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Bending of beams with symmetrically varying mechanical properties under generalized load – shear effect

100%

Magnucki K. , Lewinski J.

tom Vol. 67, iss. 3

441--457

The paper is devoted to simply supported beams with symmetrically varying mechanical properties in the depth direction. Generalized load of the beams includes the load types from uniformly distributed to point load (three-point bending). This load is analytically described with the use of a certain function including a dimensionless parameter. The value of the parameter is decisive for the load type. The individual nonlinear “polynomial” hypothesis is applied to deformation of a planar cross section. Based on the definitions of the bending moment and the shear transverse force the differential equation of equilibrium is obtained. The equation is analytically solved and the deflections are calculated for an exemplary beam family. The results of the study are specified in tables.

A shear deformation theory of beams with bisymmetrical Cross-sections based on the Zhuravsky shear stress formula

80%

Magnucki K. , Lewinski J. , Magnucka-Blandzi E.

tom Vol. 68, iss. 4

353--370

This paper is devoted to simply supported beams with bisymmetrical cross-sections under a generalized load. Based on the Zhuravsky shear stress formula, the shear deformation theory of a planar beam cross-section is formulated. The deflections and the shear stresses of exemplary beams are determined. Moreover, the numerical-FEM computations of these beams are carried out. The results of the research are shown in figures and tables.