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 around the member's longitudinal axis ϕx and the warping ω. The list offers the following options:
- kw = 1.0 restrained against rotation around x on both member ends; free to warp on both sides
- kw = 0.7le restrained against rotation around x on both ends; warping restraint on left member end
- kw = 0.7ri restrained against rotation around 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 around x and warping ω on left member end; right member end free
- kw = 2.0ri restrained against rotation around x and warping ω on right member end; left member end free
The abbreviations "li" and "ri" refer to the left and right member ends, respectively. 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 as 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.
Compared to the RF-/STEEL EC3 add-on module (RFEM 5/RSTAB 8), the following new features have been added to the Steel Design add-on for RFEM 6 / RSTAB 9:
- In addition to Eurocode 3, other international standards are integrated (e.g. AISC 360, CSA S16, GB 50017, SP 16.13330)
- Consideration of hot-dip galvanizing (DASt guideline 027) in the fire protection design according to EN 1993-1-2
- Input option for transverse stiffeners that can be taken into account in the shear buckling analysis
- Lateral-torsional buckling can also be checked for hollow sections (e.g. relevant for slender, high rectangular hollow sections)
- Automatic detection of members or member sets valid for the design (e.g. automatic deactivation of members with invalid material or members already contained in a set of members)
- Design settings can be adjusted individually for each member
- Graphical display of the results in the gross section or the effective section
- Output of the used design check formulas (including a reference to the used equation from the standard)
- I design a set of members by using the equivalent member method in RF‑/STEEL EC3, but the calculation fails. The system is unstable, delivering the message "Non-designable - ER055) Zero value of the critical moment on the segment."What could be the reason?
- What is the meaning of the warning message ER061) Minimum amplifier of design loads <1?
- In RF‑/STEEL EC3, I get an error message saying that the node with a support does not exist in the set of members. What is the reason?
- In the RF‑/STEEL EC3 add-on module, I have selected two bracings with the same size as the shear panel type in the "Parameters" window for a beam to be designed. Thus, the beam should be supported laterally in the middle. Why is the eigenvector arbitrary anyhow?
- Why are the equivalent member designs grayed out in the Stability tab when activating the plastic designs by using the partial internal force method (RF‑/STEEL Plasticity)?
- When calculating a cable using the STEEL EC3 add‑on module, there is the error message "Incorrect characteristic stresses for material No. 1! Please correct this in Table 1.2."
- I design an asymmetric cross-section and get the message: "Non-designable: ER051) Moment about z‑axis on asymmetric cross-section, taper or set of members." Why?
- How can I perform the stability analysis in RF‑/STEEL EC3 for a flat bar supported on edges, such as 100/5? Although the cross-section is rotated by 90° in RFEM/RSTAB, it is displayed as lying flat in RF‑/STEEL EC3.
- Why is there no stability analysis displayed in the results despite the activation of the stability analysis in RF‑/STEEL EC3?
- In RF‑/STEEL EC3, is the "Elastic design (also for Class 1 and Class 2 cross-sections)" option under "Details → Ultimate Limit State" considered for a stability analysis when activated?