Example data table
| Case | P0 (kN) | L (m) | A (mm²) | E (GPa) | μ | k (1/m) | θ (deg) | Stressing | Expected behavior |
|---|---|---|---|---|---|---|---|---|---|
| Straight tendon | 1500 | 25 | 140 | 195 | 0.00 | 0.0000 | 0 | One-end | Near-linear elongation, minimal losses |
| Curved tendon | 1800 | 30 | 140 | 195 | 0.20 | 0.0015 | 12 | One-end | Reduced far-end force and elongation |
| Two-end jacking | 2000 | 40 | 280 | 195 | 0.20 | 0.0015 | 18 | Two-end | Higher net elongation due to shorter loss paths |
Formula used
Axial (constant force): Δ = (P · L) / (A · E)
Friction-loss along tendon: P(x) = P₀ · e^{-(k·x + μ·θ(x))}
Assuming uniform curvature, total exponent is k·L + μ·θ. Elastic elongation is computed by integrating strain:
Δ = (1/(A·E)) · ∫₀ᴸ P(x) dx → Δ = (P₀/(A·E·α)) · (1 − e^{−α·L}), where α = (k·L + μ·θ)/L
Net elongation: Seating loss is subtracted as Δ_net = Δ_elastic − (seating_per_end · seating_ends).
How to use this calculator
- Choose a tendon preset or enter steel area and modulus manually.
- Select the method: constant force for straight runs, friction-loss for profiles.
- Enter jacking force, tendon length, and—if using friction—μ, k, and total θ.
- Set seating loss per end and how many ends seat during stressing.
- Press Calculate to view results above the form.
- Download CSV or PDF to keep a traceable site record.
Elongation as a field acceptance check
Measured tendon elongation is compared with a calculated target to confirm stressing operations. This calculator estimates elastic elongation from jacking force, tendon length, steel area, and modulus. With friction enabled, the expected value reduces as force decays along the duct. Use the net value (after seating) when comparing to measured extension under consistent temperature conditions.
Inputs that control the computed extension
Elongation increases with force and length, and decreases with steel area and modulus. For strand tendons, modulus near 195 GPa is common, and total steel area should include all strands in the anchorage. The friction option uses wobble coefficient k (1/m), friction coefficient μ, and total angular change θ from the tendon profile. Enter θ as the sum of absolute angle changes along the duct.
Interpreting force loss and average force
The report includes far-end force, average force, and loss percentage. A larger exponent (k·L + μ·θ) increases loss and lowers average force, reducing elongation. Two-end jacking shortens each loss path, so the net elongation typically increases compared with one-end stressing at the same jacking force. Use average force when checking overall strain demand on long tendons.
Seating loss and realistic net elongation
Anchorage seating or wedge slip reduces measured extension. Enter seating loss per end and the number of ends that seat during stressing. The calculator subtracts seating from elastic elongation to produce a net elongation suited for field comparison. If net elongation becomes negative, recheck seating, units, and whether seating should apply at one end only.
Documentation and tolerance checks
CSV and PDF exports support stressing logs and audit trails. Record the selected method, units, tendon identification, and any deviations from the approved stressing plan. Compare measured elongation to the net target and confirm expected trends: straight tendons show near-linear behavior, while curved profiles show lower far-end force and reduced elongation. Where specifications allow a percent tolerance window, evaluate both the absolute difference and the trend across multiple tendons.
FAQs
1. What does this calculator output for site use?
It provides elastic elongation, net elongation after seating, far-end force, average force, stress, and loss percentage. Use the net elongation to compare against measured extension during stressing.
2. When should I select the friction-loss method?
Choose it for draped, curved, or deviated tendon profiles where friction and wobble reduce force along the duct. For straight tendons with negligible curvature and deviations, the constant-force method can be adequate for quick checks.
3. How do I enter the total angular change θ?
Sum the absolute angle changes along the tendon path from one end to the other. Use radians if your calculations are in radians; otherwise enter degrees. Consistency with the approved profile calculation is more important than the unit.
4. What is the wobble coefficient k and its unit?
k represents unintended duct deviations per unit length that add friction losses. Enter k as 1/length; the calculator converts internally to 1/m. Use values from project documents, duct type, and stressing method assumptions.
5. Why can net elongation be lower than expected?
Seating loss, higher friction parameters, longer tendon length, or larger curvature reduce net elongation. Verify jack force, steel area, modulus, and that θ reflects the full tendon profile used on drawings.
6. What should I do if the net elongation becomes negative?
A negative net value usually indicates seating loss was entered too large, applied to too many ends, or units are inconsistent. Recheck seating per end, seating ends, and length units, then recompute before using results for acceptance.