STUDY ON PERFORMNCE ND PRCTICL USE OF NEW UILDING STRUCTURL SYSTEM WITH STEEL PLTES ND CONCRETE (PLRC TECHNIUE): THE STRENGTH EVLUTION METHOD OF LONGITUDINL SLIP OF THE COLUMN 669 Tomoki FURUT 1, Tomohiko KMIMUR 2 nd Yoshiaki NKNO 3 SUMMRY W prsntd a nw structural systm - th Plat Rinforcd Concrt (PLRC) tchniqu, which is basd on th us of prcasting mmbrs that mploy stl plats instad of rinforcing bars usd in convntional rinforcd concrt structural mmbrs. Howvr, PLRC column mmbrs hav bn confirmd through invrs symmtry loading tsts of dvloping a rapid drop in strngth causd by longitudinal slip failur - a phnomnon accompanid by longitudinal cracking in th axial dirction of th mmbr at th intrnal cornrs of th cross-shapd column sction, unlss a rinforcing plat (ti-plat) is installd at th cntral ara of th mmbr. This papr proposs a mthod for valuating th longitudinal slip strngth basd on th failur mchanism discussd hrin. It was confirmd that th longitudinal slip strngth could b stimatd by using th calculation formula basd on th assumption that longitudinal slip failur occurs whn th strss working at th intrnal cornrs of th sction obtaind by th Fibr Modl bcoms qual to th shar rsistanc of th concrt at that spcific ara. INTRODUCTION Th PLRC tchniqu aims at nhancing productivity of building matrials for prmannt houss through th industrializd prcasting production of PLRC mmbrs - simpl structural mmbrs consisting of concrt and stl plats -, and offring both spatial flxibility and rigidity, by utilizing th sctional configuration and purly rigid structur of th columns and bams. s may b sn from Fig. 1, th column and bam sctions of th PLRC tchniqu us plats in plac of th main and shar rinforcmnts mployd in rinforcd concrt structurs. Th column sction is a cross-shapd sction whos width is qual to that of th bam. Rpatd loading tsts of column mmbrs conductd until now by th cantilvr bam-loading systm had rvald th proprtis of ach spcimn to b satisfactory [Oya and Furuta, 1992]. Hnc, with a viw toward bringing th stat of strsss in th column mmbrs closr to that, which would b causd by actual sismic loads on th fram, th invrs symmtry loading systm was adoptd to confirm th structural prformanc. Plat Concrt Plat Concrt Spiral Rinforcmnt Spiral Rinforcmnt (a) Column (b) am Fig. 1: Sction of column and bam It was found that unlss rinforcing plats (ti-plats) wr installd to th cntral ara of th column, longitudinal cracking would occur in th axial dirction of th mmbr at th intrnal cornrs of th cross-shapd 1 2 3 Dpt. of rchitctur, kashi National Collg of Tchnology, Hyogo, Japan Email: furuta@akashi.ac.jp Dpt. of rchitctur, Shibaura Institut of Tchnology, Tokyo, Japan Email: kamimura@sic.shibaura-it.ac.jp Inst. of Industrial Scinc, Univrsity of Tokyo, Tokyo, Japan Email: iisnak@cc.iis.u-tokyo.ac.jp
sction. Notably, in th spcimns with larg shar span ratios (M/D=1.75:), th column mmbrs wr found to split longitudinally into thr pics along th longitudinal cracks following th occurrnc of longitudinal cracking, vntually lading to brittl failur. To grasp th strss that would work on a ti-plat, which is xpctd to b capabl of prvnting longitudinal failur of th PLRC column mmbrs, this papr will xamin th mthod for calculating th longitudinal slip strngth, basd on th longitudinal slip gnrating mchanism discussd hrin. Th mchanism