Question

A rod of diameter 20 mm is subjected to a tensile load. Based on Tresca’s failure criterion, if the uniaxial yield stress of the material is 300 MPa, the failure load is

1. 20.75 kN
2. 54.00 kN
3. 94.25 kN
4. 105.50 kN

Answer 1

Correct Answer - Option 3 : 94.25 kN

Concept:

Maximum shear stress theory (Guest & Tresca’s Theory):

\({{\rm{\tau }}_{{\rm{max}}}} \le \frac{{{{\rm{σ }}_{\rm{y}}}}}{2}\) (for no failure)

\({{\rm({σ }}_1} - {{\rm{σ }}_2}),{{\rm({σ }}_2} - {{\rm{σ }}_3}),{{\rm({σ }}_3} - {{\rm{σ }}_1}) \le \left( {\frac{{{{\rm{σ }}_{\rm{y}}}}}{{{\rm{FOS}}}}} \right)\) (for design)

For uni-axial loading, (σ₂ = σ₃ = 0)

\(σ_1\le σ_{yt}\) [∵ FOS = 1]

Calculation:

Given:

d = 20 mm, σ_yt = 300 MPa

Guest & Tresca’s Theory for uni-axial loading is-

\(σ_1\le σ_{yt}\)

∴ σ₁ = 300 MPa

\(σ_1=\frac{Load}{Area}\)

Load = σ₁ × Area ⇒ \(\sigma_1\times\frac{\pi}{4}d^2\)

Load = \(300\;\times\;\frac{\pi}{4}\;\times\;20^2 \Rightarrow 94.25\; kN\)