longitu dinal steel cont ent.-71** has been taken as a gui de for

P s = 0.45A c

. (2)

C5.4 The ductility of column s reduceswit h increase in axial load level and withincreaseACI 318-the axial load level above whi ch specialtrans verse steel is require d, a columnload of 0.1P Q being an appr oxim atio n forthe 0.4Pb specified in ACI 318 -71 . Forcolum ns with steel whic h does not have adefin ite yield point, or with s teel aro undthe perim eter of the section, the def init ionof P b loses its mean ing and the spec ific atio nof column load in terms of P Q is preferable.The a/h limit specified for beam s in Sectio n4.1 is also used as a limit for columnsbecause deeper compressive stress blocksthan 0.2h may require special tra nsve rsesteel to adequately confine the c oncret e.The amount of special transverse steel is


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9 4but not less than 0.12f 0.2require special transverse steel to increasethe available curvature ductility in theend regions in case plastic hinges formthere due to circumstances unforeseen bythe designer. For examp le, in flexiblestructures points of contraflexure incolumn s can mov e wel l away from the mid-height region and may result in plastichinges forming at one end of the columns.

whe re 1^ is the maxim um unsuppor ted lengthof rectangular hoop measured between perpendicular legs of the hoop or supplementarycrossties, s^ is the hoop spacing, and p sis giv en by Eq. (2) with t he area ofrectangular core of column to outside thehoops sub stitut ed for A c and hoop yieldstrength substitut ed for fy. The mini mumsize of such reinforcement shall be 10mmdiameter (3/8 in) and the centre to centrespacing shall not exceed 10 0mm (4 i n ) .

Special transverse reinforcement mayalso be considered to act as shear reinforcement. Longitudinal steel shall bepresent around the perimeter of spirals andin the corners of rectangular hoops.6.0 DESIGN OF BEAM-COLUMN CONNECTIONS6.1 Anch ora ges for post- tensi oned tendon sshall not be placed within beam-column jointcore s.6.2 Tran sver se reinfo rcemen t around thelongitudinal column bars shall be providedthroug h the joint core for shear. The designshear force Vj shall be the maximum, horiz ontalshear force in the joint core determined fromthe column shear and the shear developed fromthe steel and concrete forces in the beams atthe formation of plastic hinges due to thecombination of design lateral and gravityloadings, taking intc account the probableoverstren gth cf the mater ials. In the jointcore of a pla ne frame , the area of shearreinforcement per layer shall not be lessthan

where V s is the design shear force to becarried by the shear reinforcement in thejoint core (equal to Vj if no allow ance ismade for the shear carried by the concreteshear resisting mechanism), f is the yieldstrength of the shear reinforcement, n isthe number cf layers cf shear reinforcementbars effectively crossing the corner tocorner crack of the joint core, and 0 is thecapacity reduction factor for shear equal to0.85. For space frames allo wanc e shall bemade for the resultant shear force acting onthe joint core due to earthquake loadingacting simulta neously in the directions ofbot h pri nci pal axes of the frame . For thisloading case the shear force to be carriedby the shear reinforcement shall not exceedthe total component of force in the shearreinfor cement acting in the direction ofthe resultant shear force crossing the planeof the corner to corner diagonal tensioncrack. At least three prestressing tendon s

