Prestressing for continuous beams - The Design of Prestressed Concrete Bridges - page 141

Figure 6.3 Concordant cables
6.5 Concordant cables
We have seen that the continuity moments due to prestress for a continuous beam
are those moments that must be applied to the ends of the released beams to render
compatible the beam end rotations, Figure 6.1. It is possible to arrange the prestressing
tendons in such a way that they create zero relative rotations at the ends of the
statically determinate beams. For instance, a prestress profi le of the general form
shown in Figure 6.3 (a) for the statically determinate beams shown in Figure 6.1 (f)
may, by suitably arranging areas of positive and negative eccentricity, be designed to
give zero relative rotations of the beam ends at the intermediate supports. Under these
circumstances, the M p would be zero. A cable profi le that gives a zero parasitic moment
is called a concordant cable.
In the early days of prestressing, when engineers had trouble understanding and
manipulating prestress parasitic moments, it was considered desirable to achieve
concordant cable profi les. In fact such profi les are almost universally uneconomical,
frequently requiring some 50 per cent more prestressing steel than a properly designed
profi le. One of the great strengths of prestressing is the facility to manipulate M p in
order to optimise the bending moment distribution between pier and mid-span.
6.6 Straight cables in built-in beams
In a span that is effectively built-in at each end (which could be a single built-in span or
the interior spans in a long continuous deck), any straight cable of constant eccentricity
will generate a parasitic moment that is equal and of opposite sign to the Pe . That
means that such a straight cable is always effectively centred, producing only a direct
compression of P and no bending moment.