When analysing a structure using traditional methods (e.g. Hardy Cross, Slope Deflection, Force Method, etc.), it is a first-order elastic analysis. My question is, how would one analyse a statically indeterminate frame by hand but taking into account the second-order effects. This is more from an academic perspective and that is why I am asking for hand calculations using traditional methods or even direct stiffness method.
After completing some further research, I have come across a few approximate methods which were described in the book: Stability Design of Steel Frames. These include the two-cycle iterative method and modified slope deflection equations which can both analyse statically indeterminate structures while taking into account second-order effects. Thanks for all the answers.