-
*Corresponding author. Tel.: 61(07)3365-3511; fax:
61(07)3354-4599.E-mail address: [email protected] (C.W.
Letchford)
Journal of Wind Engineeringand Industrial Aerodynamics 84 (2000)
197}213
Mean wind loads on porous canopy roofs
C.W. Letchford*, A. Row, A. Vitale, J. WolbersDepartment of
Civil Engineering, The University of Queensland, Brisbane,
Queensland 4072, Australia
Received 6 August 1997; accepted 7 June 1999
Abstract
Mean overall lift and drag forces on a range of canopy or open
roof forms with varyingporosities are presented. In general, lift
forces decrease while for low roof pitches (a(153) dragforces
increase as porosity is increased in the range 0}23%. Resolution of
these forces intoequivalent net roof pressures reveals that wind
load may be transferred from the leeward to thewindward areas,
leading to potential overloading of the supporting structure. Mean
and#uctuating pressure measurements were undertaken to con"rm the
inferred pressure distribu-tions on the roofs. ( 2000 Elsevier
Science Ltd. All rights reserved.
Keywords: Wind loads; Porous canopy roofs
1. Introduction
Australia has the highest incidence of skin cancer in the world,
with two out of threepeople developing skin cancers, many being
life threatening [1]. The message in sunprotection programs to date
has promoted personal protection, as evidenced by the`Slip, Slop,
Slapa summer and `Slip, Slop, Slap has got Seriousa winter
campaigns.However, making sun protection an integral part of
community planning has beenacknowledged as just as important a
preventative measure [1]. This involves theprovision of shade in
public spaces where people gather, be it sportsgrounds,
play-grounds, schoolgrounds or shopping areas. Motivation for the
provision of shadestructures has also been aided by the litigation
experiences of at least one localgovernment authority [1].
It is not only humans that su!er from lack of sun protection.
The distress and deathof many beef cattle at the Whyalla feedlot,
the largest in Queensland, in 1989,
0167-6105/00/$ - see front matter ( 2000 Elsevier Science Ltd.
All rights reserved.PII: S 0 1 6 7 - 6 1 0 5 ( 9 9 ) 0 0 1 0 3 -
8
-
impacted both economically and publicity-wise on the beef cattle
feedlot industry.The most recent research carried out at the
Brigalow Research Station in CentralQueensland indicates that
signi"cant improvement in liveweight gain and animalwelfare is
achieved by the provision of shade [2]. Currently, animal welfare
legislationis driving the need for greater provision of shade, but
the economics of increasedproductivity are catching up.
Shade and weather (hail) protection have also become
increasingly common in thefruit and vegetable growing industry
where economic devastation can follow severecrop damage. This was
the case for the plant nursery industry in North
Queenslandfollowing Cyclone Winifred where sun damage to young
plants was estimated to costup to one million dollars [3]. Similar
weather protection is now being sought in otherareas, e.g. new car
sales yards.
Whereas a large database of knowledge exists for solid suspended
structures, e.g.roofs and bridges, there is very little information
on the wind loading and structuralresponse of suspended porous
shade structures. Donnan et al. [4] report wind tunneland
structural analyses of a greenhouse structure constructed of porous
shade clothsupported on cables. Their preliminary wind tunnel study
indicated somewhat unex-pected results, viz. increasing drag force
and decreasing lift force with increasingporosity. They went on to
say that `If the results of this preliminary wind tunnelstudy are
accurate, the implications for the design of such structures are
extremelysigni"cant.a
The provision of sun protection has therefore become a
signi"cant economic andhealth issue for humans, animals and plants.
Typically of large span suspended porousroof form, these shade
structures are wind sensitive and an ongoing research project atthe
University of Queensland aims to develop a model of the response of
this class ofstructure to #uctuating wind loads and implement this
model as a rational designmethod. This design approach and newly
obtained wind loading information willreplace the current largely
ad hoc approach which has the possibility of allowingunsafe
structures to be built.
