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Introduction

This verification example studies a simple fork supported beam member with welded section (flanges: 200-12 and 100-12; web: 400-8) subjected to bending about major axis. Constant bending moment due to concentrated end moments and triangular moment distribution from concentrated transverse force is examined for both orientations of the I-section. Critical moment and force of the member is calculated by hand and by the Consteel software using both 7 DOF beam finite element model and Superbeam function.

Geometry

Normal orientation – wide flange in compression

Constant bending moment distribution

Triangular bending moment distribution – load on upper flange

Triangular bending moment distribution – load on bottom flange

Reverse orientation – narrow flange in compression

Constant bending moment distribution

Triangular bending moment distribution – load on upper flange

Triangular bending moment distribution – load on bottom flange

Calculation by hand

Factors to be used for analitical approximation formulae of elastic critical moment are taken from G. Sedlacek, J. Naumes: Excerpt from the Background Document to EN 1993-1-1 Flexural buckling and lateral buckling on a common basis: Stability assessments according to Eurocode 3 CEN / TC250 / SC3 / N1639E – rev2

Normal orientation – wide flange in compression

Constant bending moment distribution

Reverse orientation – narrow flange in compression

Computation by Consteel

Version nr: Consteel 15 build 1722

Normal orientation – wide flange in compression

Constant bending moment distribution

• 7 DOF beam element

First buckling eigenvalue of the member which was computed by the Consteel software using the 7 DOF beam finite element model (n=25). The eigenshape shows lateral torsional buckling.

Superbeam

First buckling eigenvalue of the member which was computed by the Consteel software using the Superbeam function (δ=25).

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Introduction

This verification example studies a simple fork supported beam member with welded section (flanges: 200-12; web: 400-8) subjected to bending about major axis. Constant bending moment due to concentrated end moments and triangular moment dsitribution from concentrated transverse force is examined. Critical moment and force of the member is calculated by hand and by the Consteel software using both 7 DOF beam finite element model and Superbeam function.

Geometry

Constant bending moment distribution

Triangular bending moment distribution – load on upper flange

Triangular bending moment distribution – load on bottom flange

Calculation by hand

Constant bending moment distribution

Triangular bending moment distribution

Computation by Consteel

Version nr: Consteel 15 build 1722

Constant bending moment distribution

7 DOF beam element

First buckling eigenvalue of the member which was computed by the Consteel software using the 7 DOF beam finite element model (n=16). The eigenshape shows lateral torsional buckling.

Superbeam

First buckling eigenvalue of the member which was computed by the Consteel software using the Superbeam function (δ=25).

Triangular bending moment distribution – load on upper flange

7 DOF beam element

First buckling eigenvalue of the member which was computed by the Consteel software using the 7 DOF beam finite element model (n=16).

Superbeam

First buckling eigenvalue of the member which was computed by the Consteel software using the Superbeam function (δ=25).

Triangular bending moment distribution – load on bottom flange

(more…)

Perfect the understanding of your structure with advanced buckling sensitivity results illustrated on proper mode shape and colored internal force diagrams.

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Contents

• Set analysis parameters
• Perform first and second order analysis
• Perform buckling analysis
• Analysis results in graphics and in tables
• Results: deformation, internal forces, reactions

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Part 2 – Imperfection factors

The Eurocode EN 1993-1-1 offers basically two methods for the buckling verification of members:

(1) based on buckling reduction factors (buckling curves) and

(2) based on equivalent geometrical imperfections.

In the first part of this article, we reviewed the utilization difference and showed the relationship between the two methods. It was concluded that the method of chapters 6.3.1 (reduction factor) and 5.3.2 (11) (buckling mode based equivalent imperfection) are consistent at the load level equal to the buckling resistance of the member, so when the member utilization is 100%. The basic result of the procedure in 5.3.2 (11) is the amplitude (largest deflection value) of the equivalent geometrical imperfection. However, the Eurocode gives another simpler alternative for the calculation of this amplitude for compressed members in section 5.3.2(3) b) in Table 5.1, where the amplitude of an initial bow is defined as a portion of the member length for each buckling curves (Fig. 1.). We use the first column (“elastic analysis”) including smaller amplitude values.

