Topic: Machine Design
For a plate with an elliptical hole subjected to tensile stress, as shown in the figure, the maximum tensile stress at point P is
- A. $\sigma$
- B. $2\sigma$
- C. $3\sigma$
- D. more than $3\sigma$
Answer: D. more than $3\sigma$
Explanation: The theoretical stress concentration factor $k_{t}$ for an elliptical hole is given by $k_{t} = 1 + 2\left(\frac{a}{b}\right)$, where 'a' is the semi-axis perpendicular to the applied stress and 'b' is the semi-axis parallel to the applied stress. From the figure, the major axis is $2a$ and the minor axis is $2b$, so $a > b$. Therefore, $k_{t} = 1 + 2\left(\frac{a}{b}\right) > 1 + 2(1) = 3$. The maximum stress is $\sigma_{max} = k_{t} \times \sigma_{nominal}$, which will be more than $3\sigma$.