Example based on B31.3
Carbon Steel
Expansion from 50F to 350F
From B31.3 Table C-1 Group 1 Row A:
e_-50 = 6.2 micro in/in/F
e_70 = 6.4
e_300 = 6.9
e_400 = 7.1
Interpolate to get the mean coefficients of thermal expansion for 50F and 350F.
e_50 = ((6.4 - 6.2)/(70 - -50))*(50 - -50) + 6.2 = 6.36667 micro in/in/F
e_350 = ((7.1 - 6.9)/(400 - 300))*(350 - 300) + 6.9 = 7 micro in/in/F
e_50 and e_350 above are still based on expansion from 70F.
Convert them to linear thermal expansion.
a_70to50 = e_50 * (70-50) = -127.333 micro in/in
a_70to350 = e_350 * (350-70) = 1960 micro in/in
What you will eventually need to get is the linear expansion from 50 to 350F.
To get the expansion that you are looking for, a_50to350
= a_50to70 + a_70to350
=-a_70to50 + a_70to350
= 127.333 + 1960
= 2087.33 micro in/in = 0.00208733 in/in
You can check this against CAESAR II calculated thermal expansion.
IF you start off with row B of table C-1, you'll end up with 0.002083 in/in. Close, but not exactly what you see in CAESAR II.
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