What is Us Beam Design used for in structural engineering?

Us Beam Design provides values required for steel design calculations including capacity checks, connection design, and detailing. It is referenced in structural design codes and used by practicing engineers during the design of buildings, bridges, and industrial structures.

Can I use these reference values directly in my design?

Yes, provided the values match your governing code edition and project specifications. Always cross-reference against the primary source (code document, manufacturer data, or published standard). The information on this page is for educational use — final verification by a licensed engineer is required.

How often are these reference values updated?

Reference content is maintained to align with current code editions. When a new edition of AISC 360, AS 4100, EN 1993, or CSA S16 is published, values are reviewed and updated. Check the last-modified date at the bottom of the page and verify against the current edition for your jurisdiction.

US Beam Design Guide — AISC 360-22 Flexural Design

Complete reference for flexural design of steel beams per AISC 360-22 Specification Chapter F. Covers nominal moment capacity Mn for compact, noncompact, and slender sections, lateral-torsional buckling (LTB) with the Cb equivalent moment factor, shear capacity per Chapter G, deflection criteria per IBC and ASCE 7, and a step-by-step worked example for a W18x35 simply supported roof beam.

AISC 360 Flexural Design Framework

AISC 360-22 Chapter F provides the design provisions for flexural members. The design flexural strength is:

phiMn <= phiFy*Zx (for compact sections, fully braced)

Where:

phi = 0.90 (LRFD resistance factor for flexure)
Mn = nominal flexural strength (kip-in or kip-ft)
Fy = specified minimum yield stress (ksi)
Zx = plastic section modulus about the strong axis (in^3)

The actual Mn depends on the limit state that governs: yielding (plastic moment), lateral-torsional buckling, flange local buckling, or web local buckling.

Section Classification — Compact, Noncompact, Slender

AISC 360 Table B4.1b classifies section elements based on width-to-thickness ratios. The classification determines which limit states apply.

Classification	Flange (lambda <= lambdap)	Web (lambda <= lambdap)	Limit States
Compact	lambda <= lambdap	lambda <= lambdap	Yielding only (if Lb <= Lp)
Noncompact	lambdap < lambda <= lambdar	lambdap < lambda <= lambrar	Inelastic flange or web local buckling
Slender	lambda > lambdar	lambda > lambdar	Elastic local buckling

For hot-rolled W-shapes in A992 steel (Fy = 50 ksi):

Flange compact limit: bf/(2tf) <= 0.38sqrt(E/Fy) = 0.38sqrt(29000/50) = 9.15
Web compact limit: h/tw <= 3.76sqrt(E/Fy) = 3.76sqrt(29000/50) = 90.6

Most standard W-shapes are compact for both flange and web when used in bending. Noncompact sections include some lighter W-shapes with宽 flanges (e.g., W14x22 with bf/2tf = 10.2) and all HSS with certain slenderness ratios.

Nominal Moment Capacity — Yielding

For compact sections with continuous lateral bracing of the compression flange (Lb <= Lp):

Mn = Mp = Fy*Zx

This is the full plastic moment — the entire cross-section yields in tension and compression, forming a plastic hinge. The plastic section modulus Zx accounts for the full redistribution of stress across the section.

For a W18x35 (Zx = 66.5 in^3, Fy = 50 ksi): Mn = 50 * 66.5 = 3,325 kip-in = 277 kip-ft

Lateral-Torsional Buckling — Chapter F2

LTB is the governing limit state for beams without continuous lateral bracing of the compression flange. When the unbraced length Lb exceeds Lp, the beam capacity is reduced below Mp.

Critical Lengths

Lp (plastic limiting length): Lp = 1.76rysqrt(E/Fy)

For a W18x35 (ry = 1.22 in): Lp = 1.76 _ 1.22 _ sqrt(29000/50) = 1.76 _ 1.22 _ 24.08 = 51.1 in = 4.26 ft

Lr (inelastic-to-elastic transition length): Lr = 1.95ry(E/(0.7Fy))sqrt(Jc/(Sxho) + sqrt((Jc/(Sxho))^2 + 6.76*(0.7*Fy/E)^2))

For a W18x35: Lr approx 12.6 ft (varies by section — use AISC Manual Table 3-2 for exact values).

