SHEAR STRENGTH OF RC BRIDGE DECK CANTILEVERS

Transcription

1 6 th International PhD Symposium in Civil Engineering Zurih, ugust 23-26, 26 SHE STENGTH OF C IDGE DECK CNTILEES bstrat ui az odrigues 1 n experimental and theoretial investigation o the shear strength o reinored onrete slabs ithout shear reinorement is under ay at the Eole Polytehnique Fédérale de Lausanne. The irst part o the program onsists o 6 tests on to large sale bridge dek antilevers. The speimens are tested under dierent onigurations o onentrated ores simulating trai loads. The observed ailure mode is shear. The seond part o the experimental program onsists o shear tests on 12 slab strips, to investigate the inluene o plasti hinge rotation on the shear strength. The test results sho that the shear strength dereases ith inreasing plasti hinge rotation. Keyords C slabs, shear strength, yield-line, trai loads 1 Model and bakground The model proposed by (Muttoni 23) orrelates the shear strength o beams ithout shear reinorement ith the nominal opening o a ritial rak (ε d k dg ). The ailure o beams ithout shear reinorement is onsidered to be aused by the opening o a ritial rak under inreasing deormations. The shear strength dereases ith inreasing longitudinal strains ε, hih are orrelated both to overall deletion and to the opening o the ritial rak. The longitudinal strains ε are alulated using ernoulli s hypothesis or a raked setion at a distane.5 d rom the applied load and.6 d rom the ompressed iber. The parameter k dg =48/(D max +16) inludes the inluene o the maximum aggregate size D max [mm]. total o 253 shear tests (Sozen 1959, Leonhardt 1962, Kani 1979, Elzanaty 1986, Nia 1987, Collins 1999, ngelakos 21) on beams ithout shear reinorement under onentrated loads are represented in Figure 1, along ith the predition o the model. The resisting shear ore is, the eetive depth is d, the idth o the beam is b and the onrete ompressive strength is [MPa]. good agreement as ound beteen the model and the test results on beams ithout shear reinorement. similar ormulation has been proposed or the punhing shear o lat slabs ithout shear reinorement (Muttoni 23). The punhing shear strength is this time orrelated ith θ d k dg, hih is again orrelated ith the opening o a ritial rak (Figure 1). The rotation o the slab is θ, as indiated in Figure 1. The ontrol perimeter o length u lies at a distane o.5 d rom the olumn edge. This approah is no adopted as part o the Siss design ode or onrete strutures, both or the design o beams ithout shear reinorement and or punhing shear (SI 262). 1 PhD andidate, Eole Polytehnique Fédérale de Lausanne, rui.vazrodrigues@epl.h. 1

2 b d b d = ε d k dg u d u d.75 = θ d k dg θ [mm] ε d k dg [mm] θ d k dg a) One-ay shear b) Punhing shear Figure 1 Strength as a untion o deormations o beams and slabs (punhing) ithout shear reinorement (Muttoni 23) The experimental program should provide results that are relevant to improve and ombine these to models. 2 s on large sale C bridge antilevers 2.1 Layout o experiments The antilevers have a span o 2.78 meters (distane rom the ixed end to the tip o the antilever) and a total length o 1. meters. The test onept and the load arrangement are shon in Figure 2. For slab D1, the transversal reinorement o the top layer at the ixed end onsists o 16 mm diameter bars at 75 mm spaing (reinorement ratio ρ =.79%). For slab D2, the transversal reinorement o the top layer at the ixed end onsists o 14 mm diameter bars at 75 mm spaing (reinorement ratio ρ =.6%). No vertial shear reinorement as provided. Figure 3 shos the reinorement layout and the antilever dimensions, along ith the position o the onentrated loads simulating vehile heels. The bottom reinorement onsists o 12 mm diameter bars at 15 mm spaing in both diretions or all slabs. The top longitudinal reinorement onsists o 12 mm diameter bars at 15 mm. The onrete over is 3 mm. The reinorement steel used at the transversal diretion at the top layer is hot-rolled, ith a yield strength o 515 MPa. Ordinary onrete as used in both slabs ith average measured values at the time o testing o ompressive strength o = 4 MPa and Young modulus o E = MPa. Maximum aggregate size is 16 mm. a) ridge girder ith antilever b) Large sale model under loading patterns ) D1a, under our onentrated loads Figure 2 onept and load arrangement The applied loads or the test D1a are the tin axle loads presribed by Euroode 1 ith all dimensions redued by 3/4. The subsequent tests ere perormed using only to or one onentrated load to better ous on shear and punhing shear ailure modes, as shon in Figure 3 and resumed in Table 1. The onentrated loads ere applied on the top o the slab 2

