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Pressure factors for edge regions on low rise building roofs
JOURNALOF
n~B
ELSEVIER
Journal of Wind Engineering and Industrial Aerodynamics 54/55 (1995) 337-344
~
~
Pressure factors for edge regions on low rise building roofs J.D. Ginger a, C.W. L e t c h f o r d *'b aDepartment of Civil Engineering, Texas Tech University, Lubbock, TX 79409, USA b Department of Civil Engineering, The University of Queensland, Brisbane, Qld 4072, Australia
Abstract Point and area-averaged pressures are presented for enclosed low rise (height (h)/breadth (b) = 1/3) building roof, based on 1:100 scale wind tunnel measurements obtained in a simulated suburban atmospheric surface layer. Large magnitude mean and peak suction pressures were measured close to the leading edges under the separating shear layer. Significantly larger magnitude mean and peak pressures were measured on 0.2h (wide) by 1.0h (long) rectangular edge strips compared to the pressures on 1.5h by 1,0h roof sections. Pressure factors of the order of 3.0 for suction pressures were obtained for these regions which are larger than code values. However, measured peak area-averaged suction pressures were significantly smaller than code values.
1. Introduction Wind tunnel tests carried out on low rise (height (h)/breadth (b) < ½) building roofs by Kind [1] and Ginger [2] amongst others have shown that the largest pressures were experienced close to edge discontinuities (i.e. leading edges), in regions of flow separation. Ginger [2] studied the spatial and temporal characteristics of the pressures in these regions and this is reported in Ref. [3]. Flow mechanisms over sharp edged roofs are characterized by shear layer separation and subsequent vortex formation. Ginger [2] measured large magnitude mean and fluctuating pressures under the 2D separation bubble for wind flow normal to the separating edge (i.e. fl = 0 °) and under the 3D conical vortex for oblique wind directions (i.e. fl = 15 ° to 75 °) in simulated suburban atmospheric surface layer flow conditions. Large magnitude mean and peak suction pressures were measured within a 0.2h wide region from the separating edges. The largest magnitude point suction pressures were measured for fl ,-~ 30 ° close to the apex of the 3D conical vortex.
* Corresponding author. 0167-6105/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 1 6 7 - 6 1 0 5 ( 9 4 ) 0 0 0 5 2 - F
J.D. Ginger, C.W. Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337-344
338
Most wind loading codes I-4,5] prescribe the quasi-static design approach for determining peak wind loads on low rise buildings. In this method the fluctuating surface pressures depend entirely on the fluctuating wind velocity in the atmospheric boundary layer. Although the quasi-static design is satisfactory for regions where the flow impinges directly, it is not suitable for determining peak pressures where flow separation and vortex formation takes place. Local pressure factors are prescribed to account for the variation of pressure over a surface and more particularly the highly intermittent larger magnitude pressures in the flow separation regions. Area reduction factors are specified to account for the lack of correlation of the surface pressures. Ginger [2] and Ginger and Letchford [3] showed that fluctuating suction pressures were spatially well correlated over lengths of 1.0h, on 0.2h wide rectangular strips along the separating edges under the 2D separation bubble and the 3D conical vortex. The larger magnitude pressure fluctuations under the 3D conical vortex for fl ,,~ 30 ° to 60 ° were better correlated than the pressure fluctuations under the 2D separation bubble for fl = 0 °. Furthermore, for a particular wind direction, conditionally sampled data showed that the peak suction pressures were better correlated than the time averaged pressures. The regions appropriate for applying pressure factors on low rise building roofs in turbulent boundary layer flow conditions are identified as 0.2h by 1.0h rectangular edge strips along the separating edges. The purpose of this paper is to ascertain the effectiveness of code provisions to account for pressures beneath separated flow over roofs.
2. Experimental procedure Tests were carried out in the 3 m wide by 2 m high by 12 m long Boundary Layer Wind Tunnel in the Department of Civil Engineering, University of Queensland. A terrain category 3 (ASl170.2 I-4]) zo = 0.2m boundary layer was simulated at a length scale of 1/100 as described by Ginger [2]. A 300 mm by 300 mm square planform 100 mm high (h) fiat roof enclosed building model with pressure tappings on the roof was tested in this flow. Area-averaged pressures were measured on six
C
D
o i
B *
E
*
o
A _
1GO
__
Bs
Es
As
F8
0
o
F
Cs o°I
o o
160
Fig. 1. Roof panels A to F and edge strips As to Fs.
