In-Plane Shear Behavior of SC Composite Walls: Theory vs. Experiment

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1 Tranation, MiRT, 6- November,, New Delhi, India Div-VI: Paper ID# 764 In-Plane hear Behavior of C Compoite Wall: Theory v. Experiment Amit H. Varma, ai Zhang, Hoeok Chi 3, Peter Booth 4, Tod Baker 5 Aoiate Profeor, hool of Civil Engineering, Purdue Univerity, Wet Lafayette, IN, ahvarma@purdue.edu PhD Candidate, hool of Civil Engineering, Purdue Univerity, Wet Lafayette, IN, kai-zh@purdue.edu 3 Reearh ientit, Bowen Lab, Purdue Univerity, Wet Lafayette, hhi@purdue.edu 4 PhD Candidate, hool of Civil Engineering, Purdue Univerity, Wet Lafayette, IN, boothpn@purdue.edu 5 Fellow Engineer, Wetinghoue Eletri Corporation, Cranberry Townhip, PA, bakerth@wetinghoue.om ABTRACT The in-plane hear behavior of teel-plate ompoite (C) wall i different from that of reinfored onrete (RC) wall with orthogonal grid of longitudinal and tranvere rebar. In C wall, the teel plate ontribute not only their longitudinal and tranvere trength, but alo there in-plane hear tiffne and trength to the behavior of the ompoite etion. The in-plane hear loading produe prinipal tenion and ompreion fore in the ompoite C etion. The prinipal tenion aue the onrete to rak, and after raking the onrete andwih behave like an orthotropi plate with negligible tiffne in the prinipal tenion diretion but ignifiant tiffne and ompreive trength in the prinipal ompreion diretion. Thi paper preent a imple mehaniti repreentation of thi omplex in-plane hear behavior of C ompoite wall, and a deign equation for alulating their in-plane hear tiffne and trength. Thee equation are ompared and evaluated uing exiting experimental reult. Additionally, thee equation are further onfirmed by onduting a large-ale in-plane hear tet uing a unique tet etup and approah. The experimental reult inluded the meaured yli hear fore-train repone of the C panel, the hear train, and the prinipal train meaured in the teel plate. The experimental reult are hown to verify the behavior theory. INTRODUCTION There i oniderable interet in the ue of teel plate ompoite (C) wall for afety related nulear failitie that are part of third generation nulear power plant. C ontrution an potentially be more effiient than reinfored onrete from ontrution heduling and trutural effiieny tandpoint. The in-plane hear behavior of thee C wall i the primary lateral load reiting mehanim in thee truture. The in-plane hear behavior of the C ompoite wall i governed by the plane tre behavior of the teel faeplate, and the orthotropi elati behavior of onrete raked in prinipal tenion. The teel headed tud provide ompoite ation by anhoring the teel faeplate to the onrete andwih. The deformed wire tie bar alo provide ompoite ation, but mot importantly they provide trutural integrity to keep the ompoite etion together. The teel-headed tud and the tie bar provide a eondary but important funtion to the in-plane hear behavior of C ompoite wall. BACGROUND Conduting pure in-plane hear tet i extremely hallenging, and there are only a few laboratorie in the world apable of ubjeting wall panel to pure in-plane hear loading to determine their fundamental behavior and yli performane. Ozaki et al. [] have onduted uh pure in-plane hear tet on C wall panel uing peially deigned tet etup and peimen. The tet etup wa apable of ubjeting C wall panel peimen to yli in plane hear loading. The tet peimen were 47.5 x 47.5 in. in plan, and in. in thikne. The peimen had peial grip region at the edge to failitate the appliation of in-plane hear fore. Table ummarize the detail of three of the peimen teted by Ozaki et al. [] by ubjeting them to pure in-plane hear. It i important to note that Ozaki et al. [] teted everal more peimen ubjeted to light axial ompreion ombined with in-plane hear that are not diued further here. A hown in Table, the plate lenderne (/t ) defined by the paing of the hear onnetor and the thikne of the teel plate wa approximately equal to 3. The primary variable between the three peimen wa the teel plate thikne (t ), whih alo repreent the teel reinforement ratio (alulated at t /T). The teel plate reinforement ratio were approximately equal to.3%, 3.%, and 4.5% for peimen --NN, 3--NN, and 4--NN, repetively.

