Masonry Magazine June 1975 Page. 14
This masonry bonded wall built of 4 by 4 by 12-in. units provides a through-the-wall bonder unit for every 4 sq ft of wall surface. Calculations of the Uavg of this wall is as follows:
Area of path A at the bonder unit = 4 x 4/144 = 0.1111 sq ft; a = 0.1111/4 = 0.0278.
Area of path B at the cavity = 4.0 - 0.1111 = 3.8889 sq ft; b = 3.8889/4.0 = 0.9722.
Calculate Ua at path A as follows:
Material Ra
Outside air surface = 0.17
12-in. brick = 1.32
Inside air surface = 0.68
Rat = 2.17
Ua = 1/Rat = 1/2.17 = 0.461
Calculate Ub at path B as follows:
Material Rb
Outside air surface = 0.17
4-in. brick = 0.44
4-in. vermiculite insulation = 9.08
4-in. brick = 0.44
Inside air surface = 0.68
Rbt = 10.81
Ub = 1/Rbt = 1/10.81 = 0.0925
Calculate Uavg as follows:
Uavg = a(Ua) + b(Ub)
= 0.0278(0.461) + 0.9722(0.0925)
= 0.103
If the thermal bridge at the bonder were ignored, the U value would be the same as Ub, which is 0.093. This is approximately a 10 percent differential between the series and parallel path calculated transmission coefficients.
The metal-tied cavity wall shown in Fig. 3 requires the parallel path method of calculation be run. However, a slightly different method of calculation is required. The ASHRAE Handbook of Fundamentals requires that calculations for metallic thermal bridges be done by the Zone Method. Under this method a slightly larger area is assumed to be affected by the metallic bridge than just the area of the metal. The wall is divided into two zones; zone A containing the metal, and zone B the remaining portion of the wall.
The Handbook also prescribes a method for determining the size and shape of zone A. The surface shape of zone A in the case of a metal beam would be a strip of width, W, centered on the beam. In the wall shown in Fig. 3 the shape of zone A, due to the circular tie, would be a circle of diameter W. W is calculated from the following formula:
W = m + 2d
where:
W = width or diameter of the zone,
m = width or diameter of the metal heat path,
d = distance from the panel surface to the metal in inches. The value of d should not be taken as less than 0.5 in.
Calculations for W should be run for both surfaces and the larger of the two values used. One metal tie is provided for each 4½ sq ft of wall surface.
Calculate W for the metal-tied cavity wall shown in Fig. 3.
W = m + 2d = 3/16 + 2(1.75)
= 0.1875 + 2(1.75) = 3.6875 in.
This is the diameter of zone A at the metal tie.
The areas of the zones and materials of each zone are as follows:
Area of zone A = 3.68752(π)/576 = 0.074 sq ft
Area of zone B = 4.5 - 0.074 = 4.426 sq ft
Area of steel in zone A = 0.00015
Area of wall in zone A = 0.07385
The next step in calculating the U value of this wall by the parallel path method requires sectioning the wall, the outer section 1 being the outside air surface, section 2 the outer 1.75 in. of wall, section 3 the next 2 in. of wall and steel, section 4 the 2-in. cavity and steel, section 5 the next 2 in. of wall and steel, section 6 the inner 1.75 in. of wall and section 7 the inside air surface. The next step is to figure the area times conductance and resistance divided by area of each section.