Civil Engineering Reference
In-Depth Information
from which prestress tendons are manufactured do not have distinct yield points. Despite
this fact, the strength method for determining the ultimate moment capacities of sections
checks rather well with load tests as long as the steel percentage is sufficiently small as to
ensure a tensile failure and as long as bonded strands are being considered.
In the expressions used here,
f
ps
is the average stress in the prestressing steel at the
design load. This stress is used in the calculations because the prestressing steels usually
used in prestressed beams do not have well-defined yield points (that is, the flat portions
that are common to stress-strain curves for ordinary structural steels). Unless the yield
points of these steels are determined from detailed studies, their values are normally
specified. For instance, the ACI Code (18.7.2) states that the following approximate ex-
pression may be used for calculating
f
ps
. In this expression
f
pu
is the ultimate strength of
the prestressing steel,
p
is the percentage of prestress reinforcing
A
ps
/
bd
, and
f
se
is the ef-
fective stress in the prestressing steel after losses. If more accurate stress values are
available, they may be used instead of the specified values. In no case may the resulting
values be taken as more than the specified yield strength
f
py
, or
f
se
60,000. For bonded
members,
p
p
f
pu
if
f
se
0.5
f
pu
c
d
f
ps
f
pu
1
1
d
p
(
)
f
(ACI Equation 18-3)
p
is a factor for the type of prestress tendon whose values are specified in ACI
Section 18.0 (
where
0.55 for
f
py
/
f
pu
not less than 0.80, 0.40 for
f
py
/
f
pu
not less than 0.85, and
0.28 for
f
py
/
f
pu
not less than 0.90),
d
p
p
distance from the extreme compression fiber to the
c
,
c
.
centroid of the prestress reinforcement,
If any compression reinforcing is considered in calculating
f
ps
, the terms in brackets
may not be taken less than 0.17 (see Commentary R18.7.2). Should compression reinforc-
ing be taken into account and if the term in brackets is small, the depth to the neutral axis
will be small and thus the compression reinforcing will not reach its yield stress. For this
situation the results obtained with ACI Equation 18-3 are not conservative, thus explain-
ing why the ACI provides the 0.17 limit.
Should the compression reinforcing be neglected in using the equation,
f
y
/
f
and
f
y
/
f
will equal
zero and the term in brackets may be less than 0.17. Should
d
be large, the strain in the
compression steel may be considerably less than the yield strain, and as a result the com-
pression steel will not influence
f
ps
as favorably as implied by the equation. As a result,
ACI Equation 18-3 may only be used for beams in which
d
0.15 d
p
.
For unbonded members with span to depth
35,
c
100
f
f
ps
f
se
10,000
p
but not greater than
f
py
nor (
f
se
60,000)
(ACI Equation 18-4)
For unbonded members with span to depth
35,
c
300
f
f
ps
f
se
10,000
(ACI Equation 18-5)
p
However,
f
ps
may not exceed
f
py
, or
f
se
30,000.
