Issue 50

C. C. Silva et alii, Frattura ed Integrità Strutturale, 50 (2019) 264-275; DOI: 10.3221/IGF-ESIS.50.22 270 of the bottom flange, the web lateral displacement (δ 2 ) can be determined through Eqn. (1) and, from this, the web stiffness, k 2 , is calculated. Three-dimensional models of finite elements were developed in the software ANSYS 17.0 [25]. Shell elements, SHELL181, were used to represent the steel profile. Figure 7. Plate model. The Young’s modulus of the steel, E , was considered equal to 200000 MPa and the Poisson’s ratio, ν, equal to 0.3. In order to simulate the boundary conditions, the displacements and rotations in the three directions were prevented at the top of the web. At the bottom, the nodes displacements were coupled, resulting in a uniform displacement along the lower portion of the web across the model length, condition which normally occurs due to the presence of the bottom flange. The finite element mesh was generated freely by the program, resulting in an unstructured mesh, which does not represent influence due to the great simplicity of the type of analysis. A mesh study was performed, varying the size of the elements from large values to very small values (1.52 h 0 to 0.003 h 0 , with more than 32 values). The mesh used was 0.152 h 0 once it presented results with good precision (the variation for smaller meshes is less than 0.1%) and did not present high computational time. Validation of Numerical Model Plates with solid-webs were modeled for the validation of the numerical model. The numerical web rotational stiffness without openings ( k 2, num,sol ) was calculated according to Eqn. (1), considering the applied force ( F ) equal to 1 kN and the maximum displacement of the plate (δ 2 ) obtained from the numerical analysis. The analytical web rotational stiffness without openings ( k 2, an,sol ) was calculated according to Eqn. (7). The results of the numerical analysis were compared with the analytical results and it was observed that the maximum difference between the two results was less than 0.3% (Tab. 1). Therefore, it is considered that the numerical model is suitable for simulations of web stiffness. d g (mm) t w (mm) L beam (m) δ 2 (m) k 2 ,num,sol (kN.m/m) k 2 ,an,sol (kN.m/m) k 2 ,num,sol / k 2 ,an,sol 260 6.4 2.85 4.28E-04 55393.01 55398.14 1.000 300 5.0 1.99 1.98E-03 22893.71 22818.77 0.997 600 7.5 4.85 1.93E-03 38543.48 38633.24 0.998 900 10 11.17 1.19E-03 61113.43 61050.06 1.001 1200 15 14.89 6.25E-04 154755.51 154532.97 1.001 Table 1 : Validation of numerical models.