Flat plates in buildings could appear as horizontal plates such as balconies, canopies, or vertical plates like partitioning walls in short buildings or lift shafts in mid- to high-rise buildings. Balconies are especially important in the aerodynamic performance of tall buildings [6]. The flow mechanism influencing peak pressure locations on the bluff body vertical surfaces and roof will be affected by parameters such as plate length, tilt, installation height, and location. Canopies attached to mid-rise buildings [7] had a significant impact on the building-generated turbulence and, consequently, the peak wind-induced loads. With the canopy’s presence at the leading edge of the building, the turbulence was mostly generated by the flow separation from the building edges; however, moving the canopies toward the building trailing edge resulted in loading that is dominated by flow separation from the canopy leading edge. Experimental studies on canopies attached to buildings [8] have indicated that when the canopy height-to-roof eave height ratio lies within the 0 ≤ h _c /h ≤ 0.9 range, as the ratio goes higher, the peak local min Cp _,net will increase significantly. Increasing the canopy location-to-canopy length ratio by contrast was seen to decrease the local min Cp _,net magnitudes. In a similar manner, horizontal plates will affect the design of the façade structure as well by modifying the near-façade wind flow pattern and surface pressures. Computational fluid dynamics (CFD) analysis of multi-story buildings [9] shows that the horizontal balconies were capable of increasing wind loads both on windward and leeward sides of the façade surfaces. In [10], a new method for estimating wind loads on glass handrails of mid-rise buildings was developed investigating the effects of balconies and handrails on a 15-story building. The findings of the wind tunnel experiment, including the pressure coefficient measurements, were carried out on the glass handrails of various shapes. The authors also compared their results with existing standards. The presence of balconies led to a reduction in peak negative pressure coefficients, and therefore, it was suggested that balconies act as a shield against wind. Other studies [11,12] also concluded that the aerodynamic response of buildings, the façade system, and joint design processes depends on the presence of the plates.

It is common practice in the construction industry to utilize multi-level flat roofs in building structures such as public storage structures, large-scale residential complexes, and industrial warehouses. Most studies conducted on multi-level roofs [13–15] focused on the snow drift and loads and their impact on the flat roof performance. There have been limited studies conducted to evaluate the wind pressures on such stepped-roof configurations. Stathopoulos [16] carried out an experimental study on wind pressures on the roof and wall of buildings with step-shaped roofs. The study provided important knowledge that improved the wind standards and wind load provisions for stepped-roof buildings. A comparison between the experimental data and the standards showed that peak positive pressure coefficients could not be accurately calculated using standard provisions back then. In another study, significant differences in peak minimum pressure coefficients were observed between a multi-level flat roof and a simple flat roof [17]. The minimum and maximum C _p values were predominantly dependent on the step parameters. The locations of local peak pressure coefficients were at the higher building wall–lower building roof interaction zone for the 0° wind direction. One of the main sources of turbulence in tall buildings is the setbacks in tall building cross section, which produces stepped roofs. In a CFD simulation of different multi-story buildings with setbacks [18], it was found that maximum positive pressure coefficient values for the 0° wind direction happens at the top levels of the building away from the setback. The peak negative pressure coefficient values for the 90° wind direction were on the stepped flat roof which was in compliance with an earlier study [19] carried out by the same researchers. The podium is the extended section of a high-rise building at a lower level. High torsional moments and shear forces at the podium level will be expected under the lateral loads [20] due to the cross-sectional offset that, most of the time, pushes design engineers in the application of viscous dampers to reduce torsional response [21]. According to [22], setbacks in tall buildings will affect the vortex shedding frequencies and, consequently, can lead to reduction in strong vortex shedding forces. Adding setbacks at different heights will push the vortices to try to shed at different frequencies which will help in “confusing” the vortex shedding [23]. The non-linear dynamic response of tall buildings has been investigated [24] by modeling a scaled 1:400 model of an existing 47-story building with a podium structure at the base. It was found that the gravity supporting structure and structure at the podium will improve the wind performance of the tall building.

