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Structural analysis of solar racking systems literature review

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Contents

Basic Design[edit]

Materials Used[edit]

Basic steel design with LRFD [1][edit]

Metallic Materials in Engineering [2][edit]

Designing With Structural Steel: A Guide for Architects [3][edit]

Aluminum Alloy Structures [4][edit]

Design[edit]

Unirac

Unirac Datasheet [5][edit]

Unirac Code-Compliant Installation Manual [6][edit]

Installation Recommendations

Panel Orientation [7][edit]

Solid Mechanics[edit]

Shigley's mechanical engineering design [8][edit]

Introduction to Engineering Mechanics: A Continuum Approach [9][edit]

Engineering design : a systematic approach [10][edit]

Analysis of metallurgical failures [11][edit]

Failure of materials in mechanical design : analysis, prediction, prevention [12][edit]

Mechanics of Materials: Textbook for a Fundamental Mechanics Course [13][edit]

Impact Strength of Materials [14][edit]

Engineering Mechanics and Design Applications Transdisciplinary Engineering Fundamentals [15][edit]

Design Engineer’s Handbook [16][edit]

Mechanics of Materials [17][edit]

Vibrations & Seismic Requirements[edit]

Mechanical vibrations [18][edit]

Vibration of Structures: Applications in Civil Engineering Design [19][edit]

The Seismic Design Handbook [20][edit]

STRUCTURAL SEISMIC REQUIREMENTS AND COMMENTARY FOR ROOFTOP SOLAR PHOTOVOLTAIC SYSTEMS [21][edit]

Wind Loading[edit]

Wind Effects on Structures: Fundamentals and Applications to Design [22][edit]

Wind Loading of Structures [23][edit]

Aerodynamic Mechanisms for Wind Loads on Tilted, Roof-Mounted, Solar Arrays [24][edit]

Abstract: A wind tunnel study has been performed on roof-mounted solar arrays of two different panel tilt angles. One of the arrays was also placed on the ground in order to distinguish array generated aerodynamic effects from building generated effects. It is shown that there are two main mechanisms causing the aerodynamic loads: (i) turbulence generated by the panels and (ii) pressure equalization. For higher tilt angles, significant array generated turbulence increases the net wind loads, while for low tilt angles, pressure equalization dominates. In addition, it is observed that the presence of the building changes the aerodynamic loads substantially compared to ground-mounted systems. There is a complex interaction between building generated vortices and the flow induced by the array, which depends on building height, the setback

  • Difference between wind loads experienced by roof mounted & ground mounted
  • Wind loads contributed by
  1. vortices generated by flow separations at roof edges (building generated)
  2. turbulence induced by array
  3. turbulence in atmospheric boundary layer
  • Wind loads defined by
  1. array geometry (spacing between rows, height of panel, setback)

-larger setbacks = increased loads

  1. characteristic of wind
  2. building geometry
  • Net loading for
  1. low tilt angle due to pressure equalization
  2. high tilt angle due to local flow and turbulence gen. by array
  • Northern & Southern wind directions
  1. Length of separation bubble
  2. Northern critical to ground
  3. Southern critical to roof
  • Difference in array zoning for roof vs. ground mounted

Local and Overall Wind Pressure and Force Coefficients for Solar Panels [25][edit]

Abstract This paper reports on an experimental study carried out to better understand the wind pressure distribution on stand-alone panel surfaces and panels attached to flat building roofs. A complex model capable to incorporate solar panels at different locations and various inclinations was constructed at a 1:200 geometric scale. Three model panels equipped with pressure taps on both surfaces (36 in total) for point and area-averaged pressure measurements were used. Pressure and force coefficients were computed for every pressure tap and for all the panels. Different configurations were tested under similar conditions in order to examine the effect of various parameters on the experimental results. A minimal gap occurred between the solar panels and the roof of the model. The study found that the net values of pressure coefficients corresponding to different configurations are affected by the panel inclination for the critical 135° wind direction, for which panels on the back location undergo higher suctions in comparison to those in the front. The effect of building height on the solar collector total load is minimal, whereas corner panels are subjected to higher net loads for critical azimuths. Simplified net pressure coefficients for the design of solar panels are provided.

