# Damage and Failure of a Column-Supported RC Flat Slab Subjected to Impulsive Loading
## 6 Conclusions  
The present study refers to an RC flat slab that is supported by an array of columns (4 \(\times\) 4 and 8 \(\times\) 8) and subjected to a short duration constant pressure. The slab thickness and its reinforcement are designed for static loads according to a current standard. The 35 MPa concrete is simulated by the P-\(\alpha\) model for the equation of state and the RHT model for the deviatoric behavior. The linear EOS and a bi-linear elastic plastic deviatoric model with failure at a given effective plastic strain are used for the steel rebars. A simplified model consisting of a tributary area with a span size having a single central column and \"symmetry\" boundary conditions is used for comparison. Comparison between the full-size slabs' response and the simplified model response demonstrates the accuracy of the simplified model and its reliability for this loading. All these analyses have clarified the response of the RC flat slab to the action of an impulsive load, and its damage evolution and failure characteristics. It has been shown that the velocity-time histories of the two 4 \(\times\) 4 and 8 \(\times\) 8-columns multi-span slabs are very similar, and the velocity-time history of the simplified model only slightly deviates from these curves. The calculated responses up to 10 ms are identical and the same peak and permanent velocities are reached. Furthermore, the local minor variation between the single-span and multi-span slabs is noticed in their velocity-time histories but is not noticed in their displacement-time history. Therefore, the simplified model is a reliable representation of the entire slab response to a uniformly distributed short-duration loading acting on the entire slab. It may provide considerably faster solutions compared to the full-size slab. Examination of the damage map of the full-size slab indicates that damage is developed around each column, whereas the slab domains between these zones remain almost flat and damage free; this justifies the isolation of a tributary area around a column to obtain the calculate the damage-time history, which is similar for every other slab-column connection zone. The cross-sectional damage patterns in both multi-span slabs are very similar, with the following major features: (1) the damage is concentrated at the slab-column connections, along the slab spans out of the column zones no significant damage is observed; (2) the slab damage at the column zone is characterized by 100% damage in the concrete; (3) large shear distortions of the slab are clearly observed in this zone; (4) a large displacement is observed between the slab current position and its original position crossing the column; (5) the internal spans seem to remain in a horizontal position with minor almost unnoticeable curvature. The concrete in the connection zone is fully damaged and the slab reinforcement fails at cross-sections that are close to the column circumference. This refers to the top and bottom reinforcement meshes through which the column is punching through, as well  
Figure 11: Slab-on-slab damage and failure. (**a**) Top view. (**b**) Cross-section. as to the integrity reinforcement which fails similarly to the bottom reinforcement. This failure indicates that the integrity rebars are useless and cannot arrest the slab from falling. Therefore, the integrity reinforcement cannot fulfill its expected task to support the failed slab and prevent a progressive collapse. Hence, under this loading, a following progressive collapse scenario is inevitable. The failure of all bent-up rebars indicates their limited role in enhancing shear resistance and their contribution to resisting shear is doubtful. An interesting observation refers to the difference between the failure mode due to the impulsive loading, which is entirely different from the expected failure under static loading. The static analysis demonstrates the slab bending behavior, with hogging bending moments at the supporting points and sagging bending moments in the central parts of the spans.