Figure shows the stresses acting on a element ABCD. What will be the normal stress on the plane BE which is inclined at 45° to the plane BC?

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BHEL Engineer Trainee Mechanical 24 Aug 2023 Official Paper

Answer 1

Concept:

To calculate the normal stress on an inclined plane at an angle \( \theta \), use the stress transformation equation:

\( \sigma_n = \frac{\sigma_x + \sigma_y}{2} + \frac{\sigma_x - \sigma_y}{2} \cos 2\theta + \tau_{xy} \sin 2\theta \)

Given:

\( \sigma_x = 100~\text{N/mm}^2, \quad \sigma_y = 50~\text{N/mm}^2, \quad \tau_{xy} = 30~\text{N/mm}^2, \quad \theta = 45^\circ \)

Calculation:

\( \cos 2\theta = \cos 90^\circ = 0, \quad \sin 2\theta = \sin 90^\circ = 1 \)

\( \sigma_n = \frac{100 + 50}{2} + \frac{100 - 50}{2} \cdot 0 + 30 \cdot 1 \)

\( \sigma_n = 75 + 0 + 30 = 105~\text{N/mm}^2 \)