Secondary stresses in thin-walled beams with closed cross-sections

Citation

Benscoter, Stanley U. (1950) Secondary stresses in thin-walled beams with closed cross-sections. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-02022009-084840

Abstract

An accurate method of determining secondary stresses in thin-walled, uniform beams of closed cross-section is herein presented. The cross-sections are assumed to be preserved by closely spaced rigid diaphragms. In part I the integro-differential equation governing axial displacements is formulated and solved for a beam without longitudinal stiffeners. In Part II the corresponding summation-difference equation is developed and solved for a beam with stiffeners (flanges and stringers). The cross-section, loading distribution and end conditions are assumed to be arbitrary.

By introducing generalized difference equations the mathematical analysis for the stiffened beam may be performed in a manner exactly analogous to the process used for the unstiffened beam. A separation of variables in the homogeneous equation leads to the natural stress or displacement modes for a cross-section. The solution of the non-homogeneous equation is then expressed as an expansion in terms of the natural stress modes. Particular attention is given to cross-sections with single symmetry and double symmetry.

Thesis Files