WANG Le, WANG Liang. A New Method of Obtaining Timoshenko’s Shear Coefficients[J]. Applied Mathematics and Mechanics, 2013, 34(7): 756-763. doi: 10.3879/j.issn.1000-0887.2013.07.011
 Citation: WANG Le, WANG Liang. A New Method of Obtaining Timoshenko’s Shear Coefficients[J]. Applied Mathematics and Mechanics, 2013, 34(7): 756-763.

# A New Method of Obtaining Timoshenko’s Shear Coefficients

##### doi: 10.3879/j.issn.1000-0887.2013.07.011
• Rev Recd Date: 2013-05-23
• Publish Date: 2013-07-15
• With the effects of shear deformation of slender beams considered in Timoshenko beam theory, a new method of obtaining Timoshenko’s shear coefficients was derived. First, the exact solutions of the cross section’s shear stress distribution of the cantilever beam under the action of pure bending were used, and the new expressions of various cross sections were obtained based on energy principle. Then, the exact solutions of the cross section’s shear stress distribution of the cantilever beam under action of bending and torsion were derived and the coefficients obtained. The results show that the coefficients decrease when the terminal force departs from the bending center. The results are smaller than those given by Cowper because his theory doesn’t include the influence of shear stress perpendicular to the terminal force, and solution of the new method proved better.
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