ANALYSIS OF LATERAL STIFFNESS AND CRITICAL BUCKLING FORCE OF STEPPED COLUMNS AND THEIR PRACTICAL FORMULATIONS

Telescopic crane booms and multistage cylinders of large fire trucks are typical stepped column structures. To analyze their vertical stiffness and stability status under axial loadings, differential equations of the deflection of stepped column structures based on the vertical and horizontal bending theory are established in this study. Precise expressions of the lateral deflection and buckling characteristic equations with second-order effects are obtained. More specifically, formulations for columns of less than six levels of steps are derived for practical engineering application. An equivalent component method is proposed for the stability analysis of stepped column structures, and a formulation for lateral stiffness analysis is derived by introducing the deflection influence coefficient. Examples with 5 and 8 levels of stepped column are used for the stability and stiffness analysis, and the effective length factor and the deflection at the column ends are calculated. Results calculated from the proposed formulations in this study agree well with those from literature, which demonstrates the credibility and accuracy of the proposed formulations and their applicability in engineering practice.