Flow separation is a well-understood area of fluid mechanics, and it is considered when designing all modern buildings; however, there is no research conducted on the interaction between separated bubbles with vertically oriented planes of development. Existing research on the aerodynamic performance of buildings is aimed at identifying the location and values of local peak pressure coefficients. It is also well understood that when flow separation occurs in an ABL environment, the strongest suction occurs on the leading edges of the bluff bodies [25]. However, there is no previous research that considers flow separation that occurs simultaneously at two perpendicularly attached bluff bodies and looking into the loading scheme due to the complex flow interactions. Although absolute peak pressures might not be affected significantly due to this interaction, the location at which these peak pressures occur might be very different compared to more conventional cases (e.g., roof or wall surface). This effect might have a direct implication on how we design more complex structures mostly due to the existing zoning convention that is adopted in building codes and wind standards [26]. The concept of synchronous flow separation from bluff bodies with attached plates (e.g., canopy or balcony) or bluff bodies with setbacks (e.g., stepped flat roof buildings or tall buildings with podium) is the focus of the current study. This very specific flow phenomenon occurs when wind separates simultaneously due to the interaction with both the main bluff body and the attached plate or a secondary bluff body. Right after the flows are separated, a complex interaction is initiated that results in non-conventional wind-induced loading patterns on the surfaces of both the bluff body and the plate. A preliminary experimental campaign is carried out to look into this unconventional loading scenario that might have a great influence on the aerodynamic performance of the building itself and the building components that are attached to it.

In this study, the test models were constructed as single-cubic bluff bodies with a plate extension or combined bluff bodies with variable dimensions (Figure 1). In models 1 and 2, the vertical and horizontal plate thickness is 30 mm and bluff bodies’ dimensions are 240 mm × 240 mm × 240 mm. Models 1 and 2 represent a building with a vertical and horizontal flat plate attachment (e.g., partition, balcony, and canopy). Model 3 is made of two bluff bodies with dimensions of 240 mm × 240 mm × 240 mm and 240 mm × 120 mm × 120 mm representing buildings with multi-level setbacks or stepped flat roof buildings, respectively. Models 1, 2, and 3 share the same main bluff body with the difference in the attached second body. The purpose of adding a plate to the body is to evaluate the flow mechanism at the plate–body interaction zone while allowing the oncoming flow to separate on the other side of the bluff body or underneath the plate for models 1 and 2, respectively. Flat plates are continuous along the bluff bodies to provide enough length for the flow to separate from the plate edge, mix with the flow separated from the bluff body leading edge, and provide room for a probable reattachment of mixed vortices at the downstream of the models in a 90° wind direction, which is the dominant direction for the scope of this study. The plate in model 3, on the other hand, has been replaced with a second bluff body to create a stronger separated flow due to the smaller bluff body (i.e., the flow can no longer escape from the bottom/side of the plate). Model 4 is an extension of model 3, for which the shorter bluff body has increased dimensions to resemble a podium-like structure. Flow will first separate from the podium edge and later will experience the second separation from the wall of the taller body. The extended width of the podium beyond the building will allow for any probable reattachment of the separated flows. Pressure taps were fitted on one side of the bluff body and the flat plate for models with a vertical or horizontal plate. In total, 144 pressure taps were fitted in models 1, 2, and 3 and 210 pressure taps in model 4 (Figure 1). The sides of the models that did not contain any pressure taps were made out of wood, while those that had pressure taps were made out of plexiglass. A sensitive pressure scanner system was used to obtain the pressure time histories at each pressure tap using a sampling frequency of 530 Hz and sampling time of 60 s for all wind directions.

The experimental tests were carried out in the Atmospheric Boundary Layer Wind Tunnel (ABLWT) in the Laboratory for Wind Engineering Research (LWER), located at Florida International University (FIU). The wind tunnel has a test section which is 2.5 m wide and 1.85 m high with 18 m overall length. The turntable, placed downwind of the wind tunnel, allows for housing the models and testing them in different wind directions. The spires and roughness elements can be manually adjusted to achieve the desired exposure (open, suburban, or urban). The configuration chosen for the spires and roughness elements was adjusted to reproduce an open terrain profile, and a geometric scale of 1:100 was selected for this study. The two principal angles of attacks for this study were 0° and 90°. The selection was based on the fact that the 90° wind direction will generate the desired structure for the separated flows, while the 0° wind direction will serve as a reference case where a more traditional (i.e., single) separated flow occurs. Figure 2A shows a schematic illustration of the model 3 orientation on the turntable for both directions, while Figure 2B shows the physical model in the 90° wind direction.

