INVESTIGATION ON THE SHEAR OF FIBER REINFORCED CONCRETE BEAMS CONSIDERING VARIOUS TYPES OF FIBERS

Transcription

1 - Tehnal Paper - INESTIGATION ON THE SHEAR OF FIBER REINFORCED CONCRETE BEAMS CONSIDERING ARIOUS TYPES OF FIBERS Ptha JONGIATSAKUL *, Koj MATSUMOTO *, Ken WATANABE * and Junhro NIWA * ABSTRACT Ths paper presents the evaluaton of shear arred by fbers n fber renfored onrete beams (FRC) usng tenson softenng urves. Four FRC beams wth varous knds of fbers, whh were made by steel wth length of mm and mm, polypropylene wth mm length, and polyvnyl alohol wth mm length, were tested. The tenson softenng urve was used for alulatng the fore transferred aross the dagonal rak from ts wdth, whh was measured through the mage analyzng system. The alulated shear arred by fbers showed good orrespondene wth the expermental results. Keywords: shear arred by fbers, steel fbers, polypropylene fbers, polyvnyl alohol fbers, tenson softenng urves. INTRODUCTION Shear falure of renfored onrete (RC) beams s known to be brttle and atastroph. After the ourrene of dagonal rak, the tensle stress at the rak surfaes rapdly softens and t leads the sudden falure of RC beams. To prevent the shear falure, the JSCE standard spefatons [] have requred a large amount of shear renforng bars. It auses the dffulty n fllng onrete n onstruton stes. The use of fbers as shear renforement s one of the solutons for redung the shear renforng bars n the strutures wthout losng the shear strength. Many researhers [, ] have reported the effetveness of fbers as shear renforement, foused exlusvely on steel fbers. The JSCE desgn gudelnes for renfored onrete pers wth steel fbers [] have regarded steel fbers as the renforement of onrete strutures. The nrement of shear strength by steel fbers has been expressed as a value, whh was defned as a rato of the shear arred by steel fbers to the shear arred by onrete and was equal to.. Nevertheless, Watanabe et al. [] onluded that all of the expermental values of ( exp ) were more than.. The post-rakng behavor of fber renfored onrete beams (FRC) was not onsdered n the desgn gudelnes. The authors (Jongvvatsakul et al. []) proposed the evaluaton method of shear arred by steel fbers by applyng the frature mehans wth shear behavor. The method was valdated wth the fber renfored onrete beams wth steel fbers havng length of mm. Reently, synthet fbers have beome more attratve than before due to ts effetveness for mprovng shear strength [] and relatvely nexpensve omparng wth steel fbers. However, the nfluene of synthet fbers and fber length on shear arryng mehansm of FRC beams has not been deeply nvestgated and understood. The objetve of ths paper s to nvestgate the shear arred by both steel and synthet fbers. The shear resstng mehansm of four FRC beams wth varous knds of fbers (.e. materal type and length) s examned. The evaluaton method of shear arred by fbers usng tenson softenng urves [] s verfed n order to onfrm ts applablty for nvestgatng the shear apaty of FRC beams wth varous fbers.. EXPERIMENTAL PROGRAM. Materals () Conrete The materals used n ths study were hgh-early strength portland ement, sand, oarse aggregates, and hgh-performane ar-entranng water-redung agent. Table shows the mx proporton of onrete. () Fbers Four types of fbers were norporated nto onrete nludng steel fbers wth length of mm (SF) and mm (SF), polypropylene fbers (PP) and polyvnyl alohol fbers (PA). Propertes of fbers used n ths study are summarzed n Table. The surfae of SF, SF and PA fbers was ompletely smooth, whle the surfae of PP fber was rough. The nterseton of two dagonal lnes was observed on the surfae of PP fber. The volume fraton of fbers was dental as.% of full volume of onrete n all spemens. () Renforng materals The longtudnal renforng bars were deformed steel wth. mm of the nomnal dameter and yeld strength of N/mm. The strrups wth deformed steel of mm n the nomnal dameter were arranged as * Ph. D. Canddate, Graduate Shool of Sene and Engneerng, Tokyo Insttute of Tehnology, JCI Member * Assstant Prof., Dept. of Cvl Engneerng, Tokyo Insttute of Tehnology, Dr. E., JCI Member * Assstant Senor Researher, Conrete Strutures, Ralway Tehnal Researh Insttute, Ph. D., JCI Member * Prof., Dept. of Cvl Engneerng, Tokyo Insttute of Tehnology, Dr. E., JCI Member

