Steady-State R-Value Calculation. PS-4600 PolySteel Form

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1 Steady-State R-Value Calculation Introduction R value has been established as the primary measurement of energy efficiency in building construction. Steady state R value is the traditional method to determine the energy efficiency of building materials. Thermal mass and reduced air infiltration qualities of the completed construction are conservatively ignored for simplicity. The R value based on the consideration of thermal mass and reduced air infiltration is typically referred to as effective R value. Effective R value is higher than steady state R value. Effective R value will not be considered in these calculations. The calculation of the steady state R value of a wall is typically performed by summing the R-values for each material in the wall. With PolySteel formed walls, additional consideration is required to calculate the thermal bridge effect of the steel cross ties. The method selected herein to calculate the steady state R-value for the PolySteel wall is that recognized by ASHRAE (American Society of Heating, Refrigeration, and Air Conditioning Engineers). Thermal Resistance of the PS-4000 Series PolySteel Formed Wall Discussion The calculation of the steady state R value of a wall is typically performed on uniform thickness materials by summing the R-values for each material in the wall. The PolySteel PS-4000 series wall forms are of the flat wall type, which has 2.50 uniform thickness EPS foam in the form face. The straight PS-4000 series form is 24" tall by 48" long with an overall width of 11" and 13" for the 6 and 8" PS-4000 form respectively. The EPS foam in PolySteel forms has a density of 1.5 pcf in accordance with ASTM C 578. The R-value for the 1.5 pcf density EPS foam is 4.17/inch in accordance with Table 4 of ASHRAE. The following calculations are based on the thinnest PS-4000 series PolySteel wall, which is the PS-4600 flat wall form. See Figure 1 on Page 5. The calculated steady state R value for the PS-4600 flat wall is ignoring the finish materials applied to the surfaces as well as the allowance for an air film. See Table I on page 7.

2 Thermal Resistance of the Steel Cross Tie and Furring Strip Each PolySteel PS-4000 series form is held together by eight unique steel cross tie members. Each end terminates in a galvanized steel furring strip for attaching interior and exterior wall coverings. The welded wire fabric cross tie penetrates through the concrete and the EPS foam creating a thermal break, which in effect lowers the R value of the wall. The furring strip at the end of the cross tie is recessed 1/2" below the surface of the EPS foam which contributes effectively 1 inch of EPS insulation to the wall section at each steel cross tie location. Each steel furring strip is 1.5 inch wide by 21 inches long. See Figure 2 on Page 6. There are eight strips on each side of every 48 inch long form and they are spaced at 6 inches on center. These furring strips are welded to the steel welded wire cross ties which penetrates through each form. The furring strips account for % of the exterior surface of the PolySteel Form. To calculate the thermal resistance of the Polysteel Form steel cross members and furring strips, use the ASHRAE isothermal planes method used for calculating the thermal resistance of a wall panel containing steel studs as detailed in the ASHRAE Handbook of Fundamentals. Given: Flange length, F l = 21 inches Flange width, F w = 1.5 inches Flange area, F a = 31.5 in 2 Steel Cross Tie Diameter, D = 0.120" Quantity of Steel Cross Ties N = 6 Area per cross tie, A = in 2 Total Area, A t = in 2 Transfer Path Length, P l = inches = 11.00" 2 (0.5") + 2 (0.120") Thermal Conductivity / Steel C s = Btu-inch/hr-ft 2 - F 2 of 7

3 Calculation of Equivalent Thickness: Replace the steel wire cross tie which penetrates each form with an equivalent piece of solid steel in order to use the ASHRAE calculation method for a standard steel framing member. Equivalent Thickness, T e = A t / F l = in 2 / 21 inches = inches Therefore, the steel, which transfers heat through the PolySteel Form, is equivalent to a 21 inch long vertical piece of steel that is inches thick. ASHRAE Calculation of Thermal Resistance of Steel Insert: Thermal Resistance of Steel Insert = R s R s = (F w / T e ) x (P l / C s ) = (1.5 inches / inches ) x (10.24 inches / Btu-in/hr-ft 2 - F) = hr-ft 2 - F / Btu However, the additional R value for the 1/2" thick EPS between the steel furring strip and the surface of the foam = 0.5 inch x 2 sides x 4.17 hr-ft 2 - F / Btu / inch = 4.17 hr-ft 2 - F / Btu. Therefore the R-value for the wall at the location of the steel furring strip is = = hr-ft 2 - F / Btu Sectional Analysis of the PS-4600 Series PolySteel Form Divide the PolySteel Form into sections with identical properties in order to determine the R value of each individual section of the expanded polystyrene panel that make up the form. There are two unique sections of interest within each panel; the section without a steel furring strip and steel cross tie; and the section without the steel components. Each form consists of a 24 tall x 48 long EPS panel (one on each side of the form) with eight steel furring strips that have an elevation view dimension of 1.5 wide x 21 tall. Refer to the details of the form in Figure 1 on page 5. The detailed sectional analysis is found in Table I on page 7. 3 of 7

