Beam Capacity Calculator

The beam capacity calculator checks the design flexural strength (phiMn) and design shear strength (phiVn) of a steel beam under factored loads. It classifies the section as compact, non-compact, or slender per the selected design code, determines the unbraced length regime (plastic, inelastic LTB, or elastic LTB), and applies the appropriate nominal moment equation with the Cb moment gradient factor.

What you enter: Section designation, steel grade, unbraced length (Lb), moment gradient factor (Cb), and the applied factored moment and shear.

What you get: Flexural capacity (phiMn), shear capacity (phiVn), utilization ratio (demand/capacity), and the governing limit state — yielding, inelastic LTB, elastic LTB, local flange buckling, or local web buckling. A utilization ratio below 1.00 passes; above 1.00 requires a larger section, reduced unbraced length, or revised framing.

Quick Reference — Common W-Shape Beam Capacities

Capacities below are for A992 steel (Fy = 50 ksi), Cb = 1.0, fully braced compression flange (Lb is less than or equal to Lp). These are nominal design capacities that assume a continuously-braced top flange (typical for floor beams with a composite metal deck).

When the unbraced length exceeds Lp, lateral-torsional buckling reduces the available flexural capacity. The calculator applies the full LTB reduction for your specific unbraced length, not just the tabulated fully-braced value. Use the calculator directly for the correct capacity.

For beams with a continuous concrete deck providing lateral restraint to the compression flange, Lb can be taken as zero and the full plastic moment is available.

Beam Deflection Calculator

The Beam Displacement and Sag Tool computes the maximum elastic deflection of a steel beam under service-level (unfactored) loads and compares it to standard deflection limits: L/360 for floors with plaster ceilings, L/240 for total load on floors, L/180 for roof beams without ceilings, and L/480 for floors supporting sensitive finishes or brittle partitions.

Supported beam configurations: Simply supported, cantilever, fixed-fixed (both ends), propped cantilever.

Supported load types: Uniform distributed load (UDL), point load at midspan, point load at any position along the span, partial uniform load, and triangular/hydrostatic load.

Deflection Formulas at a Glance

The cantilever is the most deflection-sensitive configuration — for the same span and load, a cantilever deflects roughly 9.6 times more than an equivalent simply supported beam. This is why cantilever beams typically require much deeper sections or reduced spans.

Standard Deflection Limits by Application

For composite beams where the concrete deck acts compositely with the steel section, use the transformed moment of inertia (I_tr) — which can be 2 to 3 times the bare steel Ix — for deflection calculations under superimposed loads. The construction-stage deflection (steel beam alone supporting wet concrete) must be checked separately using the bare steel Ix.

Beam Size Lookup — Common W-Shapes

The section properties database contains dimensional and geometric properties for over 2,000 hot-rolled steel sections across all five design regions. Use the table below to shortlist candidate W-shapes by depth and weight, then click through for the full property set including flange and web slenderness ratios, torsional constant J, warping constant Cw, and section classification per your design code.

For non-US sections, use the UB (Universal Beam) and UC (Universal Column) designations for UK, EU, and Australian projects. The section properties tool covers British UB/UC, European HEA/HEB/HEM, Australian UB/UC/CHS/RHS, and Canadian W/WW shapes. The complete database is accessible through the section properties page.

Beam Span Tables — Quick Preliminary Sizing

Use the span tables below to select a trial W-shape for a given span and floor loading before running a full design check. These tables assume simply-supported beams at 8 ft spacing, A992 steel (Fy = 50 ksi), a superimposed dead load of 20 psf (plus beam self-weight), and fully-braced compression flanges (composite metal deck). The live-load deflection limit is L/360, and the total-load deflection limit is L/240. AISC 360-22 LRFD load combinations are used.

All entries pass both strength and serviceability checks. Heavier beams may be required for longer unbraced lengths, concentrated loads, or tighter deflection limits. Always verify your final selection with the beam capacity calculator.

