 # Principal Axis Inclination

### Tips & Tricks

000836

1 July 2014

The cross‑section program SHAPE‑THIN determines the principal axis inclination alpha from the moments of inertia according to the following equation:

tan (2 × α) = 2 × Iyz / (Iz − Iy)

The axes y and z are the centroid axes parallel to the input axes y0 and z0. For a flat section (width > depth), it can thus happen that the major principal axis u points in the directions of the minor principal axis v.

The check box ‘Transform the principal axes such that I-u is always greater than I-v’ allows you to align the principal axes with the input. You don't need to rotate the section by 90°.

According to the expression above, only angles between +90° and -90° are possible. If there already are internal forces relative to the principal axes u and v, you can use another function to ensure that the orientation of the principal axes remains the same when rotating the section: ‘Keep the position of the principal axes relating to the section geometry when rotating the section’. This check box also allows you to specify alpha angles greater than +90° or less than -90°. 