A220.127.116.11 Single-Layer in Cavity and Double-Layer Walls
The U-factor of metal building walls that are insulated with a single-layer in cavity or multiple layers of mineral fiber insulation (see Figure A18.104.22.168) shall be calculated using the procedure outlined in this section. For double-layer walls, the procedure assumes that the outer layer of insulation is compressed between the wall panel and girt. There may also be a thermal spacer block or continuous insulation present. Air spaces may also exist depending on the specific drape profiles.
There are nine steps in the calculation process:
Step 1—Characterize the thermal conductivity of the mineral fiber insulation.
Step 2—Define the parabolic profiles for each insulation layer.
Step 4—Calculate the R-value inside the girt and adjacent to the web.
Step 7—Calculate the overall insulation assembly using the R-values in Steps 3 and 6.
Step 8—Calculate the U-factor from the finite element analysis results.
Step 9—Calculate the U-factor for any continuous insulation if present.
Step 1: The thermal conductivity of the mineral fiber insulation is represented by a thermal curve of the form in Equation A9.4-22:
|k||=||thermal conductivity, Btu•ft/h•ft2•°F|
|ρo||=||nominal density, lb/ft3|
|δo||=||nominal thickness, ft|
|y||=||thickness of insulation, ft|
Step 2: Assume that each layer of mineral fiber has a parabolic profile defined by Equation A9.4-23:
|x||=||distance from edge of girt, ft|
|y||=||distance from edge of wall panel, ft|
|Yo||=||insulation thickness at x = 0, ft|
|Ym||=||insulation thickness at x = Xm, ft|
Because the configuration can possibly consist of both mineral fiber insulation and an air space, the composite is given by Equation A9.4-24:
where ka is the thermal conductivity of air in Btu•ft/h•ft2•°F.
The trapezoidal integration method is used to evaluate the integral and calculate R and is given by Equation A9.4-25:
|xk||=||point to analyze along the x-axis, ft|
|xk+1||=||point ahead of the point being analyzed, ft|
|yk||=||thickness at point being analyzed, ft|
|yk+1||=||thickness at point ahead of the point being analyzed, ft|
The integral represents the combined R-value of the air space and insulation over the region 0 < x < Xa. Because the thermal conductivity of air is independent of the thickness, Equation 9.4.25 can be simplified using the air space mean thickness (Ya) to produce Equation A9.4-26:
However, if the air space is characterized by convection instead of conduction then the term Ya/ka can be replaced by the R-value for convection (R-0.92 h•ft2•°F/Btu for walls). Adding the inside and outside layers is expressed in Equation A9.4-27:
Add the air film resistances at the exterior (RAT) and interior (RAB), which are defined as Equation A9.4-28:
where hAB is the air film heat transfer coefficient at the exterior in Btu/h•ft2•°F.
where hAT is the air film heat transfer coefficient at the interior in Btu/h•ft2•°F.
The sum of the R-values for the insulation and air films beyond the girt are expressed in Equation A9.4-30.
Step 4: Calculate the R-values inside the girt and adjacent to the web.
The R-values inside the girt are the air space (RAUP) added in series with the insulation (R2UP); their combined value is then added in parallel to RPUP. Depending on the thickness of the air space, it can be modeled as conduction as shown in Equation A9.4-31:
|H3||=||thickness of the air space, ft|
|ka||=||thermal conductivity of air, Btu•ft/h•ft2•°F|
The R-value for R2UP is expressed in Equation A9.4-32. The insulation thickness is also not limited by the girt height and can extend beyond it.
where H4 is the thickness of the mineral fiber at x = 0 in feet.
The R-value of the web (RPUP) is calculated using 26.2 h•ft2•°F/Btu as the thermal conductivity of the girt in Equation A9.4-33:
|kp||=||thermal conductivity of the girt, Btu•ft/h-ft2•°F|
|Web Height||=||height of the girt, ft|
Equation A9.4-34 can be rearranged and solved for RUP as presented in Equation A9.4-35:
Because the thickness of the girt is significantly less than the flange width (Lj), Equation A9.4-35 can be simplified as Equation A9.4-36. However it is important to note that RUP will be close to 2 or lower (depending on how the air is modeled) because of the significant effects of the steel girt:
Typical construction above the girt consists of a thermal spacer block and compressed mineral fiber insulation. These two insulations are in series, and the total R-value (ROPI) is expressed as Equation A9.4-37. If there is thermal break tape present it is included as the third insulation in this series.
|H1||=||thickness of thermal spacer block, ft|
|H2||=||thickness of compressed mineral fiber insulation, ft|
|kf||=||thermal conductivity of the thermal spacer block, Btu•ft/h•ft2•°F|
|kI||=||thermal conductivity of the compressed mineral fiber insulation, Btu•ft/h•ft2•°F|
The impact of the thermal bridging associated with the outside of the girt and the insulation is to reduce the thermal resistance of the insulation. The reduction is calculated using Equation A9.4-38:
The next calculation is to add the inside and outdoor air film coefficients using Equation A9.4-40:
Step 7: Calculate the overall insulation assembly using the R-values in Steps 3 and 6.
Step 8: Calculate the U-factor from the finite element analysis results.
The overall U-factor for the insulation assembly is determined using Equation A9.4-42:
|Uadj||=||adjusted overall U-factor represented by the correlation with the finite element modeling in Btu/h•ft2•°F.|
Step 9: Calculate the overall U-factor for any continuous insulation if present.
If there is any continuous insulation present, first calculate the R-value adjacent to the flange using Equation A9.4-43:
|RBFci||=||thermal resistance of continuous insulation adjacent to the flange, h•ft2•°F/Btu|
|Rci||=||thermal resistance of the continuous insulation, h•ft2•°F/Btu|
|hci||=||thickness of the continuous insulation, ft|
Next, calculate the area-weighted R-value for the continuous insulation using Equation A9.4-44:
|Roci||=||overall thermal resistance of continuous insulation in h•ft2•°F/Btu|
Finally, calculate the overall U-factor using Equation A9.4-45: