SectionBuilder section data
- @SECTION_BUILDER_SECTION_DATA
- @SECTION_BUILDER_SECTION_NAME {SbSecName} {
- @PROPERTY_DEFINITION_TYPE {PropertyType}
- @STIFFNESS_MATRIX {k_{11}, k_{12}, k_{22}, k_{13}, k_{23}, k_{33},... k_{16}, k_{26}, ...k_{66}}
- @MASS_PER_UNIT_SPAN {m_{00}}
- @MOMENTS_OF_INERTIA {m_{33}, m_{23}, m_{22}}
- @CENTRE_OF_MASS_LOCATION {x_{m2}, x_{m3}}
- ...
- @AXIAL_STIFFNESS {S}
- @BENDING_STIFFNESSES {I_{22}^{c}, I_{33}^{c}, I_{22}^{c}}
- @TORSIONAL_STIFFNESS {J}
- @SHEARING_STIFFNESSES {K_{22}, K_{33}, K_{23}}
- @MASS_PER_UNIT_SPAN {m_{00}}
- @MOMENTS_OF_INERTIA {m_{11}, m_{22}, m_{33}}
- @CENTRE_OF_MASS_LOCATION {x_{m2}, x_{m3}}
- @SHEAR_CENTRE_LOCATION {x_{k2}, x_{k3}}
- @CENTROID_LOCATION {x_{c2}, x_{c3}}
- @DAMPING_COEFFICIENT {μ_{s}}
- @COMMENTS {CommentText}
- }
- }
Introduction
This object is part of the interface between Dymore and SectionBuilder. Its function is to transfer the stiffness and mass characteristics of a beam's cross-section computed by SectionBuilder to Dymore. Although this data object is primarily used as an interface between Dymore and SectionBuilder, it is also possible to input data computed by another sectional analysis code, or experimentally measured sectional data, as long as the input format described below is respected.
The physical mass and stiffness sectional properties of the cross-section of beams are defined in this section. Typically, the physical properties of beams vary along their span. The present section focuses on a single cross-section of the beam. Beam properties are defined in the plane of its cross-section.
Beam sectional properties can be defined in two alternative manners, depending on the value of the PropertyType parameter.
- If PropertyType = SECTION_BUILDER, the data must appear in the format defined in section SectionBuilder format. This format is used by SectionBuilder and allows the automatic transfer of the stiffness and mass characteristics of a beam's cross-section computed by SectionBuilder to Dymore.
- If PropertyType = SECTIONAL_PROPERTIES, the data must appear in the format defined in section Sectional properties format. This format focuses on the definition of engineering sectional properties such as sectional bending and torsional stiffnesses. When experimental measurements of the sectional physical properties are available, this is the preferred data input format.
The sectional properties of beams are defined in the local axis system attached to the curve defining the beam geometry. Axis e_{1} is tangent to the curve, and axes e_{2} and e_{3} define the plane of the cross-section. These properties describe the mass and stiffness characteristics of the section in the form of a 6x6 mass matrix and a 6x6 stiffness matrix, respectively. Whether defined in the SECTION_BUILDER or SECTIONAL_PROPERTIES format, sectional properties are used to construct 6x6 mass and stiffness matrices; if these matrices are not positive-definite, error messages are issued during the data checking phase.
SectionBuilder format
When PropertyType = SECTION_BUILDER, the following data items must be defined.
- @STIFFNESS_MATRIX {k_{11}, k_{12}, k_{22}, k_{13}, k_{23}, k_{33},... k_{16}, k_{26}, ...k_{66}}
- @MASS_PER_UNIT_SPAN {m_{00}}
- @MOMENTS_OF_INERTIA {m_{33}, m_{23}, m_{22}}
- @CENTRE_OF_MASS_LOCATION {x_{m2}, x_{m3}}
- @DAMPING_COEFFICIENT {μ_{s}}
Notes
- These properties are used to construct the mass and stiffness characteristics of the section in the form of a 6x6 mass matrix and a 6x6 stiffness matrix, respectively.
- The fully populated, 6x6 sectional stiffness matrix is computed by SectionBuilder. Due to symmetry, only 21 terms of the stiffness matrix are independent; they are input in a column by column format defining the upper-half of the stiffness matrix, k_{11}, k_{12}, k_{22}, k_{13}, k_{23}, k_{33},... k_{16}, k_{26}, ...k_{66}.