This paper deals speci"cally with wind tunnel measurements on
rigid models toinvestigate the e!ect of porosity and obtain loading
coe$cients on porous canopy oropen roof forms. Future papers will
examine other parameters in the response ofshade cloth structures
under wind loading, including #exibility of fabrics and tension-ing
system.
2. Experimental procedure
Porosity was deemed the dominant dimensionless parameter for the
"rst stage ofthis project. The porosity (p) or solidity (d) of the
materials studied was calculatedfrom
p"1!d" open}areatotal}enclosed}area
. (1)
198 C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213
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Total enclosed area refers to the overall roof surface in this
context. For shade clothfabrics however, porosity is di$cult to
de"ne and indeed these fabrics are classi"ed ina number of ways; by
weight, weaving type, or most commonly by cover factor. Thecover
factor is equivalent to solidity and is estimated by measuring the
amount of350 nm wavelength solar radiation (i.e. middle of the
ultra-violet region) transmittedthrough the shade cloth and does
depend on the colour of the shade cloth, due todi!erent degrees of
opaqueness of the "bres. Indeed, wind forces acting on a
porousstructure will depend not only on the porosity but also on
the shape of the &pores orholes' making up the porous surface,
for example, sharp-edged holes will havedi!erent characteristics to
woven "bres. An alternative to porosity is the pressure
losscoe$cient, which is de"ned as
K"P6!P$o;2/2
(2)
where P6
and P$
are the upstream and downstream static pressures on either side
ofthe mesh and ;M is the average approach velocity. The pressure
loss coe$cient isa measure of the resistance to #ow through a
porous surface and includes the e!ects ofporosity as well as shape
of `holesa. Thus similarity of wind loading will be bestachieved by
equality of pressure loss characteristic (K). Here, the pressure
losscharacteristics of a range of shade cloth fabrics will be
compared with those measuredfor various perforated metal plates of
known porosity to select a suitable rigidmaterial for the wind
tunnel tests.
The pressure loss measurements were performed in a small wind
tunnel, approxim-ately 300 mm square, in which the entire
cross-section was covered by the variousmaterials being tested.
Fig. 1 shows the experimental results plotted as K vs. Re.
TheReynolds number (Re) was de"ned in terms of ; and dominant "bre
diameter forfabrics and hole size for porous metal plates. The
perforated metal plates of porosity11% and 23% bracketted the
commonly used high UV reduction (solidity) shadecloths and were
selected for the wind tunnel study. The 11% porous plate had 2.4
mmdiameter holes at 6.4 mm spacing while the 23% porous plate had
0.8 mm diameterholes at 1.5 mm spacing.
Generic canopy roof forms of hip, gable and monoslope were
chosen for the studyand two are sketched in Fig. 2. Three roof
pitch angles (a) were selected for study: 73,153 and 273. The
models were constructed from thin (1 mm for solid and 0.5 mm
forporous) metal sheets 300 mm square and thus di!erent roof
pitches had di!erentprojected plan areas. This arrangement is
identical to earlier pressure measurementstudies of canopy roofs
[5,6]. All were mounted at a lower eaves height (h) of 100 mmon
four 6 mm-diameter legs. The nominal model scale was 1 : 50.
A simple, one component force balance was constructed [7] to
measure the verysmall loads. This force balance could be mounted in
several ways to obtain separately,measures of the overall drag and
lift forces on the models for various angles of attack.A paddle in
a container of a viscous #uid was used to dampen the #uctuating
loads.Only mean values of force are presented here which represent
the average of betweenthree and "ve runs of 30 s duration at a
sampling frequency of 100 Hz. The drag forces
C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213 199
-
Fig. 1. Pressure loss coe$cient K as a function of Reynolds
number for various porous materials.Perforated metal plates
speci"ed by porosity, p (%), and shade cloth fabrics speci"ed by
cover factor whichis approximately the solidity d (%).
