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The influence of small open fields on wind loads on low buildings
Journal of Wind Engineering and Industrial Aerodynamics 77&78 (1998) 233—244
The influence of small open fields on wind loads on low buildings M.A. Young*, B.J. Vickery Applied Research Associates, Inc., 811 Spring Forest Road, Suite 100, Raleigh, NC 27609, USA
Abstract In established residential areas it is not uncommon for existing schools and shopping plazas to be well shielded by trees and dwellings for most directions but to be open over a very limited fetch of a playground or a parking area. Few codes provide advice on the evaluation of loads in such circumstances; but to ignore the shielding would result in a significant overestimate of the wind loads for the design of extensions or modifications to bring existing structures up to present day standards. This study predicts the uplift loads on these types of structures through an analysis of a database of calculated reactions measured on several structures. The paper outlines the development of local exposure factors that, by accounting for effects of small open fields, can refine the prediction of uplift forces on flat roof buildings in suburban areas. A modification to the National Building Code of Canada model is used to apply these factors. A study of the flow over an array of elements was used to develop a method to apply the local exposure factors to a structural system. 1998 Elsevier Science Ltd. All rights reserved.
1. Introduction The provisions of the National Building Code of Canada (NBCC) [1] aimed at the design of low buildings were originally developed from research by Stathopoulos [2]. In his thesis, Stathopoulos conducted many tests that examined the effect of several items on low building wind loads: including upstream exposure, building geometry, internal pressure, and shielding from adjacent structures. The loads derived from open country terrain were finally adopted in a simplified format into the NBCC as the primary design guidelines.
* Corresponding author. E-mail: [email protected]. Also: Boundary Layer Wind Tunnel Laboratory, Faculty of Engineering Science, The University of Western Ontario, London, Ont., Canada N6A 5B9. 0167-6105/98/$ — see front matter 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 1 4 6 - 9
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These guidelines were incorporated in the format of a zoning system on the roof of the building that featured edge and corner zones that saw increases in pressure over the interior region of the roof. This zoning system is shown in Fig. B-9 of the User’s Guide to the National Building Code of Canada [3]. Although a complete database of loads in suburban flow was also measured in Stathopoulos’ thesis, only the open country loads were used in the code because; the [suburban] results were generally less severe and the trends were not sufficiently consistent to be worthy of a separate set of specifications. This decision [to use open country terrain loads only] was also based on the fact that enforcement often defaults to open terrain, as the inherently conservative choice [4]. However, when an existing structure requires repair or modification and the structure resides in a built up area such as a residential suburb, the “inherently conservative choice” of open country terrain wind loads becomes unnecessarily punitive since suburban wind loads are generally far less than open country loads. But care must be taken for suburban structures located near small open fields like parking lots and playgrounds. In these cases, acceleration of the wind is expected and loads higher than a uniformly shielded suburban environment may be expected. This paper presents a technique that was used to improve predictions of uplift loads on flat roofed low buildings that are specifically exposed to both suburban arrays of buildings and adjacent open fields. To distinguish between the effect of the small open field and the shielding from adjacent structures, a local exposure factor was developed and applied in a modified version of the NBCC model. The local exposure factor is intended to supplement the usual exposure coefficient that describes the variation of the boundary layer flow with roughness of terrain. The local exposure factors were derived from a database of wind tunnel tests at The University of Western Ontario (referred to hereafter as the database study), and are intended to be applied only to structures that are similar to the buildings of which the database is comprised. A separate study of the flow over an array of rectangular elements (referred to as the array study) is used as justification for a structural zoning system that facilitates application of the local exposure factors.
2. Array study The primary focus of the array experiments was to measure the variation of pressure distributions on a rectangular prism when open fields of various sizes were created in a uniform array of which the prism was a part. A wind profile above the array had a full-scale aerodynamic roughness length of 1.0 m, and a turbulence intensity of 0.32 at a height of 10 m. With the height of the building used as a typical dimension, the Reynolds number of the simulation is 2.1;10. The pressure model tested in these experiments (Fig. 1) was a flat rectangular prism with 10 pressure taps aligned in a row on the roof. At a length scale of 1 : 200, the full-scale dimensions of the model are 5;12;24 m (height;length;width). Pressure
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time series from these taps were measured, recorded, and used to calculate reactions of two joists aligned end to end along the line of taps. Wind-pressure measurements have concentrated on the joists in the “middle bay” of the building. Therefore, only one wind direction, perpendicular to the long edge, was tested because this direction has been shown to govern the uplift loading on middle joists [2]. Additionally, measurements on buildings with relative heights of 0.51H, 1.25H, and 1.5H were made. The pressure model was tested in a uniform array of rectangular elements with unequal lateral and longitudinal spacing. The array consisted of 28 rows of elements with dimensions and spacing given in Table 1. This arrangement is typical of many residential areas in North America. The pressure model was located in the middle of the 22nd row of the array, and three lengths of upstream open fields were created by cumulatively removing rows 22, 21, and 20 as shown in Fig. 2. This figure shows a field length of 0 m. Removing the array elements of row 22 would create a field length of 30 m. 2.1. Reaction coefficient Reactions for two joists arranged end to end along the row of taps on the pressure model were calculated by forming linear combinations of the pressure time series. The
Fig. 1. Geometry and pressure tapping of model in array study (dimensions in mm).
