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TRANSCRIPT
13th International Symposium on Advanced Science and Technology in Experimental Mechanics, Otc.30-Nov.2, 2018, Kaohsiung, Taiwan
1
Wind Tunnel Study of Peak Wind Force Coefficients for Designing Cladding/Components of Gable-Roofed
Open-Type Structures
Yuki TAKADATE1 and Yasushi UEMATSU1
1 Department of Architecture and Building Science, Tohoku University, Sendai 980-8579, Japan
Abstract: The present paper discusses the peak wind force coefficients for designing the claddings and its immediately
supporting structures of open type membrane structures based on a wind tunnel experiment. Three types of gable-end
configurations, i.e. enclosed, open and partially-enclosed (semi-open) types are tested. The wind tunnel experiment is carried
out in two kinds of turbulent boundary layers corresponding to open-country and urban terrains. The wind pressures are
measured simultaneously at many points both on the external and internal surfaces. First, the distributions of mean wind force
coefficients are investigated to understand the characteristics of the wind forces, focusing on the effects of gable wall
configuration. Then, the maximum and minimum peak wind force coefficients irrespective of wind direction are examined.
Furthermore, the characteristics of internal pressures on open and semi-open type structures are investigated. Based on the
results, an estimation method for evaluating the peak wind force coefficients for open and semi-open type structures is proposed.
Keywords: Wind Tunnel Experiment, Peak Wind Force Coefficient, Internal Pressure, Open-Type Gable-Roofed Structure
1. Introduction
Framed membrane structures with gable roofs are often
constructed for sports facilities and temporary buildings in
Japan. Three kinds of gable wall configurations, i.e. open,
semi-open (partially-enclosed) and enclosed types, are used
for these structures. Open and semi-open type structures refer
to the structures with no gable wall and only one gable wall,
respectively. Being light and flexible, these structures are
vulnerable to dynamic wind actions. The external pressure
coefficients on enclosed type structures are specified in codes
and standards, e.g. the Notification No. 1454 and No. 1458
of the Ministry of Construction of Japan (2000) and the AIJ
Recommendations for Loads on Buildings [1]. However, no
specifications exist for open type structure without gable
walls.
In our previous study [2], the wind loads for the main wind
force resisting systems were investigated in detail. However,
the peak wind force coefficients on the open type structures
have not been investigated sufficiently. In the present study,
focus is on the wind force coefficients for
cladding/components. In the practical design, the design
wind force coefficients for cladding/components are
specified based on the peak wind force coefficients obtained
from wind tunnel experiments. However, it is quite difficult
to make the wind tunnel models of open type structures
because of the difficulties in model making. The model
thickness should be small enough to reproduce the flow
around the structure appropriately. At the same time, the
pressure taps should be arranged properly both on the outside
and inside of the building model in order to measure the
external and internal pressures at many points
simultaneously, providing the net wind forces. Therefore,
provision of design wind force coefficients for open type
structures is important for the design of such structures.
In the present study, the peak wind force coefficients for
cladding/components of open type structures with gable
roofs are investigated in two kinds of turbulent boundary
layers. The characteristics of internal pressures on the open
type structures are examined in detail. Finally, an estimation
method of peak wind force coefficients on open type
structures from the peak external pressure coefficients on
enclosed type structures is proposed.
2. Experimental apparatus and procedures
2.1 Model buildings
The building model of the present study is a framed
membrane structure with gable roof. Fig. 1 shows the gable-
end configurations of model buildings investigated in the
present study. Fig. 2 shows the geometry of the wind tunnel
model. The span B, the length L and the mean roof height H
are 42 m, 42 m and 10.3 m, respectively. The roof pitch is
17.5o. The values of these geometric parameters are
determined based on a survey of practical membrane
structures with gable roofs that have been constructed in
Japan.
