1. Design of Steel Beams
Dr. Bashar Behnam

2. General
When a beam bends, the compression region above the neutral axis is analogous to a column and it will buckle if the member is slender enough.
The compression portion/region of the cross section is restrained by the tension portion.
The outer deflection (flexural buckling) is accompanied by twisting (torsion)

3. Lateral-Torsional Buckling
This form of instability is called lateral-torsional buckling (LTB).
Lateral-Torsional buckling can be prevented by bracing the beam against twisting at sufficiently close intervals. This can be accomplished two different types of stability bracing.

4. Stability Bracing There are two types of stability bracing
Lateral bracing:
X-bracing
Concrete deck
Torsional bracing:
Cross frame
Diaphragm

5. Lateral bracing
X-Bracing
Concrete Deck

6. Torsional bracing
Cross-Frame
Diaphragm

7. Failure Modes There are four failure modes
The cross section of the beam becomes fully plastic.
Lateral-torsional buckling (LTB), either elastically or inelastically.
Flange local buckling (FLB), either elastically or inelastically.
Web local buckling (WLB), either elastically or inelastically.

8. Classification of Shapes
AISC Manual (American institute of Steel Construction) classifies cross-sectional shapes as:
Compact
Noncompact
Slender

9. The unbraced length
The unbraced length Lb is the distance between points of lateral support, or bracing. The moment strength of compact shapes is function of the unbraced length, Lb.

10. Nominal Flexural Strength
If the unbraced length, no longer than Lp, the beam is considered to have full lateral support and the nominal flexural strength can be calculated

11. Nominal Flexural Strength
If Lb is greater than Lp but less than or equal to the parameter Lr, then the strength is based on inelastic LTB.

12. Nominal Flexural Strength
If Lb is greater than Lr, the strength is based on elastic LTB.