15.3.8 Beam element library

Products: ABAQUS/Standard ABAQUS/Explicit ABAQUS/CAE

References

Element types

Beams in a plane

B21 2-node linear beam
B21H^(S)     2-node linear beam, hybrid formulation
B22 3-node quadratic beam
B22H^(S)     3-node quadratic beam, hybrid formulation
B23^(S)     2-node cubic beam
B23H^(S)     2-node cubic beam, hybrid formulation
PIPE21^(S)     2-node linear pipe
PIPE21H^(S)     2-node linear pipe, hybrid formulation
PIPE22^(S)     3-node quadratic pipe
PIPE22H^(S)     3-node quadratic pipe, hybrid formulation

Active degrees of freedom

1, 2, 6

Additional solution variables

All of the cubic beam elements have two additional variables relating to axial strain.

The linear pipe elements have one additional variable, and the quadratic pipe elements have two additional variables relating to the hoop strain.

The hybrid beam and pipe elements have additional variables relating to the axial force and transverse shear force. The linear elements have two, the quadratic elements have four, and the cubic elements have three additional variables.

Beams in space

B31 2-node linear beam
B31H^(S)     2-node linear beam, hybrid formulation
B32 3-node quadratic beam
B32H^(S)     3-node quadratic beam, hybrid formulation
B33^(S)     2-node cubic beam
B33H^(S)     2-node cubic beam, hybrid formulation
PIPE31^(S)     2-node linear pipe
PIPE31H^(S)     2-node linear pipe, hybrid formulation
PIPE32^(S)     3-node quadratic pipe
PIPE32H^(S)     3-node quadratic pipe, hybrid formulation

Active degrees of freedom

1, 2, 3, 4, 5, 6

Additional solution variables

All of the cubic beam elements have two additional variables relating to axial strain.

The linear pipe elements have one additional variable, and the quadratic pipe elements have two additional variables relating to the hoop strain.

The hybrid beam and pipe elements have additional variables relating to the axial force and transverse shear force in the linear and quadratic elements and to the axial force only in the cubic elements. The linear and cubic elements have three and the quadratic elements have six additional variables.

Open-section beams in space

B31OS^(S)     2-node linear beam
B31OSH^(S)     2-node linear beam, hybrid formulation
B32OS^(S)     3-node quadratic beam
B32OSH^(S)     3-node quadratic beam, hybrid formulation

Active degrees of freedom

1, 2, 3, 4, 5, 6, 7

Additional solution variables

Element type B31OSH has three additional variables and element type B32OSH has six additional variables relating to the axial force and transverse shear force.

Nodal coordinates required

Beams in a plane: , , also (optional) , , the direction cosines of the normal.

Beams in space: , , , also (optional) , , , the direction cosines of the second local cross-section axis.

Element property definition

For PIPE elements use only the pipe section type.

For open-section elements use only the arbitrary, I, L, and linear generalized section types.

Local orientations defined as described in “Orientations,” Section 2.2.5, cannot be used with beam elements to define local material directions. The orientation of the local beam section axes in space is discussed in “Beam element cross-section orientation,” Section 15.3.4.

Input File Usage:	Use either of the following options:
	BEAM SECTION BEAM GENERAL SECTION

ABAQUS/CAE Usage:

Property module: Create Section: select Beam as the section Category and Beam as the section Type

Element-based loading

Distributed loads

Distributed loads are specified as described in “Distributed loads,” Section 19.4.3.

Load ID (*DLOAD):  CENT^(S)

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–2 (ML^–1T^–2)

Description:  Centrifugal force (magnitude is input as , where is the mass per unit length and is the angular velocity).

Load ID (*DLOAD):  CENTRIF^(S)

ABAQUS/CAE Load/Interaction:  Rotational body force

Units:  T^–2

Description:  Centrifugal load (magnitude is input as , where is the angular velocity).

