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The need to improve on analysis and design of structural members for overall weight, material and financial economy is indispensable. This paper presents the results of post-buckling analysis of an axially loaded prismatic column. The theory of elasticity was employed to formulate the total potential energy functional for a prismatic column in the post buckling regime. The derived functional was minimized with respect to deflection function to obtain the governing equation of equilibrium. The governing equation was then solved to obtain the deflection equation. Again, the functional was minimized with respect to the coefficient of the obtained deflection function to obtain the formula for calculating the post-buckling load of the prismatic column. A numerical example was given to demonstrate the applicability of the present formulation. The prismatic column was analyzed within the post buckling regime to determine the stiffness coefficients. It was shown that as the deflection-thickness (Δ/t) ratio increased, the combined buckling stress increased geometrically. It was found that the critical buckling load obtained from the present method and those obtained from literature showed consistency. It was also found that at the buckled state of the prismatic column, the yield strength of the column material has not been attained and deflection is very small. This gives room for the column to take on more loads before it fails either by excessive deflection or by stress exceeding the material strength. [ABSTRACT FROM AUTHOR]

The need to improve on analysis and design of structural members for overall weight, material and financial economy is indispensable. This paper presents the results of post-buckling analysis of an axially loaded prismatic column. The theory of elasticity was employed to formulate the total potential energy functional for a prismatic column in the post buckling regime. The derived functional was minimized with respect to deflection function to obtain the governing equation of equilibrium. The governing equation was then solved to obtain the deflection equation. Again, the functional was minimized with respect to the coefficient of the obtained deflection function to obtain the formula for calculating the post-buckling load of the prismatic column. A numerical example was given to demonstrate the applicability of the present formulation. The prismatic column was analyzed within the post buckling regime to determine the stiffness coefficients. It was shown that as the deflection-thickness (Δ/t) ratio increased, the combined buckling stress increased geometrically. It was found that the critical buckling load obtained from the present method and those obtained from literature showed consistency. It was also found that at the buckled state of the prismatic column, the yield strength of the column material has not been attained and deflection is very small. This gives room for the column to take on more loads before it fails either by excessive deflection or by stress exceeding the material strength. [ABSTRACT FROM AUTHOR]

Abstract: The objective of this paper is to propose a simplified approach to the evaluation of the critical buckling load of multi-story frames with semi-rigid connections. To that effect, analytical expressions and corresponding graphs accounting for the boundary conditions of the column under investigation are proposed for the calculation of the effective buckling length coefficient for different levels of frame sway ability. In addition, a complete set of rotational stiffness coefficients is derived, which is then used for the replacement of members converging at the bottom and top ends of the column in question by equivalent springs. All possible rotational and translational boundary conditions at the far end of these members, featuring semi-rigid connection at their near end as well as the eventual presence of axial force, are considered. Examples of sway, non-sway and partially-sway frames with semi-rigid connections are presented, where the proposed approach is found to be in excellent agreement with the finite element results, while the application of codes such as Eurocode 3 and LRFD leads to significant inaccuracies. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to propose improved expressions for the effective buckling length coefficient of columns in multi-story sway frames. To that effect, a complete set of rotational stiffness coefficients are derived, which are then used for the replacement of members converging at the bottom and top ends of the column in question by equivalent springs. All possible rotational and translational boundary conditions at the far end of these members, as well as the eventual presence of axial force, are considered. An analytical expression and a corresponding graph similar to those used by Eurocode 3 are then proposed for the calculation of the effective buckling length coefficient. Examples of three-story sway frames are presented, where the proposed approach is found to be in excellent agreement with finite element results, while applications of Eurocode 3 and LRFD lead to significant inaccuracies. [Copyright &y& Elsevier]

The sensitivity of laminated cylindrical shell to imperfection is considered, via the initial post-buckling analysis, on the bases of Sanders’ theory. A general code is developed and used in studying the effect of the stretching–bending coupling (B) and the flexural (D) stiffness matrices on the buckling and the post-buckling behavior of the shell, thereby improving its behavior. [Copyright &y& Elsevier]