Table 1 Geometry of uniform array Description
Model dimensions
Full-scale dimensions
Ratios
Array elements Array spacing — lateral Array spacing — along wind Lateral gap Along wind gap Elements per row Density
25 : 50 : 75 mm (H : ¸ : ¼) 100 mm centre to centre 200 mm centre to centre 25 mm 150 mm 23 18.8%
5 : 10 : 15 m (H : ¸ : ¼) 20 m centre to centre 40 m centre to centre 5m 30 m
1 : 2 : 3 (H : ¸ : ¼) 4H 8H H 6H
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Fig. 2. Layout of open-field test site for model in uniform array. Only portions of array rows are shown for clarity. Field length ¸ measured from model to upstream row.
reaction has been calculated by instantaneously summing the moments of local pressures sampled at five pressure taps along the beam, assuming that each span is a simply supported beam. No dynamic amplification load factors have been used in the analysis, and joint action among several joists has been ignored. A reaction coefficient, C , was defined as the ratio of the reaction at one end of the joist to the 0 total force of a uniform distributed load of q . Thus, if a unit load of q is applied to the entire beam, the reaction coefficient will be equal to 0.5. To calculate the reaction, R , as a force per unit width 52 R "C q l , (1) 52 0 G lr L C " C G G, (2) 0 .G s l G G where q is the mean dynamic pressure at reference height, l is the total joist roof G area exposed to pressure (per unit width), C the reaction coefficient, s is the span of 0 joist, l equals the tributary area for tap i (per unit width), r is the moment arm of G G tributary area i, C the pressure coefficient at position i referenced to mean dynamic .G pressure q , and n the number of pressure taps along joist. 2.2. Results from the array study Fig. 3 shows the variation of the peak reaction coefficient with upstream open field length, ¸ , at each of the four joist reaction locations on the roof of the pressure model.
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Fig. 3. Peak reaction coefficients for all four reactions along joist line plotted as a function of upstream field length, ¸ .
The four reaction locations are described using the relative location of the reaction from the windward edge. Three deductions can be made from Fig. 3. Firstly, the magnitude of reactions on the windward half of the roof (reaction locations Lead and 2nd) are much higher than the leeward half (reaction locations 3rd and 4th) even for a field length of 0 m. Therefore, the loads on the windward joist are going to govern the design of the leeward joist, since similar loads will be induced by winds approaching from 180°. Secondly, the windward joist reactions are seen to be dependent on the upstream field length, whereas the leeward joist reactions are hardly dependent on field length at all. Thus, these data indicate that the local exposure effect of the open field only affects the windward joist. It can be surmised that the local exposure change affects the separation bubble at the leading edge of the building and that this separation bubble reattaches to the roof somewhere along the span of the windward joist. Finally, the variation of the reaction coefficient appears to level off rapidly with increasing field length, and a constant local exposure factor can be expected to exist beyond a certain field length. Other results, that varied the ratio of the building height to the array height, indicate this variable also affects the local exposure factor [5]. However, given that most suburban buildings are not a series of flat roofed structures like this array experiment, this variation of local exposure factor with height is unclear. 2.3. Local exposure zones The above observations were taken into consideration in developing a zoning system to be used in applying the local exposure factors that were derived from the database study. While the system resembles the zoning system found in the National Building Code of Canada [3], it is focused on classifying the underlying structural
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Fig. 4. Explanations of local exposure zones.
