Structural Concrete - Hassoun

740 Chapter 19 Introduction to Prestressed Concrete
The value of C c may be taken as follows:
Concrete strength f ′ c ≤ 4ksi f′ c > 4ksi
Relative humidity % 50% 100% 50%
C c 1–2 2–4 0.7–1.5 1.5–3
Linear interpolation can be made between these values. Considering that half the creep takes
place in the first 134 days of the first 6 months after transfer and under normal humidity conditions,
the creep strain can be assumed for practical design as follows:
1. For pretensioned members, ε cr = 48 × 10 −5 stress in concrete (ksi).
2. For posttensioned members, ε cr = 36 × 10 −5 × stress in concrete (ksi). This value is used when
posttensioning is made within 2 to 3 weeks. For earlier posttensioning, an intermediate value
may be used.
These values apply when the strength of concrete at transfer is f ′ ci ≥ 4 ksi. When f ′ ci < 4ksi,
the creep strain should increase in the ratio of (4/actual strength).
Total loss of prestress due to creep = ε cr E s (19.8)
19.3.5 Loss Due to Relaxation of Steel
Relaxation of steel causes a time-dependent loss in the initial prestressing force, similar to creep
in concrete. The loss due to relaxation varies for different types of steel; its magnitude is usually
furnished by the steel manufacturers. The loss is generally assumed to be 3% of the initial steel
stress for posttensioned members and 2 to 3% for pretensioned members. If test information is not
available, the loss percentages for relaxation at 1000 h can be assumed as follows:
1. In low-relaxation strands, when the initial prestress is 0.7 f pu and 0.8 f pu , relaxation (RE) is
2.5 and 3.5%, respectively.
2. In stress-relieved strands or wire, when the initial prestress is 0.7 f pu or 0.8 f pu , relaxation (RE)
is 8 and 12%, respectively.
19.3.6 Loss Due to Friction
With pretensioned steel, friction loss occurs when wires or strands are deflected through a
diaphragm. This loss is usually small and can be neglected. When the strands are deflected to
follow a concordant profile, the friction loss may be considerable. In such cases, accurate load
measuring devices are commonly used to determine the force in the tendon.
With posttensioned steel, the effect of friction is considerable because of two main factors:
the curvature of the tendon and the lack of alignment (wobble) of the duct. The curvature effect
may be visualized if a belt around a fixed cylinder is tensioned on one end with a force P 2 ; then the
force, P 1 , at the other end to initiate slippage in the direction of P 1 is
P 1 = P 2 e μα px
(19.9)
where μ is the coefficient of static angular friction and α px is the angle between P 1 and P 2 .Itisa
general practice to treat the wobbling effect similarly:
P x = P s e −(μα+Kl x )
P px = P pj e −(Kl px +μ p α px ) (ACI 2008 Code Eq. 18.1) (19.10)