Frequencies of Beams with Elastic Warping Restraint

by Paul Christiano, Assoc. Prof.; Dept. of Civ. and Min. Engrg., Univ. of Minnesota, Minneapolis, MN,
Larry Salmela, (A.M.ASCE), Civ. Engr. Trainee; United States Steel Corp., Virginia, MN; formerly, Student, Univ. of Minnesota, Minneapolis, MN,

Serial Information: Journal of the Structural Division, 1971, Vol. 97, Issue 6, Pg. 1835-1840

Document Type: Journal Paper


The free flexural-torsional vibrations of beams of thin-walled open cross sections have been studied extensively. In previous investigations arbitrary boundary conditions on the translational displacements have been considered. However, treatment of the rational displacement which defines twist has been confined to boundary conditions where warping of the cross section is either entirely free or completely restrained. The degree to which partial fixity on warping affects the fundamental natural frequencies of the member is described herein.

Subject Headings: Beams | Elastic analysis | Warpage | Cross sections | Boundary conditions | Displacement (mechanics) | Flexural strength | Vibration

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