(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 ΔL when its temperature changes by ΔT, the stress is equal to

Where F is the tension on the rod, L₀ is the original length of the rod, A its cross-sectional area, α its coefficient of linear expansion, and Y its Young€™s modulus.

(b) A heavy brass bar has projections at its ends, as in Fig. P17.85. Two fine steel wires, fastened between the projections, are just taut (zero tension) when the whole system is at 20^oC. What is the tensile stress in the steel wires when the temperature of the system is raised to 140^oC? Make any simplifying assumptions you think are justified, but state what they are.

Figure P17.85:

Transcribed Image Text:

ΔL Υ| Lo ΥΗ- αΔΤ Ξ Steel wires Brass