Fig. 2. Sketch of model roof details.
on the four supporting legs were measured separately and were
subtracted from theoverall loads to produce loads on the roof
alone. The forces were reduced tocoe$cient form by dividing by the
mean dynamic pressure at eaves height (the upperheight for the
monoslope roof ) and the projected plan area A
p(" roof area]cos(a)):
CF" F
1/2o;M 2A1
. (3)
F is the force, lift or drag, with lift de"ned as positive
downwards to be consistent withAS1170.2 [8]. The 03 wind direction
was de"ned as normal to the ridge line or roofedge.
200 C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213
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Fig. 3. Model and pressure tapping details.
The pressure tapped models had a single row of 10 taps spaced
evenly along theroof centreline. The pressure tap arrangements are
illustrated in Fig. 3. The uppersurface tappings were all type A,
while for the underside measurements severaldi!erent tapping
variants, types A reversed, B and C, were employed in an e!ort
toobtain a true wake pressure without interference. Each tapping
has a 1.0 mm internaldiameter tube with a base mounting
approximately 4 mm in diameter. Type A wasmounted on the underside
for upper surface measurements and generally producedthe most
consistent results when reversed, ie., placed on the upper surface,
formeasurement of underside pressures. Type B su!ered from azimuth
e!ects, picking upsome stagnation pressure when turned into the
wind on the gable roof models, whiletype C su!ered larger wake
interference e!ects compared with type A. Net pressureswere
measured with type A taps on the upper surface and type B taps on
the lowersurface but displaced laterally by 10 mm.
Point and area-averaged net and separate top and bottom surface
pressuremeasurements were obtained using Scanivalves and Honeywell
pressure transducersand a 1.5 mm tubing system with a near linear
frequency response to 150 Hz.Pressures were sampled at 400 Hz for
15 s and repeated 10 times. A Fisher}Tippetttype-1 extreme value
distribution was "tted to these data and mean extremes (maximaand
minima) estimated. Pressure coe$cients were obtained by dividing by
the meandynamic pressure at eaves height.
The tests were conducted in the Department of Civil
Engineering's Boundary LayerWind Tunnel which is 3 m wide ] 2 m
high and has some 12 m of upstream fetch forboundary layer
simulation. A 300 mm fence and uniform carpet roughness
wereemployed in the smoother simulation, while a grid of 100 mm
beams at 300 mmcentres was added immediately upstream of the fence
for the rougher simulation.Except where stated only results from
the smoother simulation, where the turbulenceintensity at eaves
height was approximately 15%, are presented here. The meanvelocity
and turbulence intensity pro"les are compared with AS1170.2 [8]
values inFig. 4(a) and (b) at 1 : 50 scale. The mean dynamic
pressure was measured bya pitot-static tube mounted at eaves height
away from the in#uence of the model. It isexpected that this will
lead to approximately 4% overestimate of the true dynamicpressure
[9] for the turbulence intensities in this study.
C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213 201
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Fig. 4. (a) Mean velocity pro"les for the two simulations
compared with AS1170.2 values. (b) Turbulenceintensity pro"les for
the two simulations compared with AS1170.2 values.
3. Results and discussion
3.1. Force measurements
The drag and lift coe$cients for the gable roof at an azimuth of
03 for three roofpitches are plotted against porosity in Fig. 5.
The drag coe$cient increases slightlywith increasing porosity for
the shallower pitches but reduces for the 273 pitch roof.
202 C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213
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Fig. 5. Drag and lift coe$cients for three pitches of a gable
roof at 03 azimuth.
Fig. 6. Drag and lift coe$cients for three pitches of a hip roof
(pyramid) at 03 azimuth.
