Prestress Loss from Elastic Shortening
Prestress Loss from Elastic Shortening
When prestressing strands are released and transfer their tension into a pretensioned concrete member, the concrete itself shortens elastically under the sudden compression — and because the strands are bonded to that shortening concrete, they shorten with it, which relaxes some of their original tension. This immediate loss, called elastic shortening, happens the instant the strands are cut, well before any of the longer-term losses (creep, shrinkage, relaxation) accumulate.Elastic shortening loss is often the single largest component of total prestress loss in a pretensioned member, particularly for members with a high prestress-to-concrete-area ratio, so it has to be estimated (even if approximately, before an iterative refinement) at the very first pass of design — underestimating it leaves the beam with less effective prestress than assumed, directly affecting the bottom-fibre stress checks done elsewhere.
The elastic shortening loss is df_p = n_mod·f_c, the modular ratio times the concrete stress at the level of the strands, reflecting that the strand strain change equals the concrete strain change at that level. where n_mod is the modular ratio of steel to concrete modulus (E_p/E_c), f_c is the concrete compressive stress at the level of the prestressing strands immediately after transfer, and df_p is the resulting loss of prestress in the strands.
Inputs
n_mod := 6=6
f_c := 12 MPa=12 MPa
Because the bonded strand shortens by the same strain as the surrounding concrete, and steel is stiffer than concrete by the modular ratio, the stress lost in the strand is simply that ratio times the concrete stress at the strand location.
df_p := n_mod·f_c=72 MPa
Results
A loss of about 72 MPa here is typical in magnitude — elastic shortening losses commonly run from about 5% to 10% of the initial strand jacking stress (which is often in the 1300–1900 MPa range), so this is a plausible, moderate value. This loss is then subtracted from the initial jacking stress, before further reductions for shrinkage, creep, and relaxation are applied to reach the final effective prestress used in service stress checks. Because f_c at the strand level itself depends on the (still-unknown) prestress force, real designs often iterate this calculation once or twice for a converged answer.
Assumptions & limitations
- Simplified one-pass estimate; production design typically iterates since f_c depends on the prestress force itself.
- Applies to pretensioned members with strands bonded directly to the concrete (not post-tensioned, unbonded tendons).
- Only elastic shortening is captured — shrinkage, creep, and relaxation losses are calculated separately.
- Assumes linear-elastic concrete behavior at transfer.