Secondary Stresses in Thin-Walled Beams with Closed Cross-Sections

Citation

Benscoter, Stanley Urner (1950) Secondary Stresses in Thin-Walled Beams with Closed Cross-Sections. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XKAT-E346. https://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.

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