Structural Concrete - Hassoun

19.3 Loss of Prestress 743
2. Loss due to shrinkage:
Shrinkage strain = 0.0003
Δf s = ε sh E s = 0.0003 × 29, 000 = 8.7ksi
Percent loss = 8.7
145 = 6%
3. Loss due to creep of concrete: Assuming C c = 2.0, then Δf s = C c (ε cr E s ):
Elastic strain =
F i
A c E c
= 0.151 × 10 −3
Δf s = 2(0.151 × 10 −3 × 29, 000) =8.8ksi
Percent loss = 8.8
145 = 6.1%
Or, approximately, ε cr = 48 × 10 −5 × stress in the concrete (ksi):
( )
ε cr = 48 × 10 −5 435
= 36 × 10 −5
32 × 18
Δf s = ε cr E s = 36 × 10 −5 × 29, 000 = 10.4ksi
Percent loss = 10.4
145 = 7.2%
This is a conservative value, and the same ratio is obtained if C c = 2.38 is adopted in the
preceding calculations.
4. Loss due to relaxation of steel: For low-relaxation strands, the loss is assumed to be 2.5%.
Δf s = 0.025 × 145 = 3.6ksi
5. Assume the losses due to bending, friction of cable spacers, and the end block of the pretensioning
system are 2%.
Δf s = 0.02 × 145 = 2.9ksi
6. Loss due to friction in tendon is 0.
7. Total losses are as follows:
Elastic shortening loss 5.3 ksi 3.6%
Shrinkage loss 8.7 ksi 6.0%
Creep of concrete loss 8.8 ksi 6.1%
Relaxation of steel loss 3.6 ksi 2.5%
Other losses 2.9 ksi 2.0%
Total losses 29.3 ksi 20.2%
Effective prestress = 145 − 24 = 121 ksi
Effective prestressing force F = 121 × 3in. 2 = 363 ksi
For F = η F i , η = 0.834.
F =(1 − 0.166)F i = 0.834F i