# Support Conditions for Lateral-Torsional Buckling

## Technical Article on the Topic Structural Analysis Using Dlubal Software

### Technical Article

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.

###### Cantilever Example

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.

#### Links

Write Comment...

Write Comment...

• Views 1960x
• Updated 27 October 2021

Contact us

Do you have questions or need advice?
Contact our free e-mail, chat, or forum support or find various suggested solutions and useful tips on our FAQ page.

Eurocode 3 | Steel Structures According to DIN EN 1993-1-1

Online Training 9 December 2021 8:30 AM - 12:30 PM CET

Dlubal RFEM 6: Staalconstructies (in Dutch)

Webinar 21 December 2021 3:00 PM - 4:00 PM CET

Introduction to the New RFEM 6

Webinar 11 November 2021 2:00 PM - 3:00 PM EST

Blast Time History Analysis in RFEM

Webinar 13 May 2021 2:00 PM - 3:00 PM EST

Plate and Shell Buckling Utilizing Dlubal Software

Webinar 30 March 2021 2:00 PM - 2:45 PM

CSA S16:19 Steel Design in RFEM

Webinar 10 March 2021 2:00 PM - 3:00 PM EST

Dlubal Info Day Online | 15 December 2020

Webinar 15 December 2020 9:00 AM - 4:00 PM CET

Stability Design in Steel Construction with RFEM and RSTAB

Webinar 1 December 2020 2:00 PM - 2:45 PM CET

Programmable COM Interface for RFEM/RSTAB

Webinar 12 May 2020 3:00 PM - 3:45 PM

Tensile Membrane Structures and CFD Wind Load Simulation

Webinar 8 April 2020 2:00 PM - 3:00 PM EST

Membrane Structures with Wind Loads From CFD Wind Simulation

Webinar 24 March 2020 3:00 PM - 4:15 PM CET

Webinar 3: BIM Integration and RFEM

Webinar 20 August 2019 3:00 PM - 4:00 PM

Webinar 2: Advanced modeling features in RFEM

Webinar 31 July 2019 3:00 PM - 4:00 PM

Webinar 1: Introduction to the FEA Program RFEM

Webinar 18 June 2019 3:00 PM - 4:00 PM

Tensile Membrane Structure Design in RFEM

Webinar 20 February 2019 3:00 PM - 4:00 PM

Point Supported Glass Design in RFEM

Webinar 22 January 2019 3:00 PM - 4:00 PM

Optimal BIM Integration with Revit and RFEM

Webinar 12 December 2018 3:00 PM - 4:00 PM

AISC 360-16 Steel Member and Warping Torsion Design in RFEM

Webinar 15 November 2018 3:00 PM - 4:00 PM

Length 1:17 min

Length 0:40 min

Length 0:59 min

Length 1:11 min

Length min

Length min

Length 0:24 min

Length 0:52 min

Length 1:02 min

Length 0:40 min

Length 1:06:54 min

Length 1:56 min

Length 1:14:41 min

Length 3:02:59 min

Length 1:09 min