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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA

WIND DESIGN FOR SOLAR ARRAYS

by SEAOC Solar Photovoltaic Systems Committee Report SEAOC PV2-2017 July 2017

STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA Board of Directors, 2016-2017 Officers Chris Kamp, President Janah Risha, President Elect Michael Braund, Secretary Directors Dick Dreyer Jeff Ellis Darron Huntingdale Michelle Kam-Biron Krista Looza

Bradley Lowe, Treasurer Kelly Cobeen, Past President Don Schinske, Executive Director Robert Lyons Kate Stillwell Ryan Turner Taryn Williams

Disclaimer Documents produced by the Structural Engineers Association of California (SEAOC) are published as part of our association’s educational program. While the information presented in the document is believed to be correct, neither SEAOC nor its Board, committees, writers, editors, or individuals who have contributed to this document make any warranty, expressed or implied, or assume any legal liability or responsibility for the use, application of, and/or reference to opinions, findings, conclusions, or recommendations expressed herein. The material presented in this document should not be used or relied upon for any specific application without competent examination and verification of its accuracy, suitability, and applicability by qualified professionals. Users of information from this document assume all liability arising from such use.

Structural Engineers Association of California © 2017 SEAOC All rights reserved. This document or any part thereof may not be reproduced in any form without the written permission of the Structural Engineers Association of California.

STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA 921 11th Street, Suite 1100 Sacramento, CA 95814 Phone: (916) 447-1198 Fax: (916) 444-1501 Email: [email protected] http://www.seaoc.org

Wind Design for Solar Arrays Report SEAOC PV2-2017

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Wind Design for Solar Arrays This report was written by the SEAOC Solar Photovoltaic Systems Committee, a subcommittee of the SEAOC Wind Committee. SEAOC Solar Photovoltaic Systems Committee Voting Members Andreas Karlsson, SunPower Gwenyth Searer, Wiss, Janney, Elstner Associates, Inc. James Adams, Solar-Roof-Check.com James S. Lai, Retired structural engineer Joe Cain, Solar Energy Industries Association Joe Maffei (Chair), Maffei Structural Engineering Karl Telleen (Vice Chair), Maffei Structural Engineering Associate Members Adam Saidel, DPW Solar Ajay Friesen, SunPower Amir Massoumi, Tesla Annika Chase, QuickMount PV Anurang Jain, Thornton Tomasetti Bryan Cusick, SunPower Colin Blaney, Buehler & Buehler David Banks, CPP Wind Engineering Consultants Dick Davis, FM Global Don Scott, PCS Structural Solutions Emily Guglielmo, Martin/Martin Consulting Engineers Eric Thomas, City of Portland Gregory Kopp, University of Western Ontario Hernando Montoya, TJC and Associates, Inc. Hossein Mostafaei, FM Global Jeni Hall, Energy Trust of Oregon Jennifer Carey, Unirac Jeremy Rogelstad, Tesla Joel Schafer, Blue Oak Energy, LLC John Wolfe, Mar Structural Design Jonathan Lam, LA County Building and Safety Division Justin Rupley, ZFA Structural Engineers Karen Roberts, Division of the State Architect Kristin Norman, LA County Building and Safety Div.

Ken Luttrell, CYS Structural Engineering Mason Walters, Forell/Elsesser Engineers Nader Namdar, Namdar Structural, Earthquake Eng. Norm Scheel, Norman Scheel Structural Engineer Rob Ward, SunLink Ron LaPlante, Division of the State Architect

Lakshmana Doddipatla, FM Global Logan Boutilier, DNV GL Mark Gies, Centroplan Matt Danning, Everest Solar Systems Matt Gilliss, Engineered Power Solutions Mika Jovanovic, PanelClaw Murray Morrison, Institute for Business & Home Safety Osama Younan, City of Los Angeles Paul Zacher, PZSE Structural Engineers Pete Fischer, Division of the State Architect Philip Patnude, Tesla Philip Yin, City of Long Beach Rick Hanson, RHCE Rob D'Anastasio, Ecolibrium Solar Sage Lopez, Sunrun Inc. Samuel Truthseeker, Truthseeker Consulting Scott Mulligan, Buehler & Buehler Stephen Kerr, Josephson-Werdowatz & Associates Steve Bauer, Unirac Thomas Lundin, Structural Systems Solutions Thorsten Kray, I.F.I. Institut für Industrieaerodynamik GmbH Veronica Crothers, Maffei Structural Engineering Wolfgang Fritz, Schletter Yarrow Fewless, CPP Wind Engineering Consultants

SEAOC Wind Committee Anurag Jain, Thornton Tomasetti Gwenyth Searer, Wiss Janney Elstner Associates, Inc. James Adams, Solar-roof-check.com James S. Lai (Chair), Retired structural engineer Joe Maffei, Maffei Structural Engineering Alternates Emily Guglielmo, Martin/Martin Consulting Engineers Nader Namdar, Namdar Structural, Earthquake Eng.

Wind Design for Solar Arrays Report SEAOC PV2-2017

Ken Luttrell (Co-Chair), CYS Structural Engineering Norm Scheel, Norman Scheel Structural Engineer Ron LaPlante, Division of the State Architect Stephen Kerr, Josephson-Werdowatz & Associates, Inc.

Karl Telleen, Maffei Structural Engineering Manny Sinha, Parsons

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Preface and Acknowledgements This report was developed by the Structural Engineers Association of California’s (SEAOC) Solar Photovoltaic Systems Committee (PV committee), a subcommittee of the SEAOC Wind Committee. The PV committee was formed in September 2011 with the principal goal of addressing the lack of specific requirements in applying structural building code provisions to solar photovoltaic systems. The committee directed its initial efforts on low-profile photovoltaic installations on low-slope roofs and produced Report PV1-2012 on seismic-structural design, and Report PV2-2012 on wind design. Joe Maffei directed the development of the PV1 report, and Ron LaPlante directed the development of the PV2 report. One objective of the 2012 reports was to develop provisions for the next ASCE 7 standard, and this was achieved in ASCE 7-16. As part of the ASCE 7 development and adoption process, the provisions proposed in SEAOC PV2-2012 were in some cases refined and/or simplified. This report, PV2-2017, supersedes PV2-2012 by referencing the provisions in ASCE 7-16, including knowledge from research since 2012, and making recommendations beyond those in ASCE 7-16. As an aid to the user, some of the relevant ASCE 7-16 wind-load provisions for solar are excerpted in this report. Engineers should use ASCE 7 itself for the definitive requirements and for the many related requirements that are not included here (such as risk categories or load combinations). This report should not be considered a substitute for directly using the ASCE 7 standard. Substantial new information is included in this report that is not in PV2-2012 or ASCE 7-16, such as updated terminology, a general requirement for effective wind area determination, and a number of additional requirements for wind load determination and for wind-tunnel studies. We have added provisions to clarify or provide extensions to the ASCE 7-16 requirements. In most cases, the added provisions are “optional refinements” that typically result in smaller wind loads compared to ASCE 7-16 and can potentially be used as part of an approved alternate method of design via Section 104.11 of the International Building Code. In a few cases, added provisions are “recommended additional requirements”

Wind Design for Solar Arrays Report SEAOC PV2-2017

where the ASCE 7-16 requirements may be incomplete or unconservative. For brevity, much of the background discussion in PV2-2012 on the nature of wind loads on low-profile roof-mounted systems was not included in the ASCE 7 commentary. We have kept and refined that discussion here. The example problems on designing solar arrays for wind loads have been significantly revised from PV2-2012, with sections designed to illustrate specific aspects of the methods. David Banks of CPP Wind Engineering Consultants is the principal author of this update, with substantial assistance from Karl Telleen of Maffei Structural Engineering. These two authors did a fabulous job, both in technical quality and in keeping the project moving forward. I am deeply grateful to them both, and equally grateful to the broad participation in our efforts from numerous engineers in consulting and in the solar industry. The long list of committee members at the beginning of this document is a testament to the active involvement and wide-ranging support that have made this effort possible and worthwhile. While numerous committee members have contributed to this report, I would also like to express special thanks to Jennifer Carey of Unirac for her efforts in coordinating and developing the example problems, to Gwenyth Searer of WJE for her careful review, and to David’s fellow wind gurus, Greg Kopp of University of Western Ontario, Thorsten Kray of I.F.I. Institut für Industrieaerodynamik GmbH, and Yarrow Fewless of CPP for their help in understanding the physics and improving the methods. We would like to express our appreciation to the SEAOC Wind Committee, chaired by James Lai, and to the SEAOC Board of Directors who oversee and support the work of the PV Committee. Sincerely, Joe Maffei Chair of SEAOC Photovoltaic Systems Committee July 2017

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Contents Requirements and Commentary 1. Scope...................................................................................................................................................................................................... 1 1.1. Thickness of solar panels ............................................................................................................................................................... 1 2. Terminology........................................................................................................................................................................................... 1 3. Effective wind area ................................................................................................................................................................................ 2 4. Tilted panels on flat or low-slope roofs ................................................................................................................................................. 2 4.1. ASCE 7-16 procedures ................................................................................................................................................................... 2 4.2. Recommended additional requirements (not included in ASCE 7-16) .......................................................................................... 5 4.3. Optional refinements (not included in ASCE 7-16) ....................................................................................................................... 5 5. Flush-mounted arrays on flat or sloped roofs....................................................................................................................................... 13 5.1. ASCE 7-16 procedures ................................................................................................................................................................. 13 5.2. Recommended additional requirements (not included in ASCE 7-16) ........................................................................................ 13 5.3. Optional refinements (not included in ASCE 7-16) ..................................................................................................................... 14 6. Design of the roof ................................................................................................................................................................................ 15 7. Wind tunnel procedure ......................................................................................................................................................................... 15 7.1. ASCE 7-16 procedures ................................................................................................................................................................. 15 7.2. Recommended additional requirements (not included in ASCE 7-16) ........................................................................................ 17 8. Wind dynamic effects on ground-mounted solar arrays ...................................................................................................................... 19 8.1. ASCE 7-16 procedures ................................................................................................................................................................. 19 8.2. Recommended additional requirements (not included in ASCE 7-16) ........................................................................................ 19 9. References ............................................................................................................................................................................................ 21 Example Problems A. B. C. D. E. F. G. H. I. J.

Roof wind zones ............................................................................................................................................................................. 22 Normalized wind area (An) ............................................................................................................................................................. 23 Nominal net pressure coefficient ((GCrn)nom) ................................................................................................................................. 23 Parapet factor (γP) ........................................................................................................................................................................... 24 Chord factor (γC)............................................................................................................................................................................. 24 Edge factor (γE) .............................................................................................................................................................................. 25 Effective wind area (A) and design wind pressure (p) .................................................................................................................... 25 Design of an unattached (ballast-only) array to resist uplift ........................................................................................................... 27 Design of an unattached (ballast-only) array to resist sliding......................................................................................................... 29 Parallel-to-roof (flush-mounted) modules ...................................................................................................................................... 30

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Requirements and Commentary Legend ASCE 7-16 excerpts

designs under the ASCE 7-10 standard. The recommendations for flush-mounted solar installations, in Section 5, can only be used with ASCE 7-16 component and cladding wind pressures.

SEAOC recommendations

This document does not address tilted panels (including reverse-tilt panels) on roofs with slope greater than 7 degrees. See Section 5.2.1.

SEAOC commentary

1.1. Thickness of solar panels

1. Scope

Wind loads calculated in accordance with ASCE 7-16 Sections 29.4.3 and 29.4.4 are applicable to solar panels having thickness of 4 inches (101 mm) or less.

This report addresses wind loads for low-profile photovoltaic arrays with tilted panels on flat or low-slope roofs of buildings (Section 4). It also addresses parallel-to-roof (flush-mounted) arrays on roofs of any slope (Section 5). Roofs supporting solar arrays shall be designed according to Section 6. Wind tunnel procedures shall meet the requirements of Section 7. Ground-mounted solar arrays shall be designed according to Section 8. Commentary: Design wind loads for solar photovoltaic arrays on the roof types described above are covered by the 2016 version of ASCE 7 Minimum Design Loads and Associated Criteria for Buildings and Other Structures. The ASCE 7-16 provisions for wind loads on tilted panels on flat roofs, wind loads on the roof itself, and wind tunnel testing of rooftop solar arrays are based on the 2012 version of SEAOC PV2, with some modifications. This 2017 version of PV2 is intended to extend and clarify the ASCE 7-16 provisions. This PV2 report includes the relevant excerpts from ASCE 7-16 along with SEAOC’s recommended modifications or additions and commentary explaining the SEAOC recommendations. SEAOC PV2-2012 indicated that cladding loads for the roof itself could be used for flush-mounted solar panels. ASCE 7-16 introduces a new procedure for adapting roof-cladding loads to apply to flushmounted solar panels, which is an advancement of what was recommended in PV2-2012. In applying this new procedure, this current PV2 report provides guidance on how to distinguish a flushmounted system from a tilted low-profile system. This report includes SEAOC recommended additional steps, which are optional but provide more accurate wind loads. Some of these optional steps are aspects of PV2-2012 that were omitted from ASCE 7-16 for simplicity.

Commentary: While ASCE 7-16 does not specify a maximum thickness of panel for which these provisions are applicable, we recommend the limit stated above based dimensions of commonlyused modules and what has been tested in wind tunnel experiments upon which these provisions are based.

2. Terminology This report uses the following terms, symbols, and notation defined in ASCE 7-16: ASCE 7-16: 26.2 DEFINITIONS EFFECTIVE WIND AREA, A: The area used to determine the external pressure coefficient, (GCp), and (GCrn). For component and cladding elements, the effective wind area in Figs. 30.3-1 through 30.3-7, 30.4-1, 30.5-1, and 30.7-1 through 30.7-3 is the span length multiplied by an effective width that need not be less than one-third the span length. For rooftop solar arrays, the effective wind area in Figure 29.4-7 is equal to the tributary area for the structural element being considered, except that the width of the effective wind area need not be less than one-third its length. For cladding fasteners, the effective wind area shall not be greater than the area that is tributary to an individual fastener. 26.3 SYMBOLS A = effective wind area, in ft2 (m2) An = normalized wind area for rooftop solar panels in Figure 29.4-7. d1 = for rooftop solar arrays, horizontal distance orthogonal to the panel edge to an adjacent panel or the building edge, ignoring any rooftop equipment in Figure 29.4-7, in ft (m).

This report also includes a number of important requirements for wind tunnel testing of solar arrays, which are based on the committee’s experience conducting and peer-reviewing such testing, and which are additional to ASCE 7-16 requirements.

d2 = for rooftop solar arrays, horizontal distance from the edge of one panel to the nearest edge in the next row of panels in Fig. 29.4-7, in ft (m).

The report includes a recommendation for consideration of dynamic effects for wind design of ground-mounted solar arrays.

(GCrn) = net pressure coefficient for rooftop solar panels, in Eqs. (29.4-5) and (29.4-6).

This report refers to the ASCE 7-16 standard. Some of the recommendations in this report could be used, as applicable, with

(GCrn)nom = nominal net pressure coefficient for rooftop solar panels determined from Fig. 29.4-7.

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA h = mean roof height of a building or height of other structure, except that eave height shall be used for roof angle θ less than or equal to 10°, in ft (m) h1 = height of a solar panel above the roof at the lower edge of the panel, in ft (m). h2 = height of a solar panel above the roof at the upper edge of the panel, in ft (m). hpt = mean parapet height above the adjacent roof surface for use with Eq. (29.4-6), in ft (m). Lb = normalized building length, for use with Figure 29.4-7, in ft (m). Lp = panel chord length for use with rooftop solar panels in Fig. 29.47, in ft (m). WL = width of a building on its longest side in Fig. 29.4-7, in ft (m). WS = width of a building on its shortest side in Fig. 29.4-7, in ft (m).

γc = panel chord factor for use with rooftop solar panels in Eq. (29.4-6).

γE = array edge factor for use with rooftop solar panels in Fig. 29.4-7 and Eqs. (29.4-6) and (29.4-7).

