Influence of Parameters for Lateral-Torsional Buckling on Design in RF-/STEEL EC3

Cantilever with Lateral Support

My previous article showed the effects of the lateral intermediate supports as well as the effective lengths L_cr,y/z.

• KB | Input and Effect of Lateral Supports in RF-/STEEL EC3

The parameters for lateral-torsional buckling additionally include the lengths L_w and L_T as well as the effective length factor k_z and the warping length factor k_w for a more detailed definition.

Input Window of RF-/STEEL EC3

Effective Length Factor k_z

An internal eigenvalue solver can be used to determine the ideal lateral-torsional buckling moment. It requires an internal member model with four degrees of freedom (u_y, φ_z, φx, ω).

Axis Definition

The factor k_z controls the support at the member start and member end with regard to the degrees of freedom u_y (displacement in y) and φ_z (rotation around z). In this example, both parameters are fixed at the member start. At the member end, it can only be assumed that the displacement in u_y is restricted. This situation corresponds to the definition k_z = 0.7le.

Effective Length and Warping Length Factors

Warping Length Factor k_w

This parameter is also used to support the internal member model. It controls the two remaining degrees of freedom φ_x (rotation around x) and ω (warping). Due to the restraint of the beam, both degrees of freedom are fixed at the start. At the free end, neither φ_x nor ω will be fixed. This corresponds to the definition k_w = 2.0le.

Warping Length L_w

The warping length is included in the determination of M_cr. It corresponds to the distance of the lateral and torsional restraints and is thus not necessarily identical to the effective length L_cr,z. This also becomes apparent when comparing the elastic critical moments M_cr between RF-/STEEL EC3 and LTBeamN (a program to determine critical loads).

• Website LTBeamN

The effective length L_cr,z = 0.7 ⋅ L (analogous to Euler Case 3). In contrast to this, the warping length is applied with L_w = L. In RF-/STEEL EC3, the M_cr for this results in 105.90 kNm. This corresponds to the result of the program LTBeamN, which calculates M_cr = 105.77 kNm. Compare: Using the warping length of 0.7 ⋅ L would have resulted in M_cr = 174 kNm.

Comparison of RF-/STEEL EC3 and LTBeamN

Torsional Length L_T

The torsional length is the governing length for the torsional buckling analysis according to 6.3.1.4 [1]. It is performed for compressive force only. It has no effect on the lateral-torsional buckling analysis. In the example, it is applied equal to the member length.

Comparison with Input by Means of Nodal Supports Analogous to Window 1.7

By designing sets of members according to 6.3.4 [1], RF-/STEEL EC3 offers the possibility to define the internal member model directly by means of nodal supports. The four degrees of freedom are available here. In the following comparison of the input options, we want to clarify that it is possible to have the same result. The structural system will remain identical for this purpose. Only the loading as well as the cross-section will be changed. Instead of IPE 160, a simple symmetric T-section is selected. Thus, the design according to 6.3.4 [1] will be necessary. In the image below, you can see a comparative overview of the input by effective lengths on the left and by nodal supports on the right. The result proves the assumption made at the beginning.

Comparison of Input Options

Conclusion

RF-/STEEL EC3 generally assumes a single-span beam with lateral and torsional restraint. The default parameters are aligned with it. With these preset factors, the user has the option to display other structural systems. It is finally up to the user to decide which degrees of freedom will remain in the respective nodal points.