# The Benefit of Horizontal Photovoltaic Panels in Reducing Wind Loads on a Membrane Roofing System on a Flat Roof

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## Abstract

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## 1. Introduction

## 2. Investigated Building and Roofing System

_{p}) and thickness (t

_{p}) of the parapets were both 0.15 m (see Figure 5). The waterproofing membrane was a polyvinyl chloride (PVC) resin sheet of approximately 1.5 mm in thickness, reinforced by glass fibers of 560 dTex with a density of 3.6 fibers per 10 mm in both the longitudinal and transverse directions. The mass per unit area was 2.044 kg/m

^{2}. Figure 6 shows the stress (σ)–strain (ε) relationship for the longitudinal, lateral, and diagonal directions obtained from a tensile test with No. 2 dumbbell-type specimens 10 mm wide. Note that we also tested with No. 3 dumbbell-type specimens 5 mm wide to obtain the material properties of the membrane. Regarding the specimens for the longitudinal and lateral directions, the tensile strength rapidly changed at ε $\approx $ 15%. This phenomenon was due to the fracture of glass fibers. After the glass fibers broke, the σ–ε curves were almost the same as that for the diagonal (45°) direction, which was further found to be almost the same as that for the unreinforced membrane. The membrane was anchored to the structural substrate using PVC-coated circular steel disks 65 mm in diameter and 1.2 mm in thickness and fasteners (i.e., screws). The disks were arranged in a square lattice-like form with a spacing of 0.6 m, to which the membrane was attached with a solvent.

## 3. Wind Tunnel Experiment of Wind Pressure Distributions

#### 3.1. Experimental Method

_{L}= 1/100. The PV system was not modeled. Figure 7 shows the arrangement of pressure taps. The diameter of the pressure taps was 0.5 mm. It is well-known that very large suction pressures are generated near the windward corner in oblique winds [23,24,25,26]. Therefore, the pressure taps were densely arranged in the corner and edge zones. The wind direction (θ), defined as shown in Figure 7, was changed from 0 to 45° at an increment of 5°.

_{Z}), normalized by a value at a reference height of Z = 600 mm, and the turbulence intensity, I

_{Z}. The power-law exponent α of the mean wind speed profile was approximately 0.27. The turbulence intensity, I

_{Z}, at Z = 100 mm was approximately 0.16. Figure 8b shows the normalized spectral energy density distribution at Z = 100 mm, which corresponded well to the Karman-type spectrum with an integral length scale, L

_{x}, of approximately 0.2 m. The present study did not focus on a specific building in a specific area. However, these values were compared to the specified values in the AIJ Recommendations for Loads on Buildings [27] for Terrain Category III (suburban exposure). According to the Recommendations, these values are specified as α = 0.20, I

_{Z}= 0.24, and L

_{x}= 57.7 m (at full scale). The value of α of the wind tunnel flow was larger than the specified value, while the values of I

_{Z}and L

_{x}of the wind tunnel flow were smaller than the specified values. Such discrepancies can be accepted, because the main purpose of this study was to discuss the application of PV panels for the improvement of the wind resistance of mechanically attached single-ply membrane roofing systems and not to evaluate wind loads for designing a PV system and a roofing system.

_{H}at Z = H, was determined based on the AIJ Recommendations for Loads on Buildings [27], assuming that the “Basic wind speed” U

_{0}was 35 m/s and the terrain category was III. Indeed, U

_{H}was calculated as 27.8 m/s. The value of U

_{H}was set to 8 m/s in the wind tunnel experiment. The Reynolds number defined by $\mathrm{Re}={U}_{H}\xb7H/\nu $ was approximately 5.3 × 10

^{4}, where $\nu $ represents the coefficient of the kinematic viscosity of air. The blockage ratio (Br) of the model, with respect to the wind tunnel working section area, was approximately 0.8%. The Reynolds number and the blockage ratio satisfied the experimental criteria recommended in Wind Tunnel Testing for Buildings and Other Structures [28]; that is, Re was larger than 1.1 × 10

^{4}, and Br was smaller than 5%. The velocity and time scales, λ

_{V}and λ

_{T}, of the wind tunnel experiment were 1/3.48 and 1/28.8, respectively. Wind pressures at all pressure taps were sampled simultaneously at a rate of 800 Hz for a time duration of 10 min at full scale (approximately 20.8 s at model scale) using a multi-channel pressure measuring system (Wind Engineering Institute, MAPS-02). The internal diameter and length of the tubes connecting the pressure taps and the pressure transducers were 1 mm and 1 m, respectively. A low-pass filter with a cut-off frequency of 300 Hz was used to remove high-frequency noise from the signals. The measurements were repeated 10 times. The measured wind pressure was converted to a pressure coefficient (C

_{pe}) defined in terms of the velocity pressure (q

_{H}) of the approach flow at Z = H. Ensemble averaging was applied to the results of the 10 consecutive measurements in order to obtain the statistical values of C

_{pe}and others. The distortion of the measured wind pressures due to the tubing was compensated in the frequency domain by using the frequency response function of the measuring system.