2.2 Wind tunnel model
The wind tunnel model is made of thin plastic plates with a
geometric scale of 1/200. Figs. 3 and 4 show the layout of
(a) Enclosed type (b) Semi-open
type (c) Open type
Fig. 1 Gable-end configurations
Fig. 2 Model building Fig. 3 Pressure taps
Fig. 4 Cross section of the wind tunnel model
q = 0o q = 0o q = 0o
B
h DH
q =0o
q =180o Line
1
2
3
4
5
6
7
q
3.18
1
100 100 4
210
12.51
2.5
525
5
35
31.3
25 5
525
2525
255
525
2525
4
17.5o
Pressure taps
13th International Symposium on Advanced Science and Technology in Experimental Mechanics, Otc.30-Nov.2, 2018, Kaohsiung, Taiwan
2
pressure taps on the roof and the cross section of the wind
tunnel model, respectively. Sixteen pressure taps are
installed both on the external and internal surfaces along each
of the seven lines (Lines 1 – 7). As shown in Fig. 4, the model
has sandwich structure with a thickness of 4 mm, in which
bronze tubes introducing the tap pressures to the pressure
transducers are installed.
2.3 Wind tunnel flow
The wind tunnel experiment was carried out in a closed-type
boundary-layer wind tunnel, which has a working section 2.0
m high, 3.0 m wide and 25 m long. Two kinds of turbulent
boundary layers corresponding to open-country and
suburban terrains were generated on the wind tunnel floor.
There flows are called Flows I and II, hereafter. Fig. 5 shows
the vertical profiles of mean wind velocity Uz, normalized by
U1000, and turbulence intensity for these flows. The wind
velocity at the mean roof height UH is approximately 6 m/s.
The corresponding Reynolds number is approximately
84,000. The power law exponent for the mean wind
velocity profile and the turbulence intensity IuH at the mean
roof height H are respectively 0.15 and 15.6 % for Flow I and
0.27 and 22.4 % for Flow II. The wind direction q is changed
from 0o to 180o with an increment of 5o (see Fig. 3). It should
be noted that ‘q = 0o’ for the semi-open type structure
represents a wind direction normal to the opened gable wall,
as shown in Fig. 1(b).
2.4 Experimental procedure
The pressure taps installed on the wind tunnel model were
connected to pressure transducers via bronze tube of 0.5 mm
ID and PVC tube of 1.4 mm ID. The total length of the tube
was 1 m. Wind pressures at all pressure taps were measured
simultaneously at a sampling frequency of 1 kHz for
approximately 14 sec, which corresponds to 10 min in full
scale. The measurement was repeated 10 times under the
same condition. The tubing effect was compensated in the
frequency domain by using the frequency response function
of the measuring system that had been obtained beforehand.
The wind pressure obtained at each pressure tap is
normalized to wind pressure coefficient Cp, defined by the
reference pressure qH (=UH2/2, with being the air density)
at the mean roof height H. The wind force coefficient Cf is
defined by the difference between the external and internal
pressure coefficients. Note that the internal pressure of
enclosed type is assumed to be zero, because it is difficult to
generalize the condition of openings and/or gaps on the
enclosed type structure.
(a) Flow I (b) Flow II
Fig. 5 Profiles of wind tunnel flows
3. Experimental Results
3.1 Distributions of mean wind force coefficients
Fig. 6 shows the distributions of mean wind force
coefficients Cf for typical wind directions. Regarding the
open type structure, the results for both Flows I and II are
presented in the figure.
