Calculation of a multi-span frame for stability

Abstract

Abstract The loss of stability of the first kind as applied to the longitudinal bending of the supports of a flat one-story free multispan frame under the action of vertical forces is considered. The elements of the frame have arbitrary stiffnesses constant along the length of the elements. The system of nonlinear equations of displacement method is solved. The matrix of coefficients of the system of equations is presented in block form. Formulas of generalized coefficients for each block of matrix are determined, and then one or another element of general stability equation matrix. A slight correction of generalized coefficients formulas makes it possible to extend the methodology to calculate the stability of non-free frames (overpasses). Compact notation of generalized coefficients of stability equation matrix makes it possible to considerably simplify development of algorithms and computer programs designed for solution of such tasks. The algorithm is implemented in Excel. To verify the obtained results, test calculations of stability frames for which the exact solution is known have been performed. Stability calculation of plane frame of periodic structure has been done by the suggested method. The diagram of the boundary curve has been made and the areas of frame stability and instability under the action of the given system of forces have been determined. Stability calculations of the model in the software package ANSYS, with subsequent comparison of the calculation results, have been performed.