,I.D. Ginger, C. W Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337-344
339
100 mm by 150 mm panels (labelled A, B, C, D, E, F) using six uniformly spaced tappings, as shown in Fig. 1. Area averaged pressures were also measured on 100 mm by 20 mm rectangular edge strips (labelled As to Fs) surrounding the parent panels using five uniformly spaced tappings also shown in Fig. 1. The effect of wind orientation (fl), was studied over the range 0 ° to 360 °. The point and area-averaged pressure measurement systems had good frequency response beyond 100 Hz at which point they were lowpass filtered and sampled at 250 Hz for 30 s. The rooftop reference velocity was approximately 10 m/s. The positive direction was defined as downwards. The results presented here are the average of five runs.
3. Results
The variation of mean, standard deviation, maximum and minimum area-averaged pressure coefficients with wind direction on the six panels (A to F) is summarized in two cases: a roof corner panel F and a roof middle panel E in Figs. 2 and 3, respectively. For roof corner section F, Fig. 2 shows that the formation of a 2D separation bubble for fl = 0 ° and 90 ° and 3D conical vortices for other wind directions generate large magnitude mean and fluctuating suction pressures. The location of the pressure tappings in relation to the flow separation regions generate the largest magnitude mean, maximum and minimum pressure coefficients of -0.29, 0.64 and -1.16, for fl = 345 °, 285 ° and 75 °, respectively. For roof middle panel E, Fig. 3, shows that the formation of a 2D separation bubble for fl = 0 ° and 3D conical vortices for other wind directions again generate large magnitude mean and fluctuating suction pressures. The largest magnitude mean, maximum and minimum pressure coefficients of -0.32, 0.68 and -1.26, were measured for fl = 0 °, 75 ° and 30 °, respectively. It is worth
"1"
0.5
o
-
-
-
-
-
-
-
-
-
-
0
~, -0.5 CL
-1 c
-1.5
0
go
1:~o
18o
24o
Wind Direction,
I
'-=-- Mean
- - * - - Std. Dev.
~
abo
a6o
Min.
[
deg
Max.
~
Fig. 2. Pressure coefficient variation for roof corner panel F.
340
J.D. Ginger, C.W.. Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337-344 1
~___Z
¸
~-~_._~.___ ~
~
0.5~
O'
~l_..__.ll_~
__
--
-0.5'
-1'
-I .5
6o
12o
180
Wind Direction, deg
I
'm-
Mean
~
Std. Dev. ~
Max.
[]
[
Min.
Fig. 3. Pressure coefficient variation for roof middle panel E. 1
=
~_
-1.5
-2. -2.5 _31
,
0
[
' - ~ - Mean
,
60
,
,
,
120 180 240 Wind Direction, deg
--~
Std. Dev. +
Max.
+
J
,
300
360
Min.
]
Fig. 4. Pressure coefficient variation for roof corner strip F~.
noting that there are not inconsiderable positive peak pressure coefficients (0.6) generated over both the corner and middle roof panels (~ of the roof area). Kasperski [6] has pointed out design problems that arise for structures where the direction of the wind load changes. In particular, the load can align itself with the relevant influence coefficient distribution to produce a maximum load effect. The variation of mean, standard deviation, maximum and minimum area averaged pressure coefficient with wind direction on the six edge strips (As to Fs) is summarized in two cases: a roof corner edge strip Fs and a roof middle edge strip Es in Figs. 4 and 5, respectively.
J.D. Ginger, C.W. Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337 344
341
w.
0 . 5 i ~
:
o. . . . .
. ~ = _ 4 . . ~
-0.51 --]-
-1.5 . . . .
~
"
13-
-2.5-3
0
6'o
1i0
180
Wind Direction, deg
I - - ~ - Mean
~ Std. Dev. +
Max.
+
Min.
I
Fig. 5. Pressure coefficient variation for roof middle strip Es.