Three Regions of LTB

Lb <= Lp (plastic range): Mn = Mp (full plastic moment, no reduction)

Lp < Lb <= Lr (inelastic range): Mn = Cb * [Mp - (Mp - 0.7FySx) * ((Lb - Lp)/(Lr - Lp))] <= Mp

Lb > Lr (elastic range): Mn = Cb * (pi^2E/(Lb/ry)^2) _ sqrt(1 + 0.078_(Jc/(Sx*ho))*(Lb/ry)^2)

Cb Factor — Equivalent Uniform Moment Factor

The Cb factor accounts for the shape of the bending moment diagram between brace points. A uniform moment (Cb = 1.0) is the worst case. A moment gradient that varies significantly can increase Cb up to 3.0, substantially increasing LTB resistance.

Moment Diagram	Cb Value
Uniform moment (no gradient)	1.00
Linear gradient, Mmax at one end	1.30-1.67
Uniform load, simply supported	1.14
Central point load, simply supported	1.32
Double curvature (reverse moments)	1.67-3.00

AISC 360 Equation F2-1 provides the general formula: Cb = 12.5Mmax / (2.5Mmax + 3MA + 4MB + 3*MC)

Where Mmax is the absolute maximum moment in the unbraced segment, and MA, MB, MC are the absolute moments at the quarter, mid, and three-quarter points of the segment.

Shear Capacity — Chapter G

The design shear strength for unstiffened webs:

phiVn = phi * 0.6Fy*Aw*Cv1

Where:

phi = 1.00 (resistance factor for shear)
Aw = d*tw (web area)
Cv1 = ratio of shear stress to shear yield stress

For webs with h/tw <= 2.24*sqrt(E/Fy) = 53.9 (A992): Cv1 = 1.0 (full shear yield)

For most standard W-shapes, the web is stocky enough that Cv1 = 1.0 and shear yielding governs. For example, W18x35: h/tw = 45.6 < 53.9, so Cv1 = 1.0 and phi*Vn = 1.0 * 0.6 _ 50 _ (17.7*0.300) = 159 kips.

For slender webs where h/tw > 2.24sqrt(E/Fy): Cv1 = 2.24sqrt(E/Fy) / (h/tw) (elastic buckling)

Deflection Limits

AISC 360 does not prescribe specific deflection limits — these come from building codes and project specifications. Common limits per IBC and ASCE 7 Table 1604.3:

Member Type	Live Load	Total Load	Notes
Roof members (no ceiling)	L/180	L/120	Ponding check required
Roof members (with ceiling)	L/240	L/180	Prevents cracking
Floor members	L/360	L/240	Prevents cracking and vibration
Exterior walls	L/240	—	Wind drift
Masonry wall supporting	L/600	L/400	Prevents cracking

For a simply supported beam under uniform load: Delta = 5wL^4 / (384EIx)

For a W18x35 (Ix = 510 in^4) spanning 20 ft with a 1.0 kip/ft live load: Delta = 5*(1.0/12)(240)^4 / (38429000*510) = 0.46 in Limit = L/360 = 240/360 = 0.67 in — passes (69% utilized)

Worked Example — W18x35 Roof Beam

Given:

W18x35, A992 steel (Fy = 50 ksi, Fu = 65 ksi)
Simply supported, span L = 20 ft
Roof dead load wD = 0.20 kip/ft (including self-weight)
Roof live load wL = 0.30 kip/ft
Compression flange braced at supports only (Lb = 20 ft)

Load Combinations (LRFD — ASCE 7-22)

