Issue 78

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

patch loading above a closed flange on the web behavior. To enable measuring the enhancement, a study is first conducted on an I-section with a conventional flange plate before transforming it to closed flanges. The typical I-section has a flange plate width (b f ) and thickness (t f ) of 120 mm and 8 mm, respectively. The dimensions of the plate and the angle used to create the closed flange are chosen to stiffen the web laterally at 100 mm below the top flange. This dimension is denoted as the depth of the stiffener (d s ). The beam span (a) is taken as 500 mm, and the overall depth of the web (d w ) is also typically taken as 500 mm, giving a ratio of 0.2 for the depth of stiffened web to total web depth ratio. The beam depth is extended in the study to 350 and 200 mm, covering ratios of 0.3 and 0.5 for the stiffened web depth -to- total web depth. The thickness of stiffeners is selected from 1 to 24 mm, covering different slenderness ratios of the stiffeners and various stiffener-to-web thickness ratios. The web thickness is taken as 4, 6, and 8 mm, following the limit of width-to-thickness ratios of the compression element per code, avoiding slender section classification. The length of the patch loading (W) is chosen between 0 and 150 mm, where 0 denotes a concentrated load. The patch load is assigned on the whole width of the flange. Unstiffened girders using a flange plate are modelled as pilot models to be compared with the stiffened girders that have a closed flange. A total of 39 models is performed for unstiffened girders using W = 0, 75, and 150 mm, h w = 500, 350, and 200 mm, t w = 4, 6, and 8 mm. A sample of a load-deflection curve is shown in Fig. 7. The deflection is measured at the point under the load at the midspan of the top flange. The behaviour of the unstiffened plate girder subjected to concentrated local loading exhibits a sharp linear-elastic rise, then a distinct peak, followed by a post-peak softening. The ultimate (failure) load is defined as the peak load attained on the load-displacement curve for each girder. It is the highest value on the vertical axis prior to the softening of the curve. As shown in the figure, the failure load of model U-500-4-0 is 147.2 kN at a deflection equal to 1.5 mm. For model U-500-6-0, the curve rapidly peaks at 240 kN at a deflection of 4.5 mm. For the thickest web in model U-500-8-0, the ultimate load is 343.2 kN at a deflection of 10.5 mm. A summary of the ultimate load of these models along with the dominant failure mode is tabulated in Tab. 2. The von Mises stress distribution at the ultimate load and the U1 deformation pattern are used to categorize failure types. When the critical stress concentration is confined beneath the applied load without a noticeable instability pattern, yielding-dominated behavior is considered. Significant localized out-of-plane deformation in the web beneath the patch load is indicative of web crippling, whereas situations with both significant local deformation and an extended out-of-plane action are categorized as web crippling with local buckling. The examined unstiffened models show no signs of global instability. For clarity in the table, the name of the model, U-111-2-3, uses a letter at the beginning to define if the top flange is unstrengthened as a flat plate (U). The letter is followed by groups of numbers in millimeters denoting the beam depth, firstly, then the web thickness, and lastly the width of the patch load.

Figure 7: Load versus vertical displacement under the loaded point for unstrengthened models with W = 0 mm. It is noticed from the results that, for variable loaded length, the wider the loaded length, the higher the girder strength recorded for the same web height and thickness. Failure mode and behavior vary as the loaded length grows, as shown in Fig. 8. For a small load width, a high local stress gradient directly beneath the flange-to-web interface controls the failure at W = 0 and 25 mm. Because the force is centered on a single spot or narrow band, the web experiences early localized buckling. By increasing the load width, the failure changes into a combination of web buckling and localized yielding at longer loaded lengths, as shown for W = 50, 75, and 100 mm. The web panel's stress fields start to disperse diagonally. For the largest load width, the instability of a bigger horizontal part of the web is the primary cause of failure, as shown for W = 125 and 150 mm. A significant horizontal yield/buckling lobe forms slightly below the flange instead of localized buckling

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