## 2 Materials and Methods
### Continuity Joint Repair  
Once damage was induced, the connected girder specimens were repaired with each of the specialty concretes described in Section 2.1. The continuity joints were repaired by encapsulating all sides with a 76 mm thick section of the repair material. This thickness was chosen due to the approximately half scale size of the specimens and allowing for a minimum of 25 mm clear cover for the reinforcing steel bars in the repair. The repair encapsulated the sides of the joints from the bottom of the deck to the bottom of the girder. This repair layout was chosen based on what portion of an in-service continuity joint would be accessible for repair. Due to interference from the girder supports, there would be no way to wrap a repair around the bottom of the joint without lifting the girders off the supports. Also, an in situ repair would have to stop at the bottom of the bridge deck, or else extensive demolition would be required. Figure 4: Initial crack test setup. The intent of the repair was to provide an additional load path for the compressive forces induced by the negative moment developed by traffic, provide additional support for any positive moments caused by expansion and contraction of the bridge due to temperature gradients, and to protect the joint reinforcement from corrosion. Therefore, reinforcing steel was placed only in the lower portion of the repair, since the tensile forces from live loads would be carried by the reinforcing steel in the bridge deck. The eighth edition of the AASHTO LRFD Bridge Design Specifications [3] was used to design the reinforcing steel to resist the effects of a temperature gradient on the bridge. The flexural deformation caused by a specified temperature gradient on the cross section of a girder and the moment caused by the deformation were determined using equations C4.6.6-3 (below as Equation (1)) and C4.6.6-7 (below as Equation (2)) in the AASHTO specification [3], respectively. Each equation is shown below. \[\phi=\frac{\alpha}{I_{c}}\iint T_{G}zdwdz \tag{1}\]  
\[M_{c}=\frac{3}{2}EI_{c}\phi \tag{2}\]  
where \(\phi\) is beam rotation per unit length, \(\alpha\) is the concretes coefficient of thermal expansion, \(T_{G}\) is the temperature gradient, \(z\) is the vertical distance from the center of gravity, and \(E\) is the modulus of elasticity. The temperature induced moment was calculated using the dimension of the actual connected girder test specimen. The material properties of the concrete were determined using the AASHTO specification, assuming a concrete compressive strength of 27.6 MPa, the design strength of the Class AA concrete. With a temperature gradient of 7.8 \({}^{\circ}\)C determined using AASHTO Figure 3.12.3-1 [3], the beam rotation induced by the temperature gradient was determined to be 0.000008429 radians, causing a moment of 85,240 N-m. This moment would require a minimum of 357 mm\({}^{2}\) of Grade 420 reinforcing steel in the tension region. To facilitate placement of the reinforcing steel in two layers, a total of four #13 bars in two layers was chosen for reinforcement. Two different sized U-bars were used as reinforcement for each layer. The bottom layer consisted of two 356 mm long bars (measured from outside of hook to outside of hook) with 165 mm long hooks, which were epoxied into the bottom bell 114 mm using Hilti HIT-HY 200-R structural epoxy. One U-bar was place on either side of the bottom bell. The top layer consisted of two 330 mm long bars (measured from outside of hook to outside of hook) with 356 mm long hooked legs. A hole was drilled through the 76 mm wide web and the straight bar was fed through. The hooks were then added to the bar using a manual rebar bender. These bars were designed for the legs to lap 240 mm.