ACI STRUCTURAL JOURNAL. _ TECHNICAL PAPER Reexaminatin f Dwel Behavir f Steel Bars Embedded in Cncrete T identify the mechanisms f the bearing and failure f steel bars embedded in cncrete subjected t transverse lad, static lading tests using 24 cncrete blcks cntaining dwel bars, blted platemunted bars, r welded studs were cnducted. The behavir up t failure is examined based n the results btainedfrm the tests and analysis using the traditinal beam n elastic fundatin (BEF) analgy. This paper describes the pst-yield behavir f dwel bars and welded studs invlving the spalling f cncrete under the bars and the plastic hinge f the bars. The elastic analgy prvides further interesting implicatins t illustrate the behavir f the bars in cncrete, even beynd yielding. where M = Pg; and g is the distance frm the face f the cncrete t the lading pint (negative value). Likewise, the mment f the welded studs in the cncrete may be predicted n the assumptin that the slpe at the face f cncrete shuld be zer because f the restraint f rtatin due t the welding t steel plates. When the studs have enugh height, the mment is given by3 Keywrds: beam n elastic fundatin; dwel actin; shear anchr; stud; subgrade stiffness. INTRODUCTION Friberg l applied the thery f beam n elastic fundatin (BEF) t represent the behavir f dwel steel bars installed in jints fr cncrete pavements. Timshenk0 2 intrduced the BEF analgy as fllws El d4y =-ky dx 4 where x is the depth frm the surface f the cncrete (Fig. 1); y is the transverse displacement; k is the mdulus f fundatin in MPa (lbin. 2 ); E is the elastic mdulus f the steel bar; and I is the mment f inertia f the steel bar. Friberg,l hwever, substituted Kd fr the factr k, where K is the mdulus f supprt in the elastic mass r sub grade stiffness in MPalmm Obin. 3 ); and d is the diameter f the steel bar. The slutin can be btained frm using Eq. (2) The influence f a shrtage in height is mentined in a later sectin f this paper. Friberg I stated that the values f K ranged frm 80 t 400 MPalmm (300,000 t 1,500,000 Ibin. 3 ) and that the K-values wuld mst likely increase with the increased size f the steel bar. Friberg I implied, hwever, that the K-values wuld nt be sensitive enugh t represent the stress distributin f dwel bars in cncrete pavements because K appears in p related t the quarter pwer f K. I The reprt by ACI Cmmittee 325 4 shwed that the K-values ranged frm 80 t 2300 MPalmm (300,000 t 8,500,000 Ibin. 3 ); the average was apprximately 600 t 700 MPalmm (2,200,000 t 2,600,000 Ibin. 3 ). The reprt 4 described that the larger the diameter.f the dwel bars, the smaller the value f K. The cmpressive strength f rdinary cncrete fr pavements previusly seemed t be y = ellx(acspx + Bsinpx) + e-~x(ccspx + Dsinpx) where p = (k4el)1i4 = (Kd4El) 114. It was described that the value f K is the pressure intensity n the elastic mass that is required t cause a -unit settlement. I The bearing lad distributin acting n the cncrete under the bar R x is expressed by Kdy in Nmm (kipin.). Fr instance, the transverse displacement, slpe, and mment f dwel bars embedded in the cncrete subjected t a transverse lad P are Fig. I-Definitins f mment and displacement f steel bar in cncrete fr BEF e = (e- Ilx 2p2 EI){(2PM - p)cspx- PSinpx} (3b) ACI Structural Jurnal, V. 108. N.6, Nvember-December 2011. MS N. S-2008-346.R4 received June 9, 2010, and reviewed under Institute publicatin plicies. Cpyright 20 II, American Cncrete Institute. All rights reserved, including the making f cpies unless permissin is btained frm the cpyright prprietrs. Pertinent discussin including authr's clsure, if any, will be published in the September-Octber 2012 ACl Structural Jurnal if the discussin is received by May 1,2012.
