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)

346 Prestressed concrete simple beams
(since V = dM/dx}, or
1
es = 2P [Mimax + Mimin + 2Md] + C
e
(9.2-28)
where Cis a constant of integration. Since the shear force V P depends only
on the shape of the tendon profile es but not on its absolute value, we are
free to choose C such that the profile lies within the permissible tendon
zone. If a profile of the ideal shape cannot be accommodated within the
permissible zone, then a shape close to the ideal but lying within the zone
may be used.
For the ideal profile of eqn (9.2-28), we have, from eqns (9.2-24) to
(9.2-26),
Ycmax} _ +l[V V ]
V . - -"2 imax - imin
cmm
(9.2-29)
Consider an example: Suppose Vimax = 1500 kN, Vimin = 300 kN, Vd = 400
kN. Then without prestressing, Vcmax = 1500 + 400 1900 kN. With
prestress and an ideal profile, Ycmax = -!(1500 - 300] = 600 kN only.
9.3 Stresses at transfer
Service stresses were considered in Section 9.2. In design it is necessary to
consider also the stresses at transfer. The stress criteria at transfer are
expressed by eqns (9.2-4} to (9.2-7); if the subscript t is used to denote
stresses at transfer and if the terms Mimax and Mimin are neglected (since
they are negligible at transfer), then these equations become
Md
Itt - z 1
;:::: lamint (9.3-1}
f Md <"
tt - z 1
- Jamaxt (9.3-2)
f Md <"
2t + z2 - Jamaxt (9.3-3)
Md
ht + z2 ;:::: lamint (9.3-4)
where eqns (9.3-1) and (9.3-3) are normally not critical.
Comments on eqns (9.3-1) to (9.3-4)
These four stress conditions at transfer, and the four in service (eqns 9.2-4
to 9.2-7} can be reduced to only four, with some loss of generality. See the
simplified design procedure in Problem 9.1 at the end of this chapter.
The prestresses Itt and /2 1 at transfer are due to the prestressing force P,
namely
I P Pes
tt=A+~ (9.3-5)