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Wind interference effects of high-rise building on low-rise building with flat roof
Journal of Wind Engineering & Industrial Aerodynamics 183 (2018) 88–113
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Wind interference effects of high-rise building on low-rise building with flat roof Bo Chen a, *, Luxi Shang a, b, Mengyi Qin a, Xinzhong Chen c, d, Qingshan Yang a, d a
Beijing's Key Laboratory of Structural Wind Engineering and Urban Wind Environment, School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China China Mobile Group Beijing Company Limited, Beijing, 100007, China National Wind Institute, Department of Civil, Environmental and Construction Engineering, Texas Tech University, Lubbock, TX, 79409, USA d School of Civil Engineering, Chongqing University, Chongqing, 400044, China b c
A R T I C L E I N F O
A B S T R A C T
Keywords: Wind interference Low-rise building High-rise building Wind tunnel test Pressure coefficient
Wind pressure measurements were conducted in a wind tunnel to investigate interference effects of a high-rise building on a low-rise building with a flat roof. The influences of the building spacing ratio, building height ratio and wind direction are examined. The results show that positive pressures are observed on the roof of the low-rise building when it is located in front of the high-rise building with small spacing. Increasing the height of the high-rise building or decreasing the spacing induces an increase in positive pressures. The critical condition of the sign change of wind pressures on the roof is presented. Significant amplification of suction is observed when the low-rise building is right behind the high-rise building with small spacing and large height ratio. Increasing the height of the high-rise building greatly amplifies the suction on the whole roof of the low-rise building. The mean lift coefficient on the roof is about 2.5 times that on an isolated low-rise building roof when the spacing ratio is small and the height ratio is large. The maximum interference factors of the most unfavorable minimum and maximum coefficients in the roof area near the high-rise building are larger than 1.5 and 3.5, respectively.
1. Introduction Extensive studies have been conducted on wind pressures on isolated low-rise buildings (Stathopoulos, 1984a; Tieleman et al., 1997; Uematsu and Isyumov, 1999; Banks et al., 2000; Ginger and Holmes, 2003; Alrawashdeh and Stathopoulos, 2015). The findings of these studies have been reflected in the provisions of many building codes and standards. Due to the small height of low-rise buildings, the wind flow around them is prone to interference from surrounding buildings. Both shielding effects and amplification effects have been observed, causing the wind pressures on building surface to be very different from those on an isolated building (e.g., Stathopoulos, 1984b; Pindado et al., 2011). Interference effects are influenced by the geometry of the target building and interfering buildings, building spacing and wind direction (Khanduri et al., 1998). Previous studies on interference effects on low-rise buildings include three kinds of building configurations: a group of low-rise buildings, two or three low-rise buildings, and a low-rise building and a high-rise building. Wind loads on the roof of a low-rise building embedded among a group of similar buildings are generally expected to experience shielding effects and be smaller than those on an isolated
building, while quite adverse effects appear when it is interfered by one or two other buildings (Khanduri et al., 1998). Hussain and Lee (1980) described the surface pressures on a large group of low-rise buildings for three types of flow regimes, including isolated roughness flow, wake interference flow and skimming flow, by varying building spacing and building aspect ratio. Holmes (1994) studied the effects of a group of tropical low-rise gable-roof buildings with different configurations. A significant increase in roof suction occurred for a row of buildings, and shielding effects occurred when a row of upstream buildings was added. Case and Isyumov (1998) showed that the high suction region on the roof of a low-rise gable-roof building experienced reduced loads when it was embedded in an array of similar buildings, except when it was located at the corner of the array. Ahmad and Kumar (2001) examined interference effects on a low-rise hip-roof building due to a similar building or three similar buildings, and reported significant amplification and shielding effects in different roof zones. Chang and Meroney (2003) pointed out that the effects of a lot of surrounding buildings significantly reduced wind pressures when building spacing was small, and increasing the number of upstream building rows tended to increase shielding effects. Jia and Sill (1998); Kim et al. (2012);
* Corresponding author. E-mail address: [email protected] (B. Chen). https://doi.org/10.1016/j.jweia.2018.10.019 Received 26 March 2018; Received in revised form 19 October 2018; Accepted 19 October 2018 0167-6105/© 2018 Elsevier Ltd. All rights reserved.
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Journal of Wind Engineering & Industrial Aerodynamics 183 (2018) 88–113
Fig. 1. Information on incident flow.
Fig. 2. Building configuration and pressure tap arrangement.
interference of an upstream building on the mean wind suction on the flat roof of a low-rise building for building height ratios from 1.0 to 3.0, clear spacing from 0 to 4 times the low-rise building height, and wind attack angle for two buildings arranged side by side when the high-rise building was located immediately upstream of the low-rise building. The results showed that the mean suction on the roof of the low-rise building was amplified, and the amplification increased as the height of the upstream building increased. But the interference effects were not investigated for the low-rise building located in front of the high-rise building. It was found that a nearby high-rise building can cause severe interference effects on a low-rise building. For an isolated low-rise flat-roofed building, the roof experiences large wind suction, and such upward wind loads are combined with downward dead loads for structural design. Ignoring the amplification effects on wind suction will underestimate these combined loading effects. When the inference effects change the wind loading sign from negative to positive, the wind pressures act on the roof in the same direction as the dead loads. These combined loading effects may be more dangerous than the combination of wind suction and dead load when large positive wind pressures act on the roof. Furthermore, such combined loading effects become more dangerous when heavy snow loads are included. The severe interference effects due to a nearby high-rise building severely threaten structural safety if the design wind loads on the low-rise building are determined as for an isolated building. This work presents a comprehensive study on the interference effects on a low-rise building with a flat roof due to a nearby high-rise building. The influences of building spacing, relative height ratio and wind direction varying over much wider ranges are covered. The characteristics of mean, standard deviation (STD), peak pressure coefficients on the flat roof of a low-rise building are analyzed. Emphases are placed on the
Kim and Tamura (2013) investigated the interference effects on flat roofs of low-rise buildings influenced by incoming flow, building density, and building position. It was pointed out that the mean pressure coefficients on the target building decrease as building area density increases. The pressure coefficients on the downstream side were less affected by incident flows than those of an isolated building was. Quan et al. (2014) investigated wind pressures on the flat roof of a low-rise building embedded among a group of similar buildings, and studied the influence of building area density, relative height and arrangement. It was pointed out that the shielding factors of peak pressure coefficients in most cases were smaller then 1.0, and the influence of building area density and relative height were larger than that of the arrangement pattern. Li et al. (2017) carried out CFD simulation to investigate the interference effects on a gable roof of a low-rise building, and pointed out that largest interference effects occurred for two same buildings, and the corner or outer building of the group experienced larger interference effects. Fewer studies have been conducted on wind interference effects on low-rise buildings due to the presence of nearby high-rise buildings than on interference effects among a group of similar low-rise buildings. Stathopoulos (1984b) evaluated the interference effects of a large nearby building on wind loads on a low-rise gable-roof building with three building configurations, and pointed out the possibilities of roof suction amplification and sign change from negative to positive. Significant amplification of suctions on the roof was noted in the side-by-side configuration and the configuration of the low-rise building being located behind the high-rise building. Roof suction was significantly decreased, and mean positive pressures appeared in the configuration of the low-rise building located in front of the high-rise building, but the extents of such positive pressures and the dependence on building parameters were not discussed. Pindado et al. (2011) investigated the 89
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Fig. 3. Pressure coefficients of roof for wind direction 0 . (a) Mean wind pressure coefficients (b) STD wind pressure coefficients (c) Minimum pressure coefficients (d) Maximum pressure coefficients.
Fig. 4. Pressure coefficients of roof for wind direction 45 degrees. 90
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buildings were carried out for wind directions from 0 to 180 at intervals of 15 . As shown in Fig. 2, a total of 377 pressure taps was arranged on the roof and walls of the low-rise building, and 12 pressure taps were arranged on the four sides of the high-rise building at a height of 0.096 m, which is 4 mm lower than the eaves height of the low-rise building. The fluctuating pressures were measured simultaneously at a sampling frequency of 312 Hz. The mean wind speed at eaves height of the low-rise buildings was 6.8 m/s. Ten time history samples were obtained with a time duration of about 10 min for each sample corresponding to the prototype model for a geometrical scale of 1:200 and a velocity scale of 1:4. All measured fluctuating pressures were corrected with the frequency transfer function of the tube system. Among all building configurations, the maximum blockage ratio was 5.2%, and no blockage correction was conducted. The wind pressures were normalized by the mean velocity wind pressure at eaves height of the low-rise building to obtain the pressure coefficients. For each of ten samples, a sample minimum and maximum pressure coefficients were obtained. The minimum peak and maximum peak pressure coefficients were calculated using the Cook-Mayne method, where the distribution of peak values was assumed as FisherTippet Type 1 (Cook, 1982). No moving time average of fluctuating pressures was conducted during the calculation of these point peak pressure coefficients.
