Engineering Transactions, 68, 2, pp. 119–135, 2020

Bending of Beams with Consideration of a Seventh-Order Shear Deformation Theory

Krzysztof MAGNUCKI
Łukasiewicz Research Network - Institute of Rail Vehicles “TABOR”

Włodzimierz STAWECKI
Łukasiewicz Research Network - Institute of Rail Vehicles “TABOR”

Poznań University of Technology

The subject of the paper is a simply- supported prismatic beam with bisymmetrical crosssections under non-uniformly distributed load. The shapes of the cross-sections and the nonuniformly distributed load are described analytically. The individual seventh-order shear deformation theory-hypothesis of the planar beam cross-sections is assumed. Based on the principle of stationary potential energy two differential equations of equilibrium are obtained. The system of the equations is analytically solved, and the shear and deflection coefficients of the beam are derived. Moreover, the shear stress patterns for selected cross-sections are determined and compared with stresses determined by Zhuravsky’s formula. The results of example calculations are presented in tables and figures.
Keywords: nonlinear hypothesis; shear deformation theory; shear stresses
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DOI: 10.24423/EngTrans.1129.20200214