  • Critical wind locations & panel inclination
  • Building height correlation to suction of front vs. back panels
  • Greatest net force coefficient for panels near roof edges
  • Greater pressure coefficients occur between 105-180 degree wind direction; critical at 135 degrees

Wind Design Practice and Recommendations for Solar Arrays on Low-Slope Roofs [26][edit]

Abstract: Currently, ASCE standards do not provide specific guidance on wind loads for solar arrays of photovoltaic panels, in terms of either prescriptive design or requirements for wind tunnel testing. Guidance is needed, particularly for arrays of low-profile tilted panels on flat or low-slope roofs, because they are markedly different aerodynamically from structures currently addressed in the building code. This paper presents recommendations for the structural design of these solar arrays for wind-loading. Recommendations include (1) categorizing solar array support-systems according to their height above the building roof and how they distribute forces to the roof, (2) developing pressure coefficients that are applicable to structurally interconnected roof-bearing support systems, (3) considering load cases that include uniform wind pressure on the array and nonuniform (gust) patterns, (4) determining appropriate stiffness and boundary conditions for structural analysis, and (5) use of testing to verify behavior and calibrate analytical models.

  • Types of PV support structures
  1. Roof-bearing systems (paper's focus) including: Unattached(ballast only), Attached, Attached with added ballast
  2. Fully framed systems
  3. Building-integrated systems

Structural Analysis and Application of Wind Loads to Solar Arrays[27][edit]

Abstract This paper reports on an experimental study carried out to better understand the wind pressure distribution on stand-alone panel surfaces and panels attached to flat building roofs. A complex model capable to incorporate solar panels at different locations and various inclinations was constructed at a 1:200 geometric scale. Three model panels equipped with pressure taps on both surfaces (36 in total) for point and area-averaged pressure measurements were used. Pressure and force coefficients were computed for every pressure tap and for all the panels. Different configurations were tested under similar conditions in order to examine the effect of various parameters on the experimental results. A minimal gap occurred between the solar panels and the roof of the model. The study found that the net values of pressure coefficients corresponding to different configurations are affected by the panel inclination for the critical 135° wind direction, for which panels on the back location undergo higher suctions in comparison to those in the front. The effect of building height on the solar collector total load is minimal, whereas corner panels are subjected to higher net loads for critical azimuths. Simplified net pressure coefficients for the design of solar panels are provided.

  • 2 main PV mkts = ground & building
  • Ensure natural frequency of array (and thus mounting) >> nat. freq. of experienced wind pressures
  • Pressure tap model (WTT -wind tunnel testing)
  • Dynamic analysis does not consider changes in wind pressure due to movement of PV system
  • Use of non-linear response-history analysis
  1. importance of variables (damping, friction, energy dissapation)
  • Wind load complexities
  1. friction on roof
  2. uplift
  3. load sharing and flexibility of structure & connections
  • Max uplift at corners and edges (critical locations)
  • Self arresting behavior of uplift

The Role of Corner Vortices in Dictating Peak Wind Loads on Tilted Flat Solar Panels Mounted on Large, Flat Roofs [28][edit]

Abstract Uplift wind loads on tilted flat PV panels mounted on the roofs of wide, rectangular, low-rise flat-roofed building were measured in an atmospheric boundary layer wind tunnel. The results indicate that for panels aligned with the building axes, the bubble separation that occurs for winds normal to a building face does not significantly increase these loads. Conversely, wind loads associated with the corner vortices are significantly higher than in the absence of the vortex. The direction of panel tilt relative to the vortex swirl, the position of the panel relative to the vortex reattachment, and the proximity of the panel to the vortex-originating corner together control the peak uplift. It is through changes to the vortices that the parapets affect wind loads. Vortex-related winds loads so dominate the uplift patterns on the roof that they need to be the primary consideration in any method designed to calculate these loads. This includes both experiments designed to study wind loads on this kind of PV racking system, and any calculation methods currently being codified in standards around the world