critical condition of sign change of wind pressures and the magnitudes of positive pressures when the low-rise building is located in front of the high-rise building, and on the amplification effects of wind suction when the low-rise building is located behind the high-rise building. 2. Experimental program Wind pressure measurements were conducted in a close circuit boundary layer wind tunnel in Beijing Jiaotong University of China, with a working section of 3.0 m wide and 2.0 m high. Roughness elements, carpets, spires and barriers were employed to simulate the atmospheric boundary layer over an open country terrain. Fig. 1 shows the measured longitudinal turbulence intensity profile and the mean wind velocity profile with a power law exponent of 0.147. The integral lengths scale at a height of 0.1 m is 0.36 m in the wind tunnel. The geometric scale of the simulated flow and the building models was 1:200. The experimental building configuration is displayed in Fig. 2, which includes a target low-rise building and an interfering highrise building. These two buildings have the same square plan with a side width of 0.2 m. The target building has a flat roof with an eaves height of h ¼ 0.1 m. To investigate the effects of the relative height of the high-rise building and the spacing between these two buildings on the interference effects, nine different height ratios of H/h ¼ 1, 1.5, 2, 3, 4, 5, 6, 8 and 10, i.e., the ratio of the height of the high-rise building to that of the low-rise building, and eleven spacing ratios of D/h ¼ 0, 0.25, 0.5, 1, 1.5, 2, 3, 4, 6, 8 and 10, i.e., the ratio of the clear spacing to the height of the low-rise buildings, were considered. For comparison, tests on an isolated low-rise building and high-rise buildings with nine different heights were also carried out. In total, there are 109 building configurations. For each building configuration, the pressure measurements on these two
3. Results and discussions 3.1. Isolated single low-rise building Figs. 3 and 4 display the distributions of mean, STD, minimum and
Fig. 5. Mean pressure coefficients for D/h ¼ 0.5 for wind direction 0 degrees. 91
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When H/h is 2, a positive pressure zone is noted near the leeward roof edge near the interfering building. The positive pressures and the corresponding roof area increase as the height ratio H/h increases, which leads to a decrease in negative pressures in the windward roof area. When H/h is 10, half of the roof experiences positive pressures, and the positive and negative mean pressure coefficients reach 0.7 and 0.3, respectively. These positive pressures are attributed to the large standing vortex produced by the leeward high-rise building. Fig. 6 and Fig. 7 respectively display the distributions of minimum and maximum pressure coefficients on the roof of a low-rise building for different height ratios H/h at a clear space ratio of D/h ¼ 0.5. In comparison to the peak pressure distribution of an isolated building shown in Fig. 3, it is observed from Figs. 6 and 7 that increasing the height of the downstream high-rise building decreases the magnitude of the minimum pressure coefficients on the roof of the low-rise building, and the roof area near the high-rise building is more sensitive to the height of the high-rise building. The minimum pressure coefficients on the upstream roof edge and on the downstream roof edge of the low-rise building are respectively 70% and 15% of those on the isolated building when the building height ratio is 10. Increasing the height of the downstream highrise building increases the maximum pressure coefficients on the roof of the low-rise building. The maximum pressure coefficients on the whole roof almost become positive when the building height ratio H/h is 2.0, and the values on the downstream central roof edge are about three times of those on the isolated building when H/h is larger than 4.0. Stathopoulos (1984b) also mentioned the appearance of positive pressures on the gable roof of a low-rise building when it is located right in front of a nearby high-rise building, and showed that positive pressures may be high due to the impact of the large standing vortex produced by the high-rise building on the low building roof.
maximum pressure coefficients on the roof of an isolated low-rise building at two typical wind directions: 0 and 45 . At a wind direction of 0 , large negative pressures are observed near the leading edge of the roof associate with flow separation. The STD pressure coefficient reaches a maximum around the inflexion point of the mean pressure coefficient curve, and the pressure distribution around a blunt flat plate (Li and Melbourne, 1999) exhibits a similar phenomenon. This point is considered to be the reattachment point of the separated flow from the windward roof edge. The STD pressure coefficients decrease rapidly with distance from the windward edge, but the change in gradient is much smaller than that of the mean pressure coefficients. The windward roof area experiences large negative peak pressures, and the minimum pressure coefficients on the windward quarter of the roof are smaller than 2.0. At a wind direction of 45 , the pressure distribution is associated with a conical vortex from the corner, two windward edge areas experience large negative pressures, and the minimum pressure coefficient at the windward corner edge reaches 4.6. 3.2. Low-rise building located right in front of high-rise building This section discusses the interference effects on the roof of a low-rise building when it is right in front of a high-rise building, i.e., wind direction is 0 . 3.2.1. Pressure distribution on roof of low-rise building Fig. 5 shows the mean pressure distribution on the roof of a low-rise building for different height ratios H/h at a clear space ratio of D/h ¼ 0.5. When the height of the target low-rise building is the same as the interfering building, i.e., height ratio H/h ¼ 1, the interference effects are small, and the pressure distribution is close to that of an isolated building.
Fig. 6. Minimum pressure coefficients for D/h ¼ 0.5 for wind direction 0 degrees. 92
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Fig. 7. Maximum pressure coefficients for D/h ¼ 0.5 for wind direction 0 degrees.
coefficients gradually recover close to the value for the isolated low-rise building roof. The STD pressure coefficients decrease as the height ratio H/h increases for a fixed spacing ratio. It is clear that the interference effects on the STD pressure coefficients are very different from those on the mean pressure coefficients. Fig. 10 shows the distribution of minimum pressure coefficients. Due to the increase in mean and decrease in STD values, the minimum pressure coefficients are reduced in magnitude compared to those on the isolated building roof. This reduction is more significant when the spacing ratio D/h is smaller than 2.0. The minimum pressures on the leeward roof even become positive when D/h is smaller than 0.25 and H/ h is larger than 3.0. However, the interference effects result in an increase in maximum pressures, as shown in Fig. 11.
3.2.2. Pressure distribution on roof center line Fig. 8 shows the variation of mean pressure coefficients on the roof center line for different height and spacing ratios. It is observed that increasing the height of the interfering building or reducing the building spacing makes interference effects more significant. Larger values and a larger roof area with positive pressures are noted when the spacing is small and the height ratio is large. The maximum mean positive pressure reaches 0.9 when the spacing ratio D/h is 0.25. The interference effects are very sensitive to the height ratio when D/h is smaller than 1.0. The suction decreases and the positive pressure increases as the height ratio increases. The interference effects become stable and are not sensitive to the height ratio when H/h and D/h are larger than 4.0. Fig. 9 shows the distribution of STD pressure coefficients. The maximum STD pressure coefficient on the roof appears at almost the same position as that on the isolated building roof. When the spacing ratio D/h is smaller than 0.25, the distribution and variation of the STD pressure coefficients on the roof are significantly different from those on the isolated building roof. The maximum STD value increases by 60% when the spacing ratio D/h is 0.25 with a large height ratio H/h. The STD values are also very large near the leeward roof area where large mean positive pressures are observed. The STD pressure coefficients in the leeward roof area increase with height ratio H/h up to H/h ¼ 2.0, and then decreases as H/h increases. This is very different from the effects on the mean pressure coefficients shown in Fig. 8(a), where the positive mean pressure coefficients increase monotonically as H/h increases. When the spacing ratio D/h increases from 0 to 1.0, the maximum STD pressure coefficients in both negative and positive pressure areas decrease rapidly, and the distribution gradually becomes similar to that on the isolated low-rise building roof but with smaller amplitude. When the spacing ratio D/h increases from 1.0 to 10.0, the STD pressure
3.3. Low-rise building located right behind high-rise building This section discusses the interference effects on the roof of a low-rise building when the building is right behind the high-rise building, i.e., wind direction is 180 . 3.3.1. Wind pressure distribution on low-rise building roof Fig. 12 shows the mean pressure distribution on the low-rise building roof for six height ratios H/h when the spacing ratio D/h is 0.5. For height ratio H/h ¼ 1, the pressure coefficients are very small in magnitude due to shielding effects from the interfering building. As height ratio H/h increases, the values of the negative pressures significantly increase in magnitude, and larger negative pressures are observed in the roof area near the high-rise building. For H/h ¼ 10, large negative pressures on the whole roof are noted, which are much larger than those on the isolated building roof. 93
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Fig. 8. Mean pressure coefficients on roof center line for wind direction 0 degrees.
that of the isolated building shown in Fig. 3. Increasing the height of the upstream high-rise building amplifies the magnitude of minimum pressure coefficients on the whole roof of the low-rise building, especially in the two roof edge areas parallel to the wind direction. Increasing the height of the high-rise building reduces the change in gradient of
Fig. 13 and Fig. 14 respectively show the distribution of minimum and maximum pressure coefficients on the roof of a low-rise building for different height ratios H/h with a clear space ratio of D/h ¼ 0.5. It is observed that the upstream high-rise building makes the peak pressure coefficient distribution on the low-rise building be much different from 94
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Fig. 9. STD pressure coefficients on roof center line for wind direction 0 degrees.
3.3.2. Pressure distribution on roof center line Fig. 15 shows the distribution of mean pressure coefficients. It is observed that for small spacing ratios, the pressures on the low-rise building roof are dominated by the wake flow of the high-rise building. As a result, the mean pressure coefficients on the roof are negative and have small change in gradient, which are very different from those on the
pressure coefficients along the roof center line parallel to the wind direction. Increasing the height of the upstream high-rise building decreases maximum pressure coefficients in the upstream roof area on the low-rise building, increases maximum pressure coefficients in the downstream roof area when H/h is smaller than 2.0, then decreases them after H/h is larger than 2.0.