The uplift (negative Cl) reduces as porosity increases and for
the 273 pitch roof is no
longer an uplift but a downward load which increases with
porosity.The drag and lift coe$cients for hip roofs, in e!ect
pyramids for the two shallower
pitches, for an azimuth of 03 for three roof pitches are
presented in Fig. 6. Again withincreasing porosity, drag increases
for the shallower pitches but decreases for thesteepest pitch while
uplift changes to a downward load.
The drag and lift coe$cients for monoslope roofs of three
pitches at azimuths of 03and 1803 are presented in Figs. 7 and 8.
Like the gable roof, for increasing porosity,
C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213 203
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Fig. 7. Drag and lift coe$cients for three pitches of a
monoslope roof at 03 azimuth.
Fig. 8. Drag and lift coe$cients for three pitches of a
monoslope roof at 1803 azimuth.
drag slightly increases for the shallower pitches but reduces
slightly for the 273 pitchroof, while lift reduces in magnitude
with porosity.
A regression of the mean drag coe$cients for the various roof
con"gurations,pitches, porosities and azimuths for the smoother TC1
(15%) and rougher TC2 (20%)
204 C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213
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Fig. 9. Regression of mean drag coe$cients for the two di!erent
simulations.
Fig. 10. Regression of mean lift coe$cients for the two di!erent
simulations.
simulations is presented in Fig. 9 and for lift coe$cients in
Fig. 10. The increasedturbulence leads to an increase in drag and
lift coe$cient of approximately 9%. Thisresult somewhat contradicts
the general observation that increased turbulence leadsto earlier
reattachment (for elongated bodies) and hence reduced wake
pressures and
C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213 205
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Table 1Comparison between the present study, earlier pressure
studies and AS1170.2 [8] for the meanwindward and leeward net
pressure coe$cients on solid gable roofs
Roof type and pitch Source Azimuth C18
C1-
Gable 73 AS1170.2 03 !0.48 to 0.32 !0.56Gumley [5] 03 !0.08
!0.52Letchford et al. [6] 03 0.07 !0.31Present study 03 0.14
!0.30
Gable 153 AS1170.2 03 !0.32 to 0.48 !0.80Gumley [5] 03 0.034
!0.80Letchford et al. [6] 03 0.12 !0.41Present study 03 0.19
!0.65
Gable 273 AS1170.2 03 !0.32 to 0.68 !0.92Gumley [5] 03 0.59
!0.59Letchford et al. [6] 03 0.60 !0.60Present study 03 0.69
!0.57
consequently lower overall drag. Clearly the #ow mechanisms here
are more complex,with net (upper!lower pressures) and
windward/leeward interactions making extra-polation of simple
arguments unacceptable.
Table 1 presents for solid gable roofs the mean lift and drag
force measurementsresolved into windward and leeward net pressure
coe$cients. Positive values ofC
1are de"ned as downward for both windward and leeward faces. The
present results
are compared with those from the Australian wind load code
AS1170.2 [8] and earliermean pressure measurement studies of gable
canopy roofs by Gumley [5] andLetchford and Ginger [6]. The 273
roof pitch results have been interpolated from22.53 and 303 results
for both pressure measurement studies. The code values repres-ent
envelope results and were largely derived from the yuctuating
pressure measure-ments of Gumley as indicated by the range of
pressure coe$cients on the windwardroof and large suctions on the
leeward roof. Here the code values have been multipliedby an area
reduction factor K
A"0.8. In addition, the force measurements include
both normal and tangential stresses while the code and pressure
studies cover onlynormal stresses or pressures.
The agreement between the di!erent studies is encouraging given
the di!erenttechniques used. The steeper pitch has the best
agreement while there is rather a lot ofscatter for both windward
and leeward coe$cients for the 153 pitch roof. Discrepan-cies
between the pressure studies [5,6] have been attributed by
Letchford et al. [6] tointerference from the overly large supports
on the Gumley model. This is not the casefor the force measurements
where the legs were in correct scale. Discrepancies betweenforce
and pressure studies can also arise from the distorted roof
thickness (&8 mm)required to conceal tubing for both pressure
measurement models whereas the forcebalance models were more
realistically scaled being only 1 mm thick. Additionally,
206 C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213
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Table 2Comparison between the present study, Gumley [5] and
AS1170.2 [8] for the mean lift and drag on solidmonoslope roofs.