was studid using, as th objcts of study, th spcimns that had undrgon longitudinal slip failur. GENERTION OF LONGITUDINL SLIP FILURE Column spcimns that had vntually rsultd in longitudinal slip failur (Tabl 1) consistd of four mmbrs with shar span ratios (M/D) ranging btwn.5 and 1.75, for which, no ti-plats wr installd. For rprsntativ spcimns (, ), Fig. 2 shows th stat in which longitudinal slip failur had occurrd. In all spcimns, flxural cracks occurrd first in th column had and bas aras at thir boundary with th loading stubs. Thn, diagonal cracks dvlopd, running from th nighborhood of th cntr of th plat locatd on th outr sid of th sction toward th column cntr. Latr, th dirction of th diagonal cracks changd into th axial dirction of th column mmbr at th intrnal cornrs of th cross-shapd sction. Maximum strngth was rachd at th point whr longitudinal cracking bcam significant. For th spcimn with a larg shar span ratio (M/D), it was confirmd that, at th point longitudinal cracking bcam significant, th dgs of th plat locatd on th outr sid of th sction yildd in tnsion at th column capital and bas, and th comprssion-sid concrt crushd. y contrast, for C5S, and C1S spcimns with a small M/D, no yilding of plat, or crushing of concrt wr confirmd. For all spcimns, it was found that at maximum displacmnt, longitudinal cracking bcam significant and longitudinal slip dvlopd along th longitudinal crack. Th load and angls of mmbr at gnration of cracking, crushing, yilding of plat, tc. ar shown in Tabl 1. For furthr dtails on th spcimns, th radr is rqustd to rfr to Rfrncs [Furuta and Yamamoto, 1993]. Fig. 3 shows th load-displacmnt hystrisis loops (M-R: M=nding momnt of critical sction and R=ngl of mmbr) for rprsntativ spcimns (, ). Whil th maximum strngth of th spcimn with a larg shar span ratio (M/D) bcoms qual to th flxural strngth that of othr spcimns with small M/D ratios was found to b lowr than th flxural strngth. In whos M/D is larg, significant splitting (into thr pics) was obsrvd in th axial dirction of th mmbr at maximum strngth, du to longitudinal slip accompanid by longitudinal cracking. From thr onward, strngth dtrioratd rapidly. Spcimn (M/D) C5S (.5) (.75) C1S (1.) (1.75) Tabl 1: Column mmbrs faild in longitudinal slip Yilding of plat Crushing of concrt Ultimat load (kn/r) (kn/r) (kn/r) (kn/r) 264 254 255 289 1/14 1/25 1/3 1/1 166 186 182 192 1/15 1/25 1/3 1/2 137 145 161 161 1/15 1/15 1/5 1/5 127 138 13 138 1/2 1/15 1/15 1/15 (Uppr row: Gnratd load, Lowr row: ngl of mmbr) Mod of failur 2 669
(Column sharing forc) Wing Positiv loading Ngativ loading (ngl of mmbr: 1/5) (=182kN, 1 cycl) (ngl of mmbr: 1/15) (=13kN, 6 cycl) Fig. 2: failur 12 9 6 FƒvƒŒ[ƒĝ³ k ~ š :Comp. yilding of plat FƒvƒŒ[ƒĝø ~ š G H :Tns. œf c yilding Ð ÑŠ of êplat I M(kN Em) Man axial ² Í forc ½ Ï= 725.7kN :Flxural F È cracking Ð ÑŠ ê C E :Diagonal FÎ ß cracking Ð ÑŠ ê :Longitudinal Fˆ ³ ó cracking 3 œ:crushing -3 1/8-6 1/125 1/5 1/3-9 -12-4. -2.. 2. R i 1-2 rad) 4. (a) M(kN Em) Man axial ² Í forc ½ Ï= 739.4kN 8 :Flxural F È cracking Ð ÑŠ ê C E G I K M 6 :Diagonal FÎ ß Ð cracking ÑŠ ê :Comp. FƒvƒŒ[ƒĝ³ yilding of k plat ~ š 4 :Tns. FƒvƒŒ[ƒĝø yilding of plat ~ š œf c Ð ÑŠ ê :Longitudinal 2 Fˆ ³ ó cracking œ:crushing -2-4 1/8-6 1/125 1/5 1/3-8 -4. -2.. 