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Fig. 10. Minimum pressure coefficients on roof center line for wind direction 0 degrees.
coefficients are normalized by the incoming velocity pressure at the eaves height of the low-rise building. It is demonstrated that the height of the windward high-rise building has little effects on the pressures on the windward wall, but has significant effects on the pressures on the leeward and side walls. Increasing the building height results in an increase in magnitude of suction on the leeward and side walls, and suction on the roof of the leeward interfered low-rise building.
isolated building roof. The increase in building height ratio results in an increase in the magnitude of negative pressures. The suction on the whole roof is even larger than that on the windward roof area of the isolated building roof when the building height ratio H/h is larger than 8.0. This phenomenon can be understood from the pressure distribution on the high-rise building shown in Fig. 16, where the results for the isolated high-rise building are shown for comparison. The pressure
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Fig. 11. Maximum pressure coefficients on roof centerline for wind direction 0 degrees.
D/h reaches 10.0, the pressures on the whole roof are very close to those on the isolated building roof. Fig. 17 shows the STDs of pressure coefficients on the center line of the low-rise building roof. In general, the variation of the STDs of pressure coefficients on the roof along the center line parallel to the wind direction is very different from that on the isolated building roof. When the spacing ratio D/h is smaller than 1.0, the STDs of pressure coefficients
As building spacing increases, the pressure change in gradient on the low-rise building roof increases, and the windward flow separation gradually recovers. The amplification effects on the leeward roof area and the shielding effects on the windward roof area decrease. The interference effects decrease more quickly in the leeward area. When spacing ratio D/h is larger than 4.0, the pressure coefficients in the leeward area become close to those on the isolated building roof. When
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Fig. 12. Mean pressure coefficients for D/h ¼ 0.5 for wind direction 180 degrees.
are very small for height ratios of H/h > 2.0. The STDs of pressure coefficients are not sensitive to the spacing ratio. Increase in height ratio induces an increase in RMS pressures, and the increase in the leeward area is more significant than that in the windward area. As a result, the STDs of pressure coefficients in the leeward area are larger than those in the windward area when the height ratio is larger than 3.0. This distribution is adverse to that on the isolated building roof. When the spacing ratio D/h is larger than 1.0, the STDs of pressures become sensitive to both the spacing ratio and height ratio. They are more sensitive to the spacing ratio for larger height ratios. As the spacing ratio increases, the amplification effects of leeward vortex shed from the high-rise building are smaller, and separation flow in the windward area appears gradually. This induces a significant decrease in STDs of pressures in the leeward
area for a large H/h, but a slow increase in the windward area for a smaller H/h. As a result, the distribution of STDs of pressure coefficients tend to be similar to those on an isolated building roof. The magnitude of minimum pressure coefficients on the roof is much larger than that of maximum pressure coefficients when the low-rise building is located right behind the high-rise building. Only minimum pressure coefficients are discussed here, as shown in Fig. 18. When the building clear spacing ratio D/h is smaller than 0.5, the peak pressures are not sensitive to the spacing ratio, but are very sensitive to the relative height ratio H/h. When D/h is larger than 0.5, the peak pressure coefficients are sensitive to both D/h and to H/h, and increasing D/h induces a significant decrease in the peak suction in the leeward area where H/h is larger than 5.0, and a slow increase in the windward area where
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Fig. 13. Minimum pressure coefficients for D/h ¼ 0.5 for wind direction 180 degrees.
These eight pressure taps represent the corner, middle edge and central roof area, and experience the largest negative peak pressures in these roof areas respectively. The most unfavorable peak pressure coefficients at these eight pressure taps of the isolated low-rise building are listed in Table 1. The pressure coefficients at two symmetric points are not the same, and they may be attributed to the imperfect symmetry of the mode and the non-uniformity of the approach flow. Interference effects on the most unfavorable peak pressure coefficients are evaluated by the interference factor (IF), which is defined as the ratio of the peak Cp in the case with an interfering high-rise building to that of the isolated low-rise building. Fig. 21 shows interference factors of the most unfavorable minimum pressure coefficients. Pressure taps P1 and P2 far away from the high-rise building mainly exhibit shielding effects except the cases when D/ h ¼ 0.25 and H/h > 8.0. Interference effects decrease with an increase in D/h, and are not sensitive to H/h when H/h ranges from 3.0 to 6.0. The minimum interference factor is around 0.7. Pressure taps P6 and P7 near
H/h is smaller than 5.0. 4. Most unfavorable peak pressure coefficients among all wind directions The most unfavorable peak (minimum and maximum) pressure coefficients of the roof among all wind directions are critical for the cladding design. Fig. 19 displays the most unfavorable peak pressure coefficients on the roof of an isolated low-rise building. The corner roof area experiences large negative peak pressures, and the largest value reaches 5.0. Minimum pressure coefficients in the central roof area are much smaller in magnitude, and vary around 2.0. The change in gradient of the most unfavorable positive peak pressure coefficients is small, and positive peak pressure coefficients vary around 0.5. According to the peak pressure coefficient distribution shown in Fig. 19, interference effects on peak pressures of eight typical pressure taps on the roof of low-rise building shown in Fig. 20 are investigated. 99
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Fig. 14. Maximum pressure coefficients for D/h ¼ 0.5 for wind direction 180 degrees.
P5 and P8 experience significant amplification effects in the cases with a small D/h and a large H/h. Increasing H/h or decreasing D/h strengthens the amplification effects. Pressure taps P3 and P8 exhibit shielding effects in the cases with a small D/h when H/h is smaller than 4.0. When H/h is 10, the maximum interference factors of these four taps are almost larger than 1.5. Fig. 22 displays the interference factors of the most unfavorable maximum pressure coefficients. Amplification effects appear in most cases when H/h > 1.5. The interference factors at the eight typical pressure taps tend to decrease as D/h increases. When D/h is smaller than 2.0, the amplification effects are very significant and sensitive to D/h.
the high-rise building mainly exhibit shielding effects when D/h is smaller than 1.0. Increasing H/h weakens such shielding effects. The most unfavorable minimum pressure occurs at an oblique wind direction, and the shielding effects appear at this oblique wind direction for small H/h, although amplification effects may be observed at the wind direction of 180 shown in Fig. 18. When D/h is larger than 1.0, pressure taps P6 and P7 mainly experience amplification effects. Increasing H/h or D/h strengthens such amplification effects when D/h is up to around 4.0–6.0. It is attributed to the accelerated flow passing through the two buildings. Amplification effects become smaller as D/h increases. The maximum interference factors of P6 and P7 are larger than 1.5. Pressure taps P3, P4,
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Fig. 15. Mean pressure coefficients on roof centerline for wind direction 180 degrees.
5. Lift coefficients and positive pressures on roof of low-rise building
The interference factors increase when H/h increases up to 4.0, and then remain almost constant for H/h > 4.0. As the distance from the pressure taps to the high-rise building decreases, the amplification effects increase, for example, the interference factors at P1, P4 and P6 decrease in turn. The maximum interference factors at P6 and P7 are larger than 3.5. When D/h is larger than 2.0, the interference factors show scattered relationship with H/h.
5.1. Lift coefficients on roof of low-rise building Lift coefficients on the roof of low-rise building are calculated using the external pressures only, where the influence of the internal pressure 101
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Fig. 16. Mean pressure coefficients on high-rise building for wind direction 180 degrees.
Pindado et al. (2011) also investigated interference effects of an upstream high-rise building on a low-rise building when the wind direction ranges from 90 to 180 , the clear spacing ranges from 0 to 4 times the low-rise building height, and the building height ratio H/h ranges from 1.0 to 3.0. It is shown that the interference effects become negligible at the wind direction of 90 , H/h ¼ 1 and D/h ¼ 3, and the pressure distribution on the roof is close to that for an isolated building. Both the distribution and variation of pressure coefficients in Fig. 3(a) shows good agreement in general with those in Pindado et al. (2011), and the small difference is partly attributed to the difference between the simulated atmospheric boundary layers where the turbulence intensity at the roof eaves height is 12.7% and 4%, respectively, in this paper and Pindado et al. (2011). In view of the maximum absolute values of the mean pressure coefficients, Pindado et al. (2011) showed that the upstream high-rise building produces larger suction than that on an isolated building when D/h is smaller than 4.0, and this becomes more significant for larger building height ratios. Moreover, the influence of the upstream high-rise building becomes very small when the clear spacing ratio D/h is larger than 4.0. It can be found from Figs. 15 and 23 and the experiment results not shown in these two figures that the condition of the clear building spacing corresponding to small interference effects depends on the building height ratio, and the interference effects when H/h is larger than 3.0 can not be ignored even when D/H is larger than 4.
is not included. Positive sign of the lift coefficient represents the upward direction of the lift force. Mean lift coefficients on the low-rise building roof are plotted as a function of the wind direction, spacing ratio and height ratio in Fig. 23, where mean lift coefficients are defined as the weighted average value of mean pressure coefficients on the roof weighted by the tributary area of each pressure tap. Mean lift coefficients on the isolated building are not sensitive to the wind direction and varies around 0.6. For spacing ratios smaller than 0.5, negative lift coefficients are noted for wind directions ranging from 0 to 30 when the height ratio is larger than 3.0. They increase rapidly to a maximum positive lift coefficient when the wind direction increases to 90 . This large positive lift coefficient decreases with an increase in the wind direction for height ratios smaller than 6.0, but remains almost constant for height ratios larger than 6.0. When the wind direction ranges from 0 to 60 , lift coefficients are sensitive to the height ratio H/h up to H/h ¼ 5.0, and then tend to be a constant value over H/h ¼ 5.0. When the wind direction ranges from 60 to 180 , the lift coefficients increase as H/h increases. As the spacing ratio D/h increases, the negative lift becomes smaller for large height ratios when the wind direction ranges from 0 to 60 , and amplification effects of the positive lift become smaller when the wind direction ranges from 60 to 180 . The mean lift coefficient on the roof is about 2.5 times that of an isolated low-rise building roof for a small spacing ratio and large height ratio.
