PULL-OUT AND SHEAR STRENGTH EQUATIONS FOR HEADED STUDS CONSIDERING EDGE DISTANCE

Transcription

1 PULL-OUT AND SHEAR STRENGTH EQUATIONS FOR HEADED STUDS CONSIDERING EDGE DISTANCE Hirokaz HIRAGI 1, Sigeyki MATSUI, Takai SATO, Abbaker AL-SAKKAF 4, Siger ISHIZAKI 5 and Yairo ISHIHARA 6 1 Member of JSCE, Dr. Eng., Ao. Profeor, Dept. of Civil Eng., Setnann Univerity (17-8 Ikeda-Nakamai, Neyagawa, Oaka , Japan) Fellow of JSCE, Dr. Eng., Profeor, Dept. of Civil Eng., Oaka Univerity (-1, Yamadaoka, Sita, Oaka , Japan) Stdent Member of JSCE, Gradate Stdent, Dept. of Civil Eng., Oaka Univerity (-1, Yamadaoka, Sita, Oaka , Japan) 4 Stdent Member of JSCE, M. Eng., Gradate Stdent, Dept. of Civil Eng., Oaka Univerity (-1, Yamadaoka, Sita, Oaka , Japan) 5 Member of JSCE, Engineer, Bridge Deign Dept., Sakai Iron Work Co. Ltd. (-1, Dezima-Niimai, Sakai, Oaka 59-81, Japan) 6 Member of JSCE, Engineer, Bridge Deign Dept., Katayama Strte Corp. (6--1, Minamiokazima,Taiyok, Oaka 551-1, Japan) Std are often ed a ear onnetor or anor between onrete and teel member at vario ompoite trtre. A te td are welded in a finite range of te teel member and ea td generally a different ditane from te edge of trtral onrete, it an be expeted tat tey do not ow te ame pll-ot and ear trengt. In ti paper, terefore, te tet data of previo invetigation inlding new data obtained by ator and exiting formlae for pll-ot and ear trengt of te td are reevalated, and te trengt eqation were revied in te ae of independent of te edge ditane. Ten for te td near te onrete edge, new inflene fator were fond and ompoed into te revied eqation a oeffiient. Key Word : td, ear onnetor, anor, ltimate apaity, ybrid trtre 1. INTRODUCTION Reently in Japan, de to intending to implify te igway bridge ytem, everal new type of ybrid trtre ompoed of teel and onrete member ave been atively developed. In order to realize new type of ybrid trtre, it i neeary not only to atify te reqired performane of joint part and/or onnetion member, bt alo to derive reliable formlae to evalate te trengt of onnetion member and etabli an arate deign metod. Te ompoite joint of ybrid trtre are deignated a te jointing part between teel girder and RC pier of a ybrid rigid frame bridge, te jointing part of teel and onrete member at a mixed bridge, anoring part of teel pier to onrete footing and ontat part between flange plate of main girder and RC-lab at a plate girder bridge ytem, et. In tee trtral part, td ear onneter ave been ed freqently a jointing element between teel and onrete. However, wen te td are ed in narrow jointing pae, it an be een tat te expeted load arrying apaity annot be obtained beae of inffiient ditane from te edge of onrete. And, in te field of bridge engineering, previo reeare on te trengt of te td are limited to te one onerning to ompoite girder, and almot all of tem are on td welded on te teel girder wit ffiient edge ditane 1). Bt, tere are a few tdie on te td trengt onidering edge ditane, and tee are only in te field of aritetral engineering ). Terefore, for te deign of ompoite joint mentioned above, it i important to larify te effet of edge ditane on te pll-ot and ear trengt of te td. Under tee irmtane, firtly in ti reear, teting metod adopted in te previo 69(69)

2 reeare and exiting propoal of pll-ot and ear trengt of te td are reevalated, and bot te dometi and foreign teted data inlding new relt obtained by ator are olleted and rearranged. And ten, baed on te tatitial analyi of tee data, te inflene fator on te trengt of te td are larified, and te etimating eqation of pll-ot and ear trengt of te td are propoed bot in te ae of ignoring edge ditane and onidering tem. However, te etimating eqation for pll-ot and ear trengt of te td wit 6mm diameter are already reported in referene ).. LITERATURE REVIEW (1) In te ae being independent of edge ditane a) Pll-ot trengt Exiting eqation to etimate te pll-ot trengt of eaded td are own in Table 1 4)-1). Tee eqation are derived by aming tat a td bjeted to pll-ot load wold fratre wit onial ear rfae, and an be baially laified into -type of wi employ eiter te gro rfae area or te effetive orizontal projetive area of te one a a parameter for evalating te trengt. And ' eiter te ear trengt ( f ) or te tenile trengt ' ( f / ) i employed a a onrete trengt. Tog, baially, te ear trengt old be ed for te gro rfae area of te one, and te tenile trengt old be ed for te effetive orizontal projetive area, treatment are not done o, in pratie. Poto 1 ow