At the extremities of x, y axes, these moments are respectively

Then, the largest bending moment is applied to the ends of the shortest principal axis of C.

The curvilinear expressions of the bending moment Mn and net shearing force Vn to apply at the contour C of the ellipse (ax, ay) define the boundaries. At any point of the contour, let a be the angle between the axis x and normal n. Since ds2 = dx2+dy2, dx sin a =--

The curvilinear moments Mn and Mnt are represented by

Mnt = Mxy(cos2a-sin2a) + (Mx - My ) sinacosa. (5.35)

After substitutions, we obtain


a4x2 + ajy2

3x4 3y

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