Choosing a Beam Cross-Section

The choice of cross-section is determined by the geometry of the cross-section and its behavior. A beam's cross-section:

  • can be solid or thin-walled;

  • if thin-walled, can be open or closed; and

  • can be defined by choosing from the Abaqus cross-section library; by specifying geometric quantities such as area, moments of inertia, and torsional constant; or by using a mesh of special two-dimensional elements, for which geometric quantities are calculated numerically.

You must consider whether the section should be treated as a solid cross-section or as a thin-walled cross-section. This choice determines the basis upon which Abaqus computes the axial and shear strains at each point in the section.

This page discusses:

 

See Also
About Beam Modeling
Beam Cross-Section Library
Meshed Beam Cross-Sections

Solid Cross-Sections

For solid sections under bending, plane (beam) sections remain plane. Under torsional loading any noncircular beam section will warp: the beam section will not remain planar. However, for solid sections the warping of the section is small enough so that the axial strain due to warping of the section can be neglected and St. Venant warping theory can be used to construct a single component of shear strain at each integration point in the section. This is done automatically for the rectangular and trapezoidal sections in the beam section library. The St. Venant warping functions are used to define the shear strain even when the response in the section is no longer purely elastic. This limits the accuracy of the modeling for cases involving noncircular solid beam sections subjected to torsional loadings that cause large amounts of inelastic deformation. When using a meshed beam profile, two shear strain components are available for output in the user-specified material system. The thick pipe section is treated as a solid cross-section.

Nonsolid (“Thin-Walled”) Cross-Sections

In Abaqus nonsolid sections are treated as “thin-walled” sections; that is, in the plane of the section, the thickness of a branch of the section is assumed to be small compared to its length. Thin-walled beam theory determines the shear in the wall of the section depending on whether the section is closed or open.

Closed Sections

A closed section is a nonsolid section whose branches form closed loops. Closed sections offer significant resistance to torsion and do not warp significantly. Abaqus ignores warping effects for closed sections.

In Abaqus predefined beam sections can model only one closed loop. Sections with multiple loops must be modeled with a meshed beam section (see Meshed Cross-Sections) or with shells.

For sufficiently small thickness of the section walls, the variation of shear stress across the thickness is negligible; the formulation of the closed sections available in Abaqus is based on this assumption.

Open Sections

An open section is a nonsolid section with branches that do not form closed loops, such as an I-section or a U-section. In such sections the shear stress is assumed to vary linearly over the wall thickness and to vanish at the center of the wall. Open sections can warp significantly and generally require the use of open-section warping theory (available with beam element types BxxOS in Abaqus/Standard) with suitable warping constraints (applied to degree of freedom 7) at supports or joints. Such warping constraints may significantly increase the torsional stiffness of the beam. Open, thin-walled sections whose branches are straight lines that meet at a single point (such as the L-section in the Abaqus beam element section library, T-sections, or X-sections) do not warp; therefore, warping constraints have no effect. Such sections always have very little torsional stiffness.

If an open section is used with a regular beam element type (not BxxOS), the open section is assumed to be free to warp and the axial strain due to warping is neglected. Consequently, the section will have very little torsional stiffness.

Section Property Calculations

Thin-walled assumptions are used when calculating nonsolid section properties. Properties for sections comprised of intersecting straight segments (arbitrary, box, channel, hat, hexagonal, I-, and L-sections) also include an approximation of the intersection geometry.

Available Beam Cross-Sections

You can specify any of the following types of beam cross-sections: an Abaqus library cross-section, a generalized cross-section for which you specify the geometric quantities directly, or a meshed cross-section.

Abaqus Beam Cross-Section Library

The Abaqus beam cross-section library contains

  • solid sections (circular, rectangular, and trapezoidal);
  • closed thin-walled sections (box, hexagonal, and pipe);
  • open thin-walled sections (channel-shaped, hat-shaped, I-shaped, L-shaped, and T-shaped); and
  • a thick-walled pipe section.

Abaqus also provides an arbitrary thin-walled section definition; Abaqus treats this section type as a closed or open section, depending on how the section is defined.

Arbitrary, channel, hat, I, and trapezoidal library sections allow you to define the location of the origin of the local coordinate system. Other section types (such as rectangular, circular, L, or pipe) have preset origins. The channel and hat sections are available only with general beam section definitions.

Generalized Cross-Sections

Abaqus also allows you to specify “generalized” cross-sections by specifying the geometric quantities necessary to define the section. Such generalized sections can be used only with linear material behavior although the section response can be linear or nonlinear.

Meshed Cross-Sections

Abaqus allows you to mesh an arbitrarily shaped solid cross-section by using warping elements (see Warping Elements) in a two-dimensional analysis to generate beam cross-section properties that can be used in a subsequent two- or three-dimensional beam analysis. Such sections permit only linear, elastic material behavior. Therefore, a meshed cross-section can be used only with a general beam section definition; for details, see Meshed Beam Cross-Sections.