Finite Element Analysis of Adhesive Steel Bar in Concrete under Tensile Load

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1 4th Intnational Confnc on Sstainabl Engy and Envionmntal Engining (ICSEEE 2015) Finit Elmnt Analysis of Adhsiv Stl Ba in Conct nd Tnsil Load Jianong Zhang1,a, Ribin Sh2,b and Zixiang Zhao3,c 1,2,3 Tongji Univsity, Shanghai, , China a zhangj@tongji.d.cn, bibin_sh@163.com, c2012zzx@tongji.d.cn Kywods: adhsiv anchoag tchnology; bond-slip lationship; finit lmnt analysis; stss distibtion; cack dvlopmnt Abstact. Accoding to th slts of pllot-tst fo adhsiv stl ba in conct, a bond-slip lationship on adhsiv intfac is stablishd. This lationship flcts ffct of som paamts, sch as ffctiv mbdmnt lngth, dill diamt, chaacts of ancho adhsiv, tc., on bonding stngth and slip of mixd intfac. Th finit lmnt mthod was sd fo th analysis of adhsiv anchoag systm. Th pll ot loading pocss was simlatd and a complt tnsion-displacmnt cv of th stl ba was obtaind by finit lmnt analysis. Th distibtion of stss and th dvlopmnt of cacks in conct can b dscibd in dtail accoding to nmical comptation. Th analytical slts coincid with th xpimntal slts which povd that th analysis modl is ffctiv and th paamts a liabl. Thogh a lag nmb of nmical calclations on adhsiv anchoag systm, th basic laws of stss distibtion in stl ba, adhsiv gl and conct a obtaind fo diffnt mbdmnt lngth. Th modl povids th analytical tools and basic mthod fo th analysis of adhsiv anchoag systm in mico-lvl. Intodction As a post-installd fixing tchnology, adhsiv ancho is widly sd in civil ngining fo installation of nonstctal componnt and bilding dcoation. Manwhil, with th sam tchniq, adhsiv stl ba is also widly sd in ngining constction o stctal bilding. Tst slts shown that th fail modls of adhsiv stl ba in conct a simila as thos of adhsiv anchos [1]. Whn th mbdmnt dpth is small, th conct co wold lad to fail. And whn th mbdmnt lngth is long than th citical lngth, th stl ba wold lad to fail. In addition to abov two fail modls, whn th mbdmnt dpth is lss than citical lngth, fail wold happn on mixd intfacs of adhsiv/conct intfac and adhsiv/stl intfac. It sms that th fail modl can b gnally contolld by th dsign of stl mbdmnt dpth, bt in fact, th fail mchanism of adhsiv stl in conct systm is comphnsiv. Whn th adhsiv stl ba is sd as infocmnt in conct stct, th stss distibtion and cack dvlopmnt in conct stctal lmnt wold b complx. Bcas of th limitations of xpimntal tchnology, many factos inflncing bonding stngth and stl dfomation cannot b obsvd o masd in micoscopic lvl. Finit lmnt analysis is an ffctiv mthod fo th stdy of intaction btwn adhsiv, conct and stl. By th slt of xpimntal sach and finit lmnt analysis, th bonding bhavio of adhsiv stl ba in conct can b dscib in dtail and in mico-lvl, with th loading pocss to fail. Basd on th nonlina finit lmnt analysis mthod, bonding dfomation of stl ba nd tnsil foctss distibtion and dvlopmnt of cack fo adhsiv stl ba in conct a obtaind. Th sach povids analytical modl in mico-lvl as th basis of sach. Bond-slip Rlationship Bond-slip lationship is th basic condition fo th finit lmnt analysis of adhsiv stl ba in conct. Th slts of pll ot tsts [1, 2] w sd to stablish bond-slip lationship. Rfnc [1] potd th pllot tst of 18 adhsiv stl spcimns. Th spcimns w gopd accoding to Th athos - Pblishd by Atlantis Pss 106

