Inductive analysis of the deflection of a beam truss allowing kinematic variation

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.