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          1 min read

          Linear Thermal Expansion Calcuations

          Be Careful! A word of caution for anyone using the 11th Edition of Architectural Graphic Standards: The coefficients of linear thermal expansion for selected materials given table A.87 on page 1035 are unitless. Without units attached to these coefficients, the values are useless. There is no clue if the values given are English, metric, or something else. Units make a difference.

          The coefficient of thermal expansion (α) is a constant for each material and is used to calculate the total movement of a given length of material over a given temperature range.

          English Measurement
          α = Material Constant (inches/inch/degree F, or 1/degree F)
          L = Length (inches)
          ΔT = Temperature Change (degree F)

          Metric Measurement
          α = Material Constant (m/m/degree C, or 1/degree C)
          L = Length (m)
          ΔT = Temperature Change (degree C)

          Then to calculate the thermal expansion ΔL, the formula is:

          ΔL = α x L x ΔT

          The result of the formula will be a value, measured in inches or meters.

          As a comparison, I checked both the 5th and the 6th edition of Architectural Graphic Standards for the same information. Unfortunately, both editions included units for the coefficient, but the units were identified incorrectly as inches/degree F. Here is what I found:

           


          Material

          Coefficient of Thermal Expansion (α)

          11th Edition (unitless)

          6th Edition (inches/degree F)

          Aluminum

          24 x 10^-6

          12.8 x 10^-6

          Brass and Bronze

          19 x 10^-6

          10.1 x 10^-6

          Copper

          17 x 10^-6

          9.8 x 10^-6

          Glass, ordinary

          9 x 10^-6

          4.7 x 10^-6

          Concrete

          12 x 10^-6

          6.5 x 10^-6

          Lead

          29 x 10^-6

          15.9 x 10^-6

          Steel

          11 x 10^-6

          6.7 x 10^-6

           

          Upon searching additional on-line sources, I discovered the coefficients for linear thermal expansion shown in the 11th edition are metric values. But there is nothing in the published table that provides this information.

          Without the units, calculations of thermal expansion may provide values that are double or half the real value.  So be careful you are working with the right units.

          With fond memory of my college structures professor, Willis W. (Big Daddy) Wertz, "Units, they must be right, or you are wrong."

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