Exact post-buckling analysis of planar and space trusses

•Some planar and space trusses with geometric nonlinearity are analyzed analytically.•For these structures, all positions of snap-through, bifurcation and snap-back points are found.•It is proved that changing the geometrical parameters may cause the secondary path removal.•It is deduced that jumping from the primary branch to the secondary one cannot be occurred.•Obtained results are useful for education and good reference for verifying numerical responses. Despite the great efforts aimed at modifying nonlinear solution methods, researchers have failed to achieve a single algorithm which can correctly trace the equilibrium path for all problems. It has been proved that the numerical algorithms, such as the Arc-length and Newton-Raphson, cannot easily deal with limit points while tracing the equilibrium path. Moreover, secondary and tertiary paths attained by these methods do not simultaneously appear in the solutions. Verifying these methods requires the exact answers of some structures’ equilibrium equations. In spite of the simplicity of structures, intricate post-buckling behaviors with different critical points are observed under the hypothesis of large displacements. Analyzing the equilibrium paths and their features along with providing exact expressions seem to be very useful. In line with this goal, a family of simple planar and space trusses can be analyzed analytically. Closed-form solution and critical points of these structures are available in detail. Additionally, a parametric study of geometrical bounds for monitoring secondary branches is given, which clarifies the effect of geometry on the truss’ behavior. While these outcomes are beneficial for educational purposes, they may also be utilized to check the computer programs’ developments.