Section Stiffness

The material model provides a way of directly entering the stiffness of a beam cross-section without direct knowledge of the geometry or materials used. It provides a method for entering data for complex geometries and cross-sections made of multiple materials. This is done by specifying the equivalent stiffness of the cross-section, as well as several other cross-sectional properties such as mass and mass moments of inertia.

Since only the stiffness is known, but not the cross-section geometry, it is not possible to deduce any sectional stresses. You can, however, provide an expression for stress computation based on the computed section forces.

For 3D models, a default Section Orientation subnode is added, in which you specify the orientation of the principal axes of the section. You can add any number of subnodes if the same section appears with different spatial orientations in the structure.

By adding the following subnodes to the node you can incorporate other effects:

Specify the components of the , S. The matrix is always assumed to be symmetric, but the number of components required vary depending on the beam formulation and the spatial dimension:

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For a 3D Euler-Bernoulli beam, enter the 4 by 4 matrix. The columns, in order, correspond to the axial force N, torsional moment Mxl, and bending moments Myl and Mzl. The rows, in order, correspond to the axial strain εn, axial twist κxl, and bending curvatures κyl and κzl.

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For a 3D Timoshenko beam, enter the 6 by 6 matrix. The columns, in order, correspond to the axial force N, shear forces Tyl and Tzl, torsional moment Mxl, and bending moments Myl and Mzl. The rows, in order, correspond to the axial strain εn, shear strains γyl and γzl, axial twist κxl, and bending curvatures κyl and κzl.

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For a 2D Timoshenko beam, enter the 3 by 3 matrix. The columns, in order, correspond to the axial force N, shear force Tyl, and bending moment Mzl. The rows, in order, correspond to the axial strain εn, shear strain γyl, and bending curvature κzl.

In 3D, enter also the , ez, and the, ey. These two inputs can be used to specify a distance between the center of mass and the shear center of the cross-section. If the inputs are non-zero, an applied edge load will also create a twisting moment on the cross-section.

Specify the , mL, and the , Im, of the beam in order to define the inertial forces. In 2D, only the , Im,zz, is needed.

In addition, specify the , m1y, and the , m1z, if the modeled point does not coincide with the center of mass; otherwise keep these inputs equal to zero.

	The inertia inputs are needed only for dynamic analysis. They are also used when computing mass forces for gravitational or rotating frame loads, and when computing mass properties (Computing Mass Properties).

If you want a certain stress value to be computed, you can enter a linear relation between section forces and stress here.

Enter the . In 3D, there are four evaluation points available in the cross-section. The second column in the table corresponds to the coefficient for the axial force N, the third to the bending moment around the local y-axis Myl, and the fourth to the bending moment around the local z-axis Mzl. In 2D, there are two evaluation points available in the cross-section. Only the coefficients for the normal force and the bending moment around the local z-axis Mzl are required.

In addition, in 3D enter a , ST, a , SSy, and a, SSz. In 2D, only the is needed.