# Experimental Analysis on Pre-Stress Friction Loss of Crushed Limestone Sand Concrete Beams
## 3 Test Result and Analysis
### Comparison of Theoretical and Measured Pre-Stress Forces  
Figures 15 and 16 show the comparison between the measured values and theoretical values predicted by the Chinese and ACI codes. In the specimen with single-wire, the predicted values for metal bellow and plastic bellow are accurate, but prediction is overestimated for the specimen with rubber hose. The actual pre-stress force only accounts for 85.26% (predicted by Chinese code) and 89.60% (predicted by ACI code). In the specimen with 19 wires, the predicted values are obviously larger. In particular, the measured values account for 74.93% (predicted by Chinese code) and 65.49% (predicted by ACI code). It can be seen that the coefficients are improperly selected for evaluating pre-stress friction loss, especially in the case of different duct materials.  
Figure 14: Average pre-stress losses: (**a**) 1 wire with straight duct; (**b**) 1 wire with curve duct; (**c**) 19 wires with straight duct; and (**d**) 19 wires with curve duct.  
Figure 15: _Cont._Generally, the pre-stress friction loss of each case is measured through a series of experiments. The variables (duct-forming material, wires of tendons and arrangement of duct) are proven to significantly affect the friction loss. The friction loss ranges 4-16% in with single-wire, and 10-40% in multi-wire. Friction between the tendons is the main factor. Due to pressure on the curved part, the friction loss in curved duct (10-30%) is surely larger than straight duct (10-20%). As for the difference in smoothness of contact surface and material stiffness, friction loss in rubber hose is the  
Figure 16: Pre-stress forces of specimens with 19 wires and curve duct based on Wujiang Bridge made of: (**a**) rubber hose; (**b**) metal bellow; and (**c**) plastic bellow.  
Figure 15: Pre-stress forces of specimens with a single-wire and curve duct based on Wujiang Bridge made of: (**a**) rubber hose; (**b**) metal bellow; and (**c**) plastic bellow.  
loss is generally 4-16% in specimens with single-wire, while this is 10-40% in specimens with multi-wire. The friction of inner tendons was shown to form the majority of the instantaneous pre-stress loss.
2. The friction in specimens with curve duct is definitely larger than that in straight duct. The proportion is 10-30% in curved duct and 10-20% in straight duct. First, large pressure is applied to the curved part. Moreover, the effective length is shortened because the location of tendon changes after tensioning. The curvature effect is the dominant factor in curve duct, which may result in additional friction.
3. When compared with different duct-forming materials, the pre-stress friction loss in specimens with rubber hose is the largest and reaches nearly 40%. The rubber hose tends to deform and wobble by extrusion, which especially occurs during the concrete pouring. As the contact surface of metal bellow and plastic bellow is smooth, the pre-stress friction loss is smaller. This part of friction loss is mainly determined by the stiffness of duct material and nature of contact surface.
4. The frictional resistance \(\kappa\) and friction coefficient \(\mu\) for CLS concrete member with post-tensioning were modified and detailed for each case. The parameters \(\kappa\) and \(\mu\) are at the ranges of 0.0017-0.007 and 0.108-0.858, respectively. We hope that this work will provide references for the design of pre-stressed concrete structure and engineering applications.  
[PERSON] conceived and designed the experiments; [PERSON] and [PERSON] performed the experiments; [PERSON] and [PERSON] analyzed the data; and [PERSON] and [PERSON] wrote the paper.  
The generous support provided by the National Natural Science Foundation of China (Grant No. 51278218) is gratefully acknowledged. The authors are especially grateful to Guizhou Provincial Transportation Department.  
The authors declare no conflict of interest.