BEAM4 Element Description

BEAM4 is a uniaxial element with tension, compression, torsion, and bending capabilities. The element has six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z axes. Stress stiffening and large deflection capabilities are included. A consistent tangent stiffness matrix option is available for use in large deflection (finite rotation) analyses.

Figure 4.1: BEAM4 Geometry

BEAM4 Input Data

The geometry, node locations, and coordinate systems for this element are shown in Figure 4.1: BEAM4 Geometry. The element is defined by two or three nodes, the cross-sectional area, two area moments of inertia (IZZ and IYY), two thicknesses (TKY and TKZ), an angle of orientation (θ) about the element x-axis, the torsional moment of inertia (IXX), and the material properties. For stiffness purposes, the torsional moment of inertia, if IXX is equal to 0.0 or not specified, is assumed to be equal to the polar moment of inertia (IYY + IZZ). For inertial purposes, the torsional (rotational) moment of inertia used is the polar moment of inertia, and is therefore not affected by the value entered for IXX. The IXX value should be positive and is usually less than the polar moment of inertia. An added mass per unit length may be input with the ADDMAS value.

The element x-axis is oriented from node I toward node J. For the two-node option, the default (θ = 0°) orientation of the element y-axis is automatically calculated to be parallel to the global X-Y plane. Several orientations are shown in Figure 4.1: BEAM4 Geometry. For the case where the element is parallel to the global Z axis (or within a 0.01 percent slope of it), the element y axis is oriented parallel to the global Y axis (as shown). For user control of the element orientation about the element x-axis, use the θ angle (THETA) or the third node option. If both are defined, the third node option takes precedence. The third node (K), if used, defines a plane (with I and J) containing the element x and z axes (as shown). If this element is used in a large deflection analysis, it should be noted that the location of the third node (K), or the angle (THETA), is used only to initially orient the element. (For information about orientation nodes and beam meshing, see Meshing Your Solid Model in the Modeling and Meshing Guide.)

The initial strain in the element (ISTRN) is given by Δ/L, where Δ is the difference between the element length, L, (as defined by the I and J node locations) and the zero strain length. The shear deflection constants (SHEARZ and SHEARY) are used only if shear deflection is to be included. A zero value of SHEAR_ may be used to neglect shear deflection in a particular direction.

KEYOPT(2) is used to activate the consistent tangent stiffness matrix (that is, a matrix composed of the main tangent stiffness matrix plus the consistent stress stiffness matrix) in large deflection analyses (NLGEOM,ON). You can often obtain more rapid convergence in a geometrically nonlinear analysis, such as a nonlinear buckling or postbuckling analysis, by activating this option. However, you should not use this option if you are using the element to simulate a rigid link or a group of coupled nodes. The resulting abrupt changes in stiffness within the structure make the consistent tangent stiffness matrix unsuitable for such applications.

KEYOPT(7) is used to compute an unsymmetric gyroscopic damping matrix (often used for rotordynamic analyses). The rotational frequency is input with the SPIN real constant (radians/time, positive in the positive element x direction). The element must be symmetric with this option (for example, IYY = IZZ and SHEARY = SHEARZ).

Element loads are described in Element Loading. Pressures may be input as surface loads on the element faces as shown by the circled numbers on Figure 4.1: BEAM4 Geometry. Positive normal pressures act into the element. Lateral pressures are input as a force per unit length. End "pressures" are input as a force. Temperatures may be input as element body loads at the eight "corner" locations shown in Figure 4.1: BEAM4 Geometry. The first corner temperature T1 defaults to TUNIF. If all other temperatures are unspecified, they default to T1. If only T1 and T2 are input, T3 defaults to T2 and T4 defaults to T1. If only T1 and T4 are input, T2 defaults to T1 and T3 defaults to T4. In both cases, T5 through T8 default to T1 through T4. For any other input pattern, unspecified temperatures default to TUNIF.

KEYOPT(9) is used to request output at intermediate locations. It is based on equilibrium (free body of a portion of the element) considerations and is not valid if:

A summary of the element input is given in "BEAM4 Input Summary". A general description of element input is given in Element Input.

BEAM4 Output Data

The solution output associated with the element is in two forms:

Several items are illustrated in Figure 4.2: BEAM4 Stress Output.

The maximum stress is computed as the direct stress plus the absolute values of both bending stresses. The minimum stress is the direct stress minus the absolute value of both bending stresses. A general description of solution output is given in Solution Output. See the Basic Analysis Guide for ways to view results.

Figure 4.2: BEAM4 Stress Output

The Element Output Definitions table uses the following notation:

A colon (:) in the Name column indicates that the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file jobname.out. The R column indicates the availability of the items in the results file.

In either the O or R columns, “Y” indicates that the item is always available, a letter or number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

The following tables list output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) of the Basic Analysis Guide and The Item and Sequence Number Table of this manual for more information. The following notation is used in Table 4.3: BEAM4 Item and Sequence Numbers (KEYOPT(9) = 0) through Table 4.8: BEAM4 Item and Sequence Numbers (KEYOPT(9) = 9):

BEAM4 Assumptions and Restrictions

BEAM4 Product Restrictions

When used in the product(s) listed below, the stated product-specific restrictions apply to this element in addition to the general assumptions and restrictions given in the previous section.

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