Abstract
A scheme of a statically determinate planar truss is proposed and an analytical calculation of its deflection and displacement of the mobile support are obtained. The forces in the rods from the external load, uniformly distributed over the nodes of the lower or upper belt, are determined by the method of cutting out nodes using the computer mathematic system Maple. In the generalization of a number of solutions of trusses with a different number of panels to the general case, the general terms of the sequence of coefficients in the formulas are found from solutions of linear homogeneous recurrence equations. To compose and solve these equations, Maple operators were used. In the process of calculation it was revealed that for even numbers of panels in half the span, the determinant of the system of equations degenerates. This corresponds to the kinematic degeneracy of the structure. The corresponding scheme of possible speeds of the truss is given. The displacement was determined by the Maxwell-Mohr’s formula. The graphs of the obtained dependences have appreciable jumps, which in principle can be used in the selection of optimal design sizes.
Highlights
Numerical methods for calculating rod systems [1-5] have an alternative
When choosing a scheme for a projected design, it is desirable to have formulas that are derived for an arbitrary number of panels
We propose an inductive approach for deriving the formulas for the dependence of the planar truss bending on the number of panels
Summary
Numerical methods for calculating rod systems [1-5] have an alternative. With the advent of mathematical systems (Maple, Mathematica, Derive, Reduce) producing symbolic operations, it became possible to derive finite formulas for various characteristics of the stress-strain state of the trusses. Formulas for concrete designs with a certain number of rods and a certain configuration are not very interesting for practical engineers. The engineer by the formulas can pick up the sizes of a design, and the optimum number of panels. Such problems arise when solving optimization problems [6-9]. We propose an inductive approach for deriving the formulas for the dependence of the planar truss bending on the number of panels. This approach was used in solving problems of planar [10-13] and spatial [14-16] trusses
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