Steel and Composite Structures
Volume 59, Number 3, 2026, pages 451-474
DOI: 10.12989/scs.2026.59.3.451
An effective simple shear deformation theory for analysis of homogeneous and sandwich beams
Krzysztof Magnucki , Krzysztof Sowiński
Abstract
The presented work concerns the analytical formulation of a shear deformation theory for beams. First, a review of recent studies on various shear deformation theories used in modelling beams, plates, and shells is provided. The principal objective is to develop an effective and simple individual shear deformation theory of beams derived from the classical shear stress formula. Unlike many existing approaches, the solution is obtained analytically in closed form without predefining specific shear deformation functions. The formulation enables the analysis of sandwich beams with constant or variable width and stiffness, including non-homogeneous materials. Parametric functions are introduced to describe these variations, allowing a broad range of beam geometries and stiffness profiles to be examined. The analytical results exhibit very good quantitative agreement with finite element analyses, with peak relative differences of 0.714 % in maximum deflection and 0.223 % in maximum shear stress. Applications include the standard I200 beam and non-homogeneous sandwich beams.
Key Words
analytical modelling; beam bending; shear deformation theory; shear effect
Address
- Krzysztof Magnucki — Łukasiewicz Research Network – Poznan Institute of Technology, Rail Vehicles Center, Poznan, Poland
- Krzysztof Sowiński — Poznan University of Technology, Institute of Applied Mechanics, Poznan, Poland
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