Last reviewed 30 Sept 2026 · 6 min read
Assumptions
- Concrete is treated as homogeneous and elastic within the working stress range (uncracked section).
- Plane sections remain plane; the steel is bonded or unbonded, but its effect on section properties is usually neglected for a first analysis (gross section) or considered by the transformed section for greater accuracy.
- Prestress is the force in the tendon (at the stage considered); the eccentricity is measured from the centroid of the concrete section to the tendon.
Stresses due to prestress
Concentric prestress: (uniform compression).
Eccentric prestress (tendon below the centroid by ):
With external moment (sagging):
Compression positive. and .
A tendon above the centroid (near the supports in a draped beam) gives compression at the top and tension at the bottom — that is why tendons are made to rise towards the ends: to reduce the tensile top stress at transfer where there is no self-weight moment to offset it.
Stages of loading
The design controls stresses at two critical stages:
- Transfer — prestress at its initial value (before time-dependent losses); the member carries only its self-weight. The risk is tension at the top (excessive ) and high compression at the bottom.
- Service — prestress reduced by the losses, (with –); the member carries dead plus live load. The risk is tension at the bottom and compression at the top.
For each stage, the four stress limits are checked: top and bottom fibres at transfer and at service (allowable values from the code: compression – at service; tension limited according to the class of prestressing).
Rectangular beam 300 × 600 mm, span 12 m ( = 180 000 mm², = 18×10⁶ mm³, = 81 kN·m, live-load moment = 100 kN·m). = 1000 kN, = 150 mm, losses 20 % ( = 0.8).
Transfer: , , N/mm². Top = 5.56 − 8.33 + 4.50 = +1.73 ; Bottom = 5.56 + 8.33 − 4.50 = +9.39.
Service: = 800 kN → , ; total moment = 181 kN·m → . Top = 4.44 − 6.67 + 10.06 = +7.83; Bottom = 4.44 + 6.67 − 10.06 = +1.05 (still compression → no cracking).