Stress checks at transfer and service

A prestressed member must be checked at two critical stages. At transfer, the prestress is at its highest, because losses have not yet occurred, while the only load acting is usually the member's self-weight. At service, the prestress has fallen to its effective value after losses, while the full dead and imposed loads act. A section that is fine at one stage can fail the other.

At each stage the top and bottom fibre stresses come from three parts: the uniform compression P over A, the bending from the eccentric prestress, P times e over Z, and the bending from the external moment, M over Z. With the tendon below the centroid, prestress bending compresses the bottom and tensions the top; gravity moment does the opposite. Each fibre at each stage is compared with the permissible compressive and tensile stresses for that stage, which gives four inequalities in all.

At transfer the risk is too much tension at the top near the supports, where self-weight moment is small, and too much compression at the bottom. Concrete at transfer is also younger and weaker, so permissible values are lower. At service the risk is tension at the bottom at mid-span under full load. The ratio of effective to initial prestress, often written as eta, links the two stages.

Plotting these inequalities, the Magnel diagram, shows the feasible range of prestress and eccentricity at once. Debonding or deflecting some strands near the ends of pre-tensioned members reduces the transfer tension at the top where self-weight cannot counter it.