Issue 78

S. M. Khalil et alii, Fracture and Structural Integrity, 78 (2026) 346-366; DOI: 10.3221/IGF-ESIS.78.20

ln(1+ ε E ), where σ E and ε E are the engineering stress and strain, respectively. The mechanical properties are set with a yield stress ( σ y ) of 320 MPa for both the web and the flanges, and Poisson’s ratio of 0.3.

Figure 2: Finite Element Model.

Figure 3: Stress-strain curve of the material.

The consideration of initial geometric imperfection is a critical aspect of nonlinear finite element analysis, especially for thin walled steel members whose structural response is determined by instability occurrences. According to Chacón et al. (2019) [14], the structural response of stiffened web panels under patch stress might show some sensitivity to the size and distribution of initial defects. In the current study, the maximum allowed imperfection as permitted by codes, which is considered the most critical case, is reflected. Imperfections in steel members beyond these limits shall not be accepted in the field, and the defective members are to be replaced. In the case of patch loading, the considered imperfections are geometric imperfections of the web. The governing imperfection to be considered is the one that leads to the lowest resistance and is found to be the initial out-of-flatness of the web panels (Chacón et al., 2009 [7]). There are several approaches for introducing similar geometric defects into numerical models, including manually defined imperfection profiles or imperfection forms scaled from eigenvalue buckling modes. The current study uses imperfection forms scaled from eigenvalue buckling modes, following EN 1993-1-1 [33], which takes the scaling as the minimum of a/200 and h w /200, where a is the span and h w is the web depth. Fig. 4 shows the first eigenmode for different types of beams: unstiffened, longitudinally stiffened, triangle- closed top flange stiffened, and rectangular- closed top flange stiffened. As for residual stresses, which can be idealized differently depending on design codes and modelling assumptions, they have a minimal influence on the ultimate patch loading capacity of plate girders, as failure is governed primarily by local geometric instability. Initial welding residual stresses are not included in the finite element models as they do not play a significant role in determining the ultimate resistance of longitudinally unstiffened or stiffened plate girders, as stated in previous research by Casanova et al. (2022) [23] and Graciano et al. (2021) [24].

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