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This monograph presents a non-linear shear deformation theory based on the classical shear stress formula for beams. It enables to solve the problem of accounting for the shear effect in beam deformation, as well as analysing the influence of this effect on the behaviour of beam-like structures. The theory can also be applied to the analytical study of plates and shells. It provides a general solutions to problems of strength, stability, and free vibrations, covering different types of beams, such as classical I-beams, multi-layer beams, and sandwich beams made of homogeneous or functionally graded materials. A number of practical examples concerning beams under atypical boundary conditions are provided. The results obtained with the use of the proposed non-linear theory are compared with those obtained using a numerical approach - the finite element method.
This work is addressed to researchers interested in analysing of beam-like structures and in the mathematical modelling of engineering problems in the field of solid mechanics. Thanks to the large number of examples, it can also serve as a guide for engineers involved in the design of beam structures, such as warehouses, frames, and individual load-bearing elements for various applications.