Principal Axis Inclination
Tips & Tricks
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°.
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Cross-Section Properties Software
Section properties, stress analysis, and plastic design of open and closed thin-walled cross-sections