The provisions of this chapter shall govern the design, materials, construction and quality of roof assemblies.
Roofs shall be covered with materials as set forth in Sections R904 and R905. Class A, B or C roofing shall be installed in jurisdictions designated by law as requiring their use or where the edge of the roof is less than 3 feet (914 mm) from a lot line. Class A, B and C roofing required by this section to be listed shall be tested in accordance with UL 790 or ASTM E108.
Exceptions:
Exceptions:
- Class A roof assemblies include those with coverings of brick, masonry and exposed concrete roof deck.
- Class A roof assemblies include ferrous or copper shingles or sheets, metal sheets and shingles, clay or concrete roof tile, or slate installed on noncombustible decks.
- Class A roof assemblies include minimum 16 ounces per square foot copper sheets installed over combustible decks.
- Class A roof assemblies include slate installed over underlayment over combustible decks.
Fire-retardant-treated wood shakes and shingles shall be treated by impregnation with chemicals by the full-cell vacuum-pressure process, in accordance with AWPA C1. Each bundle shall be marked to identify the manufactured unit and the manufacturer, and shall be labeled to identify the classification of the material in accordance with the testing required in Section R902.1, the treating company and the quality control agency.
Building-integrated photovoltaic products installed as the roof covering shall be tested, listed and labeled for fire classification in accordance with Section R902.1.
Rooftop-mounted photovoltaic panels and modules installed on or above the roof covering shall be tested, listed and identified with a fire classification in accordance with UL 1703. Class A, B or C photovoltaic panels and modules shall be installed in jurisdictions designated by law as requiring their use or where the edge of the roof is less than 3 feet (914 mm) from a lot line.
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Roof decks shall be covered with approved roof coverings secured to the building or structure in accordance with the provisions of this chapter. Roof assemblies shall be designed and installed in accordance with this code and the approved manufacturer's instructions such that the roof assembly shall serve to protect the building or structure.
Flashings shall be installed in a manner that prevents moisture from entering the wall and roof through joints in copings, through moisture permeable materials and at intersections with parapet walls and other penetrations through the roof plane.
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Flashings shall be installed at wall and roof intersections, wherever there is a change in roof slope or direction and around roof openings. A flashing shall be installed to divert the water away from where the eave of a sloped roof intersects a vertical sidewall. Where flashing is of metal, the metal shall be corrosion resistant with a thickness of not less than 0.019 inch (0.5 mm) (No. 26 galvanized sheet).
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A cricket or saddle shall be installed on the ridge side of any chimney or penetration more than 30 inches (762 mm) wide as measured perpendicular to the slope. Cricket or saddle coverings shall be sheet metal or of the same material as the roof covering.
Exception: Unit skylights installed in accordance with Section R308.6 and flashed in accordance with the manufacturer's instructions shall be permitted to be installed without a cricket or saddle.
Exception: Unit skylights installed in accordance with Section R308.6 and flashed in accordance with the manufacturer's instructions shall be permitted to be installed without a cricket or saddle.
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Parapet walls shall be properly coped with noncombustible, weatherproof materials of a width not less than the thickness of the parapet wall.
Where roof drains are required, secondary emergency overflow drains or scuppers shall be provided where the roof perimeter construction extends above the roof in such a manner that water will be entrapped if the primary drains allow buildup or any reason. Overflow drains having the same size as the roof drains shall be installed with the inlet flow line located 2 inches (51 mm) above the low point of the roof, or overflow scuppers having three times the size of the roof drains and having a minimum opening height of 4 inches (102 mm) shall be installed in the adjacent parapet walls with the inlet flow located 2 inches (51 mm) above the low point of the roof served. The installation and sizing of overflow drains, Leaders and conductors shall comply with Sections 1101 and 1103 of the state plumbing code. Overflow drains shall discharge to an approved location.
The requirements set forth in this section shall apply to the application of roof covering materials specified herein. Roof assemblies shall be applied in accordance with this chapter and the manufacturer's installation instructions. Installation of roof assemblies shall comply with the applicable provisions of Section R905.
Roof assemblies shall be of materials that are compatible with each other and with the building or structure to which the materials are applied.
Roof covering materials shall conform to the applicable standards listed in this chapter.
Roof covering materials shall be delivered in packages bearing the manufacturer's identifying marks and approved testing agency labels required. Bulk shipments of materials shall be accompanied by the same information issued in the form of a certificate or on a bill of lading by the manufacturer.
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Roof coverings shall be applied in accordance with the applicable provisions of this section and the manufacturer's installation instructions. Unless otherwise specified in this section, roof coverings shall be installed to resist the component and cladding loads specified in Table R301.2(2), adjusted for height and exposure in accordance with Table R301.2(3).
Underlayment for asphalt shingles, clay and concrete tile, metal roof shingles, mineral-surfaced roll roofing, slate and slate-type shingles, wood shingles, wood shakes and metal roof panels shall conform to the applicable standards listed in this chapter. Underlayment materials required to comply with ASTM D226, D1970, D4869 and D6757 shall bear a label indicating compliance to the standard designation and, if applicable, type classification indicated in Table R905.1.1(1). Underlayment shall be applied in accordance with Table R905.1.1(2). Underlayment shall be attached in accordance with Table R905.1.1(3).
Exceptions:
- As an alternative, self-adhering polymer-modified bitumen underlayment complying with ASTM D1970 installed in accordance with both the underlayment manufacturer's and roof covering manufacturer's instructions for the deck material, roof ventilation configuration and climate exposure for the roof covering to be installed, shall be permitted.
