Force methods for trusses with elastic boundary conditions

A structural analysis using force method is presented for trusses accounting for the flexibilities of the elastic boundary conditions. Novel zero-length dummy members to transform the truss with boundary conditions into an equivalent free-standing model without boundary conditions are employed. Newly general equilibrium equations and general kinematic relations in which the reaction forces and the displacements at the elastic boundary conditions are, respectively, taken into account are clearly derived. The compatibility conditions in terms of redundant forces in which the flexibilities of the elastic boundary conditions are considered are obtained from the minimum of complementary energy. The difference between with and without considering the effect of the elastic boundary conditions lies in the formulation of redundant forces. Both member and reaction forces are simultaneously and directly obtained. Finally, numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.