Issue 50

C. C. Silva et alii, Frattura ed Integrità Strutturale, 50 (2019) 264-275; DOI: 10.3221/IGF-ESIS.50.22 268 where D is the plate bending stiffness per unit length. According to Eqn. (1) and rearrangement of Eqn. (4), we obtain: 2 3 o D k h  (5) Figure 5. Web rotational stiffness (Calenzani [9]). The plate bending stiffness per unit length can be calculated, according to Timoshenko and Gere [28], as: 3 2 12(1 ) w Et D    (6) where E and ν are, respectively, the Young's modulus and the Poisson’s ratio of the structural steel and t w is the web thickness of the steel profile. Substituting Eqn. (6) for Eqn. (5), the value of k 2 per unit length can be determined by:   3 2 2 4 1 w o Et k h    (7) The web rotational stiffness, k 2 , determined for the plate without openings, described in Eqn. (7), should be adapted in the case of alveolar beams for the consideration of the openings, and being this adaptation the proposal of this article. The shear connection bending stiffness ( k 3 ) represents the moment in the geometric center of the top flange when a unitary rotation is imposed for the connection between the steel profile and the reinforced concrete slab (Fig. 6). The analytical determination of this stiffness is very difficult. According to Johnson and Molenstra [29] apud Calenzani [9], it tends to have a very high value when the I section has no openings, influencing less than 1% of the rotational stiffness k s for the case of shear connection with two connectors in the cross section and less than 5% for one shear connector. For this reason, the stiffness k 3 is usually disregarded in the calculations. In the case of castellated beam, in which the presence of openings reduces the web stiffness, the influence of the shear connection becomes even less relevant. The European standard EN 1994-1-1:2004 [4] does not provide an equation for the calculation of the elastic critical moment of LDB, but suggests the use of the inverted "U-frame" mechanism. The elastic critical moment of LDB is obtained, according to Brazilian standard ABNT NBR 8800:2008 [3], by Eqn. (8) (which was also presented in the previous version of the European standard, ENV 1994-1-1:1992 [29]), initially proposed in the Roik et al. [5] studies: 2 2 dist g cr s afy C L M GJ k EI L     (8) in which G is the transverse elasticity modulus, E is the Young's modulus of the structural steel, J is the St. Venant torsion constant of the profile, I afy is the second moment of area of the compressed flange in relation to the y axis (vertical axis), α g