Environmental Engineering Reference
In-Depth Information
First of all we consider the statically determinate primary system. The symmetrical
loading results in symmetrical action effects in the circular ring beam (n
o,Gk
,m
R,Gk
and
n
0,Gk
). The antisymmetrical loading results in antisymmetrical action effects in the
circular ring beam (n
o,QW,k
,m
R,QW,k
,n
0,Gk
and v
QW,k
).
Added to this are the effects of the statically indeterminate internal forces. These result
from the compatibility between the deformations of the circular ring beam and the
adjoining zones of the tower shaft. The latter are considered as cylindrical shells whose
bending action effects can be calculated based on [64].
a) Symmetric action effect:
The symmetric loading results in a residual stress state with action effects “short-circuited”
at the circular ring beam (
D
m
R,Gk
and
D
n
R,Gk
).
N
Gk
2
p
r
o
n
o
;
Gk
¼
N
Gk
2 p
r
R
m
R
;Gk
¼
ð
r
u
r
o
Þ
h
R
2
X
2;Gk
r
u
r
R
D
m
R
;Gk
¼
X
1;Gk
r
u
r
R
D
n
R
;Gk
¼
X
1;Gk
N
Gk
2 p
r
u
b) Antisymmetric action effect (see also [77]):
The antisymmetric loading results in a residual stress state with circumferential harmonic
(cosine or sine form) action effects in the circular ring beam.
n
u
;Gk
¼
M
QW
;
k
p
r
o
n
o
;
QW
;
k
¼
cos
w
M
QW
;
k
p
r
2
R
m
R
;QW;
k
¼
ð
r
u
r
o
Þ cos
w
h
R
2
X
2;QW;
k
r
u
r
R
cos
D
m
R
;QW;
k
¼
X
1;QW;
k
w
M
QW
;
k
p
r
u
n
u
;QW;
k
¼
cos
w
V
QW;
k
p
r
R
sin
v
R
;QW;
k
¼
w
where
w
is the rotation angle about the tower axis (
w¼
0 at vertex on flexural compression
side).
