Post-Tensioning Tendon Friction Loss (EN 1992-1-1)

This calculation determines the effective prestress force and stress profile along a draped post-tensioned tendon, accounting for friction losses between the tendon and its duct. It implements the friction model of EN 1992-1-1:2004 (Eurocode 2), Clause 5.10.5.2:

σ(x) = σ_pmax · e^{−μ(θ + kx)}

where μ is the curvature friction coefficient, θ the cumulative angular deviation of the tendon, k the wobble (unintentional angle) coefficient and x the distance from the jack. The sheet computes the jacking-stress limit check, the total angular change from the tendon geometry, the friction loss and the effective stress/force at the far end, and it plots the stress profile for single-end vs. double-end jacking so the benefit of stressing from both ends can be seen at a glance.

Tendon segment angles are derived parametrically from the drape and length of each parabolic segment using α = 2h/L (the change in tangent slope of a parabolic segment from its horizontal-tangent vertex to the far end).

How to use it

1. Set the workbook unit system from the dropdown (this calc is set up in SI, mm).
2. Enter the material and system inputs (blue cells) in Step 1: characteristic strength f_pk, tendon area A_p, jacking stress f_pj, and the friction coefficients μ and k. The sheet checks f_pj against the 0.8·f_pk stressing limit (PASS/FAIL).
3. Enter the tendon geometry in Step 2 — for each parabolic segment, its length L and drape h. Segment angles α, total length and total angle are calculated automatically.
4. Read the results in Step 3: friction factor, friction loss (MPa), and the effective stress and force at the far end.
5. Review Step 4 for the single- vs. double-end jacking stress profile along the tendon.

All grey/white cells are locked formulas; only the light-blue cells are meant to be edited. Change any input and the whole calculation, including the profile table, updates.

How it was validated

• Independent recomputation — every formula was reproduced by an alternate calculation and agrees (e.g. ζ = μ(θ + kL) = 0.0503, friction loss = f_pj(1 − e^−ζ) = 68.7 MPa, effective stress = 1331 MPa for the sample inputs).
• Code compliance — the exponential decay form and the placement of μ multiplying both the curvature term θ and the wobble term kx follow EN 1992-1-1:2004 Cl. 5.10.5.2 exactly.
• Geometry check — the double-end profile is symmetric about mid-span and equals the single-end profile at the jack, as expected physically.
• Assumption noted — segment angles use α = 2h/L for a parabolic tendon with horizontal tangents at the sag and mid-span. Users whose tendon profile differs (inclined anchorage tangent, reverse curvature, multiple drapes per span) should compute θ from the change in tangent slope instead.

Please note that the XLC Addin is used to render equations and must be installed to pevent #NAME! errors