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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.

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  • $\begingroup$ It is not clear what you are asking here. Second-order effects can occur in both statically determinate and indeterminate structures. Also there are many differenent types of second order effects (finite size displacements, infinitesimal displacements with finite size rotations, nonlinear material behaviour, pressure loads whose direction depends on the deformation of the structure, etc, etc...) Even Euler buckling is in some sense a "second order effect". $\endgroup$ – alephzero Oct 13 '19 at 12:07
  • $\begingroup$ Would I be able to take into account the above consideration when completing hand calculations? $\endgroup$ – Amit Oct 14 '19 at 7:48
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By hand? I believe you have to use matrixes to include all the formulae by superposition, then to solve the matrixes using our friendly Mathematics by hand instead of computer.

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  • $\begingroup$ Would you by any chance be able to suggest where I can find the matrices? Is it similar to direct stiffness method? $\endgroup$ – Amit Oct 27 '19 at 8:11
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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.

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