Prestressing for continuous beams - The Design of Prestressed Concrete Bridges - page 136

Prestressing for continuous beams

6.1 General
In this chapter, the general principles of the design of continuous bridge decks will
be explained by following the essential steps of the design of a typical box girder.
However, before this can be carried out it is necessary to explain the concept of
prestress parasitic moments.

6.2 The nature of prestress parasitic moments
Consider a three-span continuous beam that has been released by hinges over the
supports to create three statically determinate spans. The three equal spans are
subjected to uniform loads, Figure 6.1 (a). The free bending moment at the centre
of each span, M max = wl 2 /8, where w is the load per metre and l the span, and the
moment at any point may be called M iso . The beams will defl ect, and the end rotation
of each beam

= M max × l /3 EI , Figure 6.1(c). If the spans are to be made continuous,
hogging moments must be applied at each internal support such that the rotations of
the beam ends become compatible. The hogging moments for a three-span beam are
as shown in Figure 6.1 (d), with, for this particular case of three equal spans, a value
of wl 2 /10 at each internal support; that is 80 per cent of the free bending moment.
We may call these hogging moments the 'continuity moments', the values at any point
being M c . The total moment at any point along the continuous beam will be the sum
of the free bending moment and the continuity moment, or M iso + M c , Figure 6.1 (e).
This is basic theory of structures, which causes no problems to engineers or students.
The hogging continuity moments in the beam are as easy to understand as the free
bending moments, and there is no reason to label the free moments as primary and the
hogging moments as secondary.
The uniform loads on the statically determinate spans may be replaced by parabolic
prestressing cables anchored on the neutral axis at the beam ends, which apply
a uniform upwards load on the beams, Figure 6.1 (f), ( 5.18 ). The prestress force P
and the eccentricity at mid-span e c may be chosen to give an upwards distributed
force = w kN/m, and hence to produce exactly the same bending moments and beam
end rotations, although of the opposite sign, as the externally loaded beams described
above, Figure 6.1 (g) and (h). The free bending moment at the centre of each span
is Pe c and the moment at any point is Pe . In order to make the beams continuous,
numerically the same moments as for the distributed loads, that is 80 per cent of Pe c

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