  • No sig increase in loads for panels aligned with building aces (by means of bubble separation)
  • Very large wind loads due to corner vortices
  • Proximity and geometric factors related to vortex corner that determine peak uplift
  • Vortice changes and parapet effects on wind loads
  • Focus on loads calculated for ballasted systems
  • Relationship between panel tilt direction and vortex swirl
  • Increased wind loads due to bldg parapets
  • More severe wind loads for taller bldgs(see aspect ratio)

Wind loading characteristics of solar arrays mounted on flat roofs [29][edit]

Abstract With the increasing use of solar photovoltaics, wind-induced loads on rooftop solar arrays have become a problem. A series of wind tunnel experiments have been performed to evaluate wind loads on solar panels on flat roofs, mainly focusing on module forces calculated from area-averaged net pressures on solar modules of a standard size. In order to investigate the module force characteristics at different locations on the roof, solar array models, which were fabricated with pressure taps installed as densely as possible, were moved from place to place. Design parameters including tilt angle and distance between arrays, and building parameters including building depth and parapet height, have also been considered. The results show that unfavorable negative module force coefficients for single-array cases are much larger than those for multi-array cases; tilt angle and distance between arrays increase negative module forces; effects of building depth and parapet height on negative module forces are not obvious; and recommendation values in JIS C 8955 Standard correctly estimate negative mean module force coefficients but not peak values.

  • Large(wind/pressure)coefficients for single-array vs. multiple-array systems
  1. Also increased with tilt angle and spacing between arrays
  • "negative module forces"
  • In general: selecting scale for WTT tricky because of small PV system size in relation to large bldg size
  1. larger geometry scale preferred for WTT
  2. 1:50 used
  3. Also, in WTT, scale should match that of simulated BL (boundary layer)

Wind Loading on Tilted Roof-Top Solar Arrays: The Parapet Effect [30][edit]

Abstract Scale model wind tunnel testing was used to investigate the effect of parapets on the wind loading of a roof-top solar array with a tilt angle of 10°. Previous studies have indicated a correlation between parapet height and uplift wind loads acting on roof membranes and roof-top equipment. This relationship was reproduced in the current study for wind loads acting on roof-top solar arrays and is shown to be caused by building-induced aerodynamics, namely corner vortices. Increasing parapet height was shown to increase the peak wind loads acting on the array. These increases were found to be dependent on location on the roof, in the array, and geometry of the array itself. The parapet effect results in peak wind load increases for much of the array for typical parapet heights when all wind directions are considered.

  • Increase in peak wind loads acting on array with increased parapet heights
  1. Dependent on location on roof, within array, array geometry

Why Current Module Frame-Based Mounting Systems are Inadequate[31][edit]

How Structural Guidelines for Low-Slope PV Arrays Affect Mounting System Designs [32][edit]

Aerodynamic Loads on Solar Panels [33][edit]

Abstract: The existing literature has limited aerodynamic data for the evaluation of design wind loads for solar panels. Furthermore, there are no provisions in building codes and standards to guide the design of these types of structures for wind. This paper presents a systematic wind tunnel study to evaluate wind loads on solar panels mounted on low-rise gable buildings. A preliminary geometric scale effect study using a simple isolated solar panel was carried out to permit design appropriate wind tunnel experiments. Following the scale effect study, wind loads on solar panels mounted on different critical zones of low-rise residential roof are systematically investigated. The results of the current paper provide useful information for the design of the solar panels.