C6.1 Ancho rages are kep t out of beam-column joint ceres in order to avoid tensilebursti ng stresses in a region alreadysubjected to severe diagonal tension frombeam and column for ces . At exte rior jointsanchorages can be placed in stubs outsidethe joint core region.C6.2 The design shear force to be carriedby the shear reinforcement in the jointcore is V s = Vj - V c , where Vj is themaximum horizontal shear force acting acrossthe joint core and V c is the shear carriedby the concrete shear resisting mecha nism s.The Canterbury tests' have shown that,although in the first cycle of loading inthe inelastic ran ge, the joint cor e concr eteshear resisting mechanism can carry considerable shear forc e, furthe r inelastic l oading cycles can result in a degradation ofthe concrete shear resisting mechanism dueto a break down of the joint core co ncret ecaused by alter natin g bond forces anddiagonal tension cracking. The presenceof a centr al pres tres sing tendo n in thebeam was shown in those tests to be effective in helping to preve nt joint core shearfailure, because of the better control ofdiagonal tension crack s. Never theles s thepresence of a central tendon did not preventdegra datio n in the shear carried by theconcrete in all joints tests^. It may bepossi ble to mak e some allo wanc e for theshear carried by the concrete in caseswher e the joint core is wel l confi ned by ahigh axial compressive column load, or byhigh beam prestress and some central tendonsor by longitudinal column steel placedaround the perimeter of the column section,or by the presence of beams entering allfour sides of the colu mn. Ho we ver , a conservative approach to joint core shear designshould be adopted and generally V c shouldbe assumed to be zero unless there isevidence to show that some shear can becarried by the concrete shear resistingmechanis m during seismic type loading. The


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95should normally be present of which one islocated in the mid-d epth re gion of bea ms.It is desir able that longi tudi nal co lumnsteel be present around the perimeter ofcolumn section s. No allowa nce shall be madefor shear carried by the concrete shearresisting mechanisms unless further researchshows that the concrete shear re sistingmechanism can be adequately maintained duringseismic load reversals.6.3 The transverse reinforcement providedthroug h the joint core shall be not less thanthat specified in Section 5.4 regardless ofthe column load.6.4 Conn ectio ns betwe en precas t memb ers atbeam- colum n joints shall be accepta bleprovid ed that the jointing mate rial (mortar,epoxy, or cast-in-place concrete) hassufficien t strengt h to withst and the compres sive and transv erse forces to whi ch itmay be subjec ted. The interf aces shall beroughened to ensure good shear transfer andthe retention of the jointing material aftercracking.6.5 It is des ira ble that duct s for pos t-tensione d grouted tendons through beam -colu mnjoints should be corrugated.

detail s of some beam- colum n joint desi gnswhere V c was maintaine d during test loadingmay be seen elsewhere"?.The shear reinfo rcemen t is place d tocarry V s across the corner to corner crackof the joint core, tests having shown that

this is the critical failure crack 7 . Onlythe shear reinforcement within the top andbottom beam steel should be taken as beingeffe ctiv e; that is, V s is not to exceed thetotal force in the shear r einf orce mentbetween the top and bottom beam bars multiplied by the capacity reducti on factor .Strain readings taken on hoops in jointc o r e s 7 have indicated that the hoops inthe central region of the core are moreeffec tive than the hoops near the top andbotto m of the core. Thus the top and bottomhoops could be disreg arded an d the hoopsconcentrated more in the central region ofthe core. In cases wher e there is not aprestressing tendon in the mid-d epth regionof the beam, the area of shear reinf orcem entgiven by Eq, 4 may be inadeq uate , even wh enthe shear carried by the concrete is ignored,and some increase in shear reinforcement maybe neces sary. Ideally, for rever sed beamflexure and joint core shear, the tendonsshould be distribu ted down the beam sectionand not all placed at the section extre mitie sor all at mid-depth. Longitu dinal columnbars around the perime ter of the column arealso helpfu l in contro lling diago nal tensioncracks in the joint core . Henc e a numberof smaller diameter bars around the columnperim eter is prefer able to bars placed justat the corn ers of the sec tio n. Eq. 4 isnot applicable when the joint core is subjected to biaxial shear forc es due to earthquake loading acting simultaneously alongboth axes of a space frame . For that l oading case the joint core should be capableof carrying the resultant shear forc e dueto the biaxial shear forces induced whenplasti c hinges form in the beam s in bothprin cipa l directi ons of the fram e simu ltaneou sly due to earthq uake load ing ac tingin a general direc tion.C6.3 The minimum transverse reinforce mentconte nt permitted in the joint core is basedon the requir ements of ACI 31 8-71 ^,C6.4 Altho ugh only limited testi ng hasbeen performed** it is considered that precast joints at the faces of columns canfunction effectively with no other connectionthrough the jointing material other thangrouted tendons. Some form of mecha nica linter lock is desir able to hold the j ointingmateri al in place. Where possib le it ispref erab le to locate the joint ing facesaway from plastic hinge zones by use ofcruciform columns.C6.5 Corrugated ducts enable bette r bondbetwe en grout and concre te whi ch is desir able in regions of high bond stresses.

