Structural analysis for testing the resistance of sections of a structure, requires knowing the distribution of internal forces in it. The internal forces of a statically determinate structure can be found from the equations of static equilibrium. In an indeterminate structure of static equilibrium equations are not sufficient geometric conditions must meet under load. Go to Author for more information. The internal forces of a structure can be determined by elastic analysis or plastic analysis overall, although the latter only works when certain conditions are met. The internal forces are calculated by different methods, as might be neglected or not the effect of deformation on the structure. In the theory of first order, the calculations refer to the initial geometry of the structure (small strain).
The forces acting on the bars just do not vary with displacement. In the theory of second-order calculations refer to the deformed geometry of the structure under load. The displacements of the structure and its effect on the forces in the bars are no longer negligible. The theory of second order, more generally, is for all cases without restrictions. If we apply the theory of first order, and the material of the structure satisfies Hooke's law, if we are in a linear calculation, where all the displacements vary linearly with the applied forces. In this case, you can apply the principle of superposition to the stresses, strains, internal forces and displacements due to different actions. The superposition principle says that the displacements due to various loads acting simultaneously is equal to the sum of the displacements due to the action of each charge separately. This principle does not apply if the stress-strain relationship is non-linear material, or if the structure (even if the material obeys Hooke's law) does not behave linearly due to geometry changes caused by applied loads.