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where ku and kv are the radii of gyration about the principal axes and hence the semi-axes of the momental ellipse.

The N.A. can now be added to the diagram to scale. The second moment of area of the section about the N.A. is then given by Ah2, where h is the perpendicular distance between the N.A. and a tangent AA to the ellipse drawn parallel to the N.A. (see Fig. 1.11 and §1.7).

The bending moment about the N.A. is M cos «n.a. where otn.a. is the angle between the N.A. and the axis XX about which the moment is applied. The stress at P is now given by the simple bending formula

the distance n being measured perpendicularly from the N.A. to the point P in question.

As for the procedure introduced in §1.7, this method has the advantage of immediate indication of the points of maximum stress once the N.A. has been drawn. The solution does, however, involve the use of principal moments of area which must be obtained by calculation or graphically using Mohr's or Land's circle.

### 1.11. Deflections

The deflections of unsymmetrical members in the directions of the principal axes may always be determined by application of the standard deflection formulae of §5.7

For example, the deflection at the free end of a cantilever carrying an end-point-load is

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