2. R i 1-2 rad) 4. (b) Fig. 3: Load-displacmnt hystrisis loop RELTION ETWEEN PLTE STRINS ND LONGITUDINL SLIP PROPERTIES For rprsntativ spcimns (C5S, ), Fig. 4 (a) givs th load-strain (-ε : =Column sharing forc) curv of th plat at th critical positions in th sction illustratd in Fig. 4 (b). Fig. 4 (a) compars masurd plat strains with calculatd strains obtaind by bnding analysis, th fin lins rprsnting xprimntal valus, and th bold lins, calculatd valus. In th figur, th lft-sid graphs wr plottd for th whol numbr of cycls, whras, th right-sid ons wr plottd up to th numbr of cycls within th xprimntal and calculatd valus show agrmnt. Hr, bnding analysis was conductd by th Fibr Modl basd on th supposition that rnoulli-eulr s assumption (plan rtntion) would hold. It was also assumd that th strssstrain rlation of concrt would conform to th -function systm, and that th plats ar prfct lastoplastic mmbrs who ar comprssiv and tnsil yild strsss ar qual. s may b sn From Fig. 4 (a), th xprimntal and calculatd valus start to show disagrmnt whn raching th numbr of loading cycls (angl of mmbr) whr longitudinal cracking bcoms significant. This is thought to b du to th fact that rnoulli-eulr s assumption of plan rtntion no longr holds as not only has longitudinal slip causd th column mmbr to split into 3 pics along th longitudinal crack, but also bcaus th plats start to dvlop som curvatur. Sinc th tim of longitudinal crack gnration coincids with th point whr th plat strain starts to disagr with th calculatd flxural valu, it is assumd that th longitudinal slip strngth has bn rachd at th point whr longitudinal cracking bcoms significant. Whil in spcimns with a small shar span ratio (M/D), a slight ris in strngth was obsrvd vn aftr longitudinal slip failur, spcimns with a larg M/D (M/D=1.75) wr charactrizd by a rapid dtrioration of strngth following longitudinal slip failur. 3 669
(kn) (kn) 4 4 Longitudinal c slip ê 3 3 2 2 1 -ƒ Ãy 1 1/3R 1/3R ƒ Ãy -ƒ Ãy ƒ Ãy -1-1 -2-2 Exprimnt ÀŒ ± l -3-3 nalytic ð Í l -4-4 ƒ à iƒ Ê j ƒ à iƒ Ê j -6-4 -2 2-6 -4-2 2 Position of strain-gaug C5S 15 1 (kn) 15 1 (kn) Longitudinal c slip ê 5-5 -ƒ Ãy ƒ Ãy 5-5 -ƒ Ãy 1/15R 1/15R ƒ Ãy -1-1 -15-15 ƒ à iƒ Ê j ƒ à iƒ Ê j -3-1 1 3-3 -1 1 3 (a) Load-strain curv of stl plats (b) Position of strain gaug Fig. 4: Load-strain curv of stl plats and position of strain gaug EXMINTION OF EVLUTION METHOD FOR LONGITUDINL SLIP STRENGTH From th forgoing invstigation, it was confirmd that longitudinal slip failur accompanid by longitudinal cracking occurs at th point whr longitudinal cracking has furthr progrssd and bcoms significant, namly, th point whr th plat strain masurd at th critical positions of th sction no longr shows agrmnt with th calculatd strains obtaind by th Fibr Modl that postulats that rnoulli-eulr s assumption of plan rtntion holds. Hr, basd on th longitudinal slip gnrating mchanism, confirmd through th phnomna as dscribd abov, th valuation mthod for th longitudinal slip strngth will b studid for th slip phnomnon, which is accompanid by longitudinal cracking at th intrnal cornrs of th cross-shapd sction. Hypothtical Conditions First, in considration of th xprimntal rsults obtaind, th longitudinal slip rsistanc mchanism th mchanism that forms th basis for valuating th longitudinal slips strngth must satisfy th following conditions. (1) Th dirction of diagonal cracks that occur in th column