2 Table Mx proporton of onrete G max Unt weght (kg/m ) W/C (mm) W C S G SP G max = maxmum sze of oarse aggregate, W = water, C = ement, S = fne aggregate, G = oarse aggregate, SP = hgh-performane arentranng (AE) water-redung agent Table Propertes of fbers Tensle L Densty E Shape of Name (mm) (mm) (kg/m strength ) (GPa) the end (MPa) SF. 8 Hooked SF.9 8 Hooked PP.. 9 Straght PA. 9 Straght L = Length, = Dameter, E = Elast modulus : Stran gauge Test span D C L Fg. Detal of a FRC beam LED Spemen 8 Targets Fg. Preparaton of loadng test D Unt: mm Three ameras the shear renforement. The yeld strength was N/mm. Two round bars wth the dameter of mm were used as ompresson bars wth the yeld strength of N/mm.. Test Spemens Fg. shows the dmenson and renforng bars arrangement of a FRC beam. The spemens were retangular FRC beams. The shear span (a) was mm and effetve depth (d) was mm. The shear span to effetve depth rato (a/d) was.8. The longtudnal renforement rato (p w ) was.%. All spemens were ontrolled to fal n the rght shear span by provdng the less number of strrups n the rght shear span as shown n Fg.. Strrups rato n the test span (r w ) was.% n all spemens. Four FRC beams were prepared, varyng the type of fbers. The spemens were named aordng to the type of fbers used n the beams.. Loadng Methods Spemens were subjeted to a four-pont bendng wth smply-supported ondton as llustrated n Fg.. Steel plates wth mm wdth were plaed on the pn-hnge supports. Teflon sheets and grease were nserted between a spemen and supports n order to prevent the horzontal frton. At loadng ponts, the steel plate wth mm wdth and mm length were also plaed. Fg. shows the detaled loadng arrangement along wth the loatons of loadng ponts and stran gauges.. Measurements Measurng tems were the appled load, dsplaements of md span and supportng ponts usng four transduers, and stran of longtudnal steel bars and strrups. The stran of longtudnal steel bars was measured at md span by stran gauges whle the strans of strrups were measured at the loatons that dagonal rak was expeted to our as shown n Fg.. In addton, the rak surfae dsplaement (u), whh s the total dsplaement of rak on the dreton of prnpal tensle stran, was measured from the mage analyzng system developed by Hgash et al. []. A pture of loadng test s shown n Fg.. In order to perform the mage analyss, red targets wth dameter of mm were attahed on the spemen surfae wth an nterval of mm. The mage analyzng system an nvestgate the oordnate of these targets throughout the test span. As a result, the rak surfae dsplaement an be alulated. Durng the loadng test, photos of the spemen were taken by every kn of the shear fore usng three dgtal ameras fxed on trpods. However, sne the dagonal rak was expeted to open rapdly near the peak load, some ptures were taken near the peak load wth short tme nterval n order to apture the behavor at the peak exatly. Besdes, the length and angle of dagonal rak were measured from the vsble dagonal rak at the peak load by usng the software system, whh supports analytal funtons from mage measurement to statstal data proessng. The albraton proess was onduted to defne the length of one pxel n the mage for the purpose that the measurement data n a pxel an be onverted to the atual lengths. The mages taken for measurng the rak surfae dsplaements were also used to measure the rak length and angle of dagonal rak at the peak.. CALCULATION OF SHEAR FORCES AND EALUATION OF SHEAR CARRIED BY FIBERS. Calulaton of Shear Fores n FRC Beams Consderng the fore atng at the dagonal rak n a FRC beam subjeted to pont loads (Fg. ), t an be seen that the shear fore s ressted by the shear arred by onrete ( ), the shear arred by strrups ( s ) and the shear arred by fbers ( f ). Consequently, the shear apaty () of fber renfored onrete beams s smplfed as: () s f

3 Dvded elements Strrup Dagonal rak Table Propertes and expresson of tenson softenng urves C Type f ' f t G F (N/mm )(N/mm Expresson ) (N/mm).. u for u. mm SF... σ. 8. u for u. mm.. u for u. mm s f of one element SF.9.. σ T.. u for u. mm. 9. u for u. mm mm PP σ.. 8u for u. mm f L. 8. u for u. mm PA σ.. 9u for u. mm Fg. Free body dagram of a FRC beam f ': ompressve strength, f t : tensle strength, G F : frature energy C L Heght (mm) (N/mm ) Heght (mm) 8 Compresson zone Regon of nterest u (mm) (N/mm ) (a) Pture of a FRC beam at peak (b) u dstrbuton () Tenson softenng (d) Stress dstrbuton load (SF) urve Fg. Investgaton of tensle stress transferred aross the dagonal rak Regon of nterest The shear arred