When q = 0o, the Cf distribution on the semi-open type
structure is similar in pattern to that on the enclosed type
0
200
400
600
800
1000
1200
1400
0.0 0.5 1.0 1.5
z(m
m)
UZ/U1000, Iu
Mean
Iu
α=0.15
0
200
400
600
800
1000
1200
1400
0.0 0.5 1.0 1.5
z(m
m)
UZ/U1000, Iu
Mean
Iu
α=0.27
(a) Enclosed type (q =0o) (b) Semi-open type (q =0o) (c) Open type (q =0o) (d) Open type (q=0o)
(e) Enclosed type (q =45o) (f) Semi-open type (q =45o) (g) Open type (q =45o) (h) Open type (q =45o)
(i) Enclosed type (q =90o) (j) Semi-open type (q =90o) (k) Open type (q =90o) (l) Open type (q =90o)
Fig. 6 Distributions of mean wind pressure coefficients ((a)-(c), (e)-(g), (i)-(k):Flow I), ((d), (h), (l):Flow II)
-1.2-1.2
-1 -1
-0.8 -0.8
-0.6 -0.6
-0.4 -0.4
-0.2
-0.2
-0.2-0.2
q =0o
-1.8
-1.6-1.4
-1.4
-1.2 -1.2
-1 -1
q =0o-0.4 -0.4
-0.2 -0.2
0
0
0
0
0
0
0
q =0o
-0.2
0
0
0
0
0
0
00
q =0o
-2.2
-2-1
.8-1
.6-1
.4
-1.2 -1.2
-1
-1
-0.8
-0.8
-0.6
-0.6
-0.6
-0.4-0
.4
-0.4
-0.4
-0.4
-0.2
-0.2
-0.2
-0.2
-0.2
0
00
.20.4
0.6
q =45o
-2.6
-2.4
-2.2
-2
-1.8
-1.8
-1.6
-1.6
-1.4
-1.4
-1.4
-1.2
-1.2
-1.2
-1
-1
-1
-1
-1-1
-0.8
-0.8
-0.8
-0.6
-0.6
-0.4
-0.2
0
q =45o-2
-1.8-1.6
-1.6-1.4
-1.2
-1.2
-1-1
-0.8
-0.8
-0.6
-0.6
-0.4
-0.4
-0.2
-0.2
0
0
0
0
0
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.6
0.6
0.8
0.8
1
1
1.2
q =45o-2.8-2.6 -2
.4
-2.2-2-1.8
-1.6
-1.6 -1
.4
-1.4 -1
.2
-1.2
-1-1
-0.8
-0.8
-0.6-0.6
-0.4
-0.4
-0.4
-0.2
-0.2
0
0
0
0
0
0.2
0.2
0.2
0.4
0.4
0.4
0.6
0.6
0.6
0.8
0.8
1
1
1.2
1.2
1.4
1.61.8
q =45o
-0.4
-0.4
-0.2
-0.2
-0.2
-0.2
-0.2
-0.2
0
0
0
0 0.2
0.2
0.2
0.4
0.6
0.8
0.8
0.8
11
q =90o
-0.4
-0.2
-0.2
-0.2
0
0
0
00
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.6
0.6
0.8 1
1
1
1.2
q =90o
-0.2
-0.2
-0.2
-0.2
0
0
0
0
0
0 0.2
0.2
0.20.4
0.4
0.4
0.6
0.8
1
1
1
1.2
1.2
q =90o-0.6
-0.6-0.4
-0.4
-0.4
-0.4
-0.4
-0.2
-0.2
-0.2
-0.2-0
.2
0
0
0
0
0
0.2
0.2
0.2
0.4
0.4
0.4
0.6
0.6
0.6
0.8
0.8
11
.21
.41.4
1.4
1.6
1.6
1.6
q =90o
13th International Symposium on Advanced Science and Technology in Experimental Mechanics, Otc.30-Nov.2, 2018, Kaohsiung, Taiwan
3
structure. This feature indicates that the air is stagnant inside
the model because of the existence of the leeward gable wall.
Therefore, the internal pressure coefficients become positive,
which generate larger wind force coefficients on the walls
and roof. In contrast, the wind force coefficients on the open
type structure are approximately zero, because the external
and internal pressures cancel each other. When q = 45o, large
negative wind forces are induced on the leeward roof near
the gable edge. In this case, the conical vortex may be
induced due to the flow separation at the roof edge. When q
= 90o, the Cf distributions on the semi-open and open type
structures are similar to each other, in particular, on the
windward wall and roof. This result implies that the
distributions of internal pressures are similar to each other.
Regarding the effect of turbulence, the distribution pattern of
Cf in Flows I and II are similar to each other. However, the
magnitude of Cf in Flow II is generally larger than that in
Flow I. This result indicates that Cf is affected by the
turbulence of approach flow, significantly.