capital and bas aras is that of diagonal lins conncting opposit cornrs of th column capital and bas. (2) Th portion whr longitudinal slip occurs is that at th intrnal cornrs of th column s cross-shapd sction. (3) s may b sn from th load-displacmnt curvs shown in Fig. 5, th smallr th shar span ratio (M/D), th highr th longitudinal slip strngth and maximum strngth will bcom, with strngth dtrioration aftr maximum strngth is rachd bcoming lss rapid. (4) Th stat of strsss in th column capital and bas aras up to longitudinal slip failur agrs with th rsults of bnding analysis, which postulats that rnoulli-eulr s assumption of plan rtntion holds. Fig. 6 (a) shows th xtrnal forcs that act on th column mmbr, togthr with th rlatd stat of strsss causd by sctional forcs at th column capital and bas positions. Manwhil, Fig. 6 (b) illustrats th column mmbr s rsistanc mchanism in opposing xtrnal forcs. Lt us assum hr that longitudinal slip occurs at th n-m (n -m ) surfac, and th mod of failur is shar slip. That is, it is supposd that th shar strss of concrt at th failur surfac (n-m) has rachd th lvl (τ ) at which shar slip taks plac. Lt us furthr assum that th longitudinal (axial) sharing forc ( F ) acting on th longitudinal slip surfac (n-m) is th sum of th vrtical componnt (C C2 ) of th concrt comprssion strut, th comprssiv strss (C S ) of th plat in th comprssion zon, and th tnsil strss (T S ) of th plat in th tnsion zon. Hr, th tnsil forc of concrt is to b ignord. Manwhil, of th vrtical componnt (C C in Fig. 6 (a)) of th concrt comprssion strut, th comprssiv strss (C C1 in Fig. 6 (b)) in th orthogonal loading ara (wing ara) of th column s crossshapd sction is ignord, sinc it is balancd within th wing ara and is considrd as having no influnc on longitudinal slip. Hnc, if, in dtrmining th strut width (l in Fig. 6 (b) hutch ara) of th concrt strut of quivalnt comprssiv strsss, th siz of th comprssiv zon (position of nutral axis: X n ) is found to xtnd as far as th wing ara, th mattr is to b xamind within th comprssiv strss rang (C C2 ) up to th wing ara. From th abov assumptions, for th cas whr th shar surfac n-m (n -m ) undrgos longitudinal slip 4 669
failur, th tim at which longitudinal slip failur accompanid by longitudinal cracking occurs will b F > R, whr, R rprsnts th sharing rsistanc acting in th longitudinal (axial) dirction of th mmbr. (kn) 3 25 2 15 1 5 1/1 1/5 1/33 1/25 R (rad) C5S (M/D=.5) (M/D=.75) C1S (M/D=.1) (M/D=1.75) Ts Cc Cs l m l Plat m Cs Ts Cc Fig. 5: Load-displacmnt curv p Ts Cc 2 Cc 1 Cs ƒ Ó n m l n' Ts H m' ƒ ÓCs Cc 1 p Cc 2 Xn X D p F m D ƒ Ó n R Xn m' X F =Cc 2 +Cs+Ts R =ƒê+ƒ Ñ H (S ctional ara of longitudinal slip n-m) (a) Forcs acting on th column (b) Rsistanc mchanism Fig. 6: Forcs acting on th column and rsistanc mchanism ` Induction of valuation formula for (longitudinal cracking-accompanid) longitudinal slip strngth Th shar strss of th longitudinal slip surfac upon th occurrnc of longitudinal slip is obtaind as follows: First, th comprssiv strss (σ N ) - shar strss (τ ) rlation of concrt is obtaind from Eq. (2) using th cofficint ( µ ) which is quivalnt to th frictional cofficint of concrt. t th sam tim, th pur sharing strngth (τ ) of concrt is obtaind from Eq. 1 th formula proposd by Gaston, t al. for obtaining th shar strngth (V U ) of mortar joints (bondd joints) subjctd to comprssiv strss [Gaston and Kriz, 1964]. V = 7.7 +. 