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Aerodynamic behaviour of one-way type hanging roofs
Journal of Wind Engineering and Industrial Aerodynamics, 13 (1983) 395--405
395
Elsevier Science Publishers B.V., A m s t e r d a m - - P r i n t e d in The Netherlands
AERODYNAMIC BEHAVIOUR OF ONE-WAY TYPE HANGING ROOFS E. KIMOTO and S. KAWAMURA Osaka City University
SUMMARY This paper is devoted to the aerodynamic behaviour of one-way type hanging roofs in the natural wind. Experiments were made on the mechanical characteristics and the aerodynamic response of this structure. The paper deals with the free vibration characteristics, and the response to low wind speeds, and makes comparison with theoretical results.
i. INTRODUCTION New kinds of structural materials have been developed and come into wide use in civil engineering and construction.
These advances have brought about new
types of structures such as hanging roofs [I], which have great potential for large spans.
However,
these structures are quite sensitive to wind force
[2,3,4] because of their small stiffness in comparison with usual structures. In particular,
one-way type hanging roofs with a single layer of cables always
have a small restoring force, which depends on the gravity alone.
On the con-
trary, other types of hanging roofs with double curvature or double layer cables have larger restoring forces, which depend on the extension of the material as well as gravity.
Moreover, one-way type hanging roofs have a simple shape and
their aerodynamic response can be treated theoretically. It is well known that these structures can be subjected to the wind-induced oscillations.
These aerodynamic problems can be classified into two parts:
(I) stability problems, and (2) response problems. roofs with single cable layers for aerodynamic
For one-way type hanging
stability,
some criteria have
already been presented from an engineering point of view [5,6]. were deduced from experimental results in wind tunnel tests, theoretical treatment
These criteria
the modified
based on the oscillating thin airfoil theory, and the
total potential energy of the system. Models used in wind tunnel tests have dimensions of the order of i00 ~n and cannot always reproduce the mechanical characteristics of a full scale structure. It seems more desirable
[7] to carry out experiments on a larger model with
similarity with the full scale structure
in the natural wind.
Furthermore, not
only stability problems but also response problems are important in design and construction. Thus, some experiments have been made on a large scale model of a one-way type hanging roof with a single layer of cables in the natural wind as a first step
0167-6105/83/$03.00
© 1983 Elsevier Science Publishers B.V.
396
in this kind of study. This paper describes some of the characteristics of tbi~ model and its response to low wind speeds. Finally, comparison will be made of these results, those in wind tunnel tests, and the stability criteria mentioned above. 2. EXPERIMENT 2.1 Model A one-way type hanging roof with a single layer of cables
and walls has been
set up at the Osaka-Nanko Wind Laboratory, Osaka City University. Good facilities for experimental tests of flexible structures exist in this Laboratory as shown in Figure I. Its surroundings are the very flat, reclaimed land of the Osaka Bay shown in Figure 2. There are factories with average roof heights o[ about I0 m along the northern road.
At greater distances up to 0.5 km or so in
the western sector, there are groups of tall buildings which are about 40 m in height.
fact°ries
I
~euma tic Structure Dome--.
I
fact°ties
~
I
Towersquare withsectionMeasurement~Station /
T~wer for H~nglng Roofs Windl60mMeasurement
Figure 1
The Osaka-Nanko Wind Laboratory, Osaka City University /..~x~J~.j.~.S/~/i-"
I Osaka City
The Osaka Bay
Figure 2
Surroundings of the Laboratory
397 As shown in Figure 3, the dimensions 5 m breadth and 2.5 m height.
of the hanging roof model are 18 m span,
The roof is covered with polyester sheet, which
is 0.6 mm in thickness and 0.7 kgf/m 2 in weight.
This sheet is clamped by thin
iron plates at the west and east edges and supported with 4 mm diameter wire rope along the north and south edges. N
The initial tension can be controlled.
