ARTICLE IN PRESS
Journal of Wind Engineering and Industrial Aerodynamics 94 (2006) 833–844 www.elsevier.com/locate/jweia
Wind loads on curved roofs P.A. Blackmore, E. Tsokri Building Research Establishment Ltd, Garston, Watford WD25 9XX, UK Available online 16 October 2006
Abstract Curved roofed buildings are increasingly used in the modern built environment because they offer aerodynamically efficient shapes and provide architects and designers with an alternative to regular rectangular building forms. However, there is little information available on the wind loads on these roof forms. The Eurocode for wind actions (EN1991-1-4) includes pressure coefficients for a limited range of aspect ratio cylindrical roofs from measurements in low-turbulence conditions but only for wind blowing normal to the eaves. There is some concern regarding the reliability of these data, consequently EN1991-1-4 allows National Choice (National Determined Parameter) for wind loads on these roofs. This paper describes a series of parametric wind tunnel studies undertaken at BRE to measure wind pressures on a wide range of curved roof models in a properly scaled atmospheric boundary layer simulation and gives an alternative to the EN1991-1-4 recommended procedure. r 2006 Elsevier Ltd. All rights reserved. Keywords: Wind tunnel testing; Wind pressures; Wind loads; Curved roofs; EN1991-1-4
1. Introduction The Eurocode for wind actions (EN1991-1-4, 2004) gives recommended values for external pressure coefficients on curved roofs. These data were measured in low-turbulence conditions, hence there is some concern regarding their reliability. EN1991-1-4 therefore allows National Choice (National Determined Parameter) for wind loads on these roofs. Each Member State must therefore decide whether to adopt the recommended procedure or to specify an alternative procedure in their National Annexes to EN1991-1-4. There is however surprisingly little information available on the pressure coefficients on these roof Corresponding author.
E-mail address:
[email protected] (P.A. Blackmore). 0167-6105/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2006.06.006
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forms, therefore it is not easy for Member States to make an informed decision on the choice of pressure coefficients. Some other National wind codes, such as the Australian and New Zealand code (Australian/New Zealand Standard, 2002), the Canadian code (User’s Guide—NBC, 1995) and the American (ASCE) code (ASCE, 1996) give external pressure coefficients for curved roofs. Pressure coefficients are also given by Cook (1995) and in EN13031-1:2001 (BS EN13031-1, 2001) for commercial greenhouses (where human occupancy levels are restricted). There are other sources of pressure coefficients on curved roofs such as research papers and commercial wind tunnel studies, but in general these are not in a form suitable for codification or they lack essential experimental details which are necessary for codification purposes. This paper compares the EN1991-1-4 data with other published data and with data measured from a series of parametric wind tunnel studies undertaken at BRE. An alternative procedure is proposed to replace the EN1991-1-4 recommended procedure in the UK National Annex. 2. Comparison of published data The Eurocode for wind actions (EN1991-1-4) gives external pressure coefficients (Cpe,10) on curved roofs with rise height to span ratios (f/d) from 0.05 to 0.5 for side wall height to span ratios (h/d) of 0 and 0.5, for wind blowing on to the eaves. No data are given for wind blowing along the ridge. Fig. 1 shows the data given in EN1991-1-4. The Australian and New Zealand code gives external pressure coefficients (Cpe) on curved roofs for rise height to span ratios (r/d) of 0.05, 0.2 and 0.5, with side wall height to rise height ratio (h/r)p2, for wind blowing on to the eaves. For wind on parallel to the ridge the data for pitched roof is used. The Canadian code has data for a single curved roof of rise height to span ratio of 0.17, and side wall height to span width ratio of 0.08. Data are given for wind onto the eaves and parallel with the ridge. The US (ASCE) code has data for rise height to span ratios (r) from 0 to 0.6 for structures with side walls (no information is given regarding the effect of side wall height) and without side walls. Cook presents data from Blessmann (1987a, b) for rise height to width ratios (R/W) of 0.1, 0.2 and 0.3 for side wall height to width