by onrete ( ) was alulated from Eq. followng the JSCE desgn gudelnes []. Shear arred by strrups ( s ) was obtaned from Eq.. Hene, the expermental value of shear arred by fbers ( fexp ) an be obtaned from Eq... f / d p b d () s Aw f wy zotθ/s () fexp () exp s where, f s the ompressve strength of onrete (N/mm ), d s the effetve depth (mm), p w s the longtudnal renforement rato, b w s the web thkness (mm), A w s the ross seton area of strrups (mm ), f wy s the yeld strength of strrups (N/mm ), z s the dstane from loaton of ompressve stress resultant to entrod of tenson steel (z=/8d) (mm), s the angle between the dagonal rak and horzontal lne (degree) (see n Fg. ), s s the strrups spang (mm), and exp s the expermental value of shear apaty (kn). Furthermore, aordng to the JSCE desgn gudelnes [], the shear apaty of FRC members an be predted by usng Eq.. Thus, the expermental value of exp ) an be alulated by Eq.. However, t s noted that Eq. was proposed for steel fber renfored onrete members. w w al exp κ s () κ / () fexp where, al s the predted shear apaty (kn) and s the oeffent representng the effet of fbers (=.) [].. Evaluaton Method of Shear Carred by Fbers The authors [] have proposed the evaluaton method of shear arred by steel fbers usng tenson softenng urves. Tensle stress transferred aross the dagonal rak () an be onverted from the rak surfae dsplaement (u) usng relatonshp between tensle stress and rak openng dsplaement of tenson softenng urves as shown n Fg.. In order to evaluate the shear arred by fbers presely, the spemens were dvded nto elements wth a heght of mm (Fg. ) orrespondng to the nterval of red targets n the mage analyss. Crak surfae dsplaement (u ), length (L ), angle of prnpal tensle stran ( ), and angle of a dagonal rak ( ) of eah element were nvestgated. By onsderng the fore atng at a dagonal rak n a FRC beam due to the effet of fbers (Fg. ), the fore ressted by fbers was equal to the stress multpled by the area of rak surfae normal to dreton of. The stress and shear fores were alulated for element by element. The fore along the dagonal rak was obtaned from the porton below the ompresson zone to the tp of

4 Stress, (N/mm ) Experment Expresson.. Crak surfae dsplaement, (a) SF dagonal rak n the tenson zone and ths zone was alled the regon of nterest as seen n Fg.. The ompresson zone was the heght of spemens from the top surfae to the loaton of neutral axs at the peak, whh was alulated from the dsplaements of targets obtaned through the mage analyss. The tp of dagonal rak stopped at the loaton of tensle bars. The summaton of fores n regon of nterest was the shear arred by fbers. Consequently, the shear arred by fbers ( fal ) an be expressed as follows []: n fal σ b L β θ 9snβ w os () where, n s number of elements n the regon of nterest (n=), s the tensle stress of element (N/mm ), L s the length of dagonal rak of element (mm), s the angle of prnpal tensle stran of element (degree), and s the angle of dagonal rak of element (degree). Ths method [] was valdated for evaluaton of shear arred by steel fbers havng length of mm wth hgh auray. However, t has not been extended to fber renfored onrete beams wth varous types of fbers yet.. TENSION SOFTENING CURES.. Crak surfae dsplaement, The tenson softenng urves were obtaned from the bendng tests of nothed beams onduted aordng to the standard of JCI []. The tenson softenng urves of four types of fber renfored onrete are shown n Fg.. Table lsts the ompressve strength and frature energy of onrete of those nothed beams. By usng a least-square Stress, (N/mm ) Stress, (N/mm ) Stress, (N/mm ).. Crak surfae dsplaement, data-fttng proedure based on soluton of an nverse, the shape of blnear urves of tenson softenng dagram an be obtaned as shown n Table. As seen n Fg., the tenson softenng behavor was dfferent dependng on type of fbers. SF an resst the hghest stress n post-peak regon. Steel fbers (SF and SF) an transfer hgher stress than synthet fbers (PP and PA). Two knds of fbers falure were observed n the nothed beam tests. SF and SF were faled n pulled-out mehansm whle PP and PA showed both pulled-out and ut-off mehansm. It was beause steel fbers had hgher tensle strength than PP and PA.. EXPERIMENTAL RESULTS.. Crak surfae dsplaement, (b) SF () PP (d) PA Fg. Tenson softenng urves Table Summary of the alulaton and expermental results Conrete propertes Informaton of dagonal rak Calulaton and