For roof corner edge strip Fs, Fig. 4 shows the familiar formation of a 2D separation bubble for fl = 0 ° and 3D conical vortices for other wind directions. The largest magnitude mean, m a x i m u m and minimum pressure coefficients of - 0.79, 0.57 and - 2.75 were measured for fl = 15 °, 285 ° and 0 °, respectively. For roof middle edge strip Es, Fig. 5 again shows the formation of a 2D separation bubble for fl = 0 ° and 3D conical vortices for other wind directions. The largest magnitude mean, m a x i m u m and minimum pressure coefficients of - 0 . 5 6 , 0.77 and - 2 . 6 8 were measured for fl = 0 °, 90 ° and 0 °, respectively. When comparing these area averaged pressures with the point pressure measurements presented as smoothed contours in Ref. [3], consistent trends are in evidence. Generally the means are in good agreement, while the point rms and peak pressures are larger in magnitude because of the spatial filtering of the relatively few pressure taps in the area averaged measurements. AS1170.2 [4] suggests a local pressure factor KI of 1.5 for areas of size a 2 within a of the edge and 2.0 for areas of size a2/4 within a/2 of the edge. The definition of a is the lessor dimension of 20% of the plan dimension or the roof height. Here a takes the value 0.2 x 300 m m = 60 mm, and a 2 = 3600 m m 2 and a2/4 = 900 m m 2. The pressure factors prescribed in AS1170.2 [4] are used with local mean pressure coefficients and gust dynamic pressures. When the actual area of application exceeds 10 m 2 an area reduction factor KA is introduced tapering from 1.0 to 0.8 for areas greater than 100 m 2. It is interesting to note in passing that the United States standard [5] uses a combined approach to local pressure and area reduction factors but there is no reduction factor for areas greater than 100 ft 2 ~ 10 m 2, which is where the Australia code factor begins. An effort to evaluate local pressure factors has been made using the results of this study. These factors are for edge strip areas 0.2h by 1.0h based on the area-averaged pressure over the parent panel. The strips shown in Fig. 1 have areas of 2000 m m 2,
342
J.D. Ginger, C. W Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337-344 3.5 3 ¸
8. 2.s 2
~[ 1.5
0,5
0
6'o
t~o
tso
2~.o
360
360
Wind Direction, dog
I --B-- Max ~
Min
J
Fig. 6. Estimated local pressure factors for corner strip regions.
3:t
2.51
L)
2
. . . .
L~
0,5
0
60
1'20
180
Wind Direction, deg
l+
Max
~ ' Min
I
Fig. 7. Estimated local pressure factors for middle strip regions.
thus lying between the provisions of the code [4]. Values of K I c a n be estimated from the ratios of the peak strip pressure to peak panel pressure (maxima/maxima and minima/minima) and are shown in Figs. 6 and 7, respectively. Fig. 6 indicates a value of Kl of ~ 3.0 for suction pressures for fl = 0 ° to 60 ° and ~ 1.4 for positive pressures for /Y = 90 ° for the roof corner edge strip regions. Fig. 7 indicates Kl of ~ 2.0 is appropriate for suction pressures for fl = 0 ° to 60 ° and 1.2 for positive pressures for fl = 90 ° for the roof middle edge strip regions. These are somewhat higher than might be anticipated from the code [4], however a better comparison will be found through area-averaged pressure coefficients. Fig. 8 shows the measured area-averaged mean pressure coefficients for the strips and panels compared with the ASl170.2 envelop incorporating both K~ and KA factors. The
.I.D. Ginger, C. I,E. Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337-344
343
-0.5 cL 0 a)
E ~ ~ ' ~
-1.5
-2
0
~,$1170.2values
01s
i
115
2
21s
3
y/h
[~.\\\\'~measured- -
Ka*Kl*Cp ]
Fig. 8. Comparison of mean area-averaged pressure coefficients.
u~ -1-2c). -3-
o
-~
-4-
o.
=5-6-
-7-
-8
0
015
[kN~-~area-averagedCp
i
÷
115 y/h
pointCp
2
215
--
3
Ka*KI*Gu^2*Cp ]
Fig. 9. Comparison of peak area-averaged pressure coefficients.
angle of attack is 0 °. The area reduction factor, KA, has been determined based on the area defined by the distance from the leading edge and a unit width of one building height. It is clear that the measured area-averaged mean pressures are smaller than those predicted in the code. Fig. 9 compares the measured and code I-4] peak area-averaged roof pressure coefficients. The peak code values have been obtained by multiplying the values in Fig. 9 by the gust factor squared, where the gust factor, G, takes the value 1.89 at 10 m height in terrain category 3. Once again the code envelop significantly overestimates the area-averaged pressures. Also shown in Fig. 9 are the peak point pressure
344
J.D. Ginger, C.W. Letchford/J. WindEng. lnd. Aerodyn. 54/55 (1995) 337-344
coefficients along the building centreline for fl = 0 °. It is apparent that the code envelop relates more to peak point pressures than area-averaged values.