Wire Strain Gauges No.3
~
~ ' m a g n e t i c lDispiacement ITransducer.
anemometer - ---
[r [I /~
H FI ~
'l~nhagnetic i _ l
[
Displacement i~ucer |
I S
it O p ~ t i ~ ~ I i] u x s p l a c e m e n ~ II H "_Transdueer~]~ ~ L Wire~rain Gau~e No.l , Wire Strain ~ g e [ 4 5m l 4 5m I 4.5m 1 4.5m 1
l
i I
Wire Strain Gauges No.4
" II II
1
[ 7.5~:
, ] No.2
~
~
.
.
.
.
.
18.Ore
(a) plan
anemometer
(b) Section Figure 3 2.2 Experimental
Model of one-way type hanging roofs with walls
method
In the experiments,
the experimental
apparatus
described following has been
used. The wind speed and direction were measured by an anemometer mounted on a 2.5 m mast lying 7.5 m west of model.
The wire strain gauges were used to reveal the
change in tension in the wire rope at the four corners,
i.e. both ends of each
rope. Response parameters of displacement one.
such as displacement
transducers;
and period were measured by two kinds
i.e. an electromagnetic
transformer and an optical
These transducers were installed at three representative
which were at the i/4, 2/4 and 3/4 points of span.
roof points,
An oscillograph was used to
record them. Also, the behaviour projecting
at the 2/4 point was filmed by a 8 mm cine-camera.
these pictures on a screen, displacements
After
and periods were measured
with a rule and stop watch.
3. RESULTS Experimental aerodynamic
runs were carried out for both the free oscillation
behaviour.
However,
and the
strong winds have not yet been observed during
398
the experiment.
Therefore, these results contain no data on the response in
strong winds, but cover the low range of wind speed only. Figure 4 shows an example of free oscillation induced by impact loading. A typical example of the behaviour under natural wind is s h o ~ records were obtained from the oscillograph.
in Figure 5. These
Figure 6, taken by a 8 mm cine-
camera, shows that the roofs were oscil]ating about the deflected state, i.e. the neutral state.
Moreover, this figure reveals clearly the initial state in
contrast to the osci]lograph records•
/ ~
~
~
~ ~
/
\ V
, -10p ~ +fOp
.
.
.
Wire Strain Gauge No.2 r -10p
Displacement a t ~2 L +2cmLower Process " ~ _ ~ ; p e r Process 3 Displacement at ~ L ~ isec ~ •
r~
J
Wire Strain Gauge No.l .
/
.
Figure 4
Direction ~ S E ~ No.I ~ No.2
A record of free oscillation
~ bm ESE
_____,. ~ ~ _
E
No.3 N o . 4
-2 L
~
---7.0m/s
4 L ve±ocity o&.JmL . ~2 7 m / s Figure 5
~-~ 6.7m/s --
~
-
5 3 /s
L Isec ~ A record of roof
behaviour under natural wind
399
Displacement
3001
(mm)
2OO
I 0
Time (sec)
;o
2'o
4'o
;o
-
-40 Figure 6 D i s p l a c e m e n t at 2/4 L (a record taken by a 8 m m cine-camera)
3.1 C h a r a c t e r i s t i c s of the model The natural period of the model was found to be 1.4 sec from some runs.
It is
always better to estimate this value in the initial state because there exists no m e a n component of v e r t i c a l displacement due to wind force.
It can be seen in Figure 4 that, the decrement fair difference
of'
extreme
between the upper and the lower positions
Figure 7 shows the relation between the damping
a mpljt1~des exhibits of the initial
coefficient
and amplitude
2/4 L. Figures 7(a) and (b) correspond
to the damping coefficient
and the lower positions
It can be seen that the damping
efficient
respectively.
varies with the initial displacement,
large in comparison
although
with those of most hanging roofs.
state. at
in the upper
the values
co-
seem to be
a
400
o o
o
•
Og
u
•
..
o u
.." oo
o eo°
,- " -:-. I: :'.'"
I
C~
•
0
°
0
0 o
-,.q
©
D
o k~
•
0 0 0
I
I
C"-I 0
.
."%...~
401
3.2 Response to wind Attention is confined to the wind direction sectors, WNW to WSW and ENE to ESE.
Further,
constant.
On
the problem is simplified here by assuming that the wind speed is the basis of these conditions,
the relations between wind speed,
amplitude and its period are obtained from some experimental records. The variation of amplitude with wind speed is given in
Figure 8.
the variation of amplitude with its period is given in Figure 9.
