The exact formulas for calculating deflection and forces in the rods of the ’Molodechno’ truss with an arbitrary number of panels

Structural mechanics

 We have obtained an analytical expression for the deflection and forces in the rods of a flat truss of beam type in the elastic stage. We found that the induction method, which has been tested for a wide class of two-dimensional elastic and regular trusses, does not yield a direct and compact result for trusses with an inclined upper chord. Decomposing the deflection into a series of a small parameter characterizing the slope is only suitable for very small tilts that are not typical for real practical application. The formulas for the forces in the rods of the truss include the geometrical and physical parameters, the number of a rod in the belt or grid, and the number of panels. The asymptotics of the solution for the deflection taking into account the different rod stiffnesses (the slope of the upper belt is random) were found. All the analytical transformations were executed in the Maple computer algebra system.