Question

A composite bar is made of Steel & Aluminium strips each having 3 cm² area of cross-section. The composite bar is subjected to an axial load of 12000 N. If E_steel = 3E_Al, the stress in steel is
1. 10 N/mm²
2. 20 N/mm²
3. 30 N/mm²
4. None of the above

Answer 1

Correct Answer - Option 3 : 30 N/mm²

Concept:

For a composite bar, the strain in both the bars will be the same i.e.

\(\epsilon=\frac{P}{AE}=\rm{constant}\)

Calculation:

Given:

A_Steel = A_Almunium = 3 cm² = 300 mm², E_steel = 3E_Al, P = 12000 N.

\(\epsilon=\frac{P}{AE}=\rm{constant}\)

since area is also constant, therefore

\(\epsilon=\frac{P}{E}=\rm{constant}\)

\(⇒\frac{P_{Aluminium}}{E_{Aluminium}}=\frac{P_{Steel}}{E_{Steel}}\)

\(⇒\frac{P_{Steel}}{P_{Aluminium}}=\frac{E_{Steel}}{E_{Aluminium}}\)

\(⇒\frac{P_{Steel}}{P_{Aluminium}}=3\;\;\;[E_{steel}=3E_{Aluminium}]\)

P_steel = 3P_Aluminium

Total load acting is 12000 N, therefore;

P = P_steel + P_Aluminium ⇒ 12000 N

4P_Aluminium ⇒ 12000 N

P_Aluminum = 3000 N

P_steel = 9000 N

Stress is steel:

\(\sigma_{steel}=\frac{P_{steel}}{Area}\)

\(\sigma_{steel}=\frac{9000}{300}\Rightarrow30\;N/mm^2\)