A cylindrical boiler with an inner diameter of 1 m is subjected to an internal pressure of 400 kPa. Determine the stresses acting on the boiler wall.

The inner diameter of the boiler is $D = 1 \text{ m}$, so the inner radius is $r = \frac{D}{2} = 0.5 \text{ m}$.
The internal pressure is $p = 400 \text{ kPa} = 400 \times 10^3 \text{ Pa}$.
The condition is that the maximum in-plane shear stress at point 'a' is zero. This implies that the two principal normal stresses in the plane are equal.

We assume the boiler can be analyzed using thin-walled pressure vessel theory, as the thickness is not provided and often cancels out in