Load ID (*DLOAD):  CORIO^(S)

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–2T (ML^–1T^–1)

Description:  Coriolis force (magnitude is input as , where is the mass per unit length and is the angular velocity). The load stiffness due to Coriolis loading is not accounted for in direct steady-state dynamics analysis.

Load ID (*DLOAD):  GRAV

ABAQUS/CAE Load/Interaction:  Gravity

Units:  LT^–2

Description:  Gravity loading in a specified direction (magnitude is input as acceleration).

Load ID (*DLOAD):  PX

ABAQUS/CAE Load/Interaction:  Line load

Units:  FL^–1

Description:  Force per unit length in global -direction.

Load ID (*DLOAD):  PY

ABAQUS/CAE Load/Interaction:  Line load

Units:  FL^–1

Description:  Force per unit length in global -direction.

Load ID (*DLOAD):  PZ

ABAQUS/CAE Load/Interaction:  Line load

Units:  FL^–1

Description:  Force per unit length in global -direction (only for beams in space).

Load ID (*DLOAD):  PXNU

ABAQUS/CAE Load/Interaction:  Line load

Units:  FL^–1

Description:  Nonuniform force per unit length in global -direction with magnitude supplied via user subroutine DLOAD in ABAQUS/Standard (“DLOAD,” Section 25.2.5) and VDLOAD in ABAQUS/Explicit (“VDLOAD,” Section 25.3.1).

Load ID (*DLOAD):  PYNU

ABAQUS/CAE Load/Interaction:  Line load

Units:  FL^–1

Description:  Nonuniform force per unit length in global -direction with magnitude supplied via user subroutine DLOAD in ABAQUS/Standard (“DLOAD,” Section 25.2.5) and VDLOAD in ABAQUS/Explicit (“VDLOAD,” Section 25.3.1).

Load ID (*DLOAD):  PZNU

ABAQUS/CAE Load/Interaction:  Line load

Units:  FL^–1

Description:  Nonuniform force per unit length in global -direction with magnitude supplied via user subroutine DLOAD in ABAQUS/Standard (“DLOAD,” Section 25.2.5) and VDLOAD in ABAQUS/Explicit (“VDLOAD,” Section 25.3.1). (Only for beams in space.)

Load ID (*DLOAD):  P1

ABAQUS/CAE Load/Interaction:  Line load

Units:  FL^–1

Description:  Force per unit length in beam local 1-direction (only for beams in space).

Load ID (*DLOAD):  P2

ABAQUS/CAE Load/Interaction:  Line load

Units:  FL^–1

Description:  Force per unit length in beam local 2-direction.

Load ID (*DLOAD):  P1NU

ABAQUS/CAE Load/Interaction:  Line load

Units:  FL^–1

Description:  Nonuniform force per unit length in beam local 1-direction with magnitude supplied via user subroutine DLOAD in ABAQUS/Standard (“DLOAD,” Section 25.2.5) and VDLOAD in ABAQUS/Explicit (“VDLOAD,” Section 25.3.1). (Only for beams in space.)

Load ID (*DLOAD):  P2NU

ABAQUS/CAE Load/Interaction:  Line load

Units:  FL^–1

Description:  Nonuniform force per unit length in beam local 2-direction with magnitude supplied via user subroutine DLOAD in ABAQUS/Standard (“DLOAD,” Section 25.2.5) and VDLOAD in ABAQUS/Explicit (“VDLOAD,” Section 25.3.1).

Load ID (*DLOAD):  ROTA^(S)

ABAQUS/CAE Load/Interaction:  Rotational body force

Units:  T^–2

Description:  Rotary acceleration load (magnitude is input as , where is the rotary acceleration).

The following load types are available only for PIPE elements:

Load ID (*):  HPI^(S)

ABAQUS/CAE Load/Interaction:  Pipe pressure

Units:  FL^–2

Description:  Hydrostatic internal pressure (default closed-end condition), varying linearly with the global -coordinate.

Load ID (*):  HPE^(S)

ABAQUS/CAE Load/Interaction:  Pipe pressure

Units:  FL^–2

Description:  Hydrostatic external pressure (default closed-end condition), varying linearly with the global -coordinate.