Bold indicates in excess of AS1170.2 values
Roof type and pitch Source Azimuth C$
C-
Monoslope 73 AS1170.2 03 0 to 0.06 !0.52 to 0.16Gumley [5] 03
0.06 !0.48Present study 03 0.04 !0.17AS1170.2 1803 0 to 0.05 !0.20
to 0.40Gumley [5] 1803 0.03 0.26Present study 1803 0.05 0.32
Monoslope 153 AS1170.2 03 !0.11 to 0.17 !0.4 to !0.64Gumley [5]
03 0.21 !0.79Present study 03 0.16 !0.50AS1170.2 1803 0.13
0.48Gumley [5] 1803 1.12 0.46Present study 1803 0.19 0.60
Monoslope 273 AS1170.2 03 !0.43 to 0.60 !0.85 to !1.18Gumley [5]
03 0.79 !0.46Present study 03 0.44 !0.87AS1170.2 1803 0.44
0.85Gumley [5] 1803 0.49 1.05Present study 1803 0.53 1.01
#ow visualization indicated that reattachment was possible on
the underside of thewindward half of the shallower canopy roofs and
di!erences in #ow simulationbetween the three studies, particularly
eaves height turbulence intensities &22% inRef. [6], &20%
in Ref. [5] and &15% here, could explain the observed
di!erences.
As the mean lift and drag forces cannot be resolved into
windward and leeward netpressure coe$cients for a monoslope roof,
Table 2 presents comparisons of lift anddrag coe$cients with the
earlier pressure measurement results of Gumley [5] and thecode [8]
resolved into these force coe$cients. The 73 results for Gumley
have beeninterpolated from 03 and 153. Again the code values have
had a K
Afactor of 0.80
applied. For this roof con"guration the mean force coe$cients
from the present studylie within the bounds of the code values for
all pitches studied for the 03 azimuth (highside windward).
However, for the 1803 azimuth (high side leeward) the present
resultsare nearly 50% greater for the two steeper roof pitches. A
satisfactory explanation forthis large di!erence has yet to be
advanced. Surface oil #ow visualization wasundertaken on 1 mm thick
monoslope roof models. Along the roof centreline, theseparated #ow
region extends further, by approximately 12%, on the underside for
the1803 azimuth monoslope roof (&0.45 of roof length) than on
the topside for the 03azimuth case (&0.33 of roof length).
These surface #ow patterns are consistent witha greater resultant
force (hence lift and drag) for the 1803 azimuth. Typically
theGumley results di!er from the code values by a constant 0.8
factor, probably K
A,
except for the 153 pitch roof at 1803, where they are almost
equal.
C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213 207
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Table 3Net pressure coe$cient representation for porous gable
roofsat 03
Roof type & pitch Porosity C18
C1-
Gable 73 Solid 0.14 !0.3011% 0.35 !0.3823% 0.71 !0.64
Gable 153 Solid 0.19 !0.6511% 0.45 !0.4923% 0.58 !0.48
Gable 273 Solid 0.69 !0.5711% 0.66 !0.4823% 0.67 !0.39
Table 3 presents the pressure coe$cient representation of the
lift and drag on gableroofs as a function of porosity. It shows
that, with the exception of C
1-for the 73 roof,
there is e!ectively a transfer of wind load from the leeward to
the windward face ofporous roofs which is most evident at moderate
pitches with the e!ect increasing withporosity. Identical trends
were evident in the rougher (TC2) simulation results. Thistransfer
of load is of great signi"cance because although the overall drag
changes arerelatively small for increasing porosity, the doubling
of load on the windward face formoderate pitch roofs will have
signi"cant consequences for the roof substructuredesign. The
results for the 73 pitch are somewhat inconsistent and it must be
notedthat the conversion of force coe$cients to pressure coe$cients
is sensitive to pitchangle and relative magnitude of lift and drag
forces.