How to use this table:

1. Determine your beam span, loading category, and tributary width.
2. If your tributary width differs from 8 ft, scale the load proportionally (e.g., 10 ft trib width at 40 psf LL behaves like 50 psf LL on an 8-ft trib — use the next column to the right).
3. Select the trial section from the table.
4. Run the beam capacity calculator with your actual loads, unbraced length, and moment gradient factor.
5. Check deflection with the Beam Displacement and Sag Tool using your actual service loads and L/360 or project-specified limit.
6. If utilization exceeds 0.90, step up one row in section weight and re-check.

For cantilever spans, divide the span length by 4 and use that effective span to enter this table (e.g., a 10 ft cantilever is roughly equivalent to a 40 ft simply-supported beam). For fixed-end beams, multiply the span by 0.7 for an approximate equivalent.

Beam Optimizer — Find the Lightest Section

The beam optimizer tool searches the section database to find the lightest W, UB, or H section that satisfies your moment and shear demands. Instead of manually iterating through trial sections, enter your factored moment (Mu), factored shear (Vu), unbraced length, and code selection, and the optimizer returns the lightest adequate section along with the next two alternates.

This is particularly useful during preliminary design when you know the demands from analysis but want to minimize steel tonnage across hundreds of beams in a framing plan. The optimizer reduces weight rather than depth — for deflection-sensitive beams, manually verify the deflection after the optimizer suggests a candidate.

How to Use a Steel Beam Calculator — Step-by-Step

Follow this workflow to take a beam from concept to verified design. Each step references the specific tool or reference page you need.

Step 1 — Define your design inputs. Determine the beam span (center-to-center of supports), the tributary width (half the distance to each adjacent beam), the superimposed dead load (flooring, ceiling, MEP, partitions), and the design live load per your governing building code. For roof beams, include the appropriate snow, wind uplift, or rain load. Record the steel grade (A992 / S355 / 350 Grade / 350W) and the design standard (AISC 360 / EN 1993 / AS 4100 / CSA S16).

Step 2 — Estimate a trial section. Use the beam span tables on this page to select a trial W-shape for your span and load category. If your loading does not match the table categories, start with a depth-to-span ratio of approximately 1/20 for simply-supported floor beams (e.g., a 20 ft span suggests a depth of about 12 inches — try W12x26). For cantilevers, use a depth-to-span ratio closer to 1/8.

Step 3 — Compute factored loads. Apply the load factors from your design standard: ASCE 7 LRFD uses 1.2D + 1.6L for gravity; EN 1990 uses 1.35G + 1.5Q (or 1.25G + 1.5Q with the UK National Annex); AS 1170.0 uses 1.2G + 1.5Q; CSA S16 uses 1.25D + 1.5L. Convert the factored area loads to line loads by multiplying by the tributary width.

Step 4 — Calculate factored moment and shear. For a simply-supported beam with uniform load: Mu = wu * L^2 / 8, and Vu = wu * L / 2. For more complex loading patterns (point loads, partial UDL, overhangs), use the simple beam calculator to generate shear force and bending moment diagrams.

Step 5 — Check flexural capacity. Open the beam capacity calculator, select your design code and trial section, enter the unbraced length Lb (distance between points of lateral restraint to the compression flange), set the moment gradient factor Cb, and input Mu and Vu. The tool reports phiMn, phiVn, and the utilization ratio. If utilization exceeds 0.90, step up to a heavier section.

Step 6 — Check deflection. Use the Beam Displacement and Sag Tool with your service-level (unfactored) loads. Live-load deflection is the incremental deflection that occurs after the floor is in service and should be limited to L/360 for typical floors (plaster ceiling) or L/480 for sensitive finishes. Total-load deflection (dead plus live, unfactored) should be limited to L/240 for floors. If deflection controls, increase the moment of inertia Ix — moving to a deeper section of similar weight can increase Ix dramatically with minimal weight gain.

