Analytical Expression of the Dependence of the Multi-lattice Truss Deflection on the Number of Panels

Building constructions, buildings and structures

The object of research is a flat statically determinate trapezoidal truss with a rectilinear lower chord and four supports, one of which is a pinned, and three are roller. The purpose of this work is to analyze the dependence of the deflection of the truss and the shift of the movable support on the size, load, and number of panels. The load concentrated in the middle of the span, the load uniformly distributed over the nodes of the upper or lower belt are considered. Method. The initial forces in the elements are determined in analytical form by method of joints in the Maple computer mathematics system. The dependence of the truss performance characteristics on the number of panels is derived by induction based on analytical calculations of the sequence of trusses with different numbers of panels. External static uncertainty is revealed by adding five reactions of supports to the number of unknown components of the equilibrium system of the structure. The deflection of the truss and the displacement of the support are based on the Maxwell-Mohr formula. Results. By solving a number of problems for trusses with a different number of panels, it is found that for trusses whose number of panels is a multiple of three, the determinant of the system of equilibrium equations of nodes turns to zero, which corresponds to the instantaneous kinematic variability of the truss. The corresponding scheme of possible node speeds was found. For kinematically unchangeable trusses, formulas for deflection depending on the number of panels are obtained. The coefficients in the formula are polynomial type. The solution graphs show an abrupt increase in deflection as the number of panels increases.