Command Element

Description

Modifies a beam element.

Format

<Force_Beam

    id                   = "integer"

    i_marker_id          = "integer"

    j_marker_id          = "integer"

    length               = "real"

    E                    = "real"

    G                    = "real"

    area                 = "real"

    ixx                  = "real"

    iyy                  = "real"

    izz                  = "real"

    ASY                  = "real"

    ASZ                  = "real"

    cratio               = "real"

</Force_Beam>

Attributes

id

Element identification number (integer>0).  This number is unique among Force_Beam elements and uniquely identifies the element.

i_marker_id

Specifies the Reference_Marker at which the force is applied. This is designated as the point of application of the force.

j_marker_id

Specifies the Reference_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_marker_id defines the neutral axis of the beam.  The y- and z-axes should be oriented along the principal axes of the cross section (in other words, area products of inertial are zero).

length

Specifies the free length of the beam.  This is the distance from the origin of j_marker_id to the origin of i_marker_id.

E

Specifies the Young’s modulus of the beam material.  The beam is assumed to be homogeneous in its material properties.  E has to be strictly positive.

G

Specifies the modulus of rigidity or the shear modulus of the beam.  This is related to the Young’s modulus and POISSON's ratio by the formula:

G = E/2(1+ν), where ν is POISSON's ratio.  G has to be strictly positive.

area

Specifies the area of the cross-section that is perpendicularly oriented to the neutral axis of the beam.  This is assumed to be constant along the length of the beam.  AREA is strictly positive.

ixx

Specifies the torsional stiffness shape factor for the cross section.

For circular sections ixx is equal to the polar moment of inertia (π*Ρ4/2). 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. ixx is strictly positive.

iyy, izz

iyy 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_marker_id. iyy > 0.

izz 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_marker_id. izz > 0.

ASY, ASZ

ASY specifies the shear area ratio in the z direction for Timoshenko beams.  This quantity accounts for shear deflection in the Y direction.  It is calculated with the help of an integral.

ASZ specifies the shear area ratio in the z direction for Timoshenko beams.  This quantity accounts for shear deflection in the Z direction.  It is calculated with the help of an integral.

To calculate these factors using HyperBeam, refer to HyperBeam Help.

cratio

Defines 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], where C is the damping matrix and K is the stiffness matrix.

A value of 0.01 (or 1%) is typically used for cratio.

cratio > 0.

Example

<Force_Beam

    id     = "307017"

    length = "57.55867"

    E      = "200000."

    G      = "75000."

    area   = "314.1593"

    ixx    = "15707.96"

    iyy    = "7853.982"

    izz    = "7853.982"

    ASY    = "0."

    ASZ    = "0."

    cratio = "0.01">

</Force_Beam>

Command Element

Description

Modifies a BEAM element.

Declaration

def BEAM(ID, LABEL="", I=0, J=0, LENGTH=0.0, IXX=0.0, IYY=0.0, IZZ=0.0, AREA=0.0, ASY=0.0, ASZ=0.0, EMODULUS=0.0, GMODULUS=0.0, CMATRIX=[], CRATIO=0.0):

Attributes

id

Element identification number (integer>0).  This number is unique among all the BEAM elements.

LABEL

Modifies the name of the BEAM element.

I

Modifies the ID of the marker at which the force and moment is applied.  This is designated as the point of application of the force.

J

Modifies the ID of 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).

LENGTH

Modifies 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.

IXX

Modifies 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. IXX > 0.

IYY

Modifies 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. IYY > 0.

IZZ

Modifies 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. IZZ > 0.

AREA

Defines the beam cross sectional area.

ASY

Modifies 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. ASY > 0.

ASZ

Modifies 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. ASZ > 0.

EMODULUS

Modifies the Young’s modulus of elasticity of the beam material.  The beam is assumed to be homogeneous in its material properties. E > 0.

GMODULUS

Modifies the Shear modulus of elasticity of the beam.  This is related to the Young’s modulus of elasticity and POISSON's ratio by the formula:

G = E/2(1+v), where v is POISSON's ratio. G > 0.

CMATRIX

Specifies the damping ratio as six by six symmetric matrix.

[C11,C12,C13,C14,C15,C16,C21,C22,C23,C24,C25,C26,C31,C32...]

CRATIO

Modifies 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.

cratio> 0.

Comments

See Force_Beam

Example

The example below shows how a BEAM may be modified.

BEAM(307017, LENGTH=57.55867, IXX=15707.96, IYY=7853.982, IZZ=7853.982, AREA=314.1593, EMODULUS=200000, GMODULUS=75000, ASY=0,ASZ=0, CRATIO=0.001)