To calculate the wind speed, turbulence intensity profiles, and the power spectra, multi-hole (cobra) probes were installed at different heights. The sampling frequency was 2,500 Hz, and wind velocities were measured for a 60 s time duration. Figure 3A shows a sample time history of the wind speed at the model mean roof height. The mean wind speed at the mean roof height of all models (h = 240 mm) was 8.95 m/s. The mean wind speed and turbulence intensity profiles are shown in Figure 3B. The wind speeds were normalized against the wind speed at the reference height Z _g and compared with the power law equation (α = 1/9.8) and the ESDU (category C open terrain and a surface roughness length of z ₀ = 0.02 m) profiles showing good agreement. The turbulence intensity was estimated to be equal to I _u = 16% at the mean roof height, and the turbulence intensity profile at the wind tunnel had good agreement with the ESDU turbulence.

The power spectral density (PSD) of the wind tunnel is shown in Figure 3C. The spectral density achieved in the wind tunnel was compared to the von Karman spectrum in the atmospheric boundary layer (ABL) that was derived using [27], the wind tunnel PSD demonstrates a strong agreement at the high-frequency section of the oscillations (fh/U > 0.1), and the low-frequency cut-off signifies that the modeled turbulence is adequate for disturbances up to 5–10 times the building size. It should be noted that the increased height of the model is the reason for the discrepancy observed in the low-frequency range and that the spectrum match is even more improved at the height of the canopy in models 2, 3, and 4 (fh/U > 0.01).

Wind pressures are often expressed using dimensionless pressure coefficients (C _ps ), as in Eq. 1, where Δp is the pressure difference at the pressure tap location, ρ is the air density, and U ¯ z is the mean wind speed at a reference height (often the mean roof height of the model). In the following sections, the results from this study are presented using a similar notation. For the mean pressure coefficients C ¯ p , Eq. 2 was used, while for the peak pressure coefficients C ^ p , Eq. 3 was used. Peak Cps were obtained by using the best linear unbiased estimation (BLUE) method [28]. C p = ∆ p 0.5 ρ U ¯ z 2 , (1) C ¯ p = ∆ p ¯ 0.5 ρ U ¯ 2 , (2) C ^ p = ∆ ^ p 0.5 ρ U ^ 3   sec 2 . (3)

In the 0° wind, both the vertical plate and the roof of bluff body will experience predominately positive pressure. The roof leading edge will lead to a separated flow and negative pressure areas; however, the vertical plate will stagnate the flow, resulting in a returned flow to the roof of the model which will increase the roof area that experiences positive pressures. Mean pressure coefficient contour plots for the 0° wind (Figure 4A) show higher positive mean pressure coefficient ( C ¯ p ) values on the top and bottom parts of the vertical plate. The backward circulating flow will eventually reattach at the end of the roof, causing positive pressure despite the earlier suction due to the flow separation from the roof edge. High positive pressure coefficient values were observed at the plate–roof interaction zone, especially in the middle of both surfaces. The highest mean value happened at the higher surface of the plate and plate–roof interaction zone C ¯ p ≈0.9. Mean pressure coefficient contour plots show an interesting phenomenon on the roof of the building. Because of the presence of the vertical plate on the top of the flat roof, two positive pressure zones were formed at the leading edge and at the roof–plate interaction zone, which were separated by a narrow suction zone in the middle (Figure 4A). This narrow zone has widened at the two ends with higher negative pressure coefficients. This is due to the return flow induced by the plate and its domination over the oncoming separated flow in the roof leading edge. The return flow is not as strong on the edges as it escapes the vertical plate. Peak positive pressure coefficient C p contour plots in Figure 4B show somewhat similar flow characteristics and peak locations for the same wind direction. The plate–roof interaction zone had the highest pressure coefficients with C p values varying between 2.3 and 3.2.

