A Study of Residual Shear Strength in Severely Corroded Steel Girder Ends

Abstract

Corrosion in steel girder ends, progressing from localized thinning of the web and the lower flange to severe perforation in severe cases, can significantly affect structural integrity. This study evaluates the effects of severe corrosion, including web–lower flange disconnection and transverse flange perforation combined with web damage, on the residual shear strength of steel girder end web panels through experimental and numerical methods. Results indicate that when only the web is affected, post-buckling strength starts to decline by corrosion damaging the plastic hinge on the tension flange, disrupting the tension field action. Conversely, in cases involving simultaneous web and lower flange damage, localized yielding at fracture points near the flange damage leads to the abrupt rotation of the tension field inclination angle, causing an earlier and more pronounced decline in post-buckling strength compared to web-only damage scenarios.

1. Introduction

Corrosion in steel girder ends, caused by water leakage, humidity retention, and inadequate ventilation, is a serious issue compromising girder strength. Girder ends carry significant shear loads, and severe corrosion at support areas both on the web and lower flange can affect tension field action and significantly impact the post-buckling shear strength.

Corrosion commonly affects the web, vertical stiffener, and flange near bearings, Eiki et al. [1], affecting its load-carrying capacity. Studies by Liu et al. [2] and Chien et al. [3] reported a decline in load-carrying capacity with increasing corrosion severity, noting that failure modes and strength degradation depend on corrosion location and pattern. Nauman et al. [4] found that localized web corrosion does not significantly affect post-buckling strength, while corrosion in a small area such as pitting was considered. However, studies by Yasser et al. [5] and Rahgozar et al. [6] investigated the effect of uniform corrosion over both the lower flange and web experimentally, stating that a 25% loss in web thickness can reduce the residual web-bearing strength to around 50%. Similarly, a study by Amanda et al. [7] investigated the residual bearing strength of steel girders with web perforation patterns. The results stated that the residual strength declines as the affected area increases, also it was stated that, the effect of corrosion progressing longitudinally along the length of the girder has a more severe effect over the residual bearing strength of the steel girder.

Looking at the existing literature, most of the studies have investigated the effect of severe corrosion mainly affecting the web panel. The effect of corrosion over the lower flange is limited to mild uniform corrosion. However, in observations of actual steel bridges severely damaged by corrosion, patterns of lower flange damage can also be seen, and, in some cases, a combination of damage both on the lower flange and web can be observed. Therefore, as an investigation parameter, this study has focused on very severe cases of corrosion where the web and the lower flange have been disconnected along the girder’s longitudinal direction, combined with a perforation cutting the lower flange in the transverse direction.

This study aims to investigate the effect of such severe corrosion on the residual shear strength of steel girders. To determine the residual shear strength, the effect of severe corrosion damage on tension field action and its mechanism is studied.

2. Corrosion Damage and Model Setup

This section reviews and categorizes damage cases based on corrosion patterns. Considering the most severe cases of corrosion, the corroded girder end model for this study is set.

2.1. Categorizing Corrosion Patterns

Corrosion is a prevalent issue in steel girder ends and is caused by several factors, such as humidity retention, leaking water, and deicing agents from the surface. Corrosion in real bridges starts with mild thinning, continued by severe section loss and leading to perforations in the web and lower flange. This study considered the most severe cases of corrosion where corrosion-induced damage causes perforation in the web and lower flange, based on real bridge observations depicted in Figure 1. Figure 1a shows severe corrosion damaging the web panel and causing perforation. Figure 1b represents severe corrosion, with corrosion damage progressing longitudinally along the length of the panel and causing perforation and damage to both the web and lower flange considered in this study.

2.2. Experimental Model for Evaluation of Shear Strength

To imitate the girder end panel situation, an experimental setup, shown in Figure 2, was adopted. The girder was placed over pin and roller supports (cantilevered side) with loading jacks of each 1000 kN. The panels of interest were placed in a manner to undergo maximum shear and minimum bending moment (almost zero at the web center) recreating a girder end situation. Material properties for the main web panel consisted of Young’s Modulus 2 × 10⁵ MPa with yield stress of ${\sigma }_y=328 \mathrm{M}\mathrm{P}\mathrm{a}$. The width-to-thickness ratio ($R_{\tau }$), as in Equation (1), [8] for the target web panel used in a previous study [9] was 1.65 within the elastic range and is shown in Figure 3.

$$R_{\tau }={\displaystyle \frac{b}{t}}\ast \sqrt{{\displaystyle \frac{{\tau }_y}{E}}\ast {\displaystyle \frac{12(1-v^2)}{{\pi }^2{k}_{\tau }}}}$$

(1)

In Equation (1), (b = 500 mm) and (t = 3.2 mm) are the height and thickness of the web, respectively, (${\tau }_y={\displaystyle \frac{{\sigma }_y}{\sqrt{3}}}$) is shear stress, (E = 2 × 10⁵ MPa) is modulus of elasticity, (v = 0.3) is Poisons ratio, and buckling coefficient is $k_{\tau }=5.34+{\displaystyle \frac{4}{{\alpha }^2}}\left(\alpha \ge 1.0\right), \alpha =a/B=1$. A 500 mm × 500 mm web panel was considered for the parametric study.

