Structural Concrete - Hassoun

738 Chapter 19 Introduction to Prestressed Concrete
force during the life span of the structure. The amount of loss in tendon stress varies between 15
and 30% of the initial stress because it depends on many factors. For most normal-weight concrete
structures constructed by standard methods, the tendon stress loss due to elastic shortening, shrinkage,
creep, and relaxation of steel is about 35 ksi (241 MPa) for pretensioned members and 25 ksi
(172 MPa) for posttensioned members. Friction and anchorage slip are not included.
Two current recommendations for estimating the total loss in prestressed concrete members
are presented by AASHTO and the Posttensioning Institute (PTI). AASHTO [23] recommends a
total loss (excluding friction loss) of 45 ksi (310 MPa) for pretensioned strands and 33 ksi (228 MPa)
for posttensioned strands and wires when a concrete strength of f ′ c = 5 ksi is used. The PTI [24]
recommends a total lump-sum prestress loss for posttensioned members of 35 ksi (241 MPa) for
beams and 30 ksi (207 MPa) for slabs (excluding friction loss). These values can be used unless a
better estimate of the prestress loss by each individual source is made, as is explained shortly.
In general, the sources of prestress loss are
• Elastic shortening of concrete
• Shrinkage of concrete
• Creep of concrete
• Relaxation of steel tendons
• Friction
• Anchorage set
19.3.2 Loss due to Elastic Shortening of Concrete
In pretensioned members, estimating loss proceeds as follows. Consider a pretensioned concrete
member of constant section and stressed uniformly along its centroidal axis by a force F 0 .Afterthe
transfer of the prestressing force, the concrete beam and the prestressing tendon shorten by an equal
amount because of the bond between the two materials. Consequently, the starting prestressing
force F 0 drops to F i and the loss in the prestressing force is F 0 − F i . Also, the strain in the concrete,
ε c , must be equal to the change in the tendon strain, Δε s . Therefore, ε c = Δε s ,orf c /E c = Δf s /E s ,and
the stress loss due to the elastic shortening is
Δf s = E s
× f
E c = nf c = nF i
≈ nF 0
(19.1)
c A c A c
where
A c = area of concrete section
n = E s /E c = modular ratio
f c = stress in concrete at centroid of prestressing steel
Multiply the stress by the area of the prestressing steel, A sp , to get the total force; then the elastic
loss is
( ) nF0
ES = F 0 − F i = Δf s A sp =(nf c ) A sp ≈ A
A sp (19.2)
c
F i = F 0 −(nf c ) A sp (19.3)
For practical design, the loss in the prestressing force, Δf s per unit A sp , may be taken to be approximately
nF 0 /A c . If the force F 0 acts at an eccentricity e, then the elastic loss due to the presence of
F 0 and the applied dead load at transfer is
ES =−(nf c ) A sp (due to prestress)+(nf c ) A sp (dead load)