γp = parapet height factor for use with rooftop solar panels in Eq.

Commentary: To use the design wind pressure recommendations in this report or in ASCE 7, the structural engineer must determine the appropriate effective wind area for relevant structural members, actions (uplift, sliding, etc.), and load cases. Due to the dynamic nature of wind, pressures generated by wind are dependent on the area over which they act, with larger pressures affecting smaller areas, and smaller pressures affecting larger areas. Thus each component or fastener has an effective wind area over which wind can act and which should be considered in the design of that component or fastener. In systems with nonlinear behavior, such as ballasted solar arrays subjected to uplift, effective wind area may depend on the vertical deflection that the array is allowed to undergo. Smaller deflection limits typically require consideration of smaller effective wind areas. The calculation examples at the end of this report demonstrate the correct application of effective wind area for the case of a ballasted solar array. The SEAOC PV Committee is planning to develop further guidance regarding determining effective wind area.

4. Tilted panels on flat or low-slope roofs 4.1. ASCE 7-16 procedures

(29.4-6)

θ = angle of plane of roof from horizontal, in degrees. ω = Angle that the solar panel makes with the roof surface in Fig. 29.4-7, in degrees.

For arrays of tilted panels on flat or low-slope roofs, design wind pressure shall be determined in accordance with ASCE 7-16 Section 29.4.3, which is referenced by the components and cladding Section 30.13:

This report uses the following additional terms:

ASCE 7-16:

Solar module, panel, array: In this report the term solar module refers to an individual solid unit of a solar panel. Solar panel refers to a single plane, typically consisting of several solar modules fastened together. The term solar array refers to a collection of solar panels. In some instances, ASCE 7-16 uses the term “solar collector,” which can be considered interchangeable with the term “solar panel.”

30.13 ROOFTOP SOLAR PANELS FOR BUILDINGS OF ALL HEIGHTS WITH FLAT ROOFS OR GABLE OR HIP ROOFS WITH SLOPES LESS THAN 7°

Commentary: The terms used in this report – module, panel, and array – are defined to be consistent with common industry terminology, and generally consistent with definitions in the National Electrical Code. This report applies to solar panels that are planar (flat) and modules that are non-porous. The modules can be photovoltaic or solar thermal modules as long as they meet the dimensional limitations herein.

3. Effective wind area The Effective wind area for all relevant structural members and actions shall be established by the Engineer of Record for the solar panel support system, based on principles of mechanics and, if appropriate, suitable testing.

Wind Design for Solar Arrays Report SEAOC PV2-2017

The design wind pressure for rooftop solar modules and panels shall be determined in accordance with Section 29.4.3 for rooftop solar arrays that conform to the geometric requirements specified in Section 29.4.3.

ASCE 7-16: 29.4.3 Rooftop Solar Panels for Buildings of All Heights With Flat Roofs or Gable or Hip Roofs with Slopes Less Than 7o. As illustrated in Fig. 29.4-7, the design wind pressure for rooftop solar panels apply to those located on enclosed or partially enclosed buildings of all heights with flat roofs, or with gable or hip roof slopes with θ ≤ 7o, with panels conforming to: Lp ≤ 6.7 ft (2.04 m), ω ≤ 35o h1 ≤ 2 ft (0.61 m), h2 ≤ 4 ft (1.22 m),

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA with a minimum gap of 0.25 inches (6.4 mm) provided between all panels, and the spacing of gaps between panels not exceeding 6.7 ft (2.04 m). In addition, the minimum horizontal clear distance between the panels and the edge of the roof shall be the larger of 2(h2 – hpt) and 4 ft (1.22 m) for the design pressures in this section to apply. The design wind pressure for rooftop solar panels shall be determined by Eq. (29.4-5) and (29.4-6):

where

p = qh (GCrn) (lb/ft2)

(29.4-5)

p = qh (GCrn) (N/m2)

(29.4-5.si)

(GCrn)nom = nominal net pressure coefficient for rooftop solar panels as determined from Fig. 29.4-7. When ω ≤ 2°, h2 ≤ 0.83 ft (0.25 m), and a minimum gap of 0.25 in. (6.4 mm) is provided between all panels, and the spacing of gaps between panels does not exceed 6.7 ft (2.04 m), the procedure of Section 29.4.4 shall be permitted.

ASCE 7-16: NOTES FOR FIGURE 29.4-7

(GCrn) = (γp) (γc) (γE) (GCrn)nom

(29.4-6)

γp = min (1.2, 0.9 + hpt / h);

1. (GCrn) acts towards (+) and away from (–) the top surface of the panels.

γc = max (0.6 + 0.06 Lp , 0.8); and

2. Linear interpolation is allowed for ω between 5° and 15°.

γE

3.

= 1.5 for uplift loads on panels that are exposed and within a distance 1.5Lp from the end of a row at an exposed edge of the array; γE = 1.0 elsewhere for uplift loads and for all downward loads, as illustrated in Fig. 29.4-7. A panel is defined as exposed if d1 to the roof edge > 0.5h and one of the following applies: 1. d1 to the adjacent array > max (4h2, 4 ft (1.2m) or 2. d2 to the next adjacent panel > max (4h2, 4 ft (1.2m).

Wind Design for Solar Arrays Report SEAOC PV2-2017

1000 � 𝐴𝐴. [𝑚𝑚𝑚𝑚𝑚𝑚(𝐿𝐿𝑏𝑏 ,15𝑓𝑓𝑓𝑓 [4.6𝑚𝑚])]2

𝐴𝐴𝑛𝑛 = �

where A is the effective wind area of the structural element of the solar panel being considered, and Lb is the minimum of 0.4 (h WL)0.5 or h or Ws in ft (m).

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29.4-7

Wind Design for Solar Arrays Report SEAOC PV2-2017

Panels

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Figure 1: Building roof plan demonstrating application of roof zones to non-rectangular roofs and Roof Wind Zone 1’. Commentary: The following are steps for using ASCE 7-16 Figure 29.4-7. Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: Step 7: Step 8: Step 9:

Confirm applicability of the figure to the building and the solar installation. Determine roof zones. Determine effective wind area and normalized wind area for each element being evaluated. Compute (GCrn)nom from applicable chart, using linear interpolation for values of ω between 5o and 15o. Apply chord length adjustment factor, γc. Apply the Edge Factor, γE, if necessary. Apply parapet height factor, γpE. Calculate GCrn. Calculate pressure, p, using Equation 29.4-5.

4.2. Recommended additional requirements (not included in ASCE 7-16) The following requirements are recommended in addition to the provisions of Section 4.1. 4.2.1. Minimum design wind pressure Design wind pressure in all roof zones calculated in accordance with ASCE 7-16 Section 29.4.3 shall not be taken less than the design wind pressure calculated using the pressure coefficients in Figure 2. Linear interpolation is permitted for panel tilts between 5° and 15°. Commentary: For some building dimensions, elements with large values of effective wind area, A, may have pressure coefficients from Figure 2 that are greater than those from ASCE 7-16 Figure 29.4-7. For example, for h = 15 feet and A > 62 sf (5.8 m²), Figure 2 results in greater pressure coefficients than the Zone 1 coefficients. In these cases, it would be unconservative to use the Zone 1 coefficients. Therefore, although ASCE 7-16 does not require use of Figure 2, use of the figure to determine a minimum design pressure is strongly recommended.

Wind Design for Solar Arrays Report SEAOC PV2-2017

4.3. Optional refinements (not included in ASCE 7-16) The following refinements (Items 4.3.1 through 4.3.5) may be applied together or individually, as a supplement to the provisions of Sections 4.1 and 4.2. Commentary: These optional procedures will provide more accurate results, typically resulting smaller design wind loads compared to ASCE 7-16.

4.3.1. Roof Zone 1’ (far from roof edges) Design wind pressure in the deep-interior region defined as Zone 1’ in Figure 1 can be calculated using the pressure coefficients from Figure 2. Linear interpolation is permitted for panel tilts between 5° and 15°. Commentary: For buildings that are sufficiently wide (Ws > 10h), there is a region (Zone 1’) located sufficiently far from the roof corners that it is not significantly affected by roof corner vortices or roof edge flow separation. As a result, the roof wind pressures do not vary with building size in this region. A version of Figure 1 appears in the ASCE 7-16 commentary (Figure C29.4-1) to clarify how the provisions for roof wind zones can be applied to non-rectangular buildings, but the ASCE 7-16 provisions do not include Zone 1’. (In developing ASCE7-16, deep-interior Zone 0 from PV2-2012 was omitted from section 29.4.3 for simplicity. A deep interior Zone 1’ was introduced to the flat roof cladding loads section, however, so we have used that convention in re-introducing a deep-interior zone here.)

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA 4.3.3. Array edge factor applies to only one array edge at a time The array edge factor γE = 1.5 need only be applied to one array edge at a time. Commentary: The increase in wind pressure at array edges occurs only on the windward side of an array. If the analysis of wind loads considers separately the different directions of wind, taking the worst load pattern for each direction, the edge factor need not be applied to more than one edge of the array within a given load pattern. All directions of wind must be considered.

Figure 2:

Zone 1’ nominal net pressure coefficients, and minimum coefficients for all zones.

4.3.2. Independent corners For buildings with projecting wings, the normalized building length Lb used to calculate normalized wind area An for panels in Zone 3, is permitted to be calculated for each building corner, using WL taken as the longest building width extending from that corner. For panels in Zone 2, Lb is permitted to be taken as the larger of the Lb values from the two adjoining building corners. Figure 3 shows an example of this approach.

4.3.4. Alternate calculation of array edge factor In lieu of using the edge factor γE as either 1.0 or 1.5 as provided for by ASCE 7-16, γE may be determined according to Figure 4, using the distance to the furthest neighboring panel, divided by the maximum height of the panel above the roof. As indicated in ASCE 7-16, γE is permitted to be taken as 1.0 where the distance from the panel’s windward edge to the windward edge of the roof is less than 0.5h, where h is the mean roof height. Commentary: Panels around the perimeter of an array are subject to greater wind pressure when the spacing d2 between rows of panels (or the distance d1 from the panel’s windward edge to the edge of the next array) is large with respect to the height h2 of the upper edge of the panels above the roof. Whereas the ASCE 7-16 provisions specify γE as a step function of either 1.0 or 1.5, Figure 4 recognizes that the array edge effect increases gradually as a function of this ratio of clear spacing to height.

γE

Low-profile panels near a roof edge will not experience wind flow approaching from that roof edge. This is because the roof edge causes flow separation, which reverses the flow direction in the region near the roof edge (Figure 5). As a result, panels that are within a distance of 0.5h from the edge of the roof do not need to consider an increase in wind pressure at the edge of the array nearest the roof edge when considering wind coming from that direction. However, if other edges of the array are exposed, panels on those edges must consider an increase in wind pressure when considering wind coming from those respective directions.

Figure 3: Building roof plan demonstrating determination of normalized building length Lb for one roof edge zone of a building with projecting wings. In this example, Lb for Zone 3b is greater than that for Zone 3a because WLb is greater than WLa. Lb for the edge (Zone 2) between Zone 3a and 3b is equal to Lb for Zone 3b. Similar calculations are to be used to determine Lb for Zone 2 and Zone 3 at each of the other roof edges and corners.

Wind Design for Solar Arrays Report SEAOC PV2-2017

1.5 1.4 1.3 1.2 1.1 1 0

2 4 6 8 10 d2/h2 (or d1/h2 if d1 is distance to next array) Figure 4: Array edge factor γE as a function of spacing between rows of panels in an array (d2) or distance from the panel’s windward edge to the next adjacent array (d1), whichever is greater, divided by the height h2 of the upper edge of the panel above the roof. July 2017 Page 6

STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA 4.3.5. Gaps between modules For tilted panels on flat roofs in which a clear horizontal distance (d2) of at least 0.5h2 exists between each row of panels, it is not necessary to also provide 0.25 inch (6.4 mm) gaps between modules along the length of the row. Commentary: For the provisions of ASCE 7-16 Section 29.4.3 to apply (i.e., tilted panels on flat roofs), ASCE 7-16 requires “a minimum gap of 0.25 inches (6.4 mm) between all [modules] and… spacing of gaps between [modules] not exceeding 6.7 ft (2.04 m).” This requirement is intended to encourage providing gaps of sufficient size such that pressure equalization can occur between the top and bottom surfaces of the panels. (Pressure equalization refers to the ability of fluctuations in wind pressure to flow around the panels, so that the pressures on the top and bottom surfaces of the panels partially equalize or counteract, leading to lower net wind loads.) For arrays of tilted panels, however, the space between rows is much larger than this 0.25 inch (6.4 mm) minimum; in this case, the pressure on the underside of the panels is typically dictated by the spacing between rows, so additional 0.25 inch (6.4mm) gaps along the length of each row are inconsequential and unnecessary. Conversely, for flush-mounted arrays, it is important to provide gaps between modules, as described in Section 5.

Commentary: Background on provisions for tilted panels on flat roofs Why roof wind zones are different for low-profile tilted solar panels compared to roof components and cladding loads In ASCE 7-16 Figure 29.4-7, the roof has been split up into three distinct zones: interior zone, edge zone, and corner zone. The corner zones are located within a distance of two times the building height from the building corners, where the air flow is characterized by the most severe effects of the corner vortices. This is different from the roof wind zones for components and cladding in ASCE 7-16. This section describes wind flow characteristics to explain how wind loads on solar photovoltaic panels are affected by different phenomena than the roof members themselves, and why it is not appropriate to use the ASCE 7 components and cladding roof loads to estimate loads on tilted solar panels.

Figure 5:

Flow separation and reattachment. (Diagram courtesy of CPP)

This zone of swirling air is called a separated flow region. If the building is wide enough, the wind above the building eventually descends and meets the roof at the reattachment point. Although this point shifts around during a high wind event, on a building much wider than it is tall, it is commonly located at a distance of approximately one to two times the building height inboard from the windward roof edge (23), depending on the nature and intensity of the turbulence in the approach flow. Beyond the reattachment point, the wind flows approximately parallel to the roof. Winds approaching the building obliquely, toward one of the corners, behave somewhat differently. Oblique or cornering winds generate conical vortices above the roof. These vortices originate at the corner of the roof and radiate toward the middle of the roof (see Figure 6 and Figure 7). The core of the vortex contains significant negative (suction) pressure, which is responsible for the peak uplift on the roof itself (5). This suction directly beneath the vortices can produce uplift pressure on roof-mounted solar modules as well, but for solar modules, wind loads are typically greater just inboard of the core of the vortex, near where the vortex reattaches to the roof. Where the vortex reattaches to the roof, downward pressure occurs. Between the core and the reattachment, there is a rapid transition from high suction to downward pressure. The vortex position and intensity vary rapidly, in part due to different scales of turbulence in the approach flow. These extreme fluctuations inhibit pressure equalization in this region, so net uplift forces on solar modules are greater.

As wind flow approaches the side of a building, the structure forces the wind to flow up and over the top, as illustrated in Figure 5. The air does not, however, flow smoothly over the roof. Instead, it breaks away at the leading edge of the roof causing a shear layer (i.e. a zone where velocity changes rapidly over a short distance) and leaving a zone of swirling air beneath it.

Figure 6: Plan view of the corner of a building model in a wind tunnel test. Smoke swirls show the cores of vortices extending from the corner of the roof. (Photo courtesy of CPP) The cornering vortices reattach to the roof with higher wind speeds between the two vortices than the approach flow (10). The swirling

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA flow also significantly increases the vertical component of the wind. Depending on the orientation of the panels relative to the vortex, this can produce uplift or downforce.

Figure 7: Corner vortices on a roof top. (Figure courtesy of CPP) The phenomena described in the preceding paragraphs result in much higher wind loads on solar panels in the corner zones than those in the middle of the roof (15), and they also explain why the roof zones are wider for roof-mounted solar arrays than for the roof itself. Wind uplift on the roof itself is most severe under the vortex core, while uplift on the solar array is highest between the core and the reattachment (8). The precise location of peak uplift varies with the tilt of the panels, the parapet height, and the nature of any wind deflector devices installed as part of the array, as discussed below.

