About Prestress Losses Calculator
The prestress losses calculator evaluates the itemized time-dependent and instantaneous losses of prestress in a prestressed or post-tensioned concrete member using the AASHTO LRFD / ACI 318 refined method. It computes the elastic shortening loss at transfer, the long-term creep, shrinkage, and steel relaxation losses, sums them to the total loss, and reports the effective prestress remaining in the tendon.
Enter the jacking stress fpi, the tendon area Aps, the steel and concrete moduli (Ep, Eci, Ec), the concrete stress at the tendon centroid fcgp and the sustained superimposed dead-load stress fcds, the creep coefficient Kcr, and the shrinkage and relaxation loss magnitudes. The tool returns each loss component in MPa and as a percentage of fpi, the total loss, the effective prestress fpe, and both the initial and effective prestressing forces.
How It Works
- Compute the elastic shortening loss: dfpES = (Ep/Eci)*fcgp for pre-tension, or half that for single-stage post-tensioning.
- Compute the creep loss dfpCR = Kcr*(Ep/Ec)*(fcgp - fcds), clamped to be non-negative.
- Add the shrinkage loss dfpSH and the steel relaxation loss dfpRE (entered directly in MPa).
- Sum the four components to the total loss, express it as a percentage of fpi, and subtract it to obtain the effective prestress fpe and the effective force Pe = fpe*Aps.
Worked Example
A pre-tensioned member is jacked to fpi = 1395 MPa with Ep = 197,000 MPa, Eci = 28,000 MPa, Ec = 32,000 MPa, fcgp = 12 MPa, fcds = 2 MPa, Kcr = 2.0, dfpSH = 35 MPa, and dfpRE = 30 MPa. Elastic shortening dfpES = (197000/28000)*12 = 84.43 MPa. Creep dfpCR = 2.0*(197000/32000)*(12-2) = 123.13 MPa. The total loss = 84.43 + 123.13 + 35 + 30 = 272.55 MPa, which is 272.55/1395 = 19.54% of the jacking stress. The effective prestress fpe = 1395 - 272.55 = 1122.45 MPa.
Formulas
- Elastic shortening (pre-tension)
dfpES = (Ep/Eci) * fcgp- Elastic shortening (post-tension, single stage)
dfpES = 0.5 * (Ep/Eci) * fcgp- Creep loss
dfpCR = Kcr * (Ep/Ec) * (fcgp - fcds)- Total loss and effective prestress
total = dfpES + dfpCR + dfpSH + dfpRE ; fpe = fpi - total- Prestressing forces
Pi = fpi * Aps ; Pe = fpe * Aps
Standards & References
- AASHTO LRFD Bridge Design Specifications (refined prestress-loss method)
- ACI 318 Chapter 18/20 prestressed concrete
- PCI Design Handbook prestress-loss provisions
Frequently Asked Questions
Which prestress loss components does the calculator include?
It includes the four refined-method components: elastic shortening at transfer, long-term creep, concrete shrinkage, and steel relaxation. Anchorage seating and friction losses for post-tensioning are entered separately into the effective stress fcgp upstream of this calculation.
Why is the post-tension elastic shortening loss half the pre-tension value?
In single-stage post-tensioning the strands are stressed against the already-cast concrete, and the last strand tensioned experiences essentially no elastic shortening loss. Averaged across all tendons, the elastic shortening loss is approximately half the pre-tension value, hence the 0.5 factor.
What is fcgp and how is it different from fcds?
fcgp is the net concrete compressive stress at the centroid of the tendons due to the prestress force plus the member self-weight at transfer; it drives the elastic shortening and creep losses. fcds is the concrete stress at the same level caused by sustained superimposed dead load applied later, which partially relieves creep, so creep is proportional to (fcgp - fcds).
What units does the calculator use?
It uses SI units: stresses and moduli in MPa, the tendon area in mm^2, and the resulting prestressing forces in newtons. Loss percentages are expressed relative to the jacking stress fpi.