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Prestress Losses Calculator (ACI 318)

Calculate time-dependent prestress losses per ACI 318 including elastic shortening, shrinkage, creep, relaxation, anchorage set, and friction losses.

Prestressed Concrete Structural engineers, bridge engineers, precast concrete designers Commercial Intent: HIGH

Engineering Formulas

Jacking Force

Pj = fpj × Ap × n fpj = jacking ratio × fpu fpy = 0.90 × fpu (low relaxation)
P_j: Jacking force (kN)
f_pj: Jacking stress (MPa)
f_pu: Ultimate tensile strength (MPa)

Elastic Shortening (ES)

Pre-tension: ES = (n-1)/2 × (fpj/Ap) × (Ap/Ag + e²/Ig) × Ep/Eci Post-tension: ES = n × fcgp n = Ep/Ec
E_p: Prestressing steel modulus (MPa)
E_ci: Concrete modulus at transfer (MPa)
f_cgp: Concrete stress at strand c.g. (MPa)

Shrinkage (SH)

SH = 8.2×10⁻⁶ × Ksh × (1 - 0.06 V/S) × (100 - RH) × Ep V/S = volume/surface ratio
K_sh: Shrinkage coefficient (≈1.0)
V/S: Volume to surface ratio
RH: Relative humidity (%)

Creep & Relaxation

CR = 12 × fcgp (simplified ACI method) RE = max(0, fpj/fpy - 0.55) × 20 × Krel Low relaxation steel only
CR: Creep loss (MPa)
RE: Relaxation loss (MPa)
K_rel: Relaxation coefficient

Anchorage Slip & Friction

AS = Δ × Ep / L (post-tension) Px = P_0 × e^(-k·x - μ·α) k = wobble coeff, μ = curvature coeff
Δ: Anchorage slip (mm)
k: Wobble coefficient (per m)
μ: Curvature friction coefficient
α: Total angular change (rad)

Total Loss & Effective Prestress

ΔfpT = ES + SH + CR + RE + AS + FR fpe = fpj - ΔfpT Pe = fpe × Ap × n
f_pe: Effective prestress (MPa)
P_e: Effective prestress force (kN)

Worked Example

Post-Tensioned Beam — 20m Span

method: post-tensionfpu: 1860jackingRatio: 0.75apPerStrand: 98.7strandCount: 12beamLength: 20eccentricity: 200fci: 35fc: 50rh: 70anchorageSlip: 4wobbleCoeff: 0.0015curvatureCoeff: 0.2ductDiameter: 90
Jacking
fpj = 0.75 × 1860 = 1395 MPa Pj = 1395 × 98.7 × 12 / 1000 = 1651 kN
Elastic Shortening
f_cgp = 1395 × 1184.4 × (1/1500 + 200²/1.125e8)/1000 = 6.1MPa ES = 5.74 × 6.1 = 35.0 MPa (post-tension)
Shrinkage
V/S = 2.0, SH = 8.2e-6 × 1.0 × (1-0.06×2) × (100-70) × 195000 = 42.3 MPa
Creep & Relaxation
CR = 12 × 6.1 = 73.2 MPa RE = (1395/1674 - 0.55) × 20 = 0.28 × 20 = 5.6 MPa
Anchorage & Friction
AS = 4 × 195000 / 20000 = 39.0 MPa FR = P0(1-e^(-0.0015×20-0.20×0.044)) = 43.2 MPa
Totals
Total = 35.0 + 42.3 + 73.2 + 5.6 + 39.0 + 43.2 = 238.3 MPa Loss% = 238.3/1395 × 100 = 17.1% fpe = 1395 - 238.3 = 1156.7 MPa Pe = 1156.7 × 1184.4 / 1000 = 1370 kN
Result: Total loss = 238.3 MPa (17.1%), fpe = 1156.7 MPa, effective prestress force = 1370 kN

Engineering Notes

For long-span bridges, friction losses can exceed 20% — consider over-jacking or tensioning from both ends.
Monitor losses during stressing by comparing measured elongation with calculated values.
For seismic regions, ensure minimum effective prestress to prevent decompression under design earthquake.
Grouting of post-tensioning ducts should be done within 7 days to prevent corrosion of strands.
Camber calculations must use the effective prestress force (after all losses), not the jacking force.