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Fig. 17. RMS pressure coefficients on roof center line for wind direction 180 degrees.
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Fig. 18. Minimum pressure coefficients on roof center line for wind direction 180 degrees.
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Fig. 19. Most unfavorable peak pressure coefficients.
5.2. Amplitude and action area of positive pressures Wind suction on the flat roof of an isolated building is large and is often carefully considered in cladding design. However, positive pressures are usually considered to be small and are often neglected. However, as has been noted in the previous discussions, large positive pressures occur when the low-rise building is interfered by a high-rise building. These pressures have the same action direction as dead loads and snow loads. Therefore, they need to be carefully considered when their combination with dead loads and live loads controls the structural design. Figs. 26 and 27 show the ratio of roof area with mean positive pressures to the total roof area, and the averaged mean lift coefficients in such roof area with positive pressures. Positive pressures are noted at wind directions ranging from 0 (low-rise building right in front of highrise building) to 45 . The maximum averaged mean lift coefficient in magnitude appears at the wind direction of 15 in most cases. The maximum roof area ratio with positive pressures occurs at the wind direction of 15 or 30 . The roof area ratio and the averaged mean lift coefficients in magnitude in the area with positive pressures decrease as the spacing ratio increases. The values of these two parameters increase as the height ratio H/h increases, and then remains almost constant over H/ h ¼ 8.0. The maximum roof area ratio and the averaged mean lift coefficient are larger than 70% and 0.5, respectively, when H/h is 10.0 and D/h is 0.25. Fig. 28 shows the critical building height ratio as a function of the spacing ratio and wind direction, where mean pressures change sign and mean positive pressures on the roof begin to appear. The critical building height ratio varies from 1.5 to 8.0, and increases with an increase in the spacing ratio and wind direction.
Fig. 20. Location of eight typical pressure taps on low-rise building.
Fig. 24 and Fig. 25 respectively show the maximum and minimum lift coefficients. It is observed that the dependence of the peak lift coefficients on the wind direction, spacing ratio and height ratio is similar to that of mean lift coefficients shown in Fig. 23. The maximum and minimum lift coefficients on the isolated building are not sensitive to the wind direction and vary around 0.9 and 0.3 respectively. When the wind direction ranges from 0 to 60 , shielding effects on the maximum lift coefficients are obvious. The magnitude of the maximum lift coefficients is much smaller than that of the isolated building, and increases as the height ratio H/h increases up to H/h ¼ 5.0, and then tends to be a constant for H/h larger than 5.0. When the wind direction ranges from 0 to 30 , the maximum lift coefficients almost reduce to zero when D/ h ¼ 0.25 and H/h > 5.0. When the wind direction is larger than 70 , the amplification effects on the maximum lift coefficients are significant, and increase as H/h increases, but are not sensitive to the wind direction when H/h is larger than 2.0. The largest maximum lift coefficient reaches 2.4 when D/h ¼ 0.25 and H/h > 10. The shielding and amplification effects reduce with an increase in D/h and almost disappear when D/h reaches 10. Small minimum lift coefficient appears at the wind directions ranging from 0 to 30 for a small spacing ratio D/h. The minimum lift coefficient decreases rapidly as the H/h increases. It is smaller than 0 when H/h is larger than 3.0, and tends to be a constant when H/h is larger than 5.0. The smallest minimum lift coefficient reaches 0.7 at D/ h ¼ 0.25 and H/h ¼ 10.
6. Conclusions Wind pressure measurements were carried out to investigate interference effects of one high-rise building on the roof of a low-rise building, with building spacing ratio (D/h) varying from 0.0 to 10.0, building height ratio (H/h) from 1.0 to 10.0, and wind direction from 0 to 180 . Both buildings had the same square plan. Severe positive pressures on the roof of the low-rise building are noted when it is located in front of the high-rise building with a small
Table 1 The most unfavorable peak pressure coefficients of isolated building.
Minimum Cp Maximum Cp
P1
P2
P3
P4
P5
P6
P7
P8
3.2 0.44
4.3 0.39
4.8 0.41
2.0 0.46
2.7 0.43
3.0 0.44
4.6 0.43
5.0 0.50
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Fig. 21. Interference factors of most unfavorable minimum pressure coefficients.
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Fig. 22. Interference factors of most unfavorable maximum pressure coefficients.
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Fig. 23. Mean lift coefficients on whole roof for different wind directions.
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Fig. 24. Maximum lift coefficients on whole roof for different wind directions.
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Fig. 25. Minimum lift coefficients on whole roof for different wind directions.
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Fig. 26. Ratio of roof area with positive pressures to total roof area.
far away from the high-rise building mainly exhibit shielding effects. The roof area near the high-rise building mainly exhibits shielding effects when the building spacing ratio is smaller than 1.0, but experiences amplification effects when the building spacing ratio is larger than 1.0. The amplification effects strengthen with an increase in the building height ratio or spacing ratio when the height ratio is up to around 4.0–6.0. The most unfavorable maximum pressure coefficients mainly experience amplification effects when the building height ratio is larger than 1.5. When the building spacing ratio is smaller than 2.0, amplification effects are significant and sensitive to the building spacing ratio and the building height ratio. When the wind direction ranges from 0 to 60 , shielding effects on the maximum lift coefficients on the roof are obvious. The maximum lift coefficient almost reduces to zero for a small building spacing ratio and large building height ratio when the wind direction ranges from 0 to 30 . When the wind direction is larger than 70 , the amplification effects on the maximum lift coefficients are significant, and increase as H/h increases, but are not sensitive to the wind direction when H/h is larger than 2.0. Large minimum lift coefficient appears at the wind directions ranging from 0 to 30 for a small spacing ratio. The minimum lift coefficient in magnitude increases rapidly as H/h increases.
building spacing. Increasing the height of the high-rise building or decreasing the building spacing induces an increase in positive pressures. The critical condition for the sign change of wind pressures on the roof is presented at different wind directions. The ratio of roof area with positive pressures to total roof area and the averaged mean lift coefficients in such area reach 84% and 0.56, respectively, at a building height ratio of 10.0 and a clear building spacing ratio of 0.0. Ignoring wind interference effects will significantly underestimate structural response when wind loads are combined with downward dead loads such as weight and snow load. When the low-rise building is right behind the high-rise building with a small building spacing (D/h < 1), significant amplification of suction in the leeward roof area is observed at a large building height ratio. Increase in the height of the interfering high-rise building amplifies the magnitude of the suction on the whole roof. These interference effects are attributed to the large size of the vortex from the windward high-rise building, as can be understood from the pressure distribution on the high-rise building. The mean lift coefficient on the roof is about 2.5 times that on an isolated low-rise building roof at a small spacing ratio and large height ratio. The most unfavorable minimum pressure coefficients in the roof area
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Fig. 27. Mean force coefficients on roof zone with positive pressures.
Acknowledgments The work in this paper was partially supported by the National Natural Science Foundation of China (Grant No.51378059 and No. 51720105005), Beijing Nova Program (Grant No. Z151100000315051), and the 111 Project of China (Grant No. B13002). The authors would like to thank the reviewers of this paper for their kind improving comments and suggestions. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.jweia.2018.10.019. References Ahmad, S., Kumar, K., 2001. Interference effects on wind loads on low-rise hip roof buildings. Eng. Struct. 23 (12), 1577–1589. Alrawashdeh, H., Stathopoulos, T., 2015. Wind pressures on large roofs of low buildings and wind codes and standards. J. Wind Eng. Ind. Aerod. 147, 212–225. Banks, D., Meroney, R.N., Sarkar, et al., 2000. Flow visualization of conical vortices on flat roofs with simultaneous surface pressure measurement. J. Wind Eng. Ind. Aerod. 84 (1), 65–85.
Fig. 28. Critical building height ratio with positive pressures on roof.
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Journal of Wind Engineering & Industrial Aerodynamics 183 (2018) 88–113 Kim, Y.C., Yoshida, A., Tamura, Y., 2012. Characteristics of surface wind pressures on low-rise building located among large group of surrounding buildings. Eng. Struct. 35, 18–28. Li, Q.S., Melbourne, W.H., 1999. The effect of large-scale turbulence on pressure fluctuations in separated and reattaching flows. J. Wind Eng. Ind. Aerod. 83 (1–3), 159–169. Li, G., Gan, S., Li, Y., Wang, L., 2017. Wind-induced interference effects on low-rise buildings with gable roof. J. Wind Eng. Ind. Aerod. 170, 94–106. Pindado, S., Meseguer, J., Franchini, S., 2011. Influence of an upstream building on the wind-induced mean suction on the flat roof of a low-rise building. J. Wind Eng. Ind. Aerod. 99 (8), 889–893. Quan, Y., Gu, M., Tamura, Y., et al., 2014. Shielding effects of surrounding buildings on wind loads on low-rise building roofs. Adv. Struct. Eng. 17 (2), 275–288. Stathopoulos, T., 1984a. Wind loads on low-rise buildings: a review of the state of the art. Eng. Struct. 6 (2), 119–135. Stathopoulos, T., 1984b. Adverse wind loads on low buildings due to buffeting. J. Struct. Eng. 110 (10), 2374–2392. Tieleman, H.W., Reinhold, T.A., Hajj, M.R., 1997. Importance of turbulence for the prediction of surface pressures on low-rise structures. J. Wind Eng. Ind. Aerod. 69–71 (97), 519–528. Uematsu, Y., Isyumov, N., 1999. Wind pressures acting on low-rise buildings. J. Wind Eng. Ind. Aerod. 82 (1–3), 1–25.
