TORSIONAL BUCKLING RESPONSE OF OPEN CROSS SECTION STRUCTURES LYING ON WINKLER-PASTERNAK SOIL VIA DYNAMIC MATRIX METHOD

In view of the above, the present work deals with post buckling behavior of doubly symmetric thin-walled beams of open section and resting on Winkler-Pasternak type continuous elastic foundation. A new dynamic stiffness matrix (DSM) is developed which includes the effects of warping and Winkler-Pasternak foundation on axial compressive load. The resulting transcendental equations for all classical boundary conditions are solved for thin-walled beams of open cross section for varying values of buckling load parameter and Winkler, Pasternak foundation parameters. A new MATLAB computer program is developed based on the dynamic stiffness matrix approach to solve the highly transcendental frequency equations for all classical and various special boundary conditions. The MATLAB code developed consists of a master program based on modified BISECTION method and to call specific subroutines to set up the dynamic stiffness matrix to perform various parametric calculations. Numerical results for natural frequencies for various values of warping and Winkler and Pasternak foundation parameters are obtained and presented in graphical form showing their parametric influence clearly.