# Prestress Elongation Calculator

Control stress, length and duct friction give elongation and loss.

- Page: https://jianzhujisuan.com/en/prestress-elongation
- Category: Rebar (https://jianzhujisuan.com/en/c/rebar)
- Chinese version: https://jianzhujisuan.com/zh/prestress-elongation.md
- Data checked: 2026-10-25

## Quick result

With the default inputs (Control stress σcon 1395 MPa, Tensile strength fpk 1860 MPa, Area per tendon 140 mm², Strands per tendon 4 pcs, Tendon length 30 m, Elastic modulus Ep 195000 MPa, Wobble coefficient k 0.0015 1/m, Friction coefficient μ 0.25, Curve angle θ 0.15 rad, Anchor set 5 mm): **Theoretical elongation 206.0 mm**

## Inputs

| Parameter | Type | Default | Unit | Note |
|---|---|---|---|---|
| Control stress σcon | number | 1395 | MPa | Strand is usually 0.70-0.75 fpk, i.e. 1302-1395 MPa |
| Tensile strength fpk | number | 1860 | MPa | 1860 MPa for φs15.2 strand |
| Area per tendon | number | 140 | mm² | 140 mm² for φs15.2, 98.7 mm² for φs12.7 |
| Strands per tendon | number | 4 | pcs |  |
| Tendon length | number | 30 | m | Half the total length when stressed from both ends |
| Elastic modulus Ep | number | 195000 | MPa | 195000 MPa for strand, 200000 for rolled bar |
| Wobble coefficient k | number | 0.0015 | 1/m | 0.0015 for corrugated duct, 0.0015-0.0025 for pulled cores |
| Friction coefficient μ | number | 0.25 | — | 0.20-0.25 for bonded duct, 0.09-0.12 unbonded |
| Curve angle θ | number | 0.15 | rad | Cumulative angle from the jacking end; zero for straight |
| Anchor set | number | 5 | mm | 4-6 mm for wedge anchors |

## 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

## Worked example

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.

## Questions

### 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.

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