Topic: Strength of Materials
A solid rod of 12 mm diameter was tested for tensile strength with the gauge length of 50 mm. Final length = 80 mm; Final diameter = 4 mm; Yield load = 1130 N. What is the nearest yield stress and % reduction in area respectively?
- A. 10 MPa and 10%
- B. 90 MPa and 90%
- C. 10 MPa and 90%
- D. 90 MPa and 10%
Answer: C. 10 MPa and 90%
Explanation: Yield stress $\sigma_{y} = \frac{\text{Yield Load}}{\text{Original Area}} = \frac{1130}{\frac{\pi}{4} \times 12^{2}} = \frac{1130}{113.097} \approx 10~MPa$. Percentage reduction in area = $\frac{A_{i} - A_{f}}{A_{i}} \times 100 = \frac{d_{i}^{2} - d_{f}^{2}}{d_{i}^{2}} \times 100 = \frac{12^{2} - 4^{2}}{12^{2}} \times 100 = \frac{144 - 16}{144} \times 100 = \frac{128}{144} \times 100 \approx 88.88\% \approx 90\%$.