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Some closed-form bending formulas for elastically restrained Euler-Bernoulli beams under point and uniformly distributed loads

Yıldırım V.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 3

97--109

The transfer matrix method based on the Euler-Bernoulli beam theory is employed in order to originally achieve some exact analytical formulas for elastically supported beams under a point force together with uniformly distributed force and uniformly distributed couple moments. Those closed-form formulas can be used in a variety of engineering applications especially at the pre-design stage to get an insight into the response of the structure. Contrary to the classical boundary conditions, it is also observed that the Euler-Bernoulli solutions of a beam with elastic supports are sensitive to the ratio of length to thickness (L/h).