Determine the maximum stress in the bar:

A circular bar rigidly fixed at both of the ends is 1 m long & tapers uniformly from 20 cm diameter at one end to 10 cm diameter at the other end. Determine the maximum stress in the bar, if its temperature is grow up through 50^oC. E = 2 × 105 N/mm² and α = 12 × 10^-6  K^-1.

Solution

Here,

d₁ = 20 cm = 200 mm

d₂ = 10 cm = 100 mm

L = 1 m = 1000 mm

ΔL = 50°C

∴          σ_max = Ed₁ α ΔT/ d ₂ =( 2 ×10 ⁵× 200 ×12 ×10^-6 × 50 )/100

= 240 N/mm².