# Cyclic Tests and Numerical Analyses on Bolt-Connected Precast Reinforced Concrete Deep Beams
## 3 Test Results
### Mechanical Behavior of the Bolt Connection  
The frictional types of high-strength bolts were used in the tests to transfer the shear forces. Thus, it is important to ensure the effectiveness and reliability of the bolt connections. In this paper, the mechanical behavior of the bolt connections is divided into two main phases; they are: (1) phase I, the carried shear force of a bolt is less than its friction force; (2) phase II, the carried shear force of a bolt is larger than its friction force.  
A mechanical diagram of RDBs at phase I is presented in Figure 9c; the shear force of bolts generated from the lateral load (\(N_{\text{v}}\)) and bending moment (\(N_{\text{m}}\)) are included in the diagram. The lateral force is considered as an even distribution force on the bolts; the shear force of each bolt is determined as \(N_{\text{v}}=V_{\text{w}}/n\), where \(n\) is the number of the bolts in a support of RDBs. According to Figure 9c, \(M_{\text{w}}=V_{\text{w}}h/2=0.405V_{\text{w}}\) for the RDB-A, thus the \(N_{\text{m}}=M_{\text{w}}/4D=0.675V_{\text{w}}\), and \(N_{\text{v}}=V_{\text{w}}/3\). The largest shear force is \(0.75V_{\text{w}}\). For the mechanical diagram of RDB-B, \(M_{\text{w}}=V_{\text{w}}h/2=0.405\ V_{\text{w}}\) and \(N_{\text{m}4}=0.225V_{\text{w}}\), and \(N_{\text{v}}=V_{\text{w}}/8\). The largest shear force is \(0.26\ V_{\text{w}}\).  
At phase II, due to the carried shear force of the bolts that exceeded the friction force, the bending moment is carried by the RDB, and thus the bolts carry the shear force solely. The largest shear force of the bolts is \(0.33\ V_{\text{w}}\) and \(0.125\ V_{\text{w}}\) for the RDB-A and RDB-B, respectively.  
The shear force carried by the bolts in specimens is \(10.35\) kN and \(39.06\) kN for the RDB-A and RDB-B (Table 2), respectively. Thus the largest shear force is \(7.76\) kN and \(10.16\) kN in phase I for bolt connections in RDB-A and RDB-B, respectively, and the largest  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{**Elastic Lateral Stiffness (kN/mm)**} & \multirow{2}{*}{**Error**} \\  & \(K_{\text{e-theoretical}}\) & \(K_{\text{e-experimental}}\) & \\ \hline RDB-A & 13.08 & 11.06 & 15.4\% \\ RDB-B & 69.71 & 58.48 & 16.1\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of elastic stiffness of the theoretical and experimental test results.  
shear force is 3.42 kN and 4.88 kN in phase II for the bolt connections in RDB-A and RDB-B, respectively.  
The friction force \(N_{\text{vul}}\) in phase I and shear resistance \(N_{\text{vul}}\) in phase II of the bolts used in this paper are:  
\[N_{\text{vul}}=0.9n_{\text{f}}\mu P \tag{4}\]  
\[N_{\text{vul}}=\frac{\pi{d_{0}}^{2}}{4}f_{\text{v}} \tag{5}\]  
where \(n_{\text{f}}\) is the number of frictional faces of bolts; \(\mu\) is the anti-sliding coefficient between bolts and angles, and it is determined as 0.3 according to suggestions [8]; \(P\) is the pre-tensile force, it is 125 kN in this study; \(d_{0}\) is the clear diameter of bolts, and it is 20 mm;\(f_{\text{v}}\) is the yield shear strength of bolts, and it is 320 MPa.  
Thus \(N_{\text{vul}}\) = 67.5 kN and \(N_{\text{vul}}\) =100.5 kN can be calculated according to Equations (4) and (5), and the calculated values represent the loading resistance of a high-strength bolt at the two phases. The calculated values are larger than the maximum shear force of the bolts during tests; thus, it can be concluded that high-strength bolts are safe enough in the test specimens. According to test results recorded by the LVDTs, there was also no slipping behavior or bolt-damage failure observed in the test specimens.