- As an alternative, a minimum 4-inch-wide (102 mm) strip of self-adhering polymer-modified bitumen membrane complying with ASTM D1970, installed in accordance with the manufacturer's instructions for the deck material, shall be applied over all joints in the roof decking. An approved underlayment for the applicable roof covering for maximum ultimate design wind speeds, Vult, less than 140 miles per hour shall be applied over the entire roof over the 4-inch-wide (102 mm) membrane strips.
| ROOF COVERING | SECTION | MAXIMUM ULTIMATE DESIGN WIND SPEED, Vult < 140 MPH |
MAXIMUM ULTIMATE DESIGN WIND SPEED, Vult ≥ 140 MPH |
| Asphalt shingles | R905.2 | ASTM D226 Type I ASTM D4869 Type I, II, III or IV ASTM D6757 |
ASTM D226 Type II ASTM D4869 Type IV ASTM D6757 |
| Clay and concrete tile | R905.3 | ASTM D226 Type II ASTM D2626 Type I ASTM D6380 Class M mineral- surfaced roll roofing |
ASTM D226 Type II ASTM D2626 Type I ASTM D6380 Class M mineral- surfaced roll roofing |
| Metal roof shingles | R905.4 | ASTM D226 Type I or II ASTM D4869 Type I, II, III or IV |
ASTM D226 Type II ASTM D4869 Type IV |
| Mineral-surfaced roll roofing | R905.5 | ASTM D226 Type I or II ASTM D4869 Type I, II, III or IV |
ASTM D226 Type II ASTM D4869 Type IV |
| Slate and slate-type shingles | R905.6 | ASTM D226 Type I ASTM D4869 Type I, II, III or IV |
ASTM D226 Type II ASTM D4869 Type IV |
| Wood shingles | R905.7 | ASTM D226 Type I or II ASTM D4869 Type I, II, III or IV |
ASTM D226 Type II ASTM D4869 Type IV |
| Wood shakes | R905.8 | ASTM D226 Type I or II ASTM D4869 Type I, II, III or IV |
ASTM D226 Type II ASTM D4869 Type IV |
| Metal panels | R905.10 | Manufacturer's instructions | ASTM D226 Type II ASTM D4869 Type IV |
| ROOF COVERING | SECTION | MAXIMUM ULTIMATE DESIGN WIND SPEED, Vult < 140 MPH |
MAXIMUM ULTIMATE DESIGN WIND SPEED, Vult ≥ 140 MPH |
| Asphalt shingles | R905.2 | For roof slopes from two units vertical in 12 units horizontal (2:12), up to four units vertical in 12 units horizontal (4:12), underlayment shall be two layers applied in the following manner: apply a 19-inch strip of underlayment felt parallel to and starting at the eaves. Starting at the eave, apply 36-inch-wide sheets of underlayment, overlapping successive sheets 19 inches. Distortions in the underlayment shall not interfere with the ability of the shingles to seal. For roof slopes of four units vertical in 12 units horizontal (4:12) or greater, underlayment shall be one layer applied in the following manner: underlayment shall be applied shingle fashion, parallel to and starting from the eave and lapped 2 inches, Distortions in the underlayment shall not interfere with the ability of the shingles to seal. End laps shall be 4 inches and shall be offset by 6 feet. |
Same as Maximum Ultimate Design Wind Speed, Vult < 140 mph except all laps shall be not less than 4 inches. |
| Clay and concrete tile | R905.3 | For roof slopes from two and one-half units vertical in 12 units horizontal (21/2:12), up to four units vertical in 12 units horizontal (4:12), underlayment shall be a minimum of two layers applied as follows: starting at the eave, apply a 19-inch strip of underlayment parallel with the eave. Starting at the eave, apply 36-inch-wide strips of underlayment felt, overlapping successive sheets 19 inches. For roof slopes of four units vertical in 12 units horizontal (4:12) or greater, underlayment shall be a minimum of one layer of underlayment felt applied shingle fashion, parallel to and starting from the eaves and lapped 2 inches. End laps shall be 4 inches and shall be offset by 6 feet. |
Same as Maximum Ultimate Design Wind Speed, Vult < 140 mph except all laps shall be not less than 4 inches. |
| Metal roof shingles | R905.4 | Apply in accordance with the manufacturer's installation instructions. |
For roof slopes from two units vertical in 12 units horizontal (2:12), up to four units vertical in 12 units horizontal (4:12), underlayment shall be two layers applied in the following manner: apply a 19-inch strip of underlayment felt parallel to and starting at the eaves. Starting at the eave, apply 36-inch-wide sheets of underlayment, overlapping successive sheets 19 inches, and fastened sufficiently to hold in place. For roof slopes of four units vertical in 12 units horizontal (4:12) or greater, underlayment shall be one layer applied in the following manner: underlayment shall be applied shingle fashion, parallel to and starting from the eave and lapped 4 inches. End laps shall be 4 inches and shall be offset by 6 feet. |
| Mineral-surfaced roll roofing |
R905.5 | ||
| Slate and slate-type shingles |
R905.6 | ||
| Wood shingles | R905.7 | ||
| Wood shakes | R905.8 | ||
| Metal panels | R905.10 |
For SI: 1 inch = 25.4 mm, 1 foot = 304.8 mm
| ROOF COVERING | SECTION | MAXIMUM ULTIMATE DESIGN WIND SPEED, Vult < 140 MPH |
MAXIMUM ULTIMATE DESIGN WIND SPEED, Vult ≥ 140 MPH |
| Asphalt shingles | R905.2 | Fastened sufficiently to hold in place | The underlayment shall be attached with corrosion-resistant fasteners in a grid pattern of 12 inches between side laps with a 6-inch spacing at the side laps. Underlayment shall be attached using metal or plastic cap nails or cap staples with a nominal cap diameter of not less than 1 inch. Metal caps shall have a thickness of not less than 32-gage sheet metal. Power- driven metal caps shall have a minimum thickness of 0.010 inch. Minimum thickness of the outside edge of plastic caps shall be 0.035 inch. The cap nail shank shall be not less than 0.083 inch for ring shank cap nails and 0.091 inch for smooth shank cap nails. Staples shall be not less than 21 gage. Cap nail shank and cap staple legs shall have a length sufficient to penetrate through the roof sheathing or not less than 3/4 inch into the roof sheathing. |
| Clay and concrete tile | R905.3 | ||
| Metal roof shingles | R905.4 | Manufacturer's installation instructions. | The underlayment shall be attached with corrosion-resistant fasteners in a grid pattern of 12 inches between side laps with a 6-inch spacing at the side laps. Underlayment shall be attached using metal or plastic cap nails or cap staples with a nominal cap diameter of not less than 1 inch. Metal caps shall have a thickness of at least 32-gage sheet metal. Power-driven metal caps shall have a minimum thickness of 0.010 inch. Minimum thickness of the outside edge of plastic caps shall be 0.035 inch. The cap nail shank shall be not less than 0.083 inch for ring shank cap nails and 0.091 inch for smooth shank cap nails. Staples shall be not less than 21 gage. Cap nail shank and cap staple legs shall have a length sufficient to penetrate through the roof sheathing or not less than 3/4 inch into the roof sheathing. |
| Mineral-surfaced roll roofing | R905.5 | ||
| Slate and slate-type shingles | R905.6 | ||
| Wood shingles | R905.7 | ||
| Wood shakes | R905.8 | ||
| Metal panels | R905.10 |
For SI: 1 inch = 25.4 mm.
