Note:

• It is imperative that you follow the sign convention (given below) for the formula to work.
• z-axis must always be 90^o CCW from the y-axis.
• Moment direction must follow the right-hand rule.
• y and z are the distances of the point of interest from the centroid, along the y-axis and z-axis respectively.
• I_y and I_z are the moments of inertia about the y-axis and z-axis respectively.
• M_y and M_z are positive according to the right-hand rule, with the thumb pointing to the +ve y-axis and +ve z-axis respectively.

Due to two-directions of moments being applied, the neutral-axis (line of zero stress) tilts from the horizontal axis:

The orientation of the neutral-axis from the horizontal is set as ‘α’, and to get the formula for α we set σ_b = 0 (since the bending stress is zero at the neutral-axis).

Sometimes the moment is given in terms of its magnitude and direction. In that case:

Let’s look at an example now.