Civil Engineering Reference
In-Depth Information
E s
E c
200 000
29 961 6 : 68
α s
E L
E c
170 000
29 961 5 : 67
α L
q
5 : 67 ? 0 : 00088 6 : 67 ? 0 : 0028
2
x 5 : 67 ? 0 : 00088 6 : 67 ? 0 : 0028
160
160 6 : 67 ? 0 : 0028 ?
140
160
2 ?
5 : 67 ? 0 : 00088 ?
? 160
29 : 36 mm
Using these figures it is now possible to determine the strain in the reinforcing steel:
α N 1
=
2
α N 1
x a
d L x a
d a
=
2
a
s Lr l b
ε
sRk l b κ VB ? κ bsk ?
?
0 : 25 1
=
2
140 29 : 36
160 29 : 36
a
sRk l b 1 : 0 ? 0 : 0036 ?
0
:
25
1
=
2
ε
0 : 155
1 : 35 mm = m
?
To calculate the admissible moment, the internal lever arms are still required, which can
be determined in simplified form via the compression zone:
z L h k a ? x h 0 : 4 ? x 160 0 : 4 ? 29 : 36 148 : 26 mm
z s d k a ? x h 0 : 4 ? x 140 0 : 4 ? 29 : 36 128 : 26 mm
Therefore, the admissible moment at the flexural crack nearest the support is
1
γ BA ε
1
γ S
a
LRk l b ? E Lm ? A L ? z L ?
a
sRk l b ? E s ? A s ? z s ?
m Rd l b ε
1
1 : 5
1
1 : 15
43 ? 10 2
? 10 3
m Rd l b
1
:
40 ? 170 ? 140 ? 148
:
26 ?
1
:
35 ? 200 ? 4
:
? 128
:
26 ?
3
:
29
13
:
32
16
:
61 kNm
=
m
The acting moment results from the position of the flexural crack closest to the support
and the 'shift rule', which in this analysis according to DAfStb guideline part 1 section
9.3.1.1 (RV 10) may be assumed to be h /2 for solid slabs:
2
h
2
p ?
x cr
p ? l
2 ?
h
2
16
:
95 ? 4
:
3
0
:
16
2
m Ed
x cr
x cr
0
:
39
?
2
2
2
0
:
16
2
16
:
95 ?
0
:
39
13
:
37 kNm
=
m
2
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