In areas where there has been a history of ice forming along the eaves causing a backup of water as designated in Table R301.2(1), an ice barrier shall be installed for asphalt shingles, metal roof shingles, mineral-surfaced roll roofing, slate and slate-type shingles, wood shingles and wood shakes. The ice barrier shall consist of not fewer than two layers of underlayment cemented together, or a self-adhering polymer-modified bitumen sheet shall be used in place of normal underlayment and extend from the lowest edges of all roof surfaces to a point not less than 24 inches (610 mm) inside the exterior wall line of the building. On roofs with slope equal to or greater than 8 units vertical in 12 units horizontal, the ice barrier shall also be applied not less than 36 inches (914 mm) measured along the roof slope from the eave edge of the building.
Exception: Detached accessory structures not containing conditioned floor area.
Exception: Detached accessory structures not containing conditioned floor area.
The installation of asphalt shingles shall comply with the provisions of this section.
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Asphalt shingles shall be fastened to solidly sheathed decks.
Asphalt shingles shall be used only on roof slopes of two units vertical in 12 units horizontal (2:12) or greater. For roof slopes from two units vertical in 12 units horizontal (2:12) up to four units vertical in 12 units horizontal (4:12), double underlayment application is required in accordance with Section R905.1.1.
Underlayment shall comply with Section R905.1.1.
Asphalt shingles shall be tested in accordance with ASTM D7158. Asphalt shingles shall meet the classification requirements of Table R905.2.4.1 for the appropriate ultimate design wind speed. Asphalt shingle packaging shall bear a label to indicate compliance with ASTM D7158 and the required classification in Table R905.2.4.1.
For SI: 1 foot = 304.8 mm; 1 mph = 0.447 m/s.
Exception: Asphalt shingles not included in the scope of ASTM D7158 shall be tested and labeled to indicate compliance with ASTM D3161 and the required classification in Table R905.2.4.1.
| MAXIMUM ULTIMATE DESIGN WIND SPEED, Vult FROM FIGURE R301.2(4)A (mph) |
MAXIMUM BASIC WIND SPEED, VASD FROM TABLE R301.2.1.3 (mph) |
ASTM D7158a SHINGLE CLASSIFICATION |
ASTM D3161 SHINGLE CLASSIFICATION |
| 110 | 85 | D, G or H | A, D or F |
| 116 | 90 | D, G or H | A, D or F |
| 129 | 100 | G or H | A, D or F |
| 142 | 110 | G or H | F |
| 155 | 120 | G or H | F |
| 168 | 130 | H | F |
| 181 | 140 | H | F |
| 194 | 150 | H | F |
For SI: 1 foot = 304.8 mm; 1 mph = 0.447 m/s.
- The standard calculations contained in ASTM D 7158 assume Exposure Category B or C and building height of 60 feet or less. Additional calculations are required for conditions outside of these assumptions.
Fasteners for asphalt shingles shall be galvanized steel, stainless steel, aluminum or copper roofing nails, minimum 12-gage [0.105 inch (3 mm)] shank with a minimum 3/8-inch-diameter (9.5 mm) head, complying with ASTM F1667, of a length to penetrate through the roofing materials and not less than 3/4 inch (19.1 mm) into the roof sheathing. Where the roof sheathing is less than 3/4 inch (19.1 mm) thick, the fasteners shall penetrate through the sheathing.
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Asphalt shingles shall have the minimum number of fasteners required by the manufacturer, but not less than four fasteners per strip shingle or two fasteners per individual shingle. Where the roof slope exceeds 21 units vertical in 12 units horizontal (21:12, 175-percent slope), shingles shall be installed as required by the manufacturer.
Where required, ice barriers shall comply with Section R905.1.2.
Flashing for asphalt shingles shall comply with this section.
Base and cap flashing shall be installed in accordance with manufacturer's instructions. Base flashing shall be of either corrosion-resistant metal of minimum nominal 0.019-inch (0.5 mm) thickness or mineral-surfaced roll roofing weighing not less than 77 pounds per 100 square feet (4 kg/m2). Cap flashing shall be corrosion-resistant metal of minimum nominal 0.019-inch (0.5 mm) thickness.
Valley linings shall be installed in accordance with the manufacturer's instructions before applying shingles. Valley linings of the following types shall be permitted:
- For open valleys (valley lining exposed) lined with metal, the valley lining shall be not less than 24 inches (610 mm) wide and of any of the corrosion-resistant metals in Table R905.2.8.2.
- For open valleys, valley lining of two plies of mineral-surfaced roll roofing, complying with ASTM D 3909 or ASTM D 6380 Class M, shall be permitted. The bottom layer shall be 18 inches (457 mm) and the top layer not less than 36 inches (914 mm) wide.
- For closed valleys (valley covered with shingles), valley lining of one ply of smooth roll roofing complying with ASTM D 6380 and not less than 36 inches wide (914 mm) or valley lining as described in Item 1 or 2 shall be permitted. Self-adhering polymer modified bitumen underlayment complying with ASTM D 1970 shall be permitted in lieu of the lining material.
| MATERIAL | MINIMUM THICKNESS (inches) |
GAGE | WEIGHT (pounds) |
| Cold-rolled copper | 0.0216 nominal | — | ASTM B 370, 16 oz. per square foot |
| Lead-coated copper | 0.0216 nominal | — | ASTM B 101, 16 oz. per square foot |
| High-yield copper | 0.0162 nominal | — | ASTM B 370, 12 oz. per square foot |
| Lead-coated high-yield copper | 0.0162 nominal | — | ASTM B 101, 12 oz. per square foot |
| Aluminum | 0.024 | — | — |
| Stainless steel | — | 28 | — |
| Galvanized steel | 0.0179 | 26 (zinc coated G90) | — |
| Zinc alloy | 0.027 | — | — |
| Lead | — | — | 21/2 |
| Painted terne | — | — | 20 |
For SI: 1 inch = 25.4 mm, 1 pound = 0.454 kg.
