Answer
$σ = -135.8 MPa$, compressive stress
Work Step by Step
Given:
rod of brass 0.35 m (13.8 in.) long
$T_{0} = 15°C (60°F)$, where the rod is stress free
$T_{f} = 85°C (185°F)$
Required:
type and magnitude of stress
Solution:
Using Equation 19.8:
$σ = Eα_{l}(T_{0} - T_{f})$
From Table 6.1, the modulus of elasticity for brass is 97 GPa, and from Table 19.1, $α_{l} = 20.0 \times 10^{-6} (°C)^{-1}$.
Substituting the values:
$σ = Eα_{l}(T_{0} - T_{f}) = (97 \times 10^{3} MPa) (20.0 \times 10^{-6} (°C)^{-1})(15 °C - 85 °C) \\= -135.8 MPa$
Since the computed value is negative, the stress is compressive.