a onial pll-ot fratre mode of te onrete. A pll-ot trengt of te td i generally derived nder te amption tat te onial fratre rfae inlination i 45 degree. However, it an be een a te poto. tat te onrete jt nder te td ead ow a pre ear mode wit te arp inlination, and a te fratre Table 1 Exiting propoal for pll-ot trengt of eaded td Evalation metod for pll-ot trengt(<a f y ) Ref. Propoed by Etimating eqation F-vale 4) Leig-Univerity F ( + d ) 1.7 5) Sattler F d.95 6) Uteer F.946 7),8) CEB-ECCS F ) PCI Deign data book F ( + d ) 1.7 1) Roik,Bode,Hanenkamp F ( + d ) ) MMakin F π ( + d ).7 1) Otani F ( + d ) 11. F :Coeffiient Overall igt of te td(mm) :Lengt of te td(mm) d :Diameter of te td ead(mm)f' :Compreive trengt of onrete(n/mm ) fae get loer to te onrete rfae, te inlination of te one get to gradally flat. Wile te poto ow a relt of a peimen wit no reinforement, it an be expeted tat te fratre fae of a peimen wit reinforing me will ow more ompliate. In any ae, te inlination angle of te one doe not ow 45 degree a amed generally, o far. Witin te wole teted data of 94 olleted in ti invetigation a own in Table, 9 data exept te data affeted by edge ditane and broken at te td ank, are arranged baed on te relation propoed by te reear grop of Leig-Univerity a own in Fig. 1. Te propoal by Leig- Univerity wa adopted entirely in te PCI deign and book. In te figre, te ordinate ow a experimental vale and te abia ow a allated vale given by te etimating eqation. It an be een tat te pll-ot trengt of te td wit onial fratre rfae i arately expreed wit ig orrelation oeffiient of.96. However, te etimating eqation i inonitent beae te pll-ot trengt i etimated by ear trengt of te onrete depite of ing te effetive orizontal projetive area of te one. Meared pll-ot load P ( 1 N) 7(7) Poto 1 Cone fratre mode by pll-ot Correlation oeffiient(r ) : ( d ) ( 1 P = 1.7 ( d + ) + N mm) Fig.1 Comparion of meared pll-ot load wit te eqation propoed by Leig-Univerity

3 tage of te load. Ti rotational deformation of te plate inreae wit te inreae of loading, and te onrete at front of te td rae loally. So tat, te large deformation of te plate aed by te r of onrete inde te dereae of ear reitane. Sear tet by tenile loading for ingle ear rfae i ed freqently to obtain te ear trengt at anoring part between teel pier and onrete footing mainly in aritetral engineering field. In ti teting metod, ine te teel plate wit welded td i plled orizontally by ig trengt teel bar, te ear fore i loaded eentrially, and te plate will be bent ot of te ear rfae. Coneqently, te onrete at front of te firt td loally re in early tage de to a omplex tre tate in te diretion of td axi, and ten te ear reitane of te td dereae. b) Sear trengt baed on p-ot tet for ingle and doble ear rfae In general, ear reitane of a td a been obtained experimentally wit te teting metod a own in Fig., o far. Te mot widely ed teting metod i a p-ot tet wit te ompoite teel etion aving oter doble ear rfae, and it i jt alled P-ot ear tet. Te metod an be loaded wit a pre ear tate ntil ltimate limit, and i ardly inflened by te edge ditane beae te onrete reit by bearing trengt of te onrete nder te td ank. In addition, it i baed on te amption tat te teel plate at te td root doe not deform ntil ltimate tate a own in te rigt ide of te figre. Terefore, no rapid redtion of ear reitane i reognized de to onfined effet nder te tri-axial ompreion of te onrete at te front part of te td, even if te onrete arond te root of te td re loally. P-ot tet for te andwied onrete peimen wit two over plate i developed to determine te trengt of ear onnetor ed in andwi trtre a bmerge tnnel, arbor aion blok et. In ti metod, de to te relatively tin plate tikne of te peimen, te plate at root of te td deform loally in te early Teting metod () In te ae of onidering edge ditane a) Pll-ot trengt Wen te ditane e from te edge of onrete to te enter of td i orter tan te lengt of td ank, a one rfae formed by pll-ot load beome a partially laked one t by te onrete end. Terefore, a peified by Aritetral Intitte of Japan (AIJ), te pll-ot trengt i reded by onidering te lak of te effetive orizontal Deformation and ditribting tre of td bottom Configration of peimen Head of teting maine P-ot tet for Hig trengt bolt doble ear rfae Conrete Std StdCompreive reation Loading Plate Load ell Conrete Std (oter onrete) Web plate Bae plate Steel plate Loading plate Std P-ot tet for doble ear rfae (inner onrete) Hydrali jak Pll-ot tet for ingle ear rfae Flange plate Bedding Load ell Compreive reation Conrete Cring zone Std Cring zone Hydrali jak(enter-ole Cannel Steel Steel plate Conrete Steel plate Steel plate Free Load ell Hig-trengt -teel bar Conrete Std Cring zone Std Fig. Teting metod of te td for ear 71(71) 1),1),5) Conrete