Wind Turbulence and Load Sharing Effects on Ballasted Roof-Top Solar Arrays[34][edit]

Abstract:Solar arrays installed on roofs of low-rise commercial buildings are especially popular since it makes good use of previously unexploited real estate. These systems are usually restrained to resist wind-induced lift-off and sliding using ballast, penetrations, adhesives, or combinations thereof. In the case of ballasted systems, reducing the added weight on the roof is often the primary objective of designers, while maintaining a certain level of reliability. This can be accomplished through aerodynamic design and other methods, but sometimes more simply through the utilization of load sharing between adjacent panels. This is accomplished through the vertical bending stiffness of the racking system. This paper presents a discussion of the varied wind tunnel testing and analysis methods currently employed around the world, with a focus on the correlation effects associated with load sharing. A finite element model, in conjunction with wind tunnel data on a roof-top array, is used to demonstrate the impact of array stiffness on wind loads in a time- and spatially-varying sense. Practical guidance to determine ballast requirements is also provided.

Wind Loads on Low-Profile, Tilted, Solar Arrays Placed on Large, Flat, Low-Rise Building Roofs [35][edit]

Abstract: The author examined wind loads on low-profile, roof-mounted solar arrays, placed on large, low-rise buildings with nearly flat roofs by using scale models in a boundary layer wind tunnel. The author also examined the effects of building size and array geometry on enveloping curves of area-averaged pressure coefficients, typical of use for design. It was found that wind loads on the array increase with building size; normalizing the effective wind area by the building wall size leads to enveloping curves that collapse onto a single curve for each array geometry. For tilt angles less than 10°, there is an approximate linear increase in the pressure coefficients as the tilt angle increases. For arrays with tilt angles of 10° or more, the wind loads do not depend significantly on the tilt angle and are relatively constant. Roof zones for wind loads on solar arrays are larger than roof zones for bare roofs and depend on the array tilt angle.

Use of the Wind Tunnel Test Method for Obtaining Design Wind Loads on Roof-Mounted Solar Arrays [36][edit]

Abstract: ASCE 7 does not provide design wind loads for roof-mounted solar panels. This paper discusses the use of the wind tunnel test method, called Method 3 in ASCE 7-05, which was originally intended for obtaining design wind loads for individual buildings. Because roof-mounted solar arrays are generally mounted in many configurations on many buildings of many different shapes, additional requirements are necessary to use Method 3 in this situation. The paper describes these additional requirements

Characteristics of Wind Forces Acting on Tall Buildings [37][edit]

Abstract Nine models with different rectangular cross-sections were tested in a wind tunnel to study the characteristics of wind forces on tall buildings. The data was briefly reported (Local wind forces acting on rectangular prisms. Proceedings of 14th National Symposium on Wind Engineering, 4–6 December 1996, Japan Association for Wind Engineering, Tokyo, pp. 263–268.). In the present paper, local wind forces on tall buildings are investigated in terms of mean and RMS force coefficients, power spectral density, and spanwise correlation and coherence. The effects of three parameters, elevation, aspect ratio, and side ratio, on bluff-body flow and thereby on the local wind forces are discussed. The overall loads and base moments are obtained by integration of local wind forces. Comparisons are made with results obtained from high-frequency force balances in two wind tunnels.


Snow Loading[edit]

DEPARTMENT OF ENERGY, LABOR AND ECONOMIC GROWTH DIRECTOR’S OFFICE CONSTRUCTION CODE [38][edit]

Patents[edit]

Photovoltaic panel support assembly [39][edit]

Abstract: Provided is a support assembly for mounting an array of photovoltaic panels to a support surface such as the ground. According to the invention, there is provided a plurality of front and rear support posts, each post having an anchor portion to be driven into the support surface and a leg portion which is nested therein and longitudinally adjustable to raise or lower corresponding front and rear horizontal supports. Photovoltaic panels are mounted lengthwise across the horizontal supports in a predetermined position to minimize the stress thereon caused by wind load. The horizontal supports further comprise wiring raceways to support wiring harnesses originating from the photovoltaic panels and terminating at the end of each row of photovoltaic panels in the array.