Comb 1: 1.4D = 1.4 * 0.20 = 0.28 kip/ft Comb 2: 1.2D + 1.6L = 1.2*0.20 + 1.6*0.30 = 0.72 kip/ft (governs)

Factored moment: Mu = w*L^2/8 = 0.72 * 20^2 / 8 = 36.0 kip-ft

Flexural Capacity Check

From AISC Manual Table 3-2 (W18x35, Fy = 50 ksi):

Zx = 66.5 in^3
Mp = FyZx = 5066.5/12 = 277 kip-ft
Lp = 4.26 ft, Lr = 12.6 ft

Since Lb = 20 ft > Lr = 12.6 ft, elastic LTB governs.

From the AISC Manual for Lb = 20 ft (Cb = 1.14 for uniform load): Mn = Cb _ Mn(uncorrected) = 1.14 _ 167 = 190 kip-ft (but capped at Mp = 277 kip-ft)

phi*Mn = 0.90 * 190 = 171 kip-ft

Utilization = Mu / (phi*Mn) = 36.0 / 171 = 0.21 — passes (21% utilized)

Shear Capacity Check

phi*Vn = 1.0 * 0.6 _ 50 _ (17.7 _ 0.300) / 1000 = 159 kips Vu = 0.72 _ 20 / 2 = 7.2 kips Utilization = 7.2 / 159 = 0.045 — passes (4.5% utilized)

Deflection Check (Service Loads)

Live load deflection: Delta_L = 5*(0.30/12)(240)^4 / (38429000*510) = 0.276 in Limit = L/360 = 0.667 in Utilization = 0.276 / 0.667 = 0.41 — passes

Optimization Note

The W18x35 is significantly under-utilized at 21% for flexure with Lb = 20 ft. Adding a midspan brace point (Lb = 10 ft, between Lp and Lr) would allow inelastic LTB, increasing phi*Mn to approximately 248 kip-ft. Alternatively, a lighter section such as a W16x26 could be evaluated for economy.

Calculator

Check beam capacity instantly with our free calculator. Enter a section, steel grade, unbraced length, and loads to get phiMn, phiVn, deflection, and utilization ratios.

Try the Beam Capacity Calculator

FAQ

Q: What is the difference between Lb, Lp, and Lr in AISC 360 beam design? A: Lb is the actual unbraced length of the compression flange between brace points. Lp is the maximum unbraced length for full plastic moment capacity (yielding governs). Lr is the unbraced length at which the inelastic-to-elastic LTB transition occurs. When Lb <= Lp, Mn = Mp. When Lp < Lb <= Lr, inelastic LTB governs. When Lb > Lr, elastic LTB governs.

Q: When do I need stiffeners on a steel beam web? A: AISC 360 Chapter G requires transverse stiffeners when the required shear exceeds phiVn of the unstiffened web (h/tw > 2.24sqrt(E/Cv1*Fy)). Bearing stiffeners are required at concentrated load points and supports when web yielding (Chapter J10.2), web crippling (Chapter J10.4), or sidesway web buckling (Chapter J10.6) limits the capacity.

Q: What Cb value should I use for a simply supported beam with uniform load? A: For a simply supported beam under uniform load with no intermediate braces, Cb = 1.14. For a beam with a central point load, Cb = 1.32. The general formula uses moments at the quarter, mid, and three-quarter points of the unbraced segment. Conservatively, Cb = 1.0 may always be used.

Q: What is the LRFD resistance factor for flexure in AISC 360? A: phi = 0.90 for flexure (Chapter F). For shear, phi = 1.00 (Chapter G). For compression, phi = 0.90 (Chapter E). For tension yielding, phi = 0.90; for tension fracture, phi = 0.75.

Q: What deflection limit should I use for a floor beam? A: Per IBC Table 1604.3, floor beams typically use L/360 for live load and L/240 for total load. More restrictive limits may be required for sensitive finishes, vibration control, or if supporting masonry walls (L/600 for supporting members).