4 projetive area a own in Fig.. For referene, te general fratre model ignoring edge ditane i alo own in ti figre. For te wole olleted data of 94 own in Table, te relationip between meared pll-ot load and edge ditane i analyzed a own in Fig. 4. Tog te data widely attering, te envelope enloing pper bond of pll-ot trengt ow a tendeny tat te teted vale dereae wit te dereae of edge ditane. So a more detailed Non-Conidered Conidered 5 Meared pll-ot load P ( 1 N) Edge ditane analyi for te effet of edge ditane eem to be neeary for te deign of td by te pll-ot trengt. Te pll-ot trengt eqation propoed by Fier et al. and peified in PCI deign andbook are own in Table. For referene, te table alo ow te eqation propoed by AIJ wi i preented by lower bond of teted vale. A it i lear from te table, toe eqation are giving a imple redtion fator for te edge effet. Te proedre eem to be Conial fratre onrete Fratre model (Saded portion) Etimating eqation by AIJ PCU : Pll-ot trengt of eaded td f'c : Compreive trengt of onrete AC : Effetive orizontal projetive area(e= ) S : Lengt of td ank P'CU : Reded Pll-ot trengt of te td AC : Effetive orizontal projetive area (Conidering te edge ditane e) 1 4 Edge ditane e (mm) e : edge ditane d : Diameter of te td ead 5 6 ds : Diameter of te td ank Fig. Evalation metod for pll-ot trengt of eaded td provided in AIJ Standard Fig. 4 Relationip between meared pll-ot load and edge ditane Table Etimating eqation for pll-ot and ear trengt onidering edge ditane (Previo reear) Pll-ot trengt Propoed by Fier et al. (197) Sear trengt P ' = α γ P e αγ = 9d Q ' = α Q Q αq = (Redtion fator) PCI deign andbook (1978) AIJ Standard (1985) (Redtion fator) P ' = C γ P e 1 Cγ = Q ' = 5( e 1)λ 5 ) (Referene diagram) Q m ax =.6 A CQ Pm ax =.6 5 A r P'CU : Reded pll-ot trengt of te td onidering edge ditane PCU : Pll-ot trengt of te td ignoring edge ditane e : Edge ditane d : Diameter of te td ank ( = K λ ( + d ) ) Q' : Reded ear trengt of te td onidering edge ditane ( =. 5 A ( E ).5 ) ( (Pond and in) (Redtion fator) Q : Sear trengt of te td ignoring edge ditane e 1 8d d : Diameter of te td ead : Lengt of te td ank f' : Compreive trengt of onrete K : Coeffiient λ : Material fator λ=1. for nomal onrete λ=.85 for ligt-weigt aggregate onrete λ=.75 for ligt-weigt onrete A : Cro etion area of te td ank E : Yong' modl of te onrete Pmax : Meared lower bond of pll-ot trengt of te td onidering edge ditane = π ( + d ) + e ( + d ) e ( + d ) o 1{e ( + d )}½ Ar : Effetive orizontal projetive area ¾ Qmax : Meared lower bond of ear trengt of te td onidering edge ditane Ar : Effetive projetive area formed at end vertil rfae of te onrete (Refer to rigt ide illtration) {= (π e ) } 7(7)

5 too imple to expre te effet of edge ditane. And te eqation by AIJ eem to be too m afety ide, beae it i given by te lower bond data. b) Sear trengt baed on p-ot tet for ingle and doble ear rfae Beae te p-ot tet for doble ear rfae in tanding type i ardly inflened by edge ditane a mentioned above, te tet data wold be exlded from te objet of diion. Te trengt eqation for ear reitane of te td for te peimen wit ingle ear rfae propoed by Fier et al. and peified in PCI deign andbook are alo own in Table. Te table alo ow te AIJ eqation obtained by te ame manner a pll-ot trengt, for referene. A it i lear from te table, in te ame manner a pll-ot trengt, Fier et al. expree te ear trengt of te td onidering edge ditane by only mltiplying te eqation being independent of edge ditane by a redtion fator. And, PCI eqation alo i a mere experimental eqation, and a no lear bai. In te ame manner, te AIJ tandard give an etimating eqation for ear reitane onidering edge ditane ing te vertial effetive projetive area obtained by aming te onial fratre rfae tarting from te bearing portion at te td ank rfae a own in te rigt ide illtration of Table. And te eqation i alo irrational de to adoption of te lower bond of teted data. Wen a ear tet i arried ot by tenile loading trog reinforing bar in onrete blok, te onrete rfae of pll ide i free and te td nearet to te onrete rfae will be affeted by edge ditane. In te ame manner a pll-ot trengt, te wole 118 data own in Table 5 for ingle ear tet are olleted and arranged in ti