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)

Loss of prestress 353
p. 113 of Reference 2: 'strictly speaking, as the concrete creeps the
neutral axis in fact shifts slightly towards the tendon, since the tendon
becomes relatively stiffer. However, such slight shifting of the neutral
axis is of little significance in practice, and it makes sense to assume
that the position of the neutral axis remains unchanged.'
Example 9.4-5
The cross-section of a post-tensioned concrete beam is as shown in Fig.
9.4-1, with A = 5 X 10" mm 2 , I= 4.5 X 10 8 mm 4 , Aps = 350 mm 2 , Es =
200 kN/mm 2 , Ec = 34 kN/mm 2 • The beam is simply supported over a 10m
span and the tendon profile is as shown in Fig. 9.4-2; the effective
prestress Is immediately after transfer is 1290 N/mm 2 • Calculate the loss of
prestress c}{s for the middle third of the span, if the steel relaxation is
129 N/mm , the concrete shrinkage Ecs is 450 X 10- 6 and the creep
coefficient ljJ is 2.
SOLUTION
P = Apsis = 350 X 1290
= 451.5 kN immediately after transfer
Concrete prestress at tendon level is
lc = ~ ( 1 + ~~) (where /?- = II A)
Within the middle third of span:
~ _ 451.5 ( 1 100 2 ) k I 2
Jc - 5 X 104 + 4.5 X 108/5 X 104 N mm
= 19.06 N/mm 2
From Examples 9.4-1, 9.4-3 and 9.4-4 the total loss of prestress due to
relaxation, shrinkage and creep is
c}ls = lr + EsEcs + ael/Jic ( 1 -
a2j!c)
= 129 + 200 X 103 X 450 X 10-6
+ 200 X 1W X 2 X 19 06 ( 1 _ 200 X 1W X 2 X 19.06)
34 X 1W . 34 X 1W 2 X 1290
= 424 N/mm 2
Fig. 9.4-2