Learn how to size structural steel W-shape beams using AISC 360 and the LRFD method. Covers moment capacity, deflection limits, lateral bracing, and practical selection from AISC tables.
Steel Beam Design Overview
Sizing structural steel beams is one of the most common tasks in commercial building structural design. Wide-flange (W-shape) beams are the workhorse of structural steel framing — used for floor beams, roof beams, and girders in steel frame construction. The design process uses AISC 360 (Specification for Structural Steel Buildings) and follows either LRFD (Load and Resistance Factor Design) or ASD (Allowable Stress Design). LRFD is the current standard and produces more efficient designs.
Step 1: Determine Factored Loads
Using ASCE 7 load combinations, calculate the maximum factored moment (Mu) and shear (Vu) that the beam must resist. For a simply supported beam with uniform dead load (D) and live load (L):
- Factored load: wu = 1.2D + 1.6L (governing ASCE 7 LRFD combination)
- Factored moment: Mu = wu × L² / 8 (for uniform load)
- Factored shear: Vu = wu × L / 2
For example: a 30-foot beam with 1.5 kip/ft dead load and 2.0 kip/ft live load gives wu = 1.2(1.5) + 1.6(2.0) = 5.0 kip/ft; Mu = 5.0 × 30² / 8 = 562.5 kip-ft.
Step 2: Select a Trial Section Based on Required Zx
For compact sections with full lateral bracing, the plastic section modulus Zx must satisfy: Zx ≥ Mu / (φb × Fy), where φb = 0.90 and Fy is the yield strength (50 ksi for A992 steel). For the example above: Zx ≥ 562.5 × 12 / (0.90 × 50) = 150 in³. Consult AISC Steel Construction Manual Table 3-2 (W-shapes sorted by Zx) to find the lightest section meeting or exceeding this requirement — typically a W24×76 or W21×83.
Step 3: Check Lateral-Torsional Buckling
The moment capacity calculated above assumes full lateral bracing (or a compact section with Lb ≤ Lp). When the compression flange is unbraced over a length Lb, lateral-torsional buckling (LTB) reduces the beam's capacity. AISC 360 Chapter F defines three LTB cases:
- Lb ≤ Lp: No LTB reduction (full plastic moment Mp available)
- Lp < Lb ≤ Lr: Inelastic LTB — capacity is between Mp and 0.7FySx
- Lb > Lr: Elastic LTB — significant capacity reduction
Lp and Lr values are tabulated in AISC Manual Table 1-1 for each W-shape. If Lb exceeds Lp, either add lateral bracing (floor deck, bridging, purlins) or upsize the beam.
Step 4: Check Deflection
Deflection limits are serviceability checks, not strength checks, so use unfactored (service) loads. Typical limits: L/360 for total load (to prevent cracking of brittle finishes) and L/240 for live load only. For a simply supported beam with uniform load: δ = 5wL⁴ / (384EI), where E = 29,000 ksi and I is the moment of inertia in in⁴.
If deflection controls the design (common for longer spans or heavily loaded beams), increasing the beam depth is more effective than increasing flange width — deeper sections have larger I values relative to their weight.
Step 5: Check Shear
Shear rarely controls W-shape beam design for typical loading, but should always be verified. The shear capacity is: φVn = φ × 0.6 × Fy × Aw = 1.0 × 0.6 × 50 × (d × tw). Compare to Vu from Step 1. W-shapes with thin webs at high shear should be checked per AISC 360 Chapter G.
Composite vs. Non-Composite Beams
In steel-framed floor systems with concrete deck, composite beams use shear studs to engage the concrete slab with the steel beam, dramatically increasing moment capacity and stiffness. Composite design (per AISC 360 Chapter I) allows a lighter steel section and smaller camber requirement. Most floor beams in modern commercial buildings are designed as composite.