Flexural Strengthening of Beams and Slabs - Strengthening Design of Reinforced Concrete with FRP - page 113

3 in.

4.37 in.

5 in.

2.38 in.

FIGURE 5.16 Example 5.10 showing the section and FRP design details.

Example 5.10: Analysis

A singly reinforced section was constructed and tested by Triantafillou and
Plevris (1992). CFRP was used having E f = 26,980 ksi and f fu = 210 ksi. The
beam designation was Beam 3 with the following section properties, as seen in
Figure 5.16:

f = 6.48 ksi b = 2.38"

c f

f = 75 ksi t = 0.0079"

y f

2

A = 0.051 in ε = 0

s bi

Determine the design moment capacity of the section and compare it to the
experimental moment to have a feel for the strength reduction factors warranted
by ACI 440.

Solution:

Determine the failure mode first.

0.05 6480
1000

β= − 1.05 = 0.726

210
26980

max *
ε= ε+ε= × 0.9 C 0.9 0.95 × += 00.00665 fu E u bi

=β ε×
ε+ε

d 0.003 × 5 cu f

a

max

= 0.726 × = 1.13"

b 1

max

0.003 + 0.00665

cu fu

0.9 .9 f = C f

*

= 0.90.95 × × 210 = 179.55 ksi

fu E u

f a

max

f

f b

max c b y

ρ= 0.85 0.9 −ρ

s

f d 0.9 f

fu fu

6.48
179.55

1.13
4.37

0.051
34.37

75
179.55

f bmax ρ= × 0.85 × − × = 0.00631

×

2.38 0.0079
34.37

×
×

f b

max

ρ= = 0.00143 <ρ= 0.00631

f