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Two steel bars (Es = 200 GPa and as = 11.7 x 10- /C) are
Chapter 2, Problem 2.55(choose chapter or problem)
Two steel bars \(\left(E_{s}=200 \mathrm{GPa} \text { and } \alpha_{s}=11.7 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) are used to reinforce a brass bar \(\left(E_{b}=105 \mathrm{GPa}, \alpha_{b}=20.9 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) that is subjected to a load P = 25 kN. When the steel bars were fabricated, the distance between the centers of the holes that were to fit on the pins was made 0.5 mm smaller than the 2 m needed. The steel bars were then placed in an oven to increase their length so that they would just fit on the pins. Following fabrication, the temperature in the steel bars dropped back to room temperature. Determine (a) the increase in temperature that was required to fit the steel bars on the pins, (b) the stress in the brass bar after the load is applied to it.
Questions & Answers
QUESTION:
Two steel bars \(\left(E_{s}=200 \mathrm{GPa} \text { and } \alpha_{s}=11.7 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) are used to reinforce a brass bar \(\left(E_{b}=105 \mathrm{GPa}, \alpha_{b}=20.9 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) that is subjected to a load P = 25 kN. When the steel bars were fabricated, the distance between the centers of the holes that were to fit on the pins was made 0.5 mm smaller than the 2 m needed. The steel bars were then placed in an oven to increase their length so that they would just fit on the pins. Following fabrication, the temperature in the steel bars dropped back to room temperature. Determine (a) the increase in temperature that was required to fit the steel bars on the pins, (b) the stress in the brass bar after the load is applied to it.
ANSWER:
Step 1 of 8
(a) Required temperature change for fabrication:
Temperature change required to expand steel bar by this amount:
