About the authors
| First name, Middle name, Last name, Scientific degree, Scientific rank, Current position. Full and brief name of the organization, The organization address. | Mikhail N. Kirsanov, doctor of physical-mathematical sciences, professor of National Research University «Moscow Power Engineering Institute», Moscow, Russian Federation E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it |
| Title of the article | Analytical calculation of deflections of a planar externally statically indeterminate truss |
| Abstract. | Problem statement. A planar statically determinate lattice truss with a straight lower chord and a curvilinear upper chord has three movable and one fixed supports. The task is to derive a formula for the dependence of the amount of deflection of the truss and the horizontal displacement of the movable supports on the number of panels. To determine the forces in the rods and the reactions of the supports, a system of equilibrium equations for hinge joints is compiled and solved. The deflection is determined using the Mohrs integral. The generalization of analytical solutions for a number of trusses with a different number of panels to the case of an arbitrary number of panels is performed using Maple symbolic mathematics operators. The coefficients for similar expressions in the desired formula are determined from recursive equations compiled in this system based on the analysis of the sequence of solutions. Results. It is shown that for a certain number of panels the truss has the property of instantaneous change. This is confirmed by the found distribution of the virtual velocities of the construction hinges. The actions of a uniform distributed nodal load along the curvilinear upper or lower chords and the action of a concentrated load on the middle of the span are considered. Analytical dependences of forces in the most stretched and compressed elements on the number of panels in the truss are obtained. Conclusions. The proposed scheme of the truss, which allows obtaining the final formula for the dependence of the deflection and forces in the rods for an arbitrary number of panels. It is shown that the deflection depends abruptly on the number of panels, which makes it possible to increase the rigidity by choosing the optimal number of panels. |
| Keywords. | truss, deflection, Maple, induction, kinematic variability |
| For citations: | M.N. Kirsanov Analytical calculation of deflections of a flat outwardly statically indeterminate truss//News KSUAE No.3(61), p. 36-44, DOI: 10.52409/20731523_2022_3_36, EDN: PRRORX |
