AISC 360-22 Beam Flexural Capacity — Verification Benchmark
Complete hand calculation of a W16x31 simply supported beam flexural capacity against the Steel Calculator WASM engine, matched to AISC 360-22 Chapter F.
PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.
Problem Statement
Member: W16x31, ASTM A992 (Fy = 50 ksi, Fu = 65 ksi) Span: 20 ft, simply supported with continuous lateral bracing (concrete slab provides full restraint to compression flange) Loading: Uniformly distributed: dead load wD = 0.50 kip/ft, live load wL = 1.50 kip/ft Objective: Determine the design flexural strength phi*Mn per AISC 360-22 and verify adequacy
Section Properties — W16x31 (from AISC Steel Construction Manual, Table 1-1)
| Property | Value | Property | Value |
|---|---|---|---|
| d | 15.9 in | Zx | 54.0 in^3 |
| bf | 5.53 in | Sx | 47.2 in^3 |
| tw | 0.275 in | Ix | 375 in^4 |
| tf | 0.440 in | ry | 1.17 in |
| kdes | 0.827 in | h/tw | 51.6 |
| T | 13.5 in | bf/2tf | 6.28 |
| A | 9.12 in^2 | rts | 1.49 in |
Hand Calculation — AISC 360-22, Chapter F
Step 1: Required Flexural Strength
Per ASCE 7-22 load combination LC-2 (1.2D + 1.6L):
wu = 1.2(0.50) + 1.6(1.50) = 0.60 + 2.40 = 3.00 kip/ft
Mu = wu * L^2 / 8 = 3.00 * (20)^2 / 8 = 150.0 ft-kips
Step 2: Compactness Check — AISC 360-22 Table B4.1b
Flange (unstiffened element, Case 1):
lambda_f = bf / (2 * tf) = 5.53 / (2 * 0.440) = 6.28
lambda_pf = 0.38 * sqrt(E / Fy) = 0.38 * sqrt(29,000 / 50)
= 0.38 * 24.08 = 9.15
lambda_f = 6.28 < lambda_pf = 9.15 âÃÂàFlange is COMPACT
Web (stiffened element, Case 5):
lambda_w = h / tw = 51.6
lambda_pw = 3.76 * sqrt(E / Fy) = 3.76 * sqrt(29,000 / 50)
= 3.76 * 24.08 = 90.55
lambda_w = 51.6 < lambda_pw = 90.55 âÃÂàWeb is COMPACT
Section qualifies as compact for flexure. No reduction for flange or web local buckling.
Step 3: Plastic Moment Capacity
Mp = Fy * Zx = 50 ksi * 54.0 in^3 = 2,700 in-kips
Mp = 2,700 / 12 = 225.0 ft-kips
Step 4: Lateral-Torsional Buckling — AISC 360-22 F2.2
With continuous lateral bracing (slab), the unbraced length Lb = 0 (bracing at every point). Per Section F2.2, when Lb <= Lp:
Lp = 1.76 * ry * sqrt(E / Fy) = 1.76 * 1.17 * sqrt(29,000 / 50)
= 1.76 * 1.17 * 24.08 = 49.6 in = 4.13 ft
Lb = 0 ft < Lp = 4.13 ft âÃÂàLTB does not govern
Mn = Mp = 225.0 ft-kips
Note: For beams without continuous bracing, LTB reduction would apply. The WASM engine handles all three LTB zones (Lb <= Lp plastic, Lp < Lb <= Lr inelastic, Lb > Lr elastic) per Section F2.2 Equations F2-1 through F2-3.
Step 5: Design Flexural Strength
phi_b * Mn = 0.90 * 225.0 = 202.5 ft-kips
Check: phi*Mn = 202.5 ft-kips >= Mu = 150.0 ft-kips âÃÂàUtilization ratio: 150.0 / 202.5 = 0.741
The W16x31 is adequate for flexure at 74.1% utilization.
WASM Output Comparison
The Steel Calculator WASM engine, run with identical inputs, produced:
| Quantity | Hand Calculation | WASM Output | Difference |
|---|---|---|---|
| lambda_f | 6.28 | 6.28 | 0.00% |
| lambda_w | 51.6 | 51.60 | 0.00% |
| Flange status | COMPACT | COMPACT | Match |
| Web status | COMPACT | COMPACT | Match |
| Lp (ft) | 4.13 | 4.12 | 0.24% |
| Mp (ft-kips) | 225.0 | 225.00 | 0.00% |
| Mn (ft-kips) | 225.0 | 225.00 | 0.00% |
| phi*Mn (ft-kips) | 202.5 | 202.50 | 0.00% |
| Mu (ft-kips) | 150.0 | 150.00 | 0.00% |
| DCR (utilization) | 0.741 | 0.741 | 0.00% |
| Verdict | PASS | PASS | Match |
All 11 quantities match within 0.24%. The 0.24% difference in Lp is a rounding artefact (1.761.1724.083 = 49.556 in / 12 = 4.13 ft by hand vs 4.12 ft from double-precision float arithmetic).
Code References — AISC 360-22
| Section | Title | Application |
|---|---|---|
| B4.1b | Width-to-Thickness Ratios | Flange and web compactness limits |
| F1 | General Provisions — Flexure | Scope and member requirements |
| F2.1 | Yielding | Plastic moment Mn = Mp = Fy*Zx |
| F2.2 | Lateral-Torsional Buckling | Lp, Lr, Cb, three-zone Mn curve |
| F2.3 | Flange Local Buckling | lambda_rf limit for noncompact flanges |
| F2.4 | Web Local Buckling | Not applicable (compact web) |
| E1 | Cross-Section Properties | Zx, Sx, ry, rts, J, Cw lookup |
How to Reproduce
- Navigate to the Steel Calculator Beam Capacity tool
- Select AISC 360-22 as the design code
- Enter: W16x31, A992, L=20ft, continuous lateral bracing
- Enter: wD=0.50 kip/ft, wL=1.50 kip/ft
- Click Calculate — the WASM engine produces the output shown above
The same WASM engine also produces full step-by-step trace output showing every intermediate value, matching the hand calculation shown on this page.
Why Verification Matters
Structural engineering software must produce correct results. Every calculation engine powering Steel Calculator is verified against published textbook examples, AISC Design Examples (AISC Design Guide series), and independent hand calculations before release. These verification pages serve as public, reproducible evidence of accuracy.
Each engine covers:
- AISC 360-22 — US practice (LRFD and ASD)
- EN 1993-1-1 — European practice
- AS 4100:2020 — Australian practice
- CSA S16:24 — Canadian practice
See also: EN 1993 Column Verification, AS 4100 Bolt Verification, CSA Weld Verification, AISC Base Plate Verification.
Last verified: 2026-05-08. WASM version: core-wasm-v2 stage-4-member-design. Tolerance standard: all quantities within 1.0% of hand calculation or textbook published value.