Model Element

Class Name

Beam

Description

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

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)

Attribute Description

i

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 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.

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:

, where 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:

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:

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

id

Integer

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.

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.

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.

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

Comments

Example

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:

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)