# Reliability Analysis of the Main Pier during the Construction Period of HLCR Bridges
## 3 Reliability Analysis of the Main Pier of an HLCR Bridge with a Cradle Construction
### Project Examples
#### 3.3.1 Load Analysis  
1. Structural constant load (1) Self-weight of beam section The weights of the cantilever on both sides of Pier 8# and the length of each beam section are shown in Table 1.  
Figure 1: Layout of partial bridge. From Equation (19), the effect of the cast beam section in the main pier is calculated as:  
\[S_{N_{G}}=k_{G}p_{0}+2{\sum_{i=1}^{n}k_{G}p_{i}}_{i}=k_{G}p_{0}+2\times{\sum_{i=1 }^{17}k_{G}p_{i}}=73842.2k_{G}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Beam Section Number** & **0** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline \(P_{i}(\mathrm{KN})\) & 16,143.4 & 2345.2 & 2241.2 & 2142.2 & 2046.2 & 1955.2 & 1869.4 \\ \(l_{i}(\mathrm{m})\) & 14 & 3.5 & 3.5 & 3.5 & 3.5 & 3.5 & 3.5 \\ Beam section number & 7 & 8 & 9 & 10 & 11 & 12 & 13 \\ \(P_{i}(\mathrm{KN})\) & 2035.8 & 1934.4 & 1840.8 & 1755 & 1617.2 & 1432.6 & 1484.6 \\ \(l_{i}(\mathrm{m})\) & 4.0 & 4.0 & 4.0 & 4.0 & 4.0 & 4.0 & 4.5 \\ Beam section number & 14 & 15 & 16 & 17 & 18 & & \\ \(P_{i}(\mathrm{KN})\) & 1427.4 & 1380.6 & 1341.6 & 1315.6 & 1300 & & \\ \(l_{i}(\mathrm{m})\) & 4.5 & 4.5 & 4.5 & 4.5 & 4.5 & 4.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Weight and length of suspended beam section of Pier 8#. Figure 3: General structural drawing of main bridge box girder (m). Figure 2: Front and side design drawings of Pier 8# (m). \[S_{M_{G}}=v_{p}\sum_{i=1}^{n}k_{G}p_{i}x_{i}=v_{p}\sum_{i=1}^{17}k_{G}p_{i}x_{i}=11 75743v_{p}k_{G}\]
2. Deviation caused by unsynchronized overhanging of beam sections From Equations (20) and (21), the effect of the deviation of the girder section at the pier due to an unsynchronized suspension speed at the main pier is calculated as: \[S_{N_{k}}=2k_{G}p_{K}+v_{p}^{\prime}k_{G}p_{K}=2k_{G}p_{18}+v_{p}^{\prime}k_{G }p_{18}=2600k_{G}+1300v_{p}^{\prime}k_{G}\] \[S_{M_{k}}=\Big{(}1-v_{p}^{\prime}\Big{)}k_{G}p_{K}x_{K}=\Big{(}1-v_{p}^{\prime} \Big{)}k_{G}p_{17}x_{17}=108875\Big{(}1-v_{p}^{\prime}\Big{)}k_{G}\]
3. Self-weight of bridge pier The self-weight set of the bridge pier is calculated as follows: \[q=\rho V/H=26\times 4526.9/125=941.60\text{kN/m}\] The values of the geometric characteristics of the bridge pier sections are as follows: Pier top: \(l_{y}=343.28\) m\({}^{4}\), \(x_{0}=3.375\)m; \(l_{x}=457.03\) m\({}^{4}\), y\({}_{0}=3.75\) m; \(A=97.5\) m\({}^{2}\). Pier bottom: \(l_{y}=2967.37\) m\({}^{4}\), \(x_{0}=6.045\) m; \(l_{x}=255.67\) m\({}^{4}\), y\({}_{0}=5.04\) m. From Equation (22), the effect of the self-gravity of the bridge pier in the main pier body is calculated as: \[S_{N_{q}}=k_{G}qH=117699.4k_{G}\]
2. Live load effect (1) Construction step-by-step live load The construction distributed loads on each girder section were calculated according to Equations (23) and (24), as shown in Table 2, and then the construction distributed live loads were calculated according to the length of each girder section in Table 1.  
According to Equations (25) and (26), the load effect of each beam section is first calculated and then combined as the effect of the whole construction distribution live load. The effect of the construction distributed live load on the bridge pier of the main pier body for girder sections 0 to 14 is:  
\[S_{NQ2}=k_{Q}bQ_{20}l_{0}+2k_{Q}b\sum_{i=0}^{K-4}Q_{2i}l_{i}=k_{Q}bQ_{20}l_{0} +2k_{Q}Q_{2}b\sum_{i=1}^{14}l_{i}=149.45k_{Q}\]  
Figure 3:0  
Then, for girder sections 15 to 17, this is:  
Figure 3:1 \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**No.** & **0** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline \(Q\) (kPa) & 0.1 & 0.1 & 0.1 & 0.1 & 0.1 & 0.1 & 0.1 \\ No. & 7 & 8 & 9 & 10 & 11 & 12 & 13 \\ \(Q\) (kPa) & 0.1 & 0.1 & 0.1 & 0.1 & 0.1 & 0.1 & 0.1 \\ No. & 14 & 15 & 16 & 17 & 18 & & \\ \(Q\) (kPa) & 0.1 & 0.385925 & 0.622675 & 0.859425 & 0 & & \\ \hline \end{tabular}
\end{table} 
Table 2: Construction load on each girder section (Pa).