3 using steel plates ith dimensions 3 x 3 x 3 mm. The ixed end support as lamped by means o a vertial prestressing (7 MN total ore). The onentrated loads ere applied through holes (Ø 13 mm) in the slab, hih alloed to pull diretly rom the strong loor. hook Ø22 Ø16 s=15 Ø16 s=15 5 Ø 22 Slab D1 129 hook Ø22 Ø14 s=15 Ø14 s=15 5 Ø 18 Slab D2 129 Ø12 s= Q/4 Q/ Q y x Q/4 Q/ D1b D1a 9 D1 Ø12 s= Q y x D2b D2a 9 D vertial prestressing - vertial prestressing esults Figure 3 Slab dimensions, reinorement layout and applied loads. Dimensions in mm. Number o heel loads Table 1 esults o experiments on antilevers Failure Load Q Q Flex Q /Q Flex Failure loation Mode o ailure kn kn D1a Cantilever edge D1b Fixed end D Fixed end D2a Fixed end D2b Fixed end D Fixed end Q Flex : Theoretial lexural ailure load The results o the 6 tests are summarized in Table 1. The ailure mode or the antilever under our onentrated loads (D1a) as a brittle shear ailure at the to loads near the edge. For the other tests, the antilever also ailed in shear, hoever at the loation beteen the applied loads and the ixed end o the antilever (Figure 4). Calulations ere made o the theoretial yield-line ailure load, based on the upper bound theorem o limit analysis. This load as never reahed in any o the six tests. The ailure load in test D1a ith our onentrated loads is losest to the theoretial yield-line values (Q /Q Flex =.86, Table 1). In the ase o D1a, plasti strains ere present in both the top transversal reinorement at the ixed end and the bottom longitudinal reinorement underneath the edge loads. The loest Q /Q Flex ratio as obtained or test D2a, under to onentrated loads. More results are available in (az odrigues et al 26). 3

4 Free edge - a) D1a b) D1b b) D1 Figure 4 ailures or slab D1 Q [kn] Q [kn] D1a D2a 8 D1b 8 D2b D2 4 D [mm] [mm] Figure 5 Total load deletion urves or the six tests The load-deletion urves or the six tests are shon in Figure 5. The deletion as measured at the tip o the antilever as indiated in Figure 3. Figure 4 shos the ailure pattern obtained or the slab D1. For tests D1b and D1, the shear rak as learly visible ater ailure on the side ae o the antilever and the rak ontinues inside o the slab. ter ailure, the slab as ut and the geometry o the ritial shear rak as mapped. The position o the shear raks are shon in Figure 6 along ith the rak pattern on top and bottom suraes. For test D1a, a large shear rak is present in the region beteen the ixed end and the applied loads. Sine no ailure ourred in this region, this suggests that a proess o development o the shear rak as under ay in this region and that redistributions o the shear lo have ourred. In order to better ollo the development o the shear rak, measurements o the vertial shear rak openings inside the slab ere perormed or slab D2 (Figure 7). Top ottom Top ottom - - Figure 6 Crak pattern on the top and bottom suraes or tests D1a and D1b The measurements o slab thikness hanges onirm that the ormation o the ritial shear rak is a proess that starts at a load level signiiantly loer than the ailure load. For test 4

5 D1a, the shear rak started to gro ater Q = 66 kn, hereas the ailure took plae at Q = 96 kn. The presene o the shear rak ill probably aet the lo o shear ores, so that redistributions have ourred ater the initiation o the rak. Q [kn] 12 1 Δ h4 Δ h1 = 96 kn Q Δh Δh1 Δh2 8 Δ h2 Δ h Δh Δ h [mm] Figure 7 Measurements o the variation o slab thikness (test D2a) 3 s on C slab strips ithout shear reinorement The tests on antilevers have shon that yielding o lexural reinorement ours under ertain load onigurations. In order to investigate the inluene o yielding o lexural reinorement on the shear strength, a series o telve statially determinate slab strips have been tested. 3.1 Layout o experiments Telve beams have been tested ith a onstant retangular setion o.45 m x.25 m and a total length o 8.4 m, as shon in Figure 8. The top and bottom longitudinal reinorement onsists o 4 bars o 16 mm diameter, onstant along the beam s length. The reinorement ratio is.79% or both bottom and top bars or all tested beams. To loads, Q at mid-span, and αq at the tip o the antilever ere applied by 2 hydrauli jaks. The load introdution at mid-span (Q) as made by means o a steel plate o.1 m x.25 x.3 m. The beams ere simply supported. No shear reinorement as plaed in the measurement zone, but outside o this region, stirrups ere provided to prevent a shear ailure. The ratio α beteen the applied ores as varied through the 12 beams and kept onstant during eah test, alloing dierent shear ores and shear spans..45 m Q ending moment diagram 3. m measurement zone 8.4 m a 1 αq.45 m Cross-setion 4 Ø 16 mm = 25 mm 4 Ø 16 mm a 2.25 m Figure 8 Slab strip dimensions, loads and shear spans a i 5

