D8.A.2.6 Bending
The design bending moment capacity of a section is primarily dependent on whether the member is laterally supported or unsupported.
You can control the lateral support condition of the member by the use of LAT parameter.
If the member is laterally supported, then the design strength is calculated as per the provisions of the section 8.2.1 of IS 800:2007, based on the following factors:
 Whether section with webs susceptible to shear buckling before yielding
 Ratio of shear force to design shear strength
 Section classification
If the member is laterally unsupported, then the design strength is calculated as per the provisions of the section 8.2.2 of IS 800:2007, based on the following factors:
 Lateral Torsional Buckling
 Section Classification
Working Stress Design
Actual bending stress values are given by, about major (Z) and minor (Y) axes, respectively:
f_{bcz} = M_{z}/Z_{ecz} 
f_{btz} = M_{z}/Z_{etz} 
f_{bcy} = M_{y}/Z_{ecy} 
f_{bty} = M_{y}/Z_{ety} 
The permissible bending stress is given as follows:

For laterally supported beams:
 F_{abc} = F_{abt} = 0.66·F_{y} for Plastic or Compact sections
 F_{abc} = F_{abt} = 0.60·F_{y} for Semicompact sections
 F_{y}
=  Yield strength of steel, indicated by the FYLD parameter.

For laterally unsupported beams:

About the major axis:
f_{abcz} = 0.60·M_{d}/Z_{ecz}
f_{abtz} = 0.60·M_{d}/Z_{etz}
where M_{d}
=  Design Bending Strength as per Clause 8.2.2
= β_{b} · Z_{pz} · f_{bd}
 f_{bd}
=  χ_{LT} · F_{y} / γ_{mo}
 Z_{ez}
=  Elastic Section Modulus of the Section
 Z_{pz}
=  Plastic Section Modulus of the Section
 α_{LT}
=  0.21 for Rolled Steel Section and 0.49 for Welded Steel Section
 β_{b}
=  1.0 for Plastic and Compact Section or Z_{ez}/Z_{pz} for SemiCompact Section
 λ_{LT}
=  Nondimensional slenderness ratio
 λ_{LT}
=  (β_{b} · Z_{pz} · F_{y} / M_{cr})^{1/2} ≤ (1.2 · Z_{ez} · F_{y} / M_{cr} )^{1/2}
 ϕ_{LT}
=  0.5 · ( 1 + α_{LT} · ( λ_{LT} – 0.2 ) + λ_{LT} ^{2})
 χ_{LT}
=  The Bending Stress Reduction Factor to account for Lateral Torsional Buckling
 χ_{LTZ}
=  $\frac{1}{{\varphi}_{LTZ}+\sqrt{{\varphi}_{LTZ}^{2}{\lambda}_{LTZ}^{2}}}$
 Z_{ecz}
=  Elastic Section Modulus of the section about Major Axis for the compression side
 Z_{etz}
=  Elastic Section Modulus of the section about Major Axis for the tension side
 M_{cr}
=  ${M}_{cr}=\sqrt{\frac{{\pi}^{2}E{I}_{y}}{{L}_{LT}^{2}}(G{I}_{t}+\frac{{\pi}^{2}E{I}_{w}}{{L}_{LT}^{2}})}$
 I_{y}
=  Moment of inertia about the minor axis
 L_{LT}
=  Effective length for lateral torsional buckling as determined using either the KX or LX parameters
 I_{t}
=  Torsional constant of the section
 I_{t}
=  Warping constant of the section
 G
=  Shear modulus of the material

About the minor axis, the permissible bending stress is calculated as for a laterally supported section.

Slender Sections
For member with slender section subjected to bending, moment is taken by flanges alone. Design bending strength should be calculated with effective elastic modulus disregarding the contribution of web of the section.
Z_{ez} = 2·[B_{f} · t_{f} ^{3}/12 + (B_{f} · t_{f}) · (D/2  t_{f}/2)^{2} )] ⁄ (0.5 · D) 
Z_{ey} = 2·(B_{f} · t_{f} ^{3}/12) ⁄ (0.5 · B_{f}) 
Where:
where=  
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The Moment Capacity will be M_{d} = Z_{e}· f_{y}/γ_{m0} for "Laterally Supported" condition.
The Moment Capacity will be M_{d} = Z_{e}· f_{bd}/γ_{m0} for "Laterally UnSupported" condition.
Where, f_{bd} is defined in clause 8.2.2 of IS:8002007 (described in previous Working Stress Design section).