expermental results Spemen f ' f t u avg L β avg exp s fexp exp fal fexp / fal (N/mm ) (N/mm ) (mm) (mm) ( ) ( ) (kn) (kn) (kn) (kn) (kn) SF SF PP PA f ': ompressve strength, f t : tensle strength, u avg : average rak surfae dsplaement at the peak, L: total rak length at the peak, β avg : average angle of prnpal tensle stran at the peak, : angle between the dagonal rak and horzontal lne.. Effet of Fbers on Shear Behavor Table summarzes the onrete propertes, nformaton of dagonal rak, alulated shear fores and shear fores obtaned from the loadng tests of FRC beams. The shear apaty ( exp ) of SF was the hghest among four spemens. The dfferene of between eah spemen was slght sne the ompressve strength of onrete was not sgnfantly vared. Whereas s was ertanly dfferent n eah spemen due to the devaton of that was measured as the angle between the dagonal rak and the horzontal lne (Fg. ). The values of are presented n Table. SF provded the largest among all spemens. Fg. shows average stran of strrups n the test span. It was observed that strrups n the test span were yelded before the ultmate load. Synthet fbers (PP and PA) led the early yeldng of strrups before SF and SF due to the lower materals modulus of elastty. Consderng the shear arred by fbers, t was found that fexp of SF was the largest

5 SF SF PP PA Load (kn) Yeldng stran Load (kn) Heght of spemen (mm) Heght of spemen (mm) Dagonal rakng load Stran ( ) Defleton (mm) (a) u (mm) (b) (N/mm ) Fg. Strrups stran Fg. Load-defleton urves Fg. 8 Dstrbuton of u and at peak load u md (mm) md u md (mm) u md (mm) u md ( ( + s ) ( + s ) + s ) ( + s ) Load-defleton Defleton (mm) Defleton (mm) Defleton (mm) Defleton (mm) (a) SF (b) SF () PP (d) PA Fg. 9 Development of rak surfae dsplaement and defleton Load (kn) resultng n the largest shear apaty. The value of exp of SF and SF was more than.. On the other hand, exp of PP and PA was less than.. Steel fbers an enhane fexp more effetvely than synthet fbers. The dfferene of type of fbers aused the dfferene of exp, fexp and also the load level that strrups were yelded.. Load-Defleton Curves The relatonshp between the appled load and the md span defleton are presented n Fg.. The load-defleton response was lnear pror to rakng. After the ntaton of frst flexural rakng, the load-defleton response hanged to non-lnear behavor. Later, the dagonal rak was observed n the test span and propagated to loadng pont and support. In the pre-peak regon, the propagaton of dagonal rak stopped and the slope of load-defleton urve beame flat. Then the dagonal tenson falure ourred and onrete n ompresson zone was rushed. The same behavor of load-defleton response an be observed n all spemens.. Dagonal Crakng Behavor The dagonal rakng data, whh were u, L,, and, of eah element were nvestgated based on the ptures taken at the peak load. () Crak surfae dsplaement (u ) Fg. 8(a) presents the value of u along the heght of dagonal rak at the peak load. The dagonal rak surfae dsplaement was larger at around the mddle heght of spemens ompared wth the u at the top and the bottom of spemens beause there was Regon of nterest ompresson zone at top of spemens and restrant by longtudnal renforng bars at the bottom part of spemens. The regon of nterest was onsdered from - mm n all spemens orrespondngly n ths paper. Nevertheless, the nfluenes of types of fbers and strrup rato on the loaton of regon of nterest have not been learly understood yet. Therefore, a number of FRC beams wth varous types of fbers wll be tested n the future n order to larfy the loaton of regon of nterest. Table presents the average value of rak surfae dsplaement (u avg ) of the dagonal rak n the regon of nterest shown n Fg. 8. The result showed that u avg of SF was the wdest beause u around top surfae showed larger value than the other spemens. It s beause SF had longer length than other fbers and also effet of anhorage (hooked end). Fg. 9 shows the rak surfae dsplaements measured at the mddle heght of the spemens (u md ), where was mm, n the top horzontal axs together wth the load-defleton urve. It an be seen that u md of spemens wth both steel fbers and synthet fbers nreased drastally before the peak load. () Dagonal rak length (L) The rak length (L) s the length of a dagonal rak n the regon of nterest. PP and PA provded longer dagonal rak length than spemens wth steel fbers (SF and SF) as shown n Table beause the dagonal raks near the longtudnal steel bars had low nlnaton. () Angles of prnpal tensle stran ( ) and dagonal rak () Table presents the average value of n the regon of nterest. avg dd not hange sgnfantly

