Title: Calculation of Multispan Frame Stability With Regard to Geometric Nonlinearity

Abstract

The paper considers the methodology of determining the critical value of the load acting on a flat multi-span frame, taking into account geometric nonlinearity. The elements of the frame have arbitrary stiffnesses constant along the length. The problem is solved in two stages. At the first stage, the strain calculation of the frame is performed, the main goal of which is to obtain the values of longitudinal forces in the struts. At the second stage, loss of stability of the first kind is considered in relation to the longitudinal bending of the props under the action of vertical forces. In both calculations, practically the same system of nonlinear equations of displacement method is solved. The compact notation of generalized stiffness matrix coefficients obtained earlier by the authors facilitates the development of the algorithm and computer programs designed for solving the problems set in the paper. The algorithm is implemented in Excel spreadsheets. To verify the obtained results, test calculations for both stages of the calculation have been performed. Using the proposed methodology, the stability of a flat free one-story frame with a periodic structure has been calculated. In the ANSYS software package, the calculations of this frame according to the deformed scheme were performed, with the subsequent determination of the value of critical longitudinal force in the struts. Comparison of the results of calculations by the offered technique and in the ANSYS program complex shows their practically complete coincidence: the difference in the values of longitudinal forces in the frame struts with allowance for geometric nonlinearity is less than 0.01 %; the calculation results of the first two critical forces differ by 0.06 %. The proposed methodology allows us to use a unified approach to the formation of systems of solving nonlinear equations, both in the strain calculation and in the calculation of stability. In addition, this approach releases from the use of expensive computer programs, the use of which requires special training.