The design of reinforced concrete sections of arbitrary shape, namely with variable geometry, holes as well as with arbitrary distribution of reinforcing steel bars, is a very common task in civil engineering, reinforced concrete structures. The design of these sections requires the integration of non-linear stress fields on complex shapes, because of the non-linear behavior of concrete in compression. In this paper, a novel algorithm is proposed to compute the ultimate strength of reinforced concrete sections under biaxial bending. The algorithm includes section subdivision into trapezoidal elements using the techniques of polygon clipping algorithm proposed by Weiler-Atherton. Exact numerical integration for normal strength concrete (f(ck) <= 50 MPa) is achieved, for each trapezoid, using the change of variables theorem followed by Gauss-Legendre integration. The proposed technique is hereafter referred to as WAGL (Weiler-Atherton, Gauss-Legendre). The verification of the proposed algorithm is performed by comparing analytical results between the WAGL technique and methods proposed by other authors (five examples). Additionally, the results obtained are also compared with experimental results available in the literature. The application of the WAGL technique is illustrated with two RC cross-section design examples. (C) 2015 Elsevier Ltd. All rights reserved.

In statically indeterminate structures, yielding of flexural reinforcement in one section does not necessarily mean that the structure has reached its ultimate load. Typically this occurs in reinforced concrete slabs, which are elements that mostly do not require any kind of shear reinforcement (an exception is made in the case of punching shear). Therefore, the effect of the yielding strains of the flexural reinforcement (if they exist) should be considered when designing for shear. This effect has been studied previously, when it was shown that in 11 tested beams without shear reinforcement, the shear capacity was strongly reduced after yielding. This result is consistent with model code 2010 provisions for one-way shear without shear reinforcement, because the shear capacity decreases with longitudinal web strains and with the critical shear crack theory (CSCT). In this paper, detailed measurements of the web displacements from the same beams are analysed. These allowed quantification of the stresses and the shear force carried across the critical shear crack by aggregate interlock action for varying levels of the longitudinal reinforcement strains.

The influence of shear on the rotation capacity of one-way slabs without shear reinforcement is investigated in this paper by means of an experimental study. The experimental program consisted of 11 slab strips 8400 mm (331 in.) long and 450 mm (17.7 in.) thick with a flexural reinforcement ratio of 0.79%. The rotation capacity was investigated for various values of the shear span and for two types of flexural reinforcement (hot-rolled and cold-worked bars). The specimens developed shear failures with and without yielding of the flexural reinforcement and one specimen failed in flexure with rupture of the tensile reinforcement. The results clearly show that the rotation capacity at failure is governed by shear Based on the test results, and considering the principles of the critical shear-crack theory (CSCT), an analytical expression is proposed to estimate the rotation capacity of one-way members without transverse reinforcement accounting for shear

Ce rapport presente une etude sur le dimensionnement et la verification des dalles de roulement des ponts routiers en beton arme. L’etude commence par une description des modes de ruptures possibles dus aux charges agissantes sur la dalle et notamment dus aux charges concentrees. Suite a cette description, les differents modes de rupture sont analyses en detail. Ces modes correspondent a des ruptures par cisaillement de la dalle : poinconnement autour des charges concentrees ou ruptures par effort tranchant proche des encastrements de la dalle. Dans la SIA 262 (2003), la resistance tant au poinconnement qu’a l’effort tranchant d’une dalle sans armature transversale est estimee sur la base de la theorie de la fissure critique. En travaillant sur les hypotheses de cette theorie, une serie d’adaptations de la formulation contenue dans la SIA 262 (2003) sont proposees pour son application au cas des dalles de roulement. Ceci s’avere necessaire car la formulation de la theorie contenue dans la norme n’est applicable directement que pour des planchers-dalles. Une comparaison de la methodologie proposee avec des resultats d’essais effectues dans le cadre de cette recherche ainsi qu’avec des resultats des simulations numeriques effectues a l’aide de la methode des elements finis confirment la pertinence de l’approche. La precision des resultats obtenus peut aussi etre amelioree si des etapes supplementaires de calcul sont effectuees afin de raffiner certaines hypotheses prudentes. Le rapport est complete par trois annexes, deux contenant des abaques afin de simplifier le processus de dimensionnement ou la verification d’une dalle de roulement et la troisieme avec un exemple d’application pratique.

