Issue 48

E. Maiorana, Frattura ed Integrità Strutturale, 48 (2019) 459-472; DOI: 10.3221/IGF-ESIS.48.44 461 Figure 2: Static diagram of a plate divided into two subpanels A and B; a / h = 1.5. B ASIC CONCEPT Buckling coefficient heoretical buckling coefficients k th of simply supported plates subjected to uniform compression were analytically determined by solving the Timoshenko’s equations based on equilibrium between external and internal forces, in a deformed configuration. The lower value of the compression force N x is obtained with n = 1, and the buckling coefficient is given by Eqn. 1: k th = [( m b ) / a + a / ( m b )] 2 (1) Being stress gradient  =  t /  c the ratio between traction  t and compression  c stresses, in EN 1993-1-5 2007 [13] the following k values are proposed: k = 4 for  = 1 k = 8.2 / (1.05 +  ) for 1 >  > 0 k = 7.81 for  = 0 k = 7.81 – 6.29  + 9.7  2 for 0 >  > -1 k = 23.9 for  = -1 k = 5.98 (1 -  2 ) for -1 >  > -3 Numerically, buckling coefficient k num was found by solving the corresponding eigenvalue problem. The lower eigenvalue refers to the critical elastic load and the eigenvector defines its deformed shape. Stiffness matrix K was given by the conventional matrix in small deformations K E and the matrix K S , which takes into account the effect of stress  on the plate. The global stiffness matrix of the panel at stress level  0 may be written as follows: K (  0 ) = K E + K S (  0 ) (2) When the stress level reaches  0 , the stiffness matrix becomes: