Non linear analysis or plastic capacity of structure are aimed to assess the performance of a structure in the event of extremely adverse conditions. For example in the safety level earth quake, which are very rare events, the design aim is to avoid complete collapse of the building structure so the human life damages can be prevented.
In this case the ductility of members play an important role.
You would have heard about moment redistribution and plastic hinges. Now you take the example of a fixed ended beam by neglecting axial deformation, the degree of static indeterminacy is 2. Let assume you keep on increasing the load beyond allowable or yield point until the plastic hinges form at the two support that will turn your beam as the simply supported beam and will become a determinate structure and on further increase the load it will increase the span moment.
In short this is the situation that we utilize sure safety level eq or similar events.
Why we do so, because of cost benefit analysis. If you design the said beam for the most extreme load within elastic range then the cost may go as high as 5 times of the average cost that may turn into a non feasible design.
Thank you it is well explained...I general it is cent percent aggre with this,,, but coming to concrete non-linear fracture parameters like Gf and Cf , where it can be well suited, as like post failure investigation or can we use in any design methods.