Calculating model of a frame type planar truss having an arbitrary number of panels

ABSTRACT Introduction. The subject of the study is the kinematic variability and deformations of a planar statically-determinate elastic truss with a horizontal bolt, lateral supporting trusses and a cross-shaped grid under the action of various types of static loads. The structure has three movable supports and one fixed support. Objectives - derivation of formulas giving the dependence of the deflection of the structure in the middle of the span and the displacement of one of the three movable supports from the dimensions, load and number of panels; analysis of the kinematic variability and derivation of the analytical dependence of the forces in the rods of the middle of the span from the number of panels. Materials and methods. Forces in the rods of the truss are calculated in symbolic form by cutting out nodes using the Maple symbolic and numeric computational environment. In order to calculate the deflection, the Maxwell - Mohr formula was used. Calculation formulas for the deflection and displacement of the support were derived using the induction method based on the results of analytical calculations of a number of trusses with a different number of panels in the crossbar and lateral support trusses. The special operators of the genfunc package for managing the rational generating functions of the Maple system were used to identify and solve the recurrence equations satisfied by the sequences of coefficients of the formulas for deflection and forces. It is assumed that all the rods of the truss have the same rigidity. Results. Several variants of loads on the truss are considered. A combination of panel numbers is found in which the truss becomes kinematically variable. The phenomenon is confirmed by the corresponding scheme of possible velocities. All required dependences have a polynomial form by the number of panels. The curves of the dependence of the deflection on the number of panels and on the height of the truss are constructed in order to illustrate the analytical solutions. Conclusions. The proposed scheme of a statically determinate truss is regular, allowing a fairly simple analytic solution of the deflection problem. The curves of the identified dependencies have significant areas of abrupt changes, which can be used in problems of optimising the design by weight and rigidity.