Load ID (*):  PI^(S)

ABAQUS/CAE Load/Interaction:  Pipe pressure

Units:  FL^–2

Description:  Uniform internal pressure (default closed-end condition).

Load ID (*):  PE^(S)

ABAQUS/CAE Load/Interaction:  Pipe pressure

Units:  FL^–2

Description:  Uniform external pressure (default closed-end condition).

Load ID (*):  PENU^(S)

ABAQUS/CAE Load/Interaction:  Pipe pressure

Units:  FL^–2

Description:  Nonuniform external pressure (default closed-end condition) with magnitude supplied via user subroutine DLOAD (“DLOAD,” Section 25.2.5).

Load ID (*):  PINU^(S)

ABAQUS/CAE Load/Interaction:  Pipe pressure

Units:  FL^–2

Description:  Nonuniform internal pressure (default closed-end condition) with magnitude supplied via user subroutine DLOAD (“DLOAD,” Section 25.2.5).

ABAQUS/Aqua loads

ABAQUS/Aqua loads are specified as described in “ABAQUS/Aqua analysis,” Section 6.10.1. They are not available for open-section beams and do not apply to beams that are defined to have additional inertia due to immersion in fluid (see “Additional inertia due to immersion in fluid” in “Beam section behavior,” Section 15.3.5).

Load ID (*CLOAD/ *DLOAD):  FDD

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–1

Description:  Transverse fluid drag load.

Load ID (*CLOAD/ *DLOAD):  FD1

ABAQUS/CAE Load/Interaction:  Not supported

Units:  F

Description:  Fluid drag force on the first end of the beam (node 1).

Load ID (*CLOAD/ *DLOAD):  FD2

ABAQUS/CAE Load/Interaction:  Not supported

Units:  F

Description:  Fluid drag force on the second end of the beam (node 2 or node 3).

Load ID (*CLOAD/ *DLOAD):  FDT

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–1

Description:  Tangential fluid drag load.

Load ID (*CLOAD/ *DLOAD):  FI

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–1

Description:  Transverse fluid inertia load.

Load ID (*CLOAD/ *DLOAD):  FI1

ABAQUS/CAE Load/Interaction:  Not supported

Units:  F

Description:  Fluid inertia force on the first end of the beam (node 1).

Load ID (*CLOAD/ *DLOAD):  FI2

ABAQUS/CAE Load/Interaction:  Not supported

Units:  F

Description:  Fluid inertia force on the second end of the beam (node 2 or node 3).

Load ID (*CLOAD/ *DLOAD):  PB

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–1

Description:  Buoyancy load (closed-end condition).

Load ID (*CLOAD/ *DLOAD):  WDD

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–1

Description:  Transverse wind drag load.

Load ID (*CLOAD/ *DLOAD):  WD1

ABAQUS/CAE Load/Interaction:  Not supported

Units:  F

Description:  Wind drag force on the first end of the beam (node 1).

Load ID (*CLOAD/ *DLOAD):  WD2

ABAQUS/CAE Load/Interaction:  Not supported

Units:  F

Description:  Wind drag force on the second end of the beam (node 2 or node 3).

Foundations

Foundations are available only in ABAQUS/Standard and are specified as described in “Element foundations,” Section 2.2.2.

Load ID (*FOUNDATION):  FX^(S)

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–2

Description:  Stiffness per unit length in global -direction.

Load ID (*FOUNDATION):  FY^(S)

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–2

Description:  Stiffness per unit length in global -direction.

Load ID (*FOUNDATION):  FZ^(S)

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–2

Description:  Stiffness per unit length in global -direction (only for beams in space).

Load ID (*FOUNDATION):  F1^(S)

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–2

Description:  Stiffness per unit length in beam local -direction (only for beams in space).

Load ID (*FOUNDATION):  F2^(S)

ABAQUS/CAE Load/Interaction:  Not supported

Units:  FL^–2

Description:  Stiffness per unit length in beam local -direction.

