Review article

Improvement of methods for shear accounting in calculation of deflections and natural frequencies of elastic rods with variable cross-section








In bent rods with variable cross-section, shear stress in the cross-section depends not only on the shear force, but also on the bending moment. Existing methods to calculate deflections with regards of shear take variability of the section into account, assuming bending stiffnesses and shear stiffnesses dependant on coordinate. Such approach neglects the effect of the bending moment on the shear stress. The proposed article corrects this deficiency, introduces required improvements into the Maxwell-Mohr formula and into the Timoshenko beam theory. The improved formulas are applied to calculation of deflections and natural frequencies of a short cantilever. In the examples considered corrections due to shear calculated by means of the new formulas change in 1-1,5 times, depending on the degree of cross-section variability.


Kagan-Rosenzweig L. M. Saint Petersburg State University of Architecture and Civil Engineering