4. Conclusions Large magnitude mean and fluctuating pressures were measured within regions of flow separation on low rise building roofs. In turbulent boundary layer flows, the large magnitude mean and peak suction pressures were measured within a region 0.2h from the separating edge. These pressures were previously demonstrated I-3] to be well correlated over a distance of 1.0h. In adopting a quasi-static design approach local pressure factors are required for separated flow regions along edges. An appropriate factor on 0.2h by 1.0h edge strips referenced to 1.5h by 1.0h roof panels encompassing these edge strips is 3.0 for suction pressures for the worst wind directions. This is somewhat higher than anticipated from codes I-4]. However, when comparing actual peak area-averaged pressure coefficients with code values, the latter are significantly higher than those measured here. Much better agreement is evident between code 1-4] and peak point pressure coefficients. The influence of pressure tap distribution in regions of steep pressure gradients remains an area requiring further investigation however the trends observed here should remain as the grid resolution is increased.
Acknowledgement The financial assistance of the Australian Research Council and the Department of Civil Engineering, University of Queensland is gratefully acknowledged.
References [1] R.J. Kind, Worst suctionsnear edgesof flat rooftops on low-risebuildings,J. Wind Eng. Ind. Aerodyn. 25 (1986) 31-47. [2] J.D. Ginger, Characteristicsof large pressures in regions of flow separation on low rise building roofs, Ph.D. Thesis, Universityof Queensland, 1992. I-3] J.D. Ginger and C.W. Letchford, Characteristics of large pressures in regions of flow separation, J. Wind Eng. Ind. Aerodyn.49 (1993) 301-310. 1-4] Australian standard, SAA loading code, Part 2. Wind loads AS1170.2(1989). 1-5] AmericanSocietyof Civil Engineers,Minimum design loads for buildings and other structures, ASCE 7-88 (New York, 1990). [6] M. Kasperski, Aerodynamicsof low rise buildings and codification,J. Wind Eng. Ind. Aerodyn. 50 (1993) 253-262.
n~B
ELSEVIER
Journal of Wind Engineering and Industrial Aerodynamics 54/55 (1995) 337-344
~
~
Pressure factors for edge regions on low rise building roofs J.D. Ginger a, C.W. L e t c h f o r d *'b aDepartment of Civil Engineering, Texas Tech University, Lubbock, TX 79409, USA b Department of Civil Engineering, The University of Queensland, Brisbane, Qld 4072, Australia
Abstract Point and area-averaged pressures are presented for enclosed low rise (height (h)/breadth (b) = 1/3) building roof, based on 1:100 scale wind tunnel measurements obtained in a simulated suburban atmospheric surface layer. Large magnitude mean and peak suction pressures were measured close to the leading edges under the separating shear layer. Significantly larger magnitude mean and peak pressures were measured on 0.2h (wide) by 1.0h (long) rectangular edge strips compared to the pressures on 1.5h by 1,0h roof sections. Pressure factors of the order of 3.0 for suction pressures were obtained for these regions which are larger than code values. However, measured peak area-averaged suction pressures were significantly smaller than code values.
1. Introduction Wind tunnel tests carried out on low rise (height (h)/breadth (b) < ½) building roofs by Kind [1] and Ginger [2] amongst others have shown that the largest pressures were experienced close to edge discontinuities (i.e. leading edges), in regions of flow separation. Ginger [2] studied the spatial and temporal characteristics of the pressures in these regions and this is reported in Ref. [3]. Flow mechanisms over sharp edged roofs are characterized by shear layer separation and subsequent vortex formation. Ginger [2] measured large magnitude mean and fluctuating pressures under the 2D separation bubble for wind flow normal to the separating edge (i.e. fl = 0 °) and under the 3D conical vortex for oblique wind directions (i.e. fl = 15 ° to 75 °) in simulated suburban atmospheric surface layer flow conditions. Large magnitude mean and peak suction pressures were measured within a 0.2h wide region from the separating edges. The largest magnitude point suction pressures were measured for fl ,-~ 30 ° close to the apex of the 3D conical vortex.
