Friction losses

Due to friction between the tendon and the duct during jacking, the tendon force at the jacking end is greater than the tendon force as some distance away from the jacking end. The friction loss has two parts: the length or wobble effect and the curvature effect. The tendon force $P_{x}$ at the distance $x$ from the jacking end can be expressed as:

$P_{x}=P_{0}e^{-(\mu \alpha +Kx)}$

where:

• $P_{0}$ = tendon forces at the jacking end
• $\mu$ = curvature friction coefficient
• $\alpha$ = cumulative angle (in radians) by which tangent to the tendon profile has changed between the jacking end and location x
• $K$ = wobble friction coefficient
• $x$ = distance along tendon from jacking end to point under consideration

References

• Deepak Choudry: Analysis of Curved Nonprismatic Reinforced and Prestressed Concrete Box Girder Bridges, Report No. UCB/SEMM-86/13, December 1986; p. 42 (Section 3.4.1: Friction Losses)
• Jaroslav Navratil: Prestressed concrete structures, CERM, 2006; ISBN 80-7204-462-1; p. 53 (Section 4.1: Loss of prestressing due to friction)