layout into various zones. This method of joist classification indicates which quadrant of the wind compass will dominate the response of the joist. These zones classify the joist into one of the four main wind quadrants — north, east, south, or west — or into an interior zone where there is not one clear direction that dominates the response. Guidelines for the application of these zones are outlined in Fig. 4. The largest zones should try to follow the orientation of the main building with respect to the compass directions. For instance, in the buildings in Cases (a) and (b) of Fig. 4, the North—South zones dominate on buildings oriented in the East-West direction, and the East—West zones are dominant on buildings oriented in the North—South directions. Smaller end zones should be parallel to the joists and have a width equal to the edge zone width given in the NBCC [1,3]. The end zones should also cover whole joists, and in general, should not break the reaction points of a joist into two separate zones. Only in cases where the joists span from one side of the building to the other should the zoning system bisect the joist. For example, in Case (c), the East and West zones separate the reactions at each end of the joist into two categories. The logic for this unique case is rationalised by the fact that each reaction will be dominated by the uplift created by the separation bubble at each edge. More complicated structures should follow the guidelines of Case (d) keeping in mind the idea of maintaining whole joists within a single zone. In Case (d), the East end of the building includes two small edge zones that are influenced by the north and south winds. Note that the smaller joists in the centre of the buildings in Cases (a) and (b) are classified as “interior” joists since they are an equal distance from either edge, and no separation bubble will extend to this zone to dominate the response. Separation bubble lengths are in general limited to a distance of two building heights from the edge of a building as suggested in Fig. B-9 of the NBCC User’s Guide [3]. So if a joist is wholly away from the separation bubble from winds from all sides of the building, then it should be assigned to an interior zone. Otherwise, the inside joists should be assigned to one of the zones that will not divide up the joist, as in Case (e). The above zoning system was used to define the local exposure factor of each joist on a building in the database study. Local exposure classifications are simple and operate as follows: If the distance from the roof zone to the next major structure is more than a typical street width of 50 m, the roof area is considered to have an open local exposure; otherwise, it is shielded. For example, in Case (c), if the south side of the
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building is next to the street and across the street are residential houses, the south orientation zones are considered as shielded. However, if the other three sides of the building are facing a playground, the West, North, and East zones would be considered to be open. This zoning system is appropriate only when flow reattachment takes place on the roof. Guidelines by Hosker [6] have been used to indicate that the flow re-attaches at about the centre of the roof for low buildings with dimensions of the order of 10 by 20 m in plan.
3. Database study Nine pressure models of schools in Ontario, Canada that are of a masonry wall construction with open web steel joists were tested at a length scale of 1 : 100 in Boundary Layer Wind Tunnel II at The University of Western Ontario. Each model was tested in an appropriate suburban exposure for each site (roughness length of 0.13 m full scale), with a generic proximity model that included details of open fields and adjacent buildings within 120 m of the site. A typical layout of a proximity and pressure model from one of the nine tests is shown in Fig. 5. With the height of the
Fig. 5. Typical school and proximity model tested in database study (dimensions in mm).
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model building used as a typical dimension, the Reynolds number of the simulation is 4.2;10. Instantaneous time series of the pressure were recorded and joist uplift reactions were calculated from linear combinations of these pressures in an identical manner to Eq. (2). Internal pressures were estimated as the arithmetic sum of pressures measured on the windward wall of the building, and incorporated into the calculation of the reactions coefficient. Integration with local meteorological data yielded predictions of the 30 year return period reaction for each joist on each school. In all, 639 reactions at various locations on the roof were examined and assembled in a database. 3.1. Modification of NBCC model The predicted wind tunnel loads were compared to the NBCC model and two subsequently modified versions of the model. The basic NBCC equation for wind load reactions on the roof is formulated as follows: R " q C C C A r , (3) , !! G G G where R is the joist reaction, q the mean dynamic velocity pressure at 10 m in , !! open terrain, C the exposure factor representing the variation of gust speed with height, C the pressure factor, C the gust factor, and A and r are the tributary area G G and moment arm of pressure region i for calculation of the reaction. Like many code models, the NBCC model is based on quasi-steady theory that says that the wind pressures scale according to the peak velocity pressure at the roof height of the structure. Therefore, the exposure factor, C , is a gust pressure profile rather than a mean pressure profile. It should be noted that the NBCC does not recognise a reduction in the wind loads due to shielding effects or suburban exposures. It only uses an open exposure profile and approximates this profile with the following equation: C "(z/10) C *0.9,
(4)
where z is the height above the ground in metres. Ho [7] indicates that the ideal exposure factor, C*, would be a ratio of the peak ) to the peak velocity at roof height in an appropriate exposure for the site (»K X & velocity at 10 m height in open country (»K ): C*"(»K /»K ). X &
(5)
In this study, the Harris and Deaves [8] model for strong winds was used, with aerodynamic roughness lengths of 0.02 and 0.2 m for open country and suburban exposures respectively, to calculate a C* for a suburban profile. The peak velocity is assumed to be equal to the mean velocity plus 3.7 times the RMS velocity. At a height of 5 m, the suburban C* is approximately 0.53 compared to the 0.9 specified in the NBCC.