Figure 8: Wind zones for components and cladding on a flat roof per ASCE 7-10. The edge and corner zones have been made wider in ASCE 7-16, per Figure 9.

Figure 8 shows a diagram of the wind zones for the roof of a typical low-rise building based on ASCE 7-10. These zones are now known to be too narrow, and are revised in ASCE 7-16, as shown in Figure 9.

Figure 9: Wind zones for a flat roof for components and cladding, per ASCE 7-16. For tilted solar panels mounted on top of the roof, the zones can be twice as wide as the building is high (a ≈ 2h), as depicted in Figure 10. The roof is vulnerable to the difference between the pressure within the building and that above the roof. As discussed above, higher wind loads in the edge regions can be caused by high suction forces in the core of the vortices being transferred to the roof surface. Solar panels mounted on the roof, conversely, are vulnerable not only to the suction in the vortex cores (particularly lower tilt panels) and (as

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA detailed above) to the pressure gradient, but also to the speed and direction of the wind approaching the panel. Higher tilt panels are particularly vulnerable to the vertical component of the swirling air in the area of reattachment and near the corner vortices (23). Therefore, the edge zones for solar panels are wider (7) (22). In addition, the surface of the roof experiences significant suction forces due to “bubble separation”, a type of flow separation that occurs when the wind approaches normal to a wall and curls over the roof edge, as depicted in Figure 5. Small, tightly curled separation bubbles tend to produce more suction than those with reattachment points further from the roof edge.

Figure 10: Wind zones for a flat roof for solar photovoltaic array wind loading, per ASCE 7-16. Bubble separation affects arrays of tilted solar panels differently than roof components and cladding. For example, for a south-facing system of solar panels subjected to wind from the north, uplift loads under the bubble separation along the north edge of the building are comparable to Zone 1’ loads because the direction of swirling wind at the bottom of the bubble pushes downward on the panels, offsetting the suction forces. Conversely, under the south edge separation bubble, uplift loads on this kind of PV system can be quite high. We might therefore expect that the edge zones for roof-mounted PV would not be the same for all roof edges. The reason that Zone 2 is the same on all sides of the building in Figure 10 is for simplicity; otherwise the procedure would need to take the orientation of the panels relative to the roof into account, and zones might be different for uplift and downforce. However, roof wind zone maps from wind tunnel testing that account for panel orientation may feature asymmetric zones and may be different from the zones specified in ASCE 7-16.

Wind Design for Solar Arrays Report SEAOC PV2-2017

Why wind loads on roof-mounted arrays are different from arrays on the ground Due to the sensitivity of tilted roof-mounted panels to the swirling wind flows near the building edges, the aerodynamic forces on roofmounted arrays are very different from those on the ground. Wind tests performed without placing panels in realistic separated roof flows will not provide accurate wind loads, and should not be used for roof-mounted solar installations. Balancing breadth of applicability versus conservatism in prescriptive wind load provisions The development of a wind loading figure for roof-mounted solar photovoltaic arrays that corresponds to the prescriptive method in ASCE 7 is challenging due to the complexities of the wind flow characteristics on a roof and the numerous possible array layouts, configurations, and geometry. The goal was to make a simple, easyto-use figure that is reasonably accurate for most low-profile solar photovoltaic installations. Care was taken to not have an allencompassing range of application; otherwise the values in the figure could become overly conservative for lower profile systems. With this caveat in mind and considering the range of wind tunnel data available, it was determined that the maximum height above the roof surface (h2) for the solar panels should be limited to 4 feet (1.2 m) and the panel chord length (Lp) should be limited to 6 feet 8 inches (2.04 m). Wind tunnel data show that increasing the overall height above the roof or panel chord length increases the wind loads, so the wind load values from the figure will be unconservative for systems with higher profiles or larger chord lengths. Likewise, the height of the gap between the panels and the roof surface (h1) should not exceed 2 feet (0.6 m), otherwise the wind flow under the panels can cause uplift greater than that anticipated in the figure. For roofmounted solar photovoltaic installations that do not fall within the parameters of the wind loading figure, wind tunnel testing in accordance with Section 7 is recommended to determine design pressure coefficients. A reduction factor, γc, is included in the figure to reduce the wind loads for shorter chord lengths. The reduction factor scales down linearly from a factor of 1 to 0.8 for chords 6 feet 8 inches (2 m) long to 3 feet 4 inches (1 m), respectively. Testing indicates that this reduction is more pronounced at the higher tilt angles (15 ≤ ω ≤ 35 degrees), but it is estimated conservatively and applied uniformly to all tilts for simplicity. The behavior and physics of the wind flow contained herein can also be applied to flat- and low-slope-roofed buildings of any height. The normalized wind area will account for increased wind loads of larger buildings as described in the subsequent commentary section “Nominal net pressure coefficient.” Why wind loads are different in each roof wind zone As noted previously, there are four distinct regions or zones on the roof where the wind flow characteristics and resulting wind loading on solar panels are different. They are the deep interior (1’), interior (1), edge (2), and corner (3) zones. Only the deep interior zone is sufficiently far from the roof corners to avoid the effects of the corner vortices.

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA In the northern hemisphere, most solar arrays are oriented such that the panels are facing the south, which leaves the north edge of the panel elevated and exposed to northern winds. For illustrative purposes, this discussion assumes such an array. Wind tunnel test data have shown that the cornering winds from the northeast and northwest create the most severe uplift on the array along the east and west building edges in these respective corners due to the effects of the cornering vortices on the northern edges of the panels. The accelerated flow between the two vortices will also cause uplift. The companion vortex that forms along the north edge in either case may cause mild uplift, but is primarily a source of downward force away from the edges of the array. This is another reason for the use of simple symmetric zones in this report: these zones are intended for use with both uplift and downforce calculations. The size of the corner zones is proportional to the size and strength of the vortices formed at the roof corners, which in turn are proportional to the length and height of the walls over which the vortex is forming. The dimension of the corner zones is set at two times the building height from each corner. This will be slightly conservative for corners where Lb (the characteristic building length) is less than the height of the building, where the parapet is very low or absent, or when the panel tilt (ω) is under 10°. It is not uncommon, however, for peak uplift wind forces to be observed at a distance of more than one building height from the roof corner. The vortices form a nearly constant angle with the building edge, though the angle changes with wind direction. The highest uplift typically occurs for cornering winds between 30° and 60° from normal to the roof edge, when the vortex core forms an angle of about 15° with the roof edge. The point of reattachment will be about twice as far from the edge as the vortex core, or 30°, so the region with the highest wind loads tends to fall on a line roughly radiating at an angle of 20° to 30° from the roof corner, as shown in the wind tunnel results in Figure 11. This pattern suggests that zone width should increase with distance from the roof corner; however, the zones in Figure 1 are delineated parallel to the roof edges for simplicity. Similarly, the edge zones are continued around the perimeter of the building, rather than just at the corners. For south-facing panels, this zonation will be quite conservative along the north edge of the building. However, because the method does not stipulate or limit panel orientation, symmetrical zonation around the perimeter is necessary. For west-facing panels, the north edge uplift loads would be quite high. Elevated loads may also occur under the bubble separation along the south edge of the roof, where winds from the south create air movement from the north along the roof surface in the recirculation under the flow separation. These loads are safely enveloped by Zone 2.

Figure 11: Uplift net pressures on south-facing array for winds from the northeast. Grid lines on roof are one building height apart. (Diagram courtesy of CPP) Some clarifications have been made where building setbacks occur and where corner zones should occur. Interior reentrant corners do not require corner zonations since cornering vortices only form at outward or protruding corners. Similarly, irregularly shaped buildings with outward corners with angles greater than 90° tend to result in weakened vortices. As the corner angle becomes more obtuse, it begins to resemble more of an edge condition and less of a corner condition. The roof zoning diagram in Figure 1 indicates that corner zones can be designed as edge zones where the building corner angle is greater than or equal to 135°. Wind flow near roof edges Another important aspect of the flow separation at the roof edge is the shear layer. Above the shear layer at the leading edge of a roof, very high wind accelerations occur. Solar panels need to be kept below this shear layer; otherwise, the wind loads will significantly increase above those indicated in the figure. The shear layer curves and flutters above the roof edge, and it is not unusual for the shear layer angle to drop below 30°, or a 2:1 horizontal to vertical toward the building. As such, solar panels should never be placed closer than two times the panel height (h2) from the roof edge. Where parapets occur, the shear layer is elevated, and panels can be placed closer to the roof edge. There is also an absolute minimum set back of 4 feet (1.2 m), which is due to a lack of test data. These minimum setbacks are typically less than the setback requirements to allow fire fighter roof access. Parapet effects Low parapets have been shown to increase conical vortex wind loads on the roof itself in some situations. This effect is more pronounced for tilted roof-mounted panels, particularly on wider buildings, where significant increases in wind loads due to parapets have been observed, even for relatively tall parapets (9). Considerable additional information about parapets has been gathered since PV2-2012 was published, and the parapet factor (γp) now increases gradually with parapet height. Because much of the data used to create Figure 29.4-7 was taken from studies performed with

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA low parapets, the parapet factor decreases load on roofs with no parapet. The parapet factor levels off at 1.2 for parapets greater than 30% of the height of the roof. The data actually shows the loads reaching a maximum and then dropping as the parapet continuous to get taller. At this height, the parapet begins to resemble a wall around the roof perimeter, forming a well in which the roof surface sits, keeping the vortices high enough above the roof that their influence is diminished. The drop off happens at lower parapet heights on smaller roofs. For simplicity, no scaling with respect to building width is provided. The drop off is not expected for buildings that do not have parapets around the full perimeter. Panels placed very close to the parapets can experience some sheltering from the parapet, though this will depend on the relative height of the parapet and the panel. The impact of parapets should be considered when interpreting wind tunnel test data. Tests on a small roof with a high parapet will be unconservative for general application. Nominal net pressure coefficient, (GCrn)nom The nominal net pressure coefficient (GCrn)nom curves were generated based on wind tunnel test data within the range of parameters allowed by ASCE 7-16 Figure 29.4-7. These curves envelope the available data fairly closely, and are considered a reasonably accurate prediction of wind load on tilted solar panels on flat roofs. The subscript “n” indicates a net pressure coefficient across the panels. The coefficients shown in the design curves of the figure are denoted (GCrn)nom since these values are nominal values that generally are applicable to sheltered panels and need to be adjusted for array edge conditions, parapet height, and solar panel length. One important difference in this figure from those typically provided for roof cladding is that the effective wind area on the horizontal axis has been changed to normalized wind area. The wind tunnel test data clearly show that larger buildings have larger (GCrn)nom values than smaller buildings. This effect is not currently addressed in ASCE 7 requirements for components and cladding, although it would be equally valid for loads on the roof itself. The use of normalized wind area has several advantages. Building size is not arbitrarily capped at some height like 60 ft (18 m). It is also less conservative, since using a single value for all building sizes means applying the load from the largest building in the permitted size range to all smaller buildings. The normalized wind area is approximately equal to the effective wind area (in square feet) for ~32 ft (10-m) high buildings. For shorter buildings, the normalized wind area will be larger than the effective wind area, thereby sliding to the right on the ASCE 7-16 Figure 29.4-7 (GCrn)nom curves and reducing the (GCrn)nom values or wind load. Taller buildings have the opposite effect. A lower limit on the height of the building used in computing the normalized wind area has been set at 15 feet (4.6 m); otherwise, the calculated wind loads become lower than the data support. The ASCE 7 components and cladding GCp curves all reach a maximum value and remain constant at effective wind areas less than

Wind Design for Solar Arrays Report SEAOC PV2-2017

10 square feet (1 m²). When using normalized wind area, the GCp values cannot be capped since the factor of 10 is not an absolute area; it is a factor. Taller buildings will use the normalized wind area values in the 1 to 10 range for much of the components and cladding loads. Therefore (GCrn)nom values are instead capped at normalized wind areas of less than 1, though there is no reason to believe that the loads would stop increasing for An less than 1. The wind tunnel data available include panel tilt angles up to 30°, and since the change in wind loads on the steeper panel tilt angles is small, a maximum extrapolation to 35° is not irrational. The wind tunnel data indicate that the (GCrn)nom values are not linearly related to the panel tilt angle over the full tilt angle range. The data indicate that there is a relatively small change in (GCrn)nom values for the lower tilt panels in the 1- to 5-degree range. Then there is a rapid increase in (GCrn)nom values from 5 to 15°. There is again a relatively small change in (GCrn)nom values for higher tilt panels in the 15- to 30-degree range, because, for the higher tilt angles, upstream panels create turbulence, which increases the wind loads on all downstream panels (17). Thus, the figure was created with two (GCrn)nom curves to address this phenomenon; a (GCrn)nom curve for low tilt panels in the 0- to 5-degree range and another for high tilt panels in the 15- to 35-degree range. For panel tilt angles in the 5- to 15-degree range, interpolation is required. The (GCrn)nom curves are shown for each of the distinct roof zones previously noted. Based on the wind tunnel data, the values for Zones 2 and 3 are approximately 1.3 and 1.5 times higher than Zone 1 wind loads, respectively. At small and very large effective wind areas, these factors vary, as illustrated in the (GCrn)nom curves. The (GCrn)nom data has been typically rounded to the nearest tenth to allow easier extraction of the data from the curves. The (GCrn)nom values are for both positive and negative values. Wind tunnel test data from solar panels show positive and negative pressures that are similar, which is very different than typical roof design wind loads. Array edge factor and shielding within an array Solar panels are typically installed in large arrays with closely spaced rows. When the wind traveling above the roof surface approaches the array, the wind generally travels up and over the array. As the wind accelerates over the first panel at the array edge, it causes a large wind load on this edge panel. As the wind continues across the array, it tries to reattach to the roof, but if the panels are in closely spaced rows, the wind cannot fully recover and it rolls over the top of the remaining downwind panels in a turbulent manner, effectively shielding the inner panels. Wind tunnel tests have shown that closely spaced shielded panels experience wind loads as small as 50 percent of the loads experienced by edge panels. In the development of ASCE 7-16 Figure 29.4-7, the (GCrn)nom curves were chosen for sheltered panel areas since this represents the typical condition in large arrays. To account for the higher loading at the perimeter edge panel areas, an array edge increase factor must be applied. As noted earlier, most solar arrays in the northern hemisphere are oriented such that the panels are facing south, which leaves the north edge of the panel elevated and exposed to winds from the north. As such, the edge effects on the northern edge row July 2017 Page 11

STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA are higher than that on the southern edge row and east and west sides of the array. The same multiplier has been applied to all array sides for simplicity, however. This value is a best fit to all the data, and should not be considered universally conservative. Edge multipliers in excess of 2.0 have been measured, for example where corner vortices scour the roof surface upwind of the exposed array edge, so care should be taken if applying edge factors from this report to interior uplift pressures that do not use ASCE 7-16 roof zones. Corner vortex edge effects can extend a distance of more than 6h from the roof corner. In order to take full advantage of the shielding effect between panel rows, the space between rows needs to be less than twice the panel height above the roof (h2). As the space between rows increases, shielding decreases, and wind loads on the panels increase. The same phenomenon occurs where there are open spaces on the roof between adjacent arrays. As the open space between panels approaches approximately 8 times the panel height, sheltering from upwind rows becomes negligible. As noted in a previous section, the shear layer of wind coming up and over the edge of a building requires some distance to reattach to the building roof surface. If the roof is covered with PV panels, the reattached flow will travel across the top of the panels. If the roof is bare at the reattachment, the flow will travel along the roof surface, creating significant edge effect loading when it first hits a solar array perimeter. The corner vortices also remain above the roof surface for some distance before scouring along the roof and creating a significant edge effect. This means that the array edge facing the building edges or corners will not have an edge effect if it is close enough to the building edge or corner. It also means that testing with the roof entirely covered with panels will not capture the array edge effect. The location of the reattachment varies with the size and aspect ratio of the roof, the location on the roof, and the wind direction. It can also vary in time, as wind flow patterns above the roof are never steady. The data indicate that the edge effects are minimal within 0.5h of the building edges. Rooftop equipment, such as HVAC units, penthouses, and other roof objects can provide some sheltering benefits to solar arrays located directly downwind of the object; however, due to varied wind flow directions, the regions around edges of the units can also have accelerated wind flow. Due to the uncertainty in the wind direction and impact these objects have on the solar arrays, it is indicated in ASCE 7-16 to ignore these objects and design the surrounding panels as edge panels with the edge increase factor calculated as if the objects do not exist. This results in the panels adjacent to rooftop objects being designed for higher wind loads to account for accelerated wind flow around the objects. Ignoring very large obstructions like penthouses will tend to be unconservative, as flow acceleration around the base on the penthouse can be significant. The size of a rooftop obstruction can be characterized by its height or width, whichever is smaller. We recommend using Zone 3 values within one characteristic length of the obstruction. This recommendation is an estimate, and is not based on testing.