7 σ (1) u N Hr, from th abov formula, Eq. 2 is drivd by using th mpirically obtaind 7.7 kgf/cm 2 as th pur sharing strss of concrt (τ ), and.7, th cofficint of comprssiv strss (σ N ), as th frictional cofficint ( µ ). τ µ σ + τ = N Sinc th comprssiv strss (σ N ) is that causd by th horizontal shar forc () applid by th concrt comprssion strut and is xprssd by / th valu obtaind by dividing by th longitudinal slip ara ( ), Eq. 2 may b writtn as τ µ / + τ (3) ( ) = whr, for th frictional cofficint µ, µ =.8 as proposd by [Mattock and Hawkins, 1972] has bn adoptd. σ N : Comprssiv strss acting on concrt, µ : Frictional cofficint (=.8) [Mattock and Hawkins, 1972], τ : Pur shar strngth of concrt (=.88σ +63.4) [Watab, 1987], σ : Comprssiv strngth of concrt, : Horizontal sharing forc, : ara. (2) 5 669
Nxt, th sctional ara ( ) of th longitudinal slip-sharing surfac (n-m, n -m ) is obtaind from th following quation. = { H ( D / 2 X tan φ 2 )} (4) nd, sinc tanφ =H/(D-X ), Eq. (4) can b writtn as = X H D X ) (5) whr, H: Column hight, D: Column width, : Column dpth, φ : ngl of axial lin (>45º), X : Lngth of comprssion block for dtrmining width of quivalnt comprssiv-strss strut (l ). Fig. 7 illustrats th failur conditions of th joint surfac, xprssd by th comprssiv (axial) strss (σ N ) shar strss (τ ) rlation, basd on th strss transfr mchanism at th contact surfac of th concrt joint. Th right-sid graph in th figur shows that th mod of concrt failur changs from slip failur to comprssion failur at th boundary surfac whn th σ N -valu bcoms gratr than th τ -valu. That is, it can b xpctd that, in longitudinal slip failur discussd in this papr, too, th mod of failur will chang from longitudinal failur to comprssion failur of concrt whn σ N bcoms gratr than τ. Sinc th mod of concrt failur will b slip (longitudinal slip) whn th angl of th concrt strut to th longitudinal slip surfac is lss than 45º (which maks σ N smallr than τ ), th rang of th strut angl to th longitudinal surfac, i.., th aformntiond angl of axial lin (φ ) was st to >45º. With rfrnc to Eqs. (4) and (5), it is blivd that th strut width (l ) for quivalnt strsss would vary dpnding on th diffrnc in th shar span ratio (M/D). For th four spcimns, who had undrgon longitudinal slip failur, Fig. 8 (a) shows th stat of concrt strsss at th column capital and bas obtaind through bnding analysis for th tim of longitudinal slip failur. s may b sn from this figur, for all spcimns, not only dos th comprssion zon, i.., th position of th nutral axis (X n ), xtnd as far as th wing ara upon th gnration of longitudinal slip, but th stat of concrt strsss diffrs from spcimn to spcimn as wll. ccordingly, in this papr, th lngth of X, as shown in Fig. 8 (b), was st to a block lngth obtaind by rplacing th (C C2 ) ara (th comprssiv strss ara at th column sction s wing ara whr (C C1 ) is ignord) with an quivalnt-strss block obtaind on th basis of th comprssiv unit strss (σ m ) of concrt that occurs at sction dgs. Furthrmor, it was dcidd that, whn σ m bcoms qual to th comprssiv strngth of concrt (σ ), th ffctiv lngth of th strss block (X ) is to b multiplid by th ffctiv cofficint ( β =.85). Hr, th comprssiv strngth of concrt is st to th rang of σ < 28MPa. asd on th abov assumptions, whn th