Mean pressure coefficient results for the 90° wind direction are shown in Figure 5A. As expected, the separated flows at both the roof and plate leading edges result in higher negative pressure coefficients on the left half of the surfaces. The gradient on the roof is more uniform as it moves downwind, starting from −0.6 and ending at almost 0 on the leeward end. However, the plate pressure gradient clearly shows the more complex wind–structure interaction with higher pressure values moving at a diagonal direction from the bottom windward to the top leeward corner of the plate. The leading-edge mean pressure coefficient is also slightly increased, taking a value of −0.9. A similar distribution is shown in Figure 5B for the negative peak pressure coefficients C ^ p . The separation bubble’s diagonal pattern is evident on the plate resulting in a peak negative pressure with a value of C ^ p = −3.9 in the middle part of the plate away from the leading edge. Even on the last fourth quarter of the plate, the negative peak pressure coefficient is −2.5. These results confirm the major hypotheses of the current study, which assumed that the separated horizontal flow from the main bluff body has a direct implication on the distribution of the critical pressures on the vertically attached thin plate.

This section summarizes the findings from model 2 and 3 testing. Although each model refers to a different building structure application, because of the same dimensions for the bigger bluff body and the same cross-sectional area for the smaller bluff body, the pressure coefficient results had similarities. It was expected that the enclosed space under the plate in model 3, which practically turns its geometry into a bluff body, will drastically affect the flow in comparison to the flat plate in model 2. In terms of the central research hypothesis, model 3 was anticipated to result in a stronger separated flow on the top of the plate, therefore interacting in a different manner with the separated flow from the main bluff body.

Similar to model 1 in the 0° wind direction, both the horizontal plate and the roof of bluff bodies experience predominantly positive pressure. Mean pressure coefficient contour plots for the 0° wind in models 2 and 3 (Figures 6A, 7A) show strong positive mean C ¯ p values on the wall surface of the main bluff body. Backward rotating flow vortices cause positive pressures on the top surface of the plate and the smaller bluff body in both models due to reattachment. The mean pressure coefficients in both models had similar variation patterns at the same locations; however, C ¯ p values in model 3 were found to be 5%–10% higher than those in model 2. The maximum pressure coefficient contour plots for models 2 and 3 are shown in Figures 6B, 7B, respectively. In both cases, the distribution is very similar, but the C ^ p values were higher in model 3 (+2.6 vs +2.2 on the walls and +3.4 vs +2.8 on the plate).

In the 90° wind, mean pressure coefficients shown in Figures 8A, 9A indicate that both models are experiencing suction at the windward zones where flow separates. Clearly, the C ¯ p values are becoming positive at the leeward zones, which is an indication of flow reattachment at the end of models for this wind direction. The diagonal gradient distortion on the top plate surface is clear in both models, similar to what was captured and discussed in model 1. The enclosed space under the plate in model 3 appears not to have a significant influence on the mean C_p values or their distribution. Finally, the 90° wind peak negative pressure coefficient contour plots are shown in Figures 8B, 9B. In both cases, the gradient patterns are very similar with significant high-suction zones to be formed farther from the leading edge and away from the wall corners.

