Elastic shortening from the exact closed-form of C5.9.3.2.3a-1, the long-term creep + shrinkage lump sum with humidity factor γh and strength factor γst, and low-relaxation strand relaxation — ending at the effective prestress fpe. Built for pretensioned girders; a post-tensioning toggle applies the (N−1)/2N sequential-stressing reduction to elastic shortening.
Elastic shortening from the exact closed-form of C5.9.3.2.3a-1, the long-term creep + shrinkage lump sum with humidity factor γh and strength factor γst, and low-relaxation strand relaxation — ending at the effective prestress fpe. Built for pretensioned girders; a post-tensioning toggle applies the (N−1)/2N sequential-stressing reduction to elastic shortening.
fpu = 1860 MPa low-relaxation strand; fpy = 0.9fpu. Relaxation loss fixed at 16.5 MPa (2.4 ksi) per 5.9.3.3.
Eci = 4700√f′ci, Ep = 197,000 MPa. Gulf-coast humidity averages 50–60% on the coast, 40% inland — the default reflects Al Ain.
| fpbt before transfer | – |
| fcgp concrete at strand c.g. | – |
| ΔfpES elastic shortening | – |
| γh = 1.7 − 0.01H | – |
| γst = 34.5/(6.9 + f′ci) | – |
| ΔfpLT creep + shrinkage lump | – |
| ΔfpR relaxation | – |
| Check fpe ≤ 0.8fpy = 1339 MPa | – |
The approximate method is calibrated for ordinary precast pretensioned girders — composite decks, normal-weight concrete, strands released within a few days — and inside that envelope it lands within a few percent of the refined 5.9.3.4 time-step calc. Step outside (stage-built box girders, very high f′ci, lightweight mixes, two-stage post-tensioning) and you owe the job the refined method. Two practical anchors: total losses on a typical Gulf I-girder run 18–25% of jacking, and if elastic shortening alone exceeds about a third of the total, your release strength or strand pattern deserves a second look. The humidity factor is worth taking seriously here — inland UAE at H ≈ 40% carries roughly 10% more long-term loss than a coastal yard at 60%. Friction and anchor-set for post-tensioned tendons are a separate calculation — pair this with the PT elongation tool for the full picture.
Under Eurocode and KDS the elastic loss uses the modulus of the young concrete at transfer, and the long-term part is one combined expression (EN 1992-1-1 eq. 5.46, repeated as KDS 24 14 21 eq. 1.5-12) that adds shrinkage, creep under the concrete stress at the tendon and 80 % of the strand relaxation, then divides by the section restraint term. Creep and shrinkage respond to the humidity, the 28-day strength and the notional size 2Ac/u, so two extra sliders appear for fck and the drying perimeter. When the concrete stress at the tendon is high the creep coefficient is raised by the non-linear creep factor of each code. Relaxation is the Class 2 curve taken to 500,000 hours in both. The codes differ in the details: Eurocode uses Ep 195 GPa, fcm = fck + 8 and adds autogenous shrinkage, while KDS (the Korean concrete bridge code) uses Ep 200 GPa, fcm = fck + 4 to 6 MPa, a density-based modulus and the CEB-FIP 1990 type drying shrinkage only. The assumptions (cement type, age at loading 3 or 7 days, final values) are listed under the inputs; expect higher long-term losses than the AASHTO lump sum for early-loaded girders in dry air.