2 th mbdmnt lngth, which w 8d, 10d, 12d and 15d, wh d was th diamt of stl ba. Th stl ppad fo spcimn was a common podct as thos sd in bilding constction. Th adhsiv matial was th podct of Fisch (Taicang) Fixing Co. Ltd., FISV360S, which is a spcial podct fo mbdmnt of infocmnt in conct ngining. Th xpimnt was dsignd to pll th stl ba to fail nd tnsil load. Thogh obsving th xpimnt pocss, masing th citical loads and analyzing th fail mchanism, th bhavio of adhsiv infocmnt nd tnsil load was stdid and dscibd. Rfnc [2] potd oth 3 adhsiv stl ba spcimns in accodanc with th ffctiv mbdmnt lngth (8d, 10d and 12d). FISV360S was also sd fo th ppaation of th spcimn. Thogh obsving th xpimnt pocss, masing th displacmnt and stain of stl bas, th bhavio of adhsiv stl ba in conct was analyzd. Som poblms in adhsiv stl ba w discssdch as th fail pocss, th fail modl, th bond mchanism and th distibtion of sha stss. Th slts show that whn th ffctiv mbdmnt lngth is long than 15dtl fail wold happn. And whn th ffct mbdmnt lngth is 12d o lss, adhsiv intfac fail wold happn. Rslts fom th tst mntiond abov shown that th pllot pocss of th stl ba nd tnsil load cold b simplifid as shown in Fig.1. τ (N) τ Sliding fail phas τ τ Plastic bonding phas Elastic bonding phas Fig.1 Bond-slid lationship In Fig.1, mans th avag sha stss latd to th pll foc. s mans th displacmnt of th stl ba. Basd on nifom bond stss modl [3], th avag sha stss can b calclatd by th pll foc N : N. (1) Dh f S S S S(mm) Wh, D is dill diamt (mm); hf is ffctiv mbdmnt lngth of stl ba (mm). Fom th fom of th cv in Fig.1, th whol bond-slip pocss can b dividd into th phass, which a lastic bonding phas, plastic bonding phas and sliding fail phas. In th lastic bonding phas, th cv cold b simplifid as a amp staight thogh th oigin. Th citical point at th nd of lastic bonding phas is ( ). Cv of plastic bonding phas cold b simplifid as a paabola which vtx stands achivs bonding stngth ( ). And th cv of sliding fail phas cold b simplifid as a dcasing amp staight with th nd point ( ). By th statistic of xpimntal slts [1,2], th bond-slip lationship can b xpssd as Eqation (2) S (0 S S ) S S 0.96 S 0.52 ( S S S ) 2 S S S 5 S ( S S S ) S 5 S 5. (2) 107

3 Th Chins indsty standad, Tchnical spcification fo post-installd fastnings in conct stcts [4], gsss th dsign fomla basd on a vast tst slts of tnsion-sistanc baing capacity ( ), which is sitabl fo th pllot fail on adhsiv-conct intfac: N, pa N 5.6h D f. (3), pa f c Wh, f c is cb compssiv stngth of conct (MPa). In this way, th dsign fomla of ltimat bond stngth is: N /( Dh ) 5.6 / f. (4) f c Finit Elmnt Analysis Modl Finit lmnt analysis basd on ANSYS pogam was condctd fo th analysis of chmical anchoag systm. Th ANSYS modl diagam, with a qat of spcimn, is showd in Fig.2. In od to consid th intaction on th bonding intfac comphnsivly, th nonlina sping lmnts (Combin39 lmnt) a aangd on th cosponding nods to simlat th bond-slip lationship btwn adhsiv and conct. Th nods a btwn th intfac of adhsiv and conct. Th sis of spings psnt nomal intaction, longitdinal tangntial intaction and hoizontal tangntial intaction spctivly on th bonding intfac. Th lngth of th sping is simlatd na zo and th pfomanc of ach sping is dtmind by th foc-dfomation cv (F-D cv). Th bond-slip