ratios (H/W) of 0, 0.25 and 0.5. EN13031 has data for greenhouses with and without side walls. For greenhouses without side walls one data set is given for all height to span ratios (h/s), for greenhouses with side walls data are given for hr/sp0.4 and hr/sX0.6. It should be noted that each of the above references uses different nomenclature, hereafter the nomenclature given in EN1991-1-4 (Fig. 1) is used. Comparison of these data is not straightforward because they are presented as functions of different rise height parameters, the size of the areas over which the pressure coefficients are averaged are different, and the reference height varies. Notwithstanding these issues, Figs. 2 and 3 show comparisons for the cases of h/d ¼ 0.5, f/d ¼ 0.1 and h/d ¼ 0, f/d ¼ 0.3. From these figures it can be seen that there is a wide spread of Cpe values, especially on the windward section of the roof. In general there is a factor of 2 or more between the smallest and largest values, although in some cases even the sign of the pressure coefficient varies between different data sets. These large differences cannot be
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A
835
B C
f h
cpe,10
I
d
0.8 0.6 0.4 A(
0.2 0
h=
0)
.5)
A 0.05 0.1
0.2
d (h/
>0
0.3
0.4
0.5
f/d
-0.2 -0.4
C C
-0.6 A (h/d > 0.5)
B
-0.8 -1.0 B -1.2
A (h/d > 0.5) Fig. 1. EN1991-1-4 data for curved roofs.
1
Windward zone A
Middle zone B
Leeward zone C EN1991-1-4 ANZ (h/r=1) ANZ (h/r=2)
0.5
ASCE Cook EN13031
Cpe
0
-0.5
-1
-1.5 Roof zone Fig. 2. Comparison between Cpe values for curved roofs with h/d ¼ 0.5, f/d ¼ 0.1.
accounted for by the differences in area, reference height, etc. It is clear that there is wide variability between the data sets and further experimental data were required in order to advise on the appropriate data to be used in the UK National Annex to EN1991-1-4.
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Windward zone A
Middle zone B
Leeward zone C
0.4 0.2 0
Cpe
-0.2 -0.4 -0.6 EN1991-1-4 ANZ (h/r=1) ANZ (h/r=2) Can ASCE Cook EN13031
-0.8 -1 -1.2 -1.4
Roof zone
Fig. 3. Comparison between Cpe values for curved roofs for h/d ¼ 0, f/d ¼ 0.3.
3. Experimental details A parametric study was carried out in the BRE no. 3 boundary layer wind tunnel to measure mean, maximum and minimum external peak gust pressure coefficients on a range of curved roof models. The boundary layer simulation was representative of open country terrain with an integral length scale of approximately 1:250. The models tested had rise height/width ratios (f/d) from 0.05 to 0.5 and wall height/width ratios (h/d) from 0.06 to 1.0—see definition sketch in Fig. 4. The model linear scale was 1:250. These studies also included a range of building length/width (L/d) ratios from 1 to 10 to examine the effect of two-dimensional flow at L/d ¼ 10 and three-dimensional flow at L/d ¼ 1. Table 1 shows the full range of models tested. Sand grains were attached to the roofs of the models to promote supercritical flow separation. The sand grain size, k, was 0.6 mm, giving k/(h+f) ratios from 5 102 to 4 103. Measurements were also made without sand roughened surfaces to investigate the effect of subcritical flow, these results are reported in Breeze et al. (2004). The R3, R4 and R5 models had 46 pressure taps, and the R6 models had 55. Pressures were measured simultaneously using Scanivalve miniature pressure transducers. These sensors are piezoresistive differential sensors with a sampling rate of up to 20 kHz and a full-scale pressure range of 1250 Pa. Module type ZOC33B was used for this study. Data were sampled at 400 Hz, equivalent to 0.25 Hz at full scale. Only one pressure tapped model section was constructed for each roof shape. This had plan dimensions of 100 100 mm. To investigate the effect of building length, L, nonpressure tapped dummy models of the same shape were used. This meant that pressures could only be measured simultaneously over each 100 mm long section of model at any one time. The reference wind velocity was 10 m/s at a model scale height of 200 mm. Mean and peak pressure coefficients (for an averaging period, t, of 1 s full scale) were determined at each roof tap location using the extreme value methodology of Mayne and Cook (1979) and Cook (1982). The reference height for deriving pressure coefficients was taken as the ridge height (h+r) of the model. Measurements were made at 151 increments of
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Fig. 4. Definition sketch with key to loaded areas.