Wind Design for Solar Arrays Report SEAOC PV2-2017

Design strength Wind design of a PV panel support system includes determining with sufficient certainty that design wind loads are not greater than the system’s capacity to resist those loads. Attached systems use the strength of attachments to the roof to resist uplift and sliding/drag forces on the PV panels. Ballasted systems use the weight of the modules, racking system, and ballast blocks to resist such forces. In both cases, a complete load path must be designed from the panels, through the racking system, to attachments and/or ballast. Load factors specified in the load combinations of the International Building Code should be applied to wind loads and gravity loads to evaluate the adequacy of the system’s resistance. The governing design limit state may be associated with reaching the design strength of array components, attachments, or the weight of ballast (with load factors for minimum dead load and maximum wind uplift load combinations), or it may be associated with a deflection limit, for example if large deflections would result in increased wind loads. For sliding resistance, the coefficient of friction between the system and the roof should be suitably determined (e.g., by ASTM G115 testing as specified in SEAOC PV1), and the friction force must take into account effects of uplift on ballast. Wind loads on PV modules This report focuses on wind loads for mounting systems, and does not attempt to address micro-scale effects within modules, nor electrical or thermal performance thereof. We caution that it is not clear that the design wind loads from this report are sufficient to predict performance of individual PV modules under wind loads. For example, we are not aware of any research that defines a relationship between the wind loads calculated in this report (for structural design of the racking system) and the loads used in static loading tests such as UL1703, “Standard for Flat-Plate Photovoltaic Modules and Panels” (for evaluating performance of modules). One concern that has been raised is that the effects of cyclic and spatially variable wind loads are not captured by these static tests. Nearby structures It is assumed in these procedures that no significantly taller structures are located near the roof in question. A taller nearby building can significantly change the wind flow patterns on the roof, and such situations need to be assessed on a case-by-case basis, typically by a scale model wind tunnel study. As with rooftop obstructions, an unproven rule of thumb would be if an adjacent structure is closer than one characteristic length (i.e., the adjacent structure’s height or width, whichever is least), it is likely to cause accelerated flow. Billowing of roof membrane Mechanically attached roofing membranes can billow (locally deflect upward) between points of securement to the roof structure. The spacing between rows of roofing fasteners typically varies between 1.5 ft (0.5 m) and 11.5 ft (3.5 m) on center. Larger spacing between fasteners presumably results in greater potential for billowing. Wind-tunnel tests to establish the design wind pressures for solar arrays were conducted using scaled models of buildings with rigid July 2017 Page 12

STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA 1. d1 to the adjacent array > 4 ft (1.22m) or 2. d2 to the next adjacent panel > 4 ft (1.22m);

SEAOC is not aware of published research to evaluate the extent to which billowing of the roof membrane affects the performance of roof-mounted solar arrays, if at all, so roof billowing cannot be immediately dismissed as a potential cause of damage. Roof billowing has been observed in research and practice for membranes in the absence of solar arrays, and the pressures that cause roof billowing are in a range that exceeds the average weight of some ballasted solar arrays. Billowing of the roof membrane from internal pressure, external pressure, or a combination of the two could cause the orientation or position of solar panels to change, affecting their aerodynamics and potentially resulting in increased uplift or drag forces acting on the panels.

γa = solar panel pressure equalization factor, defined in Fig. 29.4-8.

Based on experience, we anticipate that proper wind design of the array itself, according to the provisions herein, is of primary importance for preventing damage to the array. However, roof billowing may contribute to risk, particularly for arrays or portions thereof that have very little ballast or few attachments.

5. Flush-mounted arrays on flat or sloped roofs 5.1. ASCE 7-16 procedures For arrays of flush-mounted panels on flat roofs or roofs of any slope, design wind pressure shall be determined in accordance with ASCE 7-16 Section 29.4.4. ASCE 7-16: 29.4.4 Rooftop Solar Panels Parallel to the Roof Surface on Buildings of All Heights and Roof Slopes. The design wind pressures for rooftop solar panels located on enclosed or partially enclosed buildings of all heights, with panels parallel to the roof surface, with a tolerance of 2o and with a maximum height above the roof surface, h2, not exceeding 10 inches (0.25m) shall be determined in accordance with this section. A minimum gap of 0.25 inches (6.4 mm) shall be provided between all panels, with the spacing of gaps between panels not exceeding 6.7 ft (2.04 m). In addition, the array shall be located at least 2h2 from the roof edge, a gable ridge, or a hip ridge. The design wind pressure for rooftop solar collectors shall be determined by Eq. 29.4-7: p = qh (GCp)(γE)(γa)

(lb/ft2) (N/m2)

(29.4-7)

where (GCp) = external pressure coefficient for C&C of roofs with respective roof zoning, determined from Figs. 30.3-2A-I through 30.3-7, or 30.5-1;

γE = array edge factor = 1.5 for uplift loads on panels that are exposed and within a distance 1.5(Lp) from the end of a row at an exposed edge of the array; γE = 1.0 elsewhere for uplift loads and for all downward loads, as illustrated in Figure 29.4-7. A panel is defined as exposed if d1 to the roof edge > 0.5h and one of the following applies:

Wind Design for Solar Arrays Report SEAOC PV2-2017

Solar Array Pressure Equalization Factor, γa

simulated roof surfaces. As such, the conditions in these tests did not simulate the potential effects of billowing of the roof membrane.

1 0.8 0.6 0.4 0.2 0 1

10 100 Effective Wind Area, ft²

1000

Figure 29.4-8 Solar Panel Pressure Equalization Factor, γa, for Enclosed and Partially Enclosed Buildings of All Heights. Commentary: The method of ASCE 7-16 Section 29.4.4 is only as accurate as the external pressure coefficients (GCp) used in equation 29.4-7. The components and cladding roof zones and pressure coefficients for flat roofs changed considerably from ASCE 7-10 to ASCE 7-16. Use of ASCE 7-16 cladding values and roof zoning is required for appropriate use of Section 29.4.4. Wind loads on roof-mounted solar arrays that are close to and parallel to the roof surface tend to be lower than the loads on a bare roof due to pressure equalization (14),(17), except at the perimeter of the array. The solar array pressure equalization factor, γa, accounts for this reduction, based on data from wind tunnel testing (18). For pressure equalization to occur, the panels cannot be too large, there needs to be a minimum gap between adjacent panels, and the height above the roof surface cannot be too large. The requirements of ASCE 7-16 Section 29.4.4 are based on panel sizes not exceeding 6.7 ft (2.04 m), panel height above the roof surface not exceeding 10 inches (0.25 m), and a gap of 0.25 inches (6.4 mm) or greater around the edges of each panel. Larger gaps and lower panel heights above the roof surface could further decrease the wind loads, as described in Section 5.3.5.

5.2. Recommended additional requirements (not included in ASCE 7-16) The following requirements are recommended in addition to the provisions of Section 5.1. 5.2.1. Tolerance for panel tilt Solar arrays designed in accordance with ASCE 7-16 Section 29.4.4 (flush-mounted arrays), shall be parallel to the roof surface such that the height of each panel edge above the roof is no more than one inch greater than the height of each adjacent panel edge: h2 - h1 ≤ 1”. Commentary: Flush mounted solar panels experience wind loads in a manner similar to air-permeable cladding. As such, they generally

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA interact with wind flow above the roof in a manner similar to the roof itself without solar panels. The 2° tolerance (between the slope of the roof and the slope of the panels) permitted in ASCE 7-16 Section 29.4.4 will not guarantee that the wind flow is largely unaffected by the panels, particularly if the rows of panels are widely spaced, or if the high edge of the panels juts appreciably above the adjacent panel. The additional limitation of 1” maximum difference between adjacent panel edges, as recommended here, is intended to address this concern. While the gaps between panels are not critical for wind loads on tilted panels, they are an important part of local pressure equalization for flush mounted systems, so that the minimum gap size specified in ASCE 7-16 Section 29.4.4 (0.25 inches, 6.4 mm) and maximum spacing between gaps (6.7 ft, 2.04 m) is essential.

5.2.2. Definition of h1 and h2 Heights h1 and h2, as defined in ASCE 7-16, are measured from the roof surface to the top surface of the panel. Commentary: ASCE 7-16 defines h1 and h2 as the height of a solar panel above the roof at the upper edge (h1) and lower edge (h2) of the panel. In the ASCE 7-16 definition, “upper” and “lower” refer to the high end and low end of tilted panels. For flush-mounted arrays, panels are parallel to the roof, so h1 and h2 are equal (within a tolerance per Section 5.2.1). The ASCE 7-16 definition is not adequately clear that h1 and h2 are measured to the top surface of the panel (not, for example, to the bottom of the module frame). This clarification becomes important for determining the pressure equalization factor per ASCE 7-16 Section 29.4.4 as well as in the optional refinement described below in Section 5.3.5.

5.2.3. Definition of exposed panels for array edge factor Panels shall be considered exposed if the distance to the next adjacent array is greater than 2h2. Commentary: The edge factor provisions for flush-mounted panels in ASCE 7-16 were copied from those for tilted panels on flat roofs, which in turn were based on provisions in SEAOC PV2-2012. Some of the simplifications introduced in ASCE 7-16 for tilted panels are not appropriate for flat panels. For flat panels close to the roof, edge factors will apply for distances less than the 4 ft limit specified in ASCE 7-16.

5.3. Optional refinements (not included in ASCE 7-16) The following refinements (items 5.3.1 through 5.3.5) may be applied together or individually, as a supplement to the provisions of Sections 5.1 and 5.2. Commentary: These optional refinements will provide more accurate results, typically resulting in smaller wind loads compared to ASCE 7-16.

Wind Design for Solar Arrays Report SEAOC PV2-2017

5.3.1. Array edge factor applies to only one array edge at a time The provisions of Section 4.3.3 also apply to flush-mounted arrays. 5.3.2. Array edge factor The provisions of Section 4.3.4 also apply to flush-mounted arrays. 5.3.3. Width of array perimeter strip for applying array edge factor For flush-mounted panels, γE may be taken as 1.5 for the portion of exposed panels that is within a distance 2h2 from the edge of the array. Commentary: ASCE 7-16 Section 29.4.4 (flush-mounted arrays) defines the width of the array perimeter strip for applying the array edge factor γE in the same way that it is defined in Section 29.4.3 (tilted panels on flat roofs): 1.5 times the panel chord length, Lp. However, for flush-mounted arrays, the height h2 of the top of panels above the roof surface is more influential than the panel chord length. (Also Lp is not well-defined for the continuous surface created by flush-mounted panels.) Thus, for flush-mounted arrays, we recommend defining the array perimeter strip in terms of the height h2 of the top of panels above the roof surface. For flush-mounted systems, elevated pressures at array edges are largely the result of flow separation from the roof and reattachment on the top of the panels, which occurs over a distance roughly 2h2 from the edge of the array.

5.3.4. Open buildings The design wind pressures for rooftop solar panels located on open buildings and satisfying the requirements of ASCE 7-16 Section 29.4.4 shall be determined in accordance with ASCE 7-16 Section 29.4.4. Commentary: ASCE 7-16 Section 29.4.4 is restricted to enclosed or partially enclosed buildings. This restriction is not necessary; the procedure is accurate for and may be applied to solar panels parallel to any roof surface.

5.3.5. Pressure equalization factor for arrays with greater porosity The solar panel pressure equalization factor, γa, is permitted to be determined from Figure 12. Interpolation between the solid line and the dashed line is permitted. Commentary: Figure 12 is the same as ASCE 7-16 Figure 29.4-8 except that the dashed line is added in Figure 12 to provide greater reduction in design pressure for arrays that have sufficiently wide gaps between panels and sufficiently low height above the roof such that greater pressure equalization can occur compared to the case with minimum gaps and maximum height above the roof permitted in ASCE 7-16 Section 29.4.4.

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA Test data shows that a larger gap between panels will reduce the net wind loads, as does reducing the height of the panels above the roof surface (26). As can be seen from Figure 12, to achieve the lowest wind pressures racking hardware for flush-mounted solar arrays should be designed to produce a gap between modules of at least 0.75 inches (19 mm) and a maximum height of panels above the roof of 5 inches (127 mm). For gaps between 0.25 and 0.75 inches (6.4 and 19 mm), and for h2 between 5 and 10 inches (127 and 254 mm), interpolation between the solid line and the dashed line can be computed using the equation below. For example, for gap of 0.5 inches (13 mm) and h2 equal to 7.5 inches (191 mm), γa = 0.7 for effective wind area less than 10 ft2 (0.93 m2).

6. Design of the roof Per ASCE 7-16 Section 29.4.3 (tilted solar panels on flat roofs) and Section 29.4.4 (flush-mounted arrays on flat or sloped roofs): ASCE 7-16: The roof shall be designed for both of the following: 1.

The case where solar collectors are present. Wind loads acting on solar collectors in accordance with this section shall be applied simultaneously with roof wind loads specified in other sections acting on areas of the roof not covered by the plan projection of solar collectors. For this case, roof wind loads specified in other sections need not be applied on areas of the roof covered by the plan projection of solar collectors.

2.

Cases where the solar arrays have been removed.

For effective wind area less than 10 ft2 (0.93 m2),

γa = 0.8 – 0.2(1/2)[(gap – 0.25in)/0.5in + (10in – h2)/5in] γa = 0.8 – 0.2(1/2)[(gap – 6.4mm)/13mm + (254mm – h2)/127mm] The value for gap used in the above equation must be between 0.25 and 0.75 inches (6.4 and 19 mm). For values of gap greater than 0.75 inches, use 0.75 inches (19 mm) in the calculation. For values of gap less than 0.25 inches (6.4 mm), the provisions of ASCE 7-16 Section 29.4.4 do not apply. The value for h2 used in the above equation must be between 5 and 10 inches (127 and 254 mm). For h2 less than 5 inches, use 5 inches (127 mm) in the calculation. For h2 greater than 10 inches (254 mm), the provisions of ASCE 7-16 Section 29.4.4 do not apply. For effective wind area greater than 100 ft2 (9.3 m2), γa = 0.4. For effective wind area between 10 and 100 ft2 (0.93 and 9.3 m2), use straight line interpolation on the log plot in Figure 12 between the values calculated above.

Commentary: These two sections of ASCE 7-16, applying to two types of solar arrays, indicate how wind loads on rooftop solar arrays are to be considered along with the roof components and cladding wind loads. (The language is the same in the two ASCE sections.) Wind tunnel studies have shown that the wind loads on rooftop solar arrays need not be applied simultaneously with the roof components and cladding wind loads covering the same area. Where a portion of the roof is covered by a solar array and the remainder is not covered, then the roof is to be designed with the solar array wind load on the covered portion with simultaneous application of roof components and cladding load on the uncovered portion. In a separate load case, roof structures are also to be checked for the applicable components and cladding wind loads assuming that the photovoltaic panels are not present, to address the possibility that the solar arrays are removed or are never installed. For installations of solar panels on existing buildings, this separate load case to check the capacity of the existing roof structure to resist the roof components and cladding wind loads applied over the entire roof area (i.e., assuming that the solar panels are not present) is not required.