It is an obvious expectation that these two standard procedures should yield at least similar results for the same problem. However, this is by far not the case in general.

In order to show the significance of the imperfection amplitudes this part is dealing with these two calculation methods, the variation of their values and the effect on the buckling utilization.

Let’s see again the simple example of Part 1: a simply supported, compressed column with a Class 2 cross-section (plastic resistance calculation allowed). The column is 6 meters high and has an IPE300 cross-section made of S235 steel. The two methods are implemented into Consteel and on Figure 2. it can be seen, that the two values for the amplitude of the geometrical imperfection is very different – e₀ = 24 mm by the 5.3.2(3) b) Table 5.1 (L/250) and e₀ = 13,4 mm by the 5.3.2 (11) (same as in Part 1).

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Click the button bellow to download and read the full article at page 187-195.

In this paper a numerical study is presented which examines a steel frame with two different finite element programs. Stability failure is more frequent in a lot of cases than strength failure hence it is important to focus on these failure modes: global, in-plane-, out-of-plane -, lateral-torsional- and local buckling. Three models were used with different elements such as shell elements and 7 DOF beam elements. 7 DOF beam elements were used in the first model, shell elements were used in the other two. The first of the shell models gave too much local buckling shapes therefore it was improved with local constraints and that is the third model where global buckling shapes can be examined. There are three different procedures to calculate the resistance: (i) the general method, (ii) the method of the reduction factors, and (iii) the simulation. The analysis results of the different programs and design methods were compared to each other and to the manual calculation based on the Eurocode 3 standards.

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The new versions of the EN 1993-1-1 (EC3-1-1) and the EN 1993-1-5 (EC3-1-5) standards have introduced the general method designing beam-column structures; see [1] and [2]. The design method requires 3D geometric model and finite element analysis. In a series of papers we present this general design approach. The parts of the series are the following:

• Part 1: 3D model based analysis using general beam-column FEM

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The EN 1993 Part 1-1 (EC3-1-1) has introduced a new approach (called the “General Method”) to perform lateral-torsional buckling (LTB) assessment of beam-column structural components on the basis of elastic stability analysis. In the last years great research investigations went into the development of the method, see for instance [11,12] and also into the improvement of appropriate design software that is suitable to include the method and applicable for practical solutions [10]. The general objective of this paper is to review this issue from the point of view of the practice and contribute more effectively to understanding and resolving issues in the fields of practical application of the General Method. It is essentially significant to define the minimal analysis tools for the practice which are required for the accuracy of the method but on the other hand simple enough to make the modeling and calculation efficient. The paper briefly presents the theoretical background and the practical application of the elastic stability analysis of beam-columns that is necessary for the accurate evaluation of the General Method. The elastic stability analysis is verified by benchmark examples and also by shell finite element analysis. The application of the design method is demonstrated in the field of irregular structural members, especially web-tapered members and frames. The paper analyses the new theoretical results in the field of LTB of webtapered members that have led to prohibitive statements in some National Annex for EC3-1-1 concerning the segment method in the analysis of these members. It is shown that a comprehensive design method that is based on an appropriate segmented model and the General Method is efficient as well as reliable for conceptual design and with some restrictions also for detailed design.

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Stability analysis and design have always played a key role in the process of verification of steel structures. The possible analysis methods and design procedures have a long history with plentiful literature providing various proposals for the engineers. This paper concentrates on the use of different types of eigenvalue analysis as a simple and powerful tool for stability design. Nowadays almost all the engineering software products have some kind of eigenvalue analysis options so these tools are easily available for the practicing engineers providing them a deeper look on the structural behavior. Various types of application possibilities are reviewed and new methods are proposed supporting the most up-to-date standard procedures of different levels from the isolated member design to the partial or global structural stability design. The suitable theoretical (both mathematical and mechanical) background is developed and the numerical procedure is implemented. The technique is applicable for a wide range of structural types and stability problems making the automatic effective length calculation possible in general without the use of any iterative process or tabulated values for certain cases. An application example is presented showing the comprehensiveness of the methods, and special efficiency indicators are presented in order to supply information about the adequacy of the applied design method.

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