tdy, and te relationip between meared ear apaity and edge ditane i own in Fig. 5. From te figre, tog te teted data are widely attering, te pper bond of teted vale dereae linearly wit te dereae of edge ditane, and te inflene of te edge ditane on te ear trengt of te td i lear.. PROPOSAL OF PULL-OUT AND SHEAR STRENGTH EQUATIONS FOR HEADED STUD (1) Inflene fator on pll-ot and ear trengt and bai tatitial data of previo tet a) Pll-ot trengt From te trengt eqation propoed o far a own in Table 1, it an be ppoed tat te ignifiant inflene fator on te pll-ot trengt Meared ear apaity Q ( 1 N) Edge ditane e (mm) Fig. 5 Relationip between meared ear apaity and edge ditane of te td are ank diameter (d ), lengt of td ank ( ), diameter of td ead (d ), ompreive trengt of te onrete (f' ), effetive orizontal projetive area parameter of te one (d + ) and edge ditane (e). Te bai tatitial data fond o far bot in te dometi and foreign paper for pll-ot trengt inlding new data obtained by ator are 94 a own in Table 5),1),1),15),18). b) P-ot ear trengt A for te ear trengt baed on te p-ot tet for te peimen wit doble ear rfae, te aft diameter (d ), overall lengt (), tenile trengt (f ) of te td and ompreive trengt of te onrete (f' ) wold be te ignifiant fator. Beae, for te p-ot ear tet, it an be onidered tat te ear trengt i ardly inflened by edge ditane, ine te fore ating on H-aped teel i reited by bearing trengt of te onrete nder te td ank. Te bai tatitial data for te p-ot ear trengt by te tet for doble ear rfae inlding by ator relt (wole nmber : 197) are own in Table 4 19). ) Sear trengt for ingle ear rfae For te ear trengt baed on te p-ot tet for te peimen wit ingle ear rfae, te aft diameter (d ), overall lengt (), diameter of td ead (d ), ompreive trengt of te onrete (f' ) and edge ditane (e) wold be te ignifiant fator. And bai tatitial data for p-ot ear trengt by ingle ear tet inlding by ator (wole nmber : 118) are own in Table 5 11),),). () Derivation of trengt eqation for pll-ot trengt of te td a) Std embedded deeply from onrete edge Te appropriate experimental data of 1 wa tatitially analyzed by logaritmi mltiple regreion analyi. Baed on te parameter in te exiting trengt 7(7)

6 Table Bai tatitial data of td for pll-ot tet Nmber of data : 94 Mean Standard deviation Min Max Diameter of td ank d (mm) Lengt of te td ank (mm) Diameter of td ead d (mm) Compreive trengt of onrete f' (N/mm ) Projetive aream parameter +d (mm) edge ditane e(mm) Table 4 Bai tatitial data of td for p-ot ear tet of doble ear fae Nmber of data : 197 Mean Standard deviation Min Max Diameter of td ank d (mm) Overall lengt (mm) Tenile trengt of td f (N/mm ) Compreive trengt of onrete f' (N/mm ) Table 5 Bai tatitial data of td for p-ot tet of te td of ingle ear fae Nmber of data : 118 Mean Standard deviation Min Max Diameter of td ank d (mm) Overall lengt (mm) Diameter of td ead d (mm) Compreive trengt of onrete f' (N/mm ) Edge ditane e(mm) eqation and te ator jdgment, te pll-ot trengt of te td finally old be ompoed a te following exponential mltivariate regreion model. Namely, Were, a ( d + ) b P = α (1) P : Pll-ot trengt (N), : Lengt of te td ank (mm), d : Diameter of te td ead (mm), f' : Compreive trengt of te onrete (N/mm ), α: Coeffiient. Ten, Eq.() an be derived by te mltiple regreion analyi P = 1.61 ( d + ) () vale6.7 for 1.967, and.75 for.16 Were, te ignifiane of te exponential part in te regreion eqation i examined by te t vale, and it i jdged tat a bigger t-vale give a iger ignifiane. In addition, te mltiple orrelation oeffiient wa.974. Ten, from taking te previo trengt eqation into aont, ea exponential part an be ronded off for pratial age a Eq.(). P = α ( d + ) () Meared pll-ot load P ( 1 N) Ten, te 9 data owing te ig orrelation were rearranged ing te relation of Eq.() a own in Fig. 6. From te figre, it wa larified tat te regreion eqation give te medim vale (median) of teted data in all range. Te validity of Eq.() wa onfirmed by te Fig. 6. However, te eqation form of PCI deign andbook wa alo invetigated in order to keep te oniteny a a pll-ot trengt eqation. Te eqation of PCI deign andbook are derived nder te amption of two fratre mode tat te td ank are broken itelf and te onrete one fratre arond te td. Te tenile trengt of te td ank i te pper bond. Ten PCI eqation are given by Eq. (4). P = F A P = F one π ( d + ) A f A f (4) Were, F : Coeffiient, A one : Area of an amed onial fratre rfae of te onrete (mm ), A : Cro-etional area of td te ank (mm ), f : Te tenile trengt of te td (N/mm ). Here, in Eq.(4) making te ating diretion of te external fore oinide wit te reiting diretion, and by aming tat te trengt eqation i given in te form of te prodt of projeted area of te ear one on a onrete fae (A ) and te tenile trengt of te onrete (f t ), te form of bai eqation i expreed a follow. P = F π ( d + ) f A f (5) R=.9678 ( d + ) ( 1 P =.897 ( d + ) t N mm) Fig. 6 Relation obtained by mltiple regreion analyi 74(74)

