Did you know that you could use Consteel to perform local and distortional buckling checks for cold-formed members?

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This paper discusses a combination of best practices and procedures from recent work in Europe and the US, providing rational and economical calculations addressing the complexities associated with frame design using nonprismatic members. Recommendations are provided in the context of US design practice. A primary objective is to achieve maximum simplicity, transparency, and design speed while facilitating rigor of the underlying calculations. The paper provides several focused examples illustrating the recommended design verification procedures.

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The practical use of the ‘General method’ of EN 1993-1-1 6.3.4 for the buckling design of global structural models is still a challenging issue requiring several problems to solve. In this paper we propose a fully developed methodology presenting solutions for the application topics such as the suitable FE model, specific modeling issues to capture the true 3D behavior of the members and the whole model and the final evaluation of the design parameters. The presented methodology consistently uses a unique model for the evaluation of all analysis and design parameters and results and yields a fully automatic design process controlled solely by the properly created structural model.

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Warehouse building example for Overall Imperfection Method in Consteel

Watch our user guide about How to use the Overall Imperfection Method to learn more.

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Overall Imperfection Method in Consteel

The Overall Imperfection Method is an alternative way to carry out the buckling design for a structural member. With this method the buckling phenomenon is considered on the effect side of the equation, instead of on the resistance side, compared to the general method and the member check method. In the following video we explain the theoretical background for this calculation. After that we present application examples starting with the simplest ones, all the way to the most general case in a real-world building structure, showcasing the several extra capabilities and advantages of the Overall Imperfection Method.

Check out our user guide to learn more!

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Consteel 14 is a powerful analysis and design software for structural engineers. Watch our video how to get started with Consteel.

Contents

• Set design parameters
• Perform cross section check
• Examine the design results in the Section Module
• Stability design according to the general method
• Member check – stability design for members
• Serviceability check

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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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Introduction

There are different ways to evaluate the stability of a structure. It is important to know the differences between those methods and the limits of applicability but it is also important to recognize the equalities in pure cases.

Methods of stability design

In Eurocode 1993-1-1, and so in Consteel, there are 3 methods to verify the stability of a model:

• Imperfection approach (described in Section 5.2 and 5.3)

The structural model is subjected to appropriate geometrical imperfections and after completing a second order analysis, only the cross section resistances need to be checked

• Isolated member approach ( described in section 6.3.1, 6.3.2 and 6.3.3)

       The method is based on two essential simplifications:

1. Structural member isolation: The relevant member is isolated from the global structural model by applying special boundary conditions (supports, restraints or loads) at the connection points which are taken into account in the calculation of the buckling resistance
2. Buckling mode separation: The buckling of the member is calculated separately for the pure modes: flexural buckling for pure compression and lateral-torsional buckling for pure bending. The two effects are connected by applying special interaction factors.

• General method (described in section 6.3.4)

The basic idea behind the general method is that it no longer isolates members and separates the pure buckling modes, but considers the complex system of forces in the member and evaluates the appropriate compound buckling modes. The method offers the possibility to provide solutions where the isolated member approach is not entirely appropriate:

-The general method is applicable not only for single, isolated members, but also for sub frames or complete structural models where the governing buckling mode involves the complete frame.

-The general method can examine irregular structural members such as tapered members, haunched members, and built up members.

-The general method is applicable for any irregular load and support system where separation into the pure buckling modes is not possible.

Implementation of different approaches in Consteel

Isolated member approach is basically the reduction factor method and it can be performed in Member checks function in Consteel where it is possible to define the design parameters (e.g. effective length) by hand.

In Global checksfunction, cross-section and global buckling checks can be executed automatically according to the General method which does not require the direct introduction of effective lengths and other parameters depending on the distribution and combination of stresses along the member.

However, in pure cases (pure compression, or pure bending), buckling length calculated from general method can be equated with isolated member approach. In the following, a “how to” example will be shown on a pure compression column:

How can I get the buckling length of a certain member?

Both the Isolated member approach and the General method require to calculate the slenderness value of the member. In case of the first method this is done through the use of buckling lengths. By using the General Method, the slenderness is calculated as the ratio of two amplifiying factors.

For the calculation of the equivalent buckling length we will need the first amplifier only, called critical elastic factor or alpha critical factor, obtained through a numerical analysis called linear buckling analysis.

Determination of alpha critical factor with buckling analysis:

Alpha critical factor: Minimum amplifier for the design loads to reach the elastic critical resistance of the structural component with regards to lateral buckling.

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After introducing the Eurocode standards several theses have been published on the now much-discussed phenomenon of lateral-torsional buckling of steel structural elements under pure bending. According to that, researchers are working on the development of such new design methods which can solve the problems of the design formulae given by the EN 1993-1-1. This paper gives a detailed review of the proposals for novel hand calculation procedures for the prediction of LT buckling resistance of beams. Nowadays, the application of structural design softwares in practical engineering becomes more common and widespread. Recognizing this growing interest, the main objective of our research work is the development of a novel, computer-aided design method. In this paper, the details of a general type stability design procedure for the determination of the LT buckling resistance of members under pure bending are introduced. Here, the theoretical basis of the proposed method is clarified, the calculation procedure is detailed and some results for the evaluation of the appropriateness of the method are also presented. Based on the evaluations it can be stated that the new, general type design method is properly accurate and has several advantages on the stability check of beams under bending

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In the second article of this series, Dr József Szalai of ConSteel Solutions demonstrates practical examples where the “General Method” of EN 1993-1-1 shows advantages compared to the conventional approaches.

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