7. Wind tunnel procedure 7.1. ASCE 7-16 procedures Design of rooftop solar arrays using the wind tunnel procedure shall be in accordance with ASCE 7-16 Section 31.6. ASCE 7-16: 31.6 ROOF-MOUNTED SOLAR COLLECTORS FOR ROOF SLOPES LESS THAN 7 DEGREES

Figure 12: Solar Panel Pressure Equalization Factor, γa, with proposed alternative to ASCE 7-16 Figure 29.4-8 to permit smaller design pressures for conditions with larger gaps between modules and smaller height above the roof.

Wind Design for Solar Arrays Report SEAOC PV2-2017

31.6.1 Wind Tunnel Test Requirements Wind loads on roof-mounted solar collectors with roof slope less than 7 degrees are permitted to be determined by wind tunnel tests as generic loads applicable to a range of buildings, by determining load coefficients for use in the analysis equations of the Directional Procedure in Chapters 27 and 29 for MWFRS and in Part 5 of Chapter 30 for C&C. Alternatively, the generic loads are permitted to

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA be specified with an analysis method defined in the wind tunnel test report. It is not required to include specific nearby buildings in the testing when results are to be used for multiple sites.

•

The peer reviewer shall be independent from the wind tunnel laboratory that performed the tests and report and shall bear no conflict of interest.

Wind tunnel tests shall satisfy ASCE 49, shall meet requirements specific to roof-mounted solar collectors, and shall meet the additional requirements specific to roof-mounted solar collectors including the following variables. These requirements include accurately scaled models of solar collectors including collector tilt angle, row-to-row spacing, aisles or gaps between collector rows, height above the roof, setback from roof edge, alignment of collector rows compared to the main axes of the building, deflector/shroud shapes, and the geometry of the collector support structure. The tests shall include at least eight rows of collectors, where more than eight rows are applicable, mounted on the roof of representative generic buildings. The models of generic buildings shall be large enough in plan area to capture the wind flow environment over different roof zones. The test matrix shall include the range of building plan dimensions, eave height, parapet height, roof slope, and open or enclosed buildings.

•

The peer reviewer shall have technical expertise in the application of wind tunnel studies on buildings similar to that being reviewed.

•

The peer reviewer shall have experience in performing or evaluating boundary layer wind tunnel studies and shall be familiar with the technical issues and regulations governing the wind tunnel procedure in ASCE 49 as it is applied to systems similar to solar photovoltaic arrays that use generalized wind tunnel data for design.

Data analysis shall consider wind loads from all wind directions. Generic load coefficients shall be calculated to be consistent with coefficients in Chapters 27, 29, and 30 or shall be defined to apply to an analysis procedure specified in the test report. The test report shall include data collection methods, data analysis, boundary layer modeling, collector and building modeling, measured wind loads and their relationship to effective wind area, conversion of data into generic coefficients, and conditions of applicability of results to different buildings types and collector geometry. Wind tunnel results shall not be extrapolated to geometric configurations that were not anticipated by the wind tunnel study. Interpolation between two or more tests shall be permitted. The limitations of the wind tunnel study, such as the range of array collector and building geometry parameters that were tested, shall be clearly reported. 31.6.1.1 Limitations on Wind Loads for Rooftop Solar Collectors For photovoltaic solar collector systems that meet the limitations and geometry requirements of Figure 29.4-7, the minimum design wind load based on a wind tunnel study shall not be less than 65% of the values resulting from Figure 29.4-7, subject to the conditions of Section 31.6.1.2. The minimum design wind force based on a wind tunnel study for roof-mounted solar panel systems need not comply with the minimum net pressure of 16 psf (0.77 kN/m2) per Section 30.2.2. 31.6.1.2 Peer Review Requirements for Wind Tunnel Studies of Roof-Mounted Solar Collectors Wind load values lower than the minimums indicated in Section 31.6.1.1 shall be permitted when an independent peer review of the wind tunnel test is performed in accordance with this section. The independent peer review is an objective, technical review by knowledgeable reviewer(s) experienced in performing wind tunnel studies on buildings and similar systems, in properly simulated atmospheric boundary layers. The minimum qualifications for the peer reviewer shall be the following:

Wind Design for Solar Arrays Report SEAOC PV2-2017

The peer reviewer shall review the wind tunnel report, including but not limited to data collection methods, data analysis, boundary layer modeling, collector and building modeling, resulting wind loads and their relationship to effective wind area, conversion of data into GCrn values, and conditions of applicability of results to different building types, collector geometry, and other relevant issues identified by the reviewer. The peer reviewer shall submit a written report to the Authority Having Jurisdiction and the client. The report shall include, at a minimum, statements regarding the following: scope of peer review with limitations defined; the status of the wind tunnel study at time of review; conformance of the wind tunnel study with the requirements of ASCE 49 and Section 31.6.1; conclusions of the reviewer identifying areas that need further review, investigation, and/or clarification; recommendations; and whether, in the reviewer’s opinion, the wind loads derived from the wind tunnel study are in conformance with ASCE 7-16 for the intended use(s). Commentary: The wind tunnel provisions in ASCE 7-16 Section 31.4 prescribe the test conditions for developing wind loads for a specific building located at a specific site. Typically this is done by modeling the surrounding buildings and topography and their effects on a specific building. When applying the wind tunnel procedure for solar panel installations, a different approach is necessary. For solar panel installations, it is typically desired to model a generic building with the solar array on the roof of a scaled building, then generate GCrn pressure coefficients that are applicable to any site, a wide range of building sizes, and a varied array layout. The approach needs to be similar to that used to develop the GCp figures in ASCE 7 by modeling generic buildings with various features to capture a wide range of effects. References (14) and (16) provide guidance regarding how to apply the wind tunnel procedure to obtain generalized wind design parameters for solar arrays. Typically, studies performed with full-scale solar panels on the floor of the wind tunnel (as has often been done by aerospace or automotive wind tunnels) will not satisfy the requirements of this section. Such studies are of limited value because of the complexities described in prior sections. There have been significant improvements in the test methods and understanding of wind loads on low profile roof-mounted systems since the publication of the previous edition of this report (SEAOC PV2-2012). Wind tunnel testing reports issued prior to 2012

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA are unlikely to adequately consider the scaling of wind loads with building size, for example. We recommend that these reports be reviewed and reissued by the originator before reusing the reports for new projects. Given the current pace of changes in this field, it is recommended that wind tunnel testing reports be reviewed by the originator every 3 or 4 years from the date of the report to assess the appropriateness and accuracy of the report for continued use.

Commentary: The effect of building size can be accounted for by defining (GCrn)nom values that scale with building size, or by defining the maximum building dimensions to which the test results are applicable.

7.2. Recommended additional requirements (not included in ASCE 7-16)

Commentary: ASCE 7-16 Section 29.4.3 contains a parapet factor, γp.

7.2.1. Flush-mounted solar arrays on roofs of any slope Wind loads determined by wind tunnel tests on flush-mounted solar arrays on roofs of any slope shall satisfy the requirements of ASCE 7-16 Section 31.6 and this Section 7.2. Exceptions: 1.

The minimum design wind load in ASCE 7-16 Section 31.6.1.1 shall be based on ASCE 7-16 Section 29.4.4, not Figure 29.4-7.

Commentary: While the provisions of ASCE 7-16 Section 31.6 were written with flat and low-slope roofs in mind, they are also applicable to wind tunnel testing of flush-mounted solar arrays on sloped roofs. Consistent with the provisions of ASCE 7-16 Section 29.4.4, pressure coefficients for flush-mounted solar arrays are permitted to be determined using methods similar to those used to develop pressure coefficients for Components and Cladding in ASCE 7-16.

7.2.2. Minimum number of rows Fewer than eight rows of solar panels may be used in the testing if it is demonstrated that the array interior loads are not a function of the number of rows for the applicable array size. Commentary: The use of eight or more rows of solar panels in testing, while recommended, need not be strictly met if a fewer number of rows can rationally justified. Particular care should be taken for tilts above 5°, where the effects of array-generated turbulence on the interior of the array are most pronounced (15) (17).

7.2.3. Effects to account for in determining design wind pressure Wind loads on tilted solar panels on flat or low-slope roofs, determined using wind tunnel testing in accordance with ASCE 7-16 Section 31.6, shall account for all of the following in the determination of design wind pressure: Commentary: The effects listed below have been shown to be significant in determining design wind pressures for solar arrays. If the effects listed below are not explicitly captured in the wind tunnel test program, procedures from ASCE 7-16 Section 29.4.3 and 29.4.4, where applicable, can be adapted to account for these items.

1.

The effect of building size on wind pressure coefficients.

Wind Design for Solar Arrays Report SEAOC PV2-2017

2.

3.

The effect of building parapets on wind pressure coefficients.

The potential for greater wind pressure acting on the edges of arrays.

Commentary: ASCE 7-16 Sections 29.4.3 and 29.4.4 contain an array edge factor γE.

4.

The effect of building size on the size of roof wind zones.

Commentary: ASCE 7-16 Sections 29.4.3 and 29.4.4 define roof wind zones as a function of building height.

5.

Peak value statistics consistent with the consensus of research recommendations.

Commentary: ASCE 7-16 does not include specific requirements for the statistical details associated with the peak pressure coefficients. While there is some expectation, based on conventional building studies, that the peak values should be based on a 60-minute duration, wind tunnel practice for solar arrays has been based on shorter durations because the large model scales that are typically used lead to a turbulence length scale mismatch (11)(24). ASCE 49-12, equation (2-5) specifies that the ratio of integral length scale to characteristic length of a structure at model scale and at full scale shall be met within a factor of 3. This has not typically been met in wind tunnel studies for roof-mounted arrays, and it is not known if using conventional methods with a factor of 3 mismatch in turbulence length scale is appropriate for solar structures. In most wind tunnel studies, common practice is to measure pressure coefficients referenced to a mean wind speed. Pressure coefficients can also be measured with a direct reference to the fluctuating or gust wind speeds, which has the effect of reducing many of the duration effects (6)(24). Such approaches are acceptable if sufficient justification is provided that the results are equivalent to the consensus of research recommendations. One indication that the peak pressure coefficient calculation method is suitable is to verify that the peak GCrn values (i.e., referenced to 3second gust speeds at the mean roof height) are not less than the mean coefficients (referenced to the mean speed at the mean roof height), as required by quasi-steady theory for such small structures. SEAOC recommends that the upcoming editions of ASCE 7 and/or ASCE 49 provide more specific guidance on this issue. In the absence of such provisions, alternative rational procedures for analysis of peak pressure coefficients may be justified by testing or peer reviewed literature.

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA 7.2.4. Minimum loads from wind tunnel testing If wind load values used are lower than the minimums indicated in ASCE 7-16 Section 31.6.1.1, the wind tunnel laboratory that performed the tests shall provide for peer review an explanation for the reduced loads. Commentary: ASCE 7-16 Section 31.6.1.2 permits design wind loads from wind tunnel testing to be taken less than 65% of the prescriptive values from ASCE 7-16 Figure 29.4-7 if a peer review of the wind tunnel report is performed (item 1 above). SEAOC recommends the additional requirement of an explanation for the reduced loads. Figure 29.4-7 represents an envelope of wind loads measured in wind tunnel tests of solar arrays without deflectors or shrouds. Solar panel systems that have aerodynamic devices or more efficient profiles (such as east-west systems) can have wind tunnel-based loads less than the 65% lower bound, and the presence of such devices is an example of a credible reason for a reduction in wind load coefficients.

7.2.5. Building shape and size The building size and aspect ratio (i.e., building side length versus roof height) modeled in wind tunnel tests shall be representative of the range of buildings for which the test results are used for design. Pressure coefficients shall be adjusted for building size through the effective wind area normalization procedure provided in ASCE 7-16 Section 29.4.3 or through an alternative rational procedure justified by the testing or by recognized literature. Commentary: Wind loads on solar panels in Roof Zones 1, 2 and 3 must be determined through testing on the roof of a building that generates conical vortices at its corners. To capture the full effect of the corner vortices, it is necessary that the aspect ratio of the building (Ws/h) be 4.0 or more. Little additional vortex strength is expected for aspect ratios greater than 6.0. Conversely, the effects of bubble separation can be more severe for buildings with smaller aspect ratios, particularly in high turbulence. Therefore testing on a range of building sizes and configurations is recommended if the test results are intended to be applicable to a range of buildings. Wind loads in Zone 3 are significantly higher for buildings with an aspect ratio (Ws/h) of 6.0 than at the same height with an aspect ratio of 2.0 (7). Similarly, wind loads will increase with building height if the width is kept constant (15). As a result, wind pressure coefficients measured on a particular building size will be too low for larger buildings, and so must either be scaled with building size as described in ASCE 7-16 Section 29.4.3, or must not be used for buildings larger than that represented by the test building. Testing on multiple building sizes can demonstrate the manner in which the loads scale with An, and can be expected to generate wind pressure versus normalized area relationships comparable to those in Figure 29.4-7. If testing is done on only one building size, a larger building is required, as tests on smaller buildings can underestimate

Wind Design for Solar Arrays Report SEAOC PV2-2017

wind load coefficients, particularly for single modules, even when normalized by An. The relationship between An and GCrn should also be examined as the number of modules in the effective wind area is increased. Buildings with shorter aspect ratios will also reduce the parapet factor by forming a well on the roof and keeping the corner vortices high above the panels. Also, if the roof is not wide enough, the entire test roof will consist of Zone 2 and/or Zone 3, so wind loads in Zone 1 cannot be measured. A wider building is also needed to capture edge effects. Arrays need to be offset one roof height or more from the roof corner to capture the full effect of flow reattachment on array edge factors. The array should be kept close enough to one of the building edges, however, to remain under the vortex along that edge, as this is where the edge effect is most severe. Edge factors typically vary for each side of an array. For systems with no wind deflectors, the highest values generally occur on the high (north) edge, but the other edges can be more severe if a north-side deflector is present, so edge factors should be assessed for all sides. These requirements mean that, for example, the results of wind tunnel testing performed on small roofs completely filled with solar panels need to be adjusted for building size and edge factors in order to address applications on larger buildings and roofs with discrete arrays.

7.2.6. Wind tunnel testing report The wind tunnel test report provided for peer review shall include all of the following, except for items that are demonstrated to be not applicable: 1.

A description of the simulated atmospheric boundary layer (ABL) including mean velocity and longitudinal turbulence intensity profiles, and a spectrum of longitudinal turbulence, with a comparison to approved atmospheric models in due consideration of the model scale used in the testing.

Commentary: Wind tunnel testing of rooftop solar arrays is typically performed with 1:25 to 1:50 scale building models. At these scales, the turbulence length scale cannot be correctly simulated in most wind tunnels, and modification to typical wind tunnel test and analysis procedures may be necessary (6) (20) (24).

2. A description of the test methods that includes (where applicable): • wind tunnel dimensions, cross section, position of test section and turntable; • vertical profiles of velocity and turbulence in the wind tunnel, and along-wind spectrum at roof height. Also provide information concerning components such as flow straighteners, turbulence screens, turbulence generators, barrier wall, floor roughness and other devices relevant to the generation of the atmospheric boundary layer;

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA • • • • • • • • • • •

drawings of the array model with dimensions; building model dimensions; overview of test configurations and test photographs; consideration of blockage effects; consideration of Reynolds number effects; reference static pressure; for pressure tests, the number and locations of pressure taps and consideration of frequency response of tubing instrumentation specifications; sampling rate and filters; wind directions tested; and length and number of time series measured in the wind tunnel and conversion to full scale in due consideration of the model and velocity scales.

3. Details of the method of data analysis, including: • calculation of peak pressure or force coefficients; • conversion of these peak values into GCrn values; and • the load cases considered (e.g lift, sliding). 4. Limitations to the applicability of the results, including but not limited to building size, building shape, and array geometry. Commentary: The report content required in this section is needed to facilitate an appropriate peer review. In documenting the data analysis as required in item 3, providing sample calculations can be helpful. Not all of the information listed will be available in all cases; for example, peak coefficients are not available from failure tests. In such cases, comparable details concerning the interpretation of the results are to be provided in the report, and/or it is to be demonstrated that the listed item is not applicable.