Similarly,
The enveloping
line can be drawn in by eye, in spite of a large amount of scatter in these experimental values.
These diagrams reveal the trend of amplitude variation
with wind speed, and show a gradual increase within a certain wind speed range and a rapid growth beyond it.
Moreover,
the trend is for the amplitude to
increase with period and reach a peak at a period larger than the natural period. The displacement velocity, which means the velocity of the roof membrane,
is
deduced from the amplitude and the period. The displacement velocity is plotted versus period in Figure i0.
The envelop-
ing line shows the trend that the displacement velocity has a similar peak as the period.
A similar trend is seen in the relation between wind speed and
displacement velocity,
as far as these results indicate.
4. DISCUSSION 4.1 Mechanical characteristics In a model where the initial tension is only controlled by the weight of the roof, the mechanical characteristics
such as damping and restoring force seem to
vary with the sign and the extent of displacement.
This can be seen by the fact
that the roof is oscillating about the neutral state and its dominant period is slightly larger than the natural period in the initial state, as illustrated in Figures 6 to 9.
It is notable that the damping coefficient varies with the sign
and the magnitude of amplitude.
In the structural design of these roofs, it
seems worthwhile to give adequate consideration to these characteristics.
4.2 Response to wind The natural wind varies not only in speed but also in direction as time advances. effects.
The response has been influenced by these phenomena and by hysteresis However,
some relations between wind speed, amplitude, etc., can be
established. Apart from some amount of scatter in experimental values, the response curve in Figure 8 is not in conflict with the experimental results in wind tunnel tests.
The amplitude increases rapidly beyond a certain wind velocity which has
been called the starting velocity. qualitatively.
Thus, previous work has been confirmed
402
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v
2 ~d
~oX Qe
el
H
•
•
•
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•
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,~
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,,-4
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c~
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~
~8
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-M
°
. •
oO
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0
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•
• m
•
•
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•
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0 •
abe
•
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eo
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- o...a ~ _.o
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oo
_ ~
I:::: o -M
•
.M
6 0
OX~
•
c~ •
oo
::s
.= I
t
l
I
403
Displacement
Velocity
(~/sec)
400 /
\
,
/
g
/ •
\ \
•
\ \Q
\ \ \
300
~
• 0
V
: Values taken by 8mm Cine Camera : Values taken by Oscillograph
o 0oo
O
200
I• I
• •
.~.
j"
0°
•
i00
0
•
•
e
•
•
O ee
OO
e~o
eeo O
0 0
Q
° 0 ~eSr OeA
-
~
ee o o 0
°0
o.i o . . 8 , o e
°ee
0
•
$
.
•
o
o
0
0
•
Period i
i
|
I
I
I
I
1
2
3
4
5
6
7
Figure I0
VariatioD
(sec)
of displacement velocity with period
404
Both amplitude and displacement velocity show a tendency to have a dominant period in these experiments.
This behaviour would be relevant to the various
kinds of problems such as fatigue and tear in the roof sheeting.
However, more
attention should be paid to this behaviour in future, owing to the lack of aata in strong wind.
4.3 The starting velocity The starting and the peak velocities have alreaay been given as aerodynamic criteria of one-way type hanging roofs.
For the model in these experiments,
the
values of two velocities are deduced according to the calculation proceaure in the previous work.
The value of starting velocity is 2.8 to 3.9 m/sec and the
value of peak velocity is 3.0 to 15.1 m/sec. On the other hand, the starting velocity can be found to be 2.8 m/sec from Figure 8.
It was observed that the roof was oscillating with large amplituae
and experienced divergence from 11:14 to 11:47 on 19 October 1979. Unfortunately, these phenomena were not recorded. However,
it is encouraging that the experimental data was close to the theore~
ical values.
Therefore,
this paper shows that theoretical treatment is useful
for the prediction of aerodynamic stability criteria,
in spite of the small
number of tests.
