Environmental Engineering Reference
In-Depth Information
There are a number of ways to analyse buckling of which two are described
here. The first is the ASCE [
13
] guidelines for regular polygon sections which
correlate the results of experiments to determine the limiting values of a/t where
a is the side length. For octagons, a = d/(1 ? H2). For octagonal sections with
specified maximum yield stress F
Y
(measured in MPa) the basic condition is:
p
F
Y
a
t
680
for r
a
\6
:
9MPa
\
ð
10
:
11
Þ
630
otherwise
where r
a
is the (axial) stress due to the axial load of the turbine and tower mass. If
the inequality holds, then F
Y
may be used for design and there will be no buckling.
If the left side is larger than the specified limits but still smaller than 960, then the
allowable stress considering the local buckling strength of the structure F
a
is
p
F
Y
1
:
42F
Y
1
:
0
4
:
34
10
4
t
for r
a
\6
:
9MPa
p
F
Y
F
a
\
ð
10
:
12
Þ
1
:
45F
Y
1
:
0
4
:
91
10
4
t
otherwise
The tests did not extend to values (a/t)HF
y
[ 960. By comparing this corre-
lation to the FEA determination of the linear buckling factor, the ratio of the load
required to induce elastic buckling divided by the maximum load, Clifton-Smith
and
t \ 4.3 9 10
-3
Wood
[
11
]
found
that
(
10.12
)
over-predicted
F
a
for
m
approximately. They suggested the following modification:
for t\4
:
3
10
3
ð
414t
0
:
7842
Þ
F
a
F
a
;
corr
\
ð
10
:
13
Þ
F
a
otherwise
which will be used here. Many structural codes use a ''capacity factor'', CF, which
can be thought of as the inverse of a safety factor. It is the ratio of the maximum
calculated stress to the maximum allowable stress, F
A
. For present purposes, F
A
is
the minimum of the yield stress and Eq.
10.12
or
10.13
:
F
A
¼
min
ð
F
Y
;
F
a
Þ
ð
10
:
14
Þ
and
CF
¼
r
max
=
F
A
ð
10
:
15
Þ
where r
max
is given by (
10.9
). Typically, CF B 0.6 if the ultimate tensile strength
is used and this value will be used here for illustrative design calculations. Note
that the implied safety factor of 1.67 is much less than allowed in the SLM,
implying that its use for tower design would result in a massively over-designed
tower. This remains a major unresolved issue for small turbine safety assessment.
At least two further quantities must be calculated. The first is the tower top
deflection which is obviously the maximum deflection of the turbine and tower. It
must remain small to justify the assumption that the structural shape does not alter
under the load and hence does not alter the load. The deflection, x in this case, can
be calculated according to standard beam theory as,
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