Beam Optimizer — Find Lightest Steel Section

Q: How does the optimizer handle lateral-torsional buckling?

The optimizer evaluates lateral-torsional buckling (LTB) per the selected design code. For AISC 360 Chapter F, the nominal moment capacity Mn is reduced based on the unbraced length Lb relative to Lp and Lr limits. If Lb exceeds Lp, the optimizer recalculates the available moment capacity using the LTB equations, which depend on the section's moment of inertia, torsional constant, and section modulus. Sections with insufficient LTB resistance are eliminated from consideration, encouraging the selection of deeper or more compact sections for longer unbraced lengths.

Q: Can I optimize for fabrication cost instead of just weight?

Yes, the optimizer estimates relative fabrication cost using a weighted formula that includes material weight, section availability, and fabrication complexity. Common shapes and readily available sections are ranked higher. For example, W21x50 is preferred over W18x40 if weight difference is small but the W21 is more common. The cost-weight optimization factor can be adjusted from 0 (weight-only) to 1.0 (cost-dominant). This feature helps avoid exotic sections that would increase project cost despite marginal weight savings.

Design the most economical steel beam with the free Beam Optimizer tool. Enter your span, loading, and constraints — the optimizer automatically finds the lightest section that satisfies bending strength, shear capacity, deflection limits, and slenderness requirements.

Quick links: Beam capacity → | Beam deflection → | All beam sizes →

Core calculations run via WebAssembly in your browser with step-by-step derivations across AISC 360, AS 4100, EN 1993, and CSA S16 design codes. Results are preliminary and must be verified by a licensed engineer.

How the Beam Optimizer Works

The beam optimizer implements a sorted iterative search through the selected section database. When a user specifies design loads, span length, and constraints, the tool performs the following sequence:

Section database filtering — The selected shape library (W-shapes, UB, IPE, HEA, HEB, etc.) is filtered by any user-specified constraints (depth range, weight range, or section type).
Sorting by weight — All qualifying sections are sorted from lightest to heaviest weight per unit length.
Constraint checking — Starting with the lightest section, each shape is evaluated against all specified design constraints using the selected design code.
First-pass selection — The first section passing all checks is returned as the optimal candidate. This is guaranteed to be the lightest section meeting all requirements because the search starts from the minimum weight.
Depth constraint adjustment — If no section passes all checks, the tool automatically relaxes depth constraints (if specified) and widens the search pool. If still no section is found, the user is prompted to increase member size or reduce span/load.

The search algorithm is deterministic and typically completes in under 100 milliseconds for a full W-shape database of 280+ sections.

Bending Strength Check

Per AISC 360 Chapter F, the nominal flexural strength Mn depends on the limit state of yielding, lateral-torsional buckling (LTB), flange local buckling (FLB), and web local buckling (WLB). The optimizer checks each section against these limit states:

Compact section check (AISC B4.1) — The flange width-thickness ratio λf = bf/(2tf) must be ≤ λpf = 0.38√(E/Fy). The web slenderness λw = h/tw must be ≤ λpw = 3.76√(E/Fy). For compact sections, Mn = Mp = Fy × Zx.

Lateral-torsional buckling (AISC F2) — For compact I-shaped members, the nominal moment Mn = Cb × [Mp - (Mp - 0.7Fy × Sx) × (Lb - Lp)/(Lr - Lp)] ≤ Mp for Lp < Lb ≤ Lr, and Mn = Cb × π/Lb × √(E × Iy × G × J + (π × E/Lb)² × Iy × Cw) ≤ Mp for Lb > Lr. The limiting lengths Lp and Lr are computed per AISC F2-5 and F2-6.

Shear check (AISC G2) — For unstiffened webs, φvVn = φv × 0.6 × Fy × Aw × Cv, where Cv = 1.0 for h/tw ≤ 2.24√(E/Fy). For slender webs, Cv is reduced per AISC G2-9.

Deflection Check

The optimizer computes both live load and total load deflection using elastic beam theory. For simply supported beams under uniform load: Δ = 5wL⁴/(384EI). For point loads: Δ = PL³/(48EI) at midspan. Deflection limits are user-configurable: L/360 (typical for roof beams with plaster ceilings), L/240 (typical for floor beams), L/180 (typical for industrial floor beams), or custom values. The optimizer checks both instantaneous (elastic) deflection and long-term deflection (where applicable for composite beams).