ACI member Yshiki Tanaka is a Senir Research Engineer in the Bridge Structure Research Grup at the Public Wrks Research Institute (PWRl), Tsukuba, Japan. His research interests include shear transfer at jints in cncrete fr highway bridges. in reinfrced cncrete. The backgrund f the equatin, hwever, was nt addressed. Jun Murakshi is a Chief Researcher in the Bridge Structure Research Grup at PWRI. He received his BS and MS in civil engineering frm the Tky Institute f Technlgy, Tky, Japan, in 1985 and 1987, respectively. His research interests include the design and maintenance technlgy f steelcncrete superstructures fr highway bridges. apprximately 21 MPa (3000 psi).s Currently, fr designing jints in cncrete pavements in the U.S., the K-value f 400 MPalmm (1,500,000 Ibin. 3 ) seems t be ppular. 4,6 Dei Pli et al. 7 prpsed Eq. (5) fr estimating the K-values based n the relatinships between the lads and the measured displacement btained frm their experiments, in which the displacement at several pints f the steel bars in the cncrete was directly measured Several researchers 11. 13 examined the behavir f welded studs in cncrete. The K-values, hwever, were expressed by a nnlinear relatin with respect t the 10ads. 13 Rasmussen 9 presented the fllwing equatins fr estimating the ultimate transverse lads f dwel bars embedded in cncrete where = -3(gld)ifc'ly)0.5; C is the cefficient; andy is the yield pint f the steel bar. If the gap g is zer, wherefc' is the cmpressive cylinder strength f the cncrete; and Puis the ultimate lad. The ultimate lad was estimated by Dulacska's8 methd based n Rasmussen's9 equatin. The prprtinal limit n the relatinship was determined t be OAP u ' Dei Pli et a1. 7 als attempted t estimate the apparent K-values fr expressing nnlinear behavir beynd OAP u ' Then, the K-values were expressed by using the rati PIP u ' Qureshi and Maekawa 10 used Eq. (6) t represent the elastic behavir f the reinfrcing bars acrss the cracks I 125 I 125 I t5!" is Pu =cd 2 ( )0.5 fj)' then the cefficient c is 2.5 fr blted plate-munted bars and 1.3 fr dwel bars. In this paper, d2if;y)0.5 is termed the "dwel index." The equatin was derived frm the equilibrium f the applied transverse lad, the bearing frce f the cncrete, and the plastic mment f the bar n the assumptin that the ultimate failure wuld depend n the plastic hinge f the bar. Bth the cefficients c f p S~:D:s~trn,. 1. d 2.5 and 1.3 were determined based n the experimental results.9 Several researchers 8,14 verified the equatin. In additin, Rasmussen 9 stated that the spalling f the cncrete under the dwel bars was bserved at the lad crrespnding t the cefficient c ranging frm 0.7 t 0.9. \ 15d~ T identify the mechanisms f the bearing and the l. LVDT d failure f the steel bars embedded in cncrete subjected t I 125 I 125 I transverse lad, the authrs cnducted cncrete blck tests (a) Dwel bars (Series N) '" using 24 specimens cntaining dwel bars, blted platemunted bars, r studs, and analysis using the cnventinal ::~~J!l BEF analgy. IS This paper describes nt nly the reevaluatin f the traditinal analgy t illustrate the elastic behavir f dwel bars and welded studs, but als the capability f the elastic analgy t make sme interesting implicatins abut the behavir f the bars beynd yielding. RESEARCH SIGNIFICANCE Steel anchrs subjected t shear are ften bserved in _._.~J:e_cti9nn:ep<tir WQrks.The research reveflls several issues cncerning the mechanisms f the bearing and failure f steel bars embedded in cncrete subjected t transverse lad. A certain understanding f such a basic structure will cntribute t a mre reliable design fr varius cncrete members cntaining the related structure. Nte: The cntact surfaces between steel plates and cncrete were greased in Series Band S. 1 mm = 0.0394 in. TEST PROGRAM The cnfiguratins f specimens fr three series- Series N, B, and S-are shwn in Fig. 2 and Table 1. The name f each specimen represents the test series, the target cmpressive cylinder strength f the cncrete, the size f the steel bars, and the specified yield pint f the
Series Specimens Cncrete cylinder strengthfc', MPa Size f steel bar Nminal diameter, mm Yield pint f steel bar Jy, MPa N2419 24.5 N.6 19.1 342 N3010 33.8 N.3 9.53 355 N3013 31.2 N.4 12.7 338 N3016 32.8 N.5 15.9 345 N3019 33.3 N.6 19.1 342 N3019-345 33.3 N.6 19.1 374 Series N, dwel bars N3019-390 33.3 N.6 19.1 445 N4019 45.8 N.6 19.1 342 N5010 59.2 N.3 9.53 355 N5013 59.2 NO.4 12.7 338 N5016 59.2 N.5 15.9 345 N5019 59.1 N.6 19.1 342 N5019-345 59.1 N.6 19.1 374 N5019-390 59.1 N.6 19.1 445 B2419 24.5 N.6 19.1 342 B3013 33.8 N.4 12.7 338 Series B, B3019 33.8 N.6 19.1 342 blted platemunted bars B4019 45.8 N.6 19.1 342 B5013 59.5 N.4 12.7 338 B5019 59.5 N.6 19.1 342 S24 24.5-19.0 279 Series S: S30 33.8-19.0 279 welded studs S40 45.8-19.0 279 S50 59.5-19.0 279 -Diameter f stud is mitted in name because f n variatin f size in used studs. Ntes: I MPa = 145 psi; I nun = 0.0394 in.; name f specimens indicates fllwing meanings: (fr example, in Specimen N3019-345) "N" is type f series; "30" is target cylinder strength f cncrete; "19" is diameter f bars; "-345" is specified yield pint f steel bars (n indicatin means "295"). Dia f bar.'-- Size f screw thread #4 MI2 #6 MI6,:-;':;,9'~ ~'): ;:;~(._.._-_._--_.j...- f~;;:~:~jh:)'" (b) ad + 27 ad Dia. f hle in plate.mm 15 23 1 mm = 0.0394 in. Fig. 3-Details f' (a) dwel bars; and (b) blted platemunted bars. steel bars, as described in the ftnte f Table 1. The size f the cncrete blcks and the arrangement f the reinfrcement, except the main steel bars, are the same as in Rasmussen's9 study. The specimen was simply set n the platen f a lading machine, as shwn in Fig. 2. All the specimens were mntnically laded. Series N was prepared t examine the dwel behavir f steel bars and determine the K-values. The arrangement f the dwel bars is the same as Rasmussen's9 tests, except the embedded length was changed frm 6d t 8d l,5 and defrmed bars were used instead f rund bars. The lngitudinal ribs f the defrmed bar were vertically aligned, as shwn in.. Fig. J. Lading was directly. applied t the steel bar with a 12 mm (0.47 in.) thick steel plate. Series B was similar t anther series in Rasmussen's9 tests, in which steel plates were munted n bth sides f the cncrete. The steel plates were blted n, as shwn in Fig. 3. The prtruding regin f the defrmed bars was threaded fr tightening the steel plates. The diameter f a hle in the steel plate had a clearance f apprximately 2 t 4 mm (0.08 t 0.16 in.) fr the bar. Just befre lading, the steel plates were slightly tightened with nuts, as the strains f the defrmed bars at a depth f Id frm the surface were apprximately 100!-LE. Lading was applied t the tp f bth munted plates.
