Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 91

area for an applied bending moment. A critical parameter in all these
calculations is the tension reinforcement index, ω f , defined as

f
f

A
bd

f
f

fu f fu

ω=ρ =

f f

′ ′

c
In case a, ω f is known and the strength can be defined as a function of it.
In case b, unknown parameters are derived as functions of ω f that may be
known or unknown at first. Another dimensionless parameter is defined as

c

ε
ε

fu

e = ; ε= 0.003

cu

cu

Case a—calculation of nominal flexural strength of an existing member
( a1 ) Failure is initiated by concrete crushing if

0.85
1

β
+ e

1

ω≥ω=

f fb

In this case the stress level in the reinforcement can be calculated as

3.4 β

ω

e

1

1 + − 1

f
f

f

f

f == ≤ 1

2 e

fu

And the nominal flexural strength is

ω

′ ω− ′

f

M = 1 f bd

2

′ n c

f

1.7

where

ω= ω f

f f

Example 4.1

Calculate the nominal flexural strength of the following beam:

Concrete: f ′ c = 4.0 ksi

β 1 = 0.85

Reinforcement: f fu = 60 ksi

E f = 6,000 ksi
ε fu = 0.010
A f = 4#10 = 5.08 in. 2

Size: b = 16.0 in.

h = 25.0 in.
c = 3.0 in.
d = h−c = 22.0 in.

Continued