Entering Lateral Supports and Their Effects in RF-/STEEL EC3

Technical Article

When designing steel columns or steel beams, it is usually necessary to carry out cross-section and stability analyses. In most cases, cross-section design can be carried out without giving further details; the stability design, however, needs additional user-defined specifications. To a certain extent, the member is cut out from the structure and therefore, the support conditions have to be specified. This is particularly important to determine the ideal critical moment for lateral torsional buckling Mcr. In addition, the correct effective lengths Lcr have to be defined. They are necessary for the internal calculation of the slenderness ratios.

This article shows entering these two governing parameters by means of an example and explains their effects on the results. We take a closer look at the following structure.

Structure

Figure 01 - Structure

A steel beam with a length of 6 m has a lateral and torsional restraint at both ends. A coupling member connects perpendicular in the middle of the member. It does not introduce force into the structure, but only serves as support against lateral buckling. The main beam is loaded by uniaxial bending and compression.

The design is carried out in RF-/STEEL EC3. The focus is on the design according to 6.3.3 (uniform structural elements subjected to bending and compression). Several modul cases are analyzed by specifying the boundary conditions on a case by case basis. The aim is to point out the effects of the settings on the calculation. A set of member is defined for the main beam which is selected for the design. Since the module always assumes a single-span beam with lateral and torsional restraints regardless of the given situation, the correct member length of 6 m is saved for the vertical buckling.

Case Study

Case 1: Set of members design without intermediate support

The lateral support will not be considered in the first case. No manual adjustments are necessary. The effective lengths are included in the calculation with 6 m which has been set automatically.

Figure 02 - Window "1.4 Intermediate Lateral Restraints"

The input window for the lateral intermediate supports will not be considered as well.

Figure 03 - Window "1.6 Effective Lengths - Sets of Members"

The elastic critical load for buckling around the z-axis Ncr,z as well as the elastic critical moment for lateral-torsional buckling Mcr are taken to compare the results. These intermediate results are included as governing in the calculation of the reduction factors Χz and ΧLT as well as the interaction factors kyz and kzz which can be found in the design formulas according to 6.3.3. In case 1 they result in:

Ncr,z = 347.6 kN
Mcr = 78.7 kNm
ratio = 99 %

Case 2: set of members design with adjusted effective length Lcr,z = 0.5 ⋅ L

Case 2 considers that the main beam will not buckle about the z-axis in its full length due to the coupling member, but is likely to have a sinusoidal buckling mode. Therefore, the effective length Lcr,z is reduced to 0.5 ⋅ L = 3 m in Window 1.6. However, no data are still entered in the intermediate lateral restraint.

Ncr,z = 1,390.5 kN
Mcr = 78.7 kNm
ratio = 77 %

It is clear that the elastic critical buckling load Ncr,z is increased due to the modification of the effective length. In other words, this means that by halving the effective length, the member would buckle laterally only at a far greater axial force. It is also apparent that Mcr is the same. It can be concluded that an adaptation of the effective length does not change the structural system (which is the basis for the calculation of Mcr).

Case 3: set of members design with defining an intermediate lateral restraint uy at 3 m

Based on case 1, only one intermediate lateral restraint is defined in Window 1.4 for case 3. A user-defined support at the end of member 1 is applied where only the lateral support uy is activated. As in case 1, the effective lengths are 6 m.

Ncr,z = 347.6 kN
Mcr = 187.0 kNm
ratio = 76 %

Compared to case 2, it is clear that defining a lateral intermediate support has an effect on Mcr. The structural system has been changed in the background from a simple single-span beam to a single-span beam with lateral support in the center. At the same time, it can be stated that defining the intermediate lateral restraint must not necessarily have an effect on the elastic crital buckling loads for the buckling. Ncr,z corresponds again with the result from case 1.

Case 4: set of members design including intermediate lateral restraint and adjusted effective length

In case 4, the adjustments of the cases 2 and 3 are combined. It results in the following intermediate values:

Ncr,z = 1,390.5 kN
Mcr = 187.0 kNm
ratio = 53 %

They are based, as expected, on the results of the two previous cases. Due to their combination, the ratio is, however, reduced again from 76 % and 77 % to 53 %.

Summary

Even if the development of the ratio through the cases can only be displayed as a snapshot for this special case, it should be, however, highlighted that the member as a whole has to be considered correctly for the design. It means that the effective lengths are checked and the internal structural system is supported adequately. In this example, only the effective length about the z-axis and the support by lateral intermediate restraints were described in detail. If the basic structure is no single-span beam with lateral and torsional restraints at the end points, the support conditions have to be defined in detail here. Find more information about it in the manual or the linked articles below.

Keywords

Stability, Intermediate Lateral Restraint, Support

Reference

Links

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