Cable profiles

In a post-tensioned member, the tendon need not be straight. Its profile is chosen so that the prestress works against the load where the load is largest. A tendon draped in a parabola between the supports of a uniformly loaded beam, low at mid-span and near the centroid at the ends, mirrors the bending moment diagram, giving most help at mid-span and none where it is not needed.

A curved tendon pushes on the concrete along its length. A parabolic tendon with sag e over span L exerts an upward uniform load equal to 8 P e over L squared. This is the load-balancing idea: if the upward load from the tendon equals the downward permanent load, the beam carries that load with no bending at all, only uniform compression, and it neither sags nor hogs. Only the extra load is resisted by bending.

The tendon must stay within limits. If the prestress resultant falls outside the kern of the section, the opposite fibre goes into tension. The kern points for a rectangle are a sixth of the depth above and below the centroid. Combined with the moment from loads, this leads to a cable zone, an envelope inside which the tendon centroid must lie along the member for no tension, or for limited tension.

Continuous members add secondary, or parasitic, moments: the supports restrain the deformation the prestress tries to cause, adding moments that must be included in design. Profiles are also limited by cover, duct radius, anchorage positions and the need to avoid sharp curvature, which raises friction.