Analytical method comparison on critical force of the stepped column model of telescopic crane

Abstract

The calculation of the critical force of the stepped column model of telescopic boom crane is the key to stability calculation of all-terrain crane. In slightly bending theory, differential equation can be built up, and then the deflection curve of ideal column can be obtained. Using this curve and the Rayleigh–Ritz method, the Euler force of the ideal column can be obtained. For n-stepped columns, Euler forces and the effective length coefficients can be acquired using the deflection curve of the ideal column and parabolic curve, respectively, combined with the Rayleigh–Ritz method. Differential equations of the n-stepped telescopic boom are established based on the vertical and horizontal buckling theory. The recursive formula of the stability of the n-stepped telescopic boom is deduced by the mathematical induction method. For the transcendental equation in the recursive formula, combined with the structural force characteristics and supplementary formulas, the Levenberg–Marquardt numerical optimization algorithm is used to solve the equations with n unknowns. Length coefficients obtained by the three methods are compared using GB3811-2008 and ANSYS 17.0. The results show that the accuracy of the numerical algorithm is the highest, and the first two algorithms will produce large errors when the stepped columns have more steps.