7.2.7. Effective wind area If the wind tunnel test report includes assumptions about effective wind area, such assumptions shall be validated by the Engineer of Record for the solar panel support system, per the requirements of Section 3. 8. Wind dynamic effects on ground-mounted solar arrays Commentary: This report is not intended to address all aspects of wind design for ground-mounted solar arrays. In general, such arrays are designed using applicable provisions of ASCE 7-16, such as the provisions for open buildings. However, the following addresses one aspect – vortex shedding and dynamic resonant effects – that is not fully addressed in ASCE 7-16 and merits additional consideration for the design of ground-mounted solar arrays of large horizontal extent.

Wind Design for Solar Arrays Report SEAOC PV2-2017

8.1. ASCE 7-16 procedures Commentary: ASCE 7-16 includes the following statements that, in some cases, have been interpreted by engineers to apply to the determination of wind loads on ground-mounted solar arrays: ASCE 7-16: 26.2 DEFINITIONS BUILDING OR OTHER STRUCTURE, RIGID: A building or other structure whose fundamental frequency is greater than or equal to 1 Hz. 26.11.1 Gust-Effect Factor: The gust-effect factor for a rigid building or other structure is permitted to be taken as 0.85. Commentary: The Commentary to ASCE 7-16 describes limitations for cases where prescriptive design wind loads do not apply: ASCE 7-16: C26.1.2 General Limitations. The provisions given under Section 26.1.2 apply to the majority of site locations and buildings and other structures, but, for some projects, these provisions may be inadequate. Examples of site locations and buildings and other structures (or portions thereof) that may require other approved standards, special studies using applicable recognized literature pertaining to wind effects, or using the wind tunnel procedure of Chapter 31, include: 1. Site locations that have channeling effects or wakes from upwind obstructions… 2. Buildings with unusual or irregular geometric shape… 3. Buildings or other structures with response characteristics that result in substantial vortex-induced and/or torsional dynamic effects, or dynamic effects resulting from aeroelastic instabilities such as flutter or galloping … 4. Bridges, cranes, electrical transmission lines, guyed masts, highway signs and lighting structures, telecommunications towers, and flagpoles. When undertaking detailed studies of the dynamic response to wind forces, the fundamental frequencies of the building or other structure in each direction under consideration should be established using the structural properties and deformational characteristics of the resisting elements in a properly substantiated analysis, and not utilizing approximate equations based on height.

8.2. Recommended additional requirements (not included in ASCE 7-16) Wind design of ground-mounted solar arrays or other facilities with large horizontal extent and numerous repetitive structures shall include consideration of vortex shedding and consequent dynamic resonant effects, if applicable, in the determination of design wind loads. The ASCE 7-16 definition of “rigid structure” based on the frequency of 1 Hz shall not be taken to apply to such arrays. The prescriptive calculations of the gust July 2017 Page 19

STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA effect factor specified in ASCE 7-16 shall not be taken to account for dynamic resonant effects for such arrays. Commentary: The ASCE 7-16 definition of “rigid structure” based on the frequency of 1 Hz is not necessarily appropriate for large solar arrays because the repetitive geometry of the array can cause vortex shedding at frequencies greater than 1 Hz. ASCE 7-16 Commentary (excerpted above) identifies vortex shedding as an issue in Limitation #3, but the details of this limitation focus on tall buildings or similar structures. To clarify that vortex shedding can also be significant for groundmounted solar arrays, we recommend modifying ASCE 7-16 Commentary Section C26.1.2 as follows: 1) Modify the text of Limitation #3 as follows: Buildings or other structures with response characteristics that result in substantial vortex-induced and/or torsional dynamic effects, or dynamic effects resulting from aeroelastic instabilities such as flutter or galloping. Such dynamic effects are difficult to anticipate, being dependent on many factors but. For tall buildings or similar structures, dynamic effects should be considered when any one or more of the following apply… 2) Add the following Limitation #5: Ground-mounted solar arrays or other facilities with large horizontal extent and numerous repetitive structures. Such structures can be subject to vortex shedding and consequent dynamic resonance effects. The high-frequency turbulent energy is generated by vortices shed from the repetitive upwind structures, rather than coming from gust energy inherent in the wind as is the case for isolated structures. The resulting buffeting can introduce dynamic resonance effects which are most pronounced when the reduced natural frequency of the structures St is between 0.05 and 0.20, where St = n1L/U, where U is the hourly mean wind speed at the mean height of the panels, L is the vertical projected height and/or width, and n1 is the natural frequency. (27).

Wind Design for Solar Arrays Report SEAOC PV2-2017

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA 9. References (1) American Society of Civil Engineers, “Minimum design loads for buildings and other structures.” ASCE7-05, 2006. (2) American Society of Civil Engineers, “Minimum design loads for buildings and other structures.” ASCE7-10, 2010. (3) American Society of Civil Engineers, “Minimum design loads and associated criteria for buildings and other structures.” ASCE 7-16, 2017. (4) American Society of Civil Engineers, “Wind Tunnel Testing for Buildings and Other Structures.” ASCE 49-12, 2012. (5) Banks, D., Meroney, R.M. A model of roof-top surface pressures produced by conical vortices: Model development, Wind and Structures, Vol. 4, No. 2, 2001. (6) Banks, D, “Measuring Peak Wind Loads on Solar Power Assemblies”, Proceedings of the 13th International Conference on Wind Engineering, Amsterdam, Netherlands, 2011. (7) Banks, D. “The role of corner vortices in dictating peak wind loads on tilted flat solar panels mounted on large, flat roofs.” Journal of Wind Engineering & Industrial Aerodynamics, vol 123, 192-201, 2013. (8) Banks, D., “Wind loads on tilted flat panels on commercial roofs: The effects of corner vortices”, Advances in Hurricane Engineering, ed. C.P. Jones and L.G. Griffiths, ASCE, October 2012. (9) Browne, M, Gibbons, M., Gamble, S, Galsworthy, J., Wind loading on tilted roof-top solar arrays: The parapet effect, Journal of Wind Engineering and Industrial Aerodynamics, vol. 123, 202-213, 2013. (10) Cochran, L., Peterka, J. Derickson, R, Roof Surface Wind Speed Distributions in Low-rise Buildings, Architectural Science Review, Vol 42, 1999. (11) Dyrbye, C., Hansen, S., Wind Loads on Structures, Wiley & Sons, Chichester, England, 1997. (12) International Code Council Evaluation Service AC 428 “Acceptance Criteria for Modular Framing Systems Used to Support Photovoltaic (PV) Modules.” ICC-ES AC 428, 2011

(16) Kopp, G., Banks, D. “Use of the Wind Tunnel Test Method for Obtaining Design Wind Loads on Roof-Mounted Solar Arrays”, Journal of Structural Engineering, 2012 (17) Kopp, G.A., 2013, Wind loads on low profile, tilted, solar arrays placed on large, flat, low-rise building roofs, Journal of Structural Engineering, doi: 10.1061/(ASCE)ST.1943541X.0000821. (18) Kray, T. Peak net pressure coefficients on roof-parallel photovoltaic arrays mounted on a low-rise, 10° gable roof, Proceedings of the 14th International Conference on Wind Engineering, Porto Alegre, Brazil, 2015. (19) Maffei, J., Telleen, K., Ward, R., Kopp, G.A., and Schellenberg, A. “Wind design practice and recommendations for solar arrays on low-slope roofs.” Journal of Structural Engineering, vol. 140, Issue 2, February 2014 (20) Mooneghi, M.A., Irwin, P., Chowdhury, A.G., “Partial Turbulence Simulation Method for Small Structures”, Proceedings of the 14th International Conference on Wind Engineering, Porto Alegre, Brazil, 2015. (21) National Fire Protection Association, 2011 National Electrical Code, NFPA 70, 2011 (22) O’Brien, C., Banks, D. “Wind Load Analysis for Commercial Roof-Mounted Arrays”, SolarPro Magazine, 2012 (23) Pratt and Kopp, 2013, Velocity measurements around lowprofile, tilted, solar arrays mounted on large flat-roofs, for wall normal wind directions, Journal of Wind Engineering and Industrial Aerodynamics, vol 123, 226-238, 2013. (24) Richards, P., Hoxey, R.P., Connell, B.D., Lander, D.P., “Windtunnel modelling of the Silsoe Cube,” Journal of Wind Engineering and Industrial Aerodynamics, 95(9-11), pp. 13841399. 2007. (25) Richards, P.C., Mooneghi, M.A., Chowdhury, A.G., “Combining Directionally Narrow Band Wind Loading Data in order to Match Wide Band Full-Scale Situations”, Proceedings of the 14th International Conference on Wind Engineering, Porto Alegre, Brazil, 2015.

(13) International Code Council, International Building Code, IBC, 2012.

(26) Stenabaugh, S.E., Iida, Y., Kopp, G.A. & Karava, P, Wind loads on photovoltaic arrays mounted on sloped roofs of low-rise buildings, parallel to the roof surface, Journal of Wind Engineering and Industrial Aerodynamics. vol 139, 16-26, 2015.

(14) Kopp, G., Maffei, J., Tilley, C. “Rooftop Solar Arrays and Wind Loading: A Primer on Using Wind Tunnel Testing as a Basis for Code Compliant Design per ASCE 7”, Boundary Layer Wind Tunnel Laboratory, The University of Western Ontario, Faculty of Engineering, 2011

(27) Strobel, K., Banks, D., Effects of Vortex Shedding in Arrays of Long Inclined Flat Plates and Ramifications for GroundMounted Photovoltaic Array, Proceedings of the 12th Americas Conference on Wind Engineering 2013 (12ACWE): Seattle, June 2013.

(15) Kopp, G.A., Farquhar, S. & Morrison, M.J., Aerodynamic mechanisms for wind loads on tilted, roof-mounted, solar arrays, Journal of Wind Engineering and Industrial Aerodynamics, vol. 111, pp. 40-52. 2012

(28) Structural Engineers Association of Washington, SEAW Commentary on Wind Code Provisions, SEAW/ATC 60, 2004

Wind Design for Solar Arrays Report SEAOC PV2-2017

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA

Example Problems The following examples illustrate the application of selected aspects of the SEAOC PV2-2017 design provisions. Each example is independent of the other examples, unless stated otherwise. Each example is intended to address a specific aspect of the provisions. The examples do not address every aspect of design of solar PV arrays. The examples refer to the 2016 edition of ASCE 7 (ASCE 7-16), unless stated otherwise. To the extent practical, the examples provide solutions based on ASCE 7 provisions, as well as solutions based on supplementary provisions of SEAOC PV2 that are not included in ASCE 7-16. Consistent with the recommendations of SEAOC PV2, for solar arrays designed per ASCE 7-16 Section 29.4.3 and 29.4.4, these examples do not apply the minimum net pressure of 16 psf from ASCE 7 Components and Cladding provisions. A. Roof wind zones

Solution (i) ASCE 7-16: Using Figure 29.4-7, Roof Wind Zones 3, 2, and 1 can be identified. The width of roof edge zones and corner zones is calculated as: 2h = 2 (10 ft) = 20 ft Figure A2(a) shows the roof wind zones per ASCE 7-16. Solution (ii) SEAOC PV2-2017: SEAOC PV2-2017 defines the same roof wind zones as ASCE 7-16, except that SEAOC PV2-2017 Figure 1 provides for the additional Zone 1’, where design wind pressure may be lower. The distance from the edge of the building to Zone 1’ is calculated as: 5h = 5 (10 ft) = 50 ft Figure A2(b) shows the roof wind zones per SEAOC PV22017.

Given: A solar array is to be placed on the flat roof of a building with plan dimensions shown in Figure A1. The mean roof height, h, of the building is 10 feet. The array will be low-profile, with dimensions such that ASCE 7-16 Section 29.4.3 is applicable (Lp ≤ 6.7 ft, ω ≤ 35 degrees, h1 ≤ 2 ft, h2 ≤ 4 ft, etc.). The array consists of rows of tilted panels.

Figure A1: Plan dimensions of an example building. Problem: Identify the roof wind zones for rooftop solar arrays for the building shown in Figure A1 using (i) ASCE 7-16 and (ii) SEAOC PV2-2017. Wind Design for Solar Arrays Report SEAOC PV2-2017

Figure A2: Roof wind zones. (a) Per ASCE 7-16. (b) Including Zone 1’ per SEAOC PV2-2017. July 2017 Page 22

STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA Discussion: While ASCE 7-16 Figure 29.4-7 shows roof wind zones for a rectangular building, ASCE 7-16 Commentary and SEAOC PV2-2017 Figure 1 provide guidance for buildings with other plan shapes, as used in the solution to this problem. When selecting location(s) on a building roof to position a solar array, identifying the roof wind zones can help identify where the array will be most economical from a wind design standpoint. B. Normalized wind area (An) Given: A solar array is to be placed on the flat roof of a building with plan dimensions shown in Figure A1. The mean roof height, h, of the building is 12 feet. The array will be low-profile, with dimensions such that ASCE 7-16 Section 29.4.3 is applicable (Lp ≤ 6.7 ft, ω ≤ 35 degrees, h1 ≤ 2 ft, h2 ≤ 4 ft, etc.). The array consists of rows of tilted panels. The area of one 39 inch x 66 inch module is 17.9 ft2. Problem: Determine the normalized wind area, An, for a structural element whose effective wind area A is equal to the area of one module. Solution: The normalized wind area, An, is determined by the equations in ASCE 7-16 Section 29.4.3. Using Figure A1 and a building height, h, of 12 feet, 1000 � 𝐴𝐴 [max(𝐿𝐿𝑏𝑏 , 15𝑓𝑓𝑓𝑓)]2 𝐿𝐿𝑏𝑏 = min(0.4(ℎ × 𝑊𝑊𝐿𝐿 )0.5 , ℎ, 𝑊𝑊𝑠𝑠 ) 𝐿𝐿𝑏𝑏 = min(0.4(12𝑓𝑓𝑓𝑓 × 273𝑓𝑓𝑓𝑓)0.5 , 12𝑓𝑓𝑓𝑓, 205𝑓𝑓𝑓𝑓) 𝐿𝐿𝑏𝑏 = min(23𝑓𝑓𝑓𝑓, 12𝑓𝑓𝑓𝑓, 205𝑓𝑓𝑓𝑓) 𝐿𝐿𝑏𝑏 = 12ft 1000 𝐴𝐴𝑛𝑛 = � � 17.9𝑓𝑓𝑓𝑓 2 [max(12𝑓𝑓𝑓𝑓, 15𝑓𝑓𝑓𝑓)]2 𝐴𝐴𝑛𝑛 = 79.6

𝐴𝐴𝑛𝑛 = �

Discussion: An is used to determine the Nominal Net Pressure Coefficient, (GCrn)nom for design of structural element(s) having effective wind area A, as discussed in subsequent examples. An is nondimensional because it is normalized to account for the effect that the size of the building can have on wind pressure on rooftop solar arrays. As shown in this example, a structural element with effective wind area 17.9 ft2 can have greater An (resulting in lesser wind pressure) if the array is located on a building with small height and/or small plan dimensions, or it can have smaller An (resulting in greater wind pressure) if the array is located on a building with large height and large plan dimensions. Wind Design for Solar Arrays Report SEAOC PV2-2017

In this example, An is calculated based on the worst case (longest building side) for the building, per ASCE 7-16. In some cases, SEAOC PV2 Section 4.3.2 allows calculation of An considering the length of the building side at each corner individually, which may result in reduced wind pressure. C. Nominal net pressure coefficient ((GCrn)nom) Given: A solar array is to be placed on the flat roof of a building. The array will be low-profile, with dimensions such that ASCE 7-16 Section 29.4.3 is applicable (Lp ≤ 6.7 ft, ω ≤ 35 degrees, h1 ≤ 2 ft, h2 ≤ 4 ft, etc.). The array consists of rows of tilted panels. The area of one 39 inch x 66 inch module is 17.9 ft2. Testing or analysis of the solar panel support system demonstrates that effective wind area, A, for a ballast on the corner of an array to resist uplift is equal to the area of one module. Based on that effective wind area and the building dimensions, the normalized wind area, An, for that ballast has been calculated as 79.6. The angle between the roof and solar panel, ω, is 7 degrees. Problem: Determine the Nominal Net Pressure Coefficient, (GCrn)nom for design of the weight of a ballast on the corner of an array in Zone 3, Zone 2, Zone 1 and Zone 1’. Solution: Because the tilt angle of the panels, ω, is between 5 and 15 degrees, it is necessary to interpolate between graphs for (0 ≤ ω ≤ 5) and (15 ≤ ω ≤ 35) in ASCE 7-16 Figure 29.4-7 for Roof Zones 3, 2, 1, and SEAOC PV2-2017 Figure 2 for Zone 1’. First, we determine (GCrn)nom for the 0-5 degree graph and the 15-35 degree graph. To aid in the calculation of (GCrn)nom from these graphs, Tables C1 and C2 provide numeric expressions for the lines plotted in the graphs. Tables C3 and C4 calculate (GCrn)nom corresponding to An = 79.6 and A = 17.9 ft2. The last column of Tables C3 and C4 calculates (GCrn)nom for ω = 7 degrees by interpolating between the values from the graphs. Discussion: As shown in the last column of Tables C3 and C4, for a given normalized wind area, the Nominal Net Pressure Coefficient, (GCrn)nom (and consequently the design wind pressure) is greatest near the edges and corners of the roof (Zones 2 and 3) and less in the center of the roof (Zone 1). Pressure coefficients are affected by building dimensions in Zones 1, 2, and 3, but not in Zone 1’. For this reason, effective wind area, A, is the input for calculating pressure coefficients in Zone 1’ (SEAOC PV2-2017 Figure 2), whereas normalized wind area An is the input for calculating pressure coefficients in Zones 1, 2, and 3 (ASCE 7-16 Figure 29.4-7).

