# D14.C.6.6 Bending

The laterally unsupported length of the compression flange for the purpose of computing the factored moment resistance is specified using the parameters UNB and UNT.

## Laterally Supported Members

Per section 13.5, the factored moment resistance, Mr , developed by a member subjected to uniaxial bending moments about a principal axis and where continuous lateral support is provided to the compressive flange shall be taken as:

1. For class 1 and class 2 sections:

Mr = ϕZplfy = ϕMp

2. For class 3 sections:

Mr = ϕZefy = ϕMy

## Laterally Unsupported Members

Per section 13.6, where continuous lateral support is not provided to the compression flange of a member subjected to uniaxial strong axis bending, the factored moment resistance, Mr , may be taken as follows:

1. For doubly symmetric class 1 and class 2 sections, except closed square and circular sections:

1. When Mcr > 0.67Mp ,

$M r = 1.15 ϕ M p ( 1 − 0.28 M p M c r )$

but not greater than ϕMp .

2. When Mcr ≤ 0.67Mp ,

Mr = ϕMcr

where
 Mcr = = the critical elastic moment of the unbraced member, $= ω 2 π K L E I y G J + ( π E K L ) 2 I y C w$ KL = = the effective length of the unbraced portion of the beam, in mm. ω2 = = 1.75 + 1.05κ + 0.3κ2 ≤ 2.5 for unbraced lengths subjected to end moments, or = 1.0 when the bending moment at any point within the unbraced length is larger than the end moment or when the re is no effective lateral support for the compression flange at one of the ends of the unsupported length. Note: The value for ω2 can be specified using the CB parameter. Otherwise, it is calculated as indicated here. κ = = the ratio of the smaller factored moment to the larger factored moment at opposite ends of the unbraced length, positive for double curvature and negative for single curvature. Cw = = the ratio of the smaller factored moment to the larger factored moment at opposite ends of the unbraced length, positive for double curvature and negative for single curvature.
Note: Alternatively, E may be specified directly.
2. For doubly symmetric class 3 sections, except closed square and circular sections, and for channels:

1. When Mcr > 0.67Mp ,

$M r = 1.15 ϕ M y ( 1 − 0.28 M y M c r )$

but not greater than ϕMy for class 3 sections and the value given in 13.5(c)(iii) for class 4 sections.

2. When Mcr ≤ 0.67My ,

Mr = ϕMcr

where Mcr and ω2 are as defined in 13.6(a).

3. For closed sections and circular sections, Mcr shall be determined in accordance with section 13.5.

4. For biaxial bending, the member shall meet the following criterion:

$M u x M r x + M u y M r y ≤ 1.0$
5. For monosymmetric sections, a rational method of analysis should be used.

Note: STAAD.Pro uses AISC LRFD guidelines for the design of channels, double angles, tees, and single angle sections.
1. For tees and double angles:

$= π E I y G J L b ( B + 1 + B 2 )$ (AISC LRFD equation F1-15)

where
 B = $− 2.3 ( d / UNL ) I y / J$ minus sign considered for conservative side
2. For channel sections:

When Mcr ≤ 0.67My :

$M r = 1.15 ϕ M y [ 1 − 0.28 M y M c r ] ≤ 0.9 M y$

When Mcr > 0.67My

Mr = 0.9Mcr

3. For angle sections:

When Mob ≤ My :

$M n = M o b [ 0.92 − 0.17 M o b M y ]$

When Mob > My

$M n = M y [ 1.92 − 1.17 M y M o b ] ≤ 1.5 M y$
where
 Mob = $= 4.9 E I z l 2 CB [ β w 2 + 0.052 ( l t / r z ) 2 + β w ]$ for unequal leg angles.Note: βw is conservatively assumed as zero. $= CB 0.46 E b 2 t 2 l$ for equal leg angles. Iz = minor principal axis moment of inertia rz = radius of gyration for minor principal axis βw = 0 (conservative assumption) CB = The design parameter corresponding to ω2 . b = width of the angle leg t = thickness of the angle