Surface-based loading

Distributed loads

Surface-based distributed loads are specified as described in “Distributed loads,” Section 19.4.3.

Load ID (*DSLOAD):  P

ABAQUS/CAE Load/Interaction:  Pressure

Units:  FL^–1

Description:  Force per unit length in beam local 2-direction. The distributed surface force is positive in the direction opposite to the surface normal.

Load ID (*DSLOAD):  PNU

ABAQUS/CAE Load/Interaction:  Pressure

Units:  FL^–1

Description:  Nonuniform force per unit length in beam local 2-direction with magnitude supplied via user subroutine DLOAD in ABAQUS/Standard (“DLOAD,” Section 25.2.5) and VDLOAD in ABAQUS/Explicit (“VDLOAD,” Section 25.3.1). The distributed surface force is positive in the direction opposite to the surface normal.

Incident wave loading

Incident wave loading is also available for these elements. See “Acoustic loads,” Section 19.4.5.

Element output

See “Beam cross-section library,” Section 15.3.9, for a description of the beam element output locations.

Stress, strain, and other tensor components

Stress and other tensors (including strain tensors) are available for elements with displacement degrees of freedom. All tensors, except for meshed sections, have the same components. For example, the stress components are as follows:

S11	Axial stress.

S22	Hoop stress (available only for pipe elements).

S12	Shear stress caused by torsion (available only for beam-type elements in space). This component is not available when thin-walled, open sections are employed (I-section, L-section, and arbitrary open section).

Stress and strain for section points for meshed sections

S11	Axial stress.

S12	Shear stress along the second cross-section axis caused by shear force and, for beam elements in space, torsion.

S13	Shear stress along the first cross-section axis caused by shear force and torsion (available only for beams in space).

Section forces, moments, and transverse shear forces

SF1	Axial force.

SF2	Transverse shear force in the local 2-direction (not available for B23, B23H, B33, B33H).

SF3	Transverse shear force in the local 1-direction (available only for beams in space, not available for B33, B33H).

SM1	Bending moment about the local 1-axis.

SM2	Bending moment about the local 2-axis (available only for beams in space).

SM3	Twisting moment about the beam axis (available only for beams in space).

BIMOM

Bimoment due to warping (available only for open-section beams in space).

ESF1	Effective axial force for beams subjected to pressure loading (available for all ABAQUS/Standard stress/displacement analysis types except response spectrum and random response).

See “Beam element formulation,” Section 3.5.2 of the ABAQUS Theory Manual, for the definitions of the section forces and moments.

The effective axial section force for beams subjected to pressure loading is defined as

where

and

are the external and the internal pressures, respectively, and

and

are the external and the internal pipe areas as defined in the load definition. The pressure loadings (with a closed-end condition) that are relevant to the effective axial force are external/internal pressure (load types PE, PI, PENU, and PINU); external/internal hydrostatic pressure (load types HPE and HPI); and, in an ABAQUS/Aqua environment, buoyancy pressure, PB, which includes dynamic pressure if waves are present.

For beams that are not subjected to pressure loading, the effective axial force ESF1 is equal to the usual axial force SF1.

Section strains, curvatures, and transverse shear strains

SE1	Axial strain.

SE2	Transverse shear strain in the local 2-direction (not available for B23, B23H, B33, and B33H).

SE3	Transverse shear strain in the local 1-direction (available only for beams in space, not available for B33 and B33H).

SK1	Curvature change about the local 1-axis.

SK2	Curvature change about the local 2-axis (available only for beams in space).

SK3	Twist of the beam (available only for beams in space).

BICURV

Bicurvature due to warping (available only for open-section beams in space).

Node ordering on elements

For beams in space an additional node may be given after a beam element's connectivity (in the element definition—see “Element definition,” Section 2.2.1) to define the approximate direction of the first cross-section axis, . See “Beam element cross-section orientation,” Section 15.3.4, for details.