#### 3.2. Experimental Results

_{pe}

_{,cr}, irrespective of wind direction and tap location. We found that the value of C

_{pe}

_{,cr}was −4.8 at a pressure tap near the windward roof corner when θ = 35°. Figure 9 shows the distribution of the minimum peak pressure coefficients in this wind direction, together with the pressure tap location represented by “+”. Note that the value at each pressure tap was the ensemble average applied to the ten results of the minimum peak pressure coefficients for a period of 10 min at full scale. It was clear that conical vortices generated large suction pressures near the windward corner as previous studies indicated [23,24,25,26]. However, the value of C

_{pe}

_{,cr}was somewhat smaller in magnitude than those obtained in the previous studies. This may be due to the effect of the parapets [29,30,31]. Ten sets of the time history of wind pressure coefficients at θ = 35° were used for evaluating the layer pressures in Section 4 and the wind-induced responses of the roofing system in Section 5.

## 4. Simulation of Wind Pressures on PV Panels and Waterproofing Membrane

#### 4.1. Method of Simulation

_{e}= effective depth (slug length) of the gap; d

_{e}= gap width;

_{e}U

_{i,j}= flow speed in the gap; t = time;

_{e}P

_{i,j}and P

_{i,j}, respectively, represent the external pressure at the gap and the layer pressure of Room (i, j); C

_{Le}= pressure loss coefficient of the gap (shape resistance coefficient), depending on the gap shape; λ represents a friction coefficient, which is approximately given by the following equation assuming that the gap flow is a Hagen–Poiseuille flow [32]:

_{e}may be given by the following equation [33]:

_{0}and A

_{e}represent the actual depth and area of the gap, respectively.

_{i,j}= distance from the center of a Room to that of the next Room; d = distance between the bottom surface of the PV panel and the roof;

_{i}

_{,j}U

_{i+}

_{1,j}= wind speed in the x direction from Room (i, j) to Room (i+1, j); P

_{i,j}and P

_{i+}

_{1,j}represent the layer pressures of Rooms (i, j) and (i+1, j), respectively; C

_{L}= shape resistance coefficient in the horizontal direction. When the boundary of a Room corresponds to the periphery of the array of PV panels, the subscript should be replaced by “e” in Equations (6) and (7). Similar equations can be obtained for the cavity flow in the y direction, not shown here to save space.

_{e}C = external pressure coefficient at the gap location; C = layer pressure coefficient; the subscript of C represents the Room location. The pressure loss coefficient C

_{Le}for the 3 mm gap between the PV panels was determined based on an experiment using a pressure loading actuator (PLA) [34] and a full-scale model of the gap. In the experiment, a full-scale model of a 3 mm gap (the length was 1000 mm) was attached to the testing wall of a chamber (the size was 900 × 830 × 200 mm), a PLA generated fluctuating pressure in the chamber using the time history of the wind pressure coefficient obtained from the wind tunnel experiment, and the pressures on both sides of the gap were measured. Then, the fluctuating pressure on the opposite side of the chamber was simulated based on the above-mentioned equation, changing the values of C

_{Le}incrementally. Comparing the simulated results with the experimental ones, we found that C

_{Le}= 1.42 provided results similar to the experimental ones. Regarding the details of this experiment, see Yambe et al. [21]. For wider gaps, we assumed that C

_{Le}= 1.0. Because the building had parapets and the installation area of the PV panels was immersed in a separated flow, it was thought that the speeds of the gap and cavity flows were relatively low. Thus, the gap and cavity flows were assumed to be laminar [17,35]. The external pressure coefficients at the gap location in Equations (9)–(11) were obtained from the above-mentioned wind tunnel experiment. Because the location of the gaps did not coincide with that of pressure taps installed on the wind tunnel model, the cubic spline function was applied to the experimental data of the wind pressure coefficients for interpolation; the value at the center of each gap was used as a representative value for the gap.

_{0}is the atmospheric pressure; V

_{0}is the volume of the Room; Q

_{m}and U

_{m}are the flow rate and flow speed at gap m, respectively; k

_{m}and A

_{m}represent the discharge coefficient and area of gap m, respectively; and M is the total number of gaps. Note that the sign of Q

_{m}is positive for inflow and negative for outflow. The discharge coefficient k

_{m}was determined from an experiment using a full-scale gap model and the PLA in which the flow rate and speed were measured. We found from the experiment using a full-scale model with a 3 mm gap that k

_{m}= 0.55 simulated the experimental results relatively well. Regarding the details of the experiment, see Yambe et al. [21]. For wider gaps, we assumed that k

_{m}= 1.0. From Equation (12), we can obtain the following equation for the layer pressure coefficient C

_{i,j}of Room (i, j) which has a vertical gap and four adjacent Rooms:

_{pi}, defined in terms of q

_{H}, in the same manner as C

_{pe}. The wind force coefficient, C

_{f}, of the PV panel may be given by:

_{pe}was obtained from the wind tunnel experiment, while C

_{pi}was obtained from the above-mentioned numerical simulation. Similarly, the net wind pressure on the waterproofing membrane was given by the difference between pressures acting on the top and bottom surfaces of the membrane. The pressure on the top surface corresponded to the external pressure when no PV panels were placed, while it corresponded to the layer pressure when PV panels were placed. Because the pressure on the bottom surface of the membrane depended on the structural system and air tightness of the roof structure significantly, it was difficult to estimate the value generally, which may be positive or negative. Therefore, the value was assumed to be zero for simplicity. In this case, the wind force coefficient, C

_{f}, of the membrane corresponded to the layer pressure coefficient, C

_{pi}, or the external pressure coefficient, C

_{pe}, whether the PV panels were installed or not.

_{pi}and C

_{f}for a period of 600 s at full scale. The results were used for analyzing the statistics of wind forces on the PV panels and the wind pressures on the waterproofing membrane as well as for the dynamic response analysis of the roofing system.

#### 4.2. Results

_{f}

_{,panel}, for each panel at θ = 35° was first computed. For computing the area-averaged wind pressure coefficient, C

_{pt}

_{,panel}, on the top surface of a PV panel, we used the distribution of the external wind pressure coefficients obtained by applying the cubic spline function to the experimental data for interpolation. Similarly, we computed the area-averaged wind pressure coefficient, C

_{pb,}

_{panel}, on the bottom surface of the PV panel using the layer pressure coefficients for the Rooms existing under the PV panel. The area-averaged wind force coefficient, C

_{f}

_{,panel}, was provided by the difference between C

_{pt}

_{,panel}and C

_{pb}

_{,panel}. Note that the sign for C

_{f}

_{,panel}was the same as that for C

_{pt}

_{,panel}. We found from the results that the minimum peak value, ${\widehat{C}}_{f,\mathrm{panel}}$, of C

_{f}

_{,panel}was −1.2, which occurred on Panel 5 (regarding the panel location, see Figure 11b). This value was the ensemble average of ten results for ${\widehat{C}}_{f,\mathrm{panel}}$ obtained under the same condition. The positive (downward) and negative (upward) wind force coefficients of PV panels installed on flat roofs are specified in JIS C 8955 [38] as a function of the tilt angle β of PV panels. The negative value for panels with β = 0° installed near the roof corner was specified as −0.6. It should be noted that the wind force coefficient specified in the standard is defined by the minimum peak area-averaged wind force coefficient divided by a gust effect factor that depends on the terrain category and the mean roof height (H). Therefore, the present result corresponding to the minimum peak wind force coefficient should be compared with the product of the specified value and a gust effect factor. The gust effect factor for a building with H = 10 m located in an area of Terrain Category III is specified as 2.5. Therefore, the peak wind force coefficient was calculated as −0.6 × 2.5 = −1.5. This value was larger in magnitude than the minimum peak area-averaged wind force coefficient, ${\widehat{C}}_{f,\mathrm{panel}}$, obtained in this study, i.e., −1.2. This result implies that the gaps between the PV panels could reduce wind loads on the PV panels due to the effect of pressure equalization.

## 5. Finite Element Analysis of the Wind-Induced Behavior of the Roofing System

#### 5.1. Analytical Model and Procedure

#### 5.2. Results and Discussion

_{H}) acting on the fastener was provided by the following equation:

_{x}and F

_{y}, respectively, represent the forces acting on the fastener in the x and y directions, which are provided by the sum of the x and y components of the forces at the nodes along the disk’s circumference. The vertical force (F

_{V}) acting on the fastener was provided by the sum of the z components of the forces at the nodes along the disk’s circumference and the force acting on the disk itself. Figure 19 shows the trajectory of the F

_{V}–F

_{H}relationship at each fixing point (see Figure 15). It was found that horizontal forces nearly equal to or larger than the vertical ones were generated on the fasteners when the PV panels were not installed. This feature corresponds well to the findings of Miyauchi et al. [9,10] and Sugiyama et al. [11]. When the PV panels were installed, the values of F

_{V}and F

_{H}were reduced significantly, except for F

_{H}at A-1.

