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001557

Dipl.-Ing. (FH) Lukas Sühnel

2019-02-06

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

When designing steel columns or steel beams, it is usually necessary to carry out cross-section design and stability analysis. While the cross-section design can usually be performed without giving further details, the stability analysis requires further user-defined entries. To a certain extent, the member is cut out of the structure; therefore, the support conditions have to be specified. This is particularly important when determining the ideal elastic critical moment M_cr. Furthermore, it is necessary to define the correct effective lengths L_cr. These are required for the internal calculation of slenderness ratios.

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

Structure

Structural System

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

The design is carried out in RF‑/STEEL EC3. The focus is placed on the design according to 6.3.3, the uniform structural elements subjected to bending and compression. Several module 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 members is defined for the main beam that 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 entered for the vertical buckling.

Case Study

Case 1: Design of Set of Members 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 was set automatically.

Window "1.4 Intermediate Lateral Restraints"

The input window for the lateral intermediate supports remains unaffected.

Window "1.6 Effective Lengths - Sets of Members"

The elastic critical load for buckling around the z-axis N_cr,z as well as the elastic critical moment for lateral-torsional buckling M_cr are taken to compare the results. These intermediate results are included as governing in the calculation of the reduction factors Χ_z and Χ_LT, as well as the interaction factors k_yz and k_zz, which can be found in the design formulas according to 6.3.3. In Case 1, they result in:

N_cr,z = 347.6 kN
M_cr = 78.7 kNm
Design ratio = 99%

Case 2: Design of Set of Members with Adjusted Effective Length L_cr,z = 0.5 ⋅ L

Case 2 considers the fact that the main beam will not buckle around 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 L_cr,z is reduced to 0.5 ⋅ L = 3 m in Window 1.6. However, no data have yet been entered in the intermediate lateral restraint.

N_cr,z = 1,390.5 kN
M_cr = 78.7 kNm
Design ratio = 77%

It is clear that the elastic critical buckling load N_cr,zis increased due to the effective length modification. In other words, this means that by halving the effective length, the member would not buckle laterally until the axial force was far greater. It is also apparent that M_cr remains 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 M_cr).

Case 3: Design of Set of Members with Definiton of Intermediate Lateral Restraint u_y 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 while only activating the lateral support u_y. As in Case 1, the effective lengths are 6 m.

N_cr,z = 347.6 kN
M_cr = 187.0 kNm
Design ratio = 76%

Compared to Case 2, it is clear that the definition of the lateral intermediate support has an effect on M_cr. The structural system has been changed in the background from a simple single-span beam to a single-span beam with a lateral support in the center. It can also be stated that the definition of the intermediate lateral restraint does not necessarily have an effect on the elastic critical buckling loads. N_cr,z corresponds again with the result from Case 1.

Case 4: Design of Set of Members Including Intermediate Lateral Restraint and Adjusted Effective Length

In Case 4, the adjustments of Case 2 and Case 3 are combined. This results in the following intermediate values:

N_cr,z = 1,390.5 kN
M_cr = 187.0 kNm
Design ratio = 53%

They are based, as expected, on the results of the two previous cases. Due to the combination, the design 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 emphasized that the member as a whole has to be considered correctly for the design. This means that the effective lengths are checked and the internal structural system is supported adequately. In this example, only the effective length around the z-axis and the support by lateral intermediate restraints were described in detail. If the basic structure is not a 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 this in the manual or the articles linked below.

Author

Mr. Sühnel is responsible for the quality assurance of RSTAB; he also participates in product development and provides technical support for our customers.

Links

References

Dlubal Software. (2020). Manual RF-/STEEL EC3. Tiefenbach: Dlubal Software.

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