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA Table C3: Calculation of (GCrn)nom for An = 79.6 and ω = 7 degrees Roof Wind Zone 0˚≤ω≤5˚ 15˚≤ω≤35˚ ω=7˚ (interpolation) Zone 3 1.03 1.60 1.14 Zone 2 0.91 1.31 0.99 Zone 1 0.69 0.98 0.75

Table C4: Calculation of (GCrn)nom for A = 17.9 ft2 and ω = 7 degrees Roof Wind Zone 0˚≤ω≤5˚ 15˚≤ω≤35˚ ω=7˚ (interpolation) Zone 1’ 0.56 0.81 0.61

Table C1: Equations for (𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟 )𝑛𝑛𝑛𝑛𝑛𝑛 graphed in ASCE 7-16 Figure 29.4-7 Roof Wind Zone 𝜔𝜔 𝐴𝐴𝑛𝑛 3 2 0° to 5° ≤ 500 −0.6669log10 (𝐴𝐴𝑛𝑛 ) + 2.300 −0.5743log10 (𝐴𝐴𝑛𝑛 ) + 2.000 0° to 5° > 500 −0.3500log10 (𝐴𝐴𝑛𝑛 ) + 1.445 −0.3000log10 (𝐴𝐴𝑛𝑛 ) + 1.260 15° to 35° ≤ 500 −1.0004log10 (𝐴𝐴𝑛𝑛 ) + 3.500 −0.8337log10 (𝐴𝐴𝑛𝑛 ) + 2.900 15° to 35° > 500 −0.3000log10 (𝐴𝐴𝑛𝑛 ) + 1.610 −0.2500log10 (𝐴𝐴𝑛𝑛 ) + 1.325 Table C2: Equations for (𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟 )𝑛𝑛𝑛𝑛𝑛𝑛 graphed in Figure 2 𝜔𝜔

0° to 5° 0° to 5° 15° to 35° 15° to 35°

A (ft2)

Roof Wind Zone

≤ 5000 > 5000 ≤ 5000 > 5000

D. Parapet factor (γP) Given: A solar array is to be placed on the flat roof of a building. The array will be low-profile, with dimensions such that ASCE 7-16 Section 29.4.3 is applicable (Lp ≤ 6.7 ft, ω ≤ 35 degrees, h1 ≤ 2 ft, h2 ≤ 4 ft, etc.). The array consists of rows of tilted panels. The mean roof height, h, is 12 feet and the parapet height, hpt, is 2 feet. Problem: Determine the Parapet Height Factor, γp, from ASCE 7-16 Section 29.4.3. Solution: 𝛾𝛾𝑝𝑝 = min(1.2, 0.9 + ℎ𝑝𝑝𝑝𝑝 /ℎ) 𝛾𝛾𝑝𝑝 = min(1.2, 0.9 + 2𝑓𝑓𝑓𝑓/12𝑓𝑓𝑓𝑓) 𝛾𝛾𝑝𝑝 = min(1.2, 1.07) 𝛾𝛾𝑝𝑝 = 1.07

Wind Design for Solar Arrays Report SEAOC PV2-2017

1 −0.4261log10 (𝐴𝐴𝑛𝑛 ) + 1.500 −0.2500log10 (𝐴𝐴𝑛𝑛 ) + 1.025 −0.5372log10 (𝐴𝐴𝑛𝑛 ) + 2.000 −0.2500log10 (𝐴𝐴𝑛𝑛 ) + 1.225

E. Chord factor (γC)

1’ −0.1892log10 (A) + 0.800 0.10 −0.2298log10 (𝐴𝐴) + 1.100 0.25

Given: A solar array is to be placed on the flat roof of a building. The array will be low-profile, with dimensions such that ASCE 7-16 Section 29.4.3 is applicable (Lp ≤ 6.7 ft, ω ≤ 35 degrees, h1 ≤ 2 ft, h2 ≤ 4 ft, etc.) The array consists of rows of tilted panels. Each module has dimensions of 39 in x 78 in (3.25 ft x 6.5 ft). Problem: Determine the Panel Chord Factor, γc, assuming that the modules are in (i) portrait orientation, and (ii) landscape orientation. Solution (i) Portrait: 𝛾𝛾𝑐𝑐 = max(0.6 + 0.06 𝐿𝐿𝑝𝑝 , 0.8) 𝛾𝛾𝑐𝑐 = max(0.6 + 0.06 × 6.5𝑓𝑓𝑓𝑓, 0.8) 𝛾𝛾𝑐𝑐 = max(0.99, 0.8) 𝛾𝛾𝑐𝑐 = 0.99

Solution (ii) Landscape: 𝛾𝛾𝑐𝑐 = max(0.6 + 0.06 𝐿𝐿𝑝𝑝 , 0.8) 𝛾𝛾𝑐𝑐 = max(0.6 + 0.06 × 3.25𝑓𝑓𝑓𝑓, 0.8) 𝛾𝛾𝑐𝑐 = max(0.8, 0.8) 𝛾𝛾𝑐𝑐 = 0.8

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA Discussion: For the provisions of SEAOC PV2 and ASCE 7-16 Figure 29.4-7 to be applicable, the panel chord length must be less than or equal to 6.7 ft (2.04 m). As shown in this example, arrays with longer chord length (such as rows of modules in portrait orientation), have greater Panel Chord Factor (and consequently greater design wind pressure) than arrays with shorter chord length (such as modules in landscape orientation). F. Edge factor (γE) Given: A solar array is to be placed on the flat roof of a building. The array will be low-profile, with dimensions such that ASCE 7-16 Section 29.4.3 is applicable (Lp ≤ 6.7 ft, ω ≤ 35 degrees, h1 ≤ 2 ft, h2 ≤ 4 ft, etc.). The array consists of rows of tilted panels. Modules are 39 in x 78 in (3.25 ft x 6.5 ft). At the upper edge of each tilted panel, the top of the panel is 10 inches (h2) above the roof, and the mean roof height, h, is 12 feet. Problem: Determine the Edge Factor, γE, for each module in the array shown in Figure F1. Solution: Per ASCE 7-16 Section 29.4.3, γE = 1.5 for a given panel if, in any plan direction: •

The distance (d1) from the panel to the roof edge is greater than 0.5h = 0.5(12 ft) = 6 ft

and • The distance (d1 or d2) to the roof edge or the next array or panel is greater than max(4h2, 4 ft) = max(4(10 in), 4 ft) = 4 ft.

For other panels, γE = 1.0. In cases where, γE = 1.5 applies at the end of a row of modules, γE = 1.5 applies over a distance 1.5 times the panel chord length, Lp: 1.5𝐿𝐿𝑃𝑃 = 1.5 × 6.5𝑓𝑓𝑓𝑓 = 9.75𝑓𝑓𝑓𝑓 (Portrait Orientation) 1.5𝐿𝐿𝑃𝑃 = 1.5 × 3.25𝑓𝑓𝑓𝑓 = 4.88𝑓𝑓𝑓𝑓 (Landscape Orientation)

For the example arrays in Figure F1, modules are in portrait orientation. Figure F1 shows the edge factor for each module.

Figure F1: Plan dimensions of an example building and array, with edge factor γE indicated by gray shading. Discussion: Whereas ASCE 7-16 defines the edge factor as a step function (either 1.0 or 1.5), SEAOC PV2-2017 Section 4.3.3 provides an optional more detailed approach in which the edge factor varies linearly between 1.0 and 1.5 as a function of distance to the next array or panel. Table F1 shows how the edge factor varies for several example values of row spacing, using the SEAOC PV2 optional approach. Table F1: Edge factors using interpolation per SEAOC PV2 Section 4.3.3. h2 (in) d2/h2 d2 (in) γE 2 20 1 4 40 1.2 10 6 60 1.3 8 80 1.5 G. Effective wind area (A) and design wind pressure (p) Given: A solar array is to be located on a building with low-slope roof. The array will be low-profile, with dimensions such that ASCE 7-16 Section 29.4.3 is applicable (Lp ≤ 6.7 ft, ω ≤ 35 degrees, h1 ≤ 2 ft, h2 ≤ 4 ft, etc.).

Wind Design for Solar Arrays Report SEAOC PV2-2017

July 2017 Page 25

STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA The velocity pressure qh at the mean roof height of the building is 23.7 psf (based on V = 110 mph, Exposure Category C, Kzt = 1.0, Kd = 0.85, Ke = 1.0). The mean roof height of the building is 20 ft. The mean parapet height above the adjacent roof surface is 2 ft. The width of the building on its longest side is 182 ft. The width of the building on its shortest side is 160 ft. The array will be in Roof Wind Zone 1. Modules are 39”x66” in landscape orientation. The panel tilt-angle is 5 degrees. The location of the array on the building, location of the array relative to other arrays, and row spacing of the array are such that the edge factor γE = 1.5 for modules on the perimeter of the array, and γE = 1.0 for modules on the interior of the array. Problem: Calculate the design wind pressure p for elements having each of the following effective wind areas A: (i) ¼ module (ii) ½ module (iii) 1 module (iv) 1.5 modules (v) 2 modules (vi) 4 modules (vii) 6 modules (viii) 9 modules (ix) 36 modules Solution: γp = min[1.2, 0.9 + hpt/h] = min[1.2, 0.9 + 2/20] = 1.0 γc = max[0.6 + 0.06Lp, 0.8] = max[0.6 + 0.06(40/12)] = 0.8 Lb = min[0.4√(hWL),h,WS] = min[0.4√(20)(182),20,160] = 20ft An/A = 1000/max[Lb, 15]2 = 1000/max[20, 15]2 = 2.5 Area of one module = (39)(66)/144 = 17.9 ft2 An = (An/A)A

= (An/A)(Area of one module)(# of modules) = (2.5)(17.9)(# of modules)

From ASCE 7-16 Figure 29.4-7 (or the equations in Table C1 of these examples), for 5-degree panel tilt, (GCrn)nom = 1.5 – 0.4261[log10(An)] (GCrn)nom = 1.025 – 0.25[log10(An)]

for An ≤ 500 for An > 500

Per SEAOC PV2 Section 4.2.1, design wind pressure calculated in accordance with ASCE 7-16 Section 29.4.3 shall not be taken less than the design wind pressure calculated using the pressure coefficients in Figure 2. From Figure 2 (or the equations in Table C2 of these examples), for 5-degree panel tilt, (GCrn)nom = 0.8 – 0.1892 [log10(A)] (GCrn)nom = 0.1

for A ≤ 5000 ft2 for A > 5000 ft2

Table G1 calculates An, (GCrn)nom, (GCrn), and p for each value of effective wind area A specified in the problem statement, and for each edge condition (pinterior for γE = 1.0, and pedge for γE = 1.5). Table G1 (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) A (modules)* ¼ 1/2 1 1.5 2 4 6 9 36 A (ft2) 4.5 8.9 17.9 26.8 35.8 71.5 107 161 644 An 11.2 22.3 44.7 67.0 89.4 179 268 402 1610 (GCrn)nom 1.05 0.93 0.80 0.72 0.67 0.54 0.47 0.39 0.27 (GCrn)int 0.84 0.74 0.64 0.58 0.53 0.43 0.37 0.31 0.22 (GCrn)edge 1.26 1.11 0.96 0.87 0.80 0.65 0.56 0.47 0.32 pinterior (psf) 20 18 15 14 13 10 8.8 7.4 5.2 pedge (psf) 30 26 23 21 19 15 13 11 7.6 * Effective wind area values listed in this example are not appropriate for all systems nor all limit states. See discussion below for applicability of assumptions for effective wind area A to limit states (uplift, downward force, or sliding). Discussion: As shown in Table G1, design wind pressure is greater for elements with small effective wind area; pressure is less for elements with large effective wind area. For example, an effective wind area of ¼ of a module may be appropriate for designing fasteners that attach modules to the racking system. Larger effective wind area may be appropriate for checking other elements of the array. Effective wind area depends on the structural characteristics of the solar panel support system, and the limit state under consideration. For checking the capacity of a 6-module by 6module array to resist sliding, an effective wind area of 36 modules may be appropriate if the array is adequately interconnected such that all modules would slide as a unit. For checking the same 6-module by 6-module array to resist uplift, smaller effective wind area is typically appropriate. Uplift resistance requires consideration of multiple load cases, such as the case where an edge row could be subject to lifting and flipping over, for example. For most interconnected arrays, the appropriate effective wind area for uplift is less for load cases with wind pressure at the edges of the array, compared to load cases with uplift at the interior of the array. This is because: • edges of arrays tend to be more flexible (easier to peel up) than interior portions of arrays, and • wind pressure demands on the edges of arrays tend to be more sensitive to uplift movement than modules on the interior of the array.

(GCrn) = (γp)( γc)( γE)(GCrn)nom = (1.0)(0.8)(γE)(GCrn)nom p = qh(GCrn) = (23.7)(GCrn) Wind Design for Solar Arrays Report SEAOC PV2-2017

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA For these reasons (in addition to the aerodynamic edge effect γE), greater ballast weight and/or attachments are often required around the edges of an array than at the array interior. Systems with stiffer and stronger structural elements can engage multiple ballasts or attachments to resist concentrated wind uplift pressure, resulting in greater effective wind area and less ballast and attachments than flexible systems. H. Design of an unattached (ballast-only) array to resist uplift Given: A 6-module by 6-module low-profile solar array is to be located on a building with flat roof. Wind loads on the array are resisted by self-weight of the array and ballast. Ballasts are located at each corner of each module, such that a ballast at the corner of the array connects to one module, ballasts around the edges of the array connect to two modules each, and other ballasts connect to four modules each. The array is not attached to the building structure. Each module is fastened to the solar panel support system with four fasteners, one near each corner of the module. (Fasteners are not shared between modules.) The area of each module is 17.9 sf. Each module weighs 41 lbs. The self-weight of the racking system (excluding modules and ballast) is 19 lbs per module. The panel tilt-angle is 5 degrees. Testing or analysis of the solar panel support system demonstrates that effective wind area to resist uplift is as follows: • Fasteners of modules to racking: ¼ module • Ballast at corner of array: 1 module • Ballast at edge of array: 1.5 modules • 2nd row of ballast: 4 modules • Ballast at interior of array: 6 modules The design wind pressure p has been calculated for each of the effective wind areas listed above, as shown in Table H1. Table H1 A (modules) pinterior (psf) pedge (psf)

¼ 20 30

1 1.5 15 14 23 21

4 6 10 8.8 15 13

Problem: (i) Calculate the design wind force (perpendicular to the plane of the module) on one fastener. (ii) Design the weight of a ballast at a corner of the array. (iii) Design the weight of a ballast at an edge of the array.

