# Beam

Model ElementBeam defines a straight, massless beam of uniform cross section acting between two markers, I and J, that belong to two different parts.

Beam

## Description

The mass of the beam is lumped at the origins of the I and J markers. The stiffness properties for the beam are derived using the Timoshenko beam theory. The beam axis is assumed to be along the x-axis of the J marker. The x-axis of the J marker is also defined to be the neutral axis of the undeformed beam. The beam is assumed to undergo small rotational deflections; large rotations are not supported.

## Attribute Summary

Name Property Modifiable by command? Designable?
id Int ()
label Str ()
i Reference (Marker)   Yes
j Reference (Marker)   Yes
length Double () Yes Yes
ixx Double () Yes Yes
iyy Double () Yes Yes
izz Double () Yes Yes
area Double () Yes Yes
asy Double () Yes Yes
asz Double () Yes Yes
emodulus Double () Yes Yes
gmodulus Double () Yes Yes
cratio Double () Yes Yes
cmatrix Double (count=36)   Yes
active Bool () Yes
force Double (count=3)   Yes
torque Double (count=3)   Yes
function Function ()
routine Routine ()
script Script ()

## Usage

Beam (i=objmarker, j=objMarker, length=double, ixx=double, iyy=double, izz=double, area=Double, asy=double, asz=double, emodulus=double, gmodulus=double, optional_attributes)

## Attributes

Beam defined by its properties.
j
Reference to an existing Marker object.
Specifies the ID of the marker at which the force and moment is applied. This is designated as the point of application of the force.
The j attribute is mandatory.
j
Reference to an existing Marker object.
Specifies the marker at which the reaction force and moment is applied. This is designated as the point of reaction of the force. The x-axis of J defines the neutral axis of the beam. The y- and z-axes should be oriented along the principal axes of the cross section (area products of inertial are zero).
The j attribute is mandatory.
length
Double
Specifies the free length of the beam. This is the distance from the origin of J to the origin of I. The corresponding vector must lie along the x-axis of J.
The length attribute is mandatory.
length > 0
ixx
Double
Specifies the torsional stiffness shape factor for the cross section. For circular sections, ixx is equal to the polar moment of inertia. For non-circular sections, the torsional stiffness constant is not equal to the polar moment of inertia. It's usually much smaller because of warping effects associated with torsion.
The ixx attribute is mandatory.
ixx > 0
iyy
Double
Defines the second moment of inertia of the beam cross sectional area about an axis on the cross section that is parallel to the y-axis of J.
The iyy attribute is mandatory.
iyy > 0
izz
Double
Defines the second moment of inertia of the beam cross sectional area about an axis on the cross section that is parallel to the z-axis of J.
The izz attribute is mandatory.
izz > 0
area
Double
Defines the beam cross sectional area.
The area attribute is mandatory.
area > 0
emodulus
Double
Specifies the Young's modulus of elasticity of the beam material. The beam is assumed to be homogeneous in its material properties.
The emodulus attribute is mandatory.
emodulus > 0
gmodulus
Double
Specifies the modulus of elasticity of the beam. This is related to the Young's modulus and POISSON's ratio by the formula:(1)

where

$v$ is POISSON's ratio.
The gmodulus attribute is mandatory.
gmodulus > 0
asy
Double
Specifies the shear area ratio in the y direction for Timoshenko beams. This quantity accounts for shear deflection in the y direction. This is defined as:(2)
${A}_{sy}=\frac{A}{{I}_{yy}^{2}}{\underset{A}{\int }\left(\frac{{Q}_{y}}{{l}_{z}}\right)}^{2}dA$
Qy is the first moment of the cross-sectional area to be sheared by a force in the y direction. lz is the cross section dimension in the z direction. Iyy is the area moment of inertia about the beam y-axis. To neglect shear deformation in the y-direction, set ASY=0.
The asy attribute is optional.
asy ≥ 0
When not specified asy=0
asz
Double
Specifies the shear area ratio in the z direction for Timoshenko beams. This quantity accounts for shear deflection in the Z direction. This is defined as:(3)
${A}_{sz}=\frac{A}{{I}_{zz}^{2}}{\underset{A}{\int }\left(\frac{{Q}_{z}}{{l}_{y}}\right)}^{2}dA$
Qz is the first moment of cross-sectional area to be sheared by a force in the z direction. ly is the cross section dimension in the y direction. Izz is the area moment of inertia about the beam z-axis. To neglect shear deformation in the z-direction, set asz=0.
The asz attribute is optional.
asz ≥ 0
When not specified asz=0
cmatrix
6x6 matrix specified as a list of 21 numbers in column or row ordered format.
Specifies the damping ratio as six by six symmetric matrix.(4)
$\left[\begin{array}{cccccc}{c}_{11}& & & & & \\ {c}_{21}& {c}_{22}& & & & \\ {c}_{31}& {c}_{32}& {c}_{33}& & & \\ {c}_{41}& {c}_{42}& {c}_{43}& {c}_{44}& & \\ {c}_{51}& {c}_{52}& {c}_{53}& {c}_{54}& {c}_{55}& \\ {c}_{61}& {c}_{62}& {c}_{63}& {c}_{64}& {c}_{65}& {c}_{66}\end{array}\right]$
This attribute is optional. When neither cmatrix or cratio are specified, MotionSolve will assume it is zero.
cratio
Double
Specifies the damping ratio for the beam. The beam damping matrix is calculated by multiplying the beam stiffness matrix with the cratio. In other words, [C] = cratio * [K]
A value of 0.01 (or 1%) is typically used for cratio.
This attribute is optional. When neither cmatrix or cratio are specified, MotionSolve will assume cratio is zero.
active
Bool
Select one from True or False
True
Indicates that the element is active in the model and it affects the behavior of the system.
False
Indicates that the element is inactive in the model and it does not affect the behavior of the system. It is almost as if the entity was removed from the model, of course with the exception that can be turned "ON" when desirable.