7 Meared pll-ot load P ( 1 N) R=.967 P =.845 π ( d + ) (.67f ' ) π ( d + ) (.67 ) ( 1 N mm ) P/P given by eq.(7) a Edge ditane parameter e Fig. 7 Comparion of meared pll-ot load wit te etimated vale wit Eq.(6) independing on edge ditane Ten, for te tenile trengt of onrete, te trengt eqation own in te Ref. 4) eem to be efl. So, Eq.(5) an be written a P = F π ( d + ) (.67 ) A f (6) Fig. 7 ow rearranging te data of Fig. 6 ing Eq.(6). A i obvio from te figre, te relt of Fig. 7 ow an eqivalent evalation in omparion wit te relt by Eq.() derived from mltiple regreion analyi wit te eqivalent orrelation oeffiient ( ). Terefore, it an be onidered tat te Eq.(6) ing te tenile trengt of te onrete give an appropriate etimation for te pll-ot trengt of te td, too. Finally, by ronding off te oeffiient of Eq.(6), Eq.(7) an be propoed, a an appropriate pll-ot trengt of te td. P =.85 π ( d + ) (.67 ) (7) wit a limitation of {(e-d /)/.} a own in te following paragrap. b) Conidering edge ditane A mentioned above, tere are many nolved problem for te inflene of edge ditane on te pll-ot trengt of te td. However, in order to etimate te redtion of pll-ot trengt de to te maller ditane from te onrete edge to te td, an edge ditane parameter wa introded and invetigated. In te PCI eqation, te vale of te edge ditane e (ditane from te onrete edge to te entral axi of te td) divided by te lengt of Fig. 8 Relationip between P/P and edge ditane parameter td ank i defined a te edge ditane parameter. In ti ae, te pre over ange depend on te diameter of te td, even if te edge ditane are ame. Terefore, a pre over ratio {(e-d /)/ } wa employed a te edge ditane parameter in order to eliminate te differene. Moreover, on formlation of pll-ot trengt of te td onidering edge ditane, te data gotten by break at td ank were exlded, and te teted data for te peimen wit reinforement arond te td were alo omitted, beae te pll-ot trengt eem to inreae by retraint of te reinforement. Taking te pre overing ratio to te abia a te new edge ditane parameter, and te normalized fore wi i divided te experimental pll-ot trengt by te allated vale given by Eq.(7) to te ordinate, teted data were plotted a own in Fig. 8. From te figre, it i obvio tat te teted data are remarkably attering. However, from general view of te figre, it i jdged tat te normalized fore of ordinate onverge rogly to 1. wen te edge ditane parameter exeed.. Namely, it an be aid tat te pll-ot trengt of te td i ardly inflened by edge ditane for te range of te edge ditane parameter above.. Terefore, by only te data of te abia vale nder., te regreion analyi by linear and exponential type were arried ot again. A a relt, it wa larified tat te relt obtained by te exponential regreion analyi ow iger orrelation, tog te teted data were attered (See Fig. 9). From ti fat, it wa onidered tat te trengt eqation for te range of {(e-d /)/.} old be given a te exponential fntion, and te following redtion fator ( p ) old be introded in order to implify te expreion. 75(75)

8 α p = P P.71 1 e e d d (8) A own in Fig. 1, te teted data wa plotted wit te pre overing a abia and te loading ratio (P/P ) a ordinate, in a imilar manner a Fig. 8, and an appliability of Eq.(9) wi i inorporated a oeffiient given by Eq.(8) into Eq.(7) wa examined (wole data of 7 wit te onrete trengt over 5N/mm ). P d 1 e.85 ( d + ) (.67 ) = π (9) wit a limitation of {(e-d /)/.}. From Fig. 1, it an be oberved tat te Eq.(7) i linked to Eq.(9) at te edge ditane parameter eqal to., bt at tat point, te relation between te edge ditane parameter and te loading ratio ange from te exponential fntion to te ontant vale. For te data ame a Fig. 1, taking te edge ditane parameter into aont, te teted pll-ot trengt were ompared wit te allated one a own in Fig. 11. A i lear from te figre, tog te allated vale give te medim of experimental one in te range of le tan 1kN, in te range of more tan 1kN, te experimental vale tend to take a le vale tan te allated one. However, beae of te ig orrelation oeffiient of.9578, it wa jdged te trengt eqation for pll-ot trengt of te td an be given by Eq.