Beam property definition

@BEAM_PROPERTY_DEFINITION {

@BEAM_PROPERTY_NAME {BldPropName} {

@COORDINATE_TYPE {CoordinateType}

@ETA_COORDINATE {η} {

@FILE_NAME {ArchiveName_SEB.h5}

}

@ETA_COORDINATE {η} {

@AXIAL_STIFFNESS {S}

...

}

@ETA_COORDINATE {η} {

...

}

@COMMENTS {CommentText}

}

}

Introduction

The physical mass and stiffness sectional properties of beams are defined in this section. The physical properties of the beam are allowed to vary along its span. To describe this variation, tables of beam sectional properties are defined. Beam properties are defined in the plane of the cross-section as defined by the beam geometry. Properties are described at discrete locations along the beam's span; each new location is introduced by keyword @ETA_COORDINATE. Plots of the beam sectional properties will be generated, if requested in the plotting control parameters data section.

It is possible to attach comments to the definition of the object; these comments have no effect on its definition.

Property definition type

The sectional properties of the beam are defined in the local axis system attached to the curve defining the geometry of the beam. Axis e₁ is tangent to the curve, and axes e₂ and e₃ define the plane of the cross-section. These properties describe the mass and stiffness characteristics of the section in the form of a 6×6 mass matrix and a 6×6 stiffness matrix, respectively.

Beam sectional properties can be defined in two alternative manners, depending on the keyword appearing first after the definition of coordinate η. value of the PropertyType parameter.

1. If keyword @FILE_NAME appears first, the sectional properties have been computed by SectionBuilder and are archived in file ArchiveName, which has been created by SectionBuilder. The input format is detailed below. This option allows the automatic transfer of the stiffness and mass characteristics of a beam's cross-section computed by SectionBuilder to Dymore.
2. If keyword @AXIAL_STIFFNESS appears first, the data must appear in the format detailed below. 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.

Coordinate definition type

Since beam properties are given along the curve that defines the geometry of the beam, table entries are associated with a parameterization of this curve. Coordinates can be defined in three alternative manners depending on the flag CoordinateType.

1. If CoordinateType = ETA_COORDINATE, positions along the curve are defined by means of the η coordinate. Each new property set must be introduced by the keyword @ETA_COORDINATE. The beam sectional properties will be defined in a table. Table entries define a sequence of η coordinates. Property sets are defined at each specific η-entry, as illustrated in fig. 1.
2. The table entries are mapped to physical locations along the beam curve by letting the η coordinate be the coordinate that parameterizes the curve defining the geometry of the beam.


Figure 1. Beam property definition using η-coordinate. The circles indicate the table entries.

3. If CoordinateType = CURVILINEAR_COORDINATE, positions along the curve are defined by means of the curvilinear coordinate, s. Each new property set must be introduced by the keyword @CURVILINEAR_COORDINATE. The beam sectional properties will be defined in a table. Table entries are define a sequence of s-coordinates. Property sets are defined at each specific s-entry, as illustrated in fig. 2.
4. The table entries are mapped to physical locations along the beam curve by letting the s-coordinate be the coordinate that parameterizes the curve defining the geometry of the beam.


Figure 2. Beam property definition using s-coordinates.

5. At the root end point of the beam curve, curvilinear variable s is zero. When the beam is defined, an offset, s_i, can be specified. In such case, the curvilinear variable along the beam becomes s_i + s, allowing the beam to use a subset of the entries of the property table, as illustrated in fig. 2. At the end point of the beam curve, the curvilinear variable is s_f = s_i + L, where L is the length of the beam. Clearly, the following inequalities must hold: s_beg <= s_i < s_end and s_beg < s_f <= s_end. When using the s-coordinate option, different beams are allowed to refer to the same beam property table, typically using adjacent portions of the table.
6. If CoordinateType = AXIAL_COORDINATE, positions along the curve are defined by means of the axial coordinate, x. Each new property set must be introduced by the keyword @AXIAL_COORDINATE. The beam section properties will be defined in a table. Table entries are define a sequence of x-coordinates. Property sets are defined at each specific x-entry. All the features of this option are identical to those detailed for the s-coordinate option.

SectionBuilder format

If keyword @FILE_NAME appears first, the following data items must be defined.

@ETA_COORDINATE {η} {

@FILE_NAME {ArchiveName_SEB.h5}

}

Notes

In this case, the 6×6 stiffness and mass matrices of the section are archived in file ArchiveName_SEB.h5. The archive file is a binary file that has been produced by SectionBuilder, as indicated by the _SEB.h5 ending in the file name.

Sectional properties format

If keyword @AXIAL_STIFFNESS appears first, the sectional properties of beams are defined 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.

@ETA_COORDINATE {η} {

@AXIAL_STIFFNESS {S}

@BENDING_STIFFNESSES {I₂₂^c, I₃₃^c, I₂₃^c}

@TORSIONAL_STIFFNESS {J}

@SHEARING_STIFFNESSES {K₂₂, K₃₃, K₂₃}

@MASS_PER_UNIT_SPAN {m₀₀}

@MOMENTS_OF_INERTIA {m₁₁, m₂₂, m₃₃}

@CENTRE_OF_MASS_LOCATION {x_m2, x_m3}

@SHEAR_CENTRE_LOCATION {x_k2, x_k3}

@CENTROID_LOCATION {x_c2, x_c3}

}

Notes

1. These properties are used to construct the 6×6 stiffness and mass matrices of the section.
2. The sectional stiffness is characterized by the following engineering constants, which are used to evaluate the 6×6 sectional stiffness matrix.
• The axial stiffness, S.
• The bending stiffnesses, I₂₂^c, I₃₃^c, and I₂₃^c, where I₂₂^c and I₃₃^c are the sectional bending stiffnesses about local unit vectors e₂ and e₃, respectively. I₂₃^c is the sectional cross-bending stiffness.
• The torsional stiffness, J.
• The shearing stiffnesses, K₂₂, K₃₃, and K₂₃, where K₂₂ and K₃₃ are the sectional shearing stiffnesses along local unit vectors e₂ and e₃, respectively. K₂₃ 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 e₂ and e₃, respectively.
• The coordinates of the location of the sectional centroid, x_c2 and x_c3. These coordinates are resolved along the local unit vectors e₂ and e₃, respectively.
3. The sectional mass is characterized by the following engineering constants, which are used to evaluate the 6×6 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, m₀₀.
• The moments of inertia per unit span, m₁₁, m₂₂, and m₃₃. The moments of inertia about local unit vectors e₂ and e₃ are denoted m₂₂ and m₃₃, respectively. The polar moment of inertia, m₁₁, should satisfy the following relationship, m₁₁ = m₂₂ + m₃₃.
• 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 e₂ and e₃, respectively.