This paper presents an experimental and numerical study which was carried out to examine the influence of the size and the layout of the web openings on the load carrying capacity and the serviceability of reinforced concrete deep beams. Five full-scale simply supported reinforced concrete deep beams with two large web openings created in shear regions were tested up to failure. The shear span to overall depth ratio was (1.1). Square openings were located symmetrically relative to the midspan section either at the midpoint or at the interior boundaries of the shear span. Two different side dimensions for the square openings were considered, mainly, (200) mm and (230) mm. The strength results proved that the shear capacity of the deep beam is governed by the size and location of web openings. The experimental results indicated that the reduction of the shear capacity may reach (66%). ABAQUS finite element software program was used for simulation and analysis. Numerical analyses provided un-conservative estimates for deep beam load carrying capacity in the range between (5-21%). However, the maximum scatter of the finite element method predictions for first diagonal and first flexural cracking loads was not exceeding (17%). Also, at service load the numerical of midspan deflection was greater than the experimental values by (9-18%).
The necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.
... Show MoreThe subject of improving the performance of services provided by government institutions of the important topics at the present time because of their direct contact at the service of citizens and the increased importance of these units as a result of the diversity of activities performed by the so governments of the countries and their people made sure to pay attention to the good use of those allocated to those sectors of resources and spending in the service prescribed and manage the highest level of efficiency and effectiveness and monitor the proper management of the money used in those sectors and evaluate their performance through the Supreme Audit Institutions so that they can play their role oversight and contribute to th
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