* * * * * * * * * * *R E F E R E N C E S1. "Prestressed Concrete" , NZSR 32:1968, 4.Standards Associati on of New Zealand.2. "General Structural Design and DesignLoadi ngs", NZS 4203:19 75, StandardsAssoc iation of New Zealand.3. "Buil ding Code Requ irem ents for Rein - 5.

forced Concret e (ACI 3 1 8 - 7 1 ) " , A m e r i c a nConcrete Institute.Blakeley, R.W.G. and Park, R. , "Responseof Prestressed Concrete Structur es toEarthquake Motions", New Zealand Enginee ring, Vol. 28, No. 2, February, 1973,pp. 42-54.Park , R. and Paulay, T., "Rei nfor ced


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Concrete Structures", John Wiley, NewYork, 1975, 769p.6. Blakeley , R.W.G. and Park, R., "Ductili tyof Prestressed Concrete Members", Bulletinof the New Zealand Society for Earth quakeEngineering, Vol. 4 , No. 1, March, 1971,pp. 145-170.7. Park , R. and Thom pson , K. J., "Prog ressReport on Cyclic Load Tests on Pre stresse dand Reinforced Concrete Interior Beam-Column Assemblies", Bulletin of the NewZealand Society for Eart hqua ke Engi neeri ng,Vol. 8, No. 1, Marc h, 1 975.8. Blakel ey, R.W.G. and Park, R., "SeismicResist ance of Prestr essed Concret e Beam-Column Assemblies", Journal of AmericanConcre te Instit ute, Vo l. 68, No. 9,September 1971, pp. 677-69 2.

V. = maximu m hori zont al shear force in-1 joint core determ ined from co lumnshear force and shear force developedfrom steel and concrete forces inbeams at formation of plastic hingesdue to combina tion of lateral loading and design gravity loading

V g = design shear force to be carriedby shear reinfo rceme nt in jointcoreV u = maxim um design shear f orce0 = capacity reductio n fact orP s = ratio of volume of spiral rein forc ement to volum e of conc rete coremeasured to outside of spirals.

N O T A T I O Na = depth of equival ent rectan gularconcre te compressiv e stress block atflexural stengthA c = area of concrete core measured tooutsi de of transve rse steelA = gross area of concr ete sectionA s h = a r e a f transverse hoop bar, one legA - area of prest ressin g steel in tensionzoneA v = area of transvers e shear re infor cemen tper layerb = widt h of sectiond = depth from extreme compres sion fibreto centro id of flexural ste el, butneed not be taken as less than 0.8hf^ = 28 day specified concrete compres sivecylinder strengthf = stress in prest ressi ng steel at design

p s loadfy = yield strength of trans verse steelh = overa ll depth of memb er1 = clea r span of beaml h = maximum, unsupp orted length of rectangula r hoop side meas ured betwe enperpendicular legs of the hoop or

supplementary crosstiesM u A ~ P r o b a t ) l e ultimate positive momentcapacity at one end of beamM u B ~ P r k a k l e ultimate negative momentcapaci ty at other end of beamn = numbe r of layers of shear rein force mentP^ axial load capacity of column atsimultaneous attainment of assumedultima te strain of concrete andyiel ding of tensi on steelP Q = axial load capacity of column withoutflexures

h= c e n t r e to centre spac ing of hoopsV c = shear force carried by concrete shearresisting mechanism

V, = shear force due to design grav ityloads actin g on beam t reated as asimply supported span

recommendations for the design and detailing fo ductile prestressed concrete frames for seismic...

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