Case, P.C., Isyumov, N., 1998. Wind loads on low buildings with 4:12 gable roofs in open country and suburban exposures. J. Wind Eng. Ind. Aerod. 77–78 (98), 107–118. Chang, C.H., Meroney, R.N., 2003. The effect of surroundings with different separation distances on surface pressures on low-rise buildings. J. Wind Eng. Ind. Aerod. 91 (8), 1039–1050. Cook, N.J., 1982. Towards better estimation of extreme winds. J. Wind Eng. Ind. Aerod. 9 (3), 295–323. Ginger, J.D., Holmes, J.D., 2003. Effect of building length on wind loads on low-rise buildings with a steep roof pitch. J. Wind Eng. Ind. Aerod. 91 (11), 1377–1400. Holmes, J.D., 1994. Wind pressures on tropical housing. J. Wind Eng. Ind. Aerod. 53 (1–2), 105–123. Hussain, M., Lee, B.E., 1980. A wind tunnel study of the mean pressure forces acting on large groups of low-rise buildings. J. Wind Eng. Ind. Aerod. 6 (3–4), 207–225. Jia, Y., Sill, B.L., 1998. Pressures on a cube embedded in a uniform roughness field of variable spacing density. J. Wind Eng. Ind. Aerod. 77, 491–501. Khanduri, A.C., Stathopoulos, T., Bedard, C., 1998. Wind-induced interference effects on buildings — a review of the state-of-the-art. Eng. Struct. 20 (7), 617–630. Kim, Y.C., Tamura, Y., 2013. Effects of incident flows on wind loads and their combinations on a low-rise building immersed in a long upstream fetch. J. Struct. Eng. 140 (5), 04014009.
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Journal of Wind Engineering & Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Wind interference effects of high-rise building on low-rise building with flat roof Bo Chen a, *, Luxi Shang a, b, Mengyi Qin a, Xinzhong Chen c, d, Qingshan Yang a, d a
Beijing's Key Laboratory of Structural Wind Engineering and Urban Wind Environment, School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China China Mobile Group Beijing Company Limited, Beijing, 100007, China National Wind Institute, Department of Civil, Environmental and Construction Engineering, Texas Tech University, Lubbock, TX, 79409, USA d School of Civil Engineering, Chongqing University, Chongqing, 400044, China b c
A R T I C L E I N F O
A B S T R A C T
Keywords: Wind interference Low-rise building High-rise building Wind tunnel test Pressure coefficient
Wind pressure measurements were conducted in a wind tunnel to investigate interference effects of a high-rise building on a low-rise building with a flat roof. The influences of the building spacing ratio, building height ratio and wind direction are examined. The results show that positive pressures are observed on the roof of the low-rise building when it is located in front of the high-rise building with small spacing. Increasing the height of the high-rise building or decreasing the spacing induces an increase in positive pressures. The critical condition of the sign change of wind pressures on the roof is presented. Significant amplification of suction is observed when the low-rise building is right behind the high-rise building with small spacing and large height ratio. Increasing the height of the high-rise building greatly amplifies the suction on the whole roof of the low-rise building. The mean lift coefficient on the roof is about 2.5 times that on an isolated low-rise building roof when the spacing ratio is small and the height ratio is large. The maximum interference factors of the most unfavorable minimum and maximum coefficients in the roof area near the high-rise building are larger than 1.5 and 3.5, respectively.
1. Introduction Extensive studies have been conducted on wind pressures on isolated low-rise buildings (Stathopoulos, 1984a; Tieleman et al., 1997; Uematsu and Isyumov, 1999; Banks et al., 2000; Ginger and Holmes, 2003; Alrawashdeh and Stathopoulos, 2015). The findings of these studies have been reflected in the provisions of many building codes and standards. Due to the small height of low-rise buildings, the wind flow around them is prone to interference from surrounding buildings. Both shielding effects and amplification effects have been observed, causing the wind pressures on building surface to be very different from those on an isolated building (e.g., Stathopoulos, 1984b; Pindado et al., 2011). Interference effects are influenced by the geometry of the target building and interfering buildings, building spacing and wind direction (Khanduri et al., 1998). Previous studies on interference effects on low-rise buildings include three kinds of building configurations: a group of low-rise buildings, two or three low-rise buildings, and a low-rise building and a high-rise building. Wind loads on the roof of a low-rise building embedded among a group of similar buildings are generally expected to experience shielding effects and be smaller than those on an isolated
building, while quite adverse effects appear when it is interfered by one or two other buildings (Khanduri et al., 1998). Hussain and Lee (1980) described the surface pressures on a large group of low-rise buildings for three types of flow regimes, including isolated roughness flow, wake interference flow and skimming flow, by varying building spacing and building aspect ratio. Holmes (1994) studied the effects of a group of tropical low-rise gable-roof buildings with different configurations. A significant increase in roof suction occurred for a row of buildings, and shielding effects occurred when a row of upstream buildings was added. Case and Isyumov (1998) showed that the high suction region on the roof of a low-rise gable-roof building experienced reduced loads when it was embedded in an array of similar buildings, except when it was located at the corner of the array. Ahmad and Kumar (2001) examined interference effects on a low-rise hip-roof building due to a similar building or three similar buildings, and reported significant amplification and shielding effects in different roof zones. Chang and Meroney (2003) pointed out that the effects of a lot of surrounding buildings significantly reduced wind pressures when building spacing was small, and increasing the number of upstream building rows tended to increase shielding effects. Jia and Sill (1998); Kim et al. (2012);
* Corresponding author. E-mail address: [email protected] (B. Chen). https://doi.org/10.1016/j.jweia.2018.10.019 Received 26 March 2018; Received in revised form 19 October 2018; Accepted 19 October 2018 0167-6105/© 2018 Elsevier Ltd. All rights reserved.
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Fig. 1. Information on incident flow.
Fig. 2. Building configuration and pressure tap arrangement.
interference of an upstream building on the mean wind suction on the flat roof of a low-rise building for building height ratios from 1.0 to 3.0, clear spacing from 0 to 4 times the low-rise building height, and wind attack angle for two buildings arranged side by side when the high-rise building was located immediately upstream of the low-rise building. The results showed that the mean suction on the roof of the low-rise building was amplified, and the amplification increased as the height of the upstream building increased. But the interference effects were not investigated for the low-rise building located in front of the high-rise building. It was found that a nearby high-rise building can cause severe interference effects on a low-rise building. For an isolated low-rise flat-roofed building, the roof experiences large wind suction, and such upward wind loads are combined with downward dead loads for structural design. Ignoring the amplification effects on wind suction will underestimate these combined loading effects. When the inference effects change the wind loading sign from negative to positive, the wind pressures act on the roof in the same direction as the dead loads. These combined loading effects may be more dangerous than the combination of wind suction and dead load when large positive wind pressures act on the roof. Furthermore, such combined loading effects become more dangerous when heavy snow loads are included. The severe interference effects due to a nearby high-rise building severely threaten structural safety if the design wind loads on the low-rise building are determined as for an isolated building. This work presents a comprehensive study on the interference effects on a low-rise building with a flat roof due to a nearby high-rise building. The influences of building spacing, relative height ratio and wind direction varying over much wider ranges are covered. The characteristics of mean, standard deviation (STD), peak pressure coefficients on the flat roof of a low-rise building are analyzed. Emphases are placed on the
Kim and Tamura (2013) investigated the interference effects on flat roofs of low-rise buildings influenced by incoming flow, building density, and building position. It was pointed out that the mean pressure coefficients on the target building decrease as building area density increases. The pressure coefficients on the downstream side were less affected by incident flows than those of an isolated building was. Quan et al. (2014) investigated wind pressures on the flat roof of a low-rise building embedded among a group of similar buildings, and studied the influence of building area density, relative height and arrangement. It was pointed out that the shielding factors of peak pressure coefficients in most cases were smaller then 1.0, and the influence of building area density and relative height were larger than that of the arrangement pattern. Li et al. (2017) carried out CFD simulation to investigate the interference effects on a gable roof of a low-rise building, and pointed out that largest interference effects occurred for two same buildings, and the corner or outer building of the group experienced larger interference effects. Fewer studies have been conducted on wind interference effects on low-rise buildings due to the presence of nearby high-rise buildings than on interference effects among a group of similar low-rise buildings. Stathopoulos (1984b) evaluated the interference effects of a large nearby building on wind loads on a low-rise gable-roof building with three building configurations, and pointed out the possibilities of roof suction amplification and sign change from negative to positive. Significant amplification of suctions on the roof was noted in the side-by-side configuration and the configuration of the low-rise building being located behind the high-rise building. Roof suction was significantly decreased, and mean positive pressures appeared in the configuration of the low-rise building located in front of the high-rise building, but the extents of such positive pressures and the dependence on building parameters were not discussed. Pindado et al. (2011) investigated the 89
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Fig. 3. Pressure coefficients of roof for wind direction 0 . (a) Mean wind pressure coefficients (b) STD wind pressure coefficients (c) Minimum pressure coefficients (d) Maximum pressure coefficients.
