Issue 78

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

According to Ć erani ć , 2022 [18] and Mirambell et al., 2012 [34] the imperfection factor was set to Fo α =1.0 , and the plateau length is Fo λ =0.5, for a target partial safety factor γ M1 = 1. In Eq. (1), F λ = the slenderness parameter, and is calculated as:

F

y

F λ =

(8)

F

cr

3

t

w

F = 0.9 E K

(9)

cr

F

h

w

K F = the buckling coefficient, for longitudinally stiffened webs subjected to concentrated transverse loading, EN 1993-1-5 accounts for the contribution of the longitudinal stiffener through the relative flexural rigidity parameter γ s as:

2

w       h a

b

1 +(5.44 -0.21) γ

K = 6+2

(10)

F

s

a

3

I

w   a     h

b

  

  

sl,1

1



γ =10.9

γ * =13

+210 0.3

(11)

s

s

 

3

a

h t

w w

The second moment of area of the stiffener nearest to the loaded flange, including contributing web pieces (15 ε t w ), is denoted as sl,1 I . The Commentary to EN 1993-1-5 covers the formulation's origins and intended application, as well as the limiting behavior associated with increasing stiffener rigidity. Once the top limit γ s * is achieved, increasing the estimated flexural rigidity does not enhance k F in the first-generation formulation, as applied by Johansson, et al., 2007 [35]. Experimental and numerical investigations have demonstrated the importance of stiffener rigidity in patch loading. While Loaiza et al., 2019 [16] found that stiffener-induced limitations on web displacements affect critical buckling load and patch loading resistance, especially for strong stiffeners, Graciano and Edlund, 2003 [36] showed that a longitudinal stiffener modifies the web failure mechanism and limits buckle size. They noted that stiffener placement and rigidities affect web crippling strength and offered design advice that focused on stiffener position and web slenderness. The uniform strengthening assumptions for patch-load length in the Eurocode are challenged by recent work by Ć erani ć et al., 2022 [18], which showed that the strengthening effect depends on several elements, such as stiffener rigidity and panel aspect ratio, and can beyond the limits established by EN 1993-1-5. These findings provide a relevant basis for the present study, which investigates triangular and rectangular closed stiffening configurations that are not explicitly distinguished in the current EN 1993-1-5 formulation. Accordingly, the present section evaluates whether the current γ s -based formulation can distinguish the structural contribution of triangular and rectangular closed stiffeners, despite their different geometrical and three dimensional stiffness characteristics. Eighteen models are chosen for this study with constant characteristics as h w = 500 mm, t w = 4 mm, t f = 8 mm, and b f = 120, while three variables are taken as stiffener thicknesses t s = 4, 6, and 8 mm for each stiffening configuration satisfying the applicability limits of the formulation. Therefore, based on Eq.11, limit of relative flexural rigidity parameter and accordingly limit of second moment of area of the stiffener nearest to the loaded flange are     3 s γ *=13 1.0 +210 0.3-0.2 = 34, accordingly, 3 4 4 s w w s1,limit γ *h t I = = 9.98×10 mm 10.9 For every configuration under investigation, the computed I sl,1 values including the required contributing portion of the web exceed this limiting value. Therefore, based on the present EC3 rigidity criterion, all stiffeners under investigation are categorized as strong stiffeners. While the limiting code parameter stays constant at γ s = 34, their actual computed stiffness varies significantly with stiffener shape and thickness. The current EC3 formulation predicts the same resistance for triangular and rectangular stiffeners with the same loaded length, since constant γ s is obtained for all examined configurations, as shown in Table 4 and Fig. 21. A sensitivity study is conducted in parallel by ignoring the upper bound of γ s and considering its actual value without limitation.

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