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Lateral-Torsional Buckling (LTB) is a phenomenon that occurs when a beam or structural member is subjected to bending and the compression flange is not sufficiently supported laterally. This leads to a combination of lateral displacement and twisting. It is a critical consideration in the design of structural elements, especially in slender beams and girders.
When a concrete slab is set upon the top flange, its effect is like a lateral support (composite construction), preventing problems of torsional buckling stability. If there is a negative distribution of the bending moment, the bottom flange is subjected to compression and the top flange is under tension. If the lateral support given by the stiffness of the web is insufficient, the angle between the bottom flange and the web intersection line is variable in this case so that there is a possibility of distortional buckling for the bottom flange.
For the stability verification of members using the equivalent member method, it is necessary to define effective or lateral-torsional buckling lengths in order to determine a critical load for stability failure. In this article an RFEM 6-specific function is presented, by which you can assign an eccentricity to the nodal supports and thus influence the determination of the critical bending moment considered in the stability analysis.
This article will show you how to use the Torsion Warping (7 DOF) add-on in combination with the Structure Stability add-on to consider cross-section warping as an additional degree of freedom when performing the stability analysis.
This technical article presents some basics for using the Torsional Warping add-on (7 DOF). It is fully integrated into the main program and allows you to consider the cross-section warping when calculating member elements. In combination with the Stability Analysis and Steel Design add-ons, it is possible to perform the lateral-torsional buckling design with internal forces according to the second-order analysis, taking imperfections into account.
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.
Very small torsional moments in the members to be designed often prevent certain design formats. In order to neglect them and still perform the designs, you can define a limit value in RF‑/STEEL EC3 from which torsional shear stresses are taken into account.
For a timber connection as shown in Figure 01, you can take into account the torsional spring rigidity (spring stiffness for rotation) of the connections. You can determine it by means of the slip modulus of the fastener and the polar moment of inertia of the connection.
In EN 1993-1-1, the General Method was introduced as a design format for stability analyses that can be applied to planar systems with arbitrary boundary conditions and variable structural height. The design checks can be performed for loading in the main load-bearing plane and simultaneous compression. The stability cases of lateral-torsional buckling and flexural buckling are analyzed from the main supporting plane; that is, about the weak component axis. Therefore, the issue often arises as to how to design, in this context, flexural buckling in the main load-bearing plane.
In the case of open cross-sections, the torsional load is removed mainly via secondary torsion, since the St. Venant torsional stiffness is low compared to the warping stiffness. Therefore, warping stiffeners in the cross-section are particularly interesting for the lateral-torsional buckling analysis, as they can significantly reduce the rotation. For this, end plates or welded stiffeners and sections are suitable.
- 000487
- Modeling | Structure
- RFEM 5
-
- RF-STEEL 5
- RF-STEEL AISC 5
- RF-STEEL AS 5
- RF-STEEL BS 5
- RF-STEEL CSA 5
- RF-STEEL EC3 5
- RF-STEEL GB 5
- RF-STEEL HK 5
- RF-STEEL IS 5
- RF-STEEL NBR 5
- RF-STEEL NTC-DF 5
- RF-STEEL SANS 5
- RF-STEEL SIA 5
- RF-STEEL SP 5
- RF-ALUMINUM 5
- RF-ALUMINUM ADM 5
- RSTAB 8
- STEEL 8
- STEEL AISC 8
- STEEL AS 8
- STEEL BS 8
- STEEL CSA 8
- STEEL EC3 8
- STEEL GB 8
- STEEL HK 8
- STEEL IS 8
- STEEL NBR 8
- STEEL NTC-DF 8
- STEEL SANS 8
- STEEL SIA 8
- STEEL SP 8
- ALUMINUM 8
- ALUMINUM ADM 8
- Steel Structures
- Process Manufacturing Plants
- Stairway Structures
- Structural Analysis & Design
- Eurocode 3
- ANSI/AISC 360
- SIA 263
- IS 800
- BS 5950-1
- GB 50017
- CSA S16
- AS 4100
- SP 16.13330
- SANS 10162-1
- ABNT NBR 800
- ADM
The support conditions of a beam subjected to bending are essential for its resistance to lateral-torsional buckling. If, for example, a single-span beam is held laterally in the middle of the span, the deflection of the compressed flange can be prevented, and a two-wave eigenmode can be enforced. The critical lateral-torsional buckling moment is increased significantly by this additional measure. In the add-on modules for member design, different types of lateral supports on a member can be defined using the "Intermediate supports" input window.
The RX‑TIMBER stand-alone program offers you the option to optimize the lateral-torsional bracing. With this selection, the program iteratively determines the required minimum length of the lateral-torsional bracing.
