Analytical Solution for Plane Trusses with Equidistant Supports

The type of plane truss considered in this paper is the continuous Warren truss resting on equidistant roller supports, subjected to transverse nodal loads. In order to uncouple the governing equation, we need to replace the original structure, which does not possess cyclic periodicity, by an equivalent system that is cyclic biperiodic. By applying the U-transformation twice, the governing equation for the equivalent system can be uncoupled and become a set of single degree of freedom equations, which leads to the explicit form solution for the supporting reaction and nodal displacement. The expressions of the solution include two numbers of substructures and supports. As an example, a Warren truss with six substructures and four supports subjected to a concentrated load acting at its center node in the symmetric line of the original structure is worked out by means of the formulas obtained in the present study. It is shown that the result is exact.