Civil Engineering Reference
In-Depth Information
Equilibrium of the internal forces enables the strain in the concrete to be subsequently
calculated:
F
s1
F
c
1338
2
c
ε
c
ε
c
0
:
85
5
?
ε
12
ε
c
:
6kN
1000
?
?
653
?
30
?
2
:
175
1
:
2
Solving the equation results in
ε
c
=
0.94mm/m. The relative depth of the compres-
sion 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
0
:
94
0
:
94
2
:
175
0
:
30
ξ
s
ε
c
x
ξ
?
d
s1
0
:
30
?
653
195
:
9mm
Using the coefficient
k
a
(for
2mm/m), i.e. the result according to Section 3.2, it is
now possible to determine the internal lever arm
z
s1
:
ε
c
>
8
ε
c
24
4
?
ε
c
8
0
:
94
24
4
?
0
:
94
0
:
35
k
a
a
k
a
?
ξ
?
d
s1
0
:
35
?
0
:
30
?
653
68
:
6mm
z
s1
d
s1
a
653
68
:
6
584
:
4mm
The moment at which the reinforcing steel begins to yield is therefore
M
Rdy
;
0
z
s1
?
F
s1
584
:
4
?
1338
:
6
780
:
3 kNm
The point at which the existing steel reinforcement reaches its yield point under the loads
in the strengthened condition (load case 3) is found by solving the parabolic moment
equation of Section 6.2:
s
s
8
2
4
l
2
4
l
2
M
Rdy
;
0
p
d
8
2
780
:
3
xM
Rdy
;
0
2
?
2
?
2
:
20 m
122
:
35
According to DAfStb guideline [1, 2] part 1, RV 6.1.3.3 (RV 2), or Fig. RV 6.12,
the analysis point should be determined taking into account the shifted tensile
force envelope. The
'
shift rule
'
is calculated according to DIN EN 1992-1-1
section 9.2.1.3:
a
l
z
?
cot
θ
cot
α
=
2
0
:
9
?
656
?
1
:
67
0
=
2
491
:
8mm
The angle of the strut for the shear design is taken here from Section 6.6. The analysis
point is therefore found to be at
x
=
1.71m.
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