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Two-way flat slabs are extensively used in many structures, such as buildings, shopping centers, and parking garages, because their static efficiency allows to attain large span-depth ratios and to have more spaced columns. The reduction of the thickness, however, is limited by serviceability requirements (resulting from deflection criteria) and by the ultimate limit state of punching shear. This collapse mode has been widely studied in the past, with reference to ordinary conditions, but very limited attention has been devoted to the punching resistance of flat slabs in fire conditions, an issue which is of primary concern, especially in the case of parking garages. This paper deals with two key aspects of slab punching in fire conditions. The first is the sizable reduction of the punching resistance in a typical slab-column assembly, because of the thermally induced damage caused by the exposure to the fire, that is modeled by means of the temperature-time curve ISO-834 (that fits very well the points given by ASTM E119-08a. The second is the sizable load increase due to the redistribution of the internal forces ensuing from the fire that is modeled through a realistic fire scenario based on the available information coming from real car fires. Even if these two phenomena do not necessarily occur simultaneously in a real fire, they both testify to what extent punching shear can be critical for reinforced concrete slabs in fire.

There are two basic assumptions for the shear force Vc in ACI 318-02: 1) Vc is the shear force at cracking; and 2) Vc is the same for members with and without shear reinforcement. By reviewing tests, it is shown that neither assumption is valid. Therefore, different terms have to be defined for the concrete contribution Vct of the shear capacity for members without shear reinforcement and Vc for members with stirrups. The size effect has to be considered for Vct for members without shear reinforcement, but plays a minor role for Vc for members with stirrups. Chapter 4, "Truss model versus Vc-term" shows that there is a clear relationship between the angle q of the inclined struts and a Vc-term. A more realistic model for the state of stress in the web, however, is described by the "truss model with crack friction," where the crack angle is different from the strut angle or angle of principal compression. There, the term Vc has a clear mechanical meaning as the vertical component Vf of friction forces along the inclined crack. In the web, an inclined biaxial tension-compression-field exists, so that the usual truss model is superimposed with a truss model with inclined concrete ties. Because the crack angles are considered, the shear design for prestressed concrete beams leads to a lower value for the angle q and less amount of stirrups than that for reinforced concrete beams.

This study presents an inelastic nonlinear beam element with axial, bending, and shear force interaction for cyclic analysis of reinforced concrete (RC) structures. The element considers shear deformation, and is based on the section discretization into fibers with hysteretic material models for the constituent materials. The shear mechanism along the beam is modeled by using a Timoshenko beam approach. The steel material constitutive law is assumed to be bilinear. The concrete constitutive law is based on the soften membrane model. This newly developed constitutive law can predict the concrete contribution Vc, which is produced by the shear resistance of concrete along the initial crack direction. The constitutive relationships of the RC element have been developed based on the smeared behavior of cracked continuous orthotropic material assumption of concrete with the inclusion of Poisson effects. This model accounts for the softening effect of concrete, as well as the tension stiffening and confining effects. Transverse strains are internal variables determined by imposing equilibrium at each fiber between concrete and vertical transverse steel reinforcement. Element forces are obtained by performing an equilibrium-based numerical integration on the section axial, flexural, and shear behaviors along the element length. The paper concludes with a correlation study between the analytical models and experimentally tested shear-critical RC columns.

The paper describes the development of models for torsion in northern Europe. After an introduction with a few historical notes, early use of nonlinear methods in Scandinavia is presented. The development of failure models for combined torsion, bending and shear is then described as well as the use of truss models. Static and kinematic methods are treated and a discrepancy in the results from different approaches is discussed. A refined model is then presented which unifies the results. Finally, some recent contributions are presented regarding prestressed high-strength circular column elements, hollow core slabs and curved bridges.

The paper reviews the application of classical plasticity theory to shear failure of structural concrete beams. The resistance of concrete to shearing deformations is described by the modified Coulomb failure criterion. For beams with shear reinforcement, this leads to an upper bound solution based on yield lines minimizing the combined work of yielding stirrups and cracking concrete, the coinciding lower bound solution corresponding to an inclined compression field (the web-crushing criterion). For beams without shear reinforcement, the optimal failure mechanism is a single yield line (straight or hyperbolic) from load to support, the coinciding lower bound solution corresponding to a compressive strut between the load and support platens. The predicted failure mechanisms and ultimate loads are compared with experimental evidence, and it is concluded that the plasticity approach goes a long way toward solving the riddle of shear failure.