2.3. Considering Corroded Patterns

Considering the most corroded patterns of steel girder ends, this study first sets the corroded girder end patterns. The model and test setup are discussed along with the results for corroded patterns. As confirmed with real bridges, in the most severe cases, corrosion propagates horizontally causing the disconnection of the web and lower flange. Also, in the most severe cases, as can be confirmed in Figure 1b, the flange is also severely affected and a transverse cut in the width direction of the lower flange occurs. To imitate a severe corrosion scenario in girder end panels based on real bridge observations a cut was introduced to the web. Showing a progression of corrosion damage along the horizontal direction of the web length (L_HC), the effect of corrosion damage in 50%, 80%, and 100% of the panel’s length (L₀) was investigated. Also to show the effect of extreme corrosion over flanges and the combined effect of flange and web corrosion over shear strength, a cut in the lower flange was provided, the parameters are shown in

Table 1. Experimental parameters.

Cases	Case Name	(%)$\mathbf{Web} \mathbf{Damage} \frac{{\mathit{L}}_{\mathit{H}\mathit{C}}}{{\mathit{L}}_0}$	$\mathbf{Flange} \mathbf{Damage} \mathbf{at} \frac{{\mathit{L}}_{\mathit{H}\mathit{C}}}{{\mathit{L}}_0}$ (%)
1	Base	-	-
2	W50	50	-
3	W80	80	-
4	W100	100	-
5	WF50	50	50

.

The corrosion patterns examined in this study, as illustrated in Figure 3, are categorized into two types. The first category pertains to corrosion damage that separates the web from the lower flange and is noted as (W-Type), as shown in Figure 1a and Figure 3a. The damage along the vertical stiffener of the panel for all types and patterns is fixed at 100 mm which is 20% of the total web height (L_VC), and the horizontal damage along the longitudinal direction of the girder is parametrically investigated. Another corrosion pattern investigated by this study is (WF-Type), as shown in Figure 1b and Figure 3b; damage affecting both the web and lower flange with the number next to the pattern, such as (WF50), means corrosion disconnecting the lower flange from the web and transversely disconnecting the lower flange by perforation at 50% of the total web length.

3. Evaluating Residual Strength of Damaged Cases

3.1. Effect of Severe Corrosion over Tension Field Action

Post-buckling shear strength is attained when the tension field undergoes yielding under diagonal tensile stresses. Theoretically, according to Equation (2), the post-buckling shear strength ($V_t$) is calculated based on the relationship between the yield stress (${\sigma }_t$), the width of the tension field (S), and the thickness of the web panel (t).

$$V_t={\sigma }_t\ast S\ast t$$

(2)

The post-buckling shear strength, which supports the web panel beyond critical elastic shear buckling, is governed by tension field action. This strength is attained when the web’s tension field fully yields under diagonal tensile stresses. As shown in the equation, it depends on the yield stress of the diagonal tension field, its width, and panel thickness. Additionally, the inclination of the tension field and the panel’s diagonal angle significantly influence the effective tension field area, plastic hinge locations, and length. However, corrosion alters these parameters, affecting the tension field action. Figure 4 illustrates this, with Figure 4a depicting an uncorroded panel and Figure 4b a corroded one. The effects of corrosion on tension field action and related parameters will be discussed in subsequent sections.

3.2. Experimental Results and Numerical Method Validation

This study also adopted a numerical approach for investigating the residual shear strength of severely corroded girder ends and used the results of five experimental cases to validate the numerical method shown in Figure 5 with parameters in Table 1. Abaqus 2022 was used for numerical modeling with a 4-node quadrilateral shell element, based on an elastic–plastic constitutive model with bilinear hardening behavior. Initial deformation of the web panel was considered for the numerical model as shown in Figure 5. The Base model with no corrosion has been previously studied and the numerical model results have already been verified [8]. However, the cases with severe corrosion on the web panel and lower flange require validation for further numerical study; the results for the shear and vertical displacement measured directly under the lower flange of loading Jack-2 (shown in Figure 2 as P2) are shown in Figure 6. Post-buckling shear strength declines at the post-buckling as the corrosion damage progresses, this mechanism will be discussed in the next section. Figure 7 shows the out-of-plane deflection and tension field action for the numerical and experimental parameters; it also shows the rotation of the tension field inclination angle, the plastic hinge of the lower flange, and the tension field width as corrosion propagates. Based on the results of both figures, a good agreement between the numerical method and experimental results can be confirmed.

