PSI - Issue 44

5

Gaetano Della Corte et al. / Procedia Structural Integrity 44 (2023) 472–479 Cantisani, Della Corte / Structural Integrity Procedia 00 (2022) 000–000

476

0.5

y f

σ =

2

0.5

y f

σ = −

r

r

1.5

1

y [-]

/ f

b)

0.5

M (Della Corte et al.) C (Della Corte et al.) KH SH

0

0

0.02

0.04

0.06

ε [-]

a)

c)

Fig. 4. (a) Steel stress-strain relationships; (b) assumed residual stresses; (c) example of longitudinal distribution of the residual stresses.

3.4. Geometrical imperfections Geometrical imperfections were included in the numerical models, following the recommendations by Eurocode 3 (CEN (2005a)). Specifically, the shape of the geometrical imperfections was assumed equal to the first buckling mode of the whole system. Regarding the maximum amplitude of the geometrical imperfections, two different values were considered. First, the maximum value was set equal to 1/1000 of the brace member (diagonal) length. This maximum imperfection value was used with the numerical model also including the residual stresses. The second value for the maximum imperfection amplitude was obtained as an equivalent one, using the EC3 approach. This second (larger) value was used with a numerical finite element model not explicitly representing the residual stresses. To calculate the equivalent imperfection, a linear buckling analysis was first carried out using an equivalent frame model (Fig. 5). Then, the equations proposed by Eurocode 3 were applied to obtain the resulting equivalent geometrical imperfection. The calculation results were a maximum equivalent imperfection amplitude of 30 mm , whilst the nominal value previously mentioned is 5 mm, approximately. With these two imperfection values, two alternative models were built and analyzed using Ansys, to quantify the differences between the two approaches.

(b)

(a)

Fig. 5. First mode buckling shape simulating the geometric imperfections: (a) global view; (b) plan view.