Bending calculation of rectangular beams using trigonometric series

The object of research is the stress-strain state arising from the bending of a rectilinear beam. A beam with a rectangular cross-section is considered. The load is applied symmetrically to the top and bottom surfaces. The beam is loaded with a uniformly distributed load with stepwise intensity, with values changing regularly along the beam's length. Method. This study uses methods of classical elasticity theory and structural mechanics. The numerical-analytical solution utilizes the theory of trigonometric Fourier series. Results. A formula is given for the analytical determination of the stress arising from the bending of a rectilinear beam. To derive the formula, the given load was expanded into a Fourier series, followed by a well-known method for solving structural mechanics equations.