* Corresponding author. 0167-6105/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 1 6 7 - 6 1 0 5 ( 9 4 ) 0 0 0 5 2 - F
J.D. Ginger, C.W. Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337-344
338
Most wind loading codes I-4,5] prescribe the quasi-static design approach for determining peak wind loads on low rise buildings. In this method the fluctuating surface pressures depend entirely on the fluctuating wind velocity in the atmospheric boundary layer. Although the quasi-static design is satisfactory for regions where the flow impinges directly, it is not suitable for determining peak pressures where flow separation and vortex formation takes place. Local pressure factors are prescribed to account for the variation of pressure over a surface and more particularly the highly intermittent larger magnitude pressures in the flow separation regions. Area reduction factors are specified to account for the lack of correlation of the surface pressures. Ginger [2] and Ginger and Letchford [3] showed that fluctuating suction pressures were spatially well correlated over lengths of 1.0h, on 0.2h wide rectangular strips along the separating edges under the 2D separation bubble and the 3D conical vortex. The larger magnitude pressure fluctuations under the 3D conical vortex for fl ,,~ 30 ° to 60 ° were better correlated than the pressure fluctuations under the 2D separation bubble for fl = 0 °. Furthermore, for a particular wind direction, conditionally sampled data showed that the peak suction pressures were better correlated than the time averaged pressures. The regions appropriate for applying pressure factors on low rise building roofs in turbulent boundary layer flow conditions are identified as 0.2h by 1.0h rectangular edge strips along the separating edges. The purpose of this paper is to ascertain the effectiveness of code provisions to account for pressures beneath separated flow over roofs.
2. Experimental procedure Tests were carried out in the 3 m wide by 2 m high by 12 m long Boundary Layer Wind Tunnel in the Department of Civil Engineering, University of Queensland. A terrain category 3 (ASl170.2 I-4]) zo = 0.2m boundary layer was simulated at a length scale of 1/100 as described by Ginger [2]. A 300 mm by 300 mm square planform 100 mm high (h) fiat roof enclosed building model with pressure tappings on the roof was tested in this flow. Area-averaged pressures were measured on six
C
D
o i
B *
E
*
o
A _
1GO
__
Bs
Es
As
F8
0
o
F
Cs o°I
o o
160
Fig. 1. Roof panels A to F and edge strips As to Fs.
,I.D. Ginger, C. W Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337-344
339
100 mm by 150 mm panels (labelled A, B, C, D, E, F) using six uniformly spaced tappings, as shown in Fig. 1. Area averaged pressures were also measured on 100 mm by 20 mm rectangular edge strips (labelled As to Fs) surrounding the parent panels using five uniformly spaced tappings also shown in Fig. 1. The effect of wind orientation (fl), was studied over the range 0 ° to 360 °. The point and area-averaged pressure measurement systems had good frequency response beyond 100 Hz at which point they were lowpass filtered and sampled at 250 Hz for 30 s. The rooftop reference velocity was approximately 10 m/s. The positive direction was defined as downwards. The results presented here are the average of five runs.
3. Results
The variation of mean, standard deviation, maximum and minimum area-averaged pressure coefficients with wind direction on the six panels (A to F) is summarized in two cases: a roof corner panel F and a roof middle panel E in Figs. 2 and 3, respectively. For roof corner section F, Fig. 2 shows that the formation of a 2D separation bubble for fl = 0 ° and 90 ° and 3D conical vortices for other wind directions generate large magnitude mean and fluctuating suction pressures. The location of the pressure tappings in relation to the flow separation regions generate the largest magnitude mean, maximum and minimum pressure coefficients of -0.29, 0.64 and -1.16, for fl = 345 °, 285 ° and 75 °, respectively. For roof middle panel E, Fig. 3, shows that the formation of a 2D separation bubble for fl = 0 ° and 3D conical vortices for other wind directions again generate large magnitude mean and fluctuating suction pressures. The largest magnitude mean, maximum and minimum pressure coefficients of -0.32, 0.68 and -1.26, were measured for fl = 0 °, 75 ° and 30 °, respectively. It is worth
"1"
0.5
o
-
-
-
-
-
-
-
-
-
-
0
~, -0.5 CL
-1 c
-1.5
0
go
1:~o
18o
24o
Wind Direction,
I
'-=-- Mean
- - * - - Std. Dev.
~
abo
a6o
Min.
[
deg
Max.
~
Fig. 2. Pressure coefficient variation for roof corner panel F.
