# Experimental Analysis on Pre-Stress Friction Loss of Crushed Limestone Sand Concrete Beams
## 2 Experimental Program
### Specimen Fabrication and Testing Technique  
An experiment on pre-stress friction loss in CLS concrete members with post-tensioning was conducted to investigate the following variables:  
(1) The number of tendons: The number of tendons is calculated by the required equivalent load [27]. In large bridge engineering, the number of tendons in one duct is usually more than 10 wires. The interactive extrusion may cause certain friction between one tendon and another. With an increase in the number of tendons, the inner friction is more obvious. As a contrast, the single-wire is necessary. (2) The arrangement of ducts: The straight duct cannot be perfectly linear due to small wobbles in the construction process, and tendons in the curve duct will produce a large normal pressure. Both two cases will lead to additional friction. First, \(\kappa\) is solved by Equation (3) in straight duct (\(\theta=0\)). Then, \(\mu\) is calculated by Equation (4) based on the obtained \(\kappa\). Thus, specimens with both straight and curve ducts are necessary. (3) The duct-forming material: The rubber hose, metal bellow and plastic bellow are widely used for the duct in pre-stress engineering nowadays. The friction is directly determined by the smoothness of contact surface. Moreover, the amplitude of wobbles relies on the stiffness of duct material, so the pre-stress friction loss can obviously differ due to the duct-forming material properties. The variables above are critical in influencing the friction loss. In this work, a series of full-scale pre-stressed concrete beams for post-tensioning were designed, including the three parameters above (Table 4). Based on the project of Malinghe Bridge, 3 concrete beams with a total of 30 ducts were constructed, which is shown in Figures 3 and 4. Based on the project of Wujiang Bridge, 23 concrete beams with a total of 37 ducts were also constructed, which is shown in Figures 5 and 6. Thus, at least 3 ducts are prepared for each case to ensure that the measured data are adequate and effective. It should be mentioned that the length of the specimen with a straight duct in the Malinghe Bridge project is shorter due to the limitations of local conditions. Figure 3: Arrangement for the duct based on the project of Malinghe Bridge: (**a**) straight tendons with 1, 3, 12, 19 and 22 wires; (**b**) curve tendons with 1 and 3 wires; and (**c**) curve tendons with 12, 19 and 22 wires (unit: mm). Figure 4: General view of the specimens: (**a**) straight tendons with 1, 3, 12, 19 and 22 wires; (**b**) curve tendons with 1 and 3 wires; and (**c**) curve tendons with 12, 19 and 22 wires. Figure 5: Arrangement for the duct based on the project of Wujiang Bridge: (**a**) straight tendons with 1 wire; (**b**) curve tendons with 1 wires; (**c**) curve tendons with 1 wire; and (**d**) curve tendons with 19 wires (unit: mm). \begin{table}
\begin{tabular}{c c c c c} \hline
\begin{tabular}{c} Metal bellow, plastic \\ bellow and rubber hose \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 4: Details of the specimen. Figure 7 shows the dimensions of specimens in Figure 4a,c (\(\theta\) = 20\({}^{\circ}\)), and the reinforcement arrangements of other specimens are similar. Due to limitations of project, the cross-section of specimens is not unified. However, the friction loss mainly occurs along the length and there are no \(y\)-axis loss concerns. The non-prestressed bars are used to support the specimen and to prevent partial crushing at two ends, it hardly affects the pre-stress friction loss. Figure 8 shows the metal bellow and plastic bellow, and the rubber hose can be seen in Figure 6c. Figure 6: General view of the specimens: (**a**) straight tendons with \(1\) wire; (**b**) curve tendons with \(19\) wires; (**c**) curve tendons with \(1\) wire; and (**d**) curve tendons with \(19\) wires. Figure 7: Dimension of specimens: (**a**) specimen for straight tendons; and (**b**) specimen for curve tendons (unit: mm). Figure 9 shows the loading and measuring system.