Dynamic Matrix of Timoshenko Beam Columns

by Franklin Y. Cheng, (A.M.ASCE), Assoc. Prof. of Civ. Engrg.; Univ. of Missouri-Rolla, Rolla, MO,
Wu-Hsiung Tseng, Grad. Asst.; Univ. of Missouri-Rolla, Rolla, MO,

Serial Information: Journal of the Structural Division, 1973, Vol. 99, Issue 3, Pg. 527-549

Document Type: Journal Paper


This paper describes the dynamic behavior of general structural frameworks subjected to lateral time-dependent excitations and static axial loads. Different static axial loads may be applied to various members which are simultaneously subjected to lateral harmonic excitations applied as nodal forces, uniform and nonuniform loads, or foundation movements. All the matrix equations are expressed in nondimensional parameters representing various effects of rotary inertia, axial load, and shear and bending deformations. The individual parameter may be dropped when the appropriate effect is not considered. Consequently, the formulation and the computer program developed may be applied to various cases of dynamic response as bending deformation only; bending deformation and axial load; rotatory inertia, bending and shear deformations; rotatory inertia, bending and shear deformations, and axial loads; etc.

Subject Headings: Axial loads | Shear deformation | Beam columns | Bending (structural) | Lateral loads | Inertia | Matrix (mathematics) | Structural behavior

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