An accurate method of determining secondary stresses in thinwalled uniform beams of closed cross section is herein presented. The cross sections are assumed to be preserved by closely spaced rigid diaphragms. In section I the integrodifferential equation governing axial displacements is formulated and solved for a beam without longitudinal stiffeners. In section 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.nBy 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 no 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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