Review article

Development of the elementary theory for shear stresses at simple bending of beams (ІІІ)








The article contains three additions to elementary theory of bending shearing stresses developed by author which is a generalization of the Zhuravsky theory. Firstly, the formula for the factor of the section form is deduced, which considers the warping effect of the section in the Mohr integrals for energy and displacements. The new factor of the form, unlike the classical one, depends on Poisson's effect and the influence of correlation of the cross section sizes` rate. Secondly, rather simple formula expressing running potential energy of deformation of the rod connected with vertical shearing stresses is given. Thirdly, this formula is applied for the power analysis of the theory developed by the author, which expands the Zhuravsky theory. It turns out that at certain values of Poisson's factor (individually for each kind of section), the Zhuravsky theory yields the exact results coinciding with results of the theory of elasticity.


Kharlab V. D. Saint Petersburg State University of Architecture and Civil Engineering

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