wind direction. Area-averaged pressures were obtained for each of the zones shown in Fig. 4 by averaging the area weighted pressure-time histories at the tap locations within each zone and performing an extreme value analysis on the averaged pressure signal. The peak pressure coefficients were then converted to pseudo-steady coefficients by dividing by K2 (where K is the gust factor ¼ V^ ðt ¼ 1Þ=V¯ ) given in Table 1. 4. Results The results presented here are limited to area averaged pressures over the zones shown in Fig. 4. 4.1. Wind normal to eaves 4.1.1. Pressures on the windward zone ‘a’ Fig. 5 shows the measured worst case positive pressure coefficients averaged over zone ‘a’ for wind directions 07451 for L/b ¼ 1.0. Also included for comparison are data from
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Table 1 Model configurations tested (all dimensions in mm) Model number
Dimensions
R3B1 R3B2 R3B3 R4B1 R4B2 R4B3 R5B1 R5B2 R5B3 R6B1 R6B2 R6B3
Gust factor K
Ratios
h
d
f
h/d
f/d
h/f
6 50 100 6 50 100 6 50 100 6 50 100
100 100 100 100 100 100 100 100 100 100 100 100
5 5 5 10 10 10 30 30 30 50 50 50
0.06 0.50 1.00 0.06 0.50 1.00 0.06 0.50 1.00 0.06 0.50 1.00
0.05 0.05 0.05 0.1 0.1 0.1 0.3 0.3 0.3 0.5 0.5 0.5
1.20 10.00 20.00 0.60 5.00 10.00 0.20 1.67 3.33 0.12 1.00 2.00
2.170 1.838 1.687 2.098 1.819 1.675 1.931 1.724 1.633 1.834 1.699 1.597
1 Measured zone a (h=0.06) Measured zone a (h/d =0.5) Measured zone a (h/d=1) EN zone A (h=0) EN zone A (h/d=0.5) ASCE windward (h=0) ASCE windward (h/d>0) Cook zone a (h=0
0.8
Cpe
0.6
0.4
0.2
0 0
0.05
0.1
0.15
0.2 0.25 0.3 0.35 rise height ratio (r/d)
0.4
0.45
0.5
Fig. 5. Positive pressure coefficients on windward zone ‘a’ for wind dir 07451.
other published sources. The measured data tend to agree closely with the EN1991-1-4 and ASCE data for h/d ¼ 0. There is a weak dependence on h/d in the measured data but for practical purposes this is so small that it can be disregarded. This h/d independence is consistent with the ANZ code, but is quite different from EN1991-1-4 and ASCE which both have a strong dependency on h/d. The measured data also agree quite closely with the data from Cook for h/d ¼ 0. The data presented in Fig. 5 are for L/b ¼ 1.0. The measured data (not presented here) are also similar for L/b ¼ 2.0, 4.0 and 10.0, which gives a high degree of confidence in the measurements. Therefore, based on the experimental data it seems to be reasonable, for codification purposes, to assume that positive pressures in windward zone ‘a’ can be considered to be independent of h/d and L/d.
