# A9.4.6.1 Single-Layer Roof and Single-Layer Compressed Wall

The *U-factor* of *metal building roofs* or *metal building walls* that are insulated with a single layer of fiberglass insulation (see Figure A9.4.6.1) shall be calculated using the procedure outlined in this section. The procedure assumes the insulation is compressed over the purlin or girt. There may also be a thermal spacer block present.

There are six steps in the calculation process:

Step 1—Characterize the thermal conductivity of the fiberglass.

Step 2—Determine the *U-factor* for the insulation in the cavity.

Step 3—Determine the *U-factor* over the structural framing member.

Step 4—Area weight the *U-factors* calculated in Steps 2 and 3.

Step 5—Determine the *U-factor* from the finite element analysis results.

Step 6—Determine the *U-factor* for any *continuous insulation* if present.

**Step 1:** The thermal conductivity of the fiberglass batt insulation is represented by a thermal curve of the form in Equation A9.4-2:

(A9.4-2) |

where

k |
= | thermal conductivity, Btu/h•ft•°F |

ρ | = | density, lb/ft^{3} |

A |
= | 0.014917 |

B |
= | 0.0004377 |

C |
= | 0.0056897 |

**Step 2:** Assume the fiberglass batt forms a parabolic profile defined by Equation A9.4-3:

(A9.4-3) |

Determine the cavity *U-factor* (*U _{c}*) using Equation A9.4-4:

(A9.4-4) |

where

ρ_{o} |
= | reference density of the fiberglass, lb/ft^{3} |

t_{o} |
= | reference thickness of the fiberglass, ft |

The properties of fiberglass insulation are presented in Table A9.4.6.1.

**Table A9.4.6.1 Fiberglass Reference Properties**

R-Value, h•ft^{2}•°F/Btu |
Weight, lb/ft^{2} |
Density, lb/ft^{3} |
Thickness, ft |
---|---|---|---|

10 | 0.149 | 0.605 | 0.2458 |

11 | 0.168 | 0.630 | 0.2667 |

13 | 0.199 | 0.628 | 0.3167 |

16 | 0.243 | 0.634 | 0.3833 |

19 | 0.297 | 0.653 | 0.4542 |

25 | 0.427 | 0.742 | 0.5750 |

30 | 0.520 | 0.766 | 0.6792 |

Include the thermal resistances of the interior (*R _{i}*) and exterior (

*R*) air films to calculate the overall cavity

_{e}*U-factor*(

*U*) using Equation A9.4-5:

_{co}(A9.4-5) |

**Step 3:** Determine the *U-factor(U _{fo}*) over the structural framing member. The variable

*Y*represents the total combined thickness of the thermal spacer block and the compressed insulation. The density of the compressed insulation is determined by Equation A9.4-6:

_{o}(A9.4-6) |

where

ρ_{c} |
= | density of the compressed insulation over the framing member, lb/ft^{3} |

t_{c} |
= | thickness of the compressed insulation over the framing member, ft |

Determine the *thermal resistance* of the compressed insulation (*R _{c}*) using Equation A9.4-7:

(A9.4-7) |

Determine the overall framing *U-factor* (*U _{fo}*) at the structural framing member, including the air film resistances, using Equation A9.4-8:

(A9.4-8) |

where

U_{fo} |
= | U-factor over the structural framing member, Btu/h•ft^{2}•°F |

R_{TB} |
= | R-value of the thermal spacer block, h•ft^{2}•°F/Btu |

R_{c} |
= | R-value of the compressed insulation, h•ft^{2}•°F/Btu |

**Step 4:** Determine the overall area-weighted *U-factor* for the entire *system* using Equation A9.4-9:

(A9.4-9) |

where

U_{es} |
= | area weighted U-factor for the entire system, Btu/h•ft^{2}•°F |

w_{f} |
= | width of purlin or girt flange, ft |

**Step 5:** Calculate the adjusted overall *U-factor* (*U _{adj}*) using Equation A9.4-10:

(A9.4-10) |

where

U_{adj} |
= | adjusted overall U-factor represented by correlation with the finite element modeling, Btu/h•ft^{2}•°F |

**Step 6:** If there is any *continuous insulation* present, calculate the overall *U-factor* using Equation A9.4-11:

(A9.4-11) |

**Figure A9.4.6.1 Geometry of single-layer fiberglass batt.**

where

X | = | distance from edge of purlin or girt, ft |

Y | = | distance from edge of roof panel or wall panel, ft |

L | = | length from edge of purlin or girt to centerline of cavity, ft |

w_{f} |
= | width of purlin or girt flange, ft |

Y_{o} |
= | distance between purlin or girt and the roof panel or wall panel, ft |

Y_{m} |
= | distance from edge of roof panel or wall panel at the cavity centerline, ft |

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