340
J.D. Ginger, C.W.. Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337-344 1
~___Z
¸
~-~_._~.___ ~
~
0.5~
O'
~l_..__.ll_~
__
--
-0.5'
-1'
-I .5
6o
12o
180
Wind Direction, deg
I
'm-
Mean
~
Std. Dev. ~
Max.
[]
[
Min.
Fig. 3. Pressure coefficient variation for roof middle panel E. 1
=
~_
-1.5
-2. -2.5 _31
,
0
[
' - ~ - Mean
,
60
,
,
,
120 180 240 Wind Direction, deg
--~
Std. Dev. +
Max.
+
J
,
300
360
Min.
]
Fig. 4. Pressure coefficient variation for roof corner strip F~.
noting that there are not inconsiderable positive peak pressure coefficients (0.6) generated over both the corner and middle roof panels (~ of the roof area). Kasperski [6] has pointed out design problems that arise for structures where the direction of the wind load changes. In particular, the load can align itself with the relevant influence coefficient distribution to produce a maximum load effect. The variation of mean, standard deviation, maximum and minimum area averaged pressure coefficient with wind direction on the six edge strips (As to Fs) is summarized in two cases: a roof corner edge strip Fs and a roof middle edge strip Es in Figs. 4 and 5, respectively.
J.D. Ginger, C.W. Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337 344
341
w.
0 . 5 i ~
:
o. . . . .
. ~ = _ 4 . . ~
-0.51 --]-
-1.5 . . . .
~
"
13-
-2.5-3
0
6'o
1i0
180
Wind Direction, deg
I - - ~ - Mean
~ Std. Dev. +
Max.
+
Min.
I
Fig. 5. Pressure coefficient variation for roof middle strip Es.
For roof corner edge strip Fs, Fig. 4 shows the familiar formation of a 2D separation bubble for fl = 0 ° and 3D conical vortices for other wind directions. The largest magnitude mean, m a x i m u m and minimum pressure coefficients of - 0.79, 0.57 and - 2.75 were measured for fl = 15 °, 285 ° and 0 °, respectively. For roof middle edge strip Es, Fig. 5 again shows the formation of a 2D separation bubble for fl = 0 ° and 3D conical vortices for other wind directions. The largest magnitude mean, m a x i m u m and minimum pressure coefficients of - 0 . 5 6 , 0.77 and - 2 . 6 8 were measured for fl = 0 °, 90 ° and 0 °, respectively. When comparing these area averaged pressures with the point pressure measurements presented as smoothed contours in Ref. [3], consistent trends are in evidence. Generally the means are in good agreement, while the point rms and peak pressures are larger in magnitude because of the spatial filtering of the relatively few pressure taps in the area averaged measurements. AS1170.2 [4] suggests a local pressure factor KI of 1.5 for areas of size a 2 within a of the edge and 2.0 for areas of size a2/4 within a/2 of the edge. The definition of a is the lessor dimension of 20% of the plan dimension or the roof height. Here a takes the value 0.2 x 300 m m = 60 mm, and a 2 = 3600 m m 2 and a2/4 = 900 m m 2. The pressure factors prescribed in AS1170.2 [4] are used with local mean pressure coefficients and gust dynamic pressures. When the actual area of application exceeds 10 m 2 an area reduction factor KA is introduced tapering from 1.0 to 0.8 for areas greater than 100 m 2. It is interesting to note in passing that the United States standard [5] uses a combined approach to local pressure and area reduction factors but there is no reduction factor for areas greater than 100 ft 2 ~ 10 m 2, which is where the Australia code factor begins. An effort to evaluate local pressure factors has been made using the results of this study. These factors are for edge strip areas 0.2h by 1.0h based on the area-averaged pressure over the parent panel. The strips shown in Fig. 1 have areas of 2000 m m 2,
342
J.D. Ginger, C. W Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337-344 3.5 3 ¸
8. 2.s 2
~[ 1.5
0,5
0
6'o
t~o
tso
2~.o
360
360
Wind Direction, dog
I --B-- Max ~
Min
J
Fig. 6. Estimated local pressure factors for corner strip regions.
3:t
2.51
L)
2
. . . .