6 among these spemens. On the other hand, by onsderng, t was found that SF and SF revealed the steepest dagonal rak than the other spemens. Steel fbers provded the steeper dagonal rak than synthet fbers.. Calulated Shear Carred by Fbers The tensle stress transferred aross the dagonal rak at the peak load was nvestgated from rak surfae dsplaement and relatonshp of tenson softenng urves lsted n Table as mentoned n Seton.. Fg. 8(b) shows the stresses aross the dagonal rak n FRC beams at the peak load. The larger stress ould be ressted at top and bottom parts of spemens due to the smaller u. SF an resst the hghest stress resultng n the largest fexp whereas PP and PA ressted relatvely lower stress aross the dagonal rak. The stress dstrbuton of PA was not vared beause the slope of tenson softenng urve of PA was almost flat when u. mm. The shear arred by fbers ( fal ) was alulated by Eq. and summarzed n Table. Fg. presents the omparson of the expermental results and alulated values. The mean value of the expermental value to alulated value of the shear arred by fbers was. wth the oeffent of varaton (C..) of.%. Therefore, t an be mpled that the proposed method an evaluate the shear arred by fbers of FRC beams. Ths method an be used even the materal types and length of fbers were vared sne the tenson softenng urve an reflet the haraterst of eah fber. The applablty of tenson softenng urves to examne the stress transferred aross the dagonal rak of FRC beams was proved. However, due to the lmtaton of number of spemens n the present study, a number of spemens wth varous types of fbers should be tested n the future n order to valdate the applablty of the proposed method.. CONCLUSIONS () Shear apaty of FRC beams wth -mm steel fbers was the largest omparng wth -mm steel fbers, polypropylene and polyvnyl alohol beause -mm steel fbers revealed the hghest shear ontrbuton by fbers. () The value of exp was more than. n ase of steel fbers. On the other hand, exp of polypropylene and polyvnyl alohol was less than.. Steel fbers were more effetve as shear renforement than synthet fbers. () The spemen wth -mm steel fbers provded the wdest rak surfae dsplaement at the peak load beause of the effets of fber length and anhorage. However, t was most effetve to transfer stress aross the rak due to the good post peak regon of ts tenson softenng urve. () The ntensty of stress transferred aross the dagonal rak of FRC beams at the peak load an be ranked from the hghest ntensty as the beam fexp (kn) 8 8 fal (kn) Fg. Comparson of fexp and fal wth -mm steel fbers, -mm steel fbers, polypropylene and polyvnyl alohol, respetvely. In FRC beams, steel fbers an transfer more stress aross the dagonal rak than synthet fbers resultng n the hgher shear transferred fore by fbers. () The evaluaton method of shear ontrbuton of fbers was presented. The alulated shear arred by fbers showed good agreement wth expermental results even varous materal types and length of fbers. ACKNOWLEDGEMENT The authors aknowledge the support from the Center for Urban Earthquake Engneerng (CUEE). REFERENCES SF SF PP PA [] JSCE, Standard Spefatons for Conrete Strutures-, Strutural Performane erfaton, JSCE Gudelnes for Conrete, No.,, pp. -8. [] L,. C., Ward, R., and Hamaza, A. M., Steel and Synthet Fbers as Shear Renforement, ACI Materals Journal, ol. 89, No., Sept.-Ot. 99, pp [] Watanabe, K., Kmura, T., Kodama, T., Kta, S., Odera, I., and Nwa, J., Shear Renforement for RC Lnear Members by a Combnaton of Steel Fbers and Shear Renforng Bars, Journal of Materals, Conrete Strutures and Pavements, JSCE, ol., Jul. 9, pp. -. (n Japanese) [] JSCE, Gudelnes of Desgn for RSF Pers, Conrete Lbrary 9, 999, p.. (n Japanese) [] Jongvvatsakul, P., Watanabe, K., Matsumoto, K., and Nwa, J., Evaluaton of Shear Carred by Steel Fbers of Renfored Conrete Beams Usng Tenson Softenng Curves, Journal of Materals, Conrete Strutures and Pavements, JSCE, ol., No., Ot., pp. 9-. [] Hgash, H., Watanabe, K., and Nwa, J., Image Analyss for Falure Mode of RC Beams wth Fratured Longtudnal Renforement, Proeedngs of the JCI, ol., No., Jul. 9, pp. -. (n Japanese) [] JCI, Method of Test for Frature Energy of Conrete by Use of Nothed Beams, Japan Conrete Insttute Standard,.