## 1 Introduction
### Shear Capacity  
Steel plates under shear loads are known to exhibit a significant amount of load-carrying capacity in the post-buckling regime [5]. This structural behaviour was thoroughly investigated by the researchers and attributed to the existence of tensile stresses acting in the diagonal direction of the plates after the onset of shear buckling [2; 6; 7]. These areas along the diagonal axis of the web plate where tensile stresses acts can also be seen in Figure 2. Their research led to the development of various models for the prediction of the post-buckling shear capacity of web plates based on the concept of a tension field along the plate diagonal. Tension field theory is often used as an umbrella term for these models. This theory is based on the observation that the stiffeners of a plate girder take up the compressive stresses resulting from the shear forces, and the web plate resists buckling owing to shear forces produced by tensile stresses forming along the diagonal axis of the plate [8; 9]. Among the models of tension field theory, the theory developed by [PERSON] [6] gained the most widespread acceptance in the research community; this model was also described in [10]. On the other hand, the model developed by [PERSON] [11] and the rotated stress field method developed by [PERSON] [12] are included in the European design codes [13].  
Figure 1: Lateral buckling of bridge plate girders in Edmonton, Alberta, Canada [4].  
Figure 2: Post-buckling deformation of stiffened plate girder under transverse loading [14].  
Figure 3 shows a schematic of the tension field on a girder panel surrounded by flanges and transverse stiffeners, where \(s\) denotes the width of the tension field of a web plate under the ultimate postbuckling shear stress \(\tau_{u}\). The plate in Figure 3 represents the unstiffened part of a plate girder web and is assumed to be simply supported (SS) at all edges. [PERSON] [6] developed an equation that predicts \(\tau_{u}\). This equation was later modified by [PERSON] [15], [PERSON] [16], and [PERSON] [17] as follows:  
\[\tau_{u}=\tau_{\sigma}+\sigma_{y}\bigg{(}1-\frac{\tau_{\sigma}}{\tau_{y}} \bigg{)}\bigg{(}\frac{sin\theta_{d}}{2+cos\theta_{d}}\bigg{)}. \tag{1}\]  
Once \(\tau_{u}\) is known, the ultimate postbuckling shear force \(V_{u}\) can be obtained as \(V_{u}=\tau_{u}Dt_{w}\), where \(D\) is the depth of the plate (see Figure 3), and \(t_{w}\) is the thickness of the web plate.  
In Equation (1), \(\theta_{d}\) is the angle of the web panel diagonal, \(\sigma_{y}\) is the yield strength of the plate material, from which the shear yield strength \(\tau_{y}\) can be obtained as \(\tau_{y}=0.6\sigma_{y}\). The elastic shear buckling strength \(\tau_{\sigma}\) in Equation (1) is calculated as follows [18]:  
\[\tau_{\sigma}=\frac{k\pi^{2}E}{12(1-\
u^{2})\big{(}\frac{D}{t_{w}}\big{)}^{2}}, \tag{2}\]  
where \(E\) is the modulus of elasticity, \(\
u\) is the Poisson's ratio, \(D/t_{w}\) is the slenderness ratio, and \(k\) is the shear buckling coefficient, which can be calculated as a function of \(a/D\) (span-to-depth ratio) and the assumed boundary conditions of the web plate. The equation for \(k\) for simply supported boundary conditions is as follows [19]:  
\[k=5.0+\frac{5.0}{\big{(}a/D\big{)}^{2}}, \tag{3}\]  
where \(a\) is the clear distance between transverse stiffeners.