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Base flashing against a vertical sidewall shall be continuous or step flashing and shall be not less than 4 inches (102 mm) in height and 4 inches (102 mm) in width and shall direct water away from the vertical sidewall onto the roof or into the gutter. Where siding is provided on the vertical sidewall, the vertical leg of the flashing shall be continuous under the siding. Where anchored masonry veneer is provided on the vertical sidewall, the base flashing shall be provided in accordance with this section and counterflashing shall be provided in accordance with Section R703.8.2.2. Where exterior plaster or adhered masonry veneer is provided on the vertical sidewall, the base flashing shall be provided in accordance with this section and Section R703.6.3.
Flashing against a vertical front wall, as well as soil stack, vent pipe and chimney flashing, shall be applied in accordance with the asphalt shingle manufacturer's printed instructions.
A drip edge shall be provided at eaves and rake edges of shingle roofs. Adjacent segments of drip edge shall be overlapped not less than 2 inches (51 mm). Drip edges shall extend not less than 1/4 inch (6.4 mm) below the roof sheathing and extend up back onto the roof deck not less than 2 inches (51 mm). Drip edges shall be mechanically fastened to the roof deck at not more than 12 inches (305 mm) o.c. with fasteners as specified in Section R905.2.5. Underlayment shall be installed over the drip edge along eaves and under the drip edge along rake edges.
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Clay and concrete roof tile shall be installed on roof slopes of two and one-half units vertical in 12 units horizontal (21/2:12) or greater. For roof slopes from two and one-half units vertical in 12 units horizontal (21/2:12) to four units vertical in 12 units horizontal (4:12), double underlayment application is required in accordance with Section R905.3.3.
Underlayment shall comply with Section R905.1.1.
Clay roof tile shall comply with ASTM C 1167.
Concrete roof tile shall comply with ASTM C 1492.
Nails shall be corrosion resistant and not less than 11 gage, 5/16-inch (11 mm) head, and of sufficient length to penetrate the deck not less than 3/4 inch (19 mm) or through the thickness of the deck, whichever is less. Attaching wire for clay or concrete tile shall not be smaller than 0.083 inch (2 mm). Perimeter fastening areas include three tile courses but not less than 36 inches (914 mm) from either side of hips or ridges and edges of eaves and gable rakes.
Tile shall be applied in accordance with this chapter and the manufacturer's installation instructions, based on the following:
- Climatic conditions.
- Roof slope.
- Underlayment system.
- Type of tile being installed.
| SHEATHING | ROOF SLOPE | NUMBER OF FASTENERS |
| Solid without battens | All | One per tile |
| Spaced or solid with battens and slope < 5:12 |
Fasteners not required | — |
| Spaced sheathing without battens |
5:12 ≤ slope < 12:12 | One per tile/every other row |
| 12:12 ≤ slope < 24:12 | One per tile |
At the juncture of roof vertical surfaces, flashing and counterflashing shall be provided in accordance with this chapter and the manufacturer's installation instructions and, where of metal, shall be not less than 0.019 inch (0.5 mm) (No. 26 galvanized sheet gage) corrosion-resistant metal. The valley flashing shall extend not less than 11 inches (279 mm) from the centerline each way and have a splash diverter rib not less than 1 inch (25 mm) in height at the flow line formed as part of the flashing. Sections of flashing shall have an end lap of not less than 4 inches (102 mm). For roof slopes of three units vertical in 12 units horizontal (25-percent slope) and greater, valley flashing shall have a 36-inch-wide (914 mm) underlayment of one layer of Type I underlayment running the full length of the valley, in addition to other required underlayment. In areas where the average daily temperature in January is 25°F (-4°C) or less, metal valley flashing underlayment shall be solid-cemented to the roofing underlayment for slopes less than seven units vertical in 12 units horizontal (58-percent slope) or be of self-adhering polymer modified bitumen sheet.
The installation of metal roof shingles shall comply with the provisions of this section.
Metal roof shingles shall be applied to a solid or closely fitted deck, except where the roof covering is specifically designed to be applied to spaced sheathing.
Metal roof shingles shall not be installed on roof slopes below three units vertical in 12 units horizontal (25-percent slope).
Underlayment shall comply with Section R905.1.1.
Where required, ice barriers shall comply with Section R905.1.2.
Metal roof shingle roof coverings shall comply with Table R905.10.3(1). The materials used for metal roof shingle roof coverings shall be naturally corrosion resistant or be made corrosion resistant in accordance with the standards and minimum thicknesses listed in Table R905.10.3(2).
Metal roof shingles shall be secured to the roof in accordance with this chapter and the approved manufacturer's installation instructions.
Roof valley flashing shall be of corrosion-resistant metal of the same material as the roof covering or shall comply with the standards in Table R905.10.3(1). The valley flashing shall extend not less than 8 inches (203 mm) from the centerline each way and shall have a splash diverter rib not less than 3/4 inch (19 mm) in height at the flow line formed as part of the flashing. Sections of flashing shall have an end lap of not less than 4 inches (102 mm). The metal valley flashing shall have a 36-inch-wide (914 mm) underlayment directly under it consisting of one layer of underlayment running the full length of the valley, in addition to underlayment required for metal roof shingles. In areas where the average daily temperature in January is 25°F (-4°C) or less, the metal valley flashing underlayment shall be solid cemented to the roofing underlayment for roof slopes under seven units vertical in 12 units horizontal (58-percent slope) or self-adhering polymer modified bitumen sheet.
The installation of mineral-surfaced roll roofing shall comply with this section.
Mineral-surfaced roll roofing shall be fastened to solidly sheathed roofs.
Underlayment shall comply with Section R905.1.1.
Where required, ice barriers shall comply with Section R905.1.2.
Mineral-surfaced roll roofing shall conform to ASTM D 3909 or ASTM D 6380, Class M.
Mineral-surfaced roll roofing shall be installed in accordance with this chapter and the manufacturer's instructions.
The installation of slate shingles shall comply with the provisions of this section.
Slate shingles shall be fastened to solidly sheathed roofs.
Underlayment shall comply with Section R905.1.1.
Where required, ice barriers shall comply with Section R905.1.2.
Slate shingles shall comply with ASTM C 406.
Minimum headlap for slate shingles shall be in accordance with Table R905.6.5. Slate shingles shall be secured to the roof with two fasteners per slate. Slate shingles shall be installed in accordance with this chapter and the manufacturer's instructions.
| SLOPE | HEADLAP (inches) |
| 4:12 ≤ slope < 8:12 | 4 |
| 8:12 ≤ slope < 20:12 | 3 |
| Slope ≤ 20:12 | 2 |
For SI: 1 inch = 25.4 mm.
