Stress transform - Mohr's circle

[yecko]

Homework Statement

For the beam and loading shown below,

(a) find the state of stress at point A in the Cartesian coordinate system indicated in the figure.

(b) use Mohr’s circle to determine (i) the principal stress and principal plane; (ii) the normal and shearing stresses acting on a plane oriented at 45 deg indicated in the figure.

Homework Equations

Solution:

The Attempt at a Solution

for part b, let me define the mohr's circle be like this:

Why not transform to point D but point B in the solution?

I think as the plane rotate 45 deg clockwise, so the point would follow point x then rotate 90 deg clockwise to point D i written.

So may I know if the answer is right for point B as the destination point, or should point D i written be right?
thanks.

 

[Valkarie]

Yes, your answer is correct. The point B in the solution follows from the transformation of the plane at 45° clockwise. The point D in the solution is the result of the transformation of the plane at 90° clockwise.