This section describes the standard beam sections that are available in
Abaqus/Standard
and
Abaqus/Explicit
for use with beam elements. A subset of the standard beam sections are
available for use with frame elements in
Abaqus/Standard.
General (nonstandard) beam cross-sections can be defined as described in
Choosing a Beam Cross-Section.
The arbitrary section type is provided to permit modeling of simple,
arbitrary, thin-walled, open and closed sections. You specify the section by
defining a series of points in the thin-walled cross-section of the beam; these
points are then linked by straight line segments, each of which is integrated
numerically along the axis of the section so that the section can be used
together with nonlinear material behavior. An independent thickness is
associated with each of the segments making up the arbitrary section.
Warping effects are included when an arbitrary section is used with
open-section beam elements (available only in
Abaqus/Standard).
An arbitrary section can be used only with beams in space
(three-dimensional models).
An arbitrary section should not be used to define closed sections with
branches, multiply connected closed sections, or open sections with
disconnected regions.
For each individual segment of an arbitrary section there is no bending
stiffness about the line joining the end points of the segment. Thus, an
arbitrary section cannot be made up of only one segment.
Geometric Input Data
First, give the number of segments, the local coordinates of points
A and B, and the thickness of the
segment connecting these two vertices. Then, proceed by giving the local
coordinates of point C and the thickness of the segment
between points B and C, followed by
the local coordinates of point D and the thickness of the
segment between points C and D, and
so on. An arbitrary section can contain as many segments as needed. All
coordinates of section definition points are given in the local 1–2 axis system
of the section.
The origin of the local 1–2 axis system is the beam node, and the position
of this node used to define the section is arbitrary: it does not have to be
the centroid.
Defining a Closed Section
A closed section is defined by making the starting and end points
coincident. Only single-cell closed sections can be modeled accurately. Closed
sections with fins (single branches attached to the cell) cannot be modeled
with the capability in
Abaqus.
Defining an Arbitrary Section with Discontinuous Branches
If the arbitrary section contains discontinuous sections (branches), a
section with zero thickness should be used to return from the ending point of
the branch to the starting point of the subsequent section. This zero thickness
section should always coincide with a nonzero thickness section. For an example
of an I-section defined using this method, see
Buckling analysis of beams.
Default Integration
A three-point Simpson integration scheme is used for each segment making up
the section. For more detailed integration, specify several segments along each
straight portion of the section.
Default Stress Output Points If a Beam Section Integrated during the Analysis Is Used
The vertices of the section.
Temperature and Field Variable Input at Specific Points through Beam Sections Integrated during the Analysis
Give the value at each vertex of the section (points A,
B, C, D in the
figure).
Nondefault Integration Input for a Beam Section Integrated during the Analysis
Beam in a plane: Give the number of points in each wall that is parallel to
the 2-axis. This number must be odd and greater than or equal to three.
Beam in space: Give the number of points in each wall that is parallel to
the 2-axis, then the number of points in each wall that is parallel to the
1-axis. Both numbers must be odd and greater than or equal to three.
Default Stress Output Points If a Beam Section Integrated during the Analysis Is Used
Beam in a plane: Bottom and top (points 1 and 5 above for default
integration).
Beam in space: 4 corners (points 1, 5, 9, and 13 above for default
integration).
Temperature and Field Variable Input at Specific Points for Beam Sections Integrated during the Analysis
Give the value at each of the points shown below.
Temperature Input for a Frame Section
Constant temperature throughout the element cross-section is assumed;
therefore, only one temperature value per node is required.
By allowing you to specify l, the origin of the local cross-section
axis can be placed anywhere on the local 2-axis. In the above figure a negative value of
l implies that the origin of the local cross-section axis is below
the lower edge of the bottom flange, which may be needed when constraining a beam
stiffener to a shell.
Beam in space: 3 points radially, 8 circumferentially (17 total; trapezoidal
rule). Integration point 1 is situated at the center of the beam and is used
for output purposes only. It makes no contribution to the stiffness of the
element; therefore, the integration point volume (IVOL) associated with this point is zero.
Nondefault Integration Input for a Beam Section Integrated during the Analysis
Beam in a plane: A maximum of 9 points are permitted.
Beam in space: Give an odd number of points in the radial direction, then an
even number of points in the circumferential direction.
Default Stress Output Points If a Beam Section Integrated during the Analysis Is Used
Beam in a plane: Bottom and top (points 1 and 5 above for default
integration).
Beam in space: On the intersection of the surface with the 1- and 2-axes
(points 3, 7, 11, and 15 above for default integration).
Temperature and Field Variable Input at Specific Points for Beam Sections Integrated during the Analysis
Give the value at each of the points shown below.
Temperature Input for a Frame Section
Constant temperature throughout the element cross-section is assumed;
therefore, only one temperature value per node is required.
By allowing you to specify l, the origin of the local cross-section
axis can be placed anywhere on the symmetry line (the local 2-axis). In the above figure a
negative value of l implies that the origin of the local
cross-section axis is below the lower edge of the bottom flanges, which may be needed when
constraining a beam stiffener to a shell.
Beam in space: 3 points in each wall segment (12 total)
Nondefault Integration Input for a Beam Section Integrated during the Analysis
Beam in a plane: Give the number of points along the section wall, moving in
the second beam section axis direction. This number must be odd and greater
than or equal to three.