Q 20-0 c ----' Q 40-0 c.3 -Side A.lO- - Side B Slpe 8 0 -._. Predicted using Eq_ (3b) First yielding.. I><lliing 0.1 per divisin (a) Bar sizes: #3, #4, #5 Slpe 8 0 ~LVDTS 50 m 8.- N4019 0 N5019 N3019-390 v N3019-345 0.05 per divisin (b) Bar size: #6 N3019 Fig. 5-Measured and predicted slpe f dwel bars at surface. (Nte: 1 kn = 0.225 kips; 1 mm = 0.0394 in.) In Series S, a headed stud welded t a steel plate was munted in each side f the cncrete blcks t examine the applicability f the K-values determined frm the results f the dwel bars t the welded studs. The effects f a certain rtatinal restraint at the welded end f ihe stucts were als examined. The lading scheme used was similar t the blted plate-munted bars. All the cncrete blcks were made f rdinary prtland cement cncrete cntaining a 20 mm (0.79 in.) maximumsized crushed aggregate. The blcks were cured using plastic sheets fr 1 week and then air cured in a labratry. The cmpressin tests f 200 mm (7.9 in.) height x 100 mm (3.9 in.) diameter cylinder specimens were carried ut befre and after all test series. The mechanical prperties f the defrmed steel bars and studs are shwn in Table 1 and Appendix A*. All material data, except steel plates, were btained frm tests, using three test pieces fr each material. The munted r studded steel plates had a yield pint f 355 MPa (51,500 psi), which was indicated by the manufacturer. The flexure tests f the defrmed bars were carried ut t determine the flexural rigidity f the defrmed bars. The measured flexural rigidity f the bars 1 ranged frm 0.94 t 1.04 f the rdinary flexural rigidity calculated based n the nminal diameter and the elastic mdulus f steel f 200 GPa (29,000 ksi). Because the studs did nt definitely shw the yield pint, the prprtinal limit is indicated in Table 1. Strain gauges with a gauge length f 1 mm (0.04 in.) were munted n the lngitudinal ribs f the steel bars, as shwn in Fig. 2. A synthetic rubber cating cntaining chlrprene was used t prtect the strain gauges in the cncrete. The measured thickness f the cating was apprximately 0.3 t 0.5 mm (0.01 t 0.02 in.) after testing. The cating f the strain gauges munted n the steel bar at Side B was cnsiderably thinner and narrwer than that at Side A. Similarly, the strains f the studs were measured. T measure the settlement and inclinatin f the steel bars at the face f the cncrete, the transverse displacements were measured 'using linear variable displacement transducers (LVDTs) at tw pints fr each side, as shwn in Fig. 2(a) (refer als t Fig. 5). The measured slpe was btained frm tw data f the transverse displacement at the surface and at 50 mm (1.97 in.) apart frm the surface, being available t cancel the influence f settlement due t the elastic defrmatin f cncrete under the bar. Displacement was measured under the nuts in Series B, being measured under the studded plates in Series S. T detect the lad at spalling, the lngitudinal displacement was measured using a LVDT n the face f the cncrete at each side f the specimens in Series N (Fig. 2(a)). Similarly, the lngitudinal displacement was measured n the steel plate at each side f the specimens in Series Band S (Fig. 2(b) and (c)). After the tests, the delaminated areas f all the specimens were sketched and determined. Every specimen was cut in half alng a lngitudinal axis with a diamnd blade after all the lading tests. Then, the maximum depth f spalling L sp and the length f the bar exhibiting residual deflectin L b were measured. Series N Figure 5 shws the measured slpe f the dwel bars at the face f cncrete 8 0 in relatin t the lads. A predicted line using Eq. (3b) is drawn fr each specimen. Then, the K-values were determined using Eq. (9), which is intrduced later in this paper. Tw symbls n each curve indicate the lad and slpe at first yielding and thse at spalling, respectively._(appendix A). The sp~llipg_ Qf c.~!!c:.rete_was. <:>bserv.ed underneath every dwel bar, as shwn in Fig. 4. The lad at spalling was determined based n the cmmencement f the measured lngitudinal displacement (Fig. 6). The lad increments became small after spalting. The lad reincreased, hwever, after the bar was extremely bent. This was caused by a wedge actin due t the bar being pushed int the delaminated surface. The lading fr every dwel bar was arbitrarily stpped when the lad increments began t increase 'The Appendix is available at www.cncrete.rg in PDF frmat as an addendum t the published paper. It is als available in hard cpy frm ACI headquarters fr a fee equal t the cst f reprductin plus handling at the time f the request.