5. CONCLUSIONS The following conclusions are deduced for the aerodynamic behaviour of one-way hanging roofs with a single layer of cables. The damping coefficient and the restoring force seem to vary with the sign and the extent of amplitude in the structure, when the initial tension is only controlled by weight of the roof. In a full-scale structure under natural wind action,
the amplitude is shown to
increase rapidly beyond a certain wind velocity, which is known as the starting velocity. The results of this experiment show that previous theoretical treatment is useful for the prediction of aerodynamic stability criteria. It is necessary to verify the occurrence of a peak velocity in future experiments.
It is desirable to establish the relationship between the roof displace-
ment and the strain in the wire rope.
Also, it is intended to test a model in
which the initial tension is controlled by the weight and the extension of cables.
ACKNOWLEDGEMENT The authors are grateful to the Department of Education and other parties for the financial support given to these experiments and facilities.
405
REFERENCES i. N. Esquillan and Y. Sailard, Hanging roofs, North Holland Pub. Comp., Amsterdam, 1963. 2. A. Siev, Experimental study of flutter in suspended roofs, Bull I.A.S.S., 23, (1965), 3-10. 3. S. Taneda, Waving motions of flags, J. Phys. Soc. Japan, 24, (1968), 392-401. 4. H.P.A.H. Irwin and R.L. Wardlaw, A wind tunnel investigation of a rectractable fabric roof for the Montreal Olympic Stadium, Proc. 5th Int. Conf. on Wind Eng., Fort Collins, 1979. 5. S. Kawamura and E. Kamoto, Aerodynamic stability of one-way type hanging roofs in smooth uniform flow, Proc. 3rd Int. Conf. on Wind Effects on Buildings and Structures, Tokyo, 1971, 1067-1076. 6. S. Kawamura and E. Kimoto, Aerodynamic stability criteria of one-way type hanging roofs in smooth uniform flow, Proc. 5th Int. Conf. on Wind Eng., Fort Collins, 1979. 7. B.V. Tryggvason, Aeroelastic modeling of pneumatic and tensioned fabric structures, Proc. 5th Int. Conf. on Wind Eng., Fort Collins, 1979.
395
Elsevier Science Publishers B.V., A m s t e r d a m - - P r i n t e d in The Netherlands
AERODYNAMIC BEHAVIOUR OF ONE-WAY TYPE HANGING ROOFS E. KIMOTO and S. KAWAMURA Osaka City University
SUMMARY This paper is devoted to the aerodynamic behaviour of one-way type hanging roofs in the natural wind. Experiments were made on the mechanical characteristics and the aerodynamic response of this structure. The paper deals with the free vibration characteristics, and the response to low wind speeds, and makes comparison with theoretical results.
i. INTRODUCTION New kinds of structural materials have been developed and come into wide use in civil engineering and construction.
These advances have brought about new
types of structures such as hanging roofs [I], which have great potential for large spans.
However,
these structures are quite sensitive to wind force
[2,3,4] because of their small stiffness in comparison with usual structures. In particular,
one-way type hanging roofs with a single layer of cables always
have a small restoring force, which depends on the gravity alone.
On the con-
trary, other types of hanging roofs with double curvature or double layer cables have larger restoring forces, which depend on the extension of the material as well as gravity.
Moreover, one-way type hanging roofs have a simple shape and
their aerodynamic response can be treated theoretically. It is well known that these structures can be subjected to the wind-induced oscillations.
These aerodynamic problems can be classified into two parts:
(I) stability problems, and (2) response problems. roofs with single cable layers for aerodynamic
For one-way type hanging
stability,
some criteria have
already been presented from an engineering point of view [5,6]. were deduced from experimental results in wind tunnel tests, theoretical treatment
These criteria
the modified
based on the oscillating thin airfoil theory, and the
total potential energy of the system. Models used in wind tunnel tests have dimensions of the order of i00 ~n and cannot always reproduce the mechanical characteristics of a full scale structure. It seems more desirable
[7] to carry out experiments on a larger model with
similarity with the full scale structure
in the natural wind.
Furthermore, not
only stability problems but also response problems are important in design and construction. Thus, some experiments have been made on a large scale model of a one-way type hanging roof with a single layer of cables in the natural wind as a first step
0167-6105/83/$03.00
© 1983 Elsevier Science Publishers B.V.
