SUMMARYIn this paper a new and innovative method for computation of longitudinal dynamic characteristics of multi-cracked bars is proposed. Cracks are modeled by equivalent axial springs with specified flexibility. Making use of the Heaviside step function and Dirac's delta distribution, a single governing equation for the whole bar is developed. The governing equation is an ordinary differential equation. With the help of Laplace Transform, a general analytical solution in terms of several unknown coefficients is determined. Boundary conditions are then used to determine the analytical solution for specific problems. Making use of the proposed governing equation a new finite element formulation is derived. In this formulation the effect of cracks is considered by adding an equivalent mass matrix to the element mass matrix. Through numerical study, the accuracy, efficiency and robustness of the work is verified.

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Liquid storage steel tanks are vertical above-ground cylindrical shells and as typical thin-walled structures, they are very sensitive to buckling under external pressures, especially when they are empty or at low liquid level. In this paper the results of numerical investigations on the effects of spiral stairway on the buckling behavior of steel cylindrical tanks subjected to external pressures are presented. Furthermore, a numerical study is performed to investigate the effects of internal corrosion on the buckling behavior of ground based steel cylindrical liquid storage tanks, subjected to both wind and vacuum pressures. It is concluded that the spiral stairway acts as an oblique stiffener on the tank wall. Contrary to the case of wind loading, the stairway has negligible effect on buckling resistance of tanks under vacuum pressure. In addition, it is found that the buckling load is markedly reduced with thinning of the shell for upper part corrosion cases, irrespective of the loading condition.