3.2. Pressure measurements
Pressure measurements were undertaken in order to estimate the
wind load distri-bution. Table 4 compares the results of the
centreline mean net area-averaged pressuredistribution for a 153
pitch gable roof at an azimuth of 03 for the three
di!erentunderside tapping arrangements shown in Fig. 2. An average
of the three results is alsopresented.
Some di$culty was experienced in obtaining undisturbed
pressures, particularly onthe underneath roof surface and this led
to the trial of three pressure tappingarrangements as discussed in
Section 2. Although there is some scatter in the data it isevident
that the trends in the force measurements are reproduced. Clearly
there is aninitial increase in windward net pressure coe$cient with
porosity while there isa signi"cant decrease in the leeward net
pressure with increasing porosity. Directcomparison with force
measurements is not really possible as only centreline
pressureswere measured and there would be signi"cant
three-dimensional e!ects over suchshort breadth roofs. However the
trends in Table 3, C
18and C
1-from the force
208 C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213
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Table 4Mean windward and leeward area-averaged net roof
pressures on a 153 pitch gable roof at an azimuth of 03
Tapping type A B C Average
Porosity C18
C1-
C18
C1-
C18
C1-
C18
C1-
solid 0.20 !0.93 0.30 !0.82 0.29 !0.80 0.26 !0.8511% 0.48 !0.47
0.48 !0.34 0.42 !0.44 0.46 !0.4223% 0.37 !0.28 0.43 !0.14 0.37
!0.23 0.39 !0.22
Fig. 11. Centreline mean net area-averaged pressure coe$cient
for one half of the solid and 23% porous,273 pitch, hip roof as a
function of wind direction.
measurements, are reproduced in Table 4 apart from the decrease
in windwardcoe$cient for the 23% porosity roof.
Fig. 11 shows the centreline mean net area-averaged pressure
distribution acrossone half of the roof for the solid and 23%
porous, 273 pitch, hip roof as a function ofwind direction. It is
evident that the porous roof experiences larger net
positivepressures (downwards) than the equivalent solid roof and
this phenomenon is reversedfor suctions (upward loads). The largest
downward load for each porosity occurs forwinds normal to the ridge
line (azimuth"03), while the largest uplifts occur for eachporosity
for a wind direction of about 1503, i.e., on the leeward roof half.
Meanmaximum and minimum net area-averaged pressures showed similar
trends. The lackof symmetry about 1803 indicates the level of
interference caused by the tappingarrangement } here type B for
underneath pressures.
C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213 209
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Fig. 12. Centreline mean net pressure coe$cient for solid and
23% porous, 273 pitch, hip roof.
Fig. 12 shows the mean net point and area-averaged pressure
distribution acrossthe centreline of the solid and 23% porous 273
pitch hip roof for an azimuth of 03. yis the distance from the
leading edge and = is the in-wind roof length as detailedin Fig. 3.
The area-averaged pressures over each roof half are signi"ed by
p.a. It isevident in both the point and area-averaged measurements
that there is an increase inwindward mean net pressure and a
decrease in leeward mean net pressure along thecentreline.
Fig. 13 shows the RMS net point and area-averaged pressure
distribution across thecentreline of the solid and 23% porous 273
pitch hip roof for an azimuth of 03. Againthe area-averaged
pressures over each roof half are signi"ed by p.a. Here the
#uctuat-ing area-averaged windward pressures are only slightly less
for the porous roofwhereas there is a signi"cant reduction in
leeward #uctuating pressures for theporous roof.
Fig. 14 shows the maximum net point and area-averaged pressure
distributionacross the centreline of the solid and 23% porous 273
pitch hip roof for an azimuth of03. Surprisingly the area-averaged
windward pressure maxima are slightly larger forthe porous roof.
