Analysis of a beam column on elastic foundation

Analytical solution for the elastic bending of beams lying on a variable Winkler support

The paper is concerned with the numerical analysis of prismatic beam/columns resting on a two-parameter subsoil. A mathematically rigorous technique is outlined which allows for the calculation of exact dynamic transfer and stiffness matrices for a broad range of practically important situations. The new stiffness matrices can easily be implemented in the libraries of any general or special-purpose finite element code.

Exact transfer and stiffness matrices for a beam/column resting on a two-parameter foundation

Dynamic response of reinforced concrete buildings

Stiffness of beam-columns on elastic foundation with exact shape functions

Analysis by means of slope-deflection equations; application of moment-distribution method to problems involving large numbers of spans is demonstrated by numerical example, and computation of critical axial force is illustrated by treatment of particular problem.

Continuous Beam-Columns on Elastic Foundation

A method is developed whereby the dynamic response of statically determinate and indeterminate elastic-plastic beams may be computed with a maximum degree of accuracy and with a minimum of computational difficulty. The development is applied to a mathematical model of the actual beam consisting of a system of concentrated masses connected by massless segments whose stiffnesses are identical to the stiffnesses of the corresponding parts of the original beam. The equations of motion are written in the usual manner, in which the structural resistance to deformation is expressed explicitly in terms of the deflections for any elastic-plastic phase of deformation. These equations of motion are solved by means of a single step forward numerical integration procedure. A method of determining the points of elastic-plastic and plastic-elastic transitions is described that, in conjunction with the numerical integration procedure, is suitable for programming on a high-speed digital computer. Several examples are given to show the versatility of the method, including the response of a continuous beam subjected to a moving load.

Dynamic Analysis of Inelastic Multi-Degree Systems

The differential equations of the inelastic bending of cantilever columns are solved by a numerical marching procedure. The curvature functions are derived for an elastic-perfectly plastic material and wide-flange or box sections. The critical load-slenderness ratio relationships are determined numerically and are approximated by semiemperical equations. These interaction equations are applied to the analysis of columns of various support and loading conditions. Numerical examples are given and, where appropriate, the results are compared with those obtained by other methods.

Buckling of Steel Columns Under Arbitrary End Loads

The load-deformation characteristics of circular cylindrical shells, made of linear isotropic strain hardening material, simply supported at both ends, and subjected to axisymmetric loading, is studied. The shell material is assumed to obey a square approximation to the exact Tresca yield curve for the axisymmetrical bending of cylindrical shells with zero end load. Depending on the value of the shell parameter and toe magnitude of the internal pressure, shells are found to deform under six different types of stress profile. The development of the stress profiles with increasing pressure and the corresponding load-deformation fields are presented for the entire range of the shell parameter, encompassing short, medium, long, and very long shells.

Linear Strain Hardening of Cylindrical Shells

The load carrying capacity of circular cylindrical shells simply supported at both ends and subjected to axisymmetric hydrostatic load is examined. The shell material is assumed to obey an inscribing hexagonal approximation to the Tresca yield curve for axisymmetrical bending of cylindrical shells with zero end load. The results of this analysis, together with those obtained on the assumption that the shell material obeys a circumscribing square approximation to the Tresca yield curve, bound the limit loads associated with the Tresca yield conditions. The values of the limit loads are plotted against a wide range of the shell parameter. For long shells, it is demonstrated that the curve is asymptotic to the limit load given by the membrane analysis. The stress profiles, as well as the corresponding statically admissible stress fields and kinematically admissible velocity fields, are also demonstrated for particular values of the shell parameter.

Sang-Lip Lee

Papers

Continuous Beam-Columns on Elastic Foundation

Dynamic Analysis of Inelastic Multi-Degree Systems

Buckling of Steel Columns Under Arbitrary End Loads

Linear Strain Hardening of Cylindrical Shells

Limit Analysis of Cylindrical Shells