Section Stiffness
The Section Stiffness 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 Section Orientation subnodes if the same section appears with different spatial orientations in the structure.
By adding the following subnodes to the Section Stiffness node you can incorporate other effects:
Section Properties
Specify the components of the Stiffness matrix, 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:
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.
For a 2D Euler-Bernoulli beam, enter the 2 by 2 matrix. The columns, in order, correspond to the axial force N and bending moments Mzl. The rows, in order, correspond to the axial strain εn, and curvature κzl.
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.
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 Distance to shear in local z direction, ez, and the Distance to shear center in local y direction, 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 Mass per unit length, mL, and the Mass moment of inertia per unit length, Im, of the beam in order to define the inertial forces. In 2D, only the Mass moment of inertia per unit length, zz component, Im,zz, is needed.
In addition, specify the First moment of mass per unit length, local y component, m1y, and the First moment of mass per unit length, local z component, m1z, if the modeled point does not coincide with the center of mass; otherwise keep these inputs equal to zero.
Stress Evaluation 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 Evaluation factors in local system. 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 Twisting moment factor, ST, a Shear force factor, local y direction, SSy, and a Shear force factor, local z direction, SSz. In 2D, only the Shear force factor, local y direction is needed.
By default, the table and the additional stress evaluation factors are populated with coefficients that correspond to a fictitious rectangular cross-section made of a single homogeneous material. The evaluation points then correspond to the four corners of the cross-section.
Location in User Interface
Context Menus
Ribbon
Physics tab with Beam selected: