### Prestressing losses-Friction losses

Applied prestressing force or jacking force will be reduced due to several reasons, the effective prestressing force will be jacking force minus prestress losses, prestress losses are categorized into, instantaneous losses such as friction, elastic shortening, anchorage setting. Time-dependent losses such as shrinkage of concrete, creep and stands relaxation.

Friction loss will occur over the whole length of the tendons, and it is related to two sources. The friction between tendon and duct due to change of duct profile. This loss is associated with the angular change of duct profile. μ is the friction coefficient, and it is used to evaluate friction losses, the value of μ related to duct material. μ is not sufficient to predict friction losses, using μ individually will not produce accurate results at the field. Wobble coefficient (K) will be used in conjunction with μ to calculate friction losses, wobble coefficient is related to friction due to unintended misalignment of ducts.

Figure 1

The friction losses can be calculated using the following equation.

where

fpj = stress in the prestressing steel at jacking (ksi, Mpa)

x = length of a prestressing tendon from the jacking end to any point under consideration (ft, m)

K = wobble friction coefficient.

μ = coefficient of friction

α = sum of the absolute values of angular change of prestressing steel path from jacking end, or
from the nearest jacking end if tensioning is done equally at both ends, to the point under investigation (rad.)

e = base of Napierian logarithms

The friction coefficient can be determined at the field by conducting friction test for a single tendon. In the event of the impossibility of doing the test for any reason, the table below provides values for friction and wobble coefficient for ducts of different materials.

Table 1