Flexural Strengthening of Beams and Slabs - Strengthening Design of Reinforced Concrete with FRP - page 100

87
87

bal

c = d

and f y is in ksi when U.S. customary units are used (5.45a)

+ f

y

600
600

bal

c = d

and f y is in MPa when S.I. units are used (5.45b)

+ f

y

= ε+ε

bal

d
c

ε

cu f f

bal

cu
bal

bal

ε= −ε−ε 1

(5.46)

f cu bi

c d

f

87
87

+ f d

d

yf

bal

ε= 0.003 −−ε 1 and f y is in ksi when U.S. customary units are used

f bi

(5.47a)

600
600

+ f d

d

yf

bal

ε= 0.003 −−ε 1 and f y is in MPa when S.I. units are used

f bi

(5.47b)

From force equilibrium:

bal bal bal

0.85 fb c β=+ Af AE ε

c 1 sy f f f

Dividing both sides by ( f y bd ) results in

E ε ρ= β

bal

f
f

87
87

f f

bal c

y

0.85 −ρ

and f y is in ksi when U.S. f 1 s

f + f

y y

customary units are used

(5.48a)

bal

E ε ρ= β f

f

600
600

f f c

bal

0.85 −ρ and f y is in MPa when S.I. units are used

f 1 s

f + f

y y y

(5.48b)

Therefore

f

( )

y

bal bal

ρ= ρ−ρ

(5.48c)

f s s

bal

f

f

where

ρ= A
bd

bal

f

bal

(5.49)

f

ρ= A
bd

s

(5.50)

s

f
f

87
87

c

bal

ρ= β 0.85 and f y is in ksi when U.S. customary units are used

s 1

+ f

y y

(5.51a)