4 Calculation of the Steady-State R-Value of the PS-4600 Series PolySteel Form: Perform the isothermal planes calculation method using Equations (2) and (3) from Chapter 20 of the ASHRAE Handbook of Fundamentals and example 3 for walls containing metal members (ASHRAE, Page 22.5). R ps = 1 1/R 1 x (% Area 1 ) + 1/R 2 x (% Area 2 )... 1/R i x (% Area i ) R ps = 1 = 1 Data from Table I R ps = hr-ft 2 - F / Btu Note: Additional calculations show that the R-value of the form without considering the steel thermal break is hr-ft 2 - F / Btu, which illustrates the thermal break, reduces the R value by (approximately 3%) resulting in the R value of hr-ft 2 - F / Btu. See Table II on page 7. Conclusion: The minimum steady state R value of the PolySteel PS-4000 series formed walls is hr-ft 2 - F / Btu (U = 1/R = Btu / hr-ft 2 -ºF = W / m 2 K) Prepared by: David R. Jarmul, PE Director of Engineering American PolySteel, LLC 6808 Academy Parkway East, NE Albuquerque, New Mexico Date: September 1, of 7

5 PS-4600 PolySteel Form Details Scale: none FRONT ELEV, 4.5" 1.5" 4.5" 1.5" 2.25".75" SECTION A.87" 4'-0" [1219.2] PLAN 3" [152.4] 4'-0" [1219.2] A 11" [279.4] FURRING STRIP ALIGNMENT GROOVES FURRING STRIP ALIGNMENT GROOVES.5" END ELEV, 3" FURRING STRIP ALIGNMENT GROOVES 1.5" 2'-0" [609.6] 1.5" 1'-9" 1.52".75" STEEL CROSS TIE A STEEL FURRING STRIP.77" Figure 1 5 of 7

6 CRIMPED VERTICAL WIRES 10.00" BENT DIMENSION 13.00" FLAT (UNBENT) 1.50" WELDED WIRE TIE PS-4600 SERIES Here is the tie after it is bent and crimped. Note the wires that are crimped. It is the verticals. Strips welded on the edges must have 2 welds on each wire and welds must not be on the bends. 1.75" 3.44" 6.12" 3.44" 0.25" EQUAL SPACES STEEL FURRING STRIP: 1 3/4" X 21" X 0.031" (22 GA) STRIP (STUD) 6.00" CLEAR 21.00" STEEL CROSS TIE: 0.120" DIA (11 GA) WIRES EACH WAY Figure 2 6 of 7

7 TABLE I Steady-State R-Value Derivation (including effect of steel cross-ties) PS-4600 Series Flat-Wall Form Section Section Section Area EPS EPS Concrete Form Sections Area Per Cent % Ro Rc Ri Total - R U Mark Width Height Per Section Thickness Volume Thickness Thickness Per Per Total Outside Concrete Inside Per ID (inch) (inch) (sq. inch) (inch) (cubic inch) (inch) check Form Form Area EPS Core EPS Section [=1/R X %Area] (EPS/S) Steel See page 2 of Calcs Totals: U = Notes: R(total) = 1/U = ) EPS Volume = Area per Section x EPS Foam Thickness 2.) Concrete Thickness = x EPS Foam Thickness 3.) Ro = Ri = 4.17 / inch x EPS Foam Thickness 4.) Rc = 0.08 / inch x Concrete Thickness TABLE II Steady-State R-Value Derivation (excluding effect of steel cross-ties) PS-4600 Series Flat-Wall Form Section Section Section Area EPS EPS Concrete Form Sections Area Per Cent % Ro Rc Ri Total - R U Mark Width Height Per Section Thickness Volume Thickness Thickness Per Per Total Outside Concrete Inside Per ID (inch) (inch) (sq. inch) (inch) (cubic inch) (inch) check Form Form Area EPS Core EPS Section [=1/R X %Area] Totals: U = Notes: R(total) = 1/U = ) EPS Volume = Area per Section x EPS Foam Thickness 2.) Concrete Thickness = x EPS Foam Thickness 3.) Ro = Ri = 4.17 / inch x EPS Foam Thickness 4.) Rc = 0.08 / inch x Concrete Thickness 7 of 7