396
in this kind of study. This paper describes some of the characteristics of tbi~ model and its response to low wind speeds. Finally, comparison will be made of these results, those in wind tunnel tests, and the stability criteria mentioned above. 2. EXPERIMENT 2.1 Model A one-way type hanging roof with a single layer of cables
and walls has been
set up at the Osaka-Nanko Wind Laboratory, Osaka City University. Good facilities for experimental tests of flexible structures exist in this Laboratory as shown in Figure I. Its surroundings are the very flat, reclaimed land of the Osaka Bay shown in Figure 2. There are factories with average roof heights o[ about I0 m along the northern road.
At greater distances up to 0.5 km or so in
the western sector, there are groups of tall buildings which are about 40 m in height.
fact°ries
I
~euma tic Structure Dome--.
I
fact°ties
~
I
Towersquare withsectionMeasurement~Station /
T~wer for H~nglng Roofs Windl60mMeasurement
Figure 1
The Osaka-Nanko Wind Laboratory, Osaka City University /..~x~J~.j.~.S/~/i-"
I Osaka City
The Osaka Bay
Figure 2
Surroundings of the Laboratory
397 As shown in Figure 3, the dimensions 5 m breadth and 2.5 m height.
of the hanging roof model are 18 m span,
The roof is covered with polyester sheet, which
is 0.6 mm in thickness and 0.7 kgf/m 2 in weight.
This sheet is clamped by thin
iron plates at the west and east edges and supported with 4 mm diameter wire rope along the north and south edges. N
The initial tension can be controlled.
Wire Strain Gauges No.3
~
~ ' m a g n e t i c lDispiacement ITransducer.
anemometer - ---
[r [I /~
H FI ~
'l~nhagnetic i _ l
[
Displacement i~ucer |
I S
it O p ~ t i ~ ~ I i] u x s p l a c e m e n ~ II H "_Transdueer~]~ ~ L Wire~rain Gau~e No.l , Wire Strain ~ g e [ 4 5m l 4 5m I 4.5m 1 4.5m 1
l
i I
Wire Strain Gauges No.4
" II II
1
[ 7.5~:
, ] No.2
~
~
.
.
.
.
.
18.Ore
(a) plan
anemometer
(b) Section Figure 3 2.2 Experimental
Model of one-way type hanging roofs with walls
method
In the experiments,
the experimental
apparatus
described following has been
used. The wind speed and direction were measured by an anemometer mounted on a 2.5 m mast lying 7.5 m west of model.
The wire strain gauges were used to reveal the
change in tension in the wire rope at the four corners,
i.e. both ends of each
rope. Response parameters of displacement one.
such as displacement
transducers;
and period were measured by two kinds
i.e. an electromagnetic
transformer and an optical
These transducers were installed at three representative
which were at the i/4, 2/4 and 3/4 points of span.
roof points,
An oscillograph was used to
record them. Also, the behaviour projecting
at the 2/4 point was filmed by a 8 mm cine-camera.
these pictures on a screen, displacements
After
and periods were measured
with a rule and stop watch.
3. RESULTS Experimental aerodynamic
runs were carried out for both the free oscillation
behaviour.
However,
and the
strong winds have not yet been observed during
398
the experiment.
Therefore, these results contain no data on the response in
strong winds, but cover the low range of wind speed only. Figure 4 shows an example of free oscillation induced by impact loading. A typical example of the behaviour under natural wind is s h o ~ records were obtained from the oscillograph.
in Figure 5. These
Figure 6, taken by a 8 mm cine-
camera, shows that the roofs were oscil]ating about the deflected state, i.e. the neutral state.
Moreover, this figure reveals clearly the initial state in
contrast to the osci]lograph records•
/ ~
~
~
~ ~
/
\ V
, -10p ~ +fOp
.
.
.
Wire Strain Gauge No.2 r -10p
Displacement a t ~2 L +2cmLower Process " ~ _ ~ ; p e r Process 3 Displacement at ~ L ~ isec ~ •
r~
J
Wire Strain Gauge No.l .
/
.