Step 7 — Check shear. For most W-shapes at typical span-to-depth ratios, shear capacity far exceeds shear demand and is not the governing limit state. However, for short, heavily loaded beams with concentrated loads near supports, check phi*Vn explicitly. The beam capacity calculator reports shear utilization automatically.

Step 8 — Document and verify. Record the selected section, utilization ratios, deflection values, and governing limit states for your calculation package. Run an independent hand-check on the critical limit state. All results are preliminary and must be verified by a licensed Professional Engineer before use in construction.

Design Code Reference Table

Each design code has different resistance factors, load factors, and serviceability limits. This table maps the key provisions for steel beam design across the five supported standards.

Each standard has unique provisions for web shear buckling (unstiffened vs. stiffened), flange local buckling, and the interaction of flexure with axial load (beam-column). The calculators apply the correct provisions for your selected code automatically. For combined loading cases, use the beam-column calculator which covers the AISC H1 interaction equations (or equivalent from other codes).

Worked Example — W12x26 Floor Beam at 20 ft Span

Problem: Check a simply-supported W12x26 floor beam spanning 20 ft at 8 ft spacing for a typical office floor. Dead load = 50 psf (includes 3-inch concrete deck, metal deck, ceiling, mechanical allowance, and beam self-weight). Live load = 40 psf (office occupancy, reducible per ASCE 7 but reduction ignored here for simplicity). Design code: AISC 360-22 LRFD. Steel: ASTM A992 (Fy = 50 ksi, Fu = 65 ksi). The compression flange is continuously braced by a composite metal deck with shear studs, so Lb may be taken as zero.

Step 1 — Compute loads.

Tributary width = 8 ft.

Service dead load: wD = 50 psf _ 8 ft = 400 plf = 0.400 kip/ft. Service live load: wL = 40 psf _ 8 ft = 320 plf = 0.320 kip/ft. Total service load: w = 0.720 kip/ft.

Factored load (ASCE 7-22 LRFD): w*u = 1.2 * 0.400 + 1.6 _ 0.320 = 0.480 + 0.512 = 0.992 kip/ft.

Step 2 — Compute factored moment and shear.

Mu = w_u * L^2 / 8 = 0.992 _ (20)^2 / 8 = 0.992 _ 400 / 8 = 49.6 kip-ft. Vu = w_u * L / 2 = 0.992 * 20 / 2 = 9.92 kips.

Step 3 — Section properties (W12x26, A992).

d = 12.2 in, bf = 6.49 in, tw = 0.230 in, tf = 0.380 in. A = 7.65 in^2. Ix = 204 in^4, Sx = 33.4 in^3, Zx = 37.2 in^3. Lp = 6.6 ft (limiting unbraced length for full plastic moment).

Step 4 — Flexural capacity check.

The compression flange is continuously braced by the concrete deck, so Lb = 0 is less than Lp = 6.6 ft. The full plastic moment is available. No LTB reduction applies.

phi*Mn = phi_b * Fy _ Zx = 0.90 _ 50 ksi * 37.2 in^3 = 1,674 kip-in = 139.5 kip-ft.

Flexure utilization = M_u / phi*Mn = 49.6 / 139.5 = 0.356 (35.6%). The beam has significant reserve in flexure. The governing limit state is yielding of the full cross-section (compact section, no local buckling).

If the beam were unbraced (e.g., roof beam without deck), Lb = 20 ft would exceed Lp = 6.6 ft and lateral-torsional buckling would govern. For W12x26 at Lb = 20 ft with Cb = 1.14 (uniform load case), the LTB-reduced capacity would be approximately 91.4 kip-ft, giving a utilization of 49.6/91.4 = 0.543 — still passing but with less reserve.

Step 5 — Deflection check (service loads).

Live load deflection (L/360 limit):

wL = 0.320 kip/ft = 0.02667 kip/in. Span L = 240 in. E = 29,000 ksi. Ix = 204 in^4.

delta*LL = 5 * wL _ L^4 / (384 _ E _ Ix) = 5 _ 0.02667 _ (240)^4 / (384 _ 29,000 _ 204) = 5 _ 0.02667 _ 3.318 _ 10^9 / (384 _ 29,000 _ 204) = 442.4 _ 10^6 / 2.272 * 10^9 = 0.195 in.