The attribute active is optional. When not specified, active defaults to True.

force
Double
Specifies the translational preload of the Beam object.
The attribute is optional. When not specified, all the translational preload will be zero.
torque
Double
Specifies the rotational preload of the Beam object.
The attribute is optional. When not specified, all the rotational preload will be zero.
Beam specified in a compiled user-written subroutine
i
Reference to an existing Marker object.
Specifies the ID of the marker at which the force and moment are applied. This is designated as the point of application of the force.
The i attribute is mandatory.
j
Reference to an existing Marker object.
Specifies the marker at which the reaction force and moment is applied. This is designated as the point of reaction of the force. The x-axis of J defines the neutral axis of the beam. The y- and z-axes should be oriented along the principal axes of the cross section (area products of inertial are zero).
The j attribute is mandatory.
function
String
The list of parameters that are passed from the data file to the user-defined subroutine.
The function attribute is mandatory.
routine
String
Specifies an alternative name for the user subroutine. The name consists of two pieces of information, separated by “∷”. The first is the pathname to the shared library containing the function that computes the force and its derivative with respect to relative displacement and velocity. The second is the name of the function in the shared library that does the computation.
An example is:
routine=”/staff/Altair/engine.dll∷myBeam
• ”/staff/Altair/ engine.dll is the DLL.
• “myBeam” is the function within this DLL that performs the calculations.
Beam specified in a Python function.
i
Reference to an existing Marker object.
Specifies the ID of the marker at which the force and moment are applied. This is designated as the point of application of the force.
The i attribute is mandatory.
j
Reference to an existing Marker object.
Specifies the marker at which the reaction force and moment is applied. This is designated as the point of reaction of the force. The x-axis of J defines the neutral axis of the beam. The y- and z-axes should be oriented along the principal axes of the cross section (area products of inertial are zero).
The j attribute is mandatory.
function
String
The list of parameters that are passed from the data file to the user-defined subroutine.
The function attribute is mandatory.
routine
It could either point to a callable function in Python or be the name of a python function (String).
The routine attribute is mandatory.
script
The path to the script which contains the python callable pointed by routine. When routine points to a callable object, script will be neglected.
The script attribute is optional.
Optional Attributes – Available to all description methods.
id
Specifies the element identification number. This number must be unique among all the Beam objects in the model.
This attribute is optional. MotionSolve will automatically create an ID when one is not specified.
Range of values: id > 0.
label
String
Specifies the name of the Beam object.
This attribute is optional. When not specified, MotionSolve will create a label for you.

## Example

Create a BEAM given the geometry and material properties below.

The example demonstrates a short, squat beam that is used as a connector between two rigid bodies. The beam connects Reference_Marker 37 on Rigid_Body 3 and Reference_Marker 47 on Rigid_Body 4. The properties of the beam are as follows:
• Length of the beam = 57.55mm.
• Radius of circular cross section = 10mm.
• Material = steel.
• The damping ratio is 0.001.

The Force_Beam definition for these specifications:

beam0 = beam (label="beam0", i=marker37, j=marker47, length=57.55, ixx=15707.96,iyy=7853.982, izz=7853.982, area=314.1593, emodulus=2E5, gmodulus=7.692308E4, asy=1.2,asz=1.2, cratio=0.001)