Environmental Engineering Reference
In-Depth Information
Integration over the circumference of the annular cross-section:
3
X
n
=
2
1
N
x
;
k
þ
1
¼
n
2
j
2
þ
4
n
2
j
1
þ
n
2
j
1
3
X
n
=
2
1
M
z
;
k
þ
1
¼
m
2
j
2
þ
4
m
2
j
1
þ
m
2
j
1
e) Calculation of the new (improved) value for concentric strain:
e
x
;
k
þ
1
¼ e
x
;
k
þ
e
x
;
k
e
x
;
k
1
N
x
;
k
N
x
;
k
1
N
x
N
x
;
k
e
x
;
0
¼
0
N
x
;
0
¼
0 applies for k
¼
1
;
Once N
x,k
N
x
, it is no longer necessary to continue the calculation. Otherwise, the
iteration process must be continued with k
!
k
þ
1 from step (b).
Figure 3.9 shows typical bending moment-curvature relationships for an annular cross-
section determined with the iteration procedure described above.
The following parameters were selected for this:
Concrete: C 35/45
Reinforcing steel: BSt 500
Outside diameter: r
a
¼
2.50m
Inside diameter: r
i
¼
2.00m
Percentage of longitudinal reinforcement (alternative):
r
s
¼
0.006/0.03
Normal forces (alternative): N
x
¼
0/
50 MN
Fig. 3.9 Bending moment-curvature relationships for an annular cross-section subjected to different
normal forces
