Comparing Critical Load Factors for Lateral-Torsional Buckling According to Different Methods and Modules

Technical Article

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.

Structural System and Loading

Given is a single-span beam with a length of 15 m. The cross-section of the single-span beam is an IPE 400 made of S355. The load is 5 kN/m. The self-weight is neglected.

Figure 01 - Structural System and Loading

Design without Stabilization

The verification can be carried out with the standard settings (single-span beam with lateral and torsional restraints) of the RF-/STEEL EC3 add-on module according to the German national annex and is not fulfilled.

The critical buckling moment is only 72.61 kNm here and this value is confirmed by common formulas from technical literature.

Figure 02 - Design without Stabilization

Design with Stabilization on the Upper Chord

By means of a virtual transverse bar, connecting at the middle of the upper chord, the displacement of the upper chord is fixed.

This stabilization can be performed in RF-/STEEL EC3 by means of a lateral intermediate restraint, without having to divide the member for this purpose.

Figure 03 - Entering the Intermediate Lateral Restraint

The subsequent design according to Section 6.3.2.3 EN 1993-1-1 [1] leads to a successful verification and a critical buckling moment of 209.52 kNm.

Figure 04 - Design with Stabilization

Comparing with the General Method as Design of Sets of Members

In the next step, the verification will be performed according to the general method as design of sets of members. For this purpose, the member can be copied in Y-direction, including supports and loading, divided once in the middle and a set of members can be created.

Figure 05 - Set of Members

In a new design case in RF-/STEEL EC3, the set of members is now selected for the design. Instead of Table "1.5 Effective Lengths - Members", Table "1.7 Nodal Support" is displayed. By default, two supports with support φ x' and u y' have been defined at the start and end of the set of design brackets.

To stabilize it in the middle, another support has to be created and provided with an eccentricity of -200 mm in the local z-direction.

The supports can be easily displayed via a button in the partial view window.

Figure 06 - Entering the Nodal Support

The verification is successful and a critical factor of 1.49 is calculated.

Figure 07 - Design According to the General Method

By using the maximum moment, the critical buckling moment of 209.54 kNm can be determined which corresponds to the last calculation.

Figure 08 - Calculating the Lateral-Torsional Buckling Moment

The slenderness ratio of the beam is given as 1.488 and is required for applying the imperfection in the following section.

Comparing with Warping Analysis

In the next step, the critical factor will be compared with the warping analysis which means that seven degrees of freedom are used instead of four degrees of freedom.

It is necessary to select the option "Perform warping analysis" in the "Details" dialog box, "Warping Torsion" tab.

Figure 09 - Activating Warping Torsion

As with the method according to 6.3.4 EN 1993-1-1, it is necessary to check the nodal supports and, if necessary, adjust them.

Figure 10 - Entering the Nodal Supports for the Warping Analysis

In Window 1.13 an imperfection value of L/400 is given.

The subsequent design is more favourable and leads to a critical factor of 1.489, which corresponds very well with the previous designs.

Figure 11 - Results of the Warping Torsion Analysis

Comparing with the RF-/FE-LTB Add-on Module

In the last step, the single-span beam (set of members) will be designed with the RF-/FE-LTB add-on module and the critical factor will be compared again here.

In RF/FE-LTB, the nodal supports which are defined at the set of members, are directly imported.

Figure 12 - Defining the Nodal Supports in RF-/FE-LTB

However, it is not possible to define an eccentricity, which is why the intermediate restraint is not defined as a nodal support, but as member end spring in Window 1.6.

Figure 13 - Entering the Upper Chord Support as Member End Spring with Eccentricity

When entering the load, pay attention to applying the eccentricity, since otherwise a too favourable calculation takes place.

Figure 14 - Load Eccentricity in RF-/FE-LTB

The imperfection is manually set to 1,875 cm for the first mode shape.

Figure 15 - Entering the Imperfection

The final calculation results in a critical factor of 1.489 and corresponds with all previous calculations.

Figure 16 - Displaying the Critical Load Factor

Keywords

Lateral-torsional buckling Warping analysis Steel structures EC3

Reference

[1]   Eurocode 3: Design of steel structures - Part 1‑1: General rules and rules for buildings; EN 1993‑1‑1:2010‑12

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