shar surfac (n-m, n -m ) undrgos longitudinal slip failur, th shar strngth ( R ) may b xprssd as = τ = µ + τ = µ + τ β X H /( D β X ) (6) R whr, σ m <σ : β =1., σ m =σ : β =.85 nd, from th assumption that th sharing forc ( F ) acting on th shar surfac (n-m, n -m ) is th sum of th vrtical componnt of th concrt comprssion strut, th comprssiv strss (C S ) of th plat in th comprssion zon, and th tnsil strss (T S ) of th plat in th tnsion zon, th sharing forc ( F ) may b writtn as F = CC + C S + T (7) 2 S Hnc, th strngth at gnration of longitudinal slip failur accompanid by longitudinal cracking may b xprssd, from th failur condition, F > R, as Eq. 8. = C + C + T τ β X H / D β X / (8) { ( )} µ C 2 S S Thrfor, th sharing forc () at longitudinal slip failur ( F > R ) accompanid by longitudinal cracking can b obtaind through bnding analysis conductd by th Fibr Modl adoptd in Eqs. (6) and (7). Mor spcifically, as may b sn from Fig. 9, th longitudinal slip strngth ( cal ) is th valu obtaind at th intrscting point whr F > R, whn R (Eq. 6) and F (Eq. 7) ar takn on th axis of ordinats and on th axis of abscissas. ƒð N (Comprssiv strss) ƒ Ñ oundary slip Comprssion failur of concrt ƒñ ƒñ ƒê Concrt failur condition curv (Shar strss) ƒð llowabl strss rang N ƒð N @@Fig. 7: Th concpt of comprssiv strss transmission 6 669
D Plat Strut C5S w 32 w 141 w 288 w 139 C1S w 27 w 14 w 239 w 134 3 Xn 2 X 1 ƒð ƒð ƒð ƒð (mm) X n (D )/2 C C2 D/2 X g Concrt unit strss ƒð m ƒð Concrt unit strss ƒð m ƒð (a) Strss stat chart of concrt on column capital (b) Equivalnt strut width and bas at longitudinal slipping failur Fig. 8: Strss stat chart of concrt and quivalnt strut width ( q, F ) F R () cal ( gnrating sharing forc) Fig. 9: Rlations btwn th sharing strss ( F ) and th rsistanc strngth ( R ) EXMINTION OF NLYTICL RESULTS For th four spcimns, who had undrgon longitudinal slip failur as a rsult of invrs symmtric loading, Tabl 2 compars th longitudinal slip gnrating strngth ( cal ) obtaind from Eqs. (7) and (8) with th longitudinal slip-gnrating load obtaind through xprimnts. lso shown in th tabl ar, th block lngth (X ) by which th width of th quivalnt-strss strut (l ) is dtrmind, as wll as th vrtical componnt (C C2 ) of th concrt comprssion strut, th comprssiv strss (C S ) of th plat in th comprssion zon, and th tnsil strss (T S ) of th plat in th tnsion zon. Manwhil, Fig. 1 illustrats th rlation of F and R with. s may b sn from Tabl 2, th xprimntal and calculatd valus agr with ach othr with xcllnt accuracy. This shows that it is highly possibl to stimat th longitudinal slip gnrating strngth by using th valuation mthod proposd hrin. Th mthod, which is basd on th mchanism of longitudinal slip gnration accompanid by longitudinal cracking in th column mmbr discussd arlir, assums that shar slip failur occurs at th longitudinal slip surfac, and also that th shar strss working on th longitudinal slip surfac is th sum of th vrtical componnt of th concrt comprssion strut, th comprssiv strss of th plat in th comprssion zon, and th tnsil strss of th plat in th tnsion zon. Tabl 2: Comparing analytical rsults with xprimntal rsults Spcimn Exprimnt nalytic (M/D) L X C C2 C S T S cal L/ cal C5S (.5) 255 141 297 61 21 261.98 (.75) 182 139 312 66 27 181 1. C1S (1.) 161 14 351 82 45 161 1. (1.75) 13 133 435 134 111 135.96 ( L, C C2, C S, T S, cal: kn, X : mm) 7 669
