In the case where a shallow foundation does not satisfy with design requirements alone, the addition of a pile may be suitable to improve the performance of the foundation design. The lack of in-situ data and the complexity of the issues caused by lagging in the research area of pile foundations are notable. In this study, different types of piles were used under the same geometric conditions to determine the load-settlement relationships with various sandy soil relative densities. The ultimate pile capacity for each selected pile is obtained from a modified California Bearing Ratio (CBR) machine to be suitable for axial pile loading. Based on the results, the values of Qu for close-ended square pile were increased by 15

The aim of this study is to construct a Mathematical model connecting the variation between the ambient temperatures and the level of consumption of kerosene in Iraq during the period (1985-1995), and use it to predict the level of this consumption during the years (2005-2015) based on the estimation of the ambient temperatures.

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

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Cantilever beams are used in many crucial applications in machinery and construction. For example, the airplane wing, the microscopic probe for atomic force measurement, the tower crane overhang and twin overhang folding bridge are typical examples of cantilever beams. The current research aims to develop an analytical solution for the free vibration problem of cantilever beams. The dynamic response of AISI 304 beam represented by the natural frequencies was determined under different working surrounding temperatures ((-100 ℃ to 400 ℃)). A Matlab code was developed to achieve the analytical solution results, considering the effect of some beam geometrical dimensions. The developed analytical solution has been verified successful