Example 2: Strengthening a beam with near-surface-mounted CFRP strips - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 75

The flexural strength is checked at mid-span for the maximummoment. In the following
calculations it is assumed that the maximum strain in the strip can be exploited. As the
strain in the strip ε LRd,max > f yd / E s , we shall continue to assume that the reinforcing steel
is yielding. Therefore, the tensile force in the reinforcing steel and the tensile force in the
externally bonded reinforcement are

30 : 79 ? 10 2

A s1 ? f yk
γ s

? 500

F s1d 1338 : 6kN

1 : 15

41 ? 200 ? 170 ? 10 3

F LRd ε LRd ; max ? A L ? E L 9 : 320 : 0kN

The prestrain at the level of the near-surface-mounted CFRP strips is calculated using
the prestrain in the reinforcement steel determined in Section 6.3:

d L d s1

d s1

690 653

653

ε L ; 0 ε s1 ; 0

? ε s1 ; 0 ε c ; 0

0 : 66 0 : 66 0 : 26 0 : 71 mm = m

?

The total strain in the cross-section at the level of the strips is therefore
ε L ; 0 ε LRd ; max 0 : 71 9 : 41 10 : 12 mm = m

Assuming a compressive strain in the concrete ε c < 2mm/m and that the compression
zone is contained completely within the slab, the compressive force in the concrete can
be expressed as follows according to Section 3.2:

F cd b ? x ? f cd ? α R b ? ξ ? d L ? f ck ? α cc

2
3 ? ε c

1

γ c ?

ε c
ε c ε L ; 0 ε LRd ; max

0 : 85
1 : 5 ?

2
3 ? ε c

1000 ? ? 690 ? 30 ? 1

Equilibrium of the internal forces enables the strain in the concrete to be subsequently
calculated:
F s1d F Ld F cd

Iteration results in ε c = 2.47mm/m. As this value is greater than the maximum
compressive strain in the concrete ε cu = 3.5 mm/m and also less than ε c = 2mm/
m, the above assumption was justified. The relative depth of the compression zone ξ and
the depth of the compression zone x can now be determined with the help of the strains.
As the depth of the compression zone is less than the depth of the slab, the above
assumption

- compression zone located fully within slab - was correct.

ε c
ε c ε L ; 0 ε L

2 : 47

ξ

41 0 : 196

2 : 47 0 : 71 9 :

x ξ ? d L 0 : 196 ? 690 135 : 4mm