Statics, Stability And Vibration Of Non-prismatic Beams And Columns

Abstract

An algorithm that evaluates the static, stability and vibration response of non-prismatic beams and columns is presented. Matrix equations are derived that can be readily included in existing computer programs on the analyses of 2-D and 3-D framed structures with prismatic and non-prismatic members. The proposed algorithm is unique because it shows that any consistent matrix (mass, damping, geometric, incremental, load vectors, etc.) of a non-prismatic straight beam can be obtained directly from its basic stiffness coefficients (four coefficients for a 2-D case or eight for a 3-D case). The proposed algorithm finds great applicability in: (1) the static, dynamic and stability analyses of framed structures made up of tapered members; (2) the static and stability analysis of framed structures supported on non-uniform elastic foundations including piles in which the soil stiffness varies with the depth; (3) static analyses of cylindrical tanks of variable wall thickness and supported on non-uniform foundations; and (4) the eigenvalue and dynamic analyses of framed structures under free-free conditions. It is shown in this paper that the analyses (static, dynamic and stability) of framed structures with non-prismatic and prismatic members under any loading and support conditions can be carried out once the main stiffness coefficients are determined. Numerical examples on the statics, stability and dynamics of non-prismatic beams are included for easy verification and compared with available results from other analytical methods to show the power of the proposed algorithm.