Laterally Unrestrained Beam
Dr. A Aziz Saim 2010 EC3
Unrestrained Beam
1
Nondimensional slenderness
Beam behaviour analogous to yielding/buckling of columns.
M Wyfy
Material yielding (inplane bending)
MEd
MEd
Elastic member buckling Mcr
Lcr
1.0
Dr. A Aziz Saim 2010 EC3
Nondimensional 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 inplane 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
Crosssection check (Inplane 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 31 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
Outof 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 34.
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 Crosssectional 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,...