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