Steel Design

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  • Topic: Buckling, Second moment of area, Beam
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STEEL BEAM DESIGN
Laterally Unrestrained Beam

Dr. A Aziz Saim 2010 EC3

Unrestrained Beam

1

Non-dimensional slenderness
Beam behaviour analogous to yielding/buckling of columns.

M Wyfy

Material yielding (in-plane bending)

MEd

MEd

Elastic member buckling Mcr

Lcr

1.0
Dr. A Aziz Saim 2010 EC3

Non-dimensional slenderness
Unrestrained Beam

 LT
2

Lateral torsional buckling
Lateral torsional buckling
Lateral torsional buckling is the member buckling mode associated with slender beams loaded about their major axis, without continuous lateral restraint. If continuous lateral restraint is provided to the beam, then lateral torsional buckling will be prevented and failure will occur in another mode, generally in-plane bending (and/or shear). Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 3

Eurocode 3
Eurocode 3 states, as with BS 5950, that both crosssectional and member bending resistance must be verified:

MEd  Mc ,Rd

Cross-section check (In-plane bending)

MEd  Mb,Rd
Dr. A Aziz Saim 2010 EC3 Unrestrained Beam

Member buckling check

4

Dr. A Aziz Saim 2010 EC3

Unrestrained Beam

5

Laterally Unrestrained Beam
The design of beam in this Lecture 3 is considering beams in which either no lateral restraint or only intermittent lateral restraint is provided to the compression flange

Dr. A Aziz Saim 2010 EC3

Unrestrained Beam

6

Lateral Torsional Buckling

Dr. A Aziz Saim 2010 EC3

Unrestrained Beam

7

Lateral Torsional Buckling
Figure 3-1 shows an unrestrained beam subjected to load increment. The compression flange unrestrained and beam is not stiff enough. There is a tendency for the beam to deform sideways and twist about the longitudinal axis. The failure mode which may occur to the beam is called lateral torsional buckling.

Dr. A Aziz Saim 2010 EC3

Unrestrained Beam

8

Involves both deflection and twisting rotation

Out-of plane buckling.
Bending Resistance M c, Rd  M pl 
W pl f y

M0

Due to the effect of LTB, the bending resistance of cross section become less. Failure may occurs earlier then expected

Dr. A Aziz Saim 2010 EC3

Unrestrained Beam

9

Examples of Laterally Unrestrained Beam

Dr. A Aziz Saim 2010 EC3

Unrestrained Beam

10

Restrained Beam
Comparsion

Dr. A Aziz Saim 2010 EC3

Unrestrained Beam

11

Intermittent Lateral Restrained

Dr. A Aziz Saim 2010 EC3

Unrestrained Beam

12

Torsional restraint Usually both flanges are held in their relative positions by external members during bending. May be provided by load bearing stiffeners or provision of adequate end connection details. See Figure 3-4.

Dr. A Aziz Saim 2010 EC3

Unrestrained Beam

13

Beam without torsional restraint

Dr. A Aziz Saim 2010 EC3

Unrestrained Beam

14

Can be discounted when:

• Minor axis bending
• CHS, SHS, circular or square bar • Fully laterally restrained beams

•  LT< 0.2 (or 0.4 in some cases)

-

Unrestrained length Cross-sectional shape End restrained condition The moment along the beam Loading – tension or compression Unrestrained Beam 16

Dr. A Aziz Saim 2010 EC3

Lateral torsional buckling resistance
Checks should be carried out on all unrestrained segments of beams (between the points where lateral restraint exists).

Lateral restraint

Lateral restraint Lcr = 1.0 L

Lateral restraint

Beam on plan
Dr. A Aziz Saim 2010 EC3 Unrestrained Beam 17

Three methods to check LTB in EC3:
• The primary method adopts the lateral torsional

buckling curves given by equations 6.56 and 6.57, and is set out in clause 6.3.2.2 (general case) and clause 6.3.2.3 (for rolled sections and equivalent welded sections). • The second is a simplified assessment method for beams with restraints in buildings, and is set out in clause 6.3.2.4. • The third is a general method for lateral and lateral torsional buckling of structural components,...
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