Question

A rod having a cross-sectional area of 100 x 10⁻⁶ m² is subjected to a tensile load. Based on the Tresca failure criterion, if the uniaxial yield stress of the material is 200 MPa, the failure load is:

• A. 10 kN
• B. 20 kN
• C. 100 kN
• D. 200 kN

Answer 1

Answer:

B. 20 kN

Given: C.S Area = $100 \times 10 ^ {- 6} m ^ 2$ = $100mm ^ 2$ , Syt = 200 MPa; Since only one tensile load is acting, it will give rise to $\sigma_{1}$ whereas $\sigma_{2}, \sigma_{3} = 0$ $\frac{S_{yt}}{2 \times FOS}=| max[ \frac{\sigma_1-\sigma_2}{2},\frac{\sigma_2-\sigma_3}{2},\frac{\sigma_3-\sigma_1}{2}]|$

[FOS=1]; $\frac{s_{yt}}{2}=\frac{\sigma_1}{2}\Rightarrow\sigma_1=S_{yt}\Rightarrow \sigma_1=200 MPa$ and

$\sigma_1=\frac{Load}{C.S.Area}$ $\Rightarrow 200=\frac{Load}{100} \Rightarrow Load=2\times 10^4 N=20kN$