8 R,F(kN) 8 R,F(kN) 6 6 4 4 2 F cal 181.3kN R (kn) 1 2 3 4 2 F R cal 135.2kN (kn) 5 1 15 2 (a) (b) Fig. 1: Rlations btwn F and R SUMMRY With a viw toward grasping th strsss that would work on a ti-plat that could b xpctd to prvnt longitudinal slip failur that would othrwis occur in PLRC column mmbrs at th intrnal cornrs of th cross-shapd sction in th axial dirction of th mmbr, th valuation mthod for longitudinal slip strngth has bn xamind in this papr. From th xprimntal rsults obtaind, it was confirmd that th hypothtical conditions to b st for studying th rsistanc mchanism to longitudinal slip would b as follows: (1) Th dirction of diagonal cracking that occurs in th column capital and bas aras would b in th dirction of th diagonal lins conncting opposit cornrs of th column capital and bas. (2) Th ara whr longitudinal slip occurs would b th intrnal cornr of th cross-shapd sction of th column. (3) Th smallr th shar span ratio (M/D), th gratr th longitudinal slip strngth and maximum strngth will bcom, with strngth dtrioration aftr maximum strngth is rachd bcoms lss rapid. nd, (4) th stat of strsss occurring in th column capital and bas aras up to longitudinal slip failur agrs with th rsults of bnding analysis conductd on th basis of rnoulli-eulr s assumption of plan rtntion. asd on th hypothtical conditions, a calculation formula for stimating th longitudinal slip strngth was stablishd, which assums that th strss working on th longitudinal slip surfac is th sum of (1) th vrtical componnt of th concrt comprssion strut obtaind by th Fibr Modl, (2) th comprssiv forc of th plat in th comprssion zon, and (3) th tnsil strss of th plat in th tnsion zon. Manwhil, th rsistanc at th longitudinal slip surfac was assumd to b th shar rsistanc of concrt subjctd to comprssiv axial strss. s a rsult, it was confirmd th calculatd rsults showd xcllnt agrmnt with th mpirical rsults. It was thus confirmd that th longitudinal slip strngth of PLRC column mmbrs can b stimatd by using th proposd calculation formula a formula basd on th assumption that longitudinal slip failur occurs whn th strsss working at th intrnal cornrs of th cross-shapd sction obtaind by th Fibr Modl bcoms qual to th shar rsistanc of concrt of that spcific ara. Du to th succssful th succssful rsults obtaind in calculating th longitudinal slip strngth, th authors bliv that it is highly possibl to stimat th strsss that work on a ti-plat that could b xpctd to prvnt longitudinal slip failur. REFERENCES Furuta, T. and Yamamoto, Y. (1993), Dvlopmnt and Rsarch on Plat Rinforcd Concrt (PLRC) Structural Systm Part15: Exprimnts on Cross-Shapd Column Subjctd to Invrs Symmtry Loads, and Summary Procdings IJ nnual Confrnc, Vol. C, Structurs 2, pp827-828. Gaston, J. R. and Kriz, L.. (1964), Connctions in Prcast Concrt Structurs Scarf Joints PCI Journal, Jun. Mattock,. H. and Hawkins, N. M. (1972), Shar Transfr in Rinforcd Concrt Rcnt Rsarch PCI Journal, March-pril. Ohya, T. and Furuta, T. (1992), Dvlopmnt and Rsarch on Plat Rinforcd Concrt (PLRC) Structural Systm Part 6: Exprimnts on Shar Failur of Cross-Shapd Column Procdings IJ nnual Confrnc, Vol. C, Structurs 2, pp459-46. Watab, S. (1987), Rsarch on Dynamic Proprtis and Durability of High strngth Concrt Procdings JCI nnual Confrnc, Vol. 9, No. 1 8 669