The derivation of the dependence of the deflection of a beam truss with lateral struts on the number of panels

Аннотация

A planar, statically indeterminate beam truss is loaded in the middle of the span. A formula is derived for the dependence of deflection on the size of the truss, the value of load and the number of panels. To solve the problem, we use the method of cutting nodes, the method of induction, and the operators of the Maple system, which allow us to compose and solve recurrent equations in deriving common terms of the sequence of coefficients of the desired formula. The displacement of the node in the upper belt is obtained according to the Maxwell-Mohr’s formula. It is assumed that all the rods of the truss have the same rigidity, and the supports are not deformed.