## 2 Experimental Program
### Loading Test Result  
Figure 4 shows the cracks before failure after 200,000 load cycles. For all the specimens in failure, the cracks exhibited a similar shape, but in a different sequence of progression for each integral and modular specimen. For the integral specimen shown in Figure 4a, the cracks first appeared at the bottom-center of the specimen. Further cracking developed towards the sides, away from the center, as the load was increased, exhibiting cracking typical of reinforced concrete beams. However, for the modular specimen, the initial cracks started with the separation of the precast concrete module from the connecting high-strength concrete with the separation distance increasing with increasing load. The cracks propagated from the loading points to the support points and rupture occurred at the cracks in the high-strength concrete section at the third point in Figure 4b.  
Cyclic loading was applied to analyze the joint behavior of the modular bridge. The test results are given in Table 1. As the cyclic loading progressed, the residual and maximum deflections increased. The overall deflection of the integral specimen increased steadily as the loading cycle progressed. However, the modular specimen exhibited a different deflection behavior, as shown in Figure 5. The deflection increased sharply for the first 100 load cycles, after which its rate of increase slowed. This continued up to the 100,000 th cycle, after which the rate of increase began to rise dramatically until the 200,000 th cycle and final static loading. This behavior was due to the crack propagation characteristics of the joint separation.  
According to Equation (1), the theoretical deflection was calculated using the effective moment of inertia to compare the deflection of the modular specimen with the values given in the design code [18].  
\[I_{e}=\left(\frac{M_{cr}}{M_{a}}\right)^{3}I_{g}+\left\{1-\left(\frac{M_{cr}}{M_ {a}}\right)^{3}\right\}I_{cr} \tag{1}\]  
Here, \(I_{e}\) is the effective moment of inertia, \(I_{g}\) the moment of inertia of the gross concrete section, \(I_{cr}\) the moment of inertia of the cracked section, \(M_{cr}\) the cracking moment, and \(M_{a}\) the applied moment.  
Table 2 gives the moments of inertia of the gross and cracked concrete sections and the cracking moment [16].  
The results are shown in Figure 6. The deflection given by the code underestimates the experimental results of the tested specimen. The specimen was more sensitive to the moment of inertia of the cracked section because it had a low thickness of 220 mm compared to general beams used by the design code for the effective moment of inertia when cracking occurred. However, the values at 79.1 kN for the integral specimen were relatively accurate as the crack progressed steadily. The difference increased with increasing load, reaching 2.41 mm at maximum load. The joint separation of the specimen during initial loading was thought to have dramatically reduced the moment of inertia, resulting in a significant difference from the effective moment of inertia suggested by the code. In addition, the design code does not take into account the modulus of elasticity of UHSC at the joints.