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Two modified versions of the NBCC model were compared to the wind tunnel tests. The first modification incorporated the ideal exposure factor, C*, into the original model: C* . (6) R "R , !! C The second modification incorporated the local exposure factors, C* , (derived below) into the suburban model: R "R C* . (7) ! A ratio called the uplift reaction ratio, URR, was used to compare the wind tunnel predicted uplift reaction, R , with the reactions calculated from the three NBCC 52 models. The ratios for the open country, suburban and local exposure model are defined as URR "R /R , URR "R /R , URR "R /R . (8) 52 , !! 52 ! 52 ! A URR equal to 1.0 indicates a perfect match between wind tunnel and predicted reactions. A URR less than 1.0 indicates over-prediction on behalf of the NBCC models, and a URR greater than 1.0 an under-prediction. The NBCC models also included allowances for internal pressure in a uniformly leaky building (Category 2 in Ref. [3]). 3.2. Local exposure factor Three joist descriptions were applied to the 639 reactions to divide the database into sub-groups that could be used for deriving local exposure factors. The three descriptions were “local exposure zone”, “location type”, and “frame location”. The local exposure zone was applied using the system outlined in Section 2.3. The location type described the location of the reaction according to the zoning system outlined in Fig. B-9 of the NBCC [3]. The frame location describes whether the joist is an “end bay” joist or a “middle bay” joist. The entire database was subdivided according to the three descriptions, and the statistics of each sub-group were calculated. Table 2 shows the average and standard deviation of URR in each of the sub-groups. For middle frame joists, Table 2 shows a slight increase in variability of URR with open local exposure but a more distinct increase in the mean values. For the end frame joists, little difference was found between the open and shielded local exposures. It was found that local exposure factors defined as two standard deviations of URR above the mean (Eq. (9)) were effective in improving the predictions of the model. The local exposure factors derived in this manner are shown for each sub-group in Table 3: C* "URR #2p . (9) 300 When the derived local exposure factors for the open and shielded conditions are compared, it is seen that there is a smaller local exposure effect on the end joists than
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Table 2 Statistics of URR from nine buildings grouped by frame location, local exposure, and location type
Table 3 Local exposure factors, C* , derived from Table 2
there is on the middle joists. In fact, the interior location types experience increases in load for the shielded case. Also note that the local exposure factor for the interior local exposure zones are small. There is little local exposure effect on these joists. For the middle joists, the increase in open field loads over suburban loads is seen to be of similar magnitude to the reduction of suburban loads from open country loads. This fact is apparent when the product of the ideal suburban exposure coefficient and the open local exposure factor (0.53;1.37"0.73) is compared with the open country exposure coefficient (0.9). The difference is only 20%, whereas the difference for the
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Fig. 6. Relative frequency and cumulative frequency distributions of URR for open country, suburban, and local exposure models.
shielded local exposure is 32%. In other words, the response of the open joists quickly becomes comparable to loads predicted for the open country terrain case upon which the original code is based. Fig. 6 shows the frequency distributions and cumulative frequency distributions of URR’s for the three models. The original model (represented as URR ) over-predicts loads by 50% on average, but can vary from as little as 5% to as much as 75%. When the suburban modification to the code is incorporated (URR ), the over-prediction reduces to 30% on average, but under-predictions occur for about 25% of the loads. However, when the local exposure factor (URR ) is incorporated into the model, the ! percentage of loads that are under-predicted is reduced to less than 5% while still reducing the loads from the original code model. By selectively increasing loads on areas affected by open local exposure, the effects of suburban terrain can be successfully incorporated into the prediction process while avoiding un-conservative predictions. These derived local exposure factors were used with the local exposure model to predict the loads on three other schools that were tested independently in the wind tunnel [5]. The 228 reactions of these three schools showed similar success in improving the wind load predictions as did the original 639 reactions from this study.
4. Conclusions The effect of suburban exposures on wind loads on roofs of low buildings is hard to incorporate into the National Building Code of Canada because of the variability of the loads. This variability is partially induced by variation of local surroundings such as small open fields. The local exposure effects due to small fields adjacent to the building have been incorporated into a code-like model by the use of local exposure factors and a structural zoning system. This modification to the NBCC code method
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has been used to refine the predicted loads on schools and shopping plazas while minimising the under-prediction of uplift loads. Loads on joists exposed to small open fields can approach loads created by open country terrain and therefore, allowance for this effect must be made. These increases are limited to the portions of the roof that are closest to the small open field, and the effect is more dominant on middle frame joists than end frame joists. These conclusions are limited to flat roofed structures with joists approximately 7 or 8 m in length, located among roughness elements of approximately the same height as the structure.
References [1] Canadian Commission on Building and Fire Codes, The National Building Code of Canada 1995, National Research Council of Canada, Ottawa, 1995. [2] T. Stathopoulos, Turbulent wind action on low rise buildings, Ph.D. Thesis, The University of Western Ontario, London, Ontario, 1979. [3] Canadian Commission on Building and Fire Codes, User’s Guide — NBC 1995 Structural Commentaries (Part 4), National Research Council of Canada, Ottawa, 1995. [4] A.G. Davenport, T.C.E. Ho, D. Surry, The codification of low rise building wind loads, 7th US National Conf. on Wind Engineering, Los Angeles, 27—30 June 1993. [5] M.A. Young, Effect of open fields on low building wind loads in a suburban environment, M.E.Sc. Thesis, The University of Western Ontario, London, Ontario, June 1997, 226 pp. [6] R.P. Hosker, Flow around isolated structures and building clusters: a review, ASHRAE Trans. Part 2B 91 (1985) 1671—1692. [7] T.C.E. Ho, Variability of low building wind loads, Ph.D. Thesis, The University of Western Ontario, London, Ontario, 1992, 364 pp. [8] R.I. Harris, D.M. Deaves, The structure of strong winds, Wind Engineering in the Eighties, Proc. CIRA Conf., 12—13 November 1980, Construction Industry Research and Information Association (CIRA), London, 1981.
