Structural Concrete - Hassoun

19.3 Loss of Prestress 741
where
P pj = prestressing tendon force at jacking end
P px = prestressing tendon force at any point x
μ p = curvature friction coefficient
α px = total angular change of prestressing tendon profile, in radians, from tendon jacking
end to any point x
length of curve
=
radius of curvature
K = wobble friction coefficient per foot of prestressing tendon
As an approximation, the ACI Code gives the following expression:
P px = P pj (1 + Kl px + μ p α px ) −1 (ACI Code 2008, Eq. 18.2) (19.11)
provided that (Kl px + μ p α px ) ≤ 0.30.
The frictional coefficients α and K depend on the type of prestressing strands or wires,
type of duct, and the surface conditions. Some approximate values for μ and K are given
in Table 19.2.
Friction loss in the jack is variable and depends on many factors, including the length of travel
of the arm over a given load range. The use of accurate load cells to measure directly the force in
the tendon is recommended. The use of pressure gauges may lead to inaccuracies unless they are
calibrated against a known force in the tendon.
The friction loss in the anchorage is dependent mainly upon the type of anchorage and the
amount of deviation of the tendon as it passes through the anchorage. This loss is usually small and
may be neglected. Guidance in particular cases should be obtained from the manufacturers.
19.3.7 Loss Due to Anchor Set
When the force in a tendon is transferred from the jack to the anchorage unit, a small inward
movement of the tendon takes place due to the seating of the gripping device or wedges. The
slippage causes a shortening of the tendon, which results in a loss in the prestressing force. The
magnitude of slippage varies between 0.1 and 0.25 in. (2.5 and 6 mm) and is usually specified by
the manufacturer. The loss due to the anchor set may be calculated as follows:
Δf s = ΔεE s = ΔL
L × E s (19.12)
Table 19.2
Friction Coefficients for Posttensioned Tendons
Type of Tendon
Wobble Coefficient K
per Foot (× 10 −3 )
Curvature Coefficient
μ (per Radian)
Tendon in flexible metal sheathing (grouted)
Wire tendons 1.0–1.5 0.15–0.25
Seven-wire strand 0.5–2.0 0.15–0.25
High-strength bars 0.1–0.6 0.08–0.30
Pregreased unbonded tendon
Wire tendons and seven-wire strand 0.3–2.0 0.05–0.15
Mastic-coated unbonded tendons
Wire tendons and seven-wire strand 1.0–2.0 0.05–0.15