3.2 Distributions of peak wind force coefficients
Fig. 7 shows the distributions of positive and negative peak
wind force coefficients irrespective of wind direction. Note
that the opened gable wall is located at the bottom of the
figure in the case of semi-open type structure. The tributary
area for evaluating the peak wind force coefficients is
assumed to be 1 m2 based on the AIJ Recommendations for
Loads on Buildings [1]. The equivalent averaging period is
given by the following TVL formula [3]:
real
c
kLT
U (1)
where Tc is the averaging period; k is decay constant (k = 6 –
8); and L is a representative length of the structure. When the
wind velocity Ureal is 36 m/s, the equivalent averaging period
is calculated as approximately 0.2 s in full scale.
The positive peak wind forces on the roof are generally
smaller than those on the wall in the enclosed and semi-open
type structures. On the roof, positive external pressures
seldom occur because the negative external pressures are
induced by the flow separation at the windward eaves edge.
In contrast, the positive peak wind forces on the open type
structure are rather large on the roof. This feature indicates
that the positive internal pressures dominate the positive peak
wind forces.
The negative peak wind force coefficients, which are
important for evaluating the wind loads for
cladding/components, are large in magnitude near the gable
wall. However, the values on the semi-open type structure
are relatively small near the closed gable wall. This result
implies that the negative wind forces induced in this area are
reduced by the negative internal pressures. From these results,
it is said that the internal pressures play an important role in
the evaluation of wind loads on open type structures.
3.3 Characteristics of internal pressure coefficient
3.3.1 Distribution of mean internal pressures
Fig. 8 shows the distributions of mean internal pressure
coefficients Cpi on the open and semi-open type structures in
Flow I. When q = 0o, the mean internal pressures are almost
constant in both cases. The values are negative for the open
type structure, while positive for the semi-open type structure.
When q = 45o, the Cpi values on the open type structure
depend significantly on the location. In contrast, the values
on the semi-open type structure are almost constant over the
whole area. When q = 90o, the negative internal pressures are
induced on the whole area and the Cpi values on the open and
semi-open type structures are similar to each other.
3.3.2 Distribution of peak internal pressures
Fig. 9 shows the distributions of positive and negative peak
internal pressure coefficients irrespective of wind direction.
The values around the ridge are generally small for the open
type structure. In contrast, the positive and negative peak
values on the semi-open type structure are almost constant,
which are approximately 1.6 and -1.2, respectively.
3.3.3 Skewness and kurtosis
The stochastic characteristics of internal pressures on the
open and semi-open type structures are discussed in detail.
Fig. 10 shows the results for the kurtosis and skewness, in
(a) Positive peak wind
force coefficients
(Enclosed type, Flow I)
(b) Negative peak wind
force coefficients
(Enclosed type, Flow I)
(c) Positive peak wind
force coefficients
(Semi-open type, Flow I)
(d) Negative peak wind
force coefficients
(Semi-open type, Flow I)
(e) Positive peak wind
force coefficients
(Open type, Flow I)
(f) Negative peak wind
force coefficients
(Open type, Flow I)
(g) Positive peak wind
force coefficients
(Open type, Flow II)
(e) Negative peak wind
force coefficients
(Open type, Flow II)
Fig. 7 Distributions of peak wind force coefficients
13th International Symposium on Advanced Science and Technology in Experimental Mechanics, Otc.30-Nov.2, 2018, Kaohsiung, Taiwan
4
which the results for all measuring points and wind directions
are plotted. Considering that the values of skewness and
kurtosis are respectively 0 and 3 if the stochastic value is
Gaussian, it is found that the internal pressures on the open
type structure are far from Gaussian at many points. In
contrast, the scatter of the data is relatively small for the
semi-open type structure. The values are close to those for
the Gaussian process. These results indicate that the
characteristics of internal pressures are significantly affected
by the condition of the gable-end configuration. Therefore, it
is hoped that a simple estimation method of design peak wind
force coefficients for cladding/components can be developed.
It will be discussed below.
