Normal stress on cantilever beam

[temaire]

Homework Statement

Homework Equations

$$\sigma_x = -\frac{M(x)y}{I}$$

$$I = \frac{bh^3}{3}$$

The Attempt at a Solution

For point A, I did the following:

$$I = \frac{t(2h)^3}{3}$$

$$I = \frac{8th^3}{3}$$

$$\sigma_x = -\frac{3\tau_0}{4th}$$

$$\tau_{yx} = -\tau_0$$

$$\sigma_y = 0$$

Are my principal stresses correct for point A? Also, would these principal stresses be the same for Point B?

 

[Mapes]

A principal stress state contains no shear. Also, it's hard to imagine why A and B would be equivalent when the applied traction is creating a moment around the fixed end of the beam.