The previous article, titled Lateral-Torsional Buckling in Timber Construction | Examples 1, explains the practical application for determining the critical bending moment Mcrit or the critical bending stress σcrit for a bending beam's lateral buckling using simple examples. In this article, the critical bending moment is determined by considering an elastic foundation resulting from a stiffening bracing.
Utilizing the RF-STEEL AISC add-on module, steel member design is possible according to the AISC 360-16 standard. The following article will compare the results between calculating lateral torsional buckling according to Chapter F and Eigenvalue Analysis.
This technical article deals with the stability analysis of a roof purlin, which is connected without stiffeners by means of a bolt connection on the lower flange to have a minimum manufacturing effort.
The article titled Lateral-Torsional Buckling in Timber Construction | Theory explains the theoretical background for the analytical determination of the critical bending moment Mcrit or the critical bending stress σcrit for the lateral buckling of a bending beam. This article uses examples to verify the analytical solution with the result from the eigenvalue analysis.
Slender bending beams that have a large h/w ratio and are loaded parallel to the minor axis tend to have stability issues. This is due to the deflection of the compression chord.
In order to consider inaccuracies regarding the position of masses in a response spectrum analysis, standards for seismic design specify rules that have to be applied in both the simplified and multi-modal response spectrum analyses. These rules describe the following general procedure: The story mass must be shifted by a certain eccentricity, which results in a torsional moment.
In this technical article, a hinged column with a centrally acting axial force and a linear load that acts on the major axis are designed according to EN 1993-1-1 with the aid of the RF-/STEEL EC3 add-on module. The column head and column base are assumed as a lateral and torsional restraint. The column is not held against rotation between the supports. The cross-section of the column is an HEB 360 from S235.
The input windows in RF-/STEEL EC3 distinguish between the flexural and lateral-torsional buckling analyses. In the following text, an example will show the parameters for lateral-torsional buckling.
The critical factor for lateral-torsional buckling or the critical buckling moment of a single-span beam will be compared according to different stability analysis methods.
The design of a torsional loaded beam according to AISC Design Guide 9 will be shown, based on a verification example. The design will be performed with the RF‑STEEL AISC add-on module and the RF‑STEEL Warping Torsion module extension with 7 degrees of freedom.
This example is described in technical literature [1] as Example 9.5 and in [2] as Example 8.5. A lateral-torsional buckling analysis must be performed for a principal beam. This beam is a uniform structural member. Therefore, the stability analysis can be carried out according to Clause 6.3.3 of DIN EN 1993‑1‑1. Due to the uniaxial bending, it would also be possible to perform the design using the General Method according to Clause 6.3.4. Additionally, the determination of the critical load factor is validated with an idealized member model in line with the method mentioned above, using an FEM model.
This example is described in technical literature [1] as Example 9.5 and in [2] as Example 8.5. A lateral-torsional buckling analysis must be performed for a principal beam. This beam is a uniform structural member. Therefore, the stability analysis can be carried out according to Clause 6.3.3 of DIN EN 1993-1-1. Due to the uniaxial bending, it would also be possible to perform the design using the General Method according to Clause 6.3.4. Additionally, the determination of the moment Mcr is validated with an idealized member model in line with the method mentioned above, using an FEM model.
RF-/JOINTS Timber – Timber to Timber allows you to design main-connected beam joints. This article explains the determination of forces in screws of a beam connected to a torsionally rigid main beam.
A single-span beam with lateral and torsional restraint is to be designed according to the recommendations of Eurocode 3 and AISC. If the beam does not reach the required load-bearing capacity, it must be stabilized.
For situations where no design is available, RF-/STEEL EC3 provides the option to neglect the respective internal forces. Examples of such situations are: bending and compression on angle sections, multi-axial bending for the design according to the General Method, torsion.
This article describes the determination of force coefficients using a wind load and the calculation of a stability factor due to lateral-torsional buckling.
Basically, you can design the structural components made of cross-laminated timber in the RF-LAMINATE add-on module. Since the design is a pure elastic stress analysis, it is necessary to additionally consider the stability issues (flexural buckling and lateral-torsional buckling).
This article explains how to determine loads on the basis of the internal force situations defined in the RF‑/STEEL Warping Torsion extension of the RF‑/STEEL EC3 add-on module. Since this new program also allows you to analyze extracted chain-like beam structures in addition to entire chain-like beam structures, it is necessary to determine the loads of the partial structure separately. To do this, a special transformation function has been developed that determines new loads of all partial structures (depending on the internal forces calculated in RFEM/RSTAB) according to each load situation for geometrically nonlinear warping torsion analysis with seven degrees of freedom.