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)

The ultimate limit state: flexure (BS 8110) 355
For unbonded tendons, values of/ph and x for use in eqn (9.5-1(a)) may
be taken as
~ 7000[1 1 7/puAps]
/pb = Jpc + 1/d - · fcubd
:S 0.7/pu
(9.5-1(b))
X = 2.47 [/puAps] [/pb] d
fcubd /pu
(9.5-1(c))
where f,pe = design effective prestress in the tendons after all losses;
!pu = characteristic strength of the tendons;
I = normally taken as the length of the tendons between the end
anchorages;
b = width of the rectangular beam or the effective width of a
flanged beam;
and the other symbols have their usual meanings.
With reference to the use of Table 9.5-1 and eqns (9.5-1), the term
effectively bonded post-tensioned beam refers to a beam in which the space
between the tendon and the duct is grouted after tensioning; similarly, an
unbonded post-tensioned beam is one where the duct or ducts are not
grouted. Where the neutral axis of a flanged beam lies outside the flange,
eqn (9.5-1(a)) is not applicable, and a more general approach is required
(see Fig. 9.5-4 and Comment (b) at the end of Example 9.5-1).
A general flexural theory
The general flexural theory in Section 4.2 may be modified for application
to prestressed concrete. Consider the beam section in Fig. 9.5-1(a). The
tendon strain fpb at the ultimate condition may be considered to be made
up of two parts: (a) the strain fpc due to the effective tendon prestress after
losses and (b) the additional strain Epa produced by the applied loading.
Thus
I· b ·I
T
T -r
X X
r-·-1-·L_·-- __L
d At failure
r=-J
1 \/ Prestress
1 •
C'cu=0·0035
I
I
I
Beam section Concrete strains
(a) (b)
Forces
(cJ
Fig. 9.5-1