It takes multiple iterations of a linear analysis to compute the final deformed shape of a structure where the P DELTA effect is significant.
To illustrate the effect, consider a case in statics, a perfectly rigid body anchored on the ground subject to small lateral forces.
During this side displacement, the top has changed position and the structure is experiencing an additional moment, P×Δ, or near the middle, P×δ.
In some sense, the P-delta effect is similar to the buckling load of an elastic, small-scale solid column given the boundary conditions of a free end on top and a completely restrained end at the bottom, with the exception that there may exist an invariant vertical load at the top of the column.
If the lateral displacement and/or the vertical axial loads through the structure are significant then a P-delta analysis should be performed to account for the non-linearities.