(7) and Eq.(9). 7% and/or 8% redtion vale of Eq.(7) and Eq.(9) are alo own in Fig. 1 and Fig. 11. From tee figre, it an be fond tat te 7% redtion rve of Fig. 1 well expree te lower bond of te teted data. Terefore, te redtion rve an be employed a te deign trengt formlae wi take te attering of teted data into aont. () Derivation of ear trengt eqation of te td a) In te ae being independent of edge ditane P-ot ear tet Te ear trengt of te td obtained by te ordinary p-ot tet metod i onidered to be ardly inflened by edge ditane de to te arateriti of teting metod. From te tatitial arrangement of te previo teted data, Hiragi and Mati propoed te trengt eqation for ear trengt of te td 19). In ti tdy, wole tet data inlding te new data obtained by te ator were rearranged aording to te above evalating metod. P/P given by eq.(7) a P/P given by eq.(7) a Meared pll-ot load P ( 1 N) Fig. 9 Fitting of etimating eqation baed on mltiple regreion analyi (e ) Edge ditane parameter e Fig. 1 Ditribtion of P/P for fll range and fratal vale ds P.6586 e α p = = ( R =.514) P Edge ditane parameter e e eq.(9) ds P.714 e α p = = ( R =.715) P d S eq.(7) Reded 8% (e -d /)/ (e -d /)/ > R =.9784 Reded 7%.5466 Reded 8% f' 5N/mm Callated pll-ot load P ( 1 N) Median Reded 7% Fig. 11 Comparion of te etimated load and meared pll-ot load by ignoring edge ditane And te relt i own in Fig. 1 (wole data of 197 own in Table 4). Te validity of te eqation by Hiragi and Mati an be ertified from te figre. Terefore, it wa jdged tat ti eqation an be adopted a te trengt eqation for p-ot ear 76(76)

9 Meared p-ot ear load Q ( 1 N) Q 1. A + 98 d = A Fig. 1 Comparion between meared p-ot ear load and etimated load propoed erein by ignoring edge ditane trengt in te ae of ignoring edge effet. Te eqation i given by Q = 1.A + 98 (1) d R=.9161 Doble ear (Oter onrete) Doble ear (Inner onrete) Single ear ( d ) ( N mm) Were, Q : P-ot ear trengt of a td (N), A :Cro-etional area of te td ank (mm ), : Overall eigt of te td (mm), d : Diameter of te td ank (mm), f' : Compreive trengt of onrete (N/mm ). For referene, bot te ear tet data obtained by doble ear rfae peimen for inner onrete and by te ingle ear rfae p-ot tet (Refer to Fig. ) are alo own in Fig. 1. From ti figre, toe tet relt eem to be obvioly a little bit lower, in omparion wit te ordinary p-ot tet relt. However, te gradient of bot relt eem to be imilar. Tat i, tog te regreion line for te ordinary p-ot ear tet relt a te interept at y-axi, te regreion line for ear trengt of doble ear rfae by inner onrete and for ingle ear tet eem to be expreed witot te interept. Hereafter, te data olleted by te new teting metod wi an repreent te tre tranfer meanim of atal trtre i trongly expeted. Sear tet of ingle ear rfae by tenile load Te ear tet relt of ingle ear rfae by tenion type loading are own wit te regreion line in Fig. 1. Te data were a few data (wole 5 data). A i lear from te figre, te interept of te Meared ingle ear load Q ( 1 N) Q =.918 A d 1 4 A Fig.1 Comparion between meared ingle ear apaity and etimated load propoed erein by ignoring edge ditane regreion eqation beome zero, and te orrelation oeffiient (R) ow a ig vale of.994. And te gradient of regreion line ow a little iger vale of.9 in omparion wit 1. wi wa obtained by te p-ot ear tet. From te relt, a te trengt eqation for ingle ear trengt of te td independent of edge ditane, te following expreion an be propoed onidering te ame parameter of te ordinary p-ot ear trengt eqation. R =.994 ' Q = 1. A f (11) d In te ear tet by tenion type loading for ingle ear rfae, te td welded on teel plate a a tendeny to develop loal bending of te plate de to te eentriity of ating fore. And te trengt beome a little bit maller tan te p-ot relt. Terefore, it an be aid tat te Eq.(11) i a ear trengt eqation for te td welded on tin teel plate. Moreover, te eqation form wa determined nder te engineering jdgment to make te gradient of te eqation oinide wit p-ot ear trengt one of Eq.(1) and to pt te interept of te eqation zero. b) Conidering edge ditane Sear tet for ingle ear rfae by tenile load A noted earlier, generally in te p-ot ear tet, te ear trengt i ardly affeted by edge ditane of te onrete. However, in te ear tet by tenion type loading for ingle ear rfae, te ear trengt of te td eem to be inflened by edge ditane. Te ratio of te pre over to te lengt of td ank {(e-d /)/ } i employed a a edge ditane parameter a well a te pll-ot ( d ) ( N mm) 77(77)