Allowable = L/360 = 240/360 = 0.667 in. Live load deflection utilization = 0.195 / 0.667 = 0.292 (29.2%). Passes with ample reserve.

Total load deflection (L/240 limit):

w*total = 0.720 kip/ft = 0.0600 kip/in. delta_total = delta_LL * (0.720/0.320) = 0.195 _ 2.25 = 0.439 in. Allowable = L/240 = 240/240 = 1.00 in. Total load deflection utilization = 0.439 / 1.00 = 0.439 (43.9%). Passes.

Step 6 — Shear capacity check.

Web area: Aw = d _ tw = 12.2 _ 0.230 = 2.81 in^2. phiVn = phi_v * 0.6 _ Fy _ Aw = 1.00 _ 0.6 _ 50 * 2.81 = 84.2 kips. Shear utilization = V_u / phiVn = 9.92 / 84.2 = 0.118 (11.8%). Shear does not govern.

Result summary for W12x26 at 20 ft span:

W12x26 is adequate for this loading with ample reserve. A W12x19 (lighter section at 19 plf) could potentially work — Ix = 130 in^4, Zx = 24.7 in^3 — but the live load deflection would be 0.195 * (204/130) = 0.306 in, utilization = 0.306/0.667 = 0.459 still passing. The W12x19 flexure utilization would be 49.6/(0.9*50*24.7/12) = 49.6/92.6 = 0.536. The W12x19 also passes all checks, but the W12x26 provides additional reserve for vibration, future loading changes, and connection detailing requirements. For final selection, consult the beam optimizer to find the lightest section that satisfies all constraints.

Common Beam Design Mistakes

Using factored loads for deflection checks. Deflection is a serviceability limit state and uses unfactored (service-level) loads. Using LRFD factored loads (1.2D + 1.6L) inflates the calculated deflection by 40-60% and forces selection of unnecessarily heavy sections. Always use service loads for deflection and factored loads for strength checks.

Neglecting lateral-torsional buckling for unbraced roof beams. Roof beams without a floor deck have no continuous lateral restraint to the compression flange. The unbraced length Lb is the full span, and LTB can reduce flexural capacity by 30-60% compared to the fully-braced tabulated value. Every beam design must account for the actual distance between lateral braces.

Selecting a section without checking deflection. For long-span beams (L/d > 24), deflection often controls the design rather than strength. A beam that passes flexure with a 0.50 utilization ratio can still fail the L/360 deflection check. Always check both strength and serviceability before finalizing a section.

Ignoring the moment gradient factor Cb. Cb accounts for the shape of the moment diagram along the unbraced length. A beam with a uniform moment (Cb = 1.0) has the lowest LTB capacity. A beam with reverse curvature (Cb > 2.0) can have more than double the LTB capacity. Do not conservatively assume Cb = 1.0 for all cases — calculate the actual Cb from your moment diagram.

Forgetting composite action in floor beams. After the concrete deck cures, shear studs mechanically connect the steel beam and the concrete deck, forming a composite section. The effective moment of inertia I_eff can be 2-3 times the bare steel Ix, dramatically reducing deflection. Failing to account for composite action in the final condition leads to over-designed beams.

Mixing metric and imperial units. Converting between kip-feet and kN-m, or between inches and millimeters, introduces errors. W-shape tables are typically published in imperial units. UB and UC tables use metric. Use the calculator's built-in unit system rather than manual conversion.

Frequently Asked Questions

What is the most common steel beam section for floor framing?

W-shapes (wide-flange beams) are the workhorse of steel floor framing in North America. For typical office floor bays at 30 ft x 30 ft with beams at 10 ft spacing, W16x26 through W21x50 are common sections, with W18x35 and W18x40 appearing most frequently. The governing limit is typically live-load deflection (L/360), not flexural strength. In the UK and Europe, UB (Universal Beam) sections in S355 steel fill the same role, with 356x171 UB and 406x178 UB being common choices for similar spans.

