Issue 78

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

at the top, showing that a considerably wider strip of the web is actively resisting the load. As a conclusion, increasing the width of the patch load causes the stress in the girder web to become more evenly distributed. Rather than being highly concentrated directly under the load, the stresses extend laterally over a broader region, which reduces intense local stress peaks and prevents deep stress penetration into the web. This improved dispersion of loading enhances the composite action between flange and web, so a larger portion of the steel cross-section contributes to carrying the load. Consequently, the girder achieves a higher ultimate load capacity and a more desirable global structural response. Moreover, the broader stress field supports the formation of stable post-buckling behavior, allowing the web panel to maintain substantial strength after buckling begins and thereby increasing the overall load resistance up to failure.

Figure 8: von-Mises stresses for unstiffened beams with h w = 500 mm, t w = 4 mm and different W.

Specimen depth 200 mm U-200-4-0 U-200-4-75

Specimen depth 350 mm U-350-4-0 U-350-4-75

Specimen depth 500 mm U-500-4-0 U-500-4-25 U-500-4-50 U-500-4-75

Specimen depth 500 mm

Load (kN) 150.2 200.7

Failure Mode

Load (kN) 152.4 203.6

Failure Mode

Load (kN) 147.2 165.8 165.2 201.5

Failure Mode

Load (kN)

Failure Mode

C+L C+L C+L

Y Y C Y Y C Y Y Y

Y

Y C

U-500-6-100 381.7 U-500-6-125 410.2 U-500-6-150 441.7

C+L C+L

U-200-4-150 244.9

U-350-4-150 268.7

C+L C+L C+L C+L C+L

U-200-6-0 U-200-6-75

239.7 356.6

U-350-6-0 U-350-6-75

233.6 349.7

Y C

U-500-8-0 U-500-8-25 U-500-8-50 U-500-8-75

343.2 383.0 450.1 512.0

Y Y Y Y Y

U-500-4-100 212.4 U-500-4-125 229.0 U-500-4-150 242.8

U-200-6-150 447.6

U-350-6-150 446.9

C+L

U-200-8-0 U-200-8-75

338.3 512.2

U-350-8-0 U-350-8-75

311.0 490.4

Y Y Y

U-500-6-0 U-500-6-25 U-500-6-50 U-500-6-75

240.0 278.7 324.2 355.3

Y C C

U-500-8-100 564.4 U-500-8-125 610.8

U-200-8-150 663.3

U-350-8-150 638.2

Y Y

U-500-8-150

656.6

C+L Table 2: Failure load for models with a flat plate flange (Y=Yielding, C = Crippling, L = Local buckling).

The load-deflection curves for different models are presented in Fig. 9, showing the effect of load width for different web thicknesses and beam depths. For t w = 4 mm, the capacities are 150, 200, and 245 kN for W = 0, 75, and 150 mm, respectively. The same behavior of increasing the capacity by increasing the load width is noticed for t w = 6 and 8 mm, which recorded 240, 357, 448 kN and 338, 512, 663 kN, respectively. As for the web height, no difference is noticed for the three different heights of 200, 350, and 500 mm. The three curves are almost identical for different loaded lengths and different web thicknesses. Regarding the web thickness, as the thickness increases, the maximum strength of the girders is obtained, and a noticeable increase in strength under the same loading length and web height is illustrated. The increase in capacity is somewhat proportional to the increase in web thickness. Increasing the thickness from 4 to 6 mm (1.5 times) shows an increase in the capacity of around 1.6 to 1.8 times. While increasing the thickness from 6 to 8 mm (1.33 times),

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