LRFD and ASD, both
Switch design format without switching skill. Both LRFD combinations are always evaluated, and the governing one is named.
AISC 360-22ASCE 7-22
Design a single-span steel beam to AISC 360-22
Describe the span, section, steel grade, loads and lateral restraints, and pick LRFD or ASD. Mia checks flexure, shear, lateral-torsional buckling and deflection, and names the governing check.
Worked exampleDesign verified: lateral-torsional buckling governs
W 16x40 · 20.0 ft · D 0.6 + L 0.4 kip/ft · LRFD
Key results
- Required moment Mu
- 68.0 kip-ft
- Design flexural strength phi_b Mn
- 94.7 kip-ft (F2-3, Cb = 1.136)
- Required shear Vu
- 13.6 kip of phi_v Vn = 146.4 kip
- Live-load deflection
- 0.096 in <= 0.667 in (l/360)
Transparent stepsStandards-basedDocument as PDF
Worked example
W 16x40 · 20.0 ft · D 0.6 + L 0.4 kip/ft · LRFD
- System
- Simply supported beam
- Section
- W 16x40 · A992 (Fy = 50 ksi)
- Span
- 20.0 ft, unbraced (Lb = 20.0 ft)
- Loads
- D = 0.6 kip/ft · L = 0.4 kip/ft
- Design format
- LRFD, ASCE/SEI 7-22 §2.3
Design a simply supported W16x40 beam in A992, span 20 ft, dead load D = 0.6 kip/ft including self-weight and live load L = 0.4 kip/ft, laterally unbraced between the supports, load applied at the top flange, per AISC 360-22 by LRFD. Check flexure, shear, lateral-torsional buckling and deflection against the AISC Commentary L2 limits.
Calculate the example with MiaKey results
- Required moment Mu
- 68.0 kip-ft
- Design flexural strength phi_b Mn
- 94.7 kip-ft (F2-3, Cb = 1.136)
- Required shear Vu
- 13.6 kip of phi_v Vn = 146.4 kip
- Live-load deflection
- 0.096 in <= 0.667 in (l/360)
- Governing utilization
- 0.718 (lateral-torsional buckling)
All values are deterministic for the stated inputs and are produced by reports/016-skl-000075-rfem-review/featured_example.py, not by a chat run. The load is applied at the top flange, so the square-root factor of F2-4 (the whole radical, not its radicand) is taken as 1.0 per AISC Commentary F1; with centroidal loading phi_b Mn = 134.9 kip-ft and the utilization is 0.504. That is a 29.8 % difference in capacity, which is why the answer always states both. RFEM 6.15.0007 does not apply the Commentary simplification and reproduces the centroidal capacity to within 0.55 %, the whole difference being Cb (1.1426 against 1.1364).
- — Section properties come from lookup_profiles, catalog row tagged [AISC 16], converted back from the catalog's metric units; the catalog rounds to six significant digits, which is the precision ceiling on every number above.
- — Both LRFD combinations were evaluated - 1.4D = 0.84 kip/ft and 1.2D + 1.6L = 1.36 kip/ft - and the second governs. 1.4D can only govern when D > 8L.
- — Flange and web are compact (lambda_f = 6.93 <= 9.15; lambda_w = 49.1 <= 90.6). The web depth uses h = d - 2*tf because the catalog returns no fillet dimension, which overstates lambda_w and can therefore only classify conservatively.
- — Shear takes G2.1(a) - a rolled I-shape with h/tw <= 2.24*sqrt(E/Fy) - so Cv1 = 1.0, phi_v = 1.00 and Omega_v = 1.50. AISC 360-22 requires no moment-shear interaction for I-shapes or channels.
- — Deflection is Euler-Bernoulli with E = 29,000 ksi and Ix = 518 in^4; shear deformation is neglected, so RFEM reports slightly larger values.
Required inputs
- Structural system and span
- Section and steel grade
- Dead and live load, and where the load is applied
- Lateral restraint of the compression flange
- Design format (LRFD or ASD) and deflection basis
What you receive
- Governing check and utilization
- Flexural strength and the limit state that produced it
- Shear strength and the branch of G2 that applies
- Deflection against the named limit and span convention
- Assumptions and clause references
Start from an input template
These templates prefill the form with typical inputs. They are not calculated results; the calculation runs in CALC.
Prepare your calculation
Configure your beam
System sketch
L = 6.096 mgk = 8.7563 kN/mqk = 5.8376 kN/m
m
All required fields completed
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Yes
kN/m
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kN
m
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m
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Inputs completeReady to calculate
What this skill checks
Flexure and shear
Yielding per F2-1, flange local buckling per F3, shear per G2 with the factors that belong to the shape type.
Lateral-torsional buckling
All three branches of F2.2 with C_b computed from the quarter-point moments, cantilevers included.
Deflection, with the source named
AISC Commentary L2 or IBC Table 1604.3 or your project limit. The two codes measure a cantilever differently, and the answer says which convention it used.
Frequently asked questions
Does the skill use LRFD or ASD?
Whichever you pick. The design method is always part of the parameter form, so it is confirmed rather than assumed, and the answer names the format in the same sentence as the governing check. Which one is stricter depends on the dead-to-live ratio, and the skill does not imply they are interchangeable.
How is Cb determined?
From Equation F1-1 using the quarter-point moments of the actual moment diagram, not from a lookup table. AISC 360-22 has no 3.0 cap on Cb; the cap belongs to a Commentary equation and is not applied. For a cantilever with warping prevented at the support and the free end unbraced, F1(c) gives Cb = 1.0.
Which deflection limit applies?
The one you choose - AISC Commentary L2, IBC Table 1604.3, or your own project limit, which overrides both. The two codes disagree on the cantilever span convention: Commentary L2 measures l/150 on the cantilever length, IBC takes l as twice the cantilever length. Every answer names the basis and the convention it used.
Can I compare the result against RFEM?
Yes, and the answer offers it as a follow-up. The reference case behind the featured example was cross-checked against RFEM 6.15 with the Steel Design add-on on AISC 360-22; Lp, Lr, c, rts and all four slenderness limits matched to the digit.
Standards & references
AISC 360-22ASCE 7-22
Ready for your first check?
Start with the example and adapt it to your structural system.
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