Modular Solar Panel Racking System [40][edit]

Abstract:Disclosed herein are embodiments of modular racking systems for solar panels and in particular, modular solar panel racks, racking systems, arrays of racks, kits and methods of use. One embodiment of a modular solar panel rack comprises a plurality of discrete ballast holders and a plurality of panel support members each having two upright portions, a transverse portion contiguously connected between the two upright portions, the connection such that the transverse portion is non-perpendicular to the two upright portions, and a retainer attached to the transverse portion and configured to retain a solar panel. Each of the plurality of ballast holders is connected to no more than four panel support members, each ballast holder perpendicularly connected to one of the upright portions.

Rack Assembly for Mounting Solar Modules[41][edit]

Abstract: A rack assembly is provided for mounting solar modules over an underlying body. The rack assembly may include a plurality of rail structures that are arrangeable over the underlying body to form an overall perimeter for the rack assembly. One or more retention structures may be provided with the plurality of rail structures, where each retention structure is configured to support one or more solar modules at a given height above the underlying body. At least some of the plurality of rail structures are adapted to enable individual rail structures o be sealed over the underlying body so as to constrain air flow underneath the solar modules. Additionally, at least one of (i) one or more of the rail structures, or (ii) the one or more retention structures are adjustable so as to adapt the rack assembly to accommodate solar modules of varying forms or dimensions.

Roof Support System for a Solar Panel[42][edit]

Abstract: A new mounting system for elevating and supporting objects such as solar panels and satellite dishes upon a roof. The mounting base for attachment to a roof rafter incorporates a threadable elongated member or stanchion and only requires a single lag bolt which is positioned directly beneath the stanchion for fastening to a roof rafter. A guide tunnel is also provided on the roof mount for proper drill angle into the rafter. The solar panel support utilizes C-shaped extruded aluminum horizontal members where, upon fastening the solar panel to the members, enhances the strength properties from a C-shape to a square structural member. The disclosed design for the solar panel support and associated equipment which are attached to at least two mounting bases, permits efficient packaging, resulting in minimal packaging time and cost.

Mounting System for a Solar Panel [43][edit]

Abstract:An integrated module frame and racking system for a solar panel is disclosed. The solar panel comprises a plurality of solar modules and a plurality of splices for coupling the plurality of solar modules together. The plurality of splices provide a way to make the connected modules mechanically rigid both during transport to the roof and after mounting for the lifetime of the system, provide wiring connections between modules, provide an electrical grounding path for the modules, provide a way to add modules to the panel, and provide a way to remove or change a defective module. Connector sockets are provided on the sides of the modules to simplify the electrical assembly of modules when the modules are connected together with splices.

Portable Solar Power System [44][edit]

Abstract: A trailer mounted, self contained solar power system having a plurality of solar panel sections that are arranged to fold about the sides and top of the trailer. The panel sections unfold and lock together through slide rams that are contained within a rack structure supporting the panel sections to form a planar array that is easily deployable at a desired angle to the horizontal. The planar array pivots about a hinge along one side of the trailer top, and the panel sections are asymmetrically arranged so that positioning of the planar array can be easily accomplished.

Adjustable Mounting Rack for Solar Collectors [45][edit]

Abstract: A rack for supportively mounting a solar collector to a mounting surface to set the angle of tilt with respect to the sun. One end of the rack is adapted to provide predominant support of the collector, while the other end is height adjustable to provide the proper angle and to accept tension and/or compression due to wind leading.

Building Codes & Guides[edit]

ASCE 7-05 Minimum Design Loads for Buildings and Other Structures [46][edit]

SOLAR PHOTOVOLTAIC INSTALLATION GUIDELINE [47][edit]

References[edit]

