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In this study, free vibration of square cross-sectioned aluminum beams is investigated analytically and numerically under four different boundary conditions: Clamped-Clamped (C-C), Clamped-Free (C-F), Clamped-Simply Supported (C-SS) and Simply Supported-Simply Supported (SS-SS). Analytical solution is carried out using Euler-Bernoulli beam theory and Newton Raphson Method. First, the equations of motion are provided. Then, solutions including the effects of the geometric characteristics, and boundary conditions are obtained and discussed for the natural frequencies of the first three modes. To confirm the reliability of the vibration analysis carried out in the present paper as well, all the analytical results are checked with the corresponding numerical results obtained from the finite-element-method (FEM) based software called ANSYS. Numerical and analytical results are found to be good agreement.

In the present study elastic buckling of steel columns with three different cross sections, i.e. square, rectangle and circle cross sections, and two different boundary conditions, i.e. fixed-free(F-F) and pinned-pinned (P-P) boundary conditions, under axial compression has been investigated. At first, the basic equations of the problem have been given. Then solutions are found and the effects of the boundary conditions, cross sections, slenderness ratios on the buckling loads of the steel columns have been discussed. For the solution of the problem not only numerical computations have been performed but also finite element modeling (FEM) has been employed. For the validation of the present study, the results of numerical computations have been compared with the results of FEM, and a very good agreement has been achieved.

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Abstract-In this study, natural frequencies of the prismatical steel beams with various geometrical characteristics under the four different boundary conditions are determined using Artificial Neural Network (ANN) technique. In that way, an alternative efficient method is aimed to develop for the solution of the present problem, which provides avoiding loss of time for computing some necessary parameters. In this context, initially, first ten frequency parameters of the beam are found, where Bernoulli-Euler beam theory was adopted, and then natural frequencies are computed theoretically. With the aid of theoretically obtained results, the data sets are formed and ANN models are constructed. Here, 36 models are developed using primary 3 models. The results are found from these models by changing the number and properties of the neurons and input data. The handiness of the present models is examined by comparing the results of these models with theoretically obtained results. The effects of the number of neurons, input data and training function on the models are investigated. In addition, multiple regression models are developed with the data, and adjusted R-square is examined for determining the inefficient input parameters

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