3.4 Peak external pressures on open and semi-open type
structures
The external pressure coefficients on the open and semi-open
(a) q =0o (Open type) (a) q =0o (Semi-open type)
(a) q =45o (Open type) (d) q =45o (Semi-open type)
(e) q =90o (Open type) (f) q =90o (Semi-open type)
Fig. 8 Distributions of mean internal pressures in Flow I
(a) Positive peak internal
pressures (Open type)
(b) Negative peak internal
pressures (Open type)
(c) Positive peak internal
pressures (Semi-open type)
(d) Negative peak internal
pressures (Semi-open type)
Fig. 9 Distributions of peak internal pressures in Flow I
(a) Open type (Flow I) (b) Open type (Flow II)
(c) Semi-open type
(Flow I)
(d) Semi-open type
(Flow II)
Fig. 10 Skewness versus kurtosis of internal pressures
(a) Positive peak values (b) Negative peak values
Fig. 11 Ratio of external pressure coefficients on the open
or semi-open type structure to those on the enclosed type
structure
type structures are examined to understand the effect of
gable-end configuration on the wind pressures. Fig. 11 shows
the ratio of peak external pressure coefficient Cpe_peak on the
open or semi-open type structure to that on the enclosed type
structure. The horizontal axis represents the peak external
pressure coefficient on the enclosed type structure. The
results for all measuring points and wind directions are
plotted in the figure. It can be seen that the Cpe_peak values for
the open and semi-open type structures are quite different
from those for the enclosed type structure at some points.
However, the magnitude of Cpe_peak on the open and semi-
open type structures are not so different from that on the
enclosed type structure. The ratio is around 1.0 at most
measuring points. Although the internal pressure varies
significantly with wind direction and gable-end
configuration, the values of peak external pressure
coefficients on the open and semi-open type structures are
similar to those on the enclosed type structure. Therefore, the
wind force coefficients on the open type structure can be
evaluated by using the external pressure coefficients on the
enclosed structure if some appropriate values of the internal
pressure coefficients on the open type structure are provided.
4. Estimation methods for wind force coefficients
4.1 Combination of peak external and internal pressure
coefficients for estimating peak wind force coefficients
The peak wind force coefficients are assumed to be given by
the combination of the maximum external pressure
coefficient and the minimum internal pressure coefficient or
that of the minimum external pressure coefficient and the
maximum internal pressure coefficient. Fig. 12 shows the
-0.2
0
q =0o
0.6
0.6
0.6 0.6
q =0o
-0.8
-0.6-0
.6
-0.6
-0.4 -0.4
-0.4-0.2
0
0.2
0.20.4
0.4
0.6
0.8
1
q =45o
0.6
0.6
0.6
0.6
0.6
0.8
q =45o
-0.6
-0.6-0
.4
-0.4
-0.2
-0.2
q =90o
-0.6
-0.6
-0.6
-0.6
-0.4
-0.4-0.2
q =90o
0.60.6
0.8
0.8
0.8
11
1
1
11
1.21.2
1.2
1.2
1.4
1.4
1.4
1.4
1.6
1.6
1.6
1.6
1.8
1.8
1.8
1.8
2
2
2
2
-3
-3
-3
-3
-3
-3
-3
-3
-2.8
-2.8
-2.8
-2.8
-2.8
-2.8
-2.8
-2.8
-2.6
-2.6
-2.6
-2.6
-2.6
-2.6
-2.6
-2.6
-2.4
-2.4
-2.4
-2.4
-2.4
-2.4
-2.2
-2.2
-2.2
-2.2
-2.2
-2
-2
-1.8
-1.8
1.4
1.41.6
1.6
1.6
1.6 1.6
1.6
1.6
1.8 1
.8
-1.2 -1.2
-2 -1.5 -1 -0.5 0 0.5 10
2
4
6
8
10
12
14
Skewness
Kurt
osis
-2 -1.5 -1 -0.5 0 0.5 10
2
4
6
8
10
12
14
Skewness
Kurt
osis
-2 -1.5 -1 -0.5 0 0.5 10
2
4
6
8
10
12
14
Skewness
Kurt
osis
-2 -1.5 -1 -0.5 0 0.5 10
2
4
6
8
10
12
14
Skewness
Kurt
osis
0 1 2 3 40
0.5
1
1.5
2
Cpe
Ra
tio
open(FlowI)
semi-open(FlowI)
open(FlowII)
semi-open(FlowII)
Cpe_peak
-10 -8 -6 -4 -2 00
0.5
1
1.5
2
Cpe
Ra
tio
Cpe_peak
13th International Symposium on Advanced Science and Technology in Experimental Mechanics, Otc.30-Nov.2, 2018, Kaohsiung, Taiwan
