Issue 33

R. Sepe et alii, Frattura ed Integrità Strutturale, 33 (2015) 451-462; DOI: 10.3221/IGF-ESIS.33.50 460 Loading condition Maximum stress [MPa] Allowable stress [MPa] 7 ± 1.5 130 8 ±21.2 130 9 69.1 130 10 37.2 130 Table 8 : Maximum von Mises stress under fatigue loading compared with the allowable limits. B UCKLING ANALYSIS he buckling problem is formulated as an eigenvalue problem, K·q = λ·K σ ·q (1) where: K structural stiffness matrix, K σ initial stress stiffness matrix, q eigenvector of displacements, λ eigenvalue (used to multiply the loads which generated K σ ). The buckling evaluation is made of two steps: the first one, static for the given load, is used by the code to calculate the initial stress stiffness matrix of the system; the second step by means of Block Lanczos method calculates eigenvalues and eigenvectors (1) that, multiplied by the load, provide the buckling loads. The calculated static load was related to longitudinal acceleration g x = 5g combined with vertical acceleration g z = -g. The first three eigenvalues, are summarized in Tab. 9. N° Eigenvalues 1 10.106 2 10.124 3 10.126 Table 9 : Buckling load eigenvalues. Being mode one 10.106, the buckling loads of mode 1 is related to g x = 50.53g and g z = -10.106g. This means that the roof structure can be considered to be safe. Buckling mode shape displays are helpful in understanding how the structure is prepared to deform for buckling. Fig. 14 and 15 show the buckling mode shape for the first eigenvalue. The maximum normalized displacement is localized in a roof sheet. Figure 14 : Buckling mode shape for the first eigenvalue. Figure 15 : Buckling mode shape for the first eigenvalue (detailed view). T