# On Flexural Performance of Girder-To-Girder Wet Joint for Lightweight Steel-UHPC Composite Bridge
## 4 Experimental Test of the Second Generation T-Shaped Joint
### Discussion
#### 4.3.2 Crack Width Prediction  
Furthermore, there are very few crack width formulas which are applicable to steel-UHPC composite structures. [PERSON] [34] investigated the applicability of calculating flexural crack width of steel-UHPC composite deck structures using the recommended formulas in AFGC-SETRA (Association Francaise de Genie Civil- Service d'etude des transports, des routes et de leurs amenagement) [35] and Haibin [36]; it is observed that the results greatly differed from the measured values due to the difference of the structural characteristics. [PERSON] et al. [30] tested 40 steel-UHPC composite plates and eight steel-UHPC composite beams. The cracking characteristics in transverse and longitudinal directions were explored, and a modified formulation based on MOHURD [37] for predicting the maximum crack width in composite (steel + UHPC) lightweight deck system was proposed as:  
\[w_{\text{max}}=\alpha_{cr}\psi\frac{\sigma_{s}}{E_{s}}l_{cr} \tag{1}\]  
\[\alpha_{cr}=\tau_{l}\tau_{s}\beta\alpha_{c} \tag{2}\]  
\[l_{cr}=1.06c_{s}+0.152\frac{d_{\alpha q}}{\rho_{te}} \tag{3}\]  
\[\psi=1.1-0.12\frac{f_{tk}}{\rho_{te}o_{s}} \tag{4}\]  
For a detailed discussion of the equations, one can refer to [PERSON] et al. [30]. While it is worth noting that [PERSON]'s formula is applicable to the composite (steel + UHPC) lightweight deck system, the LWCB proposed in this paper is slightly different:  
Figure 14: Comparison of analytical value and test results of specimen deflection in different load.  
The \(\alpha_{cr}\) is the coefficient regarding loading characteristics; \(\tau_{l}\) is the coefficient related to long-term effects of loads or actions, as for the UHPC matrix, [PERSON] et al. [30] omitted it due to the extremely low shrinkage and creep of UHPC after steam curing, while for the joint interface in the present study, the recommended value \(\tau_{l}\) = 1.5 was adopted by referring to MOHURD [37]; and \(\sigma_{s}\) is the reinforcement stress. [PERSON] et al. [30] stated that the tensile strength of UHPC should be taken into account when calculating the stress of reinforcing bar due to the bridging effect of steel fibers, while for the interface position of successively poured UHPC joints in present study, according to the stiffness analysis of the structure above, it can be seen that the cracked section can better predict the stiffness of the specimen in the serviceability limit states. Therefore, it is more reasonable to use the cracked section without taking into account the UHPC tensile strength when calculating the crack width.  
Besides, the crack width of the centroid of longitudinal reinforcement (\(w_{max}\)) should be converted to the top surface (\(w_{smax}\)):  
\[w_{\rm{smax}}=w_{\rm{max}}\frac{h-x}{h-x-c} \tag{5}\]  
where \(h\) is the height of the beam; \(x\) is the distance from the neutral axial of the composite beam to the top surface of UHPC deck; and \(c\) is the distance from the centroid of longitudinal reinforcement to the top surface of the UHPC deck. The test value and calculation results are shown in Figure 15.  
It is seen that the prediction value agrees well with the test results. While there was a small deviation at the beginning of the prediction, the reason was that the formulas ignored the tensile strength of the interface when calculating the reinforcement stress, and only took into account the section of steel bars and girders.  
From Equations (1)-(5), it is observed that the crack width depends on the reinforcement stress. From the test results in the literature above [21; 23], increasing the reinforcement ratio, enhancing the steel plate at the bottom of the joint, or applying the orthotropic steel bridge deck increased the reinforcement ratio in different forms, thereby reducing the reinforcement stress. Thus, the cracking strength of the joints was higher than that in the present study.