Flexural Strengthening of Beams and Slabs - Strengthening Design of Reinforced Concrete with FRP - page 85

TABLE 5.1
Beam Parameters of Example 15.3
of ACI 440.2R-08
Span 24 ft 7.32 m

B 12 in. 305 mm

H 24 in. 609.6 mm

d 21.5 in. 546 mm

5 ksi 34.5 MPa

f c

f y 60 ksi 414 MPa

Main bars #9 ϕ = 28.6 mm

266 k-ft 361 kN-m

ϕ M n

The beam is assumed to have sufficient shear strength and adequate deflec-
tion and crack-control serviceability requirements while resisting the additional
l oa ds. Design a flexural strengthening system to resist the upgraded moment
294.4 M = k − ft = 399 kN − m . The beam parameters are given in Table 5.1.

u

Solution:

Direct approach:

Use d f = h = 24 in.

M = 294.4 k − ft

u

2

A
bd

3in
12

s

0.01163

ρ= = = s

× 21.5

f
f

60
5

21.5
24

d
d

y
cf

Q =ρ = 0.01163 × × = 0.125

1 s

M
fbd

+Ψ−= ×
×× ×

d
d

294.412
0.9512

21.5
24

u

Q = φ Q + 0.125 × 0.85 − = 0.1079 2 1 f

2

24

2

c f f

2

a
d

0.15
0.85

a
d

2.353
0.85

−− × 21.176 × 0.125 + × 0.1079 = 0

f f

a
d

=− − 112.77 × 0.1079 = 0.163

f

a = 3.9 n

0.003 d 0.003 × 24

f

ε= − 0.003 = − 0.003 = 0.01177 f

a 3.9

0.8 β

1

ε=ε−ε= 0.01177 − 0.00061 = 0.01116

fe f bi