- The sectional mass per unit span, denoted m_{00}, is computed by SectionBuilder.
- The sectional moments of inertia per unit span, denoted m_{33}, m_{23}, and m_{22}, are computed by SectionBuilder. The moments of inertia about local unit vectors e_{2} and e_{3} are denoted m_{22} and m_{33}, respectively, and m_{23} is the cross product of inertia. The polar moment of inertia, m_{11}, need not be defined because it is obtained easily as m_{11} = m_{22} + m_{33}.
- The coordinates of the sectional center of mass location, denoted x_{m2} and x_{m3}, are computed by SectionBuilder. These coordinates are resolved along the local unit vectors e_{2} and e_{3}, respectively.
- Optionally, a viscous damping coefficient, μ_{s}, can be defined for the section. Note that SectionBuilder does not evaluate this viscous damping coefficient.
- If SectionBuilder is used to evaluate sectional properties, the following comments will appear in the definition of the object.
- @COMMENTS {Generated by SectionBuilder: Version 1.0}
- @COMMENTS {Time stamp: Sun Jul 15 11:54:51 2012}
Sectional properties format
This formatting describes the sectional properties of beams using the traditional engineering constants such as axial, bending, and torsional stiffnesses, etc. Typically, these properties are evaluated using the approximations described in strength of material textbooks, or measured in the laboratory. When PropertyType = SECTIONAL_PROPERTIES, the following data items must be defined.
- @AXIAL_STIFFNESS {S}
- @BENDING_STIFFNESSES {I_{22}^{c}, I_{33}^{c}, I_{23}^{c}}
- @TORSIONAL_STIFFNESS {J}
- @SHEARING_STIFFNESSES {K_{22}, K_{33}, K_{23}}
- @MASS_PER_UNIT_SPAN {m_{00}}
- @MOMENTS_OF_INERTIA {m_{11}, m_{22}, m_{33}}
- @CENTRE_OF_MASS_LOCATION {x_{m2}, x_{m3}}
- @SHEAR_CENTRE_LOCATION {x_{k2}, x_{k3}}
- @CENTROID_LOCATION {x_{c2}, x_{c3}}
- @DAMPING_COEFFICIENT {μ_{s}}
Notes
- These properties are used to construct the mass and stiffness characteristics of the section in the form of a 6x6 mass matrix and a 6x6 stiffness matrix, respectively.
- The sectional stiffness is characterized by the following engineering constants, which are used to evaluate the 6x6 sectional stiffness matrix.
- The axial stiffness, S.
- The bending stiffnesses, I_{22}^{c}, I_{33}^{c}, and I_{23}^{c}, where I_{22}^{c} and I_{33}^{c} are the sectional bending stiffnesses about local unit vectors e_{2} and e_{3}, respectively. I_{23}^{c} is the sectional cross-bending stiffness.
- The torsional stiffness, J.
- The shearing stiffnesses, K_{22}, K_{33}, and K_{23}, where K_{22} and K_{33} are the sectional shearing stiffnesses along local unit vectors e_{2} and e_{3}, respectively. K_{23} is the sectional cross-shearing stiffness.
- The coordinates of the location of the sectional shear center, x_{k2} and x_{k3}.These coordinates are resolved along the local unit vectors e_{2} and e_{3}, respectively.
- The coordinates of the location of the sectional centroid, x_{c2} and x_{c3}. These coordinates are resolved along the local unit vectors e_{2} and e_{3}, respectively.
- The sectional mass is characterized by the following engineering constants, which are used to evaluate the 6x6 sectional mass matrix. The consistency of the mass matrix is checked during the reading phase and some coefficients might be adjusted, in which case warning messages will be issued.
- The mass per unit span, m_{00}.
- The moments of inertia per unit span, m_{11}, m_{22}, and m_{33}. The moments of inertia about local unit vectors e_{2} and e_{3} are denoted m_{22} and m_{33}, respectively. The polar moment of inertia, m_{11}, should satisfy the following relationship, m_{11} = m_{22} + m_{33}.
- The coordinates of the location of the sectional center of mass, x_{m2} and x_{m3}. These coordinates are resolved along the local unit vectors e_{2} and e_{3}, respectively.
- Optionally, a viscous damping coefficient, μ_{s}, can be defined for the section.