6 For slab strips S-2 to S-9, the reinorement steel used as old ormed ith a proportional limit at.2% o 515 MPa and a tensile ailure strain o 14%. For slab strips S- 1 to S-12, the reinorement steel used as hot-rolled ith a yield strength o 525 MPa. 3.2 esults The main results are given in Table 2 and Figure 9 or all slab strips. Table 2 Main results or beams S-2 to S-12 eam N α a 1 a 2 Q b d δ θ Failure Loation m m kn kn - mm mrad - - S S Q S Q S Q ending S S Q S Q S S Q S S >55.8 Q : shear ore in the ailure setion; δ : mid-span deletion at ailure; θ : rotation in the ailure region, integrated along a length o 1.75 d. Type.14 S-2 S S-6 S-12.1 S-9 S-3 S-7 b d.8.6 S-4 S-8 S-5 S θ [mrad] Figure 9 Normalized shear stress versus rotation or all tested speimens eams S-2, S-6 and S-9 and S-11 ailed in shear, beore or at the onset o yielding. eams S-3, S-7, S-4 and S-8 also ailed in shear, but ater the ormation o the plasti hinge, loated bello the load Q. eam S-5 ailed in bending ith the rature o the longitudinal reinorement in tension. The beams ith hot-rolled reinorement type alloed higher hinge rotations than those ith old ormed steel, hen in presene o plasti strains. For beams ith old ormed reinorement (S-2 to S-9), the /(b d.5 ) ratio as generally smaller ith inreasing rotation θ, exept or beam S-7. Figure 1 shos the rak pattern ater ailure or all slab strips. more detailed desription o the test results is available in (az odrigues et al 25). test report (az odrigues and Muttoni 24) is also available at 6

7 Q αq ending S-2 S-3 S-4 S-5 ith bar rature S-8 S-6 S-9 S-7 S-1 S-11 S-12 Figure 1 Failure type and rak pattern or all slab strips 4 Further ork Further ork ill ous on modelling o the non-linear behaviour o C bridge deks under onentrated loads and on the riteria to predit the shear ailure o C bridge dek slabs. The alulations o the slab inner ores ill onsiderer the eet o the shear raking, as ell as the yielding o lexural reinorement. 5 Conlusions This paper desribes the results obtained on 6 tests on 2 large sale reinored onrete bridge antilevers under onentrated loads and on 12 slab strips ithout shear reinorement. The olloing onlusions an be made: ridge antilevers ithout shear reinorement tend to ail in shear under onentrated loads. The ultimate lexural load predited by the yield-line method as not reahed or any o the six tests (Q /Q Flex =.64.86). The measurements made o the slab thikness in the zone o shear ailure indiate possible redistributions o the internal shear lo, ith the progressive ormation o shear raks until equilibrium is no longer possible. The available results should ontribute to a better understanding o shear and punhing shear as similar phenomena. 7

8 The tests on slab strips sho that the shear strength o regions near plasti hinges dereases ith inreasing hinge rotation. 6 knoledgments The authors ould like to express their gratitude to the Siss Federal oads uthority (FEDO) and to the Portuguese Foundation or Siene and Tehnology (FCT) or their support. eerenes ngelakos, D., entz, E. C., Collins, M. P., 21, Eet o Conrete Strength and Minimum Stirrups on Strength o Large Members, CI Strutural Journal, ol. 98, 29-3 Collins, M. P., Kuhma, D., 1999, Ho Sae re Our Large, Lightly einored Conrete eams, Slabs, and Footings?, CI Strutural Journal, ol. 96, Elzanaty,. H., Nilson,. H., Slate, F. O., 1986, Capaity o einored Conrete eams Using High-Strength Conrete, CI Journal, ol. 83, Euroode 1: tions on strutures Part 2: Trai loads on bridges, EN : September 23 Kani, M. W., Huggins, M. W., Wittkopp,.., 1979, Kani on in einored Conrete, Toronto, Department o Civil Engineering Leonhardt, F., Walther,., 1962, eiträge zur ehandlung der Shubprobleme im Stahlbetonbau, Het 151, Deutsher usshuss ür Stahlbeton Muttoni,., 23, Shubestigkeit und Durhtanzen von Platten ohne Querkratbeehrung, eton und Stahlbetonbau 98, Februar 23, Het 2, pp Nia, J., Yamada, K., Yokozaa, K., Okamura, H., 1987, evaluation o the Equation or Strength o einored Conrete eams Without Web einorement, Conrete Library o JSCE, Nr. 9, SI Code 262, Conrete Strutures. Siss Soiety o Engineers and rhitets, 23 Sozen, M.., Zoyer, E. M., Siess, C. P., 1959, Strength in o eams Without Web einorement, ulletin Nr. 452, University o Illinois az odrigues,., Muttoni., 24, Inluene des déormations plastiques de l'armature de lexion sur la résistane à l'eort tranhant des poutres sans étriers. apport d'essai, EPFL - IS-ETON, Lausanne, 24 ( az odrigues,., urdet, O., Muttoni,.,25, Experimental investigation o the shear apaity o plasti hinges, Pro. o the ib symposium Keep Conrete ttrative, udapest, Hungary, vol. 2, pp az odrigues,., Muttoni,., urdet, O., 26, Large Sale s on ridge Slabs Cantilevers subjeted to Trai Loads, Pro. o the seond ib Congress, Naples, Italy. (aepted or publiation) 8