  1. Galambos, T. V. Basic Steel Design with LRFD. Upper Saddle River, N.J: Prentice Hall, 1996.
  2. Samans, Carl Hubert. Metallic Materials in Engineering. N.Y: Macmillan, 1963.
  3. “Designing With Structural Steel: A Guide for Architects 2nd Ed,” n.d. http://www.aisc.org/uploadedFiles/Steel_Solutions_Center/Conceptual/My_Project/Files/ArchitectsGuide.pdf.
  4. Mazzolani, Federico M. Aluminum Alloy Structures. Surveys in Structural Engineering and Structural Mechanics 3. Boston: Pitman, 1985.
  5. http://unirac.com/sites/default/files/solarmounttechdatasheet.pdf
  6. http://thesolarstore.com/manuals/SolarMount%20Installation%20Manual.pdf
  7. http://www.cooperindustries.com/content/dam/public/bline/Markets/Solar/Resources/Panel-Orientation-Landscape-vs-Portrait.pdf
  8. Budynas, Richard G. Shigley’s Mechanical Engineering Design. 9th ed. McGraw-Hill Series in Mechanical Engineering. New York: McGraw-Hill, 2011.
  9. Rossmann, Jenn Stroud, and Clive L Dym. Introduction to Engineering Mechanics: A Continuum Approach. Boca Raton, FL: CRC Press, 2009.
  10. Pahl, G. Engineering Design: A Systematic Approach. London ; New York: Springer, 1996.
  11. Colangelo, Vito J. Analysis of Metallurgical Failures. Wiley Series on the Science and Technology of Materials. New York: Wiley, 1974.
  12. Collins, J. A. Failure of Materials in Mechanical Design: Analysis, Prediction, Prevention. New York: Wiley, 1981.
  13. Thiagarajan, Ganesh. Mechanics of Materials: Textbook for a Fundamental Mechanics Course. Mission, KS: Schroff Development Corp, 2009.
  14. Johnson, W. Impact Strength of Materials. London: Edward Arnold, 1972.
  15. Ertas, Atila. Engineering Mechanics and Design Applications Transdisciplinary Engineering Fundamentals. Boca Raton, FL: CRC Press, 2012. http://services.lib.mtu.edu:2048/login?url=http://www.crcnetbase.com/doi/book/10.1201/b11110.
  16. Richards, Keith L. Design Engineer’s Handbook. Boca Raton, FL: CRC Press/Taylor & Francis Group, 2013. http://services.lib.mtu.edu:2048/login?url=http://www.crcnetbase.com/doi/book/10.1201/b12714.
  17. Vable,M. (2002). Mechanics of Materials. New York, Ny: Oxford University Press
  18. Rao, S. S. Mechanical Vibrations. 4th ed. Upper Saddle River, N.J: Pearson/Prentice Hall, 2004.
  19. Smith, J. W. Vibration of Structures: Applications in Civil Engineering Design. London ; New York: Chapman and Hall, 1988.
  20. The Seismic Design Handbook. 2nd ed. Boston: Kluwer Academic Publishers, 2001.
  21. SEAOC Solar Photovoltaic Systems Committee. "Seismic Requirements and Commentary for Rooftop Solar Photovoltaic Systems." Structural Engineers of California. Feb. 2012.
  22. Simiu, Emil. Winds Effects on Structures: Fundamentals and Applications to Design. Wiley, 1996.
  23. Holmes, John D. Wind Loading of Structures. London ; New York: Spon Press, 2003. http://services.lib.mtu.edu:2048/login?url=http://marc.crcnetbase.com/ISBN/9780203301647.
  24. Kopp, Gregory A., Steve Farquhar, and Murray J. Morrison. “Aerodynamic Mechanisms for Wind Loads on Tilted, Roof-Mounted, Solar Arrays.” Journal of Wind Engineering and Industrial Aerodynamics 111 (December 2012): 40–52. doi:10.1016/j.jweia.2012.08.004.
  25. Stathopoulos, Ted, Ioannis Zisis, and Eleni Xypnitou. “Local and Overall Wind Pressure and Force Coefficients for Solar Panels.” Journal of Wind Engineering and Industrial Aerodynamics 125 (February 2014): 195–206. doi:10.1016/j.jweia.2013.12.007.