3.3. Numerical Parametric Results

Following the validation of the damaged numerical cases, a parametric investigation was conducted using the parameters outlined in

Table 2. Numerical damage parameters.

Cases	Base	W20	W30	W40	W50	W80	W100	WF20	WF30	WF40	WF45	WF50	WF80	WF100
Damage Patterns
Web damage LHC/L0 (%)	-	20	30	40	50	80	100	20	30	40	45	50	80	100
Flange damage LHC/L0 (%)	-	-	-	-	-	-	-	20	30	40	45	50	80	100

. The analysis considered W-Type and WF-Type corrosion damage; the results are depicted in Figure 8 and Figure 9. For W-Type corrosion, Figure 8 demonstrates that post-buckling strength remains unaffected until the corrosion length ratio (Lc/L0) reaches 0.5, corresponding to corrosion affecting half of the panel’s length. Beyond this point, a gradual reduction in post-buckling strength is observed. Conversely, Figure 9 shows that WF-Type corrosion patterns exhibit negligible impact on post-buckling strength up to 40% of the panel’s length (WF40). However, corrosion exceeding this threshold results in a rotation of the inclination angle, resulting in a pronounced strength reduction which is attributed to a localized yield formed in the fracture point near the flange damage.

The post-buckling behavior for both corrosion patterns, along with experimental data for the WF50 case, is presented in Figure 10. For W-Type corrosion, post-buckling strength starts to decline once corrosion progresses to half of the panel’s length L_HC/L₀ ≥ 50% due to the damage of the plastic hinge (Ct), located on the lower flange affecting the anchorage of the tension field.

In contrast, WF-Type corrosion shows a marked decline in strength beyond L_HC/L₀ ≥ 40%. The decline between 40% and 50% is abrupt and driven by the initiation of the localized yielding causing a hinge-like rotation of the inclination angle in the vicinity of the flange cut. The mechanisms underlying these reductions are further discussed in the subsequent section.

3.4. Mechanism of the Decline in Post-Buckling Strength

To explain the effect of corrosion on web panels, the out-of-plane deflection curve showing the mode of buckling for the Base case is presented in Figure 11. It can be seen that the width of the tension field corresponds to the inflection points of the out-of-plane deflection curve. In an undamaged web panel, the width of the tension field can be theoretically determined based on Basler’s Equation (3) [10].

$$S=B\ast (sin\theta cos\theta -{\alpha }_c{sin}^2\theta )$$

(3a)

here ($\theta$) is the inclination angle of the tension field as shown in the figure, (B) is the height of the web panel, and ${\alpha }_c=\alpha \left\{1-(C_c+C_t)/a)\right\}$ shows the panel’s aspect ratio and plastic hinge location relationship.

$$C_c={\displaystyle \frac{2}{sin\theta }}\sqrt{{\displaystyle \frac{M_{pfc}}{{\sigma }_t{t}_w}}}\mathrm{and} C_t={\displaystyle \frac{2}{sin\theta }}\sqrt{{\displaystyle \frac{M_{pft}}{{\sigma }_t{t}_w}}}$$

(3b)

the Cc and Ct are the plastic hinge locations on the tension and compression flanges with ($M_{pft}$) being the plastic bending moment of the upper and lower flanges, and (${\sigma }_t$) is the stress causing yield of the tension field [8].

a. 

W-Type

When corrosion progresses horizontally along the web’s longitudinal direction and disconnects the web from the lower flange (W-Type), the post-buckling strength begins to decline gradually, as illustrated in Figure 8. This decline becomes significant once corrosion propagates beyond half the panel’s length. Prior to reaching this limit, the post-buckling strength remains unaffected due to the absence of a reduction in the tension field width (S), as described by the equation $V_t={\sigma }_t\ast S\ast t$.

However, as corrosion extends beyond half of the panel’s length, the post-buckling strength declines, as shown in Figure 8. This decline is attributed to a reduction in the tension field width, which in this study is defined as the distance between the inflection points of the out-of-plane deflection curve. As described in Equation (3), the tension field width is directly related to the inclination angle of the tension field and the position of plastic hinges, as further detailed in Equation (3b). With the progression of corrosion that disconnects the web and lower flange, the tension field width decreases, causing the panel’s horizontal axis (x-axis) to extend closer to the height of the web ($b_c$), as shown in Figure 7. Consequently, the length of the plastic hinge (Ct) declines, as depicted in Figure 12, resulting in a rotation of the tension field’s inclination angle, as shown in Figure 13, as well as panel’s diagonal angle.