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4.1.2. Suctions on the windward zones ‘a+b’ Fig. 6 shows the measured worst case negative pressure coefficients averaged over zones ‘a+b’, for wind directions 07451 for L/d ¼ 1.0. These zones are broadly comparable with those used in EN1991-1-4. The measured suctions on the windward zones ‘a+b’ reduce with increasing f/d. This is generally similar to the EN behaviour. There is a clear dependency on h/d, also supported by the data from Cook, whereas EN1991-1-4 has a single curve for all h/dX0.5. At f/d ¼ 0.2, the EN1991-1-4 Cpe values are the same as those at f/d ¼ 0.1, this trend is not supported by any other data. Unfortunately this cannot be validated from the BRE measurements because no data were measured for f/d ¼ 0.2. However, the trends in the measured data and the data from other sources agree quite well at f/d ¼ 0.2, so it is speculated that the large suction given in EN1991-1-4 at f/d ¼ 0.2 is probably incorrect. 4.1.3. Suctions on the central zones ‘c+d’ Fig. 7 shows the measured worst case negative pressure coefficients averaged over central zones ‘c+d’, for wind directions 07451, for L/d ¼ 1.0. In the central zone ‘c+d’, the measured suctions tend to increase with f/d. A similar trend is also observed with the EN1991-1-4 data, although the measured data are of the order of 50% smaller than the EN values. The data from Cook for f/dX0.25 are similar to the EN values. The ASCE values show the opposite trend of decreasing suction with increasing f/d. 4.1.4. Suctions on the leeward zones ‘e+f’ Fig. 8 shows the measured worst case negative pressure coefficients averaged over the leeward zones ‘e+f’ for wind directions 07451, for L/d ¼ 1.0. In the leeward zones ‘e+f’, the measured suctions generally seem to be independent of f/d up to f/d ¼ 0.3. For larger f/d the measured suctions show a sharp increase. It is not clear at this stage what the cause of this, but it is consistent with measurements made on other models with L/d ¼ 2.0, 4.0 and 10.0, so it appears to be a real effect.
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
-0.2
Cpe
-0.4 -0.6 -0.8 -1 -1.2 -1.4
EN zone A (h/d > = 0.5) Measured data zone a+b (h/d = 0.5) Measured data zone a+b (h/d = 1) Cook zones a+b (h/d = 0.25) Cook zones a+b (h/d = 0.5) ASCE windward (h>0)
Rise height ratio (r/d)
Fig. 6. Negative pressure coefficients on windward zones ‘a+b’ for wind direction 07451.
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840
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 -0.2
Cpe
-0.4 -0.6 -0.8 -1 Measured data zone c+d (h/d=0.06) Measured data zone c+d (h/d=1) ASCE Middle zone Cook (h/d=.25)
-1.2 -1.4
Measured data zone c+d (h/d=0.5) EN zone B Cook (h/d=0) Cook (h/d=.5)
Rise height ratio (r/d)
Fig. 7. Negative pressure coefficients on middle zones ‘c+d’ for wind dir 07451.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0
Cpe
-0.2
-0.4
-0.6 Measured datazone e+f (h/d=0.06) Measured datazone e+f (h/d=1) ASCE Leewardzone Cook (h/d=0.25)
Measured datazone e+f (h/d=0.5) EN zone C Cook (h/d=0) Cook (h/d=0.5)
-0.8 Rise height ratio (r/d) Fig. 8. Negative pressure coefficients on leeward zones ‘e+f’ for wind dir 07451.
Figs. 5–8 and the above discussion is based on models with L/d ¼ 1.0. From measurements on models with L/d ¼ 2.0, 4.0 and 10.0 it was found that the positive pressures on the windward zone ‘a’ and the suctions in leeward zones ‘e+f’ appear to be independent of L/d. However, the suctions in windward zones ‘a+b’ and the central zones ‘c+d’ increase with increasing L/d. Figs. 9 and 10 show wind tunnel measurements over windward zones ‘a+b’ and central zones ‘c+d’, respectively, for L/d of 1.0, 2.0, 4.0 and 10.0. From Fig. 9 it can be seen that the suction on zones ‘a+b’ increases by about 10% for each increase in L/d from 1.0 to 2.0 to 4.0, i.e. there is a non-linear increase in suction with L/d. The ANZ code applies a factor ¼ (L/d)0.25 to account for increasing L/d. The suctions measured on windward zones ‘a+b’ are generally fairly similar at all positions along the length of the roof.