  26. Maffei, J., Telleen, K., Ward, R., Kopp, G., and Schellenberg, A. (2014). ”Wind Design Practice and Recommendations for Solar Arrays on Low-Slope Roofs.” J. Struct. Eng., 140(2), 04013040.
  27. Schellenberg, Andreas, Joe Maffei, Karl Telleen, and Rob Ward. “Structural Analysis and Application of Wind Loads to Solar Arrays.” Journal of Wind Engineering and Industrial Aerodynamics 123, Part A (December 2013): 261–272. doi:10.1016/j.jweia.2013.06.011.
  28. Banks, David. “The Role of Corner Vortices in Dictating Peak Wind Loads on Tilted Flat Solar Panels Mounted on Large, Flat Roofs.” Journal of Wind Engineering and Industrial Aerodynamics 123, Part A (December 2013): 192–201. doi:10.1016/j.jweia.2013.08.015.
  29. Cao, Jinxin, Akihito Yoshida, Proshit Kumar Saha, and Yukio Tamura. “Wind Loading Characteristics of Solar Arrays Mounted on Flat Roofs.” Journal of Wind Engineering and Industrial Aerodynamics 123, Part A (December 2013): 214–225. doi:10.1016/j.jweia.2013.08.014.
  30. Browne, Matthew T. L., Michael P. M. Gibbons, Scott Gamble, and Jon Galsworthy. “Wind Loading on Tilted Roof-Top Solar Arrays: The Parapet Effect.” Journal of Wind Engineering and Industrial Aerodynamics 123, Part A (December 2013): 202–213. doi:10.1016/j.jweia.2013.08.013.
  31. Tilly, Christopher. "Why Current Module Frame-Based Mounting Systems are Inadequate." SunLink Corporation. 2012.
  32. Ward,Rob. “How_Structural.html How Structural Guidelines for Low-Slope PV Arrays Affect Mounting System Designs.” Solar Industry Magazine. Vol 6, No.3. April 2013.
  33. Aly, A. and Bitsuamlak, G. (2013) Aerodynamic Loads on Solar Panels. Structures Congress 2013: pp. 1555-1564.
  34. Browne, M., Gamble, S., and Gibbons, M. (2012) Wind Turbulence and Load Sharing Effects on Ballasted Roof-Top Solar Arrays. Advances in Hurricane Engineering: pp. 448-459.
  35. Kopp, G. (2014). ”Wind Loads on Low-Profile, Tilted, Solar Arrays Placed on Large, Flat, Low-Rise Building Roofs.” J. Struct. Eng., 140(2), 04013057.
  36. Kopp, G. and Banks, D. (2013). ”Use of the Wind Tunnel Test Method for Obtaining Design Wind Loads on Roof-Mounted Solar Arrays.” J. Struct. Eng., 139(2), 284–287.
  37. Lin, Ning, Chris Letchford, Yukio Tamura, Bo Liang, and Osamu Nakamura. “Characteristics of Wind Forces Acting on Tall Buildings.” Journal of Wind Engineering and Industrial Aerodynamics 93, no. 3 (March 2005): 217–242. doi:10.1016/j.jweia.2004.12.001.
  38. http://www.michigan.gov/documents/dleg/dleg_bcc_2009_009lg_building_residential_code_rules_337947_7.pdf
  39. Patent US5125608 - Photovoltaic panel support assembly.
  40. Patent US20100147359 - Modular Solar Panel Racking System.
  41. Patent US7856769 - Rack Assembly for Mounting Solar Modules.
  42. Patent US6360491 - Roof Support System for a Solar Panel.
  43. Patent US7406800 - Mounting System for a Solar Panel.
  44. Patent US5969501 - Portable Solar Power System.
  45. Patent US4371139 - Adjustable Mounting Rack for Solar Collectors.
  46. American Society of Civil Engineers. "Minimum Design Loads for Buildings and Other Structures." ASCE Press. (2006).
  47. CALIFORNIA DEPARTMENT of FORESTRY and FIRE PROTECTION OFFICE OF THE STATE FIRE MARSHAL April 2008.