Flexural Strengthening of Beams and Slabs - Strengthening Design of Reinforced Concrete with FRP - page 142

0.6525 × 0.748 0.6525 × 0.748

M = 0.22 × 60 6 − +××− 0.22 60 2 = 99.157 k-in. n

2 2

M 8.263 k-ft

= n

P 6

2

=×=×=

M 3ft 39k-ft n ,exp

2

Close values, use the M n this time:

M
M

24
8.263

n ,exp

= = 2.9

n

M
M

n ,exp =

0.7815 λ+= 12.9

n

λ = 2.431

ρ= λρ

fd
fd

2.431 × 0.00458 × 60 × 6 sy

0.00201

= =

f

20000 × 0.0125 × 8

fd f

80.0175
86

×

ρ = = 0.00292 unconservative

f ,actual

×

Perform another iteration:

f
f

c
d

f
f

y

c
fd

ρ=α− ρ f s

fd

2

α= ε×
−×ε

c ε×

−×ε

2

c

2

c c

fd fd

− = 4.682 8 − 7.306

( ) ( ) ( )

2 2

8 c

2

− c

38 c 8 − c

c

c

f

c

− 5

ε= 1.71 57,000 =× = 310 f 0.00267 c c

f

c

2

c c 7.95

250

c 60

250

0.00201 = 4.682 × − 7.306 × ×− × 0.00458

( )

( )

2

8 − c 6

8 − c

( )

2

( )

2 3

0.00311 ×− = 8 c 0.02481 c × −− 8 c 0.03872 c

3 2

0.06353 c − 0.1954 c − 0.04976 c + 0.199 = 0

c = 1.069 in.

0.0125 1.069
81.069

×

ε= = 0.001928

cf

( )

−

1
3

0.001928
12

−

× 0.00267

0.36

β= =

0.001928
30.00267

1 −

×

0.0125 6
8

(

c

)

−

0.00889 0.005 0.9

ε= = > φ= s

( )

− c

0.0125
8

) (

)

ε= − c −=− 2 .00168 s

(

c