This paper presents the results of six tests on R/C bridge cantilever slabs without shear reinforcement subjected to concentrated loading. The specimens represent actual deck slabs of box-girder bridges scaled 3/4. They were 10 in long with a clear cantilever equal to 2.78 m and with variable thickness (190 mm at the tip of the cantilever and 380 mm at the clamped edge). Reinforcement ratios for the specimens were equal to 0.78% and 0.60%. All tests failed in a brittle manner by development of a shear failure surface around the concentrated loads. The experimental results are investigated on the basis of linear elastic shear fields for the various tests. Taking advantage of the experimental and numerical results, practical recommendations for estimating the shear strength of R/C bridge cantilever slabs are proposed. (C) 2008 Elsevier Ltd. All rights reserved.

To improve the reduced available experimental data on the load capacity of full scale bridge deck slabs, 3 tests on a large scale bridge cantilever (10 x 4.2 m) were done. The cantilevers were tested under 4, 2 and 1 concentrated loads simulating traffic wheels. Neither of the tests attained the theoretical yield-line failure load. A brittle shear failure was observed for all tests.

An experimental and theoretical investigation of the shear strength of reinforced concrete slabs without shear reinforcement is under way at the Ecole Polytechnique Federale de Lausanne. The first part of the program consists of 6 tests on two large scale bridge deck cantilevers. The specimens are tested under different configurations of concentrated forces simulating traffic loads. The observed failure mode is shear. The second part of the experimental program consists of shear tests on 12 slab strips, to investigate the influence of plastic hinge rotation on the shear strength. The test results show that the shear strength decreases with increasing plastic hinge rotation.

Rapport d'essai de 11 poutres de 8.4m de long sans armature d'effort tranchant. Rupture a l'effort tranchant en presence de fortes, faibles et sans deformations plastiques. Mesures detailles des deformations dans le plan de l'âme. Conclusions: 1) Reduction de la resistance a l'effort tranchant due a la plastification des armatures de flexion. 2) La resistance a l'effort tranchant diminue avec la rotation dans la region crititque. 3) Les poutres avec armatures de type laminee a chaud (avec palier) ont eu plus de ductilite par rapport aux poutres avec acier etire a froid.

Reinforced concrete bridge deck slabs without shear reinforcement can be subjected to concentrated or distributed loads of important magnitude. Under these loads their structural response is not always ductile. In particular under concentrated loads their deformation capacity can be limited by shear or punching shear failures, which prevent them from reaching the ultimate load predicted by pure flexural analysis. This problem has been studied in this research by means of an important experimental program and theoretical modeling. The limited ductility of bridge decks was investigated by means of full scale tests on bridge deck cantilevers under groups of concentrated loads. Six large scale laboratory tests were performed on two bridge deck cantilevers with a span of 2.8 m and a length of 10.0 m. All slabs failed in a brittle manner, in shear or punching shear. The theoretical flexural failure load estimated using the yield-line method was never attained. Despite the brittle failures, the results of tests on cantilevers have shown that some amount of yielding can occur before the shear failure and therefore reduce the shear strength. This effect was quantified on eleven full scale tests on slab strips without shear reinforcement with a length of 8.4 m. The results clearly show that the increase of plastic strains in the flexural reinforcement leads to a reduction of the shear strength. The measured rotation capacity of the plastic hinge was thus limited by a shear failure. A particular problem of bridge deck slabs is the introduction of concentrated loads applied by wheels with pneumatic pressure. Punching shear with these loads is usually treated in a manner similar to punching by a column. A punching shear test was performed with a concentrated load simulating a vehicle wheel with pneumatic pressure to investigate the differences. It appears that punching shear with a wheel with pneumatic pressure is less critical because curvatures tend to be distributed over the surface of the applied load rather than concentrated near the edges of the column. In order to investigate the experimental results on slab strips without shear reinforcement, a mechanical model is proposed to predict the shear strength and rotation capacity of plastic hinges. The shear strength is formulated as a function of the opening of the shear crack and of the strength of the concrete compression zone. The results of the mechanical model are in good agreement with the measured values, both for the shear strength and for the shear carried across the shear crack. Based on the mechanical model, a simplified equation is proposed. The model can also be used to predict the shear capacity of yield-lines. A non linear finite element model was implemented during this work and used to correctly predict the measured rotations and load-displacements curves of the tested cantilevers and other full scale tests performed by other researchers. The measured failure loads are accurately estimated by using the results of the non-linear model and the one-way shear and punching shear criteria proposed by Prof. A. Muttoni (Muttoni 2003).