This document discusses the bending coefficient Cb, which accounts for the effect of different moment gradients on lateral-torsional buckling. Cb is equal to 1.0 for a uniform moment diagram, representing the worst case for compression flange buckling. The document provides an equation to calculate Cb based on the maximum moment and moments at quarter, half, and three-quarter points of an unbraced beam segment. It also lists some typical Cb values for different support conditions and load types. Finally, it addresses beam shear strength, noting the shear resistance factor and requirement that factored shear strength exceeds factored shear load.

1. 1 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Where, M max : is the largest moment in an unbraced segment
MA, MB & MC: are the moments at the 1/4, 1/2 & 3/4 point in the
segment, respectively.
Bending Coefficient (Cb)
Cb is a moment coefficient to account for the effect of different
moment gradients on lateral - torsional buckling
Cb = 1.0 for a uniform moment diagram
Which represent the worst case
of compression flange buckling,
resulting in the least beam moment resistance
In general, Cb = 12.5 M max
2.5 M max + 3 M A + 4 MB + 3 MC
+
M M
MA
MB = Mmax
MC
Lb = L
1/4 Lb 1/4 Lb 1/4 Lb 1/4 Lb
Compression flang is laterally
supported at ends only , Cb = 1.14
Lb = L/2 Lb = L/2
1/4 Lb 1/4 Lb 1/4 Lb 1/4 Lb
MA
Mmax
MB
MC
Compression flang is laterally
supported at mid span , Cb = 1.30

2. 2 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Some typical values of Cb for different type of loading and different points of
laterally supported compression flange

3. 3 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Beam shear strength
Shear resistance factor ( f v) = 0.90
LRFD strength requirement : f v Vn ≥ Vu
Area of web, Aw = d tw