# Shear Behavior of Concrete Encased Steel Truss Composite Girders
## 3 Analysis and Discussion
### Shear Failure at Truss Node  
As described earlier, in the case of the W specimen series applied with the Warren truss, the diagonal web member failed to exhibit effective shear resistance owing to the shear failure of the screw rod at the EST node. Figure 11 shows a free-body diagram at the Warren truss node. When diagonal cracking occurred, the diagonal web member was subjected to tensile force, and a shear force occurred on the screw rod. The shear strength of the specimen was calculated considering the screw rod failure and then compared with the test results. In this study, the crack angle was assumed to be 45\({}^{\circ}\), and the force of the diagonal member, which was exerted parallel to the crack direction, was disregarded for a simple calculation. In addition, because the bottom plate was fully anchored with bolts at both ends of the member and the bond stress between the steel plate and concrete was extremely small, the tensile force increment (\(\Delta T\)) of the bottom plate was disregarded as well. Under some assumptions, the tensile force acting on the diagonal web member (\(T_{w}\)) at the instant of the screw rod failure can be expressed as follows:  
\[T_{w}=V_{n,bolt}=0.6A_{wn}F_{y}, \tag{5}\]  
where \(V_{n,bolt}\) is the shear strength of the screw rod; \(A_{wn}\) and \(F_{y}\) are the section area and yield strength of the screw rod, respectively. The shear strength of the screw rod with a diameter of 16 mm and yield strength of 400 MPa was 48.23 kN, as calculated using Equation (5). The stress of the diagonal member (\(f_{s}\)) at the shear failure of the screw rod can be calculated as follows:  
\[f_{s}=\frac{V_{n,bolt}}{A_{s1}}, \tag{6}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Specimen** & \(V_{test}\)1  (kN)** & \(V_{n}\)2  (kN) & \(V_{test}\)/\(V_{n}\) & **Failure Mode** \\ \hline PV & 691.6 & 549.2 & 1.26 & Horizontal shear failure \\ \hline P & 520.5 & 483.3 & 1.08 & Horizontal shear failure \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of test and analysis results on P specimen series.  
Figure 10: Horizontal shear failure surface.  
where \(A_{s1}\) is the cross-sectional area of one diagonal member. Because the cross-sectional area of the diagonal member placed in the W specimen series was 240 mm\({}^{2}\) (40 mm \(\times\) 6 mm), the stress of the diagonal member at the shear failure of the screw rod was calculated to be 200.96 MPa. If using the equation for calculating the shear strength specified in ACI 318-19 [20], where the diagonal member is regarded as a stirrup, and the stress of the diagonal member (\(f_{s}\)) calculated using Equation (6) is substituted for the yield stress, then it can be represented by the following equation:  
\[V_{sr}=0.17\sqrt{f^{\prime}_{c}}+\frac{A_{s}f_{s}d}{s}(\sin\alpha+\cos\alpha), \tag{7}\]  
where \(f^{\prime}_{c}\) is the compressive strength of concrete; \(A_{s}\) and \(f_{s}\) are the section area and stress of the diagonal web member, respectively; \(s\) is the spacing of the web members; and \(\alpha\) is the angle of the diagonal member. Table 5 shows the shear strengths of the specimens calculated using Equations (5)-(7). The proposed equation only provided an estimation of the shear strength of the specimens. However, it is noteworthy that if the screw rod exhibits shear failure prior to the yielding of the diagonal web member, then a very brittle failure may occur in the member. In this case, a screw rod that is sufficiently large for providing the adequate diameter and strength should be used in designing the EST composite girder. For the Pratt truss specimen in this experimental program, it was discovered that horizontal shear cracks that occurred along the top chord led to the dominant failure mode of the specimen. Based on the test results, it is estimated that the horizontal shear strength of the Pratt truss specimens was less than the shear strength of the screw rods.