Beam in space: Give the number of points in each wall segment. This number
must be odd and greater than or equal to three.
Default Stress Output Points If a Beam Section Integrated during the Analysis Is Used
Beam in a plane: Bottom and top (points 1 and 5 above for default
integration).
Beam in space: Vertices (points 1, 3, 5, 7, 9, and 11 above for default
integration).
Temperature and Field Variable Input at Specific Points for Beam Sections Integrated during the Analysis
By allowing you to specify l, the origin of the local
cross-section axis can be placed anywhere on the symmetry line (the local
2-axis). In the above figures a negative value of l
implies that the origin of the local cross-section axis is below the lower edge
of the bottom flange, which may be needed when constraining a beam stiffener to
a shell.
Defining a T-Section
Input File Usage
Set
and
or
and
to zero to model a T-section.
Default Integration (Simpson)
Beam in a plane: 5 points (one in each flange plus 3 in web)
Beam in space: 5 points in web, 5 in each flange (13 total)
Nondefault Integration Input for a Beam Section Integrated during the Analysis
Beam in a plane: Give the number of points in the second beam section axis
direction. This number must be odd and greater than or equal to three.
Beam in space: Give the number of points in the lower flange first, then in
the web, and then in the upper flange. These numbers must be odd and greater
than or equal to three in each nonvanishing section.
Default Stress Output Points If a Beam Section Integrated during the Analysis Is Used
Beam in a plane: Flanges (points 1 and 5 above for default integration).
Beam in space: Ends of flanges (points 1, 5, 9, and 13 above for default
integration).
Temperature and Field Variable Input at Specific Points for Beam Sections Integrated during the Analysis
Give the value at each of the points shown below.
For a beam in space the temperature is first interpolated linearly through
the flanges based on the temperature at points 1 and 2, and then 4 and 5,
respectively. It is then interpolated parabolically through the web.
Temperature Input for a Frame Section
Constant temperature throughout the element cross-section is assumed;
therefore, only one temperature value per node is required.
Nondefault Integration Input for a Beam Section Integrated during the Analysis
Beam in a plane: Give the number of points in the second beam section axis
direction. This number must be odd and greater than or equal to three.
Beam in space: Give the number of points in the first beam section axis
direction, then the number of points in the second beam section axis direction.
These numbers must be odd and greater than or equal to three.
Default Stress Output Points If a Beam Section Integrated during the Analysis Is Used
Beam in a plane: Bottom and top (points 1 and 5 above for default
integration).
Beam in space: End of flange along positive local 1-axis; section corner;
end of flange along positive local 2-axis (points 1, 5, and 9 above for default
integration).
Temperature and Field Variable Input at Specific Points for Beam Sections Integrated during the Analysis
Give the value at each of the points shown below.
Pipe Section (Thin-Walled)
Pipe cross-sections can be associated with beam, pipe, or frame elements.
Nondefault Integration Input for a Beam Section Integrated during the Analysis
Beam in a plane: Give an odd number of points in the radial direction, then
an odd number of points (greater than or equal to 5) in the circumferential
direction.
Beam in space: Give an odd number of points in the radial direction, then an
even number of points (greater than or equal to 8) in the circumferential
direction.
Default Stress Output Points If a Beam Section Integrated during the Analysis Is Used
Beam in a plane: Bottom and top on the pipe midsurface (points 2 and 14
above for default integration).
Beam in space: On the intersection of the pipe midsurface with the 1- and
2-axes (points 2, 8, 14, and 20 above for default integration).
Temperature and Field Variable Input at Specific Points for Beam Sections Integrated during the Analysis
Nondefault Integration Input for a Beam Section Integrated during the Analysis
Beam in a plane: Give the number of points in the second beam section axis
direction. This number must be odd and greater than or equal to five.
Beam in space: Give the number of points in the first beam section axis
direction, then the number of points in the second beam section axis direction.
These numbers must be odd and greater than or equal to five.
Default Stress Output Points If a Beam Section Integrated during the Analysis Is Used
Beam in a plane: Bottom and top (points 1 and 5 above for default
integration).
Beam in space: Corners (points 1, 5, 21, and 25 above for default
integration).
Temperature and Field Variable Input at Specific Points for Beam Sections Integrated during the Analysis
Give the value at each of the points shown below.
Temperature Input for a Frame Section
Constant temperature throughout the element cross-section is assumed;
therefore, only one temperature value per node is required.
By allowing you to specify d, the origin of the local
cross-section axes can be placed anywhere on the symmetry line (the local
2-axis). In the above figures a negative value of d
implies that the origin of the local cross-section axis is below the lower edge
of the section. This may be needed when constraining a beam stiffener to a
shell.
Default Integration (Simpson)
Beam in a plane: 5 points
Beam in space: 5 × 5 (25 total)
Nondefault Integration Input for a Beam Section Integrated during the Analysis
Beam in a plane: Give the number of points in the second beam section axis
direction. This number must be odd and greater than or equal to five.
Beam in space: Give the number of points in the first beam section axis
direction, then the number of points in the second beam section axis direction.
These numbers must be odd and greater than or equal to five.
Default Stress Output Points If a Beam Section Integrated during the Analysis Is Used
Beam in a plane: Bottom and top (points 1 and 5 above for default
integration).
Beam in space: Corners (points 1, 5, 21, and 25 above for default
integration).
Temperature and Field Variable Input at Specific Points for Beam Sections Integrated during the Analysis
