Issue 50

C. C. Silva et alii, Frattura ed Integrità Strutturale, 50 (2019) 264-275; DOI: 10.3221/IGF-ESIS.50.22 272 R ESULTS AND D ISCUSSION ig. 10 shows the relationship between the results of the numerical analyses of plates with hexagonal openings and the values obtained according to the analytical formulations of web plates without openings (considering the same dimensions) for Anglo-Saxon, Litzka and Peiner typologies. The numeric stiffness of the castellated web, k 2, num,cast , was calculated according to Eqn. (1) and the analytic stiffness of the web without openings, k 2 ,an,sol , calculated by Eqn. (7). A linear relationship between the results of k 2, num,cast and k 2 ,an,sol is shown for the three typology patterns studied, with the mean of the ratio k 2, num,cast / k 2 ,an,sol equal 0.53, 0.54 and 0.55 for the Anglo-Saxon, Litzka and Peiner typologies, respectively. Figure 10. Comparison between the numerical and analytical results of the web stiffness of the Anglo-Saxon, Litzka and Peiner typologies. Adopting an adjustment coefficient (β), the Eqn. (7), used by EN 1994-1-1:2004 [4] and ABNT NBR 8800:2008 [3], can be adapted for the determination of the rotational stiffness of castellated webs, considering the total height of the castellated beam, d g , instead of the height of web without openings, h 0 , as below:   3 2 2 4 1 w g E t k d     (11) in which β is: 0.53 0.54 0.55       Anglo-Saxon Liztka Peiner (12) A dispersion analysis of the results was performed as described in the European standard EN 1990:2002 [33], and the coefficient of variation for the proposed formulation was equal to 0.22%, indicating low dispersion and homogeneous results. Adopting, conservatively, a simplified adjustment coefficient, β simplified , equal to 0.53 for Eqn. (11), can determine only one equation for the stiffness of the castellated beams (Anglo-Saxon, Peiner and Litzka typologies), in which the error obtained is less than 4%. It was also observed that the number of openings had no great influence on the rotational stiffness of the castellated web. 0 50 100 150 200 250 0 50 100 150 200 250 k 2, num,cast k 2, an,sol Anglo-Saxon Peiner Litzka F