# D4.E.6.2 Members Subject to Bending

The laterally unsupported length of the compression flange for the purpose of computing the factored moment resistance is specified in STAAD.Pro through the UNT and UNB parameters (Refer to D4.E.7 Design Parameters). The LAT parameter is used to specify if the member is laterally supported against lateral torsional buckling.
1. The factored moment resistance, Mr, developed by a member subjected to uniaxial bending moments about a principal axis where effectively continuous lateral support is provided to the compression flange or where the member has no tendency to buckle laterally, is calculated as:
1. For Class 1 and Class 2 sections (Cl. 13.5(a) ):

Mr = ϕ·Z· Fy = ϕ·Mp

2. For Class 3 sections (Cl. 13.5(b) ):

Mr = ϕ·S· Fy = ϕ·My

3. For Class 4 sections (Cl. 13.5(c) ):

Mr = ϕ·Se· Fy

where
 Se = the effective section modulus determined using an effective flange width,be , of $670 t / F y$ for flanges along two edges parallel to the direction of stress and an effective flange width,be of $200 t / F y$ for flanges supported along one edge parallel to the direction of stress. For flange supported along one edge, beIe/t shall not exceed 60.
2. For laterally unsupported members, flexural resistance is calculated as follows:
1. For doubly symmetric Class 1 and Class 2 sections (Cl 13.6(a) ):
where
 Mu = $ω 2 π L E I y G J + ( π E L ) 2 I y C w$ ω2 = $1.75 + 1.05 κ + 0.3 κ 2 ≤ 2.5$ κ = ratio of 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: The value for ω2 can be specified using the CB parameter. Otherwise, it is calculated as indicated here.
2. For doubly symmetric Class 3 and Class 4 sections –except closed square and circular sections– and for channels:
but not greater than ϕMy for Class 3 sections and the value specified in Cl.13.5(c)(iii) for Class 4 sections.
3. For singly symmetric (monosymmetric) Class 1, Class 2, or Class 3 sections and T-shape sections, lateral torsional buckling strength shall be checked separately for each flange under compression under factored loads at any point along its unbraced length:
• when Mu > Myr :
$M r = ϕ [ M p − ( M p − M y r ) ( L − L u L y r − L u ) ] ≤ ϕ M p$
where Myr = 0.7SxFy , with Sx taken as the smaller of the two potential values Lyr = length L obtained by setting Mu = Myr Lu = $1.1 r t E / F y = 490 r t F y$ rt = $b c 12 ( 1 + h c w 3 b c t c )$ hc = depth of the web in compression bc = width of the compression flange tc = thickness of the compression flange
• when M ≤ Myr :
$M r = ϕ M u$
where Mu = the critical elastic moment of the unbraced section = $ω 3 π 2 E I y 2 L 2 [ β x + β x 2 + 4 ( G J L 2 π 2 E I y + C w I y ) ]$ βx = asymmetry parameter for singly symmetric beam = $0.9 ( d − t ) ( 2 I y c I y − 1 ) [ 1 − ( I y I x ) 2 ]$ Iyc = moment of inertia of the compression flange about the y-axis Iyt = moment of inertia of the tension flange about the y-axis

when singly symmetric beams are in single curvature,

• ω3 = ω2 for beams with two flanges, = 1.0 for T-sections

in all other cases,

• ω3 = ω2[0.5 + 2(Iyc/Iy)2] f, but ≤ 2.0 for T-Sections