Determination of Neutral Axis in Biaxial Bending:

You know that in case of bending, the stress will be zero along a line that is known as the 'Neutral Axis'. To find out the equation of the neutral axis, we put f = 0 in Eq.,

f = M cos θ /I_uu. v + M sin θ/I_vv. u = 0

Thus,  V= -(I_uu/I_vv.tan θ).u

is the equation of the neutral axis. Comparing Eq. with the well known equation of a straight line y = mx + c, we find that

(a)        the neutral axis passes through the centroid G;

(b)       the slope of the neutral axis is given by

tan  α = - I_uu/I_vv⋅ tan θ ;

 (The negative sign shows that α is measured anticlockwise from axis XX if θ is positive or clockwise from YY.)

Thus, we see that the neutral axis is not perpendicular to the plane of bending moment M (as in the case of uniaxial bending) but makes an angle of (90^o - α + θ) with it.