# 3.7 The modification factor, cb

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#### Introduction to cb

${C}_{b}$ is a modification factor used in the equation for nominal flexural strength when determining Lateral-Torsional Buckling . The reason for this factor is to allow for non-uniform moment diagrams whenthe ends of a beam segment are braced. The conservative value for ${C}_{b}$ can be taken as 1.0 as according to Chapter F2a of the Specification Section of the Manual (page 16.1-32) for all cases. Also, the Manual gives a table of values for ${C}_{b}$ for some loading conditions of simply supported beams. This is located in Section 5 of the Manual (page 5-35) and is named, Table 5-1.

#### Equation for cb

If the value of ${C}_{b}$ is not given in Table 5-1, the equation in Chapter F2a of the Specification Section of the Manual (page 16.1-32), given here, can be used to find ${C}_{b}$ .

${C}_{b}=\frac{12.5{M}_{max}}{2.5{M}_{max}+3{M}_{A}+4{M}_{B}+3{M}_{C}}$

#### Where:

• ${M}_{max}$ = absolute value of maximum moment in the unbraced segment, kip-in.
• ${M}_{A}$ = absolute value of maximum moment at quarter point of the unbraced segment, kip-in.
• ${M}_{B}$ = absolute value of maximum moment at centerline of the unbraced segment, kip-in.
• ${M}_{C}$ = absolute value of maximum moment at three-quarter point of the unbraced segment, kip-in.

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