On the shear coefficient in Timoshenko's beam theory

Some existing formulations for the shear coefficient in Timoshenko's beam theory are discussed, especially through evaluation of the accuracy to which natural frequencies of simply supported, prismatic, thin walled beams can be obtained. The main conclusion drawn is that if a consistent expression for the shear coefficient, such as those given by Cowper [1] or Stephen [2], is used in Timoshenko's beam theory, then very high accuracies can be expected for the natural frequencies, even for wavelengths of the same magnitude as the transverse dimension of the beam. It is noted that no reduction of the moment of inertia due to shear lag effects should be made as these effects are included in the consistent formulas for the shear coefficient. Finally, some apparently paradoxical results indicating that a reduction in shear stiffness occurs in rare cases if more material is added to a section are discussed and explained as resulting from the use of integrated rather than pointwise deflection measures in the derivation of consistent shear coefficient expressions. The results are discussed in the light of the importance of the shear stiffness of the hull girder in ship hull vibration analysis.