2 In-Plane hear Fore (kn) In-Plane hear Fore (kn) In-Plane hear Fore (kn) Tranation, MiRT, 6- November,, New Delhi, India Div-VI: Paper ID# 764 Table. Detail of Pure In-Plane hear peimen Teted by Ozaki et al. [] peimen Plate thikne tud diameter tud paing F /t y f (t ) in. (d) in. () (ki) (ki) --NN NN NN The peimen were ubjeted to yli hear train γ hitory oniting of yle at.5,.,., 3., 4., 6., and x -3. The envelope of the yli hyterei rule for peimen --NN, 3--NN, and 4--NN are how in Figure. Table how numerial value of the experimental reult for peimen --NN, 3-- NN, and 4--NN ubjeted to pure in-plane hear loading. It inlude the meaured the pre-raking tiffne ( unr ), raking hear fore ( t ), pot-raking hear tiffne ( r ), and the hear trength orreponding to the limit tate of teel plate yielding ( ) for the peimen. Table. Experimental Reult from Ozaki et al. [] and and Comparion with Analytial Value Experimental Reult Experimental Reult Analytial Value peimen unr (kip) t (kip) r (kip) (kip) unr unr t t r r NN NN NN The experimental reult indiated that a the teel plate beome thiker, the pot-raking hear modulu, the yield trength, and the maximum trength beome higher, and the hear train at maximum trength beome maller. Overall, all the peimen howed good behavior and dutility. The ultimate hear train reahed and exeeded at leat 6. x -3 under yli loading NN NN Conrete raking teel yielding Maximum trength In-Plane hear train(mm/mm) In-Plane hear train(mm/mm) 5 4--NN 4 3 Conrete raking teel yielding Maximum trength.5..5 In-Plane hear train(mm/mm) Figure. Experimental reult from Ozaki [] tet, and omparion with analytial model

3 In-Plane hear Fore Tranation, MiRT, 6- November,, New Delhi, India Div-VI: Paper ID# 764 MECHANIC BAED THEOR The in-plane hear behavior of C ompoite wall an be predited uing ompoite plate theory, while auming (i) iotropi elati plane-tre behavior for the teel faeplate, (ii) iotropi elati behavior for the onrete andwih before raking, (iii) orthotropi elati behavior of the onrete andwih after raking with zero tiffne in the prinipal tenile diretion perpendiular to raking, and 7 perent of the elati tiffne for the prinipal ompreive diretion parallel to raking, and (iv) Von Mie yield riterion for the teel faeplate. The fundamental in-plane behavior of C ompoite wall ha been developed by Ozaki et al. [], and alo by Varma and Maluhte []. The in-plane hear trength of C ompoite wall an be etimated a the tri-linear hear fore train urve hown in Figure. t =V n in unr r unr t r V G A f in n E A E A E G A 3 4 (.7E A E A A F y ) Equation Equation G A Equation 3 Equation 4 In-Plane hear train γ Figure. In-Plane hear Behavior Model The firt part of the urve i before onrete raking our. The in-plane hear tiffne ( unr ) an be etimated uing that of the ompoite etion hown in Equation. Conrete raking our when the applied hear fore ( ) exeed the raking threhold ( t ), whih an be alulated uing Equation. The raking threhold ( t ) orrepond to a onrete prinipal tenile tre (in pi) of (f ).5, where f i the ompreive trength in pi. The eond part of the urve i after onrete raking but before teel plate yielding. The in-plane hear tiffne ( r ) an be etimated a that of ompoite etion with orthotropi propertie for the 45 o raked onrete ( ) and plane tre propertie of the teel plate ( ), ee Equation 3. The third part of the urve orrepond to the onet of teel plate Von Mie yielding, whih our when the applied in-plane hear reahe or V n in given by Equation 4. In Equation to 4, G, E, and A are the hear modulu, elati modulu, poion ratio, and area of the teel in the ompoite etion. G, E, and A are the hear modulu, elati modulu, and area of the onrete in the etion. Thi mehani baed behavior model i ummarized briefly in Figure 3, whih how ritial tep in the derivation of the model and Equation -4 above. The model i preented in more detail in Varma and Maluhte [], and not repeated here for brevity. Figure 3 how (a) the in-plane fore and train, (b) the orreponding prinipal fore and train, () reulting onrete raking and orthotropi behavior, (d) ompoite etion fore equilibrium equation after raking, (e) the free body diagram for etion fore equilibrium, and (f) the reulting teel and onrete tree in the x and y diretion. Thee reulting teel tree were ued to etablih the ourrene of Von Mie yielding of the teel plate, whih reulted in Equation 4 for the in-plane hear trength. Figure inlude omparion of the in-plane hear model hown in Figure with the experimental reult from Ozaki et al. []. Numerial omparion of the pre-raking hear tiffne ( unr ), raking threhold ( t ), pot-raking hear tiffne ( r ), and in-plane hear trength ( ) are inluded in Table. The omparion in Figure and Table indiate that the in-plane hear model i a reaonable and onervative repreentation of the inplane hear behavior of C wall with /t ratio le than or equal to 3 and reinforement ratio up to 4.5%. In order to further verify the in-plane hear model, a unique large-ale in-plane hear tet wa onduted at Purdue Univerity, Bowen Laboratory a explained in the following ub-etion. 3

