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.
- 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:
-
For Class 1 and Class 2 sections (Cl. 13.5(a) ):
Mr = ϕ·Z· Fy = ϕ·Mp
-
For Class 3 sections (Cl. 13.5(b) ):
Mr = ϕ·S· Fy = ϕ·My
-
For Class 4 sections (Cl. 13.5(c) ):
Mr = ϕ·Se· Fy
- Se
= - the effective section modulus determined using an effective flange width,be , of for flanges along two edges parallel to the direction of stress and an effective flange width,be of for flanges supported along one edge parallel to the direction of stress. For flange supported along one edge, beIe/t shall not exceed 60.
-
- For laterally unsupported
members, flexural resistance is calculated as follows:
- For doubly symmetric Class 1 and Class
2 sections (Cl 13.6(a) ):
where
- Mu
= - ω2
= - 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).
- 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.
- 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
:
where
- Myr
= - 0.7SxFy , with Sx taken as the smaller of the two potential values
- Lyr
= - length L obtained by setting Mu = Myr
- Lu
= - rt
= - hc
= - depth of the web in compression
- bc
= - width of the compression flange
- tc
= - thickness of the compression flange
-
when M ≤ Myr : where
- Mu
= - the critical elastic moment of the unbraced section =
- βx
= - asymmetry parameter for singly symmetric beam = For CSA S16-19, the approximate formula given is only valid for cases where Ix > 2Iy and where 0.1 < Iy/(Iyc + Iyt) < 0.9 and it is not valid for T sections.
- 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
- when Mu >
Myr
:
where
- For doubly symmetric Class 1 and Class
2 sections (Cl 13.6(a) ):
where