## Construction System Design and Layout Planning. Mechanical Equipment Challenges in Construction

### ANALYTICAL CALCULATION OF DEFLECTION OF RECTANGULAR SPATIAL ROOF STRUCTURE

Vestnik MGSU 5/2018 Volume 13

Pages 579-586

Subject: obtaining an analytical solution to the problem of deflection of a spatial structure with an arbitrary number of panels, which remains valid for a wide class of constructions of the proposed structure. Research objectives: the main purpose of this work is to derive dependence of truss deflection on the number of panels, on the magnitude of the load and dimensions of the structure. Materials and methods: the deformability of a truss over rectangular plan with vertical supports on all lateral sides, made of steel or aluminum alloys is estimated by the vertical displacement of the central node, to which the force is applied. The forces in the rods and supports are determined by the method of joints. Generalization of the particular solutions found for a sequence of trusses with various number of panels to an arbitrary number of panels is obtained by induction. All symbolic transformations and solutions are performed in the computer mathematics system Maple. Using special operators of the Maple software, homogeneous linear recurrence equations are derived and solved, which are satisfied by the terms in the sequences of coefficients of the desired formula. Results: the resulting deflection formula constitutes a cubic polynomial expressed in terms of the number of panels. The graphs of the dependence of deflection on the number of panels and on the height are plotted. Formulas for forces in characteristic rods are derived. Conclusions: the proposed model of a statically determinate spatial truss structure with supports all over the contour allows an analytical solution for deflection and its generalization to an arbitrary number of panels. The results are numerically verified and can be used as benchmark cases for estimation of the accuracy of numerical solutions. The obtained formulas are most effective for large number of panels, i.e., when numerical methods based on solving high-order linear systems require significant machine resources and are prone to uncontrolled accumulation of round-off errors.

DOI: 10.22227/1997-0935.2018.5.579-586