Figure 14 shows the rotation of the inclination angle as corrosion progresses as depicted in Figure 13. From around L_HC/L₀ ≥ 50%, the plastic hinge on the lower flange gets damaged by corrosion. The tension field width gradually becomes narrower and due to the damaged (Ct), the inclination angle starts to rotate and decline. Therefore, due to the rotation of the tension field angle, its effective area reduces, and post-buckling strength declines. This behavior can be explained by the dependence of post-buckling strength on the tension field width, which, in turn, is influenced by the inclination angle and the plastic hinge length. Consequently, in W-Type corrosion cases, the post-buckling strength starts to decline as soon as the plastic hinges of the lower flange (Ct) are damaged by corrosion, resulting in rotation of the tension field inclination angle and a shift in the anchorage.

b. 

WF-Type

As illustrated in Figure 9, when corrosion damages both the web and lower flange (WF-Type), the post-buckling strength remains relatively unaffected until the corrosion extends to 40% of the panel’s length. Starting at approximately L_HC/L₀ = 45%, a gradual decline in post-buckling strength is observed. However, at L_HC/L₀ = 50% the decline becomes more abrupt and severe. In W-Type corrosion cases, post-buckling strength remains stable until corrosion compromises the plastic hinge (Ct). However, as shown in Figure 12, the plastic hinge length remains unaffected by WF-Type corrosion until the damage reaches half the panel’s length. Still, the tension field inclination angle is observed to decline starting from around L_HC/L₀ = 40%, becoming more pronounced from 45% as shown in Figure 13, while the position of the plastic hinges on the lower flange (Ct) is observed to be unaffected. This is further confirmed in Figure 15, where no significant changes in tension field action are observed up to L_HC/L₀ = 50%.

The decline in post-buckling strength starting from around L_HC/L₀ = 40% is primarily attributed to excessive damage to the web and the lower flange, which reduces the overall load-carrying capacity of the panel. Although the plastic hinge in the lower flange remains unaffected at this stage, the localized yielding of the web in the vicinity of the flange damage, shown in Figure 15, causes an abrupt rotation of the tension field inclination angle, as shown in Figure 13. Hinge-like behavior results in the decline of post-buckling strength, as shown in Figure 16a. Excessive damage to both the web and lower flange contributes to the decline in post-buckling strength and is marked as Point 1 in Figure 16a. At Point 2, which represents the peak strength, the rotation in the fracture point formed in the web in the vicinity of the flange cut, results in a rotation in the inclination angle causing a decline in strength, as indicated at Point 3. A comparison of the von Mises stress contours for the Base case and the WF50 corrosion case in Figure 16c highlights the underdeveloped tension field and the location of the localized yielding of the web.

In WF-Type corrosion cases, the decline in post-buckling strength becomes more pronounced when the corrosion extends beyond L_HC/L₀ ≥ 40%. The damage to the lower flange leads to localized yielding at the fracture point in the vicinity of flange damage, resulting in a hinge-like rotation. This rotation results in altering the inclination angle, resulting in a reduction of the effective tension field area and, consequently, a decline in post-buckling strength.

As the current study has studied the effect of severe corrosion over steel girder ends, maintenance possibility and repair will be investigated as a part of future work.

4. Conclusions

This study examined the impact of the severe corrosion of steel girder ends on residual shear strength. The parametric investigation focused on corroded panels exhibiting extreme damage, including the disconnection of the web from the lower flange (W-Type). Additionally, scenarios involving combined damage to the lower flange and web (WF-Type) were analyzed to represent severe corrosion conditions. A comprehensive approach integrating numerical simulations and experimental testing was employed, with the findings presented as follows:

• In W-Type corrosion patterns, where the damage disconnects the web from the lower flange and predominantly affects the web, a gradual decline in post-buckling strength is observed beyond L_HC/L₀≥50%. This decline is attributed to the narrowing of the tension field width, which induces a shift in the plastic hinge (Ct) on the lower flange affecting the location of the anchorage. Consequently, this shift results in the rotation of the inclination angle, reducing the effective area of the tension field and leading to a reduction in post-buckling shear strength.
• In WF-Type corrosion patterns, where the web and lower flange are disconnected along with a transverse cut in the lower flange, post-buckling strength begins to decline at approximately L_HC/L₀≥40%. Corrosion damage to the lower flange, combined with web deterioration, leads to the formation of a localized yield point near the flange cut referred to as a fracture point. This fracture point results in a hinge-like rotation and causes the tension field’s inclination angle to abruptly rotate, reducing its effective area and resulting in a sudden decrease in post-buckling strength.

Future work: While this study primarily investigated severe corrosion scenarios involving web and lower flange damage with through-thickness damage. Future research will focus on the effects of gradual thinning over a large strip of the web panel.