Model 4, which is a building with a podium extension, was built based on model 3 in an effort to resemble a lower building surrounding a taller structure. In this case, both mean and peak pressure coefficient contour plots showed different flow–structure interaction patterns and local peak pressure zones when compared to model 3. In the 0° wind, mean pressure coefficient contour plots (Figure 10A) point to a large high-pressure zone at around the middle of the main building wall surface. The peak pressure zone dominates rows 2 and 3 of pressure taps from the top of the main building where the positive peaks C p stay almost consistent at around a value of +2.4 in Figure 10B. Similar to the previous models, another high-positive-pressure zone was formed at the wall–roof interaction zone where the wall of the bluff body has a perpendicular angle relative to the podium roof surface. The C p values at the wall–roof interaction zone were even higher than those on the wall surface. FromFigure 10B, two distinct high-pressure zones are observable on the podium roof top. The roof surface opposite to the wall has experienced positive pressures in the 0° wind, and the pressure gradually was increasing from the roof leading edge toward the wall–roof interaction zone. After the wind separates from the podium roof leading edge, the separated bubble will interact with the higher building wall face, and backward flowing vortices will be generated. These flow vortices move in the opposite direction of the oncoming flow. These high- and low-pressure zones are clearly visible in the roof mean pressure coefficient contour plot in Figure 10A. In this figure, C ¯ p values have positive signs varying from +0.2 to +0.9. Meanwhile, the two left and right zones of the podium roof had negative C ¯ p values, which mean that these two parts mostly experience an uplift force. Flow interaction from the roof with the wall had few effects on these two regions, and therefore, these two parts of the roof will experience wind loads similar to a simple flat roof for the specific orientation.

In the 90° wind direction, mean pressure coefficients were negative at the leading edges of both surfaces (Figure 11A), but the locations of the peak negatives were varying depending on how far the region is from the wall–roof interaction zone. A localized negative pressure zone was formed on the left corner of the wall compatible with the wind loading zones in chapter 30 of [26](Figure 11B). However, the suction zone on the wall surface has extended toward the middle and top of the wall to the extent that some parts of the wall close to the top edge, where the last pressure tap row extends, had very high C ^ p values. The podium surface, on the other hand, has experienced different wind loads than the roof of the small bluff body in model 3 in the 90° wind direction. On the podium roof surface, the extended suction zone in a diagonal direction was not as pronounced, and the separation bubble was smaller and pushed toward the wall–roof interface. When comparing Figures 9B, 11B, the locations of high-suction zones are different on the surface of the two lower buildings roofs. In the 90° wind direction, several localized suction zones were formed on the podium roof based on the peak negative pressure coefficient contour plots. These high C ^ p values were formed at the roof leading edge and at the end of zone 1 ( C ^ p = −2.9) and at the wall–roof interaction (top zone 2) with ( C ^ p = −4.4). A more detailed experimental parametric study is recommended for the particular podium-like structure.

The TPU aerodynamic database includes wind pressure coefficients that were experimentally derived for high-rise and low-rise buildings with and without eaves, which could be an isolated building or a non-isolated building [30]. The selected cases had similar dimensions to models 3 and 4 in this research study and were selected from the database of isolated low-rise buildings without eaves. The wind tunnel and TPU models have evenly distributed pressure taps at 20 mm. The TPU database procedure to calculate the C _p coefficients is described in detail in [31]. The current study’s and TPU’s reference wind directions differ 90°; therefore, the 0° wind direction cases in the current study correspond to the 90° wind direction in the TPU experiments, and the 90° wind direction in the current study should be compared to 0° in the TPU database results.

Chapter 30 of [26] provides pressure coefficient zones and their values applicable to the design of components and cladding based on the envelope and directional procedures. For pressure coefficients on the roof and wall of buildings with mean roof height ≥18.3 m (Figure 15A), the envelope procedure has been based on the [35] method of not enveloping the influence of exposure, so exposure categories B, C, or D may be used with the values of (GCp) in Figure 30.4-1 of ASCE7-22. For buildings with a mean roof height of h ≤ 18.3 m, a number of figures are introduced, among which Figures 30.3-2A introduce GCp coefficients for pitched roofs with θ ≤ 7°. For peak pressure coefficients on the roof of these types of buildings, Figure 15B shall apply.

