Tool 22 · PSC · AASHTO LRFD 5.9.3.3 + C5.9.3.2.3a

Prestress Losses — Approximate Method

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.

Strand system

Strand count40 × 15.2 mm (140 mm²)
Jacking ratio fpbt/fpu0.75

fpu = 1860 MPa low-relaxation strand; fpy = 0.9fpu. Relaxation loss fixed at 16.5 MPa (2.4 ksi) per 5.9.3.3.

Section & casting

Gross area Ag700 ×10³ mm²
Moment of inertia Ig250 ×109 mm4
Strand eccentricity em750 mm
Self-weight Mg at midspan2800 kN·m
f′ci at transfer38 MPa
Relative humidity H40 %

Eci = 4700√f′ci, Ep = 197,000 MPa. Gulf-coast humidity averages 50–60% on the coast, 40% inland — the default reflects Al Ain.

Losses

Effective fpe
MPa
Total loss
MPa
Loss ratio
%
ΔfpES
MPa

Stress waterfall

Detail

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
Field notes

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.

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