W-Shape Beam Flexure Check
Evaluate the nominal and design flexural strength (Mn and φMn) of a W-shape steel beam. Determines whether the limit state of yielding, lateral-torsional buckling, or flange local buckling governs. Computes the demand-to-capacity ratio (DCR) against the factored moment demand Mu. Handles compact, non-compact, and slender flange sections with the appropriate AISC 360-22 Chapter F equations.
What this calculates
Plastic moment (Mp), nominal flexural strength (Mn) for the governing limit state, design strength (φMn with φb = 0.90), and the demand-to-capacity ratio (DCR = Mu/φMn). Also reports Lp and Lr unbraced length limits and the Cb moment gradient factor.
Inputs
Maximum factored bending moment demand from load combinations
Minimum yield stress of the steel (typically 50 ksi for A992)
Modulus of elasticity (29000 ksi for structural steel)
Plastic section modulus about the major axis
Elastic section modulus about the major axis
Distance between points of lateral bracing
Lateral-torsional buckling modification factor (1.0 for uniform moment)
Limiting laterally unbraced length for yielding
Limiting laterally unbraced length for inelastic LTB
Outputs
Full plastic moment capacity Fy·Zx
Nominal strength for governing limit state
Design strength with φb = 0.90
Mu / φMn — must be ≤ 1.0
Methodology
For compact W-shapes, yielding strength Mp = Fy·Zx per AISC 360-22 Section F2.1. Lateral-torsional buckling capacity depends on unbraced length Lb relative to Lp and Lr per Equations F2-2 through F2-4. The moment gradient factor Cb amplifies the LTB capacity for non-uniform moment diagrams. Flange local buckling is checked per Section F3 if the flange is non-compact. The resistance factor φb = 0.90 is applied to Mn to obtain the design strength φMn.
Code References
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