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 EQUATION:
Mu = Apsfps(dp - a/2) + Asfdy(d-a/2)
(143)
and
EQUATION:
a = (Apsfps + Asfdy)/.85f'dcb
(144)
where,
Mu = ultimate moment capacity, in-lb
Aps = total area of prestress reinforcement, in2
fps = average stress in the prestressed reinforcement at
ultimate load, psi
dp = distance from extreme compression fiber to the centroid of
the prestressed reinforcement, in
a = depth of equivalent rectangular stress block, in
As = total area of non-prestressed tension reinforcement, in2
fdy = dynamic design strength of non-prestressed reinforcement,
psi
d = distance from extreme compression fiber to the centroid of
the non-prestressed reinforcement, in
f'dc = dynamic compressive strength of concrete, psi
b = width of the beam for a rectangular section or width of
the compression flange for a flanged section, in
(a) The average stress in the prestressed reinforcement at ultimate
load, fps, must be determined from a trial-and-error, stress-strain
compatibility analysis. This may be tedious and difficult especially if the
specific stress-strain curve of the steel being used is unavailable. In
lieu of such a detailed analysis, the equations below may be used to obtain
an appropriate value of fps.
For members with bonded prestressing tendons:
(145)
EQUATION: fps = fpu 1-[UPSILON]p [pp fpu + dfdy (p-p')]
K1
f'dc
dpf'dc
where,
fpu = specified tensile strength of prestressing tendon, psi
[UPSILON]p = factor for type of prestressing tendon
= 0.40 for 0.80 < /= fpy/fpu < 0.90
= 0.28 for fpy/fpu >/= 0.90
fpy = "fictitious" yield stress of prestressing tendon
corresponding to a 1 percent elongation, psi
K1 = 0.85 for f'dc up to 4000 psi and is reduced 0.05 for
each 1000 psi in excess of 4000 psi
pp = Aps/bdp, the prestressed reinforcement ratio
p = A's,/bd, the ratio of non-prestressed tension
reinforcement
p' = A's,/bd, the ratio of compression reinforcement
A's = total area of compression reinforcement, in2
2.08-221
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