Mathematical model of the truss with hardening elements

Structural mechanics

In the system of computer mathematics Maple the analytic expression for the deflection of the truss with the added belt stiffness was obtained by the method of induction. There was selected a flat beam model of a truss with uniform vertical loads along the lower belt. Stiffness of the rods was accepted equal. Hardening elements represent horizontal rods and the rack which form the additional belt at the bottom of the truss. Forces in the rods were determined in an analytical form by the method of cutting nodes. The statically indeterminate system, resulting from the introduction of hardening elements, was revealed by the method of forces. Coefficients of canonical equations and the deflection of the mid-span in the lower belt were calculated by Maxwell-Mohr formula. The article presents graphs of the dependence of deflection on dimensions of the truss and a number of panels. The asymptotic properties of these dependencies allow optimizing the construction.