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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


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


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


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


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


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


the positive and negative peak wind forces on the open type

structure in Flow II (suburban terrain)

Cpi

Wa Wb

-5.2 -3.1


-3.1 -7.3 -3.1 -7.3 -3.1 -7.3 -3.1

Cpi

Wa Wb

1.8 2.2


0.2 1.3 0.2 1.3 0.2 1.3 0.2


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


-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


1.3 0 -0.5 -0.5 1.3 0 -0.5


1.3 1.4 1.3 1.0 1.3 1.4 1.3


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


-1.3 -1.3 -1.3 -1.3 -1.3 -1.3 -1.3


-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


1.8 0.1 -0.1 0.1 1.8 0.1 -0.1


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.

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