The influence of small open fields on wind loads on low buildings M.A. Young*, B.J. Vickery Applied Research Associates, Inc., 811 Spring Forest Road, Suite 100, Raleigh, NC 27609, USA
Abstract In established residential areas it is not uncommon for existing schools and shopping plazas to be well shielded by trees and dwellings for most directions but to be open over a very limited fetch of a playground or a parking area. Few codes provide advice on the evaluation of loads in such circumstances; but to ignore the shielding would result in a significant overestimate of the wind loads for the design of extensions or modifications to bring existing structures up to present day standards. This study predicts the uplift loads on these types of structures through an analysis of a database of calculated reactions measured on several structures. The paper outlines the development of local exposure factors that, by accounting for effects of small open fields, can refine the prediction of uplift forces on flat roof buildings in suburban areas. A modification to the National Building Code of Canada model is used to apply these factors. A study of the flow over an array of elements was used to develop a method to apply the local exposure factors to a structural system. 1998 Elsevier Science Ltd. All rights reserved.
1. Introduction The provisions of the National Building Code of Canada (NBCC) [1] aimed at the design of low buildings were originally developed from research by Stathopoulos [2]. In his thesis, Stathopoulos conducted many tests that examined the effect of several items on low building wind loads: including upstream exposure, building geometry, internal pressure, and shielding from adjacent structures. The loads derived from open country terrain were finally adopted in a simplified format into the NBCC as the primary design guidelines.
* Corresponding author. E-mail: [email protected]. Also: Boundary Layer Wind Tunnel Laboratory, Faculty of Engineering Science, The University of Western Ontario, London, Ont., Canada N6A 5B9. 0167-6105/98/$ — see front matter 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 1 4 6 - 9
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These guidelines were incorporated in the format of a zoning system on the roof of the building that featured edge and corner zones that saw increases in pressure over the interior region of the roof. This zoning system is shown in Fig. B-9 of the User’s Guide to the National Building Code of Canada [3]. Although a complete database of loads in suburban flow was also measured in Stathopoulos’ thesis, only the open country loads were used in the code because; the [suburban] results were generally less severe and the trends were not sufficiently consistent to be worthy of a separate set of specifications. This decision [to use open country terrain loads only] was also based on the fact that enforcement often defaults to open terrain, as the inherently conservative choice [4]. However, when an existing structure requires repair or modification and the structure resides in a built up area such as a residential suburb, the “inherently conservative choice” of open country terrain wind loads becomes unnecessarily punitive since suburban wind loads are generally far less than open country loads. But care must be taken for suburban structures located near small open fields like parking lots and playgrounds. In these cases, acceleration of the wind is expected and loads higher than a uniformly shielded suburban environment may be expected. This paper presents a technique that was used to improve predictions of uplift loads on flat roofed low buildings that are specifically exposed to both suburban arrays of buildings and adjacent open fields. To distinguish between the effect of the small open field and the shielding from adjacent structures, a local exposure factor was developed and applied in a modified version of the NBCC model. The local exposure factor is intended to supplement the usual exposure coefficient that describes the variation of the boundary layer flow with roughness of terrain. The local exposure factors were derived from a database of wind tunnel tests at The University of Western Ontario (referred to hereafter as the database study), and are intended to be applied only to structures that are similar to the buildings of which the database is comprised. A separate study of the flow over an array of rectangular elements (referred to as the array study) is used as justification for a structural zoning system that facilitates application of the local exposure factors.
2. Array study The primary focus of the array experiments was to measure the variation of pressure distributions on a rectangular prism when open fields of various sizes were created in a uniform array of which the prism was a part. A wind profile above the array had a full-scale aerodynamic roughness length of 1.0 m, and a turbulence intensity of 0.32 at a height of 10 m. With the height of the building used as a typical dimension, the Reynolds number of the simulation is 2.1;10. The pressure model tested in these experiments (Fig. 1) was a flat rectangular prism with 10 pressure taps aligned in a row on the roof. At a length scale of 1 : 200, the full-scale dimensions of the model are 5;12;24 m (height;length;width). Pressure
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time series from these taps were measured, recorded, and used to calculate reactions of two joists aligned end to end along the line of taps. Wind-pressure measurements have concentrated on the joists in the “middle bay” of the building. Therefore, only one wind direction, perpendicular to the long edge, was tested because this direction has been shown to govern the uplift loading on middle joists [2]. Additionally, measurements on buildings with relative heights of 0.51H, 1.25H, and 1.5H were made. The pressure model was tested in a uniform array of rectangular elements with unequal lateral and longitudinal spacing. The array consisted of 28 rows of elements with dimensions and spacing given in Table 1. This arrangement is typical of many residential areas in North America. The pressure model was located in the middle of the 22nd row of the array, and three lengths of upstream open fields were created by cumulatively removing rows 22, 21, and 20 as shown in Fig. 2. This figure shows a field length of 0 m. Removing the array elements of row 22 would create a field length of 30 m. 2.1. Reaction coefficient Reactions for two joists arranged end to end along the row of taps on the pressure model were calculated by forming linear combinations of the pressure time series. The
Fig. 1. Geometry and pressure tapping of model in array study (dimensions in mm).
