TheBridgeEng

Post-tensioning — elongation & friction

PT elongation & friction

Friction and anchor-set losses along a single-span tendon, and the jack elongation to expect — P(x) = P_jack·e^−(μα+kx) per AASHTO LRFD §5.9.3.2.2b, with the wedge draw-in mirrored back into the force diagram. 15.2 mm strands (A_ps 140 mm², E_p 196.5 GPa, f_pu 1860 MPa). Compare against site elongations; calibrate μ and k by trial stressing.

Tendon profile — side view Force along tendon — at jacking vs after anchor set

Expected jack elongation (before seating)

—mm

Tendon length100m

10105200

Anchor to anchor, along the member.

Profile sag f2.5m

0 (straight)48

Single parabola; angle change 8f/L drives curvature friction.

Strands (15.2 mm) & jacking stress

Jacking stress75%fpu

AASHTO caps jacking at ~0.80 f_pu (0.90 f_py).

Duct · friction · anchor set

μ /rad

k /m

Anchor set Δset mm

Galvanized metal: μ 0.15–0.25 (0.20 used), k 0.00066/m (AASHTO).

Step	Quantity	Value	Note

Field notes — what to watch for

On site, the number that matters is measured-vs-theoretical elongation — outside about ±7% you stop and find out why before cutting strand. Short tendons are dominated by anchor set, long tendons by friction; if a long tendon comes up short on elongation, suspect a blocked or kinked duct, not the calculation.

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