Flashing and counterflashing shall be made with sheet metal. Valley flashing shall be not less than 15 inches (381 mm) wide. Valley and flashing metal shall be a minimum uncoated thickness of 0.0179-inch (0.5 mm) zinc coated G90. Chimneys, stucco or brick walls shall have not less than two plies of felt for a cap flashing consisting of a 4-inch-wide (102 mm) strip of felt set in plastic cement and extending 1 inch (25 mm) above the first felt and a top coating of plastic cement. The felt shall extend over the base flashing 2 inches (51 mm).
The installation of wood shingles shall comply with the provisions of this section.
Wood shingles shall be installed on solid or spaced sheathing. Where spaced sheathing is used, sheathing boards shall be not less than 1-inch by 4-inch (25 mm by 102 mm) nominal dimensions and shall be spaced on centers equal to the weather exposure to coincide with the placement of fasteners.
In areas where the average daily temperature in January is 25°F (-4°C) or less, solid sheathing is required on that portion of the roof requiring the application of an ice barrier.
Underlayment shall comply with Section R905.1.1.
Where required, ice barriers shall comply with Section R905.1.2.
Wood shingles shall be of naturally durable wood and comply with the requirements of Table R905.7.4.
| MATERIAL | MINIMUM GRADES | APPLICABLE GRADING RULES |
| Wood shingles of natu- rally durable wood |
1, 2 or 3 | Cedar Shake and Shingle Bureau |
Wood shingles shall be installed in accordance with this chapter and the manufacturer's instructions. Wood shingles shall be laid with a side lap not less than 11/2 inches (38 mm) between joints in courses, and two joints shall not be in direct alignment in any three adjacent courses. Spacing between shingles shall be not less than 1/4 inch to 3/8 inch (6.4 mm to 9.5 mm). Weather exposure for wood shingles shall not exceed those set in Table R905.7.5(1). Fasteners for untreated (naturally durable) wood shingles shall be box nails in accordance with Table R905.7.5(2). Nails shall be stainless steel Type 304 or 316 or hot-dipped galvanized with a coating weight of ASTM A 153 Class D (1.0 oz/ft2). Alternatively, two 16-gage stainless steel Type 304 or 316 staples with crown widths 7/16 inch (11.1 mm) minimum, 3/4 inch (19.1 mm) maximum, shall be used. Fasteners installed within 15 miles (24 km) of salt water coastal areas shall be stainless steel Type 316. Fasteners for fire-retardant-treated shingles in accordance with Section R902 or pressure-impregnated-preservative-treated shingles of naturally durable wood in accordance with AWPA U1 shall be stainless steel Type 316. All fasteners shall have a minimum penetration into the sheathing of 3/4 inch (19.1 mm). For sheathing less than 3/4 inch in (19.1 mm) thickness, each fastener shall penetrate through the sheathing. Wood shingles shall be attached to the roof with two fasteners per shingle, positioned in accordance with the manufacturer's installation instructions. Fastener packaging shall bear a label indicating the appropriate grade material or coating weight.
| ROOFING MATERIAL |
LENGTH (inches) |
GRADE | EXPOSURE (inches) | |
| 3:12 pitch to < 4:12 |
4:12 pitch or steeper |
|||
| Shingles of naturally durable wood |
16 | No. 1 | 33/4 | 5 |
| No. 2 | 31/2 | 4 | ||
| No. 3 | 3 | 31/2 | ||
| 18 | No. 1 | 41/4 | 51/2 | |
| No. 2 | 4 | 41/2 | ||
| No. 3 | 31/2 | 4 | ||
| 24 | No. 1 | 53/4 | 71/2 | |
| No. 2 | 51/2 | 61/2 | ||
| No. 3 | 5 | 51/2 | ||
For SI: 1 inch = 25.4 mm.
| SHAKES | NAIL TYPE AND MINIMUM LENGTH |
MINIMUM HEAD SIZE |
MINIMUM SHANK DIAMETER |
| 18" straight-split | 5d box 13/4" | 0.19" | .080" |
| 18" and 24" handsplit and resawn |
6d box 2" | 0.19" | .0915" |
| 24" taper-split | 5d box 13/4" | 0.19" | .080" |
| 18" and 24" tapersawn | 6d box 2" | 0.19" | .0915" |
| Shingles | Nail Type and Minimum Length |
||
| 16" and 18" | 3d box 11/4" | 0.19" | .080" |
| 24" | 4d box 11/2" | 0.19" | .080" |
Roof flashing shall be not less than No. 26 gage [0.019 inches (0.5 mm)] corrosion-resistant sheet metal and shall extend 10 inches (254 mm) from the centerline each way for roofs having slopes less than 12 units vertical in 12 units horizontal (100-percent slope), and 7 inches (178 mm) from the centerline each way for slopes of 12 units vertical in 12 units horizontal and greater. Sections of flashing shall have an end lap of not less than 4 inches (102 mm).
The installation of wood shakes shall comply with the provisions of this section.
Wood shakes shall be used only on solid or spaced sheathing. Where spaced sheathing is used, sheathing boards shall be not less than 1-inch by 4-inch (25 mm by 102 mm) nominal dimensions and shall be spaced on centers equal to the weather exposure to coincide with the placement of fasteners. Where 1-inch by 4-inch (25 mm by 102 mm) spaced sheathing is installed at 10 inches (254 mm) on center, additional 1-inch by 4-inch (25 mm by 102 mm) boards shall be installed between the sheathing boards.
In areas where the average daily temperature in January is 25°F (-4°C) or less, solid sheathing is required on that portion of the roof requiring an ice barrier.
Underlayment shall comply with Section R905.1.1.
Where required, ice barriers shall comply with Section R905.1.2.
Interlayment shall comply with ASTM D226, Type I.
