# # Beam Elements

The beam element stiffness is

These are modified for a shear beam as follows

The mass matrix is

And the geometric stiffness is

where

## # Non-symmetric Beam Sections

In a beam with a symmetric section the bending properties depend only on
the *y* or
*z* axis directions the deflection is in the direction of the loading.

When the section is not symmetric and is loaded in the *y* or *z*
direction there is a component of deflection orthogonal to the loading.
This is because the bending properties depend on

By rotating the section to principal axes this cross term can be omitted
and if the beam is loaded in the

For a beam with a non-symmetric section the user must consider if the beam is restrained (so that deflections are constrained to be in the direction of the loading) or if it will act in isolation (resulting in deflections orthogonal to the loading).

If the beam is to act as constrained the user should use the *local*
option for the bending axes. In this case the

If the beam is to act in isolation the user should use the *principal*
option for the bending axes. In this case the stiffness matrix for the
element is calculated using the principal second moments of area and is
then rotated into the element local axis system.

The effect of shear is also a tensor quantity involving the inverse of
the shear are factor

Where the user has specified section modifiers these are specified in
directions

All catalogue and standard sections except angles are symmetric.
Explicit sections are assumed to be defined such that the principal and
local axes coincide so there is no