Resultant Bending Moment

If mutually perpendicular bending-moment components $M_x$ and $M_y$ act simultaneously at a section, the magnitude of the resultant bending moment is:

$$M_b=\sqrt{M_x^2+M_y^2}.$$

For a circular section, whose geometric properties are identical about any centroidal axis in the section plane, the maximum bending normal stress can be calculated as:

$$|\sigma_b|=\frac{M_b}{W}.$$

• $M_x$, $M_y$ — bending-moment components;
• $M_b$ — resultant bending moment;
• $W$ — bending section modulus;
• $\sigma_b$ — bending normal stress.

For noncircular sections, the orientation of the bending moment and the second moments of area about the corresponding principal axes must generally be considered explicitly.