4 Tranation, MiRT, 6- November,, New Delhi, India Div-VI: Paper ID# 764 (a) In-plane fore and train (b) Prinipal fore, train, and diretion () Conrete orthotropi raking and behavior (d) etion fore equilibrium equation x y.7e T 4 x y E.7ET 4 x y Conrete raking (e) etion fore equilibrium free body diagram (f) Reulting teel and onrete tree teel tree x y t t t Conrete tree x y T T T Figure 3 ummary of in-plane hear behavior theory PECIMEN DETAIL A large-ale in-plane hear tet wa onduted to demontrate the yli behavior and dutility of C ompoite wall and to verify the mehani baed model. The thikne of the C ompoite wall peimen i denoted a T. The thikne of teel faeplate wa equal to t, and the nominal yield tre wa equal to 5 ki. The teel plate reinforement ratio (t /T) wa equal to 4.6%. hear onnetor were welded to the teel plate with a paing of.33 time of plate thikne (/t =.33). The nominal ompreion trength of infill onrete wa equal to 6 pi, and it wa made from.75-inh aggregate. The peimen wa a flanged hear wall with one web and two idential flange. The web repreented the C ompoite wall panel ubjeted to in-plane hear, and the flange wall were deigned to reit the orreponding overturning moment. Figure 4 how a piture of the tet etup with peimen in plae. The two onrete blok at the bottom were firt pot-tenioned to the peimen web. Then, the onrete blok were pot-tenioned down to the reation floor through hole in a teel bae plate. The peimen flange were further pre-tenioned to the teel bae plate through hole in the onrete bottom blok to prevent deompreion due to the overturning moment. Thu, the flange were deigned to reit the applied overturning moment, and have minimal (if any) ontribution to the in-plane hear, whih wa reited by the C wall peimen web. All the pot-tenioning wa verified to enure minimum loe. The peimen wa at along with a onrete top blok, where the onrete blok and onnetion were deigned to tranfer the applied hear fore and moment, if there i any, to the peimen. The in-plane hear fore wa applied uing four double-ating hydrauli ram. Eah ram had kip apaity for puh and 63-kip apaity for pull fore and -inh diplaement troke. The ram were attahed with levi and pin detail at both end to prevent retraint, and to large teel beam to pread the fore to the reation wall. Eletroni preure tranduer were ued to meaure the load applied by the hydrauli ram. 4

5 Tranation, MiRT, 6- November,, New Delhi, India Div-VI: Paper ID# 764 Figure 4 Photograph of In-Plane peimen and etup The tet wa terminated when the applied fore approahed kip, whih wa the deign apaity for afe operation of the tet etup. Exeive lippage of the etup on the laboratory floor wa oberved at the peak load. INTRUMENTATON Diplaement tranduer were ued to meaure the horizontal and vertial diplaement of the peimen, etup, the elongation and hortening of the web diagonal, and thu the hear train of the peimen. Clinometer were attahed to meaure the rotation of the top and bottom onrete blok and of the peimen. train gage roette and train gage were glued to meaure longitudinal, tranvere, and hear train at variou loation in the teel plate, and train in the tie bar. Intrumentation of the peimen i hown in Figure 5 (a) - (). A hown, the horizontal diplaement a the bae of the peimen jut above the onrete blok wa meaured uing DT7. The horizontal diplaement jut above the tet region of the peimen wa meaured uing DT8. The horizontal diplaement at the mid-height of the blok wa meaured uing DT9. Thu, DT8-DT7 meaure the horizontal diplaement (drift) of the 43 in. high tet region of the peimen. imilarly DT9-DT7 alo meaure the drift of the peimen. The rotation of the bottom onrete blok are meaured uing DC and DC. The rotation of the top onrete blok wa meaured uing DC3. Figure 5 (b) how the train gage layout for the wet fae of the peimen web. A hown, five point on the wet fae were intrumented with retangular train roette featuring three train gage eah. The grid of train gage roette overed an approximately 3 x 3 in. region of the peimen web. (a) enor Layout for Diplaement and Rotation (b) train Gage Layout for Wet Fae of Web Figure 5 Intrumentation of C Compoite Wall peimen 5

6 Tranation, MiRT, 6- November,, New Delhi, India Div-VI: Paper ID# 764 TET REULT The horizontal drift (DT8-DT7) were orreted to aount for the meaured bae rotation, and the intertory drift ratio were alulated. Figure 6 how the meaured lateral load intertory drift ratio for the peimen. Figure 6. hear Fore Intertory Drift Ratio Curve Figure 7 Meaured hear train on peimen Web Figure 7 how the hear train meaured on the wet fae of the web. The train are hown in mirotrain, whih i the atual train value multiplied by 6. Thee hear train were etimated a the differene between the meaured diagonal train at eah point. The train meaured by the retangular roette were orreted to aount for the effet of tranvere train enitivity uing equation in the literature. The orreted train value were ued to further ompute the prinipal diretion with referene to the vertial axi, the prinipal train, and the maximum hear train a the differene between the prinipal train. 6

