Analysis of a beam column on elastic foundation

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

Flexure of beams resting on hyperbolic elastic foundations

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

The present paper deals with the buckling and vibration of prismatic beams resting on an elastic half-space. The computational procedure developed herein utilizes the advantages of both an analytical approach and a finite element scheme. This is accomplished by deriving exact frequency and axial force dependent stiffness matrices using the analytical solutions of the governing differential equation as ‘shape functions’. The major advantages of the proposed approach over previous ones are pointed out and discussed in detail. Numerical results demonstrating the performance of the proposed method are presented in the final part of the paper.

Buckling and vibration analysis of flexible beams resting on an elastic half-space

Beam-columns of finite length resting on elastic foundation are analyzed by a series method. The series of the appropriate characteristic functions of beam vibration are used for beams with different types of end conditions. The method is shown to be applicable to continuous beam-columns and to the beam-columns with distributed axial and transverse loads. Cases of continuously varying flexural and foundation stiffnesses are also covered. A method is suggested for the calculation of the buckling loads of beam-columns. The method is illustrated by several numerical examples.

Finite Beam-Columns on Elastic Foundations

A method based on a solution in the form of a series of characteristic functions is suggested for calculating the influence coefficient for beams on elastic foundation. Using this method, a set of influence lines is obtained for the beams with free ends, such that the design of beams on elastic foundation is brought within the easy reach of an ordinary structural engineer.

Influence Lines for Beams on Elastic Foundations

The Evaluation of buckling loads of columns presents a difficult problem whose rigorous solution may be very difficult particularly when the variation of moment of inertia or the axial load does not follow a simple law. Hence approximate methods such as the variational and numerical methods will have to be employed. An approximate method is suggested in this note which offers a convenient method for the calculation of buckling loads of bars with any type of end conditions.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F73BB7E43533C1E652301C103A83F3A4/S0001924000061911a.pdf/div-class-title-buckling-of-bars-of-variable-rigidity-with-varying-axial-load-div.pdf

S. Anantharamu

Papers

Finite Beam-Columns on Elastic Foundations

Influence Lines for Beams on Elastic Foundations

Buckling of Bars of Variable Rigidity with Varying Axial Load