Losses in prestressed concrete structures
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, Pt ;
• After-transfer losses are the difference between the transfer force, P and the force at SLS, Ps =α Pt .
The calculation of losses is different for pre- and post-tensioned PSC
Losses in Pre-Tensioned PSC
1. Elastic Shortening Loss
In pre-tensioning, the strands are stressed before the concrete is cast. Therefore, after jacking ( Pjack ) 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, εc,e , with associated stress and force losses of Ep εc,e and Ap Ep εc,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’.