The Buckling panel, from the Model tab, opens a dialog box to select the desired buckling length calculating method of the column for both X and Y directions.
The Buckling panel
The selected buckling type along X and Y can be previewed in the ribbon.
The Buckling length dialog box
EC2 uses two methods to determine the buckling lengths:
1. In the case of isolated elements having a constant section in 5.8.3.2.(2), some examples of different buckling modes and corresponding effective lengths are given.
2. In the case of compression members in regular frames in article 5.8.3.2.(3), two formulas for calculating the effective length are proposed:
Braced members
Unbraced members
where:
K1, k2 are the relative flexibilities of rotational restraints at ends 1 and 2, respectively:
θ is the rotation of restraining members for bending moment M
EI is the bending stiffness of compression member
l is the clear height of compression member between end restraints
If an adjacent compression member (column) in a node is likely to contribute to the rotation at buckling, then (E Ι / l) in the definition of k should be replaced by [(E Ι / l)a+(E Ι / l)b], a and b representing the compression member (column) above and below the node. [EN 1992-1-1 §5.8.3.2.(4)]
Example of k calculation considering the article §5.8.3.2.(4) from EN 1992-1:
The two methods suggested by EN 1992-1-1 are found in the dialog as the two options Standard and Auto.
This dialog is used for entering the column height, as well as for choosing conditions for column end supports along the X-axis and the Y-axis, to automatically calculate the buckling lengths and the slenderness ratio.
Column height: define the height of the compression member between end restraints
Along X
- Buckling Length (Lx): If an adjacent compression member (column) in a node is likely to contribute to the rotation at buckling, then (E Ι /l) in the definition of k should be replaced by [(E Ι / l) a + (E Ι / l)b], a and b representing the compression member (column) above and below the node. [EN 1992-1-1 §5.8.3.2.(4)] effective length about X-axis
- Slenderness (λX): slenderness ratio about X-axis
- Standard: select this option to use effective lengths for isolated members with constant cross-section, according to chapter 5.8.3.2(2) from EN 1992-1-1
- Auto: select this option for the evaluation of the buckling length of a column in a multi-story frame, with the contribution of members converging at the bottom and top ends
Conditions for column supports:
- Free at the top, fixed at the bottom
- Pinned at the top, pinned at the bottom
- Displacement at the top, fixed at the bottom
- Pinned at the top, fixed at the bottom
- Fixed at the top, fixed at the bottom
You can choose not to use any of the options available under Standard, and input stiffness at both ends. The software will calculate the corresponding buckling length using a structure calculation method with braced or unbraced nodes. For this, you must apply the option in the supports area (with Auto selected) to open the Buckling Length Calculation dialog box.
In the Buckling Length Calculation dialog, the column considered is the column between A and B points.
For the buckling length to be automatically calculated, the user must enter the values for:
Top column length, Lt, and moment of inertia, It
Bottom column length, Lb and moment of inertia, Ib
Left span length Ll
Right span length Lr
Moment of inertia for the top left span, Ilt, top right span, Irt, bottom left span, Ilb, and bottom-right span, Irb
Manual stiffness method
The theoretical analysis uses idealized end restraints, whose translational and rotational stiffnesses are set to either zero (free end) or infinity (fixed end). In some instances, it may be acceptable for the designer to assume a column has these idealized end restraint conditions, especially for preliminary design purposes, when a more rigorous analysis is to follow.
The influence that end restraints have on the buckling capacity can be further analyzed by taking into account the fact that, for real structures, the rotational and translational stiffness of the end restraints is somewhere between rigid and free.
In Advance Design modules, the spring supports functionality can be found as the Manual stiffnesses option, which can be selected in the Buckling length dialog. When Manual stiffnesses are selected, FEM calculation is automatically activated and the effective length of the column is no longer calculated using simplified formulas.
Note: During FEM calculation, in the preliminary calculation of reinforcement (using one of the EN 1992-1-1 methods), the effective length is considered equal to the column height. The calculation starts from this assumption.
You can define nodal stiffnesses against displacement and rotation for both the top and bottom ends of the column, using the specific dialogs Nodal Stiffness along X and Nodal Stiffness along Y.
kΔx: Define nodal stiffness against displacement on X direction
kΔz: Define nodal stiffness against displacement on Z direction
kθx: Define nodal stiffness against rotation about X-axis
kθz: Define nodal stiffness against rotation about Z-axis
kΔy: Define nodal stiffness against displacement on Y direction
kθy: Define nodal stiffness against rotation about Y-axis
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