Figure 4
Direction ~ S E ~ No.I ~ No.2
A record of free oscillation
~ bm ESE
_____,. ~ ~ _
E
No.3 N o . 4
-2 L
~
---7.0m/s
4 L ve±ocity o&.JmL . ~2 7 m / s Figure 5
~-~ 6.7m/s --
~
-
5 3 /s
L Isec ~ A record of roof
behaviour under natural wind
399
Displacement
3001
(mm)
2OO
I 0
Time (sec)
;o
2'o
4'o
;o
-
-40 Figure 6 D i s p l a c e m e n t at 2/4 L (a record taken by a 8 m m cine-camera)
3.1 C h a r a c t e r i s t i c s of the model The natural period of the model was found to be 1.4 sec from some runs.
It is
always better to estimate this value in the initial state because there exists no m e a n component of v e r t i c a l displacement due to wind force.
It can be seen in Figure 4 that, the decrement fair difference
of'
extreme
between the upper and the lower positions
Figure 7 shows the relation between the damping
a mpljt1~des exhibits of the initial
coefficient
and amplitude
2/4 L. Figures 7(a) and (b) correspond
to the damping coefficient
and the lower positions
It can be seen that the damping
efficient
respectively.
varies with the initial displacement,
large in comparison
although
with those of most hanging roofs.
state. at
in the upper
the values
co-
seem to be
a
400
o o
o
•
Og
u
•
..
o u
.." oo
o eo°
,- " -:-. I: :'.'"
I
C~
•
0
°
0
0 o
-,.q
©
D
o k~
•
0 0 0
I
I
C"-I 0
.
."%...~
401
3.2 Response to wind Attention is confined to the wind direction sectors, WNW to WSW and ENE to ESE.
Further,
constant.
On
the problem is simplified here by assuming that the wind speed is the basis of these conditions,
the relations between wind speed,
amplitude and its period are obtained from some experimental records. The variation of amplitude with wind speed is given in
Figure 8.
the variation of amplitude with its period is given in Figure 9.
Similarly,
The enveloping
line can be drawn in by eye, in spite of a large amount of scatter in these experimental values.
These diagrams reveal the trend of amplitude variation
with wind speed, and show a gradual increase within a certain wind speed range and a rapid growth beyond it.
Moreover,
the trend is for the amplitude to
increase with period and reach a peak at a period larger than the natural period. The displacement velocity, which means the velocity of the roof membrane,
is
deduced from the amplitude and the period. The displacement velocity is plotted versus period in Figure i0.
The envelop-
ing line shows the trend that the displacement velocity has a similar peak as the period.
A similar trend is seen in the relation between wind speed and
displacement velocity,
as far as these results indicate.
4. DISCUSSION 4.1 Mechanical characteristics In a model where the initial tension is only controlled by the weight of the roof, the mechanical characteristics
such as damping and restoring force seem to
vary with the sign and the extent of displacement.
This can be seen by the fact
that the roof is oscillating about the neutral state and its dominant period is slightly larger than the natural period in the initial state, as illustrated in Figures 6 to 9.
It is notable that the damping coefficient varies with the sign
and the magnitude of amplitude.
In the structural design of these roofs, it
seems worthwhile to give adequate consideration to these characteristics.
4.2 Response to wind The natural wind varies not only in speed but also in direction as time advances. effects.
The response has been influenced by these phenomena and by hysteresis However,
some relations between wind speed, amplitude, etc., can be
established. Apart from some amount of scatter in experimental values, the response curve in Figure 8 is not in conflict with the experimental results in wind tunnel tests.
The amplitude increases rapidly beyond a certain wind velocity which has
been called the starting velocity. qualitatively.