7 Tranation, MiRT, 6- November,, New Delhi, India Div-VI: Paper ID# 764 The alulation indiate that a expeted the prinipal diretion varied approximately between -45 degree for puh (+) fore and +45 degree for the pull (-) fore. The alulated prinipal train were quite omparable to the meaured diagonal train, and the maximum hear train wa alo approximately equal to the differene between the meaured diagonal train. Figure 8 how the prinipal diretion, prinipal train and maximum hear train alulated for the point loated at web enter on both the eat and wet fae. Additionally, the train value on oppoite teel plate of the ame flange were demontrated to be quite omparable to eah other. Thi implie that the flange are ubjeted to axial tenion and ompreion with very little flexural bending (and hear). Thu, the peimen flange arry axial tenion and ompreion to help reit the overturning moment in the peimen, and their ontribution to reiting the in-plane hear fore applied to the peimen i minimal. VERIFICATION Figure 8 Prinipal Diretion and train at Web Center (Eat and Wet Fae) The in-plane hear behavior of the C wall peimen an be etimated uing the mehani baed theory hown in Figure. Figure 9 how omparion of the experimentally meaured in-plane hear fore-train behavior with the behavior hown in Figure. The meaured value of the teel yield tre (6.7 ki) and onrete ompreive trength (8 pi) were ued to etimate the in-plane hear behavior predition. The omparion ue the average in-plane hear behavior etimated uing the diplaement tranduer in the web region. The omparion hown in Figure 9 are quite favorable, but with ome direpanie. The experimental behavior doe not eem to have a lear unraked portion repone, whih i probably due to the yli nature of loading and loked in hrinkage train. The experimental behavior eem to indiate point-wie inelatiity for ome of the loation in the web, whih i probably due to the reidual tree produed loally in the plate by the welding proee ued in fabriating the peimen. Upon unloading, the experimental behavior eem to have a portion of vertial (infinitely tiff) repone, whih i probably jut an artifie of the enor and mounting tehnique ued to in the meaurement. 7

8 Tranation, MiRT, 6- November,, New Delhi, India Div-VI: Paper ID# 764 Theory (a) hear Fore v. hear train in Flange (b) hear Fore v. hear train in Web Figure 9. Comparion of Experimental and Theoretial In-Plane hear Behavior CONCLUION The in-plane hear behavior of C ompoite wall an be repreented uing a tri-linear hear fore-hear train repone baed on a imple mehani baed model. The model expliitly aount for the ompoite etion behavior before raking and the raked orthotropi ompoite behavior after raking. The raking threhold orrepond to a onrete prinipal tre of (f ).5 in pi, whih inlude the effet of loked in hrinkage train and direte ompoite ation. The in-plane hear trength orrepond to the limit tate of Von Mie yielding of the teel plate. Experimental reult from tet onduted in Japan orrelate well with the mehani baed tri-linear hear fore-hear train repone. An additional large-ale yli in-plane hear tet wa onduted by the author to further ompare with the imple model. The tet wa onduted uing a unique etup and peimen deign. The experimental reult ompare reaonably with the model. There are ome minor direpanie due to the yli nature of the loading and the omplexitie of the loading and boundary ondition involved in onduting the tet. Overall, the in-plane hear behavior of C ompoite wall an be predited reaonably and onervatively uing the tri-linear hear fore-hear train repone baed on the imple mehani baed model. ACNOWLEDGMENT Teting at Purdue Univerity wa partially funded by Wetinghoue Eletri Company LLC. All opinion expreed in thi paper are tritly thoe of the author. REFERENCE [] Ozaki, M., Akita,., Oouga, H., Nakayama, T., Adahi, N. (4). "tudy on teel Plate Reinfored Conrete Panel ubjeted to Cyli In-Plane hear." Nulear Engineering and Deign, Vol. 8, pp [] Varma, A.H., and Maluhte,., (9). In-Plane Behavior of Conrete Filled teel (CF) Element. Preentation. Enloure to DCP_NRC_78. Eletroni ADAM, NRC. Item ID 337. Aeion Number ML [3] ACI 38-8, Building Code Requirement for trutural Conrete and Commentary, Amerian Conrete Intitute, Farmington Hill, MI 8. [4] AIC 36-5, peifiation for trutural teel Building, 3 Edition, Amerian Intitute of teel Contrution, Chiago, IL, 5. 8