Beam element names in Abaqus begin with the letter “B.” The next character indicates the dimensionality of the element: “2” for two-dimensional beams and “3” for three-dimensional beams. The third character indicates the interpolation used: “1” for linear interpolation, “2” for quadratic interpolation, and “3” for cubic interpolation.
The use of beam elements is discussed in Using Beam Elements.
- Beam element library
Linear, quadratic, and cubic beams are available in two and three dimensions. Cubic beams are not available in Abaqus/Explicit.
- Degrees of freedom
Three-dimensional beams have six degrees of freedom at each node: three translational degrees of freedom (1–3) and three rotational degrees of freedom (4–6). “Open-section”-type beams (such as B31OS) are available in Abaqus/Standard and have an additional degree of freedom (7) that represents the warping of the beam cross-section.
Two-dimensional beams have three degrees of freedom at each node: two translational degrees of freedom (1 and 2) and one rotational degree of freedom (6) about the normal to the plane of the model.
- Element properties
All beam elements must refer to a beam section property that defines the material associated with the element as well as the beam section profile (i.e., the element's cross-sectional geometry); the nodal coordinates define only the length. You can define the beam section profile geometrically by specifying the shape and dimensions of the section. Alternatively, you can define a generalized beam section profile by specifying the section engineering properties, such as area and moment of inertia.
If you define the beam section profile geometrically, Abaqus calculates the cross-section behavior of the beam by numerical integration over the cross-section, allowing both linear and nonlinear material behavior.
If you provide the section engineering properties (area, moments of inertia, and torsional constants) instead of the cross-section dimensions, there is no need for Abaqus to integrate any quantities over the element cross-section. Therefore, this option is less expensive computationally. With this approach, the material behavior may be either linear or nonlinear. The response is calculated in terms of the force and moment resultants; the stresses and strains are calculated only when they are requested for output.
In Abaqus/Standard you can also define beams with linearly tapered cross-sections. General beam sections with linear response and standard library sections are supported.
- Formulation and integration
The linear beams (B21 and B31) and the quadratic beams (B22 and B32) are shear deformable and account for finite axial strains; therefore, they are suitable for modeling both slender and stout beams. The cubic beam elements in Abaqus/Standard (B23 and B33) do not account for shear flexibility and assume small axial strain, although large displacements and rotations of the beams are valid. They are, therefore, suitable for modeling slender beams.
Abaqus/Standard provides variants of linear and quadratic beam elements that are suitable for modeling thin-walled, open-section beams (B31OS and B32OS). These elements model the effects of torsion and warping in open cross-sections, such as I-beams or U-section channels. Open-section beams are not covered in this guide.
Abaqus/Standard also has hybrid beam elements that are used for modeling very slender members, such as flexible risers on offshore oil installations, or for modeling very stiff links. Hybrid beams are not covered in this guide.
- Element output variables
The stress components in three-dimensional, shear-deformable beam elements are the axial stress () and the shear stress due to torsion (). The shear stress acts about the section wall in a thin-walled section. Corresponding strain measures are also available. The shear-deformable beams also provide estimates of transverse shear forces on the section. The slender (cubic) beams in Abaqus/Standard have only the axial variables as output. Open-section beams in space also have only the axial variables as output, since the torsional shear stresses are negligible in this case.
All two-dimensional beams use only axial stress and strain.
The axial force, bending moments, and curvatures about the local beam axes can also be requested for output. For details of what components are available with which elements, see About Beam Modeling. Details of how the local beam axes are defined are given in Using Beam Elements.