A conceptual model for the prediction of the shear-flexural strength of slender reinforced concrete beams with and without transverse reinforcement is presented. The model incorporates the shear transferred by the un-cracked concrete chord, along the crack's length, by the stirrups, if they are, and, in that case by the longitudinal reinforcement. After the development of the first branch of the critical shear crack, failure is considered to occur when the stresses at any point of the concrete compression chord reach the assumed biaxial stress failure envelope. A physical explanation is provided for the evolution of the shear transfer mechanisms, and the contribution of each one at ultimate limit state is formulated accordingly. Simple equations are derived for shear strength verification and for designing transverse reinforcement. The method is validated by comparing its predictions with the results of 1131 shear tests, obtaining very good results in terms of mean value and coefficient of variation. Beca...

Shear-flexural strength mechanical model for the design and assessment of reinforced concrete beams

Assessing punching shear failure in reinforced concrete flat slabs subjected to localised impact loading

Compressive membrane action in progressive collapse resistance of RC flat plates

Punching of flat slabs supported on rectangular columns

This paper outlines the theoretical background of the punching shear provisions implemented in the fib Model Code 2010 and presents a practical example of its applica tion. It is the aim to explain the mechanical model that forms the basis of the punching design equations, to justify the relevance of the provisions and to show their suitability for the design and assessment of structures.

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Background to fib Model Code 2010 shear provisions - part II: punching shear

Most analytical approaches and available test data for punching shear in flat slabs assume axis-symmetrical conditions, which seems realistic for representing slabs supported on columns equally spaced in both orthogonal directions. However, in practice, there are many instances where loading, geometry and reinforcement around internal columns differ significantly from ideal axis-symmetrical conditions. Typical examples include slab bridges, flat slabs with unequal spans and footings with unequal widths. This paper presents a series of punching shear tests on slabs without transverse reinforcement and different flexural reinforcement ratios or loading conditions in each orthogonal direction. The tests show that both the type of loading and the amount of flexural reinforcement have a significant influence on the punching shear strength and symmetry of the response. Eurocode 2 and BS 8110 code formulas provided reasonable strength predictions of the tests using the recommended average reinforcement ratio between the x and y directions. A physical explanation behind this assumption is presented, based on critical shear crack theory. A rational analytical approach was developed for non-axis-symmetrical punching, which provides accurate predictions of strength and deformation capacity. The novelty of the proposed method is that it considers a non-uniform shear strength distribution per unit length along the control perimeter, which results in a redistribution of shear near failure.

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Non-axis-symmetrical punching shear around internal columns of RC slabs without transverse reinforcement

Bent-up bars were extensively used as shear reinforcement in beams and slabs from the first R/C developments up to the 1970’s. Their use was justified by the fact that they allowed enhanced development of the tensile reinforcement at the same time they acted as shear reinforcement. New reinforcing bars (with reduced development lengths) in combination with shear reinforcing systems led however to the abandon on their use. Recently, interest has again grown on the use of bent-up bars in flat slabs. This is explained by their efficiency both as shear reinforcement (alone or in combination with stirrups) and as integrity reinforcement. In this paper, the results of 7 full-scale specimens (3.0×3.0×0.25 m) reproducing the support region of an actual flat slab with different layout of bent-up bars are presented. The tests show different potential failure modes and allow understanding the contribution of this reinforcement to the shear-carrying capacity of the specimens. Additionally, the performance of bent-up bars as integrity reinforcement is discussed with reference to 9 half-scale specimens (1.5×1.5×0.125 m) where the influence of the development conditions of the bent-up bars is clearly assessed.

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Applications of bent-up bars as shear and integrity reinforcement in r/c slabs

A non-standard formulation is applied to find analytical solutions for elastic plates considering shear deformation using a computer-aided approach. Classical formulations of mechanics of elastic body solve each particular problem by obtaining standard differential equations. In contrast, the unified formulation used in this paper, which is described in Tassinari et al. [9], is based on a matrix framework inspired by the finite element method. For this reason, an implementation using mathematical software can be efficiently applied. The aim of this study is to use the proposed computer-aided method to solve analytically the problem and to compare the results with the finite element model predictions. In order to illustrate this approach, the case of the Reissner-Mindlin plate problem with simply support on two opposite edges is investigated (Reissner [6], Mindlin [7]). In addition, the general validity of the method and its applicability to several problems of structural mechanics is discussed. The analytical solution for a particular load case is presented showing the differences between the Reissner-Mindlin solution and the predictions given by the Love-Kirchhoff model (Kirchhoff [4], Love [5]). Finally, the vertical displacement field obtained analytically for different thickness-to-side ratios is compared with finite element method predictions. The results obtained from the proposed analytical method and numerical models presented in this study are comparable.

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Unified formulation for Reissner-Mindlin plates: a comparison with numerical results

The provisions for punching shear around concentrated loads in the new Model Code 2010 (MC2010) have been updated, covering a large number of design cases such as slabs with and without transverse reinforcement, different column/slab geometries and prestressed slabs amongst others. The theoretical framework used was based on the mechanical model of the Critical Shear Crack Theory (CSCT). This approach, in contrast to empirical formulas, provides the designer with a physical understanding of the phenomenon and allows an enhanced flexibility to implement new parameters, which may arise in practice when introducing innovative structural solutions to increase the punching strength. This paper summarizes the basis for the derivation of the design formulas introduced in the new Model Code 2010 and shows a comparison with test data from the literature including tests carried out at Ecole Polytechnique Federale de Lausanne. Several levels of approximation are presented depending on the complexity of the method used to estimate the slab rotations. Lastly, it is shown that approximated formulas and shear fields can be used for particular and general cases consistently with the CSCT

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Luca Tassinari

Papers

Non-axis-symmetrical punching shear around internal columns of RC slabs without transverse reinforcement

Punching of flat slabs supported on rectangular columns

Applications of bent-up bars as shear and integrity reinforcement in r/c slabs

Unified formulation for Reissner-Mindlin plates: a comparison with numerical results

New provisions for punching shear in model code 2010 based on the critical shear crack theory