Steel member design

Why it matters

Steel beams and girders frame most commercial buildings, bridges and industrial structures. A beam check combines three questions: is it strong enough in bending, strong enough in shear, and stiff enough that floors do not feel bouncy or crack finishes? This lesson walks through the simplest complete check so the structure of a real calculation is clear before you meet the many special cases.

The governing specification

In the US, structural steel buildings are designed to ANSI/AISC 360, Specification for Structural Steel Buildings (the current edition is AISC 360-22), published by the American Institute of Steel Construction (https://www.aisc.org), which makes the Specification freely downloadable. Section properties come from the AISC Steel Construction Manual or AISC's shapes database. Bridges follow AASHTO's specifications instead. Checked on 2026-10-23.

Like concrete, steel uses LRFD: a factored load effect must not exceed a reduced (design) strength:

Mu <= phi * Mn      Vu <= phi * Vn

Mu and Vu come from the load combinations of the previous lesson; Mn and Vn are the nominal strengths from the specification.

Flexure: yielding

A W-shape (wide-flange) beam that is compact (flanges and web stocky enough not to buckle locally) and laterally braced at short enough intervals can reach its plastic moment:

Mn = Mp = Fy * Zx        phi = 0.90

Fy is the yield stress (50 ksi for the common ASTM A992 grade) and Zx the plastic section modulus about the strong axis. Most rolled W-shapes are compact in flexure for 50 ksi steel; the specification gives the slenderness limits to check.

Lateral-torsional buckling

If the compression flange is not braced often enough, the beam can buckle sideways and twist before it yields. AISC 360 expresses this with the unbraced length Lb compared with limits Lp and Lr for the section: below Lp the full plastic moment applies; beyond it, the strength drops. A slab attached to the top flange usually braces it continuously in the finished building, but not during construction before the slab cures, which is why erection checks matter. This lesson's example assumes full lateral bracing.

Shear

For a rolled I-shape, shear is carried by the web:

Vn = 0.6 * Fy * Aw * Cv1     Aw = d * tw

For most rolled I-shapes with 50 ksi steel, the specification allows phi = 1.0 and Cv1 = 1.0 when the web meets its slenderness limit; you confirm that condition for the section you use. Shear rarely governs simple-span floor beams, but it often does for short, heavily loaded transfer beams and at coped connections.

Deflection

Deflection is a serviceability check with unfactored (service) loads. For a simple span with uniform load:

delta = 5 * w * L^4 / (384 * E * I)

E = 29,000 ksi for steel. Limits come from the building code and the project (L/360 under live load is a common floor criterion for members supporting plaster or brittle finishes); vibration may govern long, light floors and has its own AISC design guide.

Worked example (illustrative)

A floor beam spans 30 ft, laterally braced by the slab, with a factored load wu = 2.0 kip/ft and a service live load of 0.8 kip/ft. Try a section with properties close to a W18x35: Zx = 66.5 in^3, Ix = 510 in^4, d = 17.7 in, tw = 0.300 in, Fy = 50 ksi.

1. Flexure. Mu = 2.0 × 30^2 / 8 = 225 kip-ft. phi*Mn = 0.90 × 50 × 66.5 / 12 = 249.4 kip-ft. Ratio 0.90: OK.
2. Shear. Vu = 2.0 × 30 / 2 = 30 kips. phi*Vn = 1.0 × 0.6 × 50 × (17.7 × 0.300) = 159 kips. Ratio 0.19: OK.
3. Live-load deflection. w = 0.8 / 12 = 0.0667 kip/in, L = 360 in: delta = 5 × 0.0667 × 360^4 / (384 × 29,000 × 510) = 0.99 in. The L/360 limit is 1.00 in. Ratio 0.99: OK, just.

All three pass, but deflection is nearly at its limit. A designer might choose a slightly deeper section, or camber the beam for dead load, depending on project requirements. If the span were 32 ft, Mu would be 256 kip-ft and flexure would fail.

Common mistakes

• Assuming full bracing when the compression flange is unbraced (cantilevers, construction stage, uplift putting the bottom flange in compression).
• Using factored loads for deflection, or service loads for strength.
• Forgetting self-weight of the beam (35 lb/ft for this one) in the dead load.
• Mixing units: kip-in vs kip-ft, ksi vs psi.
• Ignoring connections. Members are often fine and connections or coped ends govern.

Professional responsibility

This is a teaching example. Real steel design covers local buckling, lateral-torsional buckling, combined forces, connections, stability, fire and fatigue under the adopted specification. Real designs need review and sealing by a licensed professional engineer (PE) under the codes your jurisdiction adopts.

Recap

• LRFD check: Mu <= phi*Mn, Vu <= phi*Vn, plus a service-load deflection limit.
• Braced compact beam: phi*Mn = 0.90 Fy Zx; unbraced length can reduce it.
• Shear on rolled shapes: 0.6 Fy d tw with the specification's factors; deflection 5wL^4/(384EI).

Try it

Open the Do tab to write a beam-check function that reports moment, shear and deflection ratios.