This article describes the determination of force coefficients using a wind load and the calculation of a stability factor due to lateral-torsional buckling.
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.
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.
The RF-/STEEL EC3 add‑on module performs a detailed cross‑section classification on each design before the design is carried out. Thus, the susceptibility to local buckling of all cross-section parts is evaluated. The defined cross-section class has an effect on the resistance and rotational capacity determination.
The classification of cross-sections is intended to determine the limits of resistance and rotational capacity due to local buckling of cross-section parts. In EN 1999‑1‑1, 6.1.4.2 (1), four classes are defined.
Shell buckling is considered to be the most recent and least explored stability issue of structural engineering. This is due less to a lack of research activities than to the complexity of the theory. With the introduction and further development of the finite element method in structural engineering practice, some engineers no longer have to deal with the complicated theory of shell buckling. Evidence of the problems and errors to which this gives rise is very well summarized in [1].
The fire resistance design can be performed according to EN 1993-1-2 in RF-/STEEL EC3. The design is carried out according to the simplified calculation method for the ultimate limit state. Claddings with different physical properties can be selected as fire protection measures. You can select the standard temperature-time curve, the external fire curve, and the hydrocarbon curve to determine the gas temperature.
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.
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.
RFEM offers the possibility to model also curved beams. To do this, a curved line must be created first (see Figure 01). This line can then be assigned a beam with a cross-section. The advantages over modeling with beam segments are easier handling during the modeling, as well as a clearer result output of the internal forces.
If a member is supported laterally to prevent buckling due to a compressive axial force, it must be ensured that the lateral support is actually able to prevent buckling. Therefore, the aim of this article is to determine the ideal spring stiffness of a lateral support using the Winter model.
The ASCE 7-16 standard requires both balanced and unbalanced snow load case scenarios for a structure's design consideration. While this may be more intuitive for flat or even gable/hip type roofs, the determination of snow loads is increasingly difficult for arch roofs due to complex geometry. However, with guidance from ASCE 7-16 on snow load calculations for curved roofs and RFEM's efficient load application tools, it is possible to consider both balanced and unbalanced snow loads for a reliable and safe structure design.
Prior to the analysis of steel cross‑sections, the cross‑sections are classified according to EN 1993‑1‑1, Sec. 5.5, with respect to their resistance and rotation capacity. Thus, the individual cross-section parts are analyzed and assigned to Classes 1 to 4. The cross-section classes are determined subsequently and usually assigned to the highest class of the cross-section parts. If plastic resistance is to be applied to further design of cross-sections of Class 1 and Class 2, you can analyze the elastic resistance of cross-sections as of Class 3. In the case of cross-sections of Class 4, local buckling occurs even before reaching the elastic moment. In order to take this effect into account, you can use effective widths. This article describes the calculation of the effective cross-section properties in more detail.
Using RF-/STEEL EC3, you can apply nominal temperature-time curves in RFEM or RSTAB. The standard time-temperature curve (ETK), the external fire curve and the hydrocarbon fire curve are implemented. Moreover, the program provides the option to directly specify the final temperature of steel. This steel temperature can be calculated using the parametric temperature-time curve, as described in the Annex to DIN EN 1992-1-2. The different fire exposures are explained in this article.
With RF-/STEEL EC3, you can utilize nominal temperature-time curves in RFEM and RSTAB. The standard time-temperature curve (ETK), the external fire curve and the hydrocarbon fire curve are implemented. Moreover, the program provides the option to directly specify the final temperature of steel.
Using the RF-TIMBER AWC module, timber column design is possible according to the 2018 NDS standard ASD method. Accurately calculating timber member compressive capacity and adjustment factors is important for safety considerations and design. The following article will verify the maximum critical buckling in RF-TIMBER AWC using step-by-step analytical equations as per the NDS 2018 standard including the compressive adjustment factors, adjusted compressive design value, and final design ratio.
In SHAPE-THIN, the calculation of stiffened buckling panels can be performed according to Section 4.5 of EN 1993-1-5. For stiffened buckling panels, the effective surfaces due to local buckling of the single panels in the plate and in the stiffeners, as well as the effective surfaces from the entire panel buckling of the stiffened entire panel, have to be considered.
The buckling analysis of plates with stiffeners is a special task for engineers. For this, EN 1993-1-5 provides three calculation methods: Effective Cross-Section Method, [1], Sect. 4-7; Reduced Stress Method, [1], Sect. 10; Finite Element Methods of Analysis (FEM), [1], Annex C.
Buckling analysis according to the effective width method or the reduced stress method is based on the determination of the system critical load, hereinafter called LBA (linear buckling analysis). This article explains the analytical calculation of the critical load factor as well as utilization of the finite element method (FEM).
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.
Using the RF-TIMBER AWC module, timber beam design is possible according to the 2018 NDS standard ASD method. Accurately calculating timber member bending capacity and adjustment factors is important for safety considerations and design. The following article will verify the maximum critical buckling in RF-TIMBER AWC using step-by-step analytical equations as per the NDS 2018 standard, including the bending adjustment factors, adjusted bending design value, and final design ratio.
Cable and tensile membrane structures are regarded as very slender and aesthetic building structures. The partly very complex double-curved shapes can be found using suitable form-finding algorithms. One possible solution is to search for the form via the equilibrium between the surface stress (provided prestress and an additional load such as self-weight, pressure, and so on) and the given boundary conditions.
The design of cold-rolled steel products is defined in EN 1993-1-3. Typical cross-section shapes are channel, C, Z, top hat, and sigma sections. These are cold-rolled steel products made of thin-walled sheet metal that has been cold-formed by roll-forming or bending methods. When designing the ultimate limit states, it is also necessary to ensure that local transverse forces do not lead to compression, crippling of the web, or local buckling in the web of the sections. These effects can be caused by local transverse forces by the flange into the web, as well as by support forces at the supported points. Section 6.1.7 of EN 1993-1-3 specifies in detail how to determine the resistance of the web Rw,Rd under local transverse forces.
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).
When calculating the internal forces for the buckling analysis with the method based on nominal curvature in RF‑CONCRETE Columns, the required eccentricities have to be determined.
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 design of cross-sections according to Eurocode 3 is based on the classification of the cross-section to be designed in terms of classes determined by the standard. The classification of cross-sections is important, since it determines the limits of resistance and rotation capacity due to local buckling of cross-section parts.
The RF‑STABILITY and RSBUCK add‑on modules for RFEM and RSTAB allow you to perform eigenvalue analysis for frame structures in order to determine critical load factors, including the buckling modes. Several buckling modes can be determined. They provide information about the model areas bearing stability risks.
The RF‑/STEEL EC3 add-on module automatically transfers the buckling line to be used for the flexural buckling analysis for a cross-section from the cross-section properties. The assignment of the buckling line can be adjusted manually in the module input for general cross-sections in particular, as well as for special cases.
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.