This research shows the experimental results of the bending moment in a flexible and rigid raft foundation rested on dense sandy soil with different embedded depth throughout 24 tests. A physical model of dimensions (200mm*200mm) and (320) mm in height was constructed with raft foundation of (10) mm thickness for flexible raft and (23) mm for rigid raft made of reinforced concrete. To imitate the seismic excitation shaking table skill was applied, the shaker was adjusted to three frequencies equal to (1Hz,2Hz, and 3Hz) and displacement magnitude of (13) mm, the foundation was located at four different embedment depths (0,0.25B = 50mm,0.5B = 100mm, and B = 200mm), where B is the raft width. Generally, the maximum bending

In this paper, a new equivalent lumped parameter model is proposed for describing the vibration of beams under the moving load effect. Also, an analytical formula for calculating such vibration for low-speed loads is presented. Furthermore, a MATLAB/Simulink model is introduced to give a simple and accurate solution that can be used to design beams subjected to any moving loads, i.e., loads of any magnitude and speed. In general, the proposed Simulink model can be used much easier than the alternative FEM software, which is usually used in designing such beams. The obtained results from the analytical formula and the proposed Simulink model were compared with those obtained from Ansys R19.0, and very good agreement has been shown. I

The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi

The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

  The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] .  Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

The aim of our study is to reveal the effect of steel reinforcement details,tensile steel reinforcement ratio, compressed reinforcing steel ratio,reinforcing steel size, corner joint shape on the strength of reinforcedconcrete Fc' and delve into it for the most accurate details and concreteconnections about the behavior and resistance of the corner joint ofreinforced concrete, Depending on the available studies and sources inaddition to our study, we concluded that each of these effects had a clearrole in the behavior and resistance of the corner joint of reinforced concreteunder the influence of the negative moment and yield stress. A studyof the types of faults that can be reinforced angle joints obtains detailsand conditions of c