Summary: The displacement of a beam can be conveniently resolved into a roto- translational section displacement and a section warping. The correct second order approximation of the strain is deduced accounting for large displacements and thus for large rotations. On the basis of displacement method, both linear and nonlinear formulations are given: the first one leads to the elastic section properties and to the correct characterization of section warping; the second one leads to the so- called geometric section stiffness, accounting for prestress. Both formulations are general with respect to elastic material properties, thus allowing to deal with anisotropic and unhomogeneous cross-sections. Elastic and geometric section rigidities here proposed can then be easily used in second order problems on beam frames: either initial buckling eigenvalue analyses, either large displacement incremental analyses.