OpenSpecEngineering

Finds the bending strength of a compact steel beam that is braced against lateral-torsional buckling, by AISC 360-16 [1]. It gives the plastic moment, the LRFD design strength and the ASD allowable strength, and checks a required moment against them. Pick a W, M, S, HP, channel, rectangular HSS, round HSS or pipe section and the page fills its plastic section modulus from the AISC Shapes Database [3] and checks that the section is compact. Designers use it for a quick strength check of a floor or roof beam.

The strength equations

M_n = M_p = F_y·Z_x
LRFD: φ_bM_n, φ_b = 0.90
ASD: M_n/Ω_b, Ω_b = 1.67

M_n is the nominal flexural strength, M_p the plastic moment, F_y the specified minimum yield strength [4] and Z_x the plastic section modulus about the major axis. This is the yielding limit state of AISC F2.1 for I-shapes and channels, F7.1 for rectangular HSS and F8.1 for round HSS and pipe [1]. The demand-capacity ratio is the required moment divided by φ_bM_n, so the LRFD check passes when it is 1 or less.

For a listed shape, the page compares the width-to-thickness ratios with the compact limits of AISC Table B4.1b, where E = 200,000 MPa: 0.38√(E/F_y) for I-shape and channel flanges, 3.76√(E/F_y) for their webs, 1.12√(E/F_y) and 2.42√(E/F_y) for HSS flanges and webs, and 0.07E/F_y for round walls. HSS ratios use the design wall thickness t_des.

Limits and common mistakes

• The page assumes the compression flange is braced at spacings no longer than L_p and C_b = 1. A beam with long unbraced lengths fails by lateral-torsional buckling below M_p; check it with the AISC Manual [2].
• If a section is not compact, the page warns you: local buckling makes the true strength lower than shown.
• A channel reaches M_p only if the load passes through its shear center or the channel is braced against twisting.
• Tees and angles are not offered. AISC limits their strength below F_yZ_x (F9, F10) [1].
• Compare a factored moment (LRFD) with φ_bM_n and a service moment (ASD) with M_n/Ω_b. The pass/fail line uses LRFD.
• The check covers bending only. Check shear and deflection separately.

Worked example

A floor beam carries a factored moment of 250 kN·m, and the slab braces its top flange along its length. Check a W16×31 in A992 steel.

1. Choose Section Type W-Shape and Section W16×31 — Zx = 54 in³.
2. Choose Steel Grade ASTM A992 (wide-flange shapes) — Fy = 345 MPa.
3. Enter Required Moment 250 kN·m.
4. Press Solve. The Solution shows: Plastic moment Mp = Fy·Zx: 305.291 kN·m
   LRFD design strength φbMn: 274.762 kN·m
   ASD allowable strength Mn/Ωb: 182.809 kN·m
   Demand-capacity ratio: 0.909879
   Result (LRFD): OK
   Flange slenderness bf/2tf: 6.28409
   Compact flange limit λpf: 9.14932
   Web slenderness h/tw: 51.6
   Compact web limit λpw: 90.5302

Check: in US units, 54 in³ × 50 ksi = 2,700 kip·in = 225 kip·ft = 305.1 kN·m, which matches M_p within the rounding of 345 MPa for 50 ksi. 0.90 × 305.29 = 274.76 kN·m, and 250 / 274.76 = 0.91.