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0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
841
0.5
0 -0.2 -0.4
Cpe
-0.6 -0.8 -1 EN zone A (h/d>=0.5) Measured data, L=100 Measured data, L=200 Measured data, L=400 Measured data, L=1000
-1.2 -1.4 -1.6 -1.8 Rise height ratio (f/d)
Fig. 9. Effect of building length on pressure coefficients on windward zones ‘a+b’.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
-0.2
Cpe
-0.4 -0.6
P1
-0.8
P2
-1 -1.2 -1.4
EN zone A (h/d >=0.5) Measured data,L/d=1 Measured data,L/d=2 Measured data,L/d=4 Measured data,L/d=10 (P1) Measured data,L/d=10 (P2) Measured data,L/d=10 (P3) Measured data,L/d=10 (P4) Measured data,L/d=10 (P5)
P3 P4 P5
Rise height ratio (r/d)
Fig. 10. Effect of building length on pressure coefficients on central zones ‘c+d’.
Fig. 10 shows that the suction on central zones ‘c+d’ generally increases with increasing L/d; again the increase is non-linear. The suctions on the central roof zones ‘c+d’, are highly dependent on the position along the roof, l. For example, at the gable end of the roof at section l ¼ 0.1L (measurement P1 in Fig. 10), Cpe ¼ 0.62, whereas halfway along the roof at the mid-section where l ¼ 0.5L, (measurement P5 in Fig. 10) Cpe ¼ 1.35, i.e. the suction more than doubles as l increases from 0.1L to 0.5L. This is evidence that the flow is changing in nature from three-dimensional flow on the end sections to twodimensional flow in the central section. The EN1991-1-4 zone B values shown in Fig. 10, are similar to the wind tunnel measurements made at l ¼ 0.5L on the central zone ‘a+b’, of the 1000 mm long model. It appears therefore that the EN values for zone B are more appropriate for long buildings with two-dimensional flow rather than shorter buildings which generate three-dimensional flow.
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-0.2 Zone I
-0.4 -0.6 Cpe,10
-0.8 Zone H
-1 Zone G
-1.2 Zone F
-1.4 -1.6 -1.8
solid symbols - EN1991-1-4 duopitch data open symbols- measurements on curved roofs
0
5
10 15 20 25 30 35 40 45 Roof pitch (average roof pitch for curved roofs) e/4
F H
Key to roof zones
wind
G
I ridge or trough
= 90° G H e/4
50
I
F
Fig. 11. Comparison between curved roof measurements and duo-pitch data for wind direction 901.
4.2. Wind parallel to the eaves EN1991-1-4 does not give any guidance for wind blowing onto the eaves of curved roofed buildings, some codes, such as ANZ treat curved roofs for this wind direction as if they were duo-pitch roofs. Fig. 11 shows a comparison between measurements made on the curved roof models for L/d ¼ 1.0, with data given in EN1991-1-4 for duo-pitch roofs. The appropriate pitch angle, a, of the curved roofs has been determined by drawing a straight line from eaves to ridge, i.e. a ¼ tan1(f/0.5d). The codified duo-pitch data are not given as a function of side wall height h, therefore for the curved roof data the worse case values for all wall heights have been used (the measured data are actually only very weakly dependent on h so this seems to be a reasonable assumption). It can be seen from Fig. 11 that there is reasonable agreement between the measured data and the EN duo-pitch data for all roof zones except zone G. Here the duopitch suctions become increasing larger than the measurements as the pitch angle increases. This is probably caused by vortices shed from the ridge of the duopitch roofs which does not occur on curved roofs. However, it is judged, for the purposes of codification of wind pressures on curved roof buildings, that it is reasonable to use the EN duopitch data for the wind parallel to the ridge, i.e. wind direction 907451. The pitch angle a of the curved roofs should be taken as a ¼ tan1(f/0.5d). 5. Proposed variation to the EN1991-1-4 recommended method From the results presented it can be seen that in most cases, with minor changes, the EN1991-1-4 values give a safe envelop to the wind tunnel measurements for L/dp1.0,
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1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -1.4 0.05
843
Zone A for all h/d
Zone A for h/d≥ 0.5 Zone C Zone B
0.1
0.15
0.2 0.25 0.3 0.35 Rise to width ratio (r/d)
0.4
0.45
0.5
Fig. 12. Proposed revision to EN199-1-4 Fig. 7.11 for curved roofs.
