Flexural Strengthening of Beams and Slabs - Strengthening Design of Reinforced Concrete with FRP - page 90

2

a
d

a
d

( )

−− 20.208 Q + 2.77 Q = 0 1 2

f f

2

a
d

a
d

− 1.966 + 0.4321 = 0

f f

a
d

1.966 − 1.966

2

− × 40.4321

= = 0.252

2 f

a = 4.54 in

4.54
0.8

16.25 −

ε= 0.003 = 0.00559 > 0.005

s

4.54
0.8

0.003 d f

0.003 0.00652

ε= − =

f

a

β

1

ε=ε−ε= 0.00652 <ε = 0.00896 (assuming 2layersofFRP). fe f bi fd

33,000 0.00652 215.15 ksi

f = × = fe

f
f

a
d

f
f

5
215.15

4.54
16.25

83.5
215.15

c
fe

y
fe

ρ= 0.85 −ρ = 0.85 × × − 0.01083 × = 0.001313

f s

A = 0.001313 × 10 × 16.25 = 0.213 in

2

f

Why is it smallerthan0.286 in

2

in Example5.3?

Because d is larger (18").

f

A
nt

0.213
20.0065

f
f

b == × = 16.42 in > b = 10" N.G. f

Either wrap around thesides or use3layers.

Usingfour layersand apartiallayer:

3100.0065 0.0065 0.213

×× +× = b

f

b = 2.77 in. ≈ .0 in.

f

5000
33310 .0065

check ε= 0.083 = 0.00732 > ε O.K.

fd fe

6

×× ×

The design in Figure 5.5 is more economical (less FRP area) than the wrapped
design in Example 5.3. However, the wrapped design has its advantages in confin-
ing the cover area and reducing the interfacial shear stresses.