Wood shakes shall comply with the requirements of Table R905.8.5.
| MATERIAL | MINIMUM GRADES |
APPLICABLE GRADING RULES |
| Wood shakes of naturally durable wood |
1 | Cedar Shake and Shingle Bureau |
| Tapersawn shakes of naturally durable wood |
1 or 2 | Cedar Shake and Shingle Bureau |
| Preservative-treated shakes and shingles of naturally durable wood |
1 | Cedar Shake and Shingle Bureau |
| Fire-retardant-treated shakes and shingles of naturally durable wood |
1 | Cedar Shake and Shingle Bureau |
| Preservative-treated tapersawn shakes of Southern pine treated in accordance with AWPA Standard U1 (Commodity Specification A, Use Category 3B and Section 5.6) |
1 or 2 | Forest Products Laboratory of the Texas Forest Services |
Wood shakes shall be installed in accordance with this chapter and the manufacturer's installation instructions. Wood shakes shall be laid with a side lap not less than 11/2 inches (38 mm) between joints in adjacent courses. Spacing between shakes in the same course shall be 3/8 inch to 5/8 inch (9.5 mm to 15.9 mm) including tapersawn shakes. Weather exposures for wood shakes shall not exceed those set in Table R905.8.6. Fasteners for untreated (naturally durable) wood shakes shall be box nails in accordance with Table R905.7.5(2). Nails shall be stainless steel Type 304, or Type 316 or hot-dipped with a coating weight of ASTM A153 Class D (1.0 oz/ft2). Alternatively, two 16-gage Type 304 or Type 316 stainless steel staples, with crown widths 7/16 inch (11.1 mm) minimum, 3/4 inch (19.1 mm) maximum, shall be used. Fasteners installed within 15 miles (24 km) of salt water coastal areas shall be stainless steel Type 316. Wood shakes shall be attached to the roof with two fasteners per shake positioned in accordance with the manufacturer's installation instructions Fasteners for fire-retardant-treated (as defined in Section R902) shakes or pressure-impregnated-preservative-treated shakes of naturally durable wood in accordance with AWPA U1 shall be stainless steel Type 316. All fasteners shall have a minimum penetration into the sheathing of 3/4 inch (19.1 mm). Where the sheathing is less than 3/4 inch (19.1 mm) thick, each fastener shall penetrate through the sheathing. Fastener packaging shall bear a label indicating the appropriate grade material or coating weight.
| ROOFING MATERIAL | LENGTH (inches) |
GRADE | EXPOSURE (inches) |
| 4:12 pitch or steeper | |||
| Shakes of naturally durable wood | 18 | No. 1 | 71/2 |
| 24 | No. 1 | 10a | |
| Preservative-treated tapersawn shakes of Southern Yellow Pine |
18 | No. 1 | 71/2 |
| 24 | No. 1 | 10 | |
| 18 | No. 2 | 51/2 | |
| 24 | No. 2 | 71/2 | |
| Taper-sawn shakes of naturally durable wood |
18 | No. 1 | 71/2 |
| 24 | No. 1 | 10 | |
| 18 | No. 2 | 51/2 | |
| 24 | No. 2 | 71/2 |
For SI: 1 inch = 25.4 mm.
- For 24-inch by 3/8-inch handsplit shakes, the maximum exposure is 71/2 inches.
The starter course at the eaves shall be doubled and the bottom layer shall be either 15-inch (381 mm), 18-inch (457 mm) or 24-inch (610 mm) wood shakes or wood shingles. Fifteen-inch (381 mm) or 18-inch (457 mm) wood shakes shall be permitted to be used for the final course at the ridge. Shakes shall be interlaid with 18-inch-wide (457 mm) strips of not less than No. 30 felt shingled between each course in such a manner that no felt is exposed to the weather by positioning the lower edge of each felt strip above the butt end of the shake it covers a distance equal to twice the weather exposure.
Roof valley flashing shall be not less than No. 26 gage [0.019 inch (0.5 mm)] corrosion-resistant sheet metal and shall extend not less than 11 inches (279 mm) from the centerline each way. Sections of flashing shall have an end lap of not less than 4 inches (102 mm).
The installation of built-up roofs shall comply with the provisions of this section.
Built-up roof covering materials shall comply with the standards in Table R905.9.2 or UL 55A.
| MATERIAL STANDARD | STANDARD |
| Acrylic coatings used in roofing | ASTM D 6083 |
| Aggregate surfacing | ASTM D 1863 |
| Asphalt adhesive used in roofing | ASTM D 3747 |
| Asphalt cements used in roofing | ASTM D 2822; D 3019; D 4586 |
| Asphalt-coated glass fiber base sheet | ASTM D 4601 |
| Asphalt coatings used in roofing | ASTM D 1227; D 2823; D 2824; D 4479 |
| Asphalt glass felt | ASTM D 2178 |
| Asphalt primer used in roofing | ASTM D 41 |
| Asphalt-saturated and asphalt-coated organic felt base sheet | ASTM D 2626 |
| Asphalt-saturated organic felt (perforated) | ASTM D 226 |
| Asphalt used in roofing | ASTM D 312 |
| Coal-tar cements used in roofing | ASTM D 4022; D 5643 |
| Coal-tar primer used in roofing, dampproofing and waterproofing | ASTM D 43 |
| Coal-tar saturated organic felt | ASTM D 227 |
| Coal-tar used in roofing | ASTM D 450, Type I or II |
| Glass mat, coal tar | ASTM D 4990 |
| Glass mat, venting type | ASTM D 4897 |
| Mineral-surfaced inorganic cap sheet | ASTM D 3909 |
| Thermoplastic fabrics used in roofing | ASTM D 5665; D 5726 |
Built-up roofs shall be installed in accordance with this chapter and the manufacturer's instructions.
The installation of metal roof panels shall comply with the provisions of this section.
Metal roof panel roof coverings shall be applied to solid or spaced sheathing, except where the roof covering is specifically designed to be applied to spaced supports.
Minimum slopes for metal roof panels shall comply with the following:
- The minimum slope for lapped, nonsoldered-seam metal roofs without applied lap sealant shall be three units vertical in 12 units horizontal (25-percent slope).
- The minimum slope for lapped, nonsoldered-seam metal roofs with applied lap sealant shall be one-half unit vertical in 12 units horizontal (4-percent slope). Lap sealants shall be applied in accordance with the approved manufacturer's installation instructions.
- The minimum slope for standing-seam roof systems shall be one-quarter unit vertical in 12 units horizontal (2-percent slope).
