Abstract
Flat bending stability problem of constant rectangular cross section wooden beam, loaded by a distributed load is considered. Differential equation is provided for the cases when load is located not in the center of gravity. The solution of the equation is performed numerically by the method of finite differences. For the case of applying a load at the center of gravity, the problem reduces to a generalized secular equation. In other cases, the iterative algorithm developed by the authors is implemented, in the Matlab package. A relationship between the value of the critical force and the position of the load application point is obtained. A linear approximating function is selected for this dependence.
Highlights
For reasons of reducing wood consumption in rectangular section wooden beams design they try to increase the ratio of the cross section height to its width
The problem of flat bending shape stability of constant rectangular section wooden beam is solved with following differential equation [3, 4]: GIt d 2 dx2
Bending moment is determined by the following formula: M y
Summary
For reasons of reducing wood consumption in rectangular section wooden beams design they try to increase the ratio of the cross section height to its width. The problem of flat bending shape stability of constant rectangular section wooden beam is solved with following differential equation [3, 4]: GIt d 2 dx. Equation (1) is written for the case when load is applied at cross section center of gravity. Karamysheva dissertation [6] following differential equation was obtained, that considers variable beam stiffness, and loading in the center of gravity as well:. A. Karamysheva considered only two cases of a load applying not at the center of gravity: a cantilever beam with concentrated force at the end, and a hinged beam loaded with a concentrated force in the middle of the span. In the paper we consider a beam of constant cross-section loaded by a uniformly distributed load q (Figure 1). The second term of the equation (2) equals zero because the beam that we calculate has constant section
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