-0 c.3 40 ~...\._.. _... Blted plate munted bar E ~ C -100 Q) E ~ -200-7~~a)\1i kn:. -Q-b) 19.2 kn - Fitting fr a) j -~\-_._-~---_. -'i--~it~~jl!rb) \" _... "'-..,b) at first yielding 0.2 0-0.2-0.4-0.6-0.8-1 Lngitudinal displacement (mm) Fig. 6-Measured lngitudinal displacement (f~ = 30 MPa; d = 19 mm). (Nte: 1 MPa = 145 psi.) again. In this paper, the ultimate state f the dwel bars is defined as the lad sustained regardless f the rapid increase in the transverse displacement befre the wedge actin began. The strain distributins n the upper and lwer extreme fibers f the dwel bar exhibited apprximate symmetry befre first yielding. The distributin f the mment f the dwel bar is btained frm using Eq. (8) where M x is the mment f the steel bar at x; and cx,,, and Cx,l are the measured strains f the upper and the lwer extreme fibers f the' bar at x, respectively. Examples f the mment distributins acting n the dwel bar are shwn in Fig, 7, Tw curves fr data sets a) and b) were fitted t Eq. (3c). The mment at the surface indicates the existence f an untuched r lesstuched regin between the steel plate and the bar. Thus, a real lading pint might have a gap g f several millimeters frm the face f the cncrete. The gap and K were set as parameters fr the fitting t the BEE The fitting curves were determined s that a higher crrelatin cefficient and smaller differences frm the measured mments were btained. Every specimen shwed gd fitting, except Specimen N5019 (Appendix B). As the lad apprached the lad at first yielding, the K-values became cnsistent. Hereafter, the measured K-value represents the measured K-value at first yielding. The measured K-values btained frm the fitting are pltted in Fig. 8 in relatin t the cylinder strength fthe cncrete!c'. Equatin (5) prpsed by Dei Pli et a1. 7 and Eq. (6) indicated by Qureshi and Maekawa 10 are als illustrated. The linear crrelatin f the measured K-values was nt s far frm bth equatins in the range f rdinary cncrete strength less than 60 MPa (8700 psi). The measured K-values are likely t increase, hwever, with the increase f the diameters f the steel bars, as Friberg! suggested. The influence f the diameters differed frm bth cncepts f Eq. (5) and (6). A relatinship between the measured K-values and fc'd is illustrated in Fig. 9. Equatin (9) is btained frm a crrelatin using all the experimental data, except Specimen N5019, which exhibited the inapprpriate fitting fr K. -300 50 100 Depth x (mm) Nte: 1 N-m = 0.738Ib-ft; 1 kn = 0.225 kips; 1 mm = 0.0394 in. Measured mment was calculated using Eq. (8), being fitted t Eq. (3c) Fig. 7-Examples f mment acting n dwel bars (f~ = 30 MPa; d = 19 mm). (Nte: 1 MPa = 145 psi.) c 0.. 12 10 'b 4 ~ 2 40 60 fe' (MPa) Fig.8-Cmparisn f measured K-values with previus equatins n relatinship between Kd and f~. (Nte: Regressin 1 was btained frm all results; Regressin 2 was btained frm all results except Specimens N5010 and N5019. Experimental results were btained frm fitting fr mment diagram at first yielding [Appendix Bl; 1 mm = 0.0394 in.) 8 G ~ 6.!!.- r- 12 0.. G 8 ~ - 6.!!.- 'b 4 ~ 2 0 0 10 20 30 fe' d 2 (N, mm) Fig. 9-Relatinship between Kd and f c 'd 2 based n experimental results. (Nte: 1mm = 0.0394 in.)
Z ::=...~ 100 "0 r.q ~ 50 E ""5.. 0 N24" 2.5 d'(fc' fy}o.5 ~~ 0 N30" :fr blted plate (!":,..~... :;. ~ N40:: :munted bars..,,... N50 -----j-- -T----l..--,\-- "-----. Senes B. i i. rupture f I. Series S 1.3d2(fc'fy)"-5 ~teelbars ---~~ fr dwel bars - --.- :~t.'.~-.~.-.'':~- - 20 40 60 d 2 (fe' f y )05 (kn) Fig. 10-Relatinship between ultimate lad and dwel index. (Nte: Specimens N24**, N30**, N40**, and N50** shw results f specimens at Side A in Series N with specified strength f cncrete f24, 30, 40, and 50 MPa, respectively; 1 MPa = 145 psi.) z ::=. 40..'fJ; Results at Side A in Series N. ~ p Sf> = 0.84 d 2 (f c ' f y )0.5 --' -' -- at spalling ~ 0 at fir~yieldin!l-- --. yielding f the dwel bars in relatin t the dwel index. The lad P y can be apprximately estimated using the dwel index. The lad P y crrespnds t OAP" presented by Dei Pli et al.,? althugh they estimated P" t be apprximately 1.3~(j:fy)s. Theretically, the lad at first yielding P y can be estimated using BEE The maximum mment f the bars is btained frm substituting the psitin f the maximum mment Lm fr Eq. (3c). where L m = (l~)tan-l(l(1-2~g)). The mment at first yielding My is given by 0..'" "0 20 r -' 20 40 60 d 2 (fe' f y )05 (kn) Fig. II-Lads at first yielding and spalling in relatin t dwel index. As shwn in Fig. 5, the slpe 8 0 predicted using Eq. (3b) and the K-values btained frm Eq. (9) are apprximately cnsistent with the measured slpe prir t the first yielding. Incidentally, bth Fig. 8 and 9 are illustrated using Kd (=k). When Friberg l applied the BEF analgy dealing with nly a plane issue t the behavir f dwel bars having a finite width in cncrete having infinite width, the width d might rather cnfuse the cncept f the analgy (Eq.