Question 2.6: If the rod BC in Example 2.5 is made of a high-strength stee......
If the rod BC in Example 2.5 is made of a high-strength steel for which α = 8.0 × 10^{-6}/°F, and if BC is uniformly heated by 100°F, through what angle θ will beam AB rotate? Assume that AB and BC are weightless, and that AB is horizontal before the heating of BC occurs.
Plan the Solution Equation 2.8 relates the temperature change ΔT to the thermal strain, and the answers in Example 2.5 relate strain to θ.
ε_T = αΔT Thermal Strain (2.8)
Therefore, we can simply combine these.
ε_T = α ΔT = (8.0 × 10^{-6}/°F)(100°F) = 800 × 10^{-6} in./in.
Since the expression in Eq. (2) of Example 2.5 is simpler than the expression in Eq. (1), let us try Eq. (2) first.
θ = \frac{25}{12}ε = \frac{25}{12} (8.0 × 10^{-4}) = 1.667 × 10^{-3} rad
or
θ = 0.0955 deg
Since this answer satisfies the requirement that θ \ll 1 rad, we do not need to resort to Eq. (1).
Review the Solution Although a tenth of a degree rotation for a temperature increase of 100°F may seem to be very small, the formulas are so simple that all we can do to check our result is just to double-check the calculations and the conversion from radians to degrees.