How do I determine the unbraced length Lb for a beam with intermittent lateral bracing?

Lb is the distance between points where the compression flange is restrained against lateral movement AND the cross-section is restrained against twist. For floor beams with a composite metal deck and shear studs, Lb = 0 (continuously braced). For beams with discrete lateral bracing at cross-frames or bridging at spacing s, Lb = s. For beams with only end connections providing torsional restraint, Lb = full span. For cantilevers, Lb is measured from the support to the tip. When in doubt, use the conservative assumption of full-span unbraced length.

When should I use a built-up plate girder instead of a rolled W-shape?

Rolled W-shapes are available up to approximately W36x925 (36 inches deep, 925 plf). Beyond this depth and weight, or when the required section properties fall between available W-shape sizes, a built-up plate girder may be more economical. Plate girders are also used when variable-depth sections are beneficial (tapered girders for long-span roofs), when web openings for mechanical ducts require reinforced panels, or when hybrid steel grades (higher-strength flanges with lower-cost web material) offer savings.

What does the Cb factor mean in practical terms?

Cb (moment gradient factor) accounts for the non-uniform distribution of moment along the unbraced length. The worst case is a constant moment along the entire unbraced length — the compression flange is stressed uniformly, and the entire segment wants to buckle simultaneously (Cb = 1.0). A simply-supported beam with uniform load has decreasing moment toward the ends, and only the central portion is highly stressed — this is less severe for buckling (Cb = 1.14). A beam with reverse curvature (moment changes sign) has one part of the flange in compression and another in tension — this is the least severe case (Cb can reach 2.27 or higher). In design, using a Cb greater than 1.0 when the moment diagram warrants it can increase your LTB capacity by up to 100% or more.

Do I need to check both LRFD and ASD for beam design?

No — either design methodology is acceptable per AISC 360. LRFD (Load and Resistance Factor Design) applies different factors to loads (1.2D + 1.6L) and resistance (phi = 0.90 for flexure). ASD (Allowable Strength Design) uses a single safety factor (Omega = 1.67 for flexure) and service-level loads. Both give the same result for the same load case when the ASD load combination is chosen correctly. Most commercial and industrial projects in the US use LRFD. The calculators on this site default to LRFD but provide ASD-equivalent results for users who prefer that methodology.

How does the beam calculator handle tapered or haunched beams?

The standard beam capacity formula assumes a prismatic (constant cross-section) member. Tapered and haunched beams require special treatment because the section properties vary along the span, and the location of maximum stress does not necessarily coincide with the location of maximum moment. For portal frame haunches (common at the eave and apex of single-story steel frames), the effective length factor for buckling changes, and the moment gradient is not captured by the standard Cb formula. Use the portal frame analysis tool for tapered and haunched members in moment-resisting frames, or consult AISC Design Guide 25 for frame stability design.

Related Pages

• Beam capacity calculator — flexure, shear, LTB checks
• Beam deflection calculator — L/360 and L/240 checks
• Beam optimizer — find the lightest section
• Beam span table — quick shortlisting by span and load
• Simple beam calculator — SFD, BMD, reactions
• Section properties database — 2,000+ sections across 5 regions
• Steel beam sizes reference — W, UB, UC, HSS tables
• Beam design workflow — full step-by-step guide
• Deflection limits explained — L/360, L/240, L/480
• Moment of inertia calculator — Ix, Iy from geometry
• Beam-column calculator — combined axial + flexure
• Portal frame analysis — haunched rafter + column frames
• Tools directory — all calculators
• How to verify calculator results
• Disclaimer — educational use only

Disclaimer — Educational Use Only

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors: loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification. You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

The site operator provides the content "as is" and "as available" without warranties of any kind. To the maximum extent permitted by law, the operator disclaims liability for any loss or damage arising from the use of, or reliance on, this page or any linked tools.