pfomanc of adhsiv-conct intfac is psntd by longitdinal tangntial sping, which F-D cv is confimd by th bond-slip lationship on adhsiv-conct intfac (Eqation 2). Considing itativ solving pocss of vaios sping lmnt lad to long comptation tim and poo astingncy, th sam F-D cv was adoptd fo diffnt longitdinal tangntial sping lmnts. On th oth hand, th adoption of simpl nifom bond stss modl can obtain an accptabl slt. (a) adhsiv spaation (b) adhsiv stoation (c) constaint imposition Fig.2 Finit Elmnt Analysis Modl Th F-D cv mntiond abov cold b divd fom th bond-slip lationship on mixd intfac fo adhsiv stl ba. Th bond-slip lationship can b obtaind by th xpimnt slt of load-displacmnt cv thoghot whol loading pocss. Accoding to th gssion analysis of tst slts, th lationship of bonding stss and slip can b dfind as th sgmntal phass. As to adhsiv band FISV360S, by statistical analysis of tst slts [1, 2] om indxs at th citical points ( ), ( ), ( ) can b calclatd ot, =6.790Mpa; =0.75 ; =0.5 ; S =1.26mm; S =0.35mm; S =5.00mm. Rplac th abov data into Eqation (3), th bond-slip lationship fo th analysis of th spcimn is: 108

4 14.44 s 0 s ( s) 2.05s 5.18s s (5) 0.91s s With th finit lmnt modl and th bond-slip lation, th loading pocss can b simlatd by comptation in vaios foms of slt. Fig 3 shows th slt of load-displacmnt lationship. Both th xpimntal slts and finit lmnt analysis slts w shown in on diagam fo compaison. With th fail modl of ba poll-ot, th displacmnt vals of spcimns with diffnt anchoing lngth nd diffnt load lvls a shown in Fig 3 (a) (b) (c). It can b sn that th calclating slts a qit coincid with th xpimntal slts. With th stl fail modl as is shown in Fig 3 (d), things is a littl bit diffnt. Bfo stl yilds, th stl displacmnt is mainly povidd by th slip on adhsiv-conct intfac and th calclating slts a qit clos to th xpimntal slts. Whn th stl yilds, th bonding foc nloading apidly, which lads to dcasing of slip on adhsiv intfac. (a)h f =8d (b) h f =10d (c) h f =12d (d) h f =15d Fig.3 Compaison of load-slip cv Bhavio of Adhsiv Anchoag Systm Bonding Stss Distibtion. With th finit lmnt analysis modl as discssd abov, th bhavio of adhsiv stl ba in conct can b analyzd in dtail. Th bonding stss distibtion fo th spcimns with diffnt mbdmnt lngth nd diffnt load lvls a shown in Fig 4, in which th ffctiv mbdmnt lngths a 8d, 10d, 12d, 15d, in accodanc to (a) (b) (c) (d). Th diffnt cvs man diffnt slid displacmnt latd to diffnt lvl of loading. Th slt psnts that in th initial phas of loading, th bonding stss distibtion is nvn and th maximm stss appad na th conct sfac of loading. In lat phas of loading, th stss distibtion along th mbdmnt dpth tnds to an vn distibtion. In addition to a stss incasing phas on loading sid and a stss dcasing phas on th nd of ba, th bonding stss sms vn distibtion along th st middl pat of th ba fo spcimns of Fig. 4(a)(b)(c), fo mixd intfac fail modl. Th intfacial bond-stss distibtion of Fig. 4(d) is diffnt fom 109