5
ratio of the estimated peak wind force coefficient Cf_est to the
practical one Cf_peak, directly obtained from the wind tunnel
experiment. The horizontal axis of the figure represents the
values of Cf_peak. It is found that the estimated values are
generally larger than the practical ones in a lower Cf_peak
range. In particular, the estimated values are rather large for
the semi-open type structure. This is because the peak wind
force coefficient is not necessarily provided by the
combination of the peak values of the external and internal
pressure coefficients. However, the ratio is close to 1.0 when
the magnitude of Cf_peak is large. This feature is important for
specifying the peak wind force coefficients for
cladding/components.
(a) Positive peak values (b) Negative peak values
Fig. 12 Ratio of estimated peak wind force coefficients to
experimental results
4.3 Internal pressures reproducing the peak wind force
coefficients on open type structure
In this section, a discussion is made of the virtual internal
pressure coefficients used for estimating the peak wind force
coefficients for cladding/components of open and semi-open
type structures by combining with the external peak pressure
coefficients on the enclosed type structure.
Fig. 13 shows the distributions of the estimated virtual
internal pressure coefficients for the open and semi-open
type structures. Note that the opened gable wall is located at
the bottom of the figure in the case of semi-open type
structure. The values of positive and negative internal
pressure coefficients, Cpi and Cpi, can be used for estimating
the positive and negative peak wind force coefficients,
respectively. As might be expected from Figs. 8 – 10, the
spatial variation of the virtual internal pressure coefficients
on the open type structure is large. On the other hand, it is
relatively small for the semi-open type structure.
4.3 Model of internal pressure coefficients for open and
semi-open type structures
In this section a discussion is made of simple model of virtual
internal pressure coefficients for estimating the peak wind
force coefficients on the open and semi-open type structures
by combining the external peak pressure coefficients on the
enclosed type structure.
Fig. 14 shows the zoning of the roof and wall areas for
providing the virtual internal pressure coefficients for the
open and semi-open type structures. The zoning is similar to
that for the external peak pressure coefficients on enclosed
type structures, specified in the AIJ Recommendations for
Loads on Buildings [1]. In the figures, the zones of wall and
roof are denoted by ‘W’ and ‘R’, respectively. In the case of
semi-open type structure, the subscripts ‘1’ and ‘2’ represent
the zones along the opened and closed gable walls,
respectively. Tables 1 – 4 summarize the values of the virtual
internal pressure coefficients, which are specified based on
Fig. 13. These values can be used for the open and semi-open
type structures in the open-country and suburban terrains.
Fig. 15 shows the ratio of the peak wind force coefficients
estimated by using the above-mentioned virtual internal
pressure coefficients and the external peak pressure
coefficients on the enclosed type structure. The vertical and
horizontal axes represent the ratio of Cf_est to Cf_peak and the
Cf_peak value respectively. The ratio ranges from 1.0 to 1.5 in
most cases. This feature implies that the proposed method
provide reasonable estimation of the peak wind force
coefficient for cladding/components of open and semi-open
type structures; this method provide somewhat conservative
estimation of the design wind forces.
