Open AccessElastic beam line with noticeable deflection
Author(s) -
Vsevolod Krepkogorskiy
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/890/1/012035
Subject(s) - bending stiffness , cantilever , beam (structure) , conjugate beam method , deflection (physics) , stiffness , elasticity (physics) , pure bending , mathematical analysis , differential equation , mathematics , bending , physics , structural engineering , classical mechanics , optics , engineering , thermodynamics
Two differential equations are considered in the article. They describe the elasticity line of a curved beam. The second is obtained from the first if the derivative of the deviation function of the beam axis from the straight line is negligible. The question of the proximity of both solutions is studied. The literature considers many options for deviations from ordinary conditions, such as composite beams, complex deformations, too much bending. In our case, the hypothesis of Kirchhoff is supposed to be fulfilled. The following cases are considered: 1) a beam supported by two supports, and 2) a cantilever beam. The load is distributed evenly. Graphs of solutions are constructed for both equations at different load densities and beam stiffness. A parameter is found, knowing which, we can indicate from the table below how many percent these two solutions differ in. Our task is to find out the limits of application of conventional calculation methods for strong beam bending.