Cross-section co-ordinate system

There are several co-ordinate systems used with cross-sections. All the sectional co-ordinate systems are two-dimensional right-handed Cartesian co-ordinate systems.

Principal (or main) axes

The principal axes correspond to the principal moments of inertia of a cross-section. They are marked u and v.

The u axis is called (according to the official Eurocode terminology) a major axis and the v axis is called a minor axis.

The principal axes are used to evaluate important sectional characteristics necessary for design and assessment to technical standards (code check), e.g. moments of inertia, radiuses of gyration, etc.

Centroidal axes

The two centroidal axes pass the centroid of a cross-section and the first moments (the static moments) of the cross-section around these axes are equal to zero.

The centroidal axes are marked y and z.

The centroidal axes are used to evaluate important sectional characteristics necessary for design and assessment to technical standards (code check), e.g. moments of inertia, radiuses of gyration, section modulus, etc.

For symmetrical cross-sections, the centroidal axes are identical to the principal axes.

For example, for steel cross-sections the centroidal y axis is parallel to the flanges and the centroidal z axis is perpendicular to the flanges.

Geometric co-ordinate system

The geometric axes are used to define co-ordinates of cross-section vertices. The axes of the system are marked y and z.

Orientation of the cross-section co-ordinate system with reference to the beam local co-ordinate system

A cross-section is oriented so that the centroidal axis y is identical with beam local axis Y and the centroidal axis z is identical with beam local axis Z. If the 1D member is being rotated around its local X axis, also the sectional centroidal axes rotate.