THE CRITICAL LOAD PARAMETER OF A TIMOSHENKO BEAM WITH ONE-STEP CHANGE IN CROSS SECTION

Abstract

The paper analyzes the transverse vibration of a Timoshenko beam with one-step change in cross-section when subjected to an axial force. The axial force is equal in both of the beam portions. Three types of beam which occur commonly in engineering application are considered. The frequency equation of the Timoshenko beam with one-step change in cross-section is expressed as the fourth order determinant equated to zero. The critical compressive axial force is expressed as a function of the critical load parameter which is tabulated for four classical boundary conditions. Apart from the results presented in Tables, the paper also provides calculated values of the critical load parameter for other values of system parameters along with the graphic representation of their dependence on the step position parameter.