Punching shear failure is considered one of the main problems that must be considered during the design of flat slabs especially at the critical slab column connection zone. This paper is part of an ongoing research program conducted at the concrete laboratory of the Faulty of Engineering, Cairo University to assess the effect of different types of shear reinforcement on the punching behavior of reinforced concrete flat slabs. In this paper, shear heads in the form of embedded steel beams were used to improve the performance of slabs against punching failure. An experimental program was carried out using six half scale specimens of flat slabs with dimensions of 1100 mm x 1100 mm and 150 mm thickness and each was provided with a central square concrete column of 150 mm x 150 mm with 400 mm height. The main investigated parameters were the arm length, configuration and dimensions of the steel beams by using two different types: hot rolled and built-up sections. The experimental results showed that using embedded steel beams at the column-slab connection significantly improved the punching shear capacity and ductility of flat slabs. The test results were compared against values obtained using the provisions of the ACI international design code.

The Nagumo equation describes a reaction-diffusion system in biology. Here, it is coupled to Burgers equation, via including convection, which is the Burgers-Nagumo equation (BNE). The first objective of this work is to present a theorem to reduce, approximately, the different versions of the fractional time derivatives (FTD) to an ordinary derivative (OD) with time dependent coefficients (non autonomous). The second objective is to find the exact solutions of the fractal and FTD-BNE is reduced to BNE with time dependent coefficient. Further similarity transformations are introduced. The unified and extended unified method are used to find the exact traveling waves solutions. Also, self-similar solutions are obtained. The novelties in this work are (i) reducing, via an analytic approximation, the different versions of FTD to non autonomous OD. (ii) Traveling and self-similar waves solutions of the FTD-BNE are derived. (iii) The effect of the order of fractional and fractal derivatives, on waves structure, are investigated. It is found that significant fractal effects hold for smaller order derivatives. While significant fractional effects hold for higher-order derivatives. It is found that, the solutions obtained show solitary wave, wrinkle soliton, solitons with double kinks or with spikes and undulated wave. Further It is shown that wrinkle soliton, with double kink configuration holds for smaller fractal order. While in the case of fractional derivative, this holds for higher orders. We mention that the results found here are completely new. Symbolic computations are carried by using Mathematica.