Example 1: Strengthening a slab with externally bonded CFRP strips - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 47

The strain in the strip is unknown and so the tensile force in the CFRP strip must be
described in relation to this:

F Ld a L ? ε L ? E L ε L ? 140 ? 170 000
The prestrain condition at the level of the strip is 0.88mm/m, as with the simplified

analysis. The compressive force in the concrete can be calculated as follows by assuming
a compressive strain in the concrete

ε L,0 =

3.5mm/m according to Section 3.2:
F cd b ? x ? f cd ? α R b ? ξ ? d L ? f ck ? α cc

ε c =

2
3 ? ε c

1

γ c ?

ε c

0 : 85
1 : 5 ?

2
3 ? ε

1000 ? ? 160 ? 20 ? 1

ε ε ε

c L L ; 0 c

Equilibrium of the internal forces results in an equation to calculate the strain in the strip:
F s1d

F Ld F cd

192 : 61 ? 10 3 ε L ? 87 : 5 ? 170 000

5
3 : 5 0 : 88 ε L

3 : 0 85

1 : 5 ?

: 2

3 ? 3 : 5

1000 ?

? 160 ? 20 ?

1

Iteration results in ε L = 8.47mm/m. As this value is less than the ultimate strain in the

strip (i.e. 10.78mm/m), the above assumption was justi ed. The relative depth of

the compression zone can now be determined with the help of the strains:

ε Lud =

ε c
ε c ε L ; 0 ε L

3 : 5
3 : 5 0 : 88 8 : 47 0 : 27

ξ

We can use the coef cient k a (for ε c < 2mm/m), which is the result according to Section
3.2, to determine the internal lever arms:

3 ? 3 : 5 2 3 ? ε 4 ? ε c 2

6 ? ε

c

4 ? 3 : 5 2
6 ? 3 : 5 2

k a

4 ? ε c

4 ? 3 : 5 0 : 42

c

a k a ? ξ ? d L 0 : 42 ? 0 : 27 ? 160 18 : 11 mm

z s1 d s1 a 140 18 : 11 121 : 89 mm

z L h a 160 18 : 11 141 : 89 mm

The moment capacity of the strengthened reinforced concrete cross-section is
therefore
m Rd z s1 ? F s1d z L ? a L ? ε L ? E L 121 : 89 ? 192 : 61 ? 10 3
141 : 89 ? 8 : 47 ? 140 ? 170 ? 10 6 52 : 09 kNm = m

As the moment capacity is greater than the acting moment of 39.18 kNm/m, the flexural
strength is veri ed.