4 Works

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

Krzysztof MAGNUCKI, Włodzimierz STAWECKI & Ewa MAGNUCKA-BLANDZI
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...

Analytical and Numerical Studies of an Unsymmetrical Sandwich Beam – Bending, Buckling and Free Vibration

Krzysztof MAGNUCKI, Ewa MAGNUCKA-BLANDZI, Jerzy LEWIŃSKI & Szymon MILECKI
The subject of the paper is an unsymmetrical sandwich beam. The thicknesses and mechanical properties of the beam faces are different. Mathematical model of the beam is formulated based on the classical broken-line hypothesis. The equations of motions of the beam is derived on the ground of the Hamilton’s principle. Bending, buckling and free-vibration are studied in detail for exemplary unsymmetrical structure of the beam. The values of deflection, critical force and natural frequency are...

Bending of Beams with Symmetrically Varying Mechanical Properties Under Generalized Load – Shear effect

Krzysztof MAGNUCKI & Jerzy LEWIŃSKI
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....

Approximate Estimation of Stability of Homogeneous Beam on Elastic Foundation

Iwona Małgorzata WSTAWSKA, Krzysztof MAGNUCKI & Piotr KĘDZIA
The paper deals with a proposition of obtaining an analytical solution for a beam on elastic foundation. The main objective of presented work was stability analysis of the axially compressed beam. The analytical model was proposed. Shape function for inhomogeneous properties of the foundation was assumed. The Galerkin method was used to calculate the values of critical forces. Main conditions have been defined. The critical loads as a function of geometric and mechanical properties of...

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  • 2020
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Affiliations

  • Tabor (Poland)
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  • Poznań University of Technology
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