# Bending Performance of a Prestressed Concrete Composite Girder Bridge with Steel Truss Webs
## 6 Calculation Method of the Flexural Bearing Capacity
### Breaking Bending Moment \(M_{u}\)  
When the section of the composite girder is broken by bending, the contribution of the web plate (or web truss) to the bending capacity of the girder should be considered [11; 13]. To calculate the contribution of steel truss webs to the compressive bearing capacity of the top plate in PC composite girders, the steel truss webs should be considered equivalent to concrete webs based on the principle of equivalent shear stiffness. This means the additional deflection caused by the axial deformation of the steel truss webs in the PC composite box, under the shear action, is equal to that caused by the shear deformation of the concrete web in the PC box girder. According to the principle of equivalent shear stiffness, the formula for calculating the equivalent thickness \(t\) when the truss steel web arranged at a given interval is equivalent to the continuous closed concrete web is as follows:  
\[t=\frac{E_{\text{s}}}{G_{\text{c}}}\cdot\frac{dh_{\text{cor}}}{\left[\frac{ \phi}{3}\left(\frac{1}{\Delta_{\text{cu}}}+\frac{1}{\Delta_{\text{cl}}}\right) n_{\text{e}}+\frac{t^{3}}{\Delta_{\text{sg}}}\right]} \tag{8}\]  
The parameters in Formula (8) are explained in Figure 20, where \(d\) is the horizontal projection length of the diagonal steel truss web member on the longitudinal bridge; \(h_{\text{cor}}\) is  
Figure 19: Mechanical schematic diagram in the yield stage. the vertical projection height of the diagonal steel truss web member on the longitudinal bridge; \(l^{*}\) is the length of the diagonal steel truss web and \(A_{\text{cu}}\) is the section area of the joint between the steel truss web and the concrete top plate; \(A_{\text{cl}}\) is the section area of the joint between the steel truss web and the concrete bottom plate; \(A_{\text{sg}}\) is the section area of the steel truss web; \(E_{\text{s}}\) is the elastic modulus of steel; and \(G_{\text{c}}\) is the shear modulus of concrete. Due to the significant cracking of the concrete bottom plate in the PC composite girder at the point of bending failure, this paper does not consider the contribution of the steel truss web to the flexural bearing capacity. Instead, the contribution of the steel truss web to the compressive bearing capacity of the top plate is considered. For either a bonded or unbonded prestressed concrete balanced-reinforced girder, it is assumed that the concrete in the compression zone reaches the compressive limit and the prestressed strand and reinforcement in the tension zone reach the tensile limit when bending failure occurs. When the composite girder section is broken due to bending, the compression zone depth can be divided into two situations: in the top plate and in the web. The force diagram is shown in Figure 21. The depth of the compression zone can be judged according to Formula (9). When Formula (9) is satisfied, the depth of the compression zone is located on the top plate; otherwise, the depth of the compression zone is located in the equivalent web. \[\sigma_{\text{sd}}A_{\text{s}}+\sigma_{\text{pu}}A_{\text{p}}\leq\sigma_{\text {cd}}b_{\text{rf}}+\sigma_{\text{sd}}^{\prime}A_{\text{s}}^{\prime} \tag{9}\]  
The ultimate stress \(\sigma_{\text{pu}}\) of external prestressed reinforcement is the key value to calculating the flexural strength of unbonded prestressed concrete composite girders. There are many factors affecting the value of \(\sigma_{\text{pu}}\), such as the effective prestress of external prestressed reinforcement, the reinforcement ratio, the height-to-span ratio of the girder, and the loading conditions. In this paper, according to the Technical Regulations for Unbonded Prestressed Concrete Structures (JGJ 92-2016) [29], the ultimate stress design value of unbonded prestressed  
Figure 21: Mechanical schematic diagram in the fracture stage: (**a**) Compression zone on the top plate; (**b**) Compression zone in the web. Figure 20: Cross-section parameter of the PC composite girder bridge with steel truss webs: (**a**) Section view; (**b**) Side view.