Metal-sheet roof covering systems that incorporate supporting structural members shall be designed in accordance with the International Building Code. Metal-sheet roof coverings installed over structural decking shall comply with Table R905.10.3(1). The materials used for metal-sheet roof coverings shall be naturally corrosion resistant or provided with corrosion resistance in accordance with the standards and minimum thicknesses shown in Table R905.10.3(2).
| ROOF COVERING TYPE | STANDARD APPLICATION RATE/THICKNESS |
| Galvanized steel | ASTM A 653 G90 Zinc coated |
| Stainless steel | ASTM A 240, 300 Series alloys |
| Steel | ASTM A 924 |
| Lead-coated copper | ASTM B 101 |
| Cold-rolled copper | ASTM B 370 minimum 16 oz/sq ft and 12 oz/sq ft high-yield copper for metal-sheet roof-covering systems; 12 oz/sq ft for preformed metal shingle systems. |
| Hard lead | 2 lb/sq ft |
| Soft lead | 3 lb/sq ft |
| Aluminum | ASTM B 209, 0.024 minimum thickness for roll-formed panels and 0.019-inch minimum thickness for pressformed shingles. |
| Terne (tin) and terne-coated stainless | Terne coating of 40 lb per double base box, field painted where applicable in accordance with manufacturer's installation instructions. |
| Zinc | 0.027 inch minimum thickness: 99.995% electrolytic high-grade zinc with alloy additives of copper (0.08 - 0.20%), titanium (0.07% - 0.12%) and aluminum (0.015%). |
For SI: 1 ounce per square foot = 0.305 kg/m2, 1 pound per square foot = 4.214 kg/m2, 1 inch = 25.4 mm, 1 pound = 0.454 kg.
| 55% aluminum-zinc alloy coated steel | ASTM A 792 AZ 50 |
| 5% aluminum alloy-coated steel | ASTM A 875 GF60 |
| Aluminum-coated steel | ASTM A 463 T2 65 |
| Galvanized steel | ASTM A 653 G-90 |
| Prepainted steel | ASTM A 755a |
- Paint systems in accordance with ASTM A 755 shall be applied over steel products with corrosion-resistant coatings complying with ASTM A 792, ASTM A 875, ASTM A 463, or ASTM A 653.
Metal roof panels shall be secured to the supports in accordance with this chapter and the manufacturer's installation instructions. In the absence of manufacturer's installation instructions, the following fasteners shall be used:
- Galvanized fasteners shall be used for steel roofs.
- Copper, brass, bronze, copper alloy and 300-series stainless steel fasteners shall be used for copper roofs.
- Stainless steel fasteners are acceptable for metal roofs.
Underlayment shall comply with Section R905.1.1.
The installation of modified bitumen roofing shall comply with the provisions of this section.
Modified bitumen roof coverings shall comply with the standards in Table R905.11.2.
| MATERIAL | STANDARD |
| Acrylic coating | ASTM D 6083 |
| Asphalt adhesive | ASTM D 3747 |
| Asphalt cement | ASTM D 3019 |
| Asphalt coating | ASTM D 1227; D 2824 |
| Asphalt primer | ASTM D 41 |
| Modified bitumen roof membrane | ASTM D 6162; D 6163; D 6164; D 6222; D 6223; D 6298; CGSB 37-GP-56M |
Modified bitumen roofs shall be installed in accordance with this chapter and the manufacturer's instructions.
The installation of thermoset single-ply roofing shall comply with the provisions of this section.
Thermoset single-ply roof coverings shall comply with ASTM D 4637, ASTM D 5019 or CGSB 37-GP-52M.
Thermoset single-ply roofs shall be installed in accordance with this chapter and the manufacturer's instructions.
The installation of thermoplastic single-ply roofing shall comply with the provisions of this section.
Thermoplastic single-ply roof coverings shall comply with ASTM D 4434, ASTM D 6754, ASTM D 6878 or CGSB CAN/CGSB 37.54.
Thermoplastic single-ply roofs shall be installed in accordance with this chapter and the manufacturer's instructions.
The installation of sprayed polyurethane foam roofing shall comply with the provisions of this section.
Spray-applied polyurethane foam insulation shall comply with ASTM C1029, Type III or IV or ASTM D7425.
Foamed-in-place roof insulation shall be installed in accordance with this chapter and the manufacturer's instructions. A liquid-applied protective coating that complies with Table R905.14.3 shall be applied not less than 2 hours nor more than 72 hours following the application of the foam.
| MATERIAL | STANDARD |
| Acrylic coating | ASTM D 6083 |
| Silicone coating | ASTM D 6694 |
| Moisture-cured polyurethane coating | ASTM D 6947 |
Foam plastic materials and installation shall comply with Section R316.
The installation of liquid-applied roofing shall comply with the provisions of this section.
Liquid-applied roofing shall comply with ASTM C 836, C 957, D 1227, D 3468, D 6083, D 6694 or D 6947.
Liquid-applied roofing shall be installed in accordance with this chapter and the manufacturer's instructions.
The installation of photovoltaic shingles shall comply with the provisions of this section, Section R324 and NFPA 70.
Photovoltaic shingles shall be applied to a solid or closely-fitted deck, except where the roof covering is specifically designed to be applied over spaced sheathing.
Photovoltaic shingles shall be used only on roof slopes of two units vertical in 12 units horizontal (2:12) or greater.
Unless otherwise noted, required underlayment shall conform to ASTM D4869 or ASTM D6757.
Underlayment shall be applied shingle fashion, parallel to and starting from the eave, lapped 2 inches (51 mm) and fastened sufficiently to hold in place.
In areas where there has been a history of ice forming along the eaves causing a backup of water, as designated in Table R301.2(1), an ice barrier that consists of not less than two layers of underlayment cemented together or of a self-adhering polymer modified bitumen sheet shall be used in lieu of normal underlayment and extend from the lowest edges of all roof surfaces to a point not less than 24 inches (610 mm) inside the exterior wall line of the building.
Exception: Detached accessory structures that contain no conditioned floor area.
Exception: Detached accessory structures that contain no conditioned floor area.
Underlayment applied in areas subject to high winds [above 140 mph (63 m/s), in accordance with Figure R301.2(4)A] shall be applied with corrosion-resistant fasteners in accordance with the manufacturer's installation instructions. Fasteners are to be applied along the overlap not farther apart than 36 inches (914 mm) on center.
Underlayment installed where the ultimate design wind speed equals or exceeds 150 mph (67 m/s) shall comply with ASTM D4869 Type IV, or ASTM D6757. The underlayment shall be attached in a grid pattern of 12 inches (305 mm) between side laps with a 6-inch (152 mm) spacing at the side laps. Underlayment shall be applied as required for asphalt shingles in accordance with Table R905.1.1(2). Underlayment shall be attached using metal or plastic cap nails with a head diameter of not less than 1 inch (25 mm) with a thickness of not less than 32-gage sheet metal. The cap-nail shank shall be not less than 12 gage (0.105 inches) with a length to penetrate through the roof sheathing or not less than 3/4 inch (19 mm) into the roof sheathing.
