find the maximum stressa circular bar rigidly

Question

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^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/d₂ = 2 ×10⁵×200×12×10^-6×50/100

= 240 N/mm².