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

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VIZAG MT Mechanical: 2013(Re-exam) Official Paper

Option 3 : 94.25 kN

CT 3: Building Materials

2894

10 Questions
20 Marks
12 Mins

**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, (σ_{2} = σ_{3} = 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-

\(σ_1\le σ_{yt}\)

∴ σ_{1} = 300 MPa

\(σ_1=\frac{Load}{Area}\)

Load = σ_{1} × Area ⇒ \(\sigma_1\times\frac{\pi}{4}d^2\)

Load = \(300\times\frac{\pi}{4}\times20^2 \Rightarrow 94.25\; kN\)