# 10. Linear Beam

Warning

The Linear Beam section is known to have limited functionality in implicit analyses.

    BEGIN LINEAR BEAM SECTION <string>section_name
      T AXIS = <real>tx <real>ty <real>tz
      AREA = <real>area
      I11 = <real>i11
      I22 = <real>i22
      I12 = <real>i12(0.0)
      J = <real>J
      SHEAR AREA 1 = <real>val(AREA)
      SHEAR AREA 2 = <real>val(AREA)
    END

The `LINEAR BEAM SECTION` command block specifies the properties for a linear beam element. If this command block is referenced in an element block of three-dimensional, two-node elements, the elements in the block will be treated as beam elements. The name, `beam_section_name`, can be used by the `SECTION` command line in a `PARAMETERS FOR BLOCK` command block.

The beam geometry properties are defined via areas and moments of inertia for the beam section. The linear beam will behave as a linear elastic element. If a linear beam has a nonlinear material, only the elastic constants of that material, such as Young’s modulus and Poisson’s ratio, will affect the beam behavior.

The beam element is formulated in a local orthogonal RST coordinate system. The R axis of the beam lies along the beam element. The T axis direction is given in the input deck. If the provided T axis is not orthogonal to R, the closest vector to T that is orthogonal to R will be used define the T axis. The S axis is then constructed orthogonal to R and T based on the right hand rule (The actual method of forming these axes is slightly different from this description.). The `T AXIS` command in the linear beam behaves identically to the `T AXIS` command in the standard beam. See the `BEAM SECTION` description in the TheusersguideSection~ref{user:ele:beamsec} for more examples and discussion on use of the `T AXIS` command.

The following cross sectional properties are available for linear beams.

- `AREA`: Cross sectional area used to define axial and shear properties.

- `I11`: Bending moment of inertia in the T direction of the beam.

- `I22`: Bending moment of inertia in the S direction of the beam.

- `I12`: Product of inertial of the beam for asymmetric sections. This value is by default set to zero.

- `J`: Polar moment of inertia used to define beam torsional properties.

- `SHEAR AREA 1`: Area used for shear resistance in the T direction. If unspecified the cross sectional area `AREA` will be used.

- `SHEAR AREA 2`: Area used for shear resistance in the S direction. If unspecified the cross sectional area `AREA` will be used.

This linear beam is a Timoshenko (also called a Reissner-Mindlin) shear deformable thick beam. If the thickness is small relative to the length, it behaves like an Euler-Bernoulli beam. The pre-integrated element stiffness was taken directly from [[1]].

Note, linear beam elements do not calculate element stress or stress based quantities. Linear beam elements generate nodal internal forces however no element specific output quantities are currently available on linear beam elements.

[1]

J.S. Przemieniecki. Theory of Matrix Structural Analysis. Dover Publications Inc., New York, NY, 1985.