L~
0,5
0
60
1'20
180
Wind Direction, deg
l+
Max
~ ' Min
I
Fig. 7. Estimated local pressure factors for middle strip regions.
thus lying between the provisions of the code [4]. Values of K I c a n be estimated from the ratios of the peak strip pressure to peak panel pressure (maxima/maxima and minima/minima) and are shown in Figs. 6 and 7, respectively. Fig. 6 indicates a value of Kl of ~ 3.0 for suction pressures for fl = 0 ° to 60 ° and ~ 1.4 for positive pressures for /Y = 90 ° for the roof corner edge strip regions. Fig. 7 indicates Kl of ~ 2.0 is appropriate for suction pressures for fl = 0 ° to 60 ° and 1.2 for positive pressures for fl = 90 ° for the roof middle edge strip regions. These are somewhat higher than might be anticipated from the code [4], however a better comparison will be found through area-averaged pressure coefficients. Fig. 8 shows the measured area-averaged mean pressure coefficients for the strips and panels compared with the ASl170.2 envelop incorporating both K~ and KA factors. The
.I.D. Ginger, C. I,E. Letchford/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 337-344
343
-0.5 cL 0 a)
E ~ ~ ' ~
-1.5
-2
0
~,$1170.2values
01s
i
115
2
21s
3
y/h
[~.\\\\'~measured- -
Ka*Kl*Cp ]
Fig. 8. Comparison of mean area-averaged pressure coefficients.
u~ -1-2c). -3-
o
-~
-4-
o.
=5-6-
-7-
-8
0
015
[kN~-~area-averagedCp
i
÷
115 y/h
pointCp
2
215
--
3
Ka*KI*Gu^2*Cp ]
Fig. 9. Comparison of peak area-averaged pressure coefficients.
angle of attack is 0 °. The area reduction factor, KA, has been determined based on the area defined by the distance from the leading edge and a unit width of one building height. It is clear that the measured area-averaged mean pressures are smaller than those predicted in the code. Fig. 9 compares the measured and code I-4] peak area-averaged roof pressure coefficients. The peak code values have been obtained by multiplying the values in Fig. 9 by the gust factor squared, where the gust factor, G, takes the value 1.89 at 10 m height in terrain category 3. Once again the code envelop significantly overestimates the area-averaged pressures. Also shown in Fig. 9 are the peak point pressure
344
J.D. Ginger, C.W. Letchford/J. WindEng. lnd. Aerodyn. 54/55 (1995) 337-344
coefficients along the building centreline for fl = 0 °. It is apparent that the code envelop relates more to peak point pressures than area-averaged values.
4. Conclusions Large magnitude mean and fluctuating pressures were measured within regions of flow separation on low rise building roofs. In turbulent boundary layer flows, the large magnitude mean and peak suction pressures were measured within a region 0.2h from the separating edge. These pressures were previously demonstrated I-3] to be well correlated over a distance of 1.0h. In adopting a quasi-static design approach local pressure factors are required for separated flow regions along edges. An appropriate factor on 0.2h by 1.0h edge strips referenced to 1.5h by 1.0h roof panels encompassing these edge strips is 3.0 for suction pressures for the worst wind directions. This is somewhat higher than anticipated from codes I-4]. However, when comparing actual peak area-averaged pressure coefficients with code values, the latter are significantly higher than those measured here. Much better agreement is evident between code 1-4] and peak point pressure coefficients. The influence of pressure tap distribution in regions of steep pressure gradients remains an area requiring further investigation however the trends observed here should remain as the grid resolution is increased.
Acknowledgement The financial assistance of the Australian Research Council and the Department of Civil Engineering, University of Queensland is gratefully acknowledged.
References [1] R.J. Kind, Worst suctionsnear edgesof flat rooftops on low-risebuildings,J. Wind Eng. Ind. Aerodyn. 25 (1986) 31-47. [2] J.D. Ginger, Characteristicsof large pressures in regions of flow separation on low rise building roofs, Ph.D. Thesis, Universityof Queensland, 1992. I-3] J.D. Ginger and C.W. Letchford, Characteristics of large pressures in regions of flow separation, J. Wind Eng. Ind. Aerodyn.49 (1993) 301-310. 1-4] Australian standard, SAA loading code, Part 2. Wind loads AS1170.2(1989). 1-5] AmericanSocietyof Civil Engineers,Minimum design loads for buildings and other structures, ASCE 7-88 (New York, 1990). [6] M. Kasperski, Aerodynamicsof low rise buildings and codification,J. Wind Eng. Ind. Aerodyn. 50 (1993) 253-262.