Technique for Formulating Beam Equations

by David W. Murray, (M.ASCE), Prof. of Civ. Engrg.; Univ. of Alberta, Edmonton, Alberta, Canada,
Sundaramoorthy Rajasekaran, Asst. Prof.; PSG Coll. of Tech, Coimbatore, India,

Serial Information: Journal of the Engineering Mechanics Division, 1975, Vol. 101, Issue 5, Pg. 561-573

Document Type: Journal Paper


A direct virtual work formulation of the beam equations is developed by starting with the general Lagrangian form of the three-dimensional virtual displacement equations of solid mechanics and introducing the specializations associated with thin-walled beam theory. The resulting beam equations are valid, within the limits of thin-walled beam theory, for arbitrary reference axes and are applicable to inelastic beam-column problems. This makes it unnecessary to consider instantaneous centroidal and shear center reference axes for incremental inelastic analysis, or to introduce transformations to these axes in achieving numerical solutions by techniques such as the finite element method.

Subject Headings: Finite element method | Beams | Inelasticity | Lagrangian functions | Displacement (mechanics) | Arbitration | Beam columns | Three-dimensional analysis

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