P-delta analysis accounts for second order effects due to equilibrium of the structure in the deflected shape. Pushover is a static nonlinear analysis method in which the structure is incrementally displaced and nonlinear elements are incorporated into the analysis.
1. Be very careful, "P-Delta" analysis usually refers to ONLY one part of the correct nonlinear analysis of structures (i.e., the influence of a structure's joint displacements on the force/moment equilibrium equations). However, what many programs do not consider are the other very important nonlinear geometric effects such as their effect on the member/element strain-displacement (compatibility), force-deformation, coupling of force and moment (such as member axial force coupled with bending moments), nonlinear material behavior (such as 3D plastic hinge formation in members by tracking the spread of yielding), etc. relationships for both static and dynamic analysis
2. Regarding push-over analysis, push-over analysis is far more than just a simple displacement controlled analysis with nonlinear elements. Proper push-over analysis must also include a force incrementation analysis procedure, an ability to track the spread of yielding when modeling "plastic hinges," an ability to account for residual stresses and strain hardening material behavior, an ability to account for both steel and reinforced concrete materials, etc.
3. Furthermore, be EXTREMELY cautious when using any kind of nonlinear analysis by computer. It is simply NOT true that all developers of structural analysis software are properly qualified to write such software. Further, unlike linear analysis, nonlinear analysis results are extremely sensitive (far more so than linear analysis) to a very wide range of parameters (e.g., small variations in initial conditions, boundary conditions, behavior assumptions, computational algorithms, computational convergence criteria, etc. can lead to very large differences in final solution results).
4. THE BOTTOM LINE; YOU BETTER BE EXTREMELY CAREFUL AND ONLY USE SOFTWARE OF THE VERY HIGHEST QUALITY AND RELIABILITY, AND THAT IS DEVELOPED BY RECOGNIZED EXPERTS AND LEADERS IN THE STRUCTURAL ANALYSIS AND SOFTWARE DEVELOPMENT PROFESSION. If you do not, then you should carry extra large amounts of professional liability insurance.