Table 1 Geometry of uniform array Description
Model dimensions
Full-scale dimensions
Ratios
Array elements Array spacing — lateral Array spacing — along wind Lateral gap Along wind gap Elements per row Density
25 : 50 : 75 mm (H : ¸ : ¼) 100 mm centre to centre 200 mm centre to centre 25 mm 150 mm 23 18.8%
5 : 10 : 15 m (H : ¸ : ¼) 20 m centre to centre 40 m centre to centre 5m 30 m
1 : 2 : 3 (H : ¸ : ¼) 4H 8H H 6H
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Fig. 2. Layout of open-field test site for model in uniform array. Only portions of array rows are shown for clarity. Field length ¸ measured from model to upstream row.
reaction has been calculated by instantaneously summing the moments of local pressures sampled at five pressure taps along the beam, assuming that each span is a simply supported beam. No dynamic amplification load factors have been used in the analysis, and joint action among several joists has been ignored. A reaction coefficient, C , was defined as the ratio of the reaction at one end of the joist to the 0 total force of a uniform distributed load of q . Thus, if a unit load of q is applied to the entire beam, the reaction coefficient will be equal to 0.5. To calculate the reaction, R , as a force per unit width 52 R "C q l , (1) 52 0 G lr L C " C G G, (2) 0 .G s l G G where q is the mean dynamic pressure at reference height, l is the total joist roof G area exposed to pressure (per unit width), C the reaction coefficient, s is the span of 0 joist, l equals the tributary area for tap i (per unit width), r is the moment arm of G G tributary area i, C the pressure coefficient at position i referenced to mean dynamic .G pressure q , and n the number of pressure taps along joist. 2.2. Results from the array study Fig. 3 shows the variation of the peak reaction coefficient with upstream open field length, ¸ , at each of the four joist reaction locations on the roof of the pressure model.
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Fig. 3. Peak reaction coefficients for all four reactions along joist line plotted as a function of upstream field length, ¸ .
The four reaction locations are described using the relative location of the reaction from the windward edge. Three deductions can be made from Fig. 3. Firstly, the magnitude of reactions on the windward half of the roof (reaction locations Lead and 2nd) are much higher than the leeward half (reaction locations 3rd and 4th) even for a field length of 0 m. Therefore, the loads on the windward joist are going to govern the design of the leeward joist, since similar loads will be induced by winds approaching from 180°. Secondly, the windward joist reactions are seen to be dependent on the upstream field length, whereas the leeward joist reactions are hardly dependent on field length at all. Thus, these data indicate that the local exposure effect of the open field only affects the windward joist. It can be surmised that the local exposure change affects the separation bubble at the leading edge of the building and that this separation bubble reattaches to the roof somewhere along the span of the windward joist. Finally, the variation of the reaction coefficient appears to level off rapidly with increasing field length, and a constant local exposure factor can be expected to exist beyond a certain field length. Other results, that varied the ratio of the building height to the array height, indicate this variable also affects the local exposure factor [5]. However, given that most suburban buildings are not a series of flat roofed structures like this array experiment, this variation of local exposure factor with height is unclear. 2.3. Local exposure zones The above observations were taken into consideration in developing a zoning system to be used in applying the local exposure factors that were derived from the database study. While the system resembles the zoning system found in the National Building Code of Canada [3], it is focused on classifying the underlying structural
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Fig. 4. Explanations of local exposure zones.
layout into various zones. This method of joist classification indicates which quadrant of the wind compass will dominate the response of the joist. These zones classify the joist into one of the four main wind quadrants — north, east, south, or west — or into an interior zone where there is not one clear direction that dominates the response. Guidelines for the application of these zones are outlined in Fig. 4. The largest zones should try to follow the orientation of the main building with respect to the compass directions. For instance, in the buildings in Cases (a) and (b) of Fig. 4, the North—South zones dominate on buildings oriented in the East-West direction, and the East—West zones are dominant on buildings oriented in the North—South directions. Smaller end zones should be parallel to the joists and have a width equal to the edge zone width given in the NBCC [1,3]. The end zones should also cover whole joists, and in general, should not break the reaction points of a joist into two separate zones. Only in cases where the joists span from one side of the building to the other should the zoning system bisect the joist. For example, in Case (c), the East and West zones separate the reactions at each end of the joist into two categories. The logic for this unique case is rationalised by the fact that each reaction will be dominated by the uplift created by the separation bubble at each edge. More complicated structures should follow the guidelines of Case (d) keeping in mind the idea of maintaining whole joists within a single zone. In Case (d), the East end of the building includes two small edge zones that are influenced by the north and south winds. Note that the smaller joists in the centre of the buildings in Cases (a) and (b) are classified as “interior” joists since they are an equal distance from either edge, and no separation bubble will extend to this zone to dominate the response. Separation bubble lengths are in general limited to a distance of two building heights from the edge of a building as suggested in Fig. B-9 of the NBCC User’s Guide [3]. So if a joist is wholly away from the separation bubble from winds from all sides of the building, then it should be assigned to an interior zone. Otherwise, the inside joists should be assigned to one of the zones that will not divide up the joist, as in Case (e). The above zoning system was used to define the local exposure factor of each joist on a building in the database study. Local exposure classifications are simple and operate as follows: If the distance from the roof zone to the next major structure is more than a typical street width of 50 m, the roof area is considered to have an open local exposure; otherwise, it is shielded. For example, in Case (c), if the south side of the
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building is next to the street and across the street are residential houses, the south orientation zones are considered as shielded. However, if the other three sides of the building are facing a playground, the West, North, and East zones would be considered to be open. This zoning system is appropriate only when flow reattachment takes place on the roof. Guidelines by Hosker [6] have been used to indicate that the flow re-attaches at about the centre of the roof for low buildings with dimensions of the order of 10 by 20 m in plan.