Thus, previous work has been confirmed
402
o
v
2 ~d
~oX Qe
el
H
•
•
•
O0
•
X .i
i
,~
¢i0
•
.~4
x e
t 0 v
•
0
0
.~
,,-4
.M
c~
0 0
I
i
I
~
oU'3
~
~8
"0
-M
°
. •
oO
O0 °° °°
0
• O0
•
• m
•
•
0
iJ
• •
•
~D
0 •
abe
•
0o
eo
• 0
0
0
0
•
- o...a ~ _.o
g0o
oo
_ ~
I:::: o -M
•
.M
6 0
OX~
•
c~ •
oo
::s
.= I
t
l
I
403
Displacement
Velocity
(~/sec)
400 /
\
,
/
g
/ •
\ \
•
\ \Q
\ \ \
300
~
• 0
V
: Values taken by 8mm Cine Camera : Values taken by Oscillograph
o 0oo
O
200
I• I
• •
.~.
j"
0°
•
i00
0
•
•
e
•
•
O ee
OO
e~o
eeo O
0 0
Q
° 0 ~eSr OeA
-
~
ee o o 0
°0
o.i o . . 8 , o e
°ee
0
•
$
.
•
o
o
0
0
•
Period i
i
|
I
I
I
I
1
2
3
4
5
6
7
Figure I0
VariatioD
(sec)
of displacement velocity with period
404
Both amplitude and displacement velocity show a tendency to have a dominant period in these experiments.
This behaviour would be relevant to the various
kinds of problems such as fatigue and tear in the roof sheeting.
However, more
attention should be paid to this behaviour in future, owing to the lack of aata in strong wind.
4.3 The starting velocity The starting and the peak velocities have alreaay been given as aerodynamic criteria of one-way type hanging roofs.
For the model in these experiments,
the
values of two velocities are deduced according to the calculation proceaure in the previous work.
The value of starting velocity is 2.8 to 3.9 m/sec and the
value of peak velocity is 3.0 to 15.1 m/sec. On the other hand, the starting velocity can be found to be 2.8 m/sec from Figure 8.
It was observed that the roof was oscillating with large amplituae
and experienced divergence from 11:14 to 11:47 on 19 October 1979. Unfortunately, these phenomena were not recorded. However,
it is encouraging that the experimental data was close to the theore~
ical values.
Therefore,
this paper shows that theoretical treatment is useful
for the prediction of aerodynamic stability criteria,
in spite of the small
number of tests.
5. CONCLUSIONS The following conclusions are deduced for the aerodynamic behaviour of one-way hanging roofs with a single layer of cables. The damping coefficient and the restoring force seem to vary with the sign and the extent of amplitude in the structure, when the initial tension is only controlled by weight of the roof. In a full-scale structure under natural wind action,
the amplitude is shown to
increase rapidly beyond a certain wind velocity, which is known as the starting velocity. The results of this experiment show that previous theoretical treatment is useful for the prediction of aerodynamic stability criteria. It is necessary to verify the occurrence of a peak velocity in future experiments.
It is desirable to establish the relationship between the roof displace-
ment and the strain in the wire rope.
Also, it is intended to test a model in
which the initial tension is controlled by the weight and the extension of cables.
ACKNOWLEDGEMENT The authors are grateful to the Department of Education and other parties for the financial support given to these experiments and facilities.
405
REFERENCES i. N. Esquillan and Y. Sailard, Hanging roofs, North Holland Pub. Comp., Amsterdam, 1963. 2. A. Siev, Experimental study of flutter in suspended roofs, Bull I.A.S.S., 23, (1965), 3-10. 3. S. Taneda, Waving motions of flags, J. Phys. Soc. Japan, 24, (1968), 392-401. 4. H.P.A.H. Irwin and R.L. Wardlaw, A wind tunnel investigation of a rectractable fabric roof for the Montreal Olympic Stadium, Proc. 5th Int. Conf. on Wind Eng., Fort Collins, 1979. 5. S. Kawamura and E. Kamoto, Aerodynamic stability of one-way type hanging roofs in smooth uniform flow, Proc. 3rd Int. Conf. on Wind Effects on Buildings and Structures, Tokyo, 1971, 1067-1076. 6. S. Kawamura and E. Kimoto, Aerodynamic stability criteria of one-way type hanging roofs in smooth uniform flow, Proc. 5th Int. Conf. on Wind Eng., Fort Collins, 1979. 7. B.V. Tryggvason, Aeroelastic modeling of pneumatic and tensioned fabric structures, Proc. 5th Int. Conf. on Wind Eng., Fort Collins, 1979.