(l)). In Fig. 10, the ultimate lads f the dwel bars are pltted in relatin t the dwel index. The ultimate lads P" are apprximately eqll~1 t the dwel in~ex:_ "... On the ther hand, the maximum lads cntammg the influence f the wedge actin were nt far frm Rasmussen's9 equatin 1.3d 2 (fc'h)0.s. The lad at first yielding P y is interesting fr predicting a prprtinal limit in the dwel behavir f a steel bar embedded in cncrete. Figure 11 shws the lad at the first The predicted lad using Eq. (14) agreed with the experimental results. Then, the K-values were determined using Eq. (9). The K-values did nt seem t be very sensitive, hwever, fr predicting the lad P y Whichever K-value is determined by Eq. (5), (6), (9), r even a cnstant value f 400 MPalmm (1,500,000 Ibin. 3 ), the predicted lad P y des nt vary significantly. The K-values given by Eq. (9) were smewhat favrable t the predictin. The lad at spalling P sp is als pltted in Fig. II. Similar t the lad P y, a gd crrelatin between P sp and the dwel index is bserved. The result shws that the spalling always happened after the firstyielding_fthedq'ivel Pw. and that the lad at spalling was apprximately twice as large as that at first yielaing. When cmpared with the ultimate lad P" (Eq. 10), it can be seen that an extra lad-carrying capacity remained at spalling. Frm the dissectin survey (Appendix C), it was fund that the measured area f spalling Asp rapidly increased with the increase f the measured depth f spalling Lsp (Asp = 28Ls)' Series Band S Frm the tests in Series Band S, the lad at first yielding f the blted plate-munted bars, the lad at the prprtinal limit f the studs, the lad at the cmmencement (r the limit
f linearity with respect t the lads) f the lngitudinal displacement f the steel plates (Fig. 6), and the ultimate lad were btained (Appendix A). The first yielding f the bars and the prprtinal limit f the studs were detected by strain readings. It shuld be nted that while the maximum strain f studs ccurred at the welded end, n strain gauge was munted just at the pint (refer t Fig. 2(c)). As shwn in Fig. 6, the lngitudinal displacement n the munted steel plates fr bth the blts and studs mderately increased when cmpared with the dwel bars. The lads at the cmmencement f the lngitudinal displacement fr the blted plate-munted bars and welded studs were ften larger than the lad at spalling under the dwel bars in each cmpanin specimen. As shwn in Fig. 10, the ultimate lad f the blted plate-munted bars is cnsistent with Eq. (7b) using the crrespnding cefficient f 2.5. The ultimate lad f the welded studs was similar t that f the blted platemunted bars. The flexural and shear rupture f the blted plate-munted bars and the welded studs was bserved at the. face f the cncrete in. all the sp~imens fr Series B and S, except Specimens B2419, S24, and S30, which had a relatively lw cncrete strength. The ultimate lad due t the rupture may be limited t the prperty f steel bars such as the ultimate shear frce VsuC=isuAsl. 73), where isu is the ultimate tensile strength; and As is the nminal area f the steel bar. The average ultimate lad due t the rupture f the blted plate-munted bars was 1.32V su ; the average ultimate lad f the welded studs was 1.67V su ' The measured and predicted mment diagrams f a stud in Specimen S30 are shwn in Fig. 12. The predicted lines are btained using BEF (Eq. (d3) in Appendix D) with the K-values frm Eq. (9). The methd and K-values seem effective t predict the behavir f the welded studs. In the mment diagram at 16.7 kn (4.0 kips), the predicted mment at the welded end (x = 8 mm [0.3 in.]) reached the prprtinal limit f the studs. The yielding ught t have ccurred at the welded end much earlier than the lad f 50.1 kn (11.3 kips) when the measured strain at a depth f 2d reached the prprtinal limit; hwever, the cmpatibility f the BEF with experimental data was fairly bserved even at the lad f 50 kn (11.3 kips). An example f the measured mment f a blted platemunted bar at first yielding is pltted in Fig. 13. Using Eq. (3c) and (4), three predicted lines are drawn. The thin slid line exhibits the behavir f dwel bars with n restraint f rtatin at the surface. The thick line exhibits the behavir f the bar with a strict restraint f the rtatin, similar t the wejded studs. This thick line crrespnds t Eq. (3c) when assuming that M is 600 N-m (443 Ib-ft). Every measured mment is between bth the predicted lines. The third line (brken line) using Eq. (3c) was apprximated t the experimental data. Then, M was 200 N-m (148Ib-ft). It was recgnized that the psitive mment due t the steel plates acted n the bars at the surface. The blted plates seemed t be insufficient t keep the rtatinal restraint cmpared with the studded plate. Althugh the lngitudinal displacement n the blted plates was similar t that n the studded plates, as shwn in Fig. 6, the clearance f the hle in the blted plates might mitigate the restraint prir t extreme deflectin. The blted plate-munted bars seemed t be ruptured wing 1000 800 E 600 ~ C 400 OJ E 0 200 ~ 0-200 0 50 1000 50 100 Depth x(mm) Nte: 1 mm = 0.0394 in.; 1 MPamm = 3680 Ibin' Predicted using Eq. (d3) in Appendix D. 1 N-m = 0.738 Ib-ft; 1 kn = 0.225 kips; Fig. 12-Measured and predicted mment acting n welded stud (Specimen S30). 