Matrix Force Analysis of Thin-Walled Structures

by Dusan Krajcinovic, Assoc. Mech. Engr.; Argonne Natl. Lab., Argonne, IL; formerly, Member of Tech. Staff, Ingersoll-Rand Res., Inc., Princeton, NJ,

Serial Information: Journal of the Structural Division, 1970, Vol. 96, Issue 1, Pg. 107-121

Document Type: Journal Paper


The Bernoulli's hypothesis of plane cross sections remaining perpendicular to the deformed center line does not adequately approximate the deformation due to the torsion of a long prismatic shell (or thin-walled structure with open cross section). Due to the warping, the pure torsion gives rise to the occurrence of normal stresses in longitudinal direction. In order to simplify the analysis, a specific design model standing in between a long shell and a classical beam is introduced. The matrix force method proves to be a powerful tool for the analysis of such thin-walled members. The flexibility, transformation, and equilibrium matrices are derived. Two different techniques of matrix force method are presented in detail. Through a limiting process (when the torsional rigidity approaches zero) it is shown that the suggested procedure presents the generalization of the method used in the case of solid beam assemblages.

Subject Headings: Structural analysis | Matrix (mathematics) | Thin wall structures | Torsion | Beams | Structural models | Warpage | Shell structures

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