EXPERIMENTAL INVESTIGATION OF THE SHEAR CAPACITY OF PLASTIC HINGES

Transcription

1 fib Symposium Keep Conrete Attrative, Budapest 25 EXPERIMENTAL INVESTIGATION OF THE SHEAR CAPACITY OF PLASTIC HINGES Rui Vaz Rodrigues, PhD andidate; Olivier Burdet, PhD; Prof. Aurelio Muttoni, PhD Strutural Conrete Laboratory Eole Polytehnique Fédérale de Lausanne CH-115 Lausanne Switzerland SUMMARY The influene of plasti in the longitudinal reinforement in presene of high shear fores in beams and slabs without stirrups was investigated performing a series of tests of eight ordinary reinfored onrete beams 8.4 meters long with.79% reinforement ratio. The tests show that the shear apaity of plasti hinges dereases with inreasing rotation. The artile presents a desription of the tests along with the main preliminary results. 1. INTRODUCTION Traditionally, the rotation apaity of plasti hinges is expressed as a funtion of the depth of the onrete ompression zone and the properties of the reinforing steel, negleting the presene of shear fores within the plasti hinge. This approah is not generally appliable in presene of large point loads, at the fixed end of a antilever or at intermediate supports. This artile presents the results obtained from beam tests performed within the framework of a omprehensive study of the shear-bending interation in dek slabs of highway bridges urrently under way at the Strutural Conrete Laboratory of the Swiss Federal Institute of Tehnology in Lausanne. The mode of failure of beams without shear reinforement is thought to be aused by the opening of a ritial rak under inreased deformations. As shown in fig. 1, the shear apaity of beams without shear reinforement dereases with inreasing longitudinal ε, whih are orrelated both to overall defletion and to the opening of the ritial rak (Muttoni, 23). Experimental test results (Sozen, 1959; Leonhardt, 1962; Kani, 1979; Niwa, 1987; Collins, 1999; Angelakos, 21; Elzanaty, 1986) are shown together with the failure riterion to illustrate its performane in determining the ultimate load for beams without plasti in the reinforement. The problem is similar in essene to that of punhing shear of flat slabs without shear reinforement, where the strong influene of large steel, this time orrelated to the overall slab rotation around the olumn has been demonstrated (Muttoni, 1991; Muttoni, 23). This approah was reently adopted as part of the Swiss design ode for onrete strutures, both for the design of beams without shear reinforement and for punhing shear (SIA, 23). 1

2 θ V.2 R b d f.15.1 τr = V R b d VR 1 = b d f ε d D 16 max + V R u d.5 f VR u d.75 = f θ d D 16 max ε d D max + 16 [mm] θ d [mm] D 16 Fig. 1 Strength as a funtion of deformations of beams and slabs (punhing) without shear reinforement (after Muttoni, 23) max + 2. EXPERIMENTAL INVESTIGATION Eight beams have been tested with a onstant retangular setion of.45 m x.25 m and a total length of 8.4 m, as shown in fig. 2. The top and bottom longitudinal reinforement onsists of 4 bars of 16 mm diameter, onstant along the beam s length. The reinforement ratio is.79% for both bottom and top bars for all tested beams. Two loads, Q at mid-span, and αq at the tip of the antilever were applied by 2 hydrauli jaks. The load introdution at the mid-span (Q) was made by means of a steel plate of.1 m x.25 m. The beams were supported on 2 supports, allowing rotation. No shear reinforement was plaed in the measurement zone, but outside of this region, stirrups were provided to prevent a shear failure. The ratio α between the applied fores was varied through the 8 beams and kept onstant during eah test, allowing different shear fores and shear spans for eah beam. Table 1 summarizes the measured material properties for eah tested beam. The maximum aggregate size was 16 mm..45 m East A Q 3. m measurement zone 8.4 m Bending moment diagram a 1 B α Q.45 m Cross-setion 4 Ø16 mm =25 mm 4 Ø16 mm a 2.25 m Fig. 2 Beam dimensions, loads and shear spans a i Tab. 1 Conrete properties for beams SR-2 to SR-9 Beam N SR-2 SR-3 SR-4 SR-5 SR-6 SR-7 SR-8 SR-9 f [MPa] f t [MPa] E [GPa] The reinforement steel used was old formed with a proportional limit at.2% of 515 MPa and a tensile failure strain of 14%. 2

3 Measurements were made mainly in the region between the applied load Q and the intermediate support B. Omega-shaped extensometers ontinuously measured the longitudinal at the top and bottom fibers on the West fae, on the onrete surfae at the level of the top and bottom reinforement (fig. 3). On the East fae, 331 manual measures were made at eah load step with a mehanial strain gauge on a triangular mesh with a base length of 12 mm (figs 2 and 3), allowing a omplete desription of the in-plane deformation of the shear span. High resolution pitures of the shear span were also taken at eah load step, using as photogrammetri targets the verties of the triangular mesh, allowing a diret omparison of both measurements. All the tests were performed under ontrolled displaements. Fig. 3 From left to right: omega-shaped extensometers (West fae), shear span with triangular mesh (East fae), testing faility at EPF Lausanne 3. RESULTS The main results from the tests are shown in figures 4 and 5 as well as in tables 2 and 3. Figure 5 shows the final raking pattern of beams SR-2, SR-3, SR-4 and SR-7. The failure mode was similar for all speimens that failed in shear, with a brittle opening of a diagonal rak, in spite of large plasti deformations in some speimens. Tab. 2 Main results for beams SR-2 to SR-9 Beam N α a 1 [m] a 2 [m] Q [kn] V R [kn] VR ( b d f ) δ R [mm] θ R [mrad] Failure Loation SR B Shear SR Q Shear SR Q Shear SR Q Bending SR B Shear SR Q Shear SR B Shear SR B Shear V R : shear fore in the failure setion; δ R: mid-span defletion at failure; θ R : rotation in the failure region, integrated along a length of 1.75 d Type 3