## 6. Conclusions

_{Le}), the shape resistance coefficient (C

_{L}), and the discharge coefficient (k

_{m}). At present, these assumptions have not been verified yet sufficiently. Furthermore, the size of the gaps between the PV panels in the longitudinal direction was fixed to 26 mm in the present paper. This is a tentative value. Because the gap size affects the layer pressures significantly, it is necessary to investigate the effect of gap size on the layer pressures and to obtain the optimum gap size for reducing the wind loads on PV panels and the roofing system. It is also necessary to discuss the most effective arrangement of PV panels with respect to the wind-load reduction effects and the power generation efficiency.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Schematic illustration of a mechanically attached single-ply membrane roofing system generally used for roofs of reinforced concrete buildings in Japan.

**Figure 4.**Schematic illustration of the wind loads on a waterproofing system and PV panels: (

**a**) without PV panels; (

**b**) with PV panels.

**Figure 8.**Characteristics of wind tunnel flow: (

**a**) profiles of mean wind speed and turbulence intensity in the longitudinal direction; (

**b**) normalized spectral energy density distribution of wind speed fluctuation at Z = 100 mm.

**Figure 11.**Installation of PV panels: (

**a**) installation position of the PV panels; (

**b**) panel numbers.

**Figure 14.**Minimum peak values of the external pressure coefficient, ${\widehat{C}}_{pe}$, (without PV panels) and the layer pressure coefficient, ${\widehat{C}}_{pi}$, (with PV panels) at θ = 35°.

**Figure 18.**Deflections of the membrane: (

**a**) measuring points; (

**b**) general view of the mean deformation; (

**c**) maximum peak value (without parapets); (

**d**) maximum peak value (with parapets); (

**e**) standard deviation (without parapets); (

**f**) standard deviation (with parapets).

Layer | t (mm) | E (N/mm^{2}) | ν | G_{12}(N/mm ^{2}) | G_{23}(N/mm ^{2}) | G_{31}(N/mm ^{2}) | |
---|---|---|---|---|---|---|---|

Longitudinal | Lateral | ||||||

PVC | 0.8 + 0.7 | 25.0 | 25.0 | 0.50 | 8.30 | 8.30 | 8.30 |

Fiberglass | 0.01 | 65.0 | 70.3 | 0.24 | 0.001 | 28,000 | 28,000 |

_{12}, G

_{23}, and G

_{31}: shear modulus.

Fastener | Without PV Panels | With PV Panels | Reduction Rate (%) |
---|---|---|---|

A-1 | 770.2 | 599.9 | 22.1 |

A-2 | 563.5 | 464.1 | 17.6 |

A-3 | 576.9 | 478.5 | 17.1 |

A-4 | 565.6 | 359.4 | 36.5 |

B-1 | 618.5 | 385.2 | 37.7 |

B-2 | 635.0 | 388.5 | 38.8 |

B-3 | 605.1 | 450.8 | 25.5 |

B-4 | 511.9 | 397.8 | 22.3 |

C-1 | 726.5 | 509.0 | 29.9 |

C-2 | 610.8 | 507.6 | 16.9 |

C-3 | 399.4 | 287.4 | 28.0 |

C-4 | 483.3 | 332.2 | 31.3 |

D-1 | 599.7 | 419.2 | 30.1 |

D-2 | 500.5 | 376.9 | 24.7 |

D-3 | 386.1 | 270.9 | 29.8 |

D-4 | 308.0 | 272.5 | 11.5 |

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**MDPI and ACS Style**

Uematsu, Y.; Yambe, T.; Watanabe, T.; Ikeda, H.
The Benefit of Horizontal Photovoltaic Panels in Reducing Wind Loads on a Membrane Roofing System on a Flat Roof. *Wind* **2021**, *1*, 44-62.
https://doi.org/10.3390/wind1010003

**AMA Style**

Uematsu Y, Yambe T, Watanabe T, Ikeda H.
The Benefit of Horizontal Photovoltaic Panels in Reducing Wind Loads on a Membrane Roofing System on a Flat Roof. *Wind*. 2021; 1(1):44-62.
https://doi.org/10.3390/wind1010003

**Chicago/Turabian Style**

Uematsu, Yasushi, Tetsuo Yambe, Tomoyuki Watanabe, and Hirokazu Ikeda.
2021. "The Benefit of Horizontal Photovoltaic Panels in Reducing Wind Loads on a Membrane Roofing System on a Flat Roof" *Wind* 1, no. 1: 44-62.
https://doi.org/10.3390/wind1010003