Cross-Code Optimization

The optimizer supports four design codes with code-specific parameters applied automatically:

AISC 360-22 LRFD — Phi factors: φb = 0.90 (bending), φv = 0.90 (shear). Resistance factor φc = 0.90 for compression flange buckling. Cb factor for non-uniform moment diagrams computed per AISC F1-1. ASD alternative: Ωb = 1.67, Ωv = 1.67.

AS 4100:2020 — Capacity factor φ = 0.90 for bending. AS 4100 uses nominal section moment capacity Ms = fy × Ze where Ze is the effective section modulus. The moment modification factor αm replaces Cb. Shear capacity Vw = 0.6 × fy × Aw × αv.

EN 1993-1-1 — Partial factors: γM0 = 1.00 (cross-section), γM1 = 1.00 (member buckling). Design moment resistance Mc,Rd = Wpl × fy/γM0. Lateral-torsional buckling is checked per 6.3.2 using the reduction factor χLT. The shear buckling resistance is computed per EN 1993-1-5 for webs with hw/tw > 72ε/η.

CSA S16:2019 — Factor φ = 0.90 for steel members. Flexural strength Mr = φ × Z × Fy for Class 1 and 2 sections. Shear strength Vr = φ × Aw × Fs where Fs = 0.66Fy for unstiffened webs.

Unbraced Length and Lateral Bracing

The optimizer requires the user to specify the unbraced length Lb for lateral-torsional buckling calculations. This is typically the distance between points of lateral restraint (cross-frames, purlins with diaphragm action, or discrete lateral braces). For floor beams with concrete slabs on deck, Lb can be taken as zero if full composite action and deck attachment provide continuous bracing to the top flange. For beams with intermittent bracing, the Lb to use is the maximum distance between brace points. The optimizer automatically accounts for the moment gradient factor Cb based on the loading pattern selected.

Practical Optimization Strategies

For economical beam design, consider these strategies that the optimizer can incorporate:

Depth constraints — For floor systems, limiting beam depth to match floor-to-floor height constraints often governs. Typical span-to-depth ratios: 20-24 for simply supported beams, 24-28 for continuous beams. Setting a maximum depth of L/20 often produces economical sections.

Deflection rather than strength — For longer spans with light loads, deflection limits rather than flexural strength often govern the section selection. This is common in roof beams and walkway beams.

Self-weight iteration — The optimizer includes the beam self-weight in the load calculation and iterates until convergence, ensuring the selected section's own weight is properly accounted for in the design.

Frequently Asked Questions

How does the beam optimizer find the lightest section? The beam optimizer iterates through all available sections in the selected shape library (W-shapes, UB, IPE, HEA, HEB), checks each against your design constraints — bending moment, shear force, deflection limit, and slenderness — and returns the lightest section that passes all checks. Constraint checking follows the selected design code (AISC 360, AS 4100, EN 1993, or CSA S16).

What constraints can I set? You can set: maximum allowable deflection (L/360, L/240, or custom), unbraced length for LTB, yield strength (Fy), whether to include self-weight, and minimum or maximum depth restrictions. The optimizer respects all code-specific phi factors and safety factors automatically.

Which beam shapes does the optimizer support? The optimizer supports all AISC W-shapes, UK UB sections, European IPE and HEA/HEB sections, and Australian UB sections. You can filter by shape type or depth range to narrow the search. Additional shapes are added regularly based on user demand.

How does the optimizer handle lateral-torsional buckling? The optimizer computes LTB capacity per the selected code using the user-specified unbraced length Lb. For AISC 360, it calculates Lp and Lr and applies the appropriate Mn formula from Chapter F. If Lb is set to zero, the optimizer assumes full lateral bracing and uses Mn = Mp. The moment gradient factor Cb is automatically computed from the loading pattern.

Can I optimize for fabrication cost instead of just weight? The current optimizer selects the least-weight section, which generally correlates with lower material cost. However, the lightest section may not always be the most economical when considering fabrication complexity, connection costs, or availability. We recommend reviewing the optimizer's output against local steel supplier pricing and checking for section availability. A future enhancement will add multi-objective optimization considering cost factors.

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice. All results must be independently verified by a licensed Professional Engineer.