1000 800.. All lines were calculated by using BEF. E 600 ~ 400 C 200 Q) E a a :2-200 - -400-600 a L Eq. (3c), M = 600 N-m. r Eq. (4) '. Eq. (3c). M 0 = 200 N-m Eq. (3c), M = 0 Depth 100 (mm) Fig. 13-Measured mment acting n blted plate-munted bar (Specimen B3019). (Nte: 1 MPa = 145 psi.) t the delayed rtatinal restraint brught n by the small clearance f the hle in the plates. Frm the dissectin survey, it was fund that the depth f spalling under the blted plate-munted bar was nt much different frm that under the dwel bar when cmpared between cmpanin specimens. While the lad at the lngitudinal displacement cmmencement f blted platemunted bars was larger than that f dwel bars, invisible cracking might develp at the lwer lad crrespnding t spalling under the dwel bars. Even if the cracking develped, the ductile behavir f the bars might be sustained due t the munted plates cnfining the cracked cncrete beneath the bars. Large initial axial tensin may generate frictin between the steel plates and cncrete but affect the yielding f the blts after slipping at the interface. The stiff behavir was bserved at nly a very lw lad. The influence f the frictin due t the intrduced axial frce f apprximately 3 t 6 kn (0.67 t 1.35 kips), hwever, seemed t be negligible fr the details in Series B. BEHAVIOR OF DOWEL BARS Spalling f cncrete A depth t the resultant f bearing lad distributin R x frm the surface t the first intercept n the x-axis L(=(l~) tan-! ((~g - 1)~g)) can be calculated by numerical integratin, similar t the center f gravity. Frm the calculatin fr 14 specimens cntaining dwel bars, it was fund that
g> 20 r c.. :::.~ 15 E : E g- ~ 10 "0 "0 ~::::l en <1l Q) ::2: -------~ -- -- 1--- 4. ' I 5> 0 ------;;-- ---;EYg,-- - -- - " -~ "SideA Side B 5 10 15 20 25 Calculated depth f resultant Leg (mm) Fig. i4-relatinship between measured depth f spalling and calculated depth f resultant f bearing stress distributin within first intercept. Z 80 6 I;l- :;,. 60 Q) 2.2 ~ 40 c <1l en.~ 20 -... <1l Q).c en 0 Fig. i5-relatinship between shear resistance frce f cncrete under dwel bar and assumed resultant at spalling. The depth f spalling is likely t be shallwer than the maximum mment pint. The previus finding implies that the resultant induces the spalling f cncrete. At spalling, the resultant f the bearing lad distributin frm the surface t the first intercept F may be apprximated by F = KdJ~ ydx (y at P sp ) = p' p [e- PL {(l- 2~g)sin~L - cs~l}+ 1] Frm Eq. (18), the ratis f F t?sp fr the specimens ranged frm 1.22 t 1.33, the average being 1.27. Assuming that the spalling depends n the shear failure f the cncrete due t the resultant f the bearing lad within the first intercept, the resultant at spalling may crrespnd t the shear resistance frce f the cncrete. Figure 15 shws the relatin f the shear resistance frce V sp with the calculated resultant at spalling F. In this study, the values f V sp were evaluated by ml\ltiplying the shear strength f cncrete vu(=2!r)15 and the area f failure having a cnical shape Msp(=rr.req(re + Lsp 2 ).5), where!r is the tensile strength f cncrete (=0.3f 213 ); and r eq is the equivalent radius calculated using the measured area f spalling Asp(=rr.req2). Figure 15 implies that the assumptins abut the resultant frce inducing the spalling and the crrespnding shear capacity f the cncrete under the dwel bar are likely t be acceptable. Plastic hinge f dwel bars The assumed plastic hinge pint f the steel bars intrduced by Rasmussen 9 mst likely has smething t d with the depth f the maximum mment pint befre yielding L m r just after spalling L ma On the assumptin that the BEF analgy wuld still be applicable t the dwel bars in the remaining cncrete after spalling, the rigin fr anther axis (x'-axis) is psitined at the delaminated surface f cncrete, as illustrated in Fig. 16. The maximum mment pint after spalling L m ' n the x' -axis may be given by fr all specimens f dwel bars, the depth f resultant Leg has a linear relatin t the depth f the first intercept L as fllws In Fig. 14, the calculated depth f resultant Leg is shwn in relatin t the measured depth f spalling L sp The depth Leg apprximately crrespnds t the depth Lsp- Because carse aggregate might ccasinally exist under the bar, the measured depth f spalling L sp has a greater ptential t vary than Leg. The result implies that the spalling always initiates arund the depth Leg. A relatinship between Leg and the maximum mment pint f steel bars L m (= (l~) tan-1(l(l - 2~g))) is represented by where g' is the distance frm the delaminated surface f the cncrete t' the lading pint (=g - Leg)' The assumed maximum mment pint just after spalling frm the riginal surface L ma is The depth L ma was calculated fr each specimen cntaining dwel bars. Frm the results, the fllwing crrelatin between L ma and the depth f the maximum mment pint befre yielding L m was btained.
