# Beam axes

## Symmetry about the axis

In most cases beams have symmetry about one axis or both axes (e.g., a rectangular, circular, I-beam or tee section). In these cases the principal axes of the beam *correspond* with the local axes. This means that the bending behaviour is governed by: $I_{yy}$ and $I_{zz}$ and the $I_{yz}$ term is zero.

## No symmetry about the axis

When a section lacks symmetry about both axes, the cross term $I_{yz}$ is no longer zero. This means that a load in the *y* direction will produce a *displacement* in *y* and *z* directions.

The angle of the principal second moments of area can be calculated from:

The second moments of area in the *u* and *v* axes are:

These relationships can be visualised using a Mohr's circle approach similar to stress.

Note:GSA gives the option to use eitherprincipalsecond moments of area, orlocalsecond moments of area (ignoring the $I_{yz}$ term). Principal moments most often apply to asymmetric or angle sections; by using this option it is possible to capture sideways deflection. Therefore, the latter option is not recommended.