Static Design Stresses -Cont.

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To insure against sudden compression failures, the reinforcement ratio, p,
must not exceed 0.75 of the ratio pb which produces balanced conditions at
ultimate strength and is given by:
0.85K1 f'dc
87,000
EQUATION:
pb=
(37)
fdy
87,000 + fdy
where,
K1 = 0.85 for f'dc up to 4,000 psi and is reduced by 0.05
for each 1,000 psi in excess of 4,000 psi.
(2) The ultimate dynamic resisting moment, Mu, of a rectangular
beam section of width, b, with compression reinforcement is given by:
EQUATION:
Mu = (As - A's)fdy(d - a/2) + A's fdy(d-d')
(38)
and
(As - A's) fdy
EQUATION:
a =
(39)
0.85b f'dc
where,
A's = total area of compression reinforcement
within the beam, in2
d'
= distance from extreme compression fiber to centroid
of compression reinforcement, in
The compression reinforcement ratio p' is defined as:
A's
EQUATION:
p' =
(40)
bd
Equation (38) is valid only when the compression reinforcement yields at
ultimate strength.  This condition is satisfied when:
f'dcd'
87,000
EQUATION:
p-p' < /= 0.85 K1
(41)
fdy d
87,000 - fdy
In addition, the quantity p-p' must not exceed 0.75 of the value of pb
given in Equation (37) in order to insure against sudden compression
failures.  If p-p' is less than the value given by Equation (41), the
ultimate resisting moment should not exceed the value given by Equation
(34).
2.08-72