The main bluff body in models 1–4 of this research study could be compared to a full-scale building with a mean roof height of 24 m, and therefore, Figure 30.4-1 of ASCE 7-22 (Figure 15A) could be used to determine wind loads on the wall surface of the full-scale building. In this figure, the wall elevation has been divided into three zones at both edges and at the center of the wall. The full-scale effective area of the higher buildings in models 1–4 will be 12× α , which is the vertical dimension multiplied by ( α ) the 10% of the horizontal dimension ( α = 10% × 24 m = 2.4 m), and therefore, the effective area would become 28.8 m². For this effective area, a peak negative coefficient value of G C ^ p ≈ −1.1 for zone 5 and G C ^ p ≈ −0.7 for zone 4 and a peak positive pressure coefficient value of G C p = +0.65 for zones 4 and 5 could be extracted from Figure 30.4-1 of ASCE 7-22. The wall surfaces of models 2, 3, and 4 have dissimilar peak negative pressure coefficient zones in comparison to the ASCE 7-22 wind loading zones in Figure 30.4-1. In all three models, there is a localized peak negative zone at the wall–roof interaction zones in Figures 7B, 9B, 11B, which was formed due to the flow separation at two perpendicular surfaces and could be compared to zone 5 in Figure 15A. However, the suction zone does not stop at the edge of the wall, and an upward dispersion of negative pressure toward the central parts of the wall was observed in models 2, 3, and 4. The peak negative zones did not occur at the leading edge as per the ASCE 7-22 wind loading zone in Figure 30.4-1 zone 5 and has shifted away from the edge. In each of the models examined, the manifestation of high suction zones was observed within a designated region referred to as “zone 5” according to ASCE 7-22 (Figures 15A as depicted in this scholarly article). Notably, however, a distinction arises when comparing these models to the provisions outlined in ASCE 7-22. Specifically, the high suction zones in these models exhibit an upward diagonal extension towards the central part of the wall, identified as “zone 4” within the ASCE 7-22 guidelines. This notable extension of the high suction zone is particularly evident in model 1 (Figures 5B). The same condition was observed for the peak positives in Figures 6B, 7B, 10B with peaks happening at the center and decreasing as getting away from the center, whereas in ASCE 7, the two zones (4 and 5) will have similar positive peaks (Figure 15A).

ASCE 7-2022 provides a figure for the peak pressure coefficient of the roof of stepped-roof buildings (Figures 30.3-3); however, the mean roof height of the top roof is limited to 18.3 m. Because, in this research, the mean roof height of top roofs of all models exceeds the ASCE 7 defined height limitation, for the peak coefficients on the surface of the lower roof in models 3 and 4 with a mean roof height of 12 m, Figures 30.3-2A of ASCE7-22 were selected, and the peak zones are shown in Figure 15B. The highest localized peak negative zones on the roof based on this figure will be formed at the four corners of the roof (zone 3) followed by zone 2, a narrow area extended along the edges of the roof. In Figures 8B, 9B, the separation bubble has shifted away from the leading edge of the plate and the lower roof, causing peak negative pressure coefficient zones to happen on an extended diagonal form at the center of the roof. The highest peak negative pressure coefficients, unlike the ASCE 7-22 defined zones, were not at the corners but away from the leading edge toward the center of the roof. In model 4, the peak negative pressure coefficients similarly were not limited to the leading edge as it is in ASCE7-22 (Figure 15B). Both the peak negative and positive zones on the roof of the podium building were formed at the roof–wall interaction zone where the main shear stress will be resulted from vortex interactions. In ASCE 7-22, for a building of roof height less than 18.3 m (Figure 15B), all four zones on a roof surface will receive the same peak positive pressure coefficient which did not happen in this research study on the roof of all four models. The contour plots of positive pressure coefficients show a sudden spike for the positive pressures at the location of two perpendicular surfaces.

The results of experiments on combined bluff bodies in this research show that wind loading on buildings will not always comply with the provisions defined by ASCE 7 which are generally for isolated buildings with simpler geometries. The envelope procedure in ASCE 7-2022 that have been used to determine wind loads on the main wind force resisting systems and, on the components, and cladding is by involving an effective area of a particular surface without considering the pressure fluctuations resulted from more complex geometries such as two perpendicular surfaces. Based on the present research study, the localized peak pressure coefficients in buildings with attached plates and buildings with variable roofs could have different zones and values than what has been defined in ASCE 7-2022. The implication of designing external elements such as roof tile connections and main force resisting systems such as roof beams and shear walls for wrong wind forces could be detrimental and costly, especially in extreme wind events.