Assumptions

• ACI 318-19 Chapter 20 refined loss method
• Low relaxation strand per ASTM A416 (unless specified)
• Simplified creep coefficient of 1.6 for normal weight concrete
• Shrinkage coefficient Ksh = 1.0 (standard conditions)
• Concrete modulus Ec = 4700√fc
• Prestressing steel modulus Ep = 195,000 MPa
• Uniform beam section (prismatic)
• Symmetric tendon profile (linear or parabolic)

Common Mistakes

✕ Using fpu instead of fpj as the starting stress for loss calculations
✕ Forgetting to include friction losses for post-tensioning (can be 5-15% of total)
✕ Applying elastic shortening fully for post-tensioning (sequential loss is less)
✕ Not accounting for the difference between short-term and long-term creep
✕ Using the wrong modulus of elasticity for prestressing steel (195 GPa, not 200 GPa)
✕ Ignoring the effect of multiple tendons on sequential elastic shortening calculations

Frequently Asked Questions

What is prestress loss?

Prestress loss is the reduction in tendon stress from the initial jacking stress to the effective stress at service. Typical total losses: 15-25% for pre-tensioning, 20-35% for post-tensioning.

What is the largest component of loss?

For pre-tensioning: elastic shortening and creep usually dominate (50-60% of total). For post-tensioning: friction and anchorage slip dominate (40-50% of total).

What is elastic shortening?

When the prestress force is transferred to the concrete, the concrete shortens elastically, reducing the tendon strain. In pre-tensioning, this is the immediate loss. In post-tensioning, it occurs as each strand is tensioned.

How does relative humidity affect losses?

Lower RH increases shrinkage and creep losses. At RH 40%, shrinkage losses are about 70% higher than at RH 80%. Dry climates (desert) have higher total losses than humid coastal areas.

What is the difference between pre- and post-tensioning losses?

Pre-tensioning has elastic shortening, shrinkage, creep, and relaxation. Post-tensioning additionally has friction and anchorage slip losses, but elastic shortening may be lower due to sequential stressing.

What is the typical effective prestress after all losses?

Typically f_pe ≈ 0.55-0.65 × f_pu after all time-dependent losses. For 1860 MPa strand, expect f_pe ≈ 1000-1200 MPa depending on conditions.

How can I reduce prestress losses?

Use low-relaxation strand (minimizes RE), stress-relieve by over-jacking (reduces friction), use larger ducts (less friction), concrete with low shrinkage/creep, or allow longer curing before transfer.

What is the wobble coefficient k?

The wobble coefficient accounts for unintended curvature in the duct. Rigid metal duct: k=0.0015/m, flexible duct: k=0.0033/m, plastic sheathing: k=0.0066/m.

How does the V/S ratio affect shrinkage?

A higher volume-to-surface ratio (thicker sections) reduces shrinkage losses because less moisture escapes. Typical V/S: slab = 0.5-1.0, beam = 2-4, column = 3-6.

Are these losses per ACI or Eurocode?

This calculator follows the ACI 318-19 Chapter 20 refined method. Eurocode 2 uses a different approach based on intrinsic creep/shrinkage functions and may give different results.

What is the relaxation loss for low relaxation strand?

Low relaxation strand (per ASTM A416) has significantly less relaxation than stress-relieved strand. Typical relaxation loss: 2-5% of initial stress vs 8-12% for stress-relieved.

When should I use post-tensioning vs pre-tensioning?

Pre-tensioning is used in precast plants for mass production of beams, slabs, and piles. Post-tensioning is used for cast-in-place construction, long-span bridges, and where curved tendon profiles are needed.

References & Standards

ACI 318-19 Ch. 20IS 1343:2012EN 1992-1-1PCI Design Handbook 8th Ed.
ACI 318-19 Chapter 20
Prestressed concrete design provisions including loss calculations
IS 1343:2012
Indian Standard for Prestressed Concrete — Code of Practice
EN 1992-1-1 (Eurocode 2)
Design of Concrete Structures — Prestress losses
PCI Design Handbook (8th Ed.)
Precast/Prestressed Concrete Institute — loss calculation methods
Collins & Mitchell
Prestressed Concrete Structures — comprehensive reference

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