4 f.14 SR-2.12 SR-6.1 SR-9 SR-3 SR-7 V b d.8.6 SR-4 SR-8 SR-5.4 τ R f θ [mrad] Fig. 4 Normalized shear stress versus rotation for all tested speimens B.4 mm (upside down) 4 mm Q p=1 p=1 p=2 p=3 p=4 p=5 p=6 p=2 p=3 p=4 p=5 p=6 p=7 p=8 p=9 p= SR SR-3 2 mm Q Q p=1 p=2 p=3 p=4 p=5 p=6 p= SR SR-7 Fig. 5 Crak pattern in the failure region, with relative displaements between the lips of the ritial rak and longitudinal onrete at the level of the tensile reinforement 4

5 From the data obtained at eah load step with the mehanial strain gauge on the East fae of the beam (fig. 3), it is possible to derive the relative displaement between the lips of the ritial rak (Muttoni, 1991). The relative displaement, the longitudinal measured at the level of the tensile reinforement and the rak pattern are shown in fig. 5. Beams SR-2, SR-6 and SR-9 failed in shear, before or at the onset of yielding (see fig. 4). Beams SR-3, SR7, SR-4 and SR-8 also failed in shear, but after the formation of the plasti hinge. Beam SR-5 failed in bending with the frature of the longitudinal reinforement in tension. Table 3 shows that the normalized shear VR/(b d f.5) was generally smaller with inreasing rotation θ, exept for beam SR-7. For a detailed desription of the test results, see the omplete test report (Vaz Rodrigues, 24). Tab. 3 Failure type, normalized shear strength and rotation at failure for all beams Failure type SR-5 Flexural with bar frature Crak pattern after failure VR b d f θ [mrad] Q SR-8 plasti SR-4 plasti SR-7 plasti *) First failure Seond failure SR-3 plasti SR Seond failure few plasti *) SR First failure Seond failure First failure few plasti *) SR-2 few plasti B *) Only the first failure is onsidered here 5

6 4. CONCLUSIONS A series of eight reinfored onrete beams without stirrups was tested at the strutural onrete laboratory of EPF Lausanne. The main parameter of the study was the plasti strain in the longitudinal tensile reinforement in the failure region. The results show that the shear apaity of plasti hinges dereases with inreasing hinge rotation. The derease is similar to that observed for punhing shear, where the punhing shear apaity dereases with inreasing plasti in the flexural reinforement. 5. ACKNOWLEDGEMENTS The authors would like to express their gratitude to the Swiss Federal Roads Authority (FEDRO) and to the Portuguese Foundation for Siene and Tehnology (FCT) for their support. 6. REFERENCES Collins M. P., Kuhma D. (1999) "How Safe Are Our Large, Lightly Reinfored Conrete Beams, Slabs, and Footings?", ACI Strutural Journal, Vol. 96, (1999), pp.2-49 Euroode 2 (22), "Design of Conrete Strutures, Part 1, General rules and rules for buildings", pren , 22 Kani M. W., Huggins M. W., Wittkopp R. R. (1979), "Kani on Shear in Reinfored Conrete", Toronto, Department of Civil Engineering, 1979 Leonhardt F., Walther R. (1962), "Beiträge zur Behandlung der Shubprobleme im Stahlbetonbau", Heft 151, Deutsher Ausshuss für Stahlbeton, 1962 Muttoni A. (23) "Shubfestigkeit und Durhtanzen von Platten ohne Querkraftbewehrung" Beton und Stahlbetonbau 98, Februar 23, Heft 2, pp Muttoni A., Shwartz J. (1991), "Behaviour of Beams and Punhing in Slabs without Shear Reinforement", IABSE Colloquium Stuttgart, Vol. 62, Zürih: International Assoiation for Bridge and Strutural Engineering, 1991, pp Niwa J., Yamada K., Yokozawa K., Okamura H. (1987), "Revaluation of the Equation for Shear Strength of Reinfored Conrete Beams Without Web Reinforement", Conrete Library of JSCE, Nr. 9 (1987), pp Sozen M. A., Zwoyer E. M., Siess C. P. (1959), "Strength in Shear of Beams Without Web Reinforement", Bulletin Nr. 452, University of Illinois, 1959 SIA Code 262 (23), Conrete Strutures. Swiss Soiety of Engineers and Arhitets, 23 Vaz Rodrigues R., Muttoni A., (24) "Influene des déformations plastiques de l'armature de flexion sur la résistane à l'effort tranhant des poutres sans étriers. Rapport d'essai", EPFL - IS-BETON, Lausanne, 24 ( 6