Prestress Elongation Calculator
Control stress, length and duct friction give elongation and loss.
Quick answer
With the default inputs: Control stress σcon 1395 MPa · Tensile strength fpk 1860 MPa · Area per tendon 140 mm² etc.Theoretical elongation 206.0 mm
Edit the inputs below to recalculate.Inputs
Result
Theoretical elongation
206.0mm
| Jacking force | 781.2kN |
| kx + μθ | 0.0825 |
| Average tension | 749.8kN |
| Friction loss | 4.0% |
| Theoretical elongation | 206.0mm |
| Less anchor set | 5mm |
| Site control elongation | 201.0mm |
| Elongation per metre | 6.87mm/m |
| Stress ratio σcon ÷ fpk | 75.0% |
Elongation is the only check that catches prestressing faults on the spot: if measured and theoretical values differ by more than ±6%, stop and investigate — blocked ducts, wire slip, faulty gauges, short jacking force. Average tension uses Pp = P·(1 − e^−(kx+μθ)) ÷ (kx+μθ), which is exactly the force eaten by duct friction. For two-end stressing take half the length and add both readings before comparing. Anchor set affects the effective prestress at the live end, not the theoretical elongation. Keep σcon at or below 0.75 fpk — beyond that the strand yields, elongation stops being linear and losses after release become large.
Formula
| Jacking force | P = σcon × area × strands |
| Friction term | kx + μθ = k × length + μ × angle |
| Average tension | Pp = P × (1 − e^−(kx+μθ)) ÷ (kx+μθ) |
| Elongation | ΔL = Pp × length ÷ (area × strands × Ep) |
| Control value | ΔL = ΔL − anchor set |
| Tolerance | Measured within ±6% of theoretical |
Four φs15.2 strands (140 mm²) at 1395 MPa over 30 m with θ = 0.15 rad, k = 0.0015 and μ = 0.25: 781.2 kN jacking force, kx+μθ = 0.0825, 4.0% friction loss, 749.8 kN average tension, 206.0 mm theoretical elongation and 201.0 mm after 5 mm of anchor set.
How to work it out
- Jacking force P = σcon × nominal area per strand × strands per tendon, with σcon typically 0.75 fpk.
- Friction exponent kx + μθ: k the wobble coefficient (0.0015 per m for duct), μ the friction coefficient (0.20-0.25), θ the angular change in radians.
- Mean force Pp = P × (1 − e^−(kx+μθ)) ÷ (kx+μθ); where kx+μθ is below 0.1, take P directly.
- Theoretical elongation ΔL = Pp × L ÷ (Ap × n × Ep), with the denominator using the full tendon area and modulus.
- Hold measured against theoretical within ±6%; outside that, investigate friction values, duct alignment and the measured modulus.
Where it goes wrong
- Using the jacking-end force — force decays along the duct through friction, so the mean force is required; the end force overstates elongation by 5-15%.
- Assuming Ep = 195 GPa — measured strand modulus falls between 190 and 200, and 2% eats a third of the ±6% tolerance.
- Ignoring anchor set — deduct the anchor draw-in (typically 3-6 mm) from the effective elongation, since the gauge reading includes it.
Material and cost
Strand runs 5,000-6,000 per tonne, anchors 60-150 per set, ducts 8-15 per metre. Equipment calibration costs 2,000-4,000 and is required every six months or 2,000 operations.
On site
- Control on both force and elongation — force governs and elongation verifies; reading one without the other is not a check.
- For two-end stressing the elongation is the sum of both gauge readings; single-end stressing reads one end but must account for the fixed anchor.
- Grout within 48 hours of stressing at M30 or better; how completely the duct is filled decides durability.
Basis
- GB 50666-2011 Code for construction of concrete structures, Chapter 6 (prestressed work)
- JGJ 92-2016 Technical specification for unbonded prestressed concrete structures
- GB 50204-2015 Code for acceptance of concrete structures, Chapter 6 (prestressing)
FAQ
Why check elongation and not just gauge pressure?
A gauge only shows jack output, not whether the force reached the far end. With a blocked duct the jack still reaches design pressure while the strand barely moves — friction and the blockage absorb everything; wire slip at the anchor behaves the same way. Elongation infers actual force from the steel's own deformation, so both must agree. Codes require measured elongation within ±6% of theoretical, and any deviation must be investigated, not just topped up.
How does elongation work with two-end stressing?
Single-end: use the full length from jack to fixed end. Two-end: each jack covers half, so compute elongation on half the length, add both readings and compare with the theoretical value for the full length (or compare each end against the half-length value). Stressing from both ends halves the friction loss and is mandatory for long or curved tendons.
What if friction loss is too high?
Three levers: cut μ and k (plastic instead of galvanised ducts, smooth bore, denser chairs so the duct cannot deform); shorten the stressed length — curve over 25-30 m should be stressed from both ends; and flatten the alignment to avoid sharp bends. If calculated loss exceeds 15%, the profile or ducting is wrong: report it rather than jacking harder, because extra force overstresses the live end and can crush the concrete under the anchor.
Results are estimating aids only and are not a design basis. Construction and final accounts must follow the drawings, the applicable standards and an approved method statement. Anything affecting structural safety, shoring or falsework must be checked by a suitably qualified engineer.