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Question on Geometric non linearity- shallow or deep truss element

Submitted by bruno-page on

Consider the attached pdf's- chapter 2 derivation.pdf(which is derivation of equations involving a shallow truss element) and Deep truss element using Green's strain.pdf.

My question is more of an intuitive one:Now considering the shallow truss eleemnt.pdf, we have the axial force "N" a part of the stiffness matriz similarly for deep truss eleemnt.My question is that a compressive reduces stiiffness and a tensile N increases stiffness, how is this reflected in the equations?

Can anyone help?