Issue 50

C. C. Silva et alii, Frattura ed Integrità Strutturale, 50 (2019) 264-275; DOI: 10.3221/IGF-ESIS.50.22 269 is a related factor to the cross-section geometry, k s is the rotational stiffness of the composite beam and C dist is a coefficient that depends on the distribution of bending moments in the length L of the analyzed composite beam span. Figure 6. Shear connection bending stiffness (Calenzani [9]). Dias [20] proposed a new procedure for the determination of the elastic critical moment of composite beams with web profile without openings subjected to uniform hogging moment according to Eq. (10):   2 2 , 2 0 g w d b cr k EC M GJ n h n L                               (9) where 4 , b w d kL EC   (10) where h 0 is the distance between the geometric centres of the steel profile flanges, G the transverse elasticity modulus, E the Young's modulus of the structural steel, J the St. Venant torsion constant of the steel profile, L the beam length, C w,d the warping constant of the steel profile, n the number of half-waves of the buckling mode, k the spring stiffness in the centre of the upper face of the top flange, η b is a dimensionless parameter and k g takes into account effects caused by the presence of the slab in the model. The new procedure proposed by Dias [20] presented excellent agreement with numerical values, with deviations below 10% in 97.29% of the analyzed models and mean error of 2.33%. Results better than the formulations of Roik et al. [5] and Hanswille et al. [8], which did not lead to satisfactory results, presenting average errors of 12.41% and 16.51%, respectively. These last two works present several simplifications and can lead to results not as precise as those of Dias [20]. Oliveira [1] extended the equation of Dias [20] for composite beams submitted to non-uniform hogging moment. N UMERICAL A NALYSIS Numerical Model he formulation of the rotational stiffness discussed in EN 1994-1-1:2004 [4] covers only composite beams composed of steel profiles without openings. This stiffness depends substantially on the web rotational stiffness ( k 2 ), which can be determined by considering the web as a plate fixed in the geometric center of the top flange and free in the geometric center of the bottom flange (Fig. 7). Thus, a simplified numerical model of plate was developed to determine the web stiffness of the castellated profiles. The numerical model represents a plate of height ( d g ), thickness t w and length varying due to the number of openings, in the case of the castellated web (Fig. 5). As described previously, by applying a horizontal force F in the geometric center T