Issue 78

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

for t s /t w = 4 and t w = 8 mm, where the capacity gain starts with 320% at W/d s = 0 and ends with 125% only at W/d s = 1.5. For t s /t w = 1, which is the advice in the previous section, the gain in capacity is almost constant for different web thicknesses and load lengths, which show 100% gain. The curves in the figure are plotted starting from a stiffener thickness of 4 mm. The smaller stiffener thicknesses, such as 1 or 2 mm, are not included, as their contribution is minor because of the weakness of these slender stiffeners. By increasing stiffener thickness to 4 mm (non-compact stiffener) for t s /t w = 1, the normalized load slightly increases to 2.5 at aspect ratio w/d s = 1, then it slightly decreases. This concludes that a non-compact stiffener has a positive effect on strength, especially when the loaded length is equal to the stiffener depth. A greater increase in stiffener-to-web thickness ratio makes the peak normalized load go to a smaller ratio of w/ds. A 6 mm thickness (compact stiffener) made the maximum normalized load at a ratio of w/d s = 0.75, an 8 mm thickness made the maximum normalized load at a ratio of w/d s = 0.5. As a conclusion, it is recommended to use a stiffener with the same thickness as the web at any load length. Still, a higher ratio of t s /t w up to 2 or 4 gives benefits for small web thickness generally for different load lengths, and for large web thickness specifically at small load lengths.

Figure 16: Normalized load versus W/d s ratio for models with h w = 500 mm and different t s /t w ratios.

Figure 17: Normalized load versus d s /h w ratio for models with different t s /t w ratios.

Effect of depth of stiffened web (ds) The parameter d s /h w was previously studied by Casanova et al. (2022) [23], who concluded that a larger d s /h w ratio increases the web area within the triangle, which lowers the height of the unstiffened web panel beneath the stiffener. The ratio in this reference was in the range of 0.1 to 0.3, while the current paper extends the ratio to cover a ratio of 0.5. Under patch loading, unstiffened narrow webs may buckle locally due to compressive forces. Shallowly placed triangle stiffeners result in higher web panels, increasing the risk of premature buckling. Deeper stiffeners increase buckling resistance by lowering the effective buckling height and establishing a rigid load-transfer system. This arrangement helps to rebalance the patch load, which reduces localized buckling and delays instability, changing the failure mode from localized buckling to a more distributed failure involving several structural components. As shown in Fig. 17, for models with t w = 4 mm, the maximum normalized load is equal to 4.5 for d s /h w = 0.2, and this value decreased at d s /h w = 0.3 to 4.35, then increased again to 4.71 at d s /h w = 0.5. These differences are considered negligible, and the d s /h w ratio is considered ineffective and has a constant normalized load for different web thicknesses. The same is noticed for t s /t w = 2.0. The three curves for t w = 4, 6, and 8 mm match each other, and have constant capacity gain for different d s /h w ratios. Still, the average capacity gain of the higher t s /t w ratio is greater than that of the one for the lower t s /t w ratio. Rectangular closed flange More models are performed to compare the stiffening using an inclined plate with the stiffening using an angle. The models with a triangular closed flange are compared to the ones with a rectangular closed flange, considering the same stiffening depth and width. By comparing the two stiffening geometries with the same stiffener thickness and beam dimension, it is found that both configurations increase the capacity of the web. As shown in Fig. 18, the rectangular and triangular closed flanges have the same normalized load at loaded length W = 0, no matter whether the stiffener thickness differs. By increasing the loaded length to 75 mm, this behaviour changes little for the thick stiffener. With a small stiffener thickness of 4 and 6 mm, triangular stiffening gives almost the same strengthening; however, by using thicker stiffeners with a

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