A steel rod 0.450 m long and an aluminum rod 0.250 m long, both with the same diameter, are placed end to end between rigid supports with no initial stress in the rods. The temperature of the rods is now raised by 60.0 C°. What is the stress in each rod? (Hint: The length of the combined rod remains the same, but the lengths of the individual rods do not. See below.) Problem: (a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount ?L ? ? when its temperature changes by ?? ?, the stress is equal to Where ?F is the tension on the rod ?L?0 is the original length of the rod, ?A its cross-sectional area, ?? its coefficient of linear expansion, and ?Y its Young’s modulus. (b) A heavy brass bar has projections at its ends, as in Figure. Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20°C. What is the tensile stress in the steel wires when the temperature of the system is raised to 140°C? Make any simplifying assumptions you think are justified, but stale what they are. Figure:

Solution 88P Introduction Since the total length is equal, the change in one rod will be equal to the change in other rod, (one will expand and other will contract). Also, since the rods will be in equilibrium, the stress in both side will be equal. Step 1 The stress on a rod due to temperature change of T and length change L is given by