Background Knowledge - Strengthening Design of Reinforced Concrete with FRP - page 36

1164
300

ρ= = 0.006053

× 641

k

k = 0.273 j = −= 1 0.909

3

kd = 0.273 × 641 = 175 mm

1
2

Mf kdbjd =

cc

M
bd kj

120

f = = cc

1
2

1
2

2

300 641

2

10

− 9

0.273 0.909

××× × ×

= 7846 kPa7.85MPa = ≈ 31% f < 70% f linear O.K. c c

MAfjd =

ss

M
Ajd

120

f = =

s

− 6 − 3

1164 × 10 × ×× 0.909 641 10

s

= 176,932 kPa = 176.93 MPa ≈ 43% f

y

Chapter Problems

Problem 2.1
Use the stress-strain curve shown below to determine α and γ for different values of
f c (3-8 ksi). Assume f c = f c . Determine the results using β1 from ACI 318 equation
and Park and Paulay's model. Please realize that the latter is only approximate, since
it is derived for the entire parabola. Hint: Integrate the area under the curve.

Linear

f c

0.15 f c

2ε c ε ε o 2

f c = f c

ε o

E c

ε cu = 0.0038

ε o = 1.8 f c / E c

Strain ε c

FIGURE 2.P.1

Problem 2.2
Repeat Problem 2.1 using the original Hognestad's parabola, that was derived in this
chapter. However, use Park and Paulay's derivation of the actual β 1 instead of the
ACI 318 equation.