R,= Kd Pint f the first yielding n Assumed max. mment U pint just after spalling " 0' ::'~':'9:':7?:.', "':~( I Ji::,c).: :~; '. ~'.- I ~b:.',0'. Q.' '''0 I,,,,, :,:~.O, ~(j.,'..v.: t' '.'.'. : : Temprary rig n fr )' re-applying BE x' i just after spalli ~ 80 - E gj.s '0.~ -.J 60...... 025.r::.- 0> ~ 40 c 0 ~'O -g '0 20...c ~.Q ~t3 2t2! 0 (l) '0 0 Side A Side B --- 20 40 60 80 Assumed depth t max. mment pint just after spalling L ma (mm) : f ned inal mng ltin lint nte: Leg = 0.61 Lm ;; Lsp Lma= 1.27 Lm Fig. I6-Assumptin f maximum mment pint just after spalling. A relatinship between the depth L ma and the measured length f residual deflectin L b is illustrated in Fig. 17. The assumed depth L ma apprximately crrespnds t the measured length Lb' Regarding the dwel bar just after spalling, the mment at L ma and the ther mment at the delaminated surface (""Leg) were tentatively estimated using the lad at spalling P sp given by Eq. (15). Bth the estimated mments at Leg and L ma were extremely beynd the plastic mment f the steel bars. The results imply that just at spalling, the full penetratin f yielding thrughut the crss sectin might develp, at least in the regin frm the delaminated surface (""Leg) t the assumed maximum mment pint after spalling (L ma ). Frm this viewpint, it can be seen that presumably further spalling was difficult t take place. The remaining lad-carrying capacity after spalling mst likely depended n the strain hardening f the steel bar prir t the beginning f the wedge actin. Frm the previus results, the prcess up t failure f the dwel bars embedded in the cncrete is schematically summarized in Appendix E. The behavir in elasticity still prvided several useful parameters t draw the behavir f the dwel bars beynd first yielding. BEHAVIOR OF WELDED STUDS Welded studs exhibited ductile behavir and a higher lad-carrying capacity cmpared with the cmpanin dwel bars. Figure 18 shws the bearing lad distributin acting n welded studs with a diameter f 19 mm (0.75 in.) in cncrete with a cylinder strength' f 30 MPa (4350 psi) using the BEF analgy (Appendix D) and that fr the cmpanin dwel bars. The rtatinal restraint due t welding t the steel plate results in a significant difference in the bearing lad diagram. Frm the figures, it can be seen that the pint f resultant acting n the studs tends t be deeper. The deeper resultant pint is mst likely effective in delaying the spalling f cncrete wing t requiring a larger failure area fr the spalling. In additin, frm Fig. 18(a), the resultant F acting n the stud is apprximately equal t the applied lad P. The rati FIP f 1.0 fr the welded studs is smaller than that fr dwel bars with a sufficient embedded length Fig. I7-Relatinship between measured length f residual deflectin f dwel bar and assumed depth t maximum mment pint just after spalling. -0-0.4 :::., :::., 0.!!..- 0.4 '"0 (\).Q 0.8 OJ c 1.2.~ -0.4 OJ..Cl 0 '"0 OJ 0.4.!::! r E 0.8 0 z 1.2 0 Pint f resultant 40 60 Depth x (mm) Calculated bearing lad distributin f stud '-.. L : Depth f the first intercept Nte: 1 mm = 0.0394 in. Predicted fr stud using Eq. (d5) in Appendix D and fr dwel bar using Eq. (3a). Fig. IS-Difference f bearing lad distributin between welded stud and dwel bar (fe' = 30 MPa; d = 19 mm). (Nte: 1 MPa = 145 psi.) (refer t the rati f 1.27 fr the dwel bars). Bth features stemming frm the elastic behavir might be reasns why the cracking f the cncrete underneath the studs was nt bviusly bserved in the dissectin survey, despite the severe defrmatin f studs. Eventually, the rtatinal restraint impacting the elastic behavir seemed t bring abut the ductile behavir and higher lad-carrying capacity f the welded studs. Using the equatin f the mment diagram fr headed s40rt studs (Appendix D), Fig. 19 indicates the influence f the height f the studs n the mment diagraridrwdded------ studs with a diameter f 19 mm (0.75 in.) in cncrete with a cylinder strength f 30 MPa (4350 psi). In this case, the studs with a height f mre than 150 mm (5.91 in.) bear negligible mment at the head. The studs with a height f 100 mm (3.94 in.), hwever, are subjected t a large mment at the head. In the dissectin survey, critical cracks frm the head f the studs were cmmnly bserved in Series S, as drawn in Fig. 19. Similar cracks were als bserved in the tests f welded studs presented by Ollgaard et al. 12 Such cracks might begin t develp due t the large mment acting n the head f such shrt studs. Tw types f failure f the welded studs that
