Combining finite element analyses and mechanical models for the assessment of reinforced concrete slabs

The influence of the level of deformation of the flexural reinforcement on the punching strength is well-established and mechanically founded since the pioneer works of Kinnunen and Nylander in the 1960’s. In code provisions, this influence is sometimes reflected by means of indirect parameters such as the flexural reinforcement ratio (as in many empirical formulae) or by means of mechanical approaches accounting for the ratio between the applied load and the flexural resistance of the specimen (as in fib’s MC2010). An accurate estimate of this parameter (level of deformation of the flexural reinforcement) is nevertheless complex in many situations, due to the determination of the moment field and the po-tential redistributions of bending moments. In order to provide a consistent approach to determine the punching strength, it has been recently proposed to couple refined finite element (FE) models describing accurately the flexural behavior of slabs (accounting for the influence of cracking, yielding and moment redistributions) with a robust strain-based failure criterion in shear. In this framework, the goal of this paper is to review specific case studies in which redistributions after cracking in bending and shear may be governing on the overall behavior of reinforced concrete slabs. Load–displacement responses of the investigated case studies are evaluated by means of FE analyses using a multi-layered shell formulation. Eventually, the numerical global response is combined with the failure criterion of the Critical Shear Crack Theory, that can directly consider the influence of the flexural response on the punching or shear capacity.

The Critical Shear Crack Theory for punching design: from a mechanical model to closed-form design expressions

Miguel Fernández Ruiz, Aurelio Muttoni

The Critical Shear Crack Theory (CSCT) is a consistent approach used for shear design of one- and two-way slabs failing in shear and punching shear respectively. The theory is based on a mechanical model allowing to determine the amount of shear force that can be carried by cracked concrete accounting for the opening and roughness of a critical shear crack leading to failure. The theory was first developed for punching design of slab-column connections without shear reinforcement. Its principles were later extended to other cases such as slabs with shear reinforcement, fibre-reinforced concrete or slabs strengthened with CFRP strips and one-way slabs without shear reinforcement. The generality, accuracy and ease-of-use of this theory led to its implementation into design codes (such as the fib Model Code 2010 or the Swiss Code for concrete structures). The design expressions of the CSCT consist of a failure criterion and a load-deformation relationship, whose intersection defines the load and the deformation capacity at punching failure. They are clear and physically understandable, and can be written in a compact manner to be used for design of new structures. With respect to the assessment of the maximum punching capacity, the conventional design expressions of the CSCT can also be used, although they required to be solved iteratively. In order to enhance the usability of the design equations of the CSCT, particularly for the punching assessment of existing structures, this paper presents closed-form design expressions developed within the frame of the CSCT. These expressions allow for direct design and assessment of the failure load. The closed-form expressions keep the generality and advantages of the CSCT approach, but they allow for a faster and more convenient use in practice. In this paper, the derivation of these expressions on the basis of the CSCT principles is presented as well as its benefits and comparison to experimental results and the original design formulation.

2016

Shear force redistributions and resistance of slabs and wide beams

Raffaele Cantone, Miguel Fernández Ruiz, Aurelio Muttoni

Redistribution of shear forces in reinforced concrete members without shear reinforcement is a key aspect for the assessment of the shear capacity of wide beams and slabs. Such redistributions are due to the nonlinear response of reinforced concrete (both in bending and shear) and have the potential to significantly modify the internal forces during loading. This phenomenon allows in many cases, as for slabs linearly supported and subjected to concentrated forces, to increase the level of load even when some regions have already attained their local shear resistance. This work introduces the results of an experimental programme performed on three cantilever slabs subjected either to strip loads or to concentrated loads. Shear redistributions close to failure are investigated on the basis of refined measurements performed on the concrete surface and on the reinforcement bars. The results show the significance of several mechanical parameters, as well as how shear redistributions occur when some regions are in softening (post-peak behavior) while others have still not attained their local shear resistance. On this basis, a comprehensive approach is presented for determining the redistributions of internal forces and to predict the shear capacity of reinforced concrete slabs subjected to concentrated loads near linear supports. The performance of such approach is eventually validated against test data and practical recommendations are proposed for design and assessment.

2021

Poinçonnement des planchers-dalles avec colonnes superposées fortement sollicitées

Roberto Guidotti

Flat slabs are commonly used in buildings due to their easiness of construction and economy. In order to keep these advantages, columns are usually not continuous through the slabs in multi-storey buildings. In these cases, the slabs are subjected to large compressive stresses at the support area of the columns, which can exceed the uniaxial compressive strength of the concrete of the slab. This critical zone is in addition subjected to large shear forces and bending moments due to the loads applied on the slab. This leads to a series of potential failure modes: crushing of the concrete of the slab between columns, flexural failures or punching shear failures. Most research has previously focused on the influence of bending of the slab on the column strength. However, no works have provided in-depth investigation of the strength of the slab when large column loads are applied. In this research, an extensive experimental program has shown that the stresses applied at the support area of the columns can be significantly larger than the uniaxial compressive strength of concrete. The test results have clearly shown that no special confinement or load transfer devices are required between columns for most cases (moderate column loads). In addition, two phenomena have been observed. The first one is a reduction on the flexural strength as column loads are applied. The second corresponds to a significant increase on the punching shear strength and deformation capacity with column loading. Existing theoretical approaches for flat slab behaviour and strength are shown not to be directly applicable for slabs subjected to large column loading. In this research, the principles of two general theories (the theory of plasticity and the critical shear crack theory) are thus used to investigate such cases. The theory of plasticity allows calculating a plastic failure envelope accounting for bending and column loading, whereas the critical shear crack theory, which in this work as been further investigated theoretically, is used to derive a failure criterion accounting for punching shear failure in presence of column loading. The results for both theories are finally presented in terms of a single interaction diagram between column loading and slab loading (bending and shear of the slab). The theoretical approaches require however the help of rather refined numerical tools for estimating the strength of a flat slab. In order to use the theoretical approaches for design, a simplified approach has been developed, allowing to calculate the strength as well as the deformation capacity of flat slabs. These tools were implemented in a design method for slab-column joints in multi-storey building. This design approach allows to derive simplified interaction diagrams that can be compared with the loading history of the structural element analysed.