Wind Design for Solar Arrays Report SEAOC PV2-2017

(iv) Design the weight of a ballast in the second row from the edge of the array. (v) Design the weight of a ballast at the interior of the array. (vi) Calculate the total ballast weight for the array based on the designs from (ii) through (v). Solution: (i) For effective wind area of ¼ module, the design wind pressure is 20 psf for modules on the interior of the array, and 30 psf for modules on the perimeter of the array. Assuming that the same fastener design will be applied to all modules, design for the worst of these cases, 30 psf. The tributary area of one fastener is ¼ of one module. The design wind force on a fastener is W = pedge(Tributary Area) = (30)(1/4)(17.9) = 134 lb. (ii) For effective wind area of 1 module, the design wind pressure is 15 psf for modules on the interior of the array, and 23 psf for modules on the perimeter of the array. The tributary area to a corner ballast is ¼ of one module. All of the tributary area to the corner ballast is on a perimeter module, so the design wind pressure is 23 psf. The design wind uplift force is Fvert

= Wcos(ω) = pedge(Tributary Area)cos(5°) = (23)(1/4)(17.9)(0.996) = 103 lb.

To resist uplift, the ballast weight must be greater than the wind uplift force, minus the tributary weight of modules and self-weight of the racking system. Using allowable stress design per the load combinations of ASCE 7-16 Section 2.4.1(7), and solving for ballast weight: Ballast weight > Fvert – (module weight)(# of tributary modules) – (racking weight per module)(# of tributary modules) > 103 – (19)(1/4) – (41)(1/4) > 88 lb. (iii) For effective wind area of 1.5 modules, the design wind pressure is 14 psf for modules on the interior of the array, and 21 psf for modules on the perimeter of the array. The tributary area to an edge ballast is ½ of one module. All of the tributary area to the edge ballast is on a perimeter module, so the design wind pressure is 21 psf. The design wind uplift force is Fvert

= Wcos(ω) = pedge(Tributary Area)cos(5°) = (21)(1/2)(17.9)(0.996) = 187 lb.

Ballast weight > Fvert – (module weight)(# of tributary modules) – (racking weight per module)(# of tributary modules)

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA > 187 – (19)(1/2) – (41)(1/2) > 157 lb. (iv) For effective wind area of 4 modules, the design wind pressure is 10 psf for modules on the interior of the array, and 15 psf for modules on the perimeter of the array. The tributary area to a ballast in the second row from the edge of the array is one module. Half of this tributary area is on perimeter modules, and half is on interior modules. The design wind uplift force is Fvert

= Wcos(ω) = [pinterior(1/2) + pedge(1/2)](Tributary Area)cos(5°) = [(10)(1/2) + 15(1/2)](1)(17.9)(0.996) = 223 lb.

Ballast weight > Fvert – (module weight)(# of tributary modules) – (racking weight per module)(# of tributary modules) > 223 – (19)(1) – (41)(1) > 163 lb. For the ballast in the second row from the corner of the array, ¾ of the tributary area is on perimeter modules, and ¼ is on an interior module. Performing similar calculations as above, the ballast weight for this location is > 185 lb. (v) For effective wind area of 6 modules, the design wind pressure is 8.8 psf for modules on the interior of the array, and 13 psf for modules on the perimeter of the array. The tributary area to an interior ballast is one module. All of the tributary area to the interior ballast is on an interior module, so the design wind pressure is 8.8 psf. The design wind uplift force is Fvert

= Wcos(ω) = pinterior(Tributary Area)cos(5°) = (8.8)(1)(17.9)(0.996) = 157 lb.

because they have greater wind pressure (smaller effective wind area, and greater aerodynamic edge effects). Effective wind area values in the problem statement are for illustration only. As discussed in the effective wind area problem, these example values are not necessarily applicable to all arrays. For wind design methodologies that are based on assigning an effective wind area to structural elements of the array, such as the approach used in this example, the effective wind area values must be validated by analysis and/or testing of the structural behavior of the racking system and consideration of what uplift displacement (if any) is acceptable under the design wind pressure (or other wind load levels of interest). For example, uplift displacement exceeding a certain threshold may change the aerodynamics of the system, which may change the wind loads. The solution demonstrated in this example is not the only valid approach. An alternative, and perhaps more direct, approach would be to apply load cases with wind “gusts” of various sizes (1 module, 2 modules, 4 modules, etc.) and to check that for each case the array has adequate ballast and interconnection strength to resist the pressure. The solution above uses allowable stress design load combination (7) from ASCE 7-16 Section 2.4.1 to determine ballast requirements. This load combination applies a load factor of 0.6 for dead load and 0.6 for wind, so the 0.6 cancels in the calculation of total ballast weight required. This calculation could also be performed using the strength design load combination (5) of ASCE 7-16 Section 2.3.1. Solar designers typically choose to use the allowable stress design load combination in this case because the strength design load combination applies a load factor of 0.9 for dead load and 1.0 for wind, resulting in slightly greater ballast requirements.

Ballast weight > Fvert – (module weight)(# of tributary modules) – (racking weight per module)(# of tributary modules) > 157 – (19)(1) – (41)(1) > 97 lb. (vi) The total ballast weight for the array is Total ballast weight > 4(88) + 20(157) + 12(163) + 4(185) + 9(97) = 7061 lb. Discussion: As shown in this example, tributary area is less than or equal to effective wind area. While ballasts near the perimeter of the array have smaller tributary area than ballasts at the interior of the array, perimeter ballasts tend to require greater weight

Wind Design for Solar Arrays Report SEAOC PV2-2017

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA I. Design of an unattached (ballast-only) array to resist sliding Given: A 6-module by 6-module low-profile solar array is to be located on a building with flat roof. Wind loads on the array are resisted by self-weight of the array and ballast. Ballasts are located at each corner of each module. The array is not attached to the building structure. The coefficient of friction µ between the array and the roof surface is 0.4. The area of each module is 17.9 sf. Each module weighs 41 lbs. The self-weight of the racking system (excluding modules and ballast) is 19 lbs per module. The panel tilt-angle is 5 degrees.

stress design per the load combinations of ASCE 7-16 Section 2.4.1(7), and solving for ballast weight: Total ballast weight > Fhoriz/µ + Fvert – (module weight)(# of modules) – (racking weight per module)(# of modules) > 320/0.4 + 3652 – 41(36) – 19(36) > 2292 lb.* * Providing adequate ballast to resist sliding does not necessarily provide adequate resistance for other limit states, such as uplift, which must be checked separately. See discussion.

Tests and/or calculations have shown that the array is adequately interconnected such that, if the friction between the array and the roof surface is exceeded, all modules would slide as a unit. For an effective wind area A equal to the area of the entire array (36 modules), the design wind pressure p has been calculated as 5.2 psf for modules on the interior of the array, and 7.6 psf for modules on the perimeter of the array.

Discussion: The total ballast weight calculated above averages to 64 lb per module in the 36-module array. For most arrays, the total ballast weight to resist sliding, as calculated in this example, will be less than the sum of the individual ballast weights required to resist uplift of smaller portions of the array. Each limit state must be checked, and the ballast design must be adequate for each.

Problem: Calculate the total ballast weight for the array that is required to resist sliding from wind.

See the wind uplift example problem for discussion of allowable stress design vs. strength design load combinations.

Solution: The horizontal component of the wind pressure acting on modules is p[sin(5 degrees)]. The vertical component is p[cos(5 degrees)]. In the 36-module array, 16 modules are on the perimeter of the array, and 16 modules are on the interior of the array. (As discussed in Section 5.3.1, applying edge factors to more than one edge at a time is conservative, but we do so in this example for simplicity.) The wind uplift force on the array is = [(# of interior modules)pinterior + (# of perimeter Fvert modules)pedge][Area of one module][cos(5°)] = [(16)5.2 + (16)7.6][17.9][0.996] = 3652 lb. The wind horizontal force on the array is = [(# of interior modules)pinterior + (# of perimeter Fhoriz modules)pedge][Area of one module][sin(5°)] = [(16)5.2 + (16)7.6][17.9][0.087] = 320 lb. To resist sliding (by friction), the total weight of the array (including ballast, modules, and self-weight of the racking system) must be such that the normal force (total weight minus wind uplift) multiplied by the coefficient of friction is greater than the horizontal force from wind. Using allowable Wind Design for Solar Arrays Report SEAOC PV2-2017

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA J. Parallel-to-roof (flush-mounted) modules Given: A proposed PV array is to be secured to a metal standing seam roof using extruded aluminum external seam clamps (See Figure J1a). The seams of the roof are spaced at 24 inches on center. The roof slope is ¼ in. per ft. The PV modules will be parallel to the roof surface. The distance between the flat part of the roof deck and the top surface of the PV module is to be 5 in. The PV modules are 39 in. wide and 66 in. long. The long dimension of the PV modules will run perpendicular to the deck ribs. Three clamps will be used to secure each long edge of the PV module to the roof deck ribs as shown in Fig. J1b. The horizontal space between modules will be 6 in. in their longitudinal direction and 1 in. in the opposite direction. A minimum of 800 modules must be installed to provide the required electrical output. The building is just slightly above sea level.

Other details are as follows: h = 33 ft, Wind Exposure Category C, Kz = 1.0 WL = 246 ft WS = 140 ft V = 110 mph, Risk Category II per ASCE 7-16 Kzt = 1.0 Kd = 0.85 per ASCE 7-16 Table 26.6-1 Ke = 1.0 per ASCE 7-16 Table 26.9-1 Clamps must be installed at each deck rib in order to follow the wind load path of the standing seam roof to which the PV modules are secured. The wind load path goes from the deck ribs to an internal clip, then through self-drilling screws securing the internal clips into the top flange of steel purlins. The fire department requires a minimum 6 ft. wide aisle every 100 ft. Problem: Determine the roof wind zones for parallel-to-roof (flushmounted) solar arrays. Determine the design wind uplift pressure in each zone for design of the external seam clamps that attach the modules to the roof. Propose a location for the array on the roof that satisfies the constraints described above while minimizing the wind loads on the array. Solution: STEP 1: ASCE 7-16 Section 29.4.4 applies because the PV modules are parallel to the roof surface, are within 10 in. of the flat part of the roof deck, and have adequate gaps between all panels to allow pressure equalization between the top and bottom surfaces of the panels. The design wind pressure is p = qh(GCp)(γE)(γa) where, per ASCE 7-16, Eq. 26.10-1) = 0.00256KzKztKdKeV2 qh = 0.00256 (1.0) (1.0) (0.85) (1.0) (110)2 = 26.3 psf STEP 2: The pressure coefficients GCp for elements of the solar array are determined from Fig. 30.3-2A of ASCE 7-16 for a low slope (≤ 7°) gable roof. The largest area supported by any clamp is less than 10 ft2, so GCp for clamp design is based on effective wind area A ≤ 10 ft2. For Zone 3, GCp = -3.2 For Zone 2, GCp = -2.3 For Zone 1, GCp = -1.7 For Zone 1’, GCp = -0.9

Figure J1: Metal standing seam roof with flush-mounted solar array. (a) Photo of an example array. (b) Dimensions used in this example calculation.

Wind Design for Solar Arrays Report SEAOC PV2-2017

STEP 3: An edge factor γE = 1.5 must be applied to the exposed PV modules located along each outer row, or adjacent to aisles > 4 ft. STEP 4: A factor γa is permitted to be applied to reduce the design wind pressure to account for pressure equalization

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STRUCTURAL ENGINEERS ASSOCIATION OF CALIFORNIA between the top and bottom surfaces of the panels. Per ASCE 7-16 Figure 29.4-8, the Pressure Equalization Factor γa = 0.8 for A ≤ 10 ft2. However, because the top surface of the modules is ≤ 5 in. from the roof surface (h1 = h2), and the minimum gap between modules in each direction is ≥ ¾ in., Figure 12 of SEAOC PV2 allows the design pressure to be further reduced using a pressure equalization factor γa = 0.6. Table J1 calculates the design wind pressure p for clamps in each roof wind zone by applying the equation from Step 1 with the coefficients from Steps 2, 3, and 4. STEP 5: A setback of 20 ft from the roof edge is selected in order to minimize wind loads on the array by locating the array in roof wind Zones 1 and 1’ as shown in Figure J2. Based on this location, design pressures shown in Table J1 for clamps are limited to the values shown for Zone 1 and Zone 1’. Modules located in an outer row or column are considered “exposed” and are designed using the higher pressures that include an edge factor of 1.5, as shown in Figure J2. Because the aisle between arrays is > 4 ft wide (per ASCE 7-16) and > 2h2 (per SEAOC PV2 Section 5.2.3), modules along this aisle also require an edge factor of 1.5. Whereas ASCE 7-16 would require the application of the edge factor 1.5 to all modules within a distance of 1.5 Lp from the edge of the array, Lp is not clearly defined in the case of a flush-mount array such as in this example. For this case, SEAOC PV2-2017 Section 5.3.3 recommends applying the edge factor to modules within 2h2 = 10 inches of the exposed edge. This example applies the edge factor 1.5 to the edge modules.

As the local fire department required a minimum 6 ft wide access aisles at maximum distances of 100 ft, the modules along each side of the aisle must use an edge factor = 1.5 since the aisle is > 4 ft. wide (per ASCE 7-16) and > 2h2 (per SEAOC PV2 Section 5.2.3). This will still allow enough room for the required minimum of 800 modules by installing the modules in two – approximate 100 by 100 ft arrays. Within each array 14 modules in each of 30 rows are used (see Fig. J2). This allows for up to 840 modules total. Table J1: Summary of design wind pressure calculations for module clamps Roof Wind Uplift Roof Wind Zone Module Edge Wind GCp Pressure Dimensions (ft) Location Factor Zone (psf) L-shaped areas at Exposed 1.5 -75.9 roof corners: 3 -3.2 6.6 ft wide, 19.8 ft Shielded 1.0 -50.6 long on each side 19.8 ft wide Exposed 1.5 -54.6 perimeter of roof 2 -2.3 (except areas in Shielded 1.0 -36.4 Roof Wind Zone 3) 19.8 ft to 39.6 ft Exposed 1.5 -40.3 -1.7 1 from roof edges Shielded 1.0 -26.9 greater than 39.6 ft Exposed 1.5 -21.3 1’ -0.9 from roof edges Shielded 1.0 -14.2

Discussion: The provisions for parallel-to-roof (flush-mount) modules used in this example apply only when used with ASCE 7-16. Pressure coefficients GCp for Components and Cladding (to which the flush-mount provisions refer) changed from ASCE 7-10 to ASCE 7-16. In this example, several options were considered in order to provide the required number of modules, while minimizing wind forces on the array. Limiting the height of the module surface above the roof surface to 5 in., and providing a minimum gap of ¾ in. between modules provides a significant reduction in the wind uplift design pressure as γa is reduced to 0.6. This is allowed per SEAOC PV2-2017, but this value is limited to 0.8 in ASCE 7-16. Another factor is the setback distance from the edge of the roof to the first row of PV modules, which often is 10 ft on all sides of the building. In reviewing Table J1, it can be noted that the wind pressure has been further reduced considerably by increasing the setback distance to 20 ft on all sides and placing the modules in Zone 1 and 1’, and not in Zone 2 or 3.

Wind Design for Solar Arrays Report SEAOC PV2-2017

Figure J2: Roof plan and array layout. Modules are colorcoded to identify the applicable roof wind zone and edge factor at each location on the array.

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