Find the maximum stress:
A circular bar rigidly fixed at both ends is 1 m long and tapers uniformly from 20 cm diameter at one end to 10 cm diameter at the other end. Find the maximum stress in the bar, if its temperature is raised through 50^{o}C. E = 2 × 10^{5} N/mm^{2} and α = 12 × 10^{-6} K^{-1}.
Solution
Here,
d_{1} = 20 cm = 200 mm
d_{2} = 10 cm = 100 mm
L = 1 m = 1000 mm
ΔL = 50°C
∴ σ_{max }= Ed_{1 }α ΔT/d_{2} = 2 ×10^{5}×200×12×10^{-6}×50/100
= 240 N/mm^{2}.