3. Database study Nine pressure models of schools in Ontario, Canada that are of a masonry wall construction with open web steel joists were tested at a length scale of 1 : 100 in Boundary Layer Wind Tunnel II at The University of Western Ontario. Each model was tested in an appropriate suburban exposure for each site (roughness length of 0.13 m full scale), with a generic proximity model that included details of open fields and adjacent buildings within 120 m of the site. A typical layout of a proximity and pressure model from one of the nine tests is shown in Fig. 5. With the height of the
Fig. 5. Typical school and proximity model tested in database study (dimensions in mm).
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model building used as a typical dimension, the Reynolds number of the simulation is 4.2;10. Instantaneous time series of the pressure were recorded and joist uplift reactions were calculated from linear combinations of these pressures in an identical manner to Eq. (2). Internal pressures were estimated as the arithmetic sum of pressures measured on the windward wall of the building, and incorporated into the calculation of the reactions coefficient. Integration with local meteorological data yielded predictions of the 30 year return period reaction for each joist on each school. In all, 639 reactions at various locations on the roof were examined and assembled in a database. 3.1. Modification of NBCC model The predicted wind tunnel loads were compared to the NBCC model and two subsequently modified versions of the model. The basic NBCC equation for wind load reactions on the roof is formulated as follows: R " q C C C A r , (3) , !! G G G where R is the joist reaction, q the mean dynamic velocity pressure at 10 m in , !! open terrain, C the exposure factor representing the variation of gust speed with height, C the pressure factor, C the gust factor, and A and r are the tributary area G G and moment arm of pressure region i for calculation of the reaction. Like many code models, the NBCC model is based on quasi-steady theory that says that the wind pressures scale according to the peak velocity pressure at the roof height of the structure. Therefore, the exposure factor, C , is a gust pressure profile rather than a mean pressure profile. It should be noted that the NBCC does not recognise a reduction in the wind loads due to shielding effects or suburban exposures. It only uses an open exposure profile and approximates this profile with the following equation: C "(z/10) C *0.9,
(4)
where z is the height above the ground in metres. Ho [7] indicates that the ideal exposure factor, C*, would be a ratio of the peak ) to the peak velocity at roof height in an appropriate exposure for the site (»K X & velocity at 10 m height in open country (»K ): C*"(»K /»K ). X &
(5)
In this study, the Harris and Deaves [8] model for strong winds was used, with aerodynamic roughness lengths of 0.02 and 0.2 m for open country and suburban exposures respectively, to calculate a C* for a suburban profile. The peak velocity is assumed to be equal to the mean velocity plus 3.7 times the RMS velocity. At a height of 5 m, the suburban C* is approximately 0.53 compared to the 0.9 specified in the NBCC.
