Flexural Strengthening of Beams and Slabs - Strengthening Design of Reinforced Concrete with FRP - page 123

No need to strengthen the positive moment region.
Negative moment section at interior support:

No. 13 @ 150 mm
No. of bars/m =

1000
150 = bars/m
Area of reinforcement/m = 133 mm 2 × 6.67 = 887 mm 2 /m
887
1000

6.67

A
b s s

-

ρ= = = 0.00507

× 175

f
f

400
25

y
c

ω=ρ= × 0.00507 = 0.0811

s

M
fbd

2 n

R =ω−ω= 0.59 0.07723 =

2

c

2

M n = 0.07723 × 25 × 1000 × 175 = 59,126,123.4N-mm/m = 59.13 kN-m/m

2 2

wL 17.884 × 5.5

un

M = = = 60.11 kN-m/m u

9 9

φ=× M 0.9 59.13 = 53.22 kN-m/m <= M 60.11 kN-m/m

n u

Thus, strengthening is needed at the interior negative region:

UseAslan 500 NSMCFRPTape.

Dimensions:16mmx2mm

f = 2068 MPa E = 124 GPa ε= 0.0167 fu f fu

Assume only DL at the time of strengthening:

2 2

wL 5.57 × 5.5

DL n

M = = = 18.72 kN-m/m

DL

9 9

fI
y

rgt

M =

cr

top
Assuming a singly reinforced section:

( )

1000 ××+ − ××

×+−×

200 100 8.51 1 887 25

y = = 97.6mm

( )

top

1000 200 8.51 1 887

3

1000 × 200

( )

2

( ) ( )

2

I = + 1000 × 200 × 100 − 97.6 .511 887 + − ××− 25 97.6

gt

12

4

= 702929149.2mm

8 4

= 7.02 × 10 mm

0.62 25 × 7.02 × 10

8

M = = 22326643.1N-mm/m = 22.33 kN-m/m > M

cr DL

97.6

Still thesectioniscracked underservice load in its priorhistory.

k = +ρ−ρ= 2 n nn

2

0.254