Answer
$T_{f} = 41.34 °C (106.41°F)$
Work Step by Step
Given:
steel wire with stress of 70 MPa (10,000psi) at $T_{0}= 20°C (68°F)$
Required:
temperature $T_{f}$ if length is held constant and the stress is to be reduced to 17 MPa (2500 psi)
Solution:
Using Equation 19.8:
$σ = Eα_{l}(T_{0} - T_{f})$
Since the stress is to be reduced from 70 MPa to 17 MPa, the resulting stress will be compressive, so:
$σ = -53 MPa$
Substituting values for steel from Table 6.1, it follows:
$(-53 MPa) = {(207 \times 10^{3} MPa) (12.0 \times 10^{-6} (°C)^{-1}) (20 °C} - T_{f})$
$T_{f} = 41.34 °C$