(a) Open type structure (b) Semi-open type
structure
Fig. 14 Zoning for providing the virtual internal pressure
coefficients for open-type structures
(a) Positive peak pressure (b) Negative peak pressure
Fig. 15 Ratio of estimated peak wind force coefficients to
experimental results
0 2 4 6 8 100
1
2
3
4
Cfpeak
Ratio
Open(FlowI)Open(FlowII)Semi-open type(FlowI)Semi-open type(FlowII)
Cf_peak
Cf_
est
/Cf_
peak
-12 -10 -8 -6 -4 -2 00
1
2
3
4
Cfpeak
Ratio
Open(FlowI)Open(FlowII)Semi-open type(FlowI)Semi-open type(FlowII)
Cf_peak
Cf_
est
/Cf_
peak
Wa
Wb
Wb Rb
Ra
Rb
Rc
Rc Rd
Rd
Rg
ReRf
Rg
Center line Center line
Wa1
Wb2
Wb1 Rb1
Ra1
Rb2
Rc1
Rc2 Rd2
Rd1
Rg1
Re2
Rf1
Rg2
Wa2
Ra2
Re1
Rf2
0 2 4 6 8 100
1
2
3
4
Cfpeak
C fp
ea
k/C
fpe
ak
Open type(FlowI)Open type(FlowII)Semi-open type(FlowI)Semi-open type(FlowII)
Cf_peak
Cf_
est/C
f_peak
-14 -12 -10 -8 -6 -4 -2 00
1
2
3
4
Cfpeak
C fp
ea
k/C
fpe
ak
Open type(FlowI)Open type(FlowII)Semi-open type(FlowI)Semi-open type(FlowII)
Cf_peak
Cf_
est
/Cf_
peak
(a) Positive peak values
(Open type (Flow I))
(b) Negative peak values
(Open type (Flow I))
(c) Positive peak values
(Semi-open type (Flow I))
(d) Negative peak values
(Semi-open type (Flow I))
Fig. 13 Distributions of internal pressure coefficients which
reproduce the maximum wind force coefficients
-3.5
-3.5
-3.5
-3.5
-3
-3
-3
-3
-2.5
-2.5
-2.5
-2.5
-2.5
-2.5
-2
-2
-2
-2
-2
-2
-2
-2
-2-1.5
-1.5
-1.5
-1.5
-1-1
-1
-1
-0.5
-0.5
-0.5 -0
.5
0
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
1
1
1
1
1
1
1
1
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
0
0
0.5
0.5
1 1
1
1
1
1
1 1
1.5 1.5
13th International Symposium on Advanced Science and Technology in Experimental Mechanics, Otc.30-Nov.2, 2018, Kaohsiung, Taiwan
6
Table 1 Virtual internal pressure coefficients for evaluating
the positive and negative peak wind forces on the open type
structure in Flow I (open-country terrain)
Cpi
Wa Wb
-3.0 -1.7
Ra Rb Rc Rd Re Rf Rg
-2.0 -4.1 -3.4 -3.3 -0.7 -3.2 -0.8
Cpi
Wa Wb
1.0 1.1
Ra Rb Ra Rb Ra Rb Ra
0.3 0.7 0.3 0.7 0.3 0.7 0.3
Table 2 Virtual internal pressure coefficients for evaluating
the positive and negative peak wind forces on the open type
structure in Flow II (suburban terrain)
Cpi
Wa Wb
-5.2 -3.1
Ra Rb Rc Rd Re Rf Rg
-3.1 -7.3 -3.1 -7.3 -3.1 -7.3 -3.1
Cpi
Wa Wb
1.8 2.2
Ra Rb Rc Rd Re Rf Rg
0.2 1.3 0.2 1.3 0.2 1.3 0.2
Table 3 Virtual internal pressure coefficients for evaluating
the positive and negative peak wind forces on the semi-open
type structure in Flow I (open-country terrain)
Cpi
Wa1 Wb1 Wb2 Wa2
-0.7 -0.9 -1.0 -0.5
Ra1 Rb1 Rc1 Rd1 Re1 Rf1 Rg1
-0.7 -0.8 -0.9 -0.8 -0.7 -0.8 -0.9
Ra2 Rb2 Rc2 Rd2 Re2 Rf2 Rg2
-0.7 -0.7 -0.5 -0.6 -0.7 -0.7 -0.5
Cpi
Wa1 Wb1 Wb2 Wa2
0 1.7 1.7 1.2
Ra1 Rb1 Rc1 Rd1 Re1 Rf1 Rg1
1.3 0 -0.5 -0.5 1.3 0 -0.5
Ra2 Rb2 Rc2 Rd2 Re2 Rf2 Rg2
1.3 1.4 1.3 1.0 1.3 1.4 1.3
Table 4 Virtual internal pressure coefficients for evaluating
the positive and negative peak wind forces on the semi-open
type structure in Flow II (suburban terrain)
Cpi
Wa1 Wb1 Wb2 Wa2
-1.4 -1.7 -1.8 -1.3
