Analytical integration of elasto-plastic uniaxial constitutive laws over arbitrary sections

We present the preliminary results of a novel approach to the state determination of polygonal sections of arbitrary shape endowed with elasto-plastic uniaxial constitutive laws. By means of a suitable application of Gauss theorem, we prove that the normal stress resultants can be computed analytically as sum of finite quantities evaluated solely at the vertices of the section. For this reason, the proposed approach has been termed fiber-free to emphasize the fact that it does not require any subdivision of the section in fibers. Numerical results show that the fiber approach is grossly inaccurate and that the number of fibers required to achieve a degree of accuracy comparable with that entailed by the fiber-free approach is at least one order of magnitude greater than the one commonly suggested in commercial software for nonlinear frame analysis