Deformations of a Triangular Trussed Rafter With an Arbitrary Number of Panels: An Analytical Solution
The object of the study is a planar, statically determinate lattice truss on two supports. The upper belt of the structure has a triangular outline. The task is to obtain formulas for the dependence of the deflection and displacement of the movable support on the number of panels. Method. To obtain the deflection value, the Maxwell-Mohr formula is used. The forces in the rods are found by cutting out nodes from the solution of a system of linear equations. All transformations and calculations are performed symbolically in the Maple computer mathematics system. The generalization of a series of particular solutions obtained for trusses with a sequentially increasing number of panels to an arbitrary case is performed by induction using Maple operators. Results. Three types of loads are considered, including lateral wind load. The calculated formulas obtained contain the coefficients in the form of polynomials in the number of panels and, in comparison with similar solutions for other structures, have a very compact form. The distribution of forces over the elements of the lattice is given. Formulas are derived for some of the rods that are most critical to the loss of strength or stability.