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Two modified versions of the NBCC model were compared to the wind tunnel tests. The first modification incorporated the ideal exposure factor, C*, into the original model: C* . (6) R "R , !! C The second modification incorporated the local exposure factors, C* , (derived below) into the suburban model: R "R C* . (7) ! A ratio called the uplift reaction ratio, URR, was used to compare the wind tunnel predicted uplift reaction, R , with the reactions calculated from the three NBCC 52 models. The ratios for the open country, suburban and local exposure model are defined as URR "R /R , URR "R /R , URR "R /R . (8) 52 , !! 52 ! 52 ! A URR equal to 1.0 indicates a perfect match between wind tunnel and predicted reactions. A URR less than 1.0 indicates over-prediction on behalf of the NBCC models, and a URR greater than 1.0 an under-prediction. The NBCC models also included allowances for internal pressure in a uniformly leaky building (Category 2 in Ref. [3]). 3.2. Local exposure factor Three joist descriptions were applied to the 639 reactions to divide the database into sub-groups that could be used for deriving local exposure factors. The three descriptions were “local exposure zone”, “location type”, and “frame location”. The local exposure zone was applied using the system outlined in Section 2.3. The location type described the location of the reaction according to the zoning system outlined in Fig. B-9 of the NBCC [3]. The frame location describes whether the joist is an “end bay” joist or a “middle bay” joist. The entire database was subdivided according to the three descriptions, and the statistics of each sub-group were calculated. Table 2 shows the average and standard deviation of URR in each of the sub-groups. For middle frame joists, Table 2 shows a slight increase in variability of URR with open local exposure but a more distinct increase in the mean values. For the end frame joists, little difference was found between the open and shielded local exposures. It was found that local exposure factors defined as two standard deviations of URR above the mean (Eq. (9)) were effective in improving the predictions of the model. The local exposure factors derived in this manner are shown for each sub-group in Table 3: C* "URR #2p . (9) 300 When the derived local exposure factors for the open and shielded conditions are compared, it is seen that there is a smaller local exposure effect on the end joists than
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Table 2 Statistics of URR from nine buildings grouped by frame location, local exposure, and location type
Table 3 Local exposure factors, C* , derived from Table 2
there is on the middle joists. In fact, the interior location types experience increases in load for the shielded case. Also note that the local exposure factor for the interior local exposure zones are small. There is little local exposure effect on these joists. For the middle joists, the increase in open field loads over suburban loads is seen to be of similar magnitude to the reduction of suburban loads from open country loads. This fact is apparent when the product of the ideal suburban exposure coefficient and the open local exposure factor (0.53;1.37"0.73) is compared with the open country exposure coefficient (0.9). The difference is only 20%, whereas the difference for the
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Fig. 6. Relative frequency and cumulative frequency distributions of URR for open country, suburban, and local exposure models.
shielded local exposure is 32%. In other words, the response of the open joists quickly becomes comparable to loads predicted for the open country terrain case upon which the original code is based. Fig. 6 shows the frequency distributions and cumulative frequency distributions of URR’s for the three models. The original model (represented as URR ) over-predicts loads by 50% on average, but can vary from as little as 5% to as much as 75%. When the suburban modification to the code is incorporated (URR ), the over-prediction reduces to 30% on average, but under-predictions occur for about 25% of the loads. However, when the local exposure factor (URR ) is incorporated into the model, the ! percentage of loads that are under-predicted is reduced to less than 5% while still reducing the loads from the original code model. By selectively increasing loads on areas affected by open local exposure, the effects of suburban terrain can be successfully incorporated into the prediction process while avoiding un-conservative predictions. These derived local exposure factors were used with the local exposure model to predict the loads on three other schools that were tested independently in the wind tunnel [5]. The 228 reactions of these three schools showed similar success in improving the wind load predictions as did the original 639 reactions from this study.
4. Conclusions The effect of suburban exposures on wind loads on roofs of low buildings is hard to incorporate into the National Building Code of Canada because of the variability of the loads. This variability is partially induced by variation of local surroundings such as small open fields. The local exposure effects due to small fields adjacent to the building have been incorporated into a code-like model by the use of local exposure factors and a structural zoning system. This modification to the NBCC code method
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has been used to refine the predicted loads on schools and shopping plazas while minimising the under-prediction of uplift loads. Loads on joists exposed to small open fields can approach loads created by open country terrain and therefore, allowance for this effect must be made. These increases are limited to the portions of the roof that are closest to the small open field, and the effect is more dominant on middle frame joists than end frame joists. These conclusions are limited to flat roofed structures with joists approximately 7 or 8 m in length, located among roughness elements of approximately the same height as the structure.
References [1] Canadian Commission on Building and Fire Codes, The National Building Code of Canada 1995, National Research Council of Canada, Ottawa, 1995. [2] T. Stathopoulos, Turbulent wind action on low rise buildings, Ph.D. Thesis, The University of Western Ontario, London, Ontario, 1979. [3] Canadian Commission on Building and Fire Codes, User’s Guide — NBC 1995 Structural Commentaries (Part 4), National Research Council of Canada, Ottawa, 1995. [4] A.G. Davenport, T.C.E. Ho, D. Surry, The codification of low rise building wind loads, 7th US National Conf. on Wind Engineering, Los Angeles, 27—30 June 1993. [5] M.A. Young, Effect of open fields on low building wind loads in a suburban environment, M.E.Sc. Thesis, The University of Western Ontario, London, Ontario, June 1997, 226 pp. [6] R.P. Hosker, Flow around isolated structures and building clusters: a review, ASHRAE Trans. Part 2B 91 (1985) 1671—1692. [7] T.C.E. Ho, Variability of low building wind loads, Ph.D. Thesis, The University of Western Ontario, London, Ontario, 1992, 364 pp. [8] R.I. Harris, D.M. Deaves, The structure of strong winds, Wind Engineering in the Eighties, Proc. CIRA Conf., 12—13 November 1980, Construction Industry Research and Information Association (CIRA), London, 1981.