Flexural Strengthening of Beams and Slabs - Strengthening Design of Reinforced Concrete with FRP - page 135

f s = 200000 × 0.00223 = 446.23 MPa

( )

0.00311 ×−

−

c
c

37

540
200000

0.00076 0.0027 No yielding of topsteel

ε= = < =

s

( )

200

f s = 200000 × 0.00076 = 152 MPa

1
3

0.00164
12

−

× 0.00209

β= = 0.363

0.00164
30.00209

1 −

×

MM M

( ) ( )

u u 6

= = = 38.510 × −= −β +Ψ N mm Af dc Af dcAf −β +β− ( cd )

n s s f ffef ss

φ 0.65

( )

6

38.510 ×= × 307.9 446.23 × 163 − 0.363 × 69.07 + 0.85 × A f × 519.4

( )

× 200 − 0.363 × 69.07 + ×× × 307.9 152 (0.363 69.07 − 37)

20107767.52
77228.78

2 2

A f = = 260.4mm >> 195 mm (actual)

Iterate one more time:

α +=+ fbcAf Af Af

c s s s s f fcd

α= ε×
−×ε

c
dc

− ε×
−ε

c
dc

2 2

2

fcd fcd

( )

( )

2

3

f c

f c

c c

2

( c 7)

−

1.488 × − 0.738 × ×× + 33 200 c 307.9 × 622 ×

( )

2

200 − c (200 − c )

200 − c

(163 −

−

c
c

)

= 307.9 × 622 × + 260.4 × 519.4

(200 )

c = 65.06 mm
0.0015

c ε= <

0.003 O.K.

ε= 0.00226 < 0.0027 No yielding of tensionsteel

f s = 200000 × 0.00226 = 451.5MPa

( )

0.00311 ×−

−

c
c

37

0.000647 0.0027 No yielding of topsteel

ε= = <

s

( )

200

f s = 200,000 × 0.000647 = 129.34 MPa

1
3

0.0015

−

12 × 0.00209

β= = 0.36

0.0015
30.00209

1 −

×

MM M

( ) ( )

u u 6

= = = 38.510 × = A fd −β+Ψ c fd −β+ β− cAfcd ( ) n s s f ffef ss

φ 0.65