Fig. 4. Pressure coefficients of roof for wind direction 45 degrees. 90
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buildings were carried out for wind directions from 0 to 180 at intervals of 15 . As shown in Fig. 2, a total of 377 pressure taps was arranged on the roof and walls of the low-rise building, and 12 pressure taps were arranged on the four sides of the high-rise building at a height of 0.096 m, which is 4 mm lower than the eaves height of the low-rise building. The fluctuating pressures were measured simultaneously at a sampling frequency of 312 Hz. The mean wind speed at eaves height of the low-rise buildings was 6.8 m/s. Ten time history samples were obtained with a time duration of about 10 min for each sample corresponding to the prototype model for a geometrical scale of 1:200 and a velocity scale of 1:4. All measured fluctuating pressures were corrected with the frequency transfer function of the tube system. Among all building configurations, the maximum blockage ratio was 5.2%, and no blockage correction was conducted. The wind pressures were normalized by the mean velocity wind pressure at eaves height of the low-rise building to obtain the pressure coefficients. For each of ten samples, a sample minimum and maximum pressure coefficients were obtained. The minimum peak and maximum peak pressure coefficients were calculated using the Cook-Mayne method, where the distribution of peak values was assumed as FisherTippet Type 1 (Cook, 1982). No moving time average of fluctuating pressures was conducted during the calculation of these point peak pressure coefficients.
critical condition of sign change of wind pressures and the magnitudes of positive pressures when the low-rise building is located in front of the high-rise building, and on the amplification effects of wind suction when the low-rise building is located behind the high-rise building. 2. Experimental program Wind pressure measurements were conducted in a close circuit boundary layer wind tunnel in Beijing Jiaotong University of China, with a working section of 3.0 m wide and 2.0 m high. Roughness elements, carpets, spires and barriers were employed to simulate the atmospheric boundary layer over an open country terrain. Fig. 1 shows the measured longitudinal turbulence intensity profile and the mean wind velocity profile with a power law exponent of 0.147. The integral lengths scale at a height of 0.1 m is 0.36 m in the wind tunnel. The geometric scale of the simulated flow and the building models was 1:200. The experimental building configuration is displayed in Fig. 2, which includes a target low-rise building and an interfering highrise building. These two buildings have the same square plan with a side width of 0.2 m. The target building has a flat roof with an eaves height of h ¼ 0.1 m. To investigate the effects of the relative height of the high-rise building and the spacing between these two buildings on the interference effects, nine different height ratios of H/h ¼ 1, 1.5, 2, 3, 4, 5, 6, 8 and 10, i.e., the ratio of the height of the high-rise building to that of the low-rise building, and eleven spacing ratios of D/h ¼ 0, 0.25, 0.5, 1, 1.5, 2, 3, 4, 6, 8 and 10, i.e., the ratio of the clear spacing to the height of the low-rise buildings, were considered. For comparison, tests on an isolated low-rise building and high-rise buildings with nine different heights were also carried out. In total, there are 109 building configurations. For each building configuration, the pressure measurements on these two
3. Results and discussions 3.1. Isolated single low-rise building Figs. 3 and 4 display the distributions of mean, STD, minimum and
Fig. 5. Mean pressure coefficients for D/h ¼ 0.5 for wind direction 0 degrees. 91
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When H/h is 2, a positive pressure zone is noted near the leeward roof edge near the interfering building. The positive pressures and the corresponding roof area increase as the height ratio H/h increases, which leads to a decrease in negative pressures in the windward roof area. When H/h is 10, half of the roof experiences positive pressures, and the positive and negative mean pressure coefficients reach 0.7 and 0.3, respectively. These positive pressures are attributed to the large standing vortex produced by the leeward high-rise building. Fig. 6 and Fig. 7 respectively display the distributions of minimum and maximum pressure coefficients on the roof of a low-rise building for different height ratios H/h at a clear space ratio of D/h ¼ 0.5. In comparison to the peak pressure distribution of an isolated building shown in Fig. 3, it is observed from Figs. 6 and 7 that increasing the height of the downstream high-rise building decreases the magnitude of the minimum pressure coefficients on the roof of the low-rise building, and the roof area near the high-rise building is more sensitive to the height of the high-rise building. The minimum pressure coefficients on the upstream roof edge and on the downstream roof edge of the low-rise building are respectively 70% and 15% of those on the isolated building when the building height ratio is 10. Increasing the height of the downstream highrise building increases the maximum pressure coefficients on the roof of the low-rise building. The maximum pressure coefficients on the whole roof almost become positive when the building height ratio H/h is 2.0, and the values on the downstream central roof edge are about three times of those on the isolated building when H/h is larger than 4.0. Stathopoulos (1984b) also mentioned the appearance of positive pressures on the gable roof of a low-rise building when it is located right in front of a nearby high-rise building, and showed that positive pressures may be high due to the impact of the large standing vortex produced by the high-rise building on the low building roof.
maximum pressure coefficients on the roof of an isolated low-rise building at two typical wind directions: 0 and 45 . At a wind direction of 0 , large negative pressures are observed near the leading edge of the roof associate with flow separation. The STD pressure coefficient reaches a maximum around the inflexion point of the mean pressure coefficient curve, and the pressure distribution around a blunt flat plate (Li and Melbourne, 1999) exhibits a similar phenomenon. This point is considered to be the reattachment point of the separated flow from the windward roof edge. The STD pressure coefficients decrease rapidly with distance from the windward edge, but the change in gradient is much smaller than that of the mean pressure coefficients. The windward roof area experiences large negative peak pressures, and the minimum pressure coefficients on the windward quarter of the roof are smaller than 2.0. At a wind direction of 45 , the pressure distribution is associated with a conical vortex from the corner, two windward edge areas experience large negative pressures, and the minimum pressure coefficient at the windward corner edge reaches 4.6. 3.2. Low-rise building located right in front of high-rise building This section discusses the interference effects on the roof of a low-rise building when it is right in front of a high-rise building, i.e., wind direction is 0 . 3.2.1. Pressure distribution on roof of low-rise building Fig. 5 shows the mean pressure distribution on the roof of a low-rise building for different height ratios H/h at a clear space ratio of D/h ¼ 0.5. When the height of the target low-rise building is the same as the interfering building, i.e., height ratio H/h ¼ 1, the interference effects are small, and the pressure distribution is close to that of an isolated building.
Fig. 6. Minimum pressure coefficients for D/h ¼ 0.5 for wind direction 0 degrees. 92
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Fig. 7. Maximum pressure coefficients for D/h ¼ 0.5 for wind direction 0 degrees.
coefficients gradually recover close to the value for the isolated low-rise building roof. The STD pressure coefficients decrease as the height ratio H/h increases for a fixed spacing ratio. It is clear that the interference effects on the STD pressure coefficients are very different from those on the mean pressure coefficients. Fig. 10 shows the distribution of minimum pressure coefficients. Due to the increase in mean and decrease in STD values, the minimum pressure coefficients are reduced in magnitude compared to those on the isolated building roof. This reduction is more significant when the spacing ratio D/h is smaller than 2.0. The minimum pressures on the leeward roof even become positive when D/h is smaller than 0.25 and H/ h is larger than 3.0. However, the interference effects result in an increase in maximum pressures, as shown in Fig. 11.
3.2.2. Pressure distribution on roof center line Fig. 8 shows the variation of mean pressure coefficients on the roof center line for different height and spacing ratios. It is observed that increasing the height of the interfering building or reducing the building spacing makes interference effects more significant. Larger values and a larger roof area with positive pressures are noted when the spacing is small and the height ratio is large. The maximum mean positive pressure reaches 0.9 when the spacing ratio D/h is 0.25. The interference effects are very sensitive to the height ratio when D/h is smaller than 1.0. The suction decreases and the positive pressure increases as the height ratio increases. The interference effects become stable and are not sensitive to the height ratio when H/h and D/h are larger than 4.0. Fig. 9 shows the distribution of STD pressure coefficients. The maximum STD pressure coefficient on the roof appears at almost the same position as that on the isolated building roof. When the spacing ratio D/h is smaller than 0.25, the distribution and variation of the STD pressure coefficients on the roof are significantly different from those on the isolated building roof. The maximum STD value increases by 60% when the spacing ratio D/h is 0.25 with a large height ratio H/h. The STD values are also very large near the leeward roof area where large mean positive pressures are observed. The STD pressure coefficients in the leeward roof area increase with height ratio H/h up to H/h ¼ 2.0, and then decreases as H/h increases. This is very different from the effects on the mean pressure coefficients shown in Fig. 8(a), where the positive mean pressure coefficients increase monotonically as H/h increases. When the spacing ratio D/h increases from 0 to 1.0, the maximum STD pressure coefficients in both negative and positive pressure areas decrease rapidly, and the distribution gradually becomes similar to that on the isolated low-rise building roof but with smaller amplitude. When the spacing ratio D/h increases from 1.0 to 10.0, the STD pressure
3.3. Low-rise building located right behind high-rise building This section discusses the interference effects on the roof of a low-rise building when the building is right behind the high-rise building, i.e., wind direction is 180 . 3.3.1. Wind pressure distribution on low-rise building roof Fig. 12 shows the mean pressure distribution on the low-rise building roof for six height ratios H/h when the spacing ratio D/h is 0.5. For height ratio H/h ¼ 1, the pressure coefficients are very small in magnitude due to shielding effects from the interfering building. As height ratio H/h increases, the values of the negative pressures significantly increase in magnitude, and larger negative pressures are observed in the roof area near the high-rise building. For H/h ¼ 10, large negative pressures on the whole roof are noted, which are much larger than those on the isolated building roof. 93
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Fig. 8. Mean pressure coefficients on roof center line for wind direction 0 degrees.
that of the isolated building shown in Fig. 3. Increasing the height of the upstream high-rise building amplifies the magnitude of minimum pressure coefficients on the whole roof of the low-rise building, especially in the two roof edge areas parallel to the wind direction. Increasing the height of the high-rise building reduces the change in gradient of
Fig. 13 and Fig. 14 respectively show the distribution of minimum and maximum pressure coefficients on the roof of a low-rise building for different height ratios H/h with a clear space ratio of D/h ¼ 0.5. It is observed that the upstream high-rise building makes the peak pressure coefficient distribution on the low-rise building be much different from 94
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Fig. 9. STD pressure coefficients on roof center line for wind direction 0 degrees.
