Issue 29

D. Addessi et al., Frattura ed Integrità Strutturale, 29 (2014) 178-195; DOI: 10.3221/IGF-ESIS.29.16 193 Figure 12 : Rectangular beam: evolution of damage over the element cross - section without (first raw) and with (second raw) warping. The case of the T-shaped section is then analyzed, using the same mesh and the same warping point distribution along the axis as in the case of the rectangular section. In this case, the fiber mesh grid and the warping points distribution shown in Fig. 13 are used over the cross-section, in order to have cubic warping interpolation functions in the principal directions over each rectangular part of the section. Four Gauss-Lobatto integration points are used in each FE. The material parameters are given in Fig. 14, where also in this case the modulus E is set so as to reproduce the experimental initial stiffness. In the same figure, the global response curves and the warping displacement profile are plotted, while the damage distributions are shown in Fig. 15. For this section, the response obtained under the hypothesis of rigid cross-sections is related to the value of the torsional inertia J = 4010 cm 4 , derived by using the semi-analytical solution based on the Fourier series. Similar considerations as in the case of the rectangular section can be made. Figure 13 : Plain concrete T-shaped beam subjected to end torsion load, warping points distribution and fiber discretization.