1000 Lading Cracking due t (0' = 33.8 MPa 800 Steel plate ~ the ~_. head f rela- ""mm K 161 MPamm E 600 tively lw stud p = 50.1 kn 2S C 400 The surtace Stud Q) f cncrete Crushed cncrete E I 0 200 :2 h = 150 mm \ 0 Nte: -200 0 50 100 150 200 250 300 Depth x (mm) 1 N-m = 0.738Ib-ft; 1 kn = 0.225 kips; 1 mm = 0.0394 in.: 1MPamm = 3680 Ibin.' Predicted using Eq. (d3) in Appendix D. Fig. 19-Infiuence f height f studs n mment at head. (Nte: 1 MPa = 145 psi.) were bserved in the pushff tests presented by Viest t 1 might be related t the mment acting n the head due t the shrt cutff. Further investigatin is needed t identify the influence f several factrs, such as the size f the head. CONCLUSIONS In this study, lading tests using 24 cncrete blcks cntaining dwel bars, blted plate-munted bars, r welded studs were carried ut, fllwed by a dissectin survey t determine the depth f spalling bserved under dwel bars and the residual deflectin regin f the bars. The behavir up t failure was investigated using the experimental data and the BEF analgy. The elastic analgy still prvides sme implicatins t illustrate the behavir f the steel bars embedded in cncrete, even beynd yielding (Appendix E). This paper, depending n the traditinal analgy, may be insufficient t fully identify the pst-yield behavir f the dwel bars. The apprach is at least likely t be useful fr engineers and researchers t draw an utline cncerning the prcess f failure f the dwel bars. ACKNOWLEDGMENTS The tests in this study were cnducted as a part f the Cperative Research Prject n Cnnectins f Precast Prestressed Cncrete Elements fr Bridges with the Japan Prestressed Cncrete Cntractrs Assciatin (JPCA). NOTATION A, area f crss sectin f steel bar, mm 2 (in. 2 ) A,p measured delaminated area f spalling n plane surface, mm 2 (in 2 ) c cefficient fr Rasmussen's9 equatin d diameter f steel bar, mm (in.) E elastic mdulus f steel bar, MPa (psi) F assumed resultant f bearing lad distributin within first intercept, kn (kip) f: cmpressive cylinder strength f cncrete, MPa (psi) isa ultimate tensile strength f steel bar, MPa (psi) f, tensile strength f cncrete, MPa (psi) y yield pint f steel bar, MPa (psi) g distance frm surface f cncrete t lading pint, mm (in.) g' distance frm failed surface t lading pint, mm (in.) h height f stud, mm (in.) I mment f inertia f steel bar, mm 4 (in.') K mdulus f supprt in elastic mass r subgrade stiffness, MPalmm (lblin]) k mdulus f fundatin, MPa (psi) L depth t first intercept f bearing lad distributin, mm (in.) L b measured length f bar exhibiting residual deflectin after testing, mm (in.) Lg depth t resultant f bearing lad distributin within first intercept n x-axis, mm (in.) Lm maximum mment pint f steel bar, mm (in.) L m ' assumed maximum mment pint after spalling frm failed surface, mm (in.) L ma assumed maximum mment pint after spalling frm riginal surface, mm (in.) L,p measured maximum depth f spalling, mm (in.) M a mment at surface, N-m (kip-in.) M,p assumed area f failed surface f cncrete after spalling, mm 2 (in 2 ) M x mment at x, N-m (kip-in.) P transverse lad, kn (kip) P,p lad at spalling, kn (kip) P" ultimate lad, kn (kip) P,. lad at first yielding, kn (kip) R, bearing lad distributin acting n cncrete at x, Nmm (kipin.) r,q equivalent radius f failed area due t spalling (=(A,lt)O.5), mm (in.) V,p shear resistance frce f cncrete under steel bar, kn (kip) V,,, ultimate shear frce f steel bar, kn (kip) Va shear strength f cncrete, MPa (psi) x depth frm surface, mm (in.) y transverse displacement, mm (in.) ~ relative stiffness f steel bar and cncrete, mm- I (in.") E Rasmussen's9 parameter Ex,L measured strain f lwer extreme fiber f bar at x, mm (in.) Ex." measured strain f upper extreme fiber f bar at x, mm (in.) e a slpe f steel bar at surface REFERENCES I. Friberg, B. E, "Design f Dwels in Transverse Jints f Cncrete Pavements," Prceedings f ASCE, Nv. 1938, pp. 1809-1828. 2. Timshenk, S., Strength f Materials. Part II: Advanced Thery and Prblems, third editin, D. Van Nstrand C., Inc., New Jersey, 1956, pp. 1-25. 3. Chang, Y. L., "Discussin n the Paper 'Lateral Pile-Lading Tests' by Feagin, L. B.," Transactins f ASCE, V. 102, 1937, pp. 272-278. 4. ACI Cmmittee 325, Subcmmittee III, "Structural Design Cnsideratins fr Pavement Jints," ACI JOURNAL,Prceedings V. 53, N.7, July 1956, pp. 1-28. 5. Marcus, H., "Lad Carrying Capacity f Dwels at Transverse Pavement Jints," ACI JOURNAL,Prceedings V. 48, N. 10, Oct. 1951, pp. 169-184. 6. Yder, E. J., and Witczak, M. w., Principles f Pavement Design, secnd editin, Jhn Wiley & Sns, Inc., New Yrk, 1975,736 pp. 7. Dei P1i, S.; Di Prisc, M.; and Garnbarva, P. 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Aka, S.; Kurita, A.; and Hiragi, H., "Effect f Directins f Cncrete Placing n Behavir f Headed Stud Shear Cnnectrs in Push-Out Tests," Jurnal f Japan Sciety f Civil Engineers, N. 380, Apr. 1987, pp. 311-320. (in Japanese) 14. Vintzeleu, E. N., and Tassis, T. P., "Mathematical Mdels fr Dwel Actin under Mntnic and Cyclic Cnditins," Magazine f Cncrete Research, V. 38, N. 134, 1986, pp. 13-22. 15. PWRI and JPCA, Cperative Research Reprt n Cnnectins f Precast Prestressed Cncrete Elements fr Bridges, PWRI Cperative Research Reprt N. 370, Tsukuba, Japan, Mar. 2008, 247 pp. (in Japanese)