Question

A circular rod of diameter 16 mm and length 200 mm is subjected to a tensile force of 20 KN. Calculate the stress and strain, respectively.

Given: E (for steel) = 200 KN/mm² , where E is the modulus of elasticity.

1. 198.94 N/mm² ; 0.0009947
2. 0.4977 N/mm² ; 0.0009947
3. 99.473 N/mm² ; 0.000497
4. 123.66 N/mm² ; 0.08865

Answer 1

Correct Answer - Option 3 : 99.473 N/mm² ; 0.000497

Concept:

Stress, σ = \(\frac {F}{A}\)

Strain, ϵ = \(\frac {\Delta L}{L}\)

Young's Modulus, E = \(\frac {σ }{ϵ}\)

A = Area of cross-section

Calculation:

Given:

d = 16 mm, L = 200 mm, F = 20 kN, E = 200 kN/mm2 

A = \(\frac {\pi}{4}d^2 = \frac {\pi}{4}{16}^2 \)

A = 201.06 mm² 

Stress, σ = \(\frac {F}{A}\)

σ = \(\frac {20}{201.06}\)

σ = 0.09947 kN/mm2 

σ = 99.47 N/mm2 

Using, E = \(\frac {σ }{ϵ}\)

\(200 = \frac {0.09947 }{ϵ}\)

ϵ = 0.000497 mm