F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

384 Prestressed concrete continuous beams
acf::r
c
(a) Bending moment diagram
(b) Shear force diagram
(c) Load diagram
Fig.10.2-3
consists oftwo straight lines, such as ac and cb in Fig. 10.2-3(a), then
from eqn (10.2-2) the shear force is constant from a to c and also
from c to b (Fig. 10.2-3(b)); therefore the load must be a
concentrated one at section c, its magnitude Q being equal to the
change in shear force from one side of c to the other (Fig. 10.2-3(c) ).
That is, Q is equal to the change in slope of the bending moment
diagram at section c.
In a prestressed concrete beam, the tendon profile represents to scale
the primary moment diagram; hence the transverse load due to the
prestressing can be worked out directly from the tendon profile, as
explained in Example 10.2-1.
Example 10.2-1
Figure 10.2-4(a) shows the tendon profile in a continuous beam of
uniform cross-section. If the prestressing force is 5000 kN, determine
the line of pressure. Hence determine the support reactions induced by the
prestressing.
SOLUTION
The loads produced by the prestressing are as shown in Fig. 10.2-4(b).
Thus, at A there is a concentrated load of 5000 kN x 0.082 radians
= 410 kN (see statement (c) above). Between A and C there is a uniformly
distributed load of (5000 kN x 0.18 radians)/25 m = 36 kN/m (see statement
(b)) and so on. The axial forces at A and B are the horizontal
components of the tendon force and, for the relatively flat tendon profiles
used in practice, are taken as equal to the tendon force. The moment of
500 kNm at B is obtained as 5000 kN x 0.1 m.
Of the forces in Fig. 10.2-4(b), only those in Fig. 10.2-4(c) produce
bending moments acting on the beam.
The beam is next analysed for the continuity moments at the supports.
Hardy Cross's moment distribution method is used here (Fig. 10.2-4(d) ),