3.3.2. Pressure distribution on roof center line Fig. 15 shows the distribution of mean pressure coefficients. It is observed that for small spacing ratios, the pressures on the low-rise building roof are dominated by the wake flow of the high-rise building. As a result, the mean pressure coefficients on the roof are negative and have small change in gradient, which are very different from those on the
pressure coefficients along the roof center line parallel to the wind direction. Increasing the height of the upstream high-rise building decreases maximum pressure coefficients in the upstream roof area on the low-rise building, increases maximum pressure coefficients in the downstream roof area when H/h is smaller than 2.0, then decreases them after H/h is larger than 2.0.
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Fig. 10. Minimum pressure coefficients on roof center line for wind direction 0 degrees.
coefficients are normalized by the incoming velocity pressure at the eaves height of the low-rise building. It is demonstrated that the height of the windward high-rise building has little effects on the pressures on the windward wall, but has significant effects on the pressures on the leeward and side walls. Increasing the building height results in an increase in magnitude of suction on the leeward and side walls, and suction on the roof of the leeward interfered low-rise building.
isolated building roof. The increase in building height ratio results in an increase in the magnitude of negative pressures. The suction on the whole roof is even larger than that on the windward roof area of the isolated building roof when the building height ratio H/h is larger than 8.0. This phenomenon can be understood from the pressure distribution on the high-rise building shown in Fig. 16, where the results for the isolated high-rise building are shown for comparison. The pressure
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Fig. 11. Maximum pressure coefficients on roof centerline for wind direction 0 degrees.
D/h reaches 10.0, the pressures on the whole roof are very close to those on the isolated building roof. Fig. 17 shows the STDs of pressure coefficients on the center line of the low-rise building roof. In general, the variation of the STDs of pressure coefficients on the roof along the center line parallel to the wind direction is very different from that on the isolated building roof. When the spacing ratio D/h is smaller than 1.0, the STDs of pressure coefficients
As building spacing increases, the pressure change in gradient on the low-rise building roof increases, and the windward flow separation gradually recovers. The amplification effects on the leeward roof area and the shielding effects on the windward roof area decrease. The interference effects decrease more quickly in the leeward area. When spacing ratio D/h is larger than 4.0, the pressure coefficients in the leeward area become close to those on the isolated building roof. When
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Fig. 12. Mean pressure coefficients for D/h ¼ 0.5 for wind direction 180 degrees.
are very small for height ratios of H/h > 2.0. The STDs of pressure coefficients are not sensitive to the spacing ratio. Increase in height ratio induces an increase in RMS pressures, and the increase in the leeward area is more significant than that in the windward area. As a result, the STDs of pressure coefficients in the leeward area are larger than those in the windward area when the height ratio is larger than 3.0. This distribution is adverse to that on the isolated building roof. When the spacing ratio D/h is larger than 1.0, the STDs of pressures become sensitive to both the spacing ratio and height ratio. They are more sensitive to the spacing ratio for larger height ratios. As the spacing ratio increases, the amplification effects of leeward vortex shed from the high-rise building are smaller, and separation flow in the windward area appears gradually. This induces a significant decrease in STDs of pressures in the leeward
area for a large H/h, but a slow increase in the windward area for a smaller H/h. As a result, the distribution of STDs of pressure coefficients tend to be similar to those on an isolated building roof. The magnitude of minimum pressure coefficients on the roof is much larger than that of maximum pressure coefficients when the low-rise building is located right behind the high-rise building. Only minimum pressure coefficients are discussed here, as shown in Fig. 18. When the building clear spacing ratio D/h is smaller than 0.5, the peak pressures are not sensitive to the spacing ratio, but are very sensitive to the relative height ratio H/h. When D/h is larger than 0.5, the peak pressure coefficients are sensitive to both D/h and to H/h, and increasing D/h induces a significant decrease in the peak suction in the leeward area where H/h is larger than 5.0, and a slow increase in the windward area where
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Fig. 13. Minimum pressure coefficients for D/h ¼ 0.5 for wind direction 180 degrees.
These eight pressure taps represent the corner, middle edge and central roof area, and experience the largest negative peak pressures in these roof areas respectively. The most unfavorable peak pressure coefficients at these eight pressure taps of the isolated low-rise building are listed in Table 1. The pressure coefficients at two symmetric points are not the same, and they may be attributed to the imperfect symmetry of the mode and the non-uniformity of the approach flow. Interference effects on the most unfavorable peak pressure coefficients are evaluated by the interference factor (IF), which is defined as the ratio of the peak Cp in the case with an interfering high-rise building to that of the isolated low-rise building. Fig. 21 shows interference factors of the most unfavorable minimum pressure coefficients. Pressure taps P1 and P2 far away from the high-rise building mainly exhibit shielding effects except the cases when D/ h ¼ 0.25 and H/h > 8.0. Interference effects decrease with an increase in D/h, and are not sensitive to H/h when H/h ranges from 3.0 to 6.0. The minimum interference factor is around 0.7. Pressure taps P6 and P7 near
H/h is smaller than 5.0. 4. Most unfavorable peak pressure coefficients among all wind directions The most unfavorable peak (minimum and maximum) pressure coefficients of the roof among all wind directions are critical for the cladding design. Fig. 19 displays the most unfavorable peak pressure coefficients on the roof of an isolated low-rise building. The corner roof area experiences large negative peak pressures, and the largest value reaches 5.0. Minimum pressure coefficients in the central roof area are much smaller in magnitude, and vary around 2.0. The change in gradient of the most unfavorable positive peak pressure coefficients is small, and positive peak pressure coefficients vary around 0.5. According to the peak pressure coefficient distribution shown in Fig. 19, interference effects on peak pressures of eight typical pressure taps on the roof of low-rise building shown in Fig. 20 are investigated. 99
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Fig. 14. Maximum pressure coefficients for D/h ¼ 0.5 for wind direction 180 degrees.
P5 and P8 experience significant amplification effects in the cases with a small D/h and a large H/h. Increasing H/h or decreasing D/h strengthens the amplification effects. Pressure taps P3 and P8 exhibit shielding effects in the cases with a small D/h when H/h is smaller than 4.0. When H/h is 10, the maximum interference factors of these four taps are almost larger than 1.5. Fig. 22 displays the interference factors of the most unfavorable maximum pressure coefficients. Amplification effects appear in most cases when H/h > 1.5. The interference factors at the eight typical pressure taps tend to decrease as D/h increases. When D/h is smaller than 2.0, the amplification effects are very significant and sensitive to D/h.
the high-rise building mainly exhibit shielding effects when D/h is smaller than 1.0. Increasing H/h weakens such shielding effects. The most unfavorable minimum pressure occurs at an oblique wind direction, and the shielding effects appear at this oblique wind direction for small H/h, although amplification effects may be observed at the wind direction of 180 shown in Fig. 18. When D/h is larger than 1.0, pressure taps P6 and P7 mainly experience amplification effects. Increasing H/h or D/h strengthens such amplification effects when D/h is up to around 4.0–6.0. It is attributed to the accelerated flow passing through the two buildings. Amplification effects become smaller as D/h increases. The maximum interference factors of P6 and P7 are larger than 1.5. Pressure taps P3, P4,
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Fig. 15. Mean pressure coefficients on roof centerline for wind direction 180 degrees.
5. Lift coefficients and positive pressures on roof of low-rise building
The interference factors increase when H/h increases up to 4.0, and then remain almost constant for H/h > 4.0. As the distance from the pressure taps to the high-rise building decreases, the amplification effects increase, for example, the interference factors at P1, P4 and P6 decrease in turn. The maximum interference factors at P6 and P7 are larger than 3.5. When D/h is larger than 2.0, the interference factors show scattered relationship with H/h.
5.1. Lift coefficients on roof of low-rise building Lift coefficients on the roof of low-rise building are calculated using the external pressures only, where the influence of the internal pressure 101
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Fig. 16. Mean pressure coefficients on high-rise building for wind direction 180 degrees.
