اختبارات التربة

 

INTRODUCTION:

Columns in a steel building are often subjected to bending moments in addition to axial compressive forces. Even when beams are connected to the column through simple connections, such as framing angles shown in Fig 7.1, they exert bending moment on the column duet eccentrically applied support reactions. Columns in moment-resisting frames, of course, are subjected to considerable bending. Members acted on simultaneously by compressive axial forces and bending moments are referred to as when a beam-column is subjected to in plane bending (figure 1a), its behavior shows an interaction between beam bending and compression member buckling, as indicated in figure 1b...

 

 The methods of mathematical solutions, of the typical behavior of beam-column elements

1. The secant formula method

 This is based on rationally developed analytical expressions by assuming that initiation of yielding caused by the applied loads and including the effect of an assumed initial crookedness or an initial accident end eccentricity will terminate the usefulness of the member. Historical this is the earliest approach

2. Interaction Equation

Which are empirically determined and experimentally tested? They relate the interaction between the axial force, bending moments, and member geometry at the limiting working stress by means of simple algebraic expressions this approach is by far the most popular in steel building specification because of its simplicity and versatility

3. Maximum strength Interaction curves

Which are theoretically developed and have been used as the basis of the plastic design concept all the three design philosophies are based on the maximum strength criterion regardless of the use of the formulas in either allowable stress or plastic design?

General description of the general method

The concept of a comprehensive, general approach (Overall concept) to check the stability of steel  structures was proposed by Rotter  in 2002, and introduced to EN 1993-1-6 [3]. A similar idea, regarding the reduced stress method used to determine the stress limits for plates, was applied in the

PN-EN 1993-1-5 [4].  Further development of this method, especially its variety called the general method [5], [6], led to

Its introduction to the new edition of the standard [1]. Description of this method and an extensive Comparative analysis with the interaction formulae were carried out in [7]. Further research to Verify safety level of the general method was carried out at the University of Coimbra [8], [9].  The general method uses a Merchant-Rankine type of empirical interaction expression to uncouple

The in-plane effects and the out-of-plane effects [10]

Procedures of the general method

 

Practical determination of the parameters needed to verify the stability of the element by general

Method can be done in two ways:

- Analytically, with the use of the general conditions of resistance/ stability, 

- With the use of the Finite Elements Method.

In the analytical determination of the minimum multiplier α

Lutsk , the following cases should be taken  Into account

LATERAL-TORSIONAL BUCKLING.

Considering the lateral-torsional behavior of an unrestrained I section beam-column bent about its Major axis it can be assumed the elastic behavior and the arrangement of applied loading and support Conditions given in figure 12.

Figure 12 – Basic case for lateral-torsional buckling. The critical combinations of N and M may be obtained from the solution of (Chen & Atsuta, 1976)

Eq. (15) reduces to the buckling of a beam when N→0 and to the buckling of a column in either flexure (PEz) or torsion (PE0) as M → 0. In the first case the critical value of M will be given by In deriving Eq. (15) no allowance was made for the amplification of the in-plane moments M by the axial load acting through the in-plane deflections

Reference:

1. Lectures of Design of steel structures by: Dr. Eng. Medhat.M. Momtaz

2. Egyptian Code of Practice LRFD, 2005

3 .Steel Structures, design & Behavior, Charles G. Salmon & John E. Johnson, Fifth Edition, 2009..

4. WWWEB Enhanced Teaching of Structural Steel Design, AISC.

5. Euro code 3: Design of steel structures - Part 1-1: General rules and rules for buildings.

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6. Euro code 3: Design of steel structures - Part 1-6: Strength and stability of shell structures

7.BS EN 1993-6: 2007 Euro code 3 Design of steel structures – Part 6: Crane supporting structures

8. BS EN 1993-1-9:2005 Euro code 3 Design of steel structures – Part 1-9 Fatigue