Leeward pressure maxima are of little interest in design.
Fig. 15 shows the minimum net point and area-averaged pressure
distributionacross the centreline of the solid and 23% porous 273
pitch hip roof for an azimuth of03. Here there is a signi"cant
reduction in area-averaged minima on the leewardporous roof when
compared with the solid roof. As might be expected the average
ofthe point pressure minima and maxima are greater in magnitude
than the corre-sponding area-averaged pressures due to reduced
correlation of the #uctuatingpressures.
210 C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213
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Fig. 13. Centreline RMS net pressure coe$cient for solid and 23%
porous, 273 pitch, hip roof.
Fig. 14. Centreline maximum net pressure coe$cient for solid and
23% porous, 273 pitch, hip roof.
C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213 211
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Fig. 15. Centreline minimum net pressure coe$cient for solid and
23% porous, 273 pitch, hip roof.
These pressure results, although for only one roof type and
pitch and subject tosome criticism in terms of tapping wake
interference, clearly illustrate that thewindward roof region
experiences increased mean and peak maxima loading while theleeward
region experiences reduced mean and peak minima loading. These
resultssupport the inferred load transfer to windward regions made
from the overall forcemeasurements.
4. Conclusions
Mean wind loading coe$cients, both lift and drag, have been
determined fora range of rigid porous canopy roof forms. Similarity
of the pressure loss characteristicwas used to match the range of
typical shade cloth materials used in the constructionof these
structures to a range of perforated metal plates used to construct
the windtunnel models. Hip, gable and monoslope roof forms were
studied for three pitchangles, 73, 153 and 273, for porosity's
ranging from 0% (solid) to 23%. The results areapplicable to shade
cloths with cover factors (UV reduction rating) ranging from 80%to
100%. In using this data for the design of other porous roof
materials the pressureloss characteristic K should be measured "rst
to determine the applicability of theseresults.
In general windward loads increase and leeward loads reduce with
increasingporosity. Flow visualization on a 153 pitch gable roof
model revealed that porosityinduces #ow through the windward roof
preventing reattachment beneath this sectionof the roof and thereby
increasing both the upper surface load through increased
212 C.W. Letchford et al. / J. Wind Eng. Ind. Aerodyn. 84 (2000)
197}213
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stagnation area and lower surface load through prevention of
pressure recovery afterreattachment. This regime occurs on
shallower pitch roofs. For steeper pitch roofsreattachment does not
occur and the possibility of increased loading on the windwardroof
is signi"cantly reduced. The leeward roof experiences reduced
loading becausethe separation bubble formed on the upper surface at
the ridge line is ventedsomewhat while the lower surface
experiences a much more signi"cant wake e!ectfrom the #ow through
the windward roof section. Pressure measurements, althoughdi$cult
in porous materials, con"rmed the trend for an increase in windward
roofload with increasing porosity and although mean and #uctuating
suctions weresigni"cantly reduced with the introduction of
porosity, mean and #uctuating pres-sures were actually maintained
or increased with the addition of porosity.
For solid monoslope roofs, the force measurements indicated
greater lift and dragfor the 1803 azimuth, high end leeward, than
for the 03 azimuth. Surface oil #owvisualization con"rmed that the
separation was larger on the underneath side for the1803 azimuth
than on the top side of the 03 azimuth which would support
theobserved force measurements. However, this "nding is opposite to
earlier pressuremeasurement studies and this discrepancy remains to
be clari"ed.
Signi"cant work remains to be undertaken to examine #uctuating
loads and inparticular the e!ect of #exibility of porous roofs on
the structural response. This is thesubject of an ongoing research
program at the University of Queensland.
Acknowledgements
The authors wish to acknowledge support for this study from the
Department ofCivil Engineering and an Australian Research Council
small grant in 1996 and 1997.
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