10 Q/Q Edge ditane parameter e = ( e d ) Fig. 14 Relationip between Q/Q and edge ditane parameter S Q e αq = =.4919 ( R =.957) Q d Q/Q given by eq.(11) a Edge ditane parameter e Fig. 16 Comparion between meared ingle ear apaity and etimated load by Eq.(1) and Eq.(11) 4 Eq.(1) Eq.(11) Reded 8% Reded 7% Q/Q a (e -d /)/ Edge ditane parameter e Fig.15 Fitting of an etimating eqation baed on mltiple regreion analyi (e) trengt. Fig. 14 ow te relationip between te ear fore ratio [experimental vale/ allated vale of Eq.(11)] and edge ditane parameter (wole data i 118 own in Table 5). It i reognized from ti figre tat te ear fore ratio of ordinate onverge rogly to 1. wen te edge ditane parameter exeed.. Ti mean te ear trengt of te td i ardly inflened by edge ditane for te range of edge ditane parameter over. a well a te pll-ot trengt. Ten, for only te data of te edge ditane parameter nder. in Fig. 14, te linear regreion eqation wa obtained wit iger orrelation wit te orrelation oeffiient of.957 (See Fig. 15). Terefore, te trengt eqation for te affeted range of edge ditane {(e-d /)/.} i given by linear fntion, and te following redtion fator ( p ) an be introded. q d e Q 1 = Q (1) A own in Fig. 16, te teted data were plotted Meared ingle ear apaity Q ( 1 N) R =.956 Reded 8% Reded 7% Callated ingle ear apaity Q ( 1 N) Fig.17 Comparion between meared ingle ear apaity and etimated load by Eq.(1) onidering edge ditane wit te pre over of edge ditane parameter a abia and te ear fore ratio a ordinate, and te Eq.(1) wit te oeffiient given by Eq.(1) and Eq.(11) for te range of {(e-d /)/.}.wa drawn on te figre (ame data nmber a Fig. 14). d 1 e Q = 1. A d (1) From Fig. 16, it i oberved tat te Eq.(11) i linked to Eq.(1) at te edge ditane parameter eqal to., and te relation between te edge ditane parameter and te ear fore ratio an be expreed a a bi-linear rve. Frtermore, 7% and/or 8% redtion vale of Eq.(11) and Eq.(1) are drawn in Fig. 16. From te figre, te 7% redtion rve of Fig. 16 eem to be te lower bond of teted data. A by all te tet data of 118 and taking te edge ditane parameter into onideration, te tet vale 78(78)

11 were ompared wit te allated one a own in Fig. 17. A i lear from te figre, tog te allated vale give te medim of experimental one in te range of le tan kn, te experimental vale in te range of more tan kn tend to take a le vale tan te allated one. However, beae of te ig orrelation oeffiient of.956, it wa jdged tat te trengt eqation for ear trengt of te td wit ingle ear rfae an be given by Eq.(11) and Eq.(1). Moreover, it an be een te 7% redtion vale of Eq.(11) and Eq.(1) well expree te lower bond of attering data. Terefore, te redtion rve an be employed a te deign trengt formlae wi take te attering of teted data into aont. 4. CONCLUSIONS Firtly, in ti paper, te trengt eqation of te pll-ot and ear trengt of te td, propoed by previo reeare and peified in deign andbook were introded, and by preenting a problem from te degree of onformity for te exiting teted data, te neeity of preenting te trengt eqation of te td wa empaized. Seondly, te tatitial proeing wa arried ot for te exiting teted data inlding te data obtained by ator, and ten, te trengt eqation for bot te pll-ot and ear trengt of te td were derived rationally. Finally, te deign trengt formlae wi take te attering of teted data into aont were alo propoed by introding te redtion fator. Ti tdy i mmarized a follow. (1) Te pll-ot trengt eqation of te td wa derived by reviing of trengt eqation peified in PCI. For te pll-ot trengt of te td ignoring edge ditane, Eq.(7) wa propoed by formlating in te form of te prodt of projeted area of te ear one and te tenile trengt of te onrete. Ten, for te pll-ot trengt eqation of te td onidering edge ditane, te vale dividing te pre over tikne by te lengt of td ank {(e-d /)/ } wa newly introded a an edge ditane parameter, and te Eq.(9) wa propoed for te edge ditane parameter nder.. In addition, te Eq.(9) i linked to te trengt eqation of Eq.(7) wi i naffeted by edge ditane at {(e-d /)/ }=.. () Te validity of te p-ot ear trengt eqation of Eq.(1) propoed by Hiragi and Mati wa ertified tatitially, and adopted erein a te p-ot ear trengt eqation of te td. Epeially, a for te p-ot ear trengt, te data inlding fine diameter td (mm) teted in ti tdy old be arately rearranged. () Sear trengt for doble ear rfae of inner onrete and for ingle ear rfae ow a little lower vale in omparion wit p-ot ear trengt. A te ear trengt eqation of tee ae, Eq.