L Combined Shear and Flexure

The transverse deformation of real beams is the sum of flexure and shear deformations. In general, numerical solutions are required to incorporate both the shear and flexural deformations in the prediction of natural frequency of beams. For beams with comparable shear and flexural deformations, the following simplified formula may be used to estimate the beam's frequency:

where f is the fundamental frequency of the beam, and ff and fs are the fundamental frequencies predicted by the flexure and shear beam theories, respectively (Rutenberg 1975). Natural Frequency of Multistory Building Frames

Tall building frames often deform more in the shear mode than in flexure. The fundamental frequencies of many multistory building frameworks can be approximated by (Rinne 1952; Housner 1963)

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