Pindado et al. (2011) also investigated interference effects of an upstream high-rise building on a low-rise building when the wind direction ranges from 90 to 180 , the clear spacing ranges from 0 to 4 times the low-rise building height, and the building height ratio H/h ranges from 1.0 to 3.0. It is shown that the interference effects become negligible at the wind direction of 90 , H/h ¼ 1 and D/h ¼ 3, and the pressure distribution on the roof is close to that for an isolated building. Both the distribution and variation of pressure coefficients in Fig. 3(a) shows good agreement in general with those in Pindado et al. (2011), and the small difference is partly attributed to the difference between the simulated atmospheric boundary layers where the turbulence intensity at the roof eaves height is 12.7% and 4%, respectively, in this paper and Pindado et al. (2011). In view of the maximum absolute values of the mean pressure coefficients, Pindado et al. (2011) showed that the upstream high-rise building produces larger suction than that on an isolated building when D/h is smaller than 4.0, and this becomes more significant for larger building height ratios. Moreover, the influence of the upstream high-rise building becomes very small when the clear spacing ratio D/h is larger than 4.0. It can be found from Figs. 15 and 23 and the experiment results not shown in these two figures that the condition of the clear building spacing corresponding to small interference effects depends on the building height ratio, and the interference effects when H/h is larger than 3.0 can not be ignored even when D/H is larger than 4.
is not included. Positive sign of the lift coefficient represents the upward direction of the lift force. Mean lift coefficients on the low-rise building roof are plotted as a function of the wind direction, spacing ratio and height ratio in Fig. 23, where mean lift coefficients are defined as the weighted average value of mean pressure coefficients on the roof weighted by the tributary area of each pressure tap. Mean lift coefficients on the isolated building are not sensitive to the wind direction and varies around 0.6. For spacing ratios smaller than 0.5, negative lift coefficients are noted for wind directions ranging from 0 to 30 when the height ratio is larger than 3.0. They increase rapidly to a maximum positive lift coefficient when the wind direction increases to 90 . This large positive lift coefficient decreases with an increase in the wind direction for height ratios smaller than 6.0, but remains almost constant for height ratios larger than 6.0. When the wind direction ranges from 0 to 60 , lift coefficients are sensitive to the height ratio H/h up to H/h ¼ 5.0, and then tend to be a constant value over H/h ¼ 5.0. When the wind direction ranges from 60 to 180 , the lift coefficients increase as H/h increases. As the spacing ratio D/h increases, the negative lift becomes smaller for large height ratios when the wind direction ranges from 0 to 60 , and amplification effects of the positive lift become smaller when the wind direction ranges from 60 to 180 . The mean lift coefficient on the roof is about 2.5 times that of an isolated low-rise building roof for a small spacing ratio and large height ratio.
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Fig. 17. RMS pressure coefficients on roof center line for wind direction 180 degrees.
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Fig. 18. Minimum pressure coefficients on roof center line for wind direction 180 degrees.
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Fig. 19. Most unfavorable peak pressure coefficients.
5.2. Amplitude and action area of positive pressures Wind suction on the flat roof of an isolated building is large and is often carefully considered in cladding design. However, positive pressures are usually considered to be small and are often neglected. However, as has been noted in the previous discussions, large positive pressures occur when the low-rise building is interfered by a high-rise building. These pressures have the same action direction as dead loads and snow loads. Therefore, they need to be carefully considered when their combination with dead loads and live loads controls the structural design. Figs. 26 and 27 show the ratio of roof area with mean positive pressures to the total roof area, and the averaged mean lift coefficients in such roof area with positive pressures. Positive pressures are noted at wind directions ranging from 0 (low-rise building right in front of highrise building) to 45 . The maximum averaged mean lift coefficient in magnitude appears at the wind direction of 15 in most cases. The maximum roof area ratio with positive pressures occurs at the wind direction of 15 or 30 . The roof area ratio and the averaged mean lift coefficients in magnitude in the area with positive pressures decrease as the spacing ratio increases. The values of these two parameters increase as the height ratio H/h increases, and then remains almost constant over H/ h ¼ 8.0. The maximum roof area ratio and the averaged mean lift coefficient are larger than 70% and 0.5, respectively, when H/h is 10.0 and D/h is 0.25. Fig. 28 shows the critical building height ratio as a function of the spacing ratio and wind direction, where mean pressures change sign and mean positive pressures on the roof begin to appear. The critical building height ratio varies from 1.5 to 8.0, and increases with an increase in the spacing ratio and wind direction.
Fig. 20. Location of eight typical pressure taps on low-rise building.
Fig. 24 and Fig. 25 respectively show the maximum and minimum lift coefficients. It is observed that the dependence of the peak lift coefficients on the wind direction, spacing ratio and height ratio is similar to that of mean lift coefficients shown in Fig. 23. The maximum and minimum lift coefficients on the isolated building are not sensitive to the wind direction and vary around 0.9 and 0.3 respectively. When the wind direction ranges from 0 to 60 , shielding effects on the maximum lift coefficients are obvious. The magnitude of the maximum lift coefficients is much smaller than that of the isolated building, and increases as the height ratio H/h increases up to H/h ¼ 5.0, and then tends to be a constant for H/h larger than 5.0. When the wind direction ranges from 0 to 30 , the maximum lift coefficients almost reduce to zero when D/ h ¼ 0.25 and H/h > 5.0. When the wind direction is larger than 70 , the amplification effects on the maximum lift coefficients are significant, and increase as H/h increases, but are not sensitive to the wind direction when H/h is larger than 2.0. The largest maximum lift coefficient reaches 2.4 when D/h ¼ 0.25 and H/h > 10. The shielding and amplification effects reduce with an increase in D/h and almost disappear when D/h reaches 10. Small minimum lift coefficient appears at the wind directions ranging from 0 to 30 for a small spacing ratio D/h. The minimum lift coefficient decreases rapidly as the H/h increases. It is smaller than 0 when H/h is larger than 3.0, and tends to be a constant when H/h is larger than 5.0. The smallest minimum lift coefficient reaches 0.7 at D/ h ¼ 0.25 and H/h ¼ 10.
6. Conclusions Wind pressure measurements were carried out to investigate interference effects of one high-rise building on the roof of a low-rise building, with building spacing ratio (D/h) varying from 0.0 to 10.0, building height ratio (H/h) from 1.0 to 10.0, and wind direction from 0 to 180 . Both buildings had the same square plan. Severe positive pressures on the roof of the low-rise building are noted when it is located in front of the high-rise building with a small
Table 1 The most unfavorable peak pressure coefficients of isolated building.
Minimum Cp Maximum Cp
P1
P2
P3
P4
P5
P6
P7
P8
3.2 0.44
4.3 0.39
4.8 0.41
2.0 0.46
2.7 0.43
3.0 0.44
4.6 0.43
5.0 0.50
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Fig. 21. Interference factors of most unfavorable minimum pressure coefficients.
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Fig. 22. Interference factors of most unfavorable maximum pressure coefficients.
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Fig. 23. Mean lift coefficients on whole roof for different wind directions.
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Fig. 24. Maximum lift coefficients on whole roof for different wind directions.
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Fig. 25. Minimum lift coefficients on whole roof for different wind directions.
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Fig. 26. Ratio of roof area with positive pressures to total roof area.
far away from the high-rise building mainly exhibit shielding effects. The roof area near the high-rise building mainly exhibits shielding effects when the building spacing ratio is smaller than 1.0, but experiences amplification effects when the building spacing ratio is larger than 1.0. The amplification effects strengthen with an increase in the building height ratio or spacing ratio when the height ratio is up to around 4.0–6.0. The most unfavorable maximum pressure coefficients mainly experience amplification effects when the building height ratio is larger than 1.5. When the building spacing ratio is smaller than 2.0, amplification effects are significant and sensitive to the building spacing ratio and the building height ratio. When the wind direction ranges from 0 to 60 , shielding effects on the maximum lift coefficients on the roof are obvious. The maximum lift coefficient almost reduces to zero for a small building spacing ratio and large building height ratio when the wind direction ranges from 0 to 30 . When the wind direction is larger than 70 , the amplification effects on the maximum lift coefficients are significant, and increase as H/h increases, but are not sensitive to the wind direction when H/h is larger than 2.0. Large minimum lift coefficient appears at the wind directions ranging from 0 to 30 for a small spacing ratio. The minimum lift coefficient in magnitude increases rapidly as H/h increases.
building spacing. Increasing the height of the high-rise building or decreasing the building spacing induces an increase in positive pressures. The critical condition for the sign change of wind pressures on the roof is presented at different wind directions. The ratio of roof area with positive pressures to total roof area and the averaged mean lift coefficients in such area reach 84% and 0.56, respectively, at a building height ratio of 10.0 and a clear building spacing ratio of 0.0. Ignoring wind interference effects will significantly underestimate structural response when wind loads are combined with downward dead loads such as weight and snow load. When the low-rise building is right behind the high-rise building with a small building spacing (D/h < 1), significant amplification of suction in the leeward roof area is observed at a large building height ratio. Increase in the height of the interfering high-rise building amplifies the magnitude of the suction on the whole roof. These interference effects are attributed to the large size of the vortex from the windward high-rise building, as can be understood from the pressure distribution on the high-rise building. The mean lift coefficient on the roof is about 2.5 times that on an isolated low-rise building roof at a small spacing ratio and large height ratio. The most unfavorable minimum pressure coefficients in the roof area
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Fig. 27. Mean force coefficients on roof zone with positive pressures.
Acknowledgments The work in this paper was partially supported by the National Natural Science Foundation of China (Grant No.51378059 and No. 51720105005), Beijing Nova Program (Grant No. Z151100000315051), and the 111 Project of China (Grant No. B13002). The authors would like to thank the reviewers of this paper for their kind improving comments and suggestions. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.jweia.2018.10.019. References Ahmad, S., Kumar, K., 2001. Interference effects on wind loads on low-rise hip roof buildings. Eng. Struct. 23 (12), 1577–1589. Alrawashdeh, H., Stathopoulos, T., 2015. Wind pressures on large roofs of low buildings and wind codes and standards. J. Wind Eng. Ind. Aerod. 147, 212–225. Banks, D., Meroney, R.N., Sarkar, et al., 2000. Flow visualization of conical vortices on flat roofs with simultaneous surface pressure measurement. J. Wind Eng. Ind. Aerod. 84 (1), 65–85.
Fig. 28. Critical building height ratio with positive pressures on roof.
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