Post-Tensioning Calculator
Stress Profile Along Tendon
| Location (ft)↕ | Stress (ksi)↕ | Friction Loss (ksi)↕ |
|---|---|---|
| 0.0 | 202.50 | 0.00 |
| 8.0 | 201.97 | 0.53 |
| 16.0 | 201.45 | 1.05 |
| 24.0 | 200.93 | 1.57 |
| 32.0 | 200.41 | 2.09 |
| 40.0 | 199.88 | 2.62 |
| 48.0 | 199.37 | 3.13 |
| 56.0 | 198.85 | 3.65 |
| 64.0 | 198.33 | 4.17 |
| 72.0 | 197.82 | 4.68 |
| 80.0 | 197.30 | 5.20 |
This post-tensioning calculator computes tendon stress losses and elongation for a prestressed concrete member using the friction equation from ACI 318 and PTI practice. It evaluates the jacking stress and force, the total angle change of the tendon profile, the friction loss along the length, the anchor-set (seating) loss, and a simplified elastic shortening loss. It returns the stress profile at eleven points so you can see how the prestress decays from the live end.
Formula
f_px = f_pj · e^(−(μ·α + K·L)) ; α = 2·atan(4·drape/span) for a parabola
- f_px
- Tendon stress at a distance L from the jacking end (ksi)
- f_pj
- Jacking stress = fpu × jacking percent (ksi)
- μ
- Curvature friction coefficient (per radian)
- α
- Cumulative angular change of the tendon (radians)
- K
- Wobble (length) friction coefficient per ft; L is the distance along the tendon
How it works
- Select the tendon profile (parabolic or harped) and enter the span length (ft), drape (in), and the wobble (K) and curvature (μ) friction coefficients.
- Enter the strand area (in²), the ultimate strength fpu (ksi), and the jacking stress as a percent of fpu (commonly 75-80%). The jacking force is jacking stress times strand area.
- The calculator computes the friction loss f_pj·e^(−(μα + KL)) along the tendon, the anchor-set loss from the seating distance and friction slope, the elastic shortening loss (about 2.5%), and the total elongation by integrating strain over the length using Eps = 28,500 ksi.
Worked example
A parabolic tendon on an 80 ft span with a 6-inch drape, K = 0.0002/ft, μ = 0.20, a 0.153 in² strand, fpu = 270 ksi, and 75% jacking.
- Jacking stress = 270 × 0.75 = 202.5 ksi; jacking force = 202.5 × 0.153 = 30.98 kips.
- Total angle change α = 2·atan(4 × 6 / (80 × 12)) = 2·atan(0.025) = 0.05 rad.
- Far-end stress = 202.5 × e^(−(0.20 × 0.05 + 0.0002 × 80)) = 202.5 × e^(−0.026) = 197.3 ksi, a 2.57% friction loss.
- Anchor-set loss ≈ 12.42 ksi, elastic shortening ≈ 5.06 ksi, and total elongation ≈ 6.733 in.
Jacking force ≈ 30.98 kips, friction loss ≈ 2.57% (stress drops to 197.3 ksi at the far end), anchor-set loss ≈ 12.42 ksi, and elongation ≈ 6.73 in.
Frequently asked questions
- What causes friction losses in a post-tensioned tendon?
- Two effects: curvature friction as the tendon bears against the duct along its intended profile, governed by μ and the angle change, and wobble friction from unintended misalignment of the duct, governed by K and length. Together they reduce the stress the further you are from the jacking end.
- What is anchor-set (seating) loss?
- When the jack is released, the strand pulls the wedges into the anchorage and slips back a small distance (the anchor set, typically about 1/4 inch). This seating reduces stress near the live end, and the loss is recovered over a length set by the friction slope.
- Why is the elongation measured during stressing?
- Elongation is a field check on the force in the tendon. The calculator integrates the strain (stress divided by the 28,500 ksi strand modulus) over the length, and the measured elongation should match the prediction within tolerance, confirming the prestress was applied correctly.
- Does this calculator include long-term losses?
- It covers the immediate losses: friction, anchor set, and a simplified elastic shortening of about 2.5%. Long-term time-dependent losses from concrete creep, shrinkage, and steel relaxation are separate and should be added for the effective service prestress.