although in some cases, particularly for the zone B values these values can be very conservative. Significant reductions in wind loads could be made by developing a more sophisticated model based on f/d and h/d ratios. However, for the purposes of codification a simple revised version of the EN approach might be more appropriate. Fig. 12 shows a proposed modified version of EN Fig. 7.11 based on the wind tunnel measurements. Fig. 12 is for L/dp1.0. The suctions on zones A and B increase with increasing L/d. For zone A this can be accounted for by subtracting the factor (1(L/d)0.25) from the values for L/d ¼ 1. For zone B this effect can be accounted for by multiplying the values for L/d ¼ 1 by (L/d2)0.35. The positive values in zone A and the suctions in zone C do not require correction for L/d. 6. Conclusions A series of parametric measurements have been carried out at BRE to measure wind pressures on curved roofs. The main conclusions that can be drawn from this study are: For wind angle 07451 (wind normal to the eaves); the EN1991-1-4 recommended procedure requires some modifications in order to give safe and economical design values of wind pressure. The proposed revision is shown in Fig. 12. For wind angle 907451 (wind parallel to the ridge); for the purposes of codification the EN1991-1-4 data for duo-pitch roofs may be used to determine wind pressures on curved roofs. The effective pitch angle a of the curved roofs should be taken as a ¼ tan1(f/0.5d). References ASCE Standard, Minimum design loads for buildings and other structures, ANSI/ASCE 7-95, American Society of Civil Engineers, June 1996. Australian/New Zealand Standard, Structural design actions, Part 2: wind actions, AS/NZS 1170.2:2002, June 2002. Blessmann, J., 1987a. Acao do vento em coberturas curvas, 1a Parte. Caderno Tecnico CT-86. Porto Alegre, Universidade Federale do Ria Grande do Sul.
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Blessmann, J., 1987b. Vento em coberturas curves—pavilhoes vizinhos, Caderno Tecnico CT-88. Porto Alegre, Universidade Federale do Ria Grande do Sul. Breeze, G., Blackmore, P., Tsokri, E., 2004. Wind tunnel tests on low-rise cylindrical roofs, 6th UK Wind Engineering Society Conference, Cranfield, September 2004. BS EN13031-1, Greenhouses—design and construction: Part 1: Commercial production greenhouses, CEN, 2001. Cook, N.J., 1982. Calibration of the quasi-static and peak-factor approaches to the assessment of wind loads against the method of Cook and Mayne. J. Wind Eng. Ind. Aero. 10, 315–341. Cook, N.J., 1995. The designers guide to wind loading of building structures, Part 2. Butterworths. EN1991-1-4, Eurocode 1: Actions on structures—Part 1–4: General Actions—wind actions, Latest draft, September 2004. Mayne, J.R., Cook, N.J., 1979. Acquisition, analysis and application of wind loading data. In: Proceedings of Fifth International Conference on Wind Engineering, CO, USA. User’s Guide—NBC 1995 Structural commentaries (Part 4), NRC-CNRC, Canadian Commission on Building and Fire Codes, National Research Council of Canada, April 2002.