Exception: As an alternative, adhered underlayment complying with ASTM D1970 shall be permitted.
Underlayment installed where the ultimate design wind speed equals or exceeds 150 mph (67 m/s) shall comply with ASTM D4869 Type IV, or ASTM D6757. The underlayment shall be attached in a grid pattern of 12 inches (305 mm) between side laps with a 6-inch (152 mm) spacing at the side laps. Underlayment shall be applied as required for asphalt shingles in accordance with Table R905.1.1(2). Underlayment shall be attached using metal or plastic cap nails with a head diameter of not less than 1 inch (25 mm) with a thickness of not less than 32-gage sheet metal. The cap-nail shank shall be not less than 12 gage (0.105 inches) with a length to penetrate through the roof sheathing or not less than 3/4 inch (19 mm) into the roof sheathing.
Exception: As an alternative, adhered underlayment complying with ASTM D1970 shall be permitted.
Photovoltaic shingles shall be listed and labeled in accordance with UL 1703.
Photovoltaic shingles shall be attached in accordance with the manufacturer's installation instructions.
Photovoltaic shingles shall be tested in accordance with procedures and acceptance criteria in ASTM D3161. Photovoltaic shingles shall comply with the classification requirements of Table R905.2.4.1 for the appropriate maximum basic wind speed. Photovoltaic shingle packaging shall bear a label to indicate compliance with the procedures in ASTM D3161 and the required classification from Table R905.2.4.1.
The use of above-deck thermal insulation shall be permitted provided such insulation is covered with an approved roof covering and complies with FM 4450 or UL 1256.
Above-deck thermal insulation board shall comply with the standards in Table R906.2.
| Cellular glass board | ASTM C552 |
| Composite boards | ASTM C1289, Type III, IV, V or VI |
| Expanded polystyrene | ASTM C578 |
| Extruded polystyrene board | ASTM C578 |
| Perlite board | ASTM C728 |
| Polyisocyanurate board | ASTM C1289, Type I or II |
| Wood fiberboard | ASTM C208 |
| Fiber-reinforced gypsum board |
ASTM C1278 |
| Glass-faced gypsum board | ASTM C1177 |
Rooftop-mounted photovoltaic panels or modules shall be installed in accordance with this section, Section R324 and NFPA 70.
Rooftop-mounted photovoltaic panel or modules systems shall be installed to resist the component and cladding loads specified in Table R301.2(2), adjusted for height and exposure in accordance with Table R301.2(3).
Rooftop-mounted photovoltaic panels or modules shall have the same fire classification as the roof assembly required in Section R902.
Rooftop-mounted photovoltaic panels or modules shall be installed in accordance with the manufacturer's instructions.
Rooftop-mounted photovoltaic panels and modules shall be listed and labeled in accordance with UL 1703 and shall be installed in accordance with the manufacturer's printed instructions.
Materials and methods of application used for re-covering or replacing an existing roof covering shall comply with the requirements of Chapter 9.
Exceptions:
Exceptions:
- Reroofing shall not be required to meet the minimum design slope requirement of one-quarter unit vertical in 12 units horizontal (2-percent slope) in Section R905 for roofs that provide positive roof drainage.
- For roofs that provide positive drainage, re-covering or replacing an existing roof covering shall not require the secondary (emergency overflow) drains or scuppers of Section R903.4.1 to be added to an existing roof.
The structural roof components shall be capable of supporting the roof covering system and the material and equipment loads that will be encountered during installation of the roof covering system.
Roof replacement shall include the removal of existing layers of roof coverings down to the roof deck.
Exception: Where the existing roof assembly includes an ice barrier membrane that is adhered to the roof deck, the existing ice barrier membrane shall be permitted to remain in place and covered with an additional layer of ice barrier membrane in accordance with Section R905.
Exception: Where the existing roof assembly includes an ice barrier membrane that is adhered to the roof deck, the existing ice barrier membrane shall be permitted to remain in place and covered with an additional layer of ice barrier membrane in accordance with Section R905.
The installation of a new roof covering over an existing roof covering shall be permitted where any of the following conditions occur:
- Where the new roof covering is installed in accordance with the roof covering manufacturer's approved instructions
- Complete and separate roofing systems, such as standing-seam metal roof systems, that are designed to transmit the roof loads directly to the building's structural system and do not rely on existing roofs and roof coverings for support, shall not require the removal of existing roof coverings.
- Metal panel, metal shingle and concrete and clay tile roof coverings shall be permitted to be installed over existing wood shake roofs where applied in accordance with Section R908.4.
- The application of a new protective coating over an existing spray polyurethane foam roofing system shall be permitted without tear-off of existing roof coverings.
A roof re-cover shall not be permitted where any of the following conditions occur:
- Where the existing roof or roof covering is water soaked or has deteriorated to the point that the existing roof or roof covering is not adequate as a base for additional roofing.
- Where the existing roof covering is slate, clay, cement or asbestos-cement tile.
- Where the existing roof has two or more applications of any type of roof covering.
Where the application of a new roof covering over wood shingle or shake roofs creates a combustible concealed space, the entire existing surface shall be covered with gypsum board, mineral fiber, glass fiber or other approved materials securely fastened in place.
Existing slate, clay or cement tile shall be permitted for reinstallation, except that damaged, cracked or broken slate or tile shall not be reinstalled. Any existing flashings, edgings, outlets, vents or similar devices that are a part of the assembly shall be replaced where rusted, damaged or deteriorated. Aggregate surfacing materials shall not be reinstalled.
Flashings shall be reconstructed in accordance with approved manufacturer's installation instructions. Metal flashing to which bituminous materials are to be adhered shall be primed prior to installation.
The installation of photovoltaic panel systems that are mounted on or above the roof covering shall comply with this section, Section R324 and NFPA 70.
Rooftop-mounted photovoltaic panel systems shall be designed to structurally support the system and withstand applicable gravity loads in accordance with Chapter 3. The roof upon which these systems are installed shall be designed and constructed to support the loads imposed by such systems in accordance with Chapter 8.
Rooftop-mounted photovoltaic systems shall be installed in accordance with the manufacturer's instructions. Roof penetrations shall be flashed and sealed in accordance with this chapter.