Timoshenko Beam Theory - Shear Coefficient

Shear Coefficient

Determining the shear coefficient is not straightforward (nor are the determined values widely accepted, i.e. there's more than one answer), generally it must satisfy:

The shear coefficient is dependent to the Poisson's Ratio. The approaches of more precise expressions are made by many scientists, including Stephen Timoshenko, Raymond D. Mindlin, G. R. Cowper, John W. Hutchinson, etc. In engineering practices, the expressions provided by Stephen Timoshenko are good enough for general cases.

For solid rectangular cross-section,

For solid circular cross-section,