Support Conditions for Lateral-Torsional Buckling
A member's boundary conditions decisively influence the elastic critical moment for lateral-torsional buckling Mcr. The program uses a planar model with four degrees of freedom for its determination. The corresponding coefficients kz and kw can be defined individually for standard-compliant cross-sections. This allows you to describe the degrees of freedom available at both member ends due to the support conditions.
The effective length coefficient kz controls the lateral displacement uy and the rotation φz at the member ends. The following options are available in the list of the table column:
- kz = 1.0 restrained against lateral displacement uy on both member ends
- kz = 0.7le restrained against displacement uy on both member ends; restraint about z on left member end
- kz = 0.7ri restrained against displacement uy on both member ends; restraint about z on right member end
- kz = 0.5 restrained against displacement uy and restraint about z on both member ends
- kz = 2.0le restrained against displacement uy and restraint about z on left member end; right member end free
- kz = 2.0ri restrained against displacement uy and restraint about z on right member end; left member end free
The warping length factor kw controls the torsion about the member's longitudinal axis ϕx and the warping ω. The list offers the following options:
- kw = 1.0 restrained against rotation about x on both member ends; free to warp on both sides
- kw = 0.7le restrained against rotation about x on both ends; warping restraint on left member end
- kw = 0.7ri restrained against rotation about x on both ends; warping restraint on right member end
- kw = 0.5 torsion and warping restraint on both member ends
- kw = 2.0le restrained against rotation about x and warping ω on left member end; right member end free
- kw = 2.0ri restrained against rotation about x and warping ω on right member end; left member end free
The abbreviations "li" and "ri" refer to the left and right member end. The abbreviation "le" always describes the support conditions at the start of the member.
A cantilever is subjected to a moment and an axial force.
In design case 1, the support conditions are defined like for a single-span beam with end fork conditions: kz = 1.0 and kw = 1.0. This results in an elastic critical moment for lateral-torsional buckling of 761.14 kNm.
The mode shape shows the lateral-torsional buckling behavior of a single-span beam.
In design case 2, the cantilever's support conditions are defined correctly: kz = 2.0le and kw = 2.0le. The program determines a significantly smaller critical moment of 371.72 kNm.
The mode shape corresponds to that of a cantilever.
Dipl.-Ing. (FH) Robert Vogl
Technical Editor, Product Engineering & Customer Support
Mr. Vogl creates and maintains the technical documentation. In addition, he is involved in the development of the SHAPE-THIN program and provides customer support.
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Very small torsional moments in the members to be designed often prevent certain design formats.
SHAPE-THIN determines the effective cross-sections according to EN 1993-1-3 and EN 1993-1-5 for cold-formed sections. You can optionally check the geometric conditions for the applicability of the standard specified in EN 1993‑1‑3, Section 5.2.
The effects of local plate buckling are considered according to the method of reduced widths and the possible buckling of stiffeners (instability) is considered for stiffened sections according to EN 1993-1-3, Section 5.5.
As an option, you can perform an iterative calculation to optimize the effective cross-section.
You can display the effective cross-sections graphically.
Read more about designing cold-formed sections with SHAPE-THIN and RF-/STEEL Cold-Formed Sections in this technical article: Design of a Thin-Walled, Cold-Formed C-Section According to EN 1993-1-3.
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