## Losses in prestressed concrete structures

**Prestressing Losses**

**Basis and Notation**

Recall that transfer is the moment at which the concrete first feels the prestress. Losses can be before or after transfer:

• Before-transfer losses are the difference between what is applied by the hydraulic jack, jack P and what the concrete feels at transfer, P_{t } ;

• After-transfer losses are the difference between the transfer force, P and the force at SLS, P_{s} =α P_{t} .

The calculation of losses is different for pre- and post-tensioned PSC

Notation

**Losses in Pre-Tensioned PSC**

**1. Elastic Shortening Loss**

In pre-tensioning, the strands are stressed before the concrete is cast. Therefore, after jacking ( P_{jack} ) has been applied, at a level y, the concrete is subjected to the stress:

At the level of the strands, y = e. Hence, the stress in the concrete at that level is:

And the concrete at the level of the strands has a strain of:

Since the strands are bonded to the concrete, they undergo a loss of strain of the same amount, ε_{c,e} , with associated stress and force losses of E_{p} ε_{c,e } and A_{p} E_{p} ε_{c,e } . Hence

The concrete never feels the full jacking force since the strands shorten as the concrete strains. Hence, elastic shortening loss in pre-tensioning is ‘before-transfer’.