Issue 50

S. R. Pereira et alii, Frattura ed Integrità Strutturale, 50 (2019) 242-250; DOI: 10.3221/IGF-ESIS.50.20 246 N UMERICAL A NALYSIS U SING THE F INITE E LEMENT M ETHOD n the present study, numerical models were developed in the ANSYS Mechanical APDL software [14]. Three types of elements were used to represent the specimens. For concrete modelling, the SOLID65 element, available in the element library, was used. This element is volumetric and has eight nodes with three degrees of freedom per node, corresponding to the displacements in three directions. The representation of the reinforcement bars was made in a discrete manner, by means of truss elements (LINK180), which share nodes of the concrete volume mesh, enabling consideration of a perfect adherence between the two materials. Finally, rigid elements (MPC184) were used for the application of the eccentric load instead of direct modelling of the concrete consoles. These elements are intended to connect the nodes of the upper face of the column to the load application node, positioned at a distance from the axis of the column equal to the eccentricity adopted in the tests. The elements used are shown in Fig. 4. In this figure, some of the volumetric elements corresponding to the concrete are omitted to allow visualization of the reinforcements. Figure 4 : Elements used in the numerical modelling of the column. SOLID65 in green, LINK180 in purple and MPC184 in red. Due to the symmetry of the problem, only one quarter of the column was modelled for each analysis, which allowed considerable gain in processing time. In addition, due to the difficulty of mesh generation, small simplifications were adopted in the cross section, as shown in Fig. 5. Figure 5 : Simplified cross section used in the numerical modelling. A mesh with a characteristic dimension equal to 20 mm was adopted and generated freely by the program. Meshes with smaller dimensions were evaluated, however the results obtained with the 20 mm mesh were deemed satisfactory, as will be seen in the next section. For modelling of the materials, the stress-strain relationship presented in the ABNT NBR 6118:2014 [3] (a parabola- rectangle diagram), with a compressive strength of 33.5 MPa was adopted for the concrete. The tensile strength of the concrete was calculated according to this standard and the adopted value was equal to 3.12 MPa, since there was no tensile test for the concrete. The Willam & Warnke criterion was used to model material behaviour. Open and closed crack shear coefficients were adopted as 0.6 and 0.9 respectively, as proposed by Contamine et al. (2011) [21]. Steel was modelled as elastic, perfectly plastic, with a yield stress of 500 MPa and a Young’s modulus of 200 GPa. I