Question

A square bar of size 10 mm × 10 mm and length 1000 mm is subjected to 200 N axial tensile force. The bar is made of mild steel having modulus of elasticity of 200 GPa. Find the strain energy density stored in the bar under this state of loading?
1. 10 J/m³
2. 20 J/m³
3. 2 J/m³
4. 5 J/m³

Answer 1

Correct Answer - Option 1 : 10 J/m³

Concept:

Strain energy stored in the bar \(\frac{1}{2}\times P\times \delta =\frac{1}{2}\times P\times \frac{PL}{AE}~\)

Strain energy density or strain energy per unit volume

\(U=\frac{1}{2}\times \frac{{{P}^{2}}L}{AE\times AL}=\frac{1}{2}\times {{\left( \frac{P}{A} \right)}^{2}}\times \frac{1}{E}\)

\(U=\frac{{{\sigma }^{2}}}{2E}\)

Calculation:

Given data, P = 200 N, A = 10 mm × 10 mm = 100 mm²

E = 200 GPa = 200 × 10³ MPa

\(\sigma =\frac{200}{100}=2~MPa\)

Strain energy density

\(U={{\left( \frac{200}{100} \right)}^{2}}\times \frac{1}{2\times 200\times {{10}^{3}}}=10~J/m{{m}^{3}}\)