Ra1 Rb1 Rc1 Rd1 Re1 Rf1 Rg1
-1.3 -1.3 -1.3 -1.3 -1.3 -1.3 -1.3
Ra2 Rb2 Rc2 Rd2 Re2 Rf2 Rg2
-1.3 -1.4 -0.9 -1.0 -1.3 -1.4 -0.9
Cpi
Wa1 Wb1 Wb2 Wa2
0.1 3.0 3.0 2.9
Ra1 Rb1 Rc1 Rd1 Re1 Rf1 Rg1
1.8 0.1 -0.1 0.1 1.8 0.1 -0.1
Ra2 Rb2 Rc2 Rd2 Re2 Rf2 Rg2
2.2 2.7 2.8 2.9 2.2 2.7 2.8
5. Concluding Remarks
Peak wind force coefficients for designing
cladding/components of open and semi-open type structures
were investigated in two kinds of boundary layers. The
results indicate that the effect of gable-end configuration on
the distribution of wind force coefficients, provided by the
difference between the external and internal pressure
coefficients, is rather large. Therefore, it is important to
understand the behavior of internal pressures for evaluating
the peak wind force coefficients on the open and semi-open
type structures appropriately. The present paper proposed the
virtual internal pressure coefficients, which can evaluate the
positive and negative peak wind force coefficients by
combining with the peak external pressure coefficients on the
enclosed type structure. This method provided somewhat
conservative estimation of the design wind loads on
cladding/components. The virtual internal pressure
coefficients can be applied to various open-type structure
because the roof shape, including the roof pitch, does not
affect the internal pressure coefficient significantly.
The characteristics of internal pressures on the open and
semi-open type structures should be investigated in more
detail to provide more accurate estimation method of wind
force coefficients for open-type structures with various
shapes. This is the subject of our future study.
Nomenclature
B span width [m]
Cf wind force coefficient
Cf mean wind force coefficient
Cp wind pressure coefficient
Cpe external pressure coefficient
Cpi internal pressure coefficient
Cpi mean internal pressure coefficient
Cpi virtual internal pressure coefficient for evaluating the
positive peak wind force
Cpi virtual internal pressure coefficient for evaluating the
negative peak wind force
H mean roof height [m]
k decay constant
L span length [m]
qH velocity pressure [kg/m2]
TC equivalent averaging period [s]
UH wind velocity at mean roof height [m/s]
U1000 wind velocity at 1000 mm from the wind tunnel floor
[m/s]
power law exponent
roof pitch []
air density [kg/m3]
q wind direction []
Subscripts
est estimated value
peak peak value
Acknowledgement
The present study is financially supported by the Japan Iron
and Steel Federation (2015). Thanks are also due to Dr.
Yasuo Okuda, Building Research Institute, for help with the
wind tunnel experiments.
References
[1] Architectural Institute of Japan: AIJ Recommendations
for Loads on Buildings, 2015.
[2] Yuki Takadate, Yasushi Uematsu, Eri Gavanski: Wind
Tunnel Study of Wind Force Coefficients for Open-type
Framed Membrane Structures, 10th International
Symposium on Advanced Science and Technology in
Experimental Mechanics, November 1 - 4, 2015.
[3] T. V. Lawson: Wind effects on buildings, Vol. 1, Applied
Science Publishers, 1980.