5 oth th, as th spcimn faild in stl yild. Th stss dcass along th mbdmnt dpth of th stl, not in vn distibtion fom. (a) h f =8d (b) h f =10d (c) h f =12d (d) h f =15d Fig.4 Bond-stss distibtion on adhsiv-conct intfac Cack Distibtion and Dvlopmnt. To val th distibtion and dvlopmnt of cack on adhsiv anchoag systm, on of th spcimns with ffctiv mbdmnt lngth of 8d, was analyzd with finit lmnt mthod. As is shown in Fig 5, 4 lvls of tnsil foc is xpssd as displacmnt of ba, 0.005mm, 0.26mm, 0.37mm, 1.02mm. Whn th tnsil foc is small, as is shown in Fig.5 (a), th tnsil stss in conct is in vn distibtion along th anchoag hight of ba. Th adhsiv lay is also in tnsion along th stl ba. With th incas of th tnsil foc, Fig 5 (b) and (c) shows th dvlopmnt of stss distibtion and cack in conct. Th slant cacks appad fist at adhsiv-conct intfac wh pak bond stss xistd. Slant cacks xtndd to conct sfac and fomd conct invtd con. In th wak of intfacial pak bond stss, cacks xtndd gadally to intio along th mbdmnt ba. Th conct invtd con fomd continosly with th dvlopmnt of cacks along th mbdmnt stl ba. Fig 5 (d) shows th stss distibtion at th lat phas of loading. Sval onds of invtd con typ cacks fomd along th mbdmnt dpth. Bcas of lack of constaint by conct at th sfac of th spcimn, th shallow invtd conct con wold b fomd ali than th dp cons. Th conct con lavs away fom th conct body as th stl was plld ot with sliding. (a) s=0.005mm (b) s=0.26mm (c) s=0.37mm (d) s=1.02mm Fig.5 Cack dvlopmnt in conct 110

6 Distibtion of Longitdinal Nomal Stss. Fig 6 is a longitdinal stss diagam on adhsiv stl ba systm whn mbdmnt lngth is 8d. Th tnsil stss of ba is dcasd with th incas of mbdmnt lngth. Majoity of ancho adhsiv is compssd and top con pat of it is in tnsion. Majoity of conct sbstat is compssd and top con pat of it is in tnsion. (a) FEA modl (b) Stl ba (c) Adhsiv gl (d) Conct block Fig.6 Axial stss distibtion Conclsions Th th-phas bond-slip lationship, basd on th slts of pllot-tst of adhsiv stl ba in conct, can b sd in finit lmnt analysis of th anchoag systm. Th bond-slip lationship flcts th ffct of paamtsch as ffctiv mbdmnt lngth, dill diamt, chaacts of adhsiv, tc., on bonding stngth and slip of adhsiv intfac. Th analytical slt coincids with th xpimntal slt, which povs that th analysis modl is ffctiv and th paamts a liabl. Th bonding bhavio and fail modl of adhsiv stl in conct can b stdid fficintly by finit lmnt analysis mthod. With th poposd FEA modl, a lot of xpimnt cold b savd and placd by digital analysis. Th bonding stss distibtion on adhsiv intfac, th distibtion and dvlopmnt of cack in conct, th distibtion of stss in stl, adhsiv and conct fo diffnt anchoing sampl in whol loading pocss can b xpssd in dtail thogh digital comptation. Acknowldgmnts This wok was financially sppotd by National Natal Scinc Fondation of China ( ). Rfncs [1] Jianong Zhang, Lizhong Shi, Jin W, Xin Zhang and Mngwi Zhang: Expimntal Rsach on th Bhavio of Adhsiv Rinfocmnt nd Tnsil Load, Stctal Engins [J]. Vol.20-5(2004), p.47-51, in Chins. [2] Jianong Zhang, Lizhong Shi, Jianha Yang, Jin W, Xin Zhang and Mngwi Zhang: Expimntal Rsach on th Bhavio of Chmical Adhsiv Stl Ba in Conct nd Tnsil Load [J]. Bilding Stct, Vol.36-3(2006), p.17-21, in Chins. [3] Ronald A. Cook, Mmb, ASCE. Bhavio of Chmically Bondd Anchos [J]. Jonal of Stctal Engining, Sptmb, 1993, Vol.119(9), [4] Tchnical Spcification fo Post-installd Fastnings in Conct Stcts(JGJ )[S], Indsty Standad of th Popl Rpblic of China, in Chins. [5] Michal McCay, Ronald A. Cook, Kailash Kishnamthy. Pllot Simlation of Post-installd Chmically Bondd Anchos [J]. Jonal of Stctal Engining, Sptmb, 1996, Vol.122(9),