(11) tat pt te interept of te p-ot ear trengt eqation to zero an be propoed in te ae of ignoring edge ditane. In addition, a te ear trengt eqation for ingle ear rfae of te td onidering edge ditane, te Eq.(1) wa propoed by ing a new edge ditane parameter {(e-d /)/ } for te parameter nder. a well a pll-ot trengt eqation. In addition, te Eq.(1) i linked to te Eq.(11) wi i naffeted by edge ditane at {(e-d /)/ }=.. (4)Te 7% redtion vale of pll-ot and ear trengt eqation of te td propoed erein an be adopted a deign vale onidering te attering of teted data. ACKNOWLEDGEMENT Ti tdy wa ondted a a joint reear of te RCJ (Reear grop of Compoite Joint). Te ator wi to expre teir gratitde to te preio ontribtion of te reear member of Nippon Std Welding Co., Mato Bridge Contrtion In. and Japan Information Proeing Co. And, te ator wold like to aknowledge tdent of Oaka Univ. and Setnan Univ. in te laboratory tet. REFERENCES 1) Maeda, Y., Mati, S. and Hiragi, H.: Effet of Conrete- Plaing Diretion on Stati and Fatige Strengt of Std Sear Connetor, Tenology Report of te Oaka Univerity, Vol., No.17, pp.97-46, 198. ) Matzaki, I.: Te Eartqake-proof Intallation Metod of te Eqipment -Type of te Anor and te Spport Load Capaity-, Te Contrtion Tenology of Aritetre, pp.1-51, 198. (In Japanee) ) Al-akkaf, A., Hiragi, H., Takabayai, K. and Mati, S.: Invetigation on Pll-ot and Sear Strengt of 6mm Std, Proeeding of te Japan Conrete Intitte, Vol., No1, pp , 1. 4) TRW, Nelon-Diviion: Embedment Propertie of Head Std, TRW-In., USA, p.47, ) Sattler, K.: Betratngen über nee Verdbelngen im Verbndba, Der Baingnier,7,H1, pp.1-8, ) Uteer, G.: Berteilnggrndlagen für Faadenveran -kerngen, Berlin, Ernt & Son, ) Eropean Convention for Contrtional Steelwork: Compoite Strtre, Te Contrtion Pre, ) Daft Eropean Reommendation on Compoite Strtre: CEB-ECCS-FIP- IABSE, Joint Committee on Compoite Strtre ) PCI Deign Handbook: Preat Pretreed Conrete, Pretreed Conrete Intitte, Ciago, Illinoi, ) Bode, H. and Roik, K.: Headed Std -Embedded in Conrete and Loaded in Tenion-, Paper preented at te ACI Annal Convention, Lo Angel, pp.61-88, ) MMakin, P. J., Sltter, R. G. and Fier, J. W.: Headed 79(79)

12 Steel Anor nder Combined Loading, AISC Engineering Jornal, pp.4-5, ) Otani, Y. and Fkmoto, Y.: Failre Beavior of Std Anor de to Pllot Tenion, Tenology Report of te Oaka Univerity, Vol.9, No.1981, pp.97-5, ) Sonoda, K., Kito, H., Nakajima, K. and Uenaka, K.: Sytemati Reear on Sear Tranfer Carateriti of Projeting Steel Plate, Jornal of Strtral meani and eartqake engineering, JSCE, No.598/I-44, pp.18-, (In Japanee) 14) AIJ: Deign Gideline and Commentary for Compoite Strtre, Part 4; Deign Gideline and Commentary for Anor Bolt, (In Japanee) 15) TRW, Nelon-Diviion: Nelon Std Projet No.8, Report No , ) TRW, Nelon-Diviion: Deign Data, Nelon Conrete Anor Std, Manal, No.1, ) Siraaka, Y., Matzaki, I., Abe, Y. and Uami, S.: Experimental Stdy on Loading Capaity of Spport Strtre (Embedding Metalli Material) for Piping Eqipment, Part-1. Pll-ot Strengt of Std Bolt Embedded in Conrete -, Te AIJ Convention Sientifi Letre Otline, pp , (In Japanee) 18) Siraaka,Y., Matzaki,I., Abe,Y. and Uami, S.: Experimental Stdy on Loading Capaity of Spport Strtre (Embedding Metalli Material) for Piping Eqipment -. Tenile and Sear Fatige Strengt of Headed Std wit 19mm diameter, Te AIJ Convention Sientifi Letre Otline, pp , (In Japanee) 19) Hiragi,H., Mati,S. and Fkmoto,Y.: Derivation of Strengt Eqation of Headed Std Sear Connetor Fatige Strengt, Proeeding of Strtral Engineering, JSCE, Vol.5A, pp.11-1, (In Japanee) ) Klingner, R. E. and Mendona, J. A. : Sear Capaity of Sort Anor Bolt and Welded Std: A Literatre Review, ACI Jornal, Proeeding Vol.79, No.4, ) Bailey, J. W. and Brdette, E. G.: Edge Effet on Anorage to Conrete, Civil Engineering Reear Serie,No.1, Te Univerity of Tenneee, Knoxville, ) Swirky, R. A., et al.: Lateral Reitane of Anor Bolt Intalled in Conrete, Report No.FHWA-CA-ST , California, Department of Tranportation, Saramento,1977. ) Kawagi, C.: An introdtion to Mlti-variable Linear Regreion Analyi, pp.-, 197. (In Japanee) 4) Okamra, H.: Limit State Deign Metod for Conrete Strtre, Conrete eminar 4, Kyorit-Sppann, pp.17, (In Japanee) 5) Takabayai, K., Al-akkaf, A., Mati, S., Kawaaki, T., Hiragi, H. and Iizaki, S.: Reear on Sear and Pll-ot Strengt of te Std wit 6mm Diameter, Pro. of te 54t Annal meeting of JSCE, I-A14, (In Japanee) (Reeived Agt 15, 1) 8(8)