How do I calculate the maximum load a beam can carry?

Maximum load capacity depends on the allowable bending stress (Fb), section modulus (S), and span length (L). For a simply supported beam with a center point load: P = 4 × Fb × S / L. For a UDL: w = 8 × Fb × S / L². Values for Fb and S come from AISC 360-22 Table J3 and AISC Steel Construction Manual Table 1-1 for W-shapes.

What is the difference between a simply supported beam and a cantilever?

A simply supported beam rests on two end supports and can rotate freely at both ends. A cantilever is fixed at one end and free at the other. Under the same span and load, a cantilever deflects approximately 4 to 5 times more than a simply supported beam because only one support carries all reactions. Per Roark's Formulas for Stress and Strain, 8th Ed., Table 8.1, cantilever maximum deflection under a tip point load is PL³/(3EI) versus PL³/(48EI) for a simply supported center point load.

What is the allowable deflection limit for a floor beam?

Per IBC 2024 Table 1604.3, floor beams must not deflect more than L/360 under live load alone, and L/240 under total load (dead plus live). For beams supporting brittle finishes such as tile or plaster, the live-load limit is L/480. L is the clear span in inches. A 20-foot floor beam has an L/360 limit of 0.667 inches.

What is the section modulus and why does it matter for beam load calculations?

Section modulus (S = I/c) is the ratio of the moment of inertia to the distance from the neutral axis to the outermost fiber. It directly determines bending capacity: M_allow = Fb × S. A W12x35 steel beam has Sx = 46.8 in³ per AISC SCM Table 1-1. Higher S values allow the beam to carry larger bending moments without exceeding the allowable fiber stress.

What is the allowable bending stress for A36 structural steel?

For compact ASTM A36 steel sections per AISC 360-22 ASD, the allowable bending stress is Fb = 0.66 × Fy = 0.66 × 36,000 = 23,760 psi. For A992 steel (Fy = 50 ksi), Fb = 0.66 × 50,000 = 33,000 psi. These values apply when full lateral support is provided and the compression flange is continuously braced per AISC 360-22 Chapter F.

How do I find the safe uniform load for a wood beam?

For a simply supported wood beam under UDL: w_allow = 8 × Fb × S / L². The allowable bending stress Fb for Douglas Fir-Larch No. 2 lumber is 875 psi per NDS 2018 Supplement Table 4A. For a 4x12 (actual 3.5 × 11.25 in), S = 3.5 × 11.25² / 6 = 73.8 in³. Over a 12-foot span, w_allow = 8 × 875 × 73.8 / (144)² = 24.8 lb/in = 298 lb/ft before deflection checks.

What is shear force in a beam and when does it govern design?

Shear force is the internal force perpendicular to the beam axis, maximum at the supports for simply supported beams. For steel beams, shear capacity is Vn = 0.6 × Fy × Aw per AISC 360-22 Section G2.1, where Aw is the web area. Shear rarely governs for long-span beams but controls for short, heavily loaded spans or beams with large concentrated loads near supports. Short wood beams under point loads near supports are particularly prone to shear failure per NDS 2018 Section 3.4.

Beam Load Calculator 2026 - Simply Supported, Cantilever & Fixed Beams

⚙ Beam Load Calculator

Enter beam geometry, load, and section properties below. Required fields are marked *.

Beam Support Condition * How is the beam held at each end?

Load Configuration * Select how the load is applied to the beam.

Load Position from Left Support (ft) *

ft

Must be less than the beam span.

Beam Span (ft) *

ft

Clear span between supports, 0.5 to 300 ft.

Applied Load (lb) *

lb

Total point load in lb, or distributed load in lb/ft for UDL.

Material * Sets allowable bending stress (Fb) and modulus of elasticity (E).

Allowable Bending Stress, Fb (psi) *

psi

For A36 steel: 23,760 psi. For Douglas Fir No. 2: 875 psi.

Modulus of Elasticity, E (psi) *

psi

Steel: 29,000,000 psi. Douglas Fir: 1,700,000 psi.

Section Properties * Select a standard section or enter custom section modulus (S) and moment of inertia (I).

Section Modulus, S (in³) *

in³

S = I/c. Found in AISC Table 1-1 or NDS Supplement.

Moment of Inertia, I (in⁴) *

in⁴

Required for deflection calculation.

Application Type * Sets the IBC 2024 Table 1604.3 deflection limit for pass/fail check.

Display Units

Results are for planning and preliminary design only. Structural members in permitted construction must be verified by a licensed engineer. See full disclaimer below.

How This Beam Load Calculator Works

⎯

Choose Support Condition

Select simply supported, cantilever, or fixed-fixed. Each produces a different bending moment formula and reaction distribution.

⇣

Define Load and Span

Enter the applied load and clear span. Select point load at center, at any position, or a uniform distributed load in lb/ft.

▊

Pick Material and Section

Choose from steel A36/A992 presets, lumber species, or enter custom Fb and E. Use the W-shape or lumber section database.

✓

Get Capacity and Code Check

Results show maximum safe load, actual vs. allowable bending stress, shear force, reaction forces, and IBC 2024 deflection pass/fail.

Allowable Bending Stress Reference by Material

Allowable bending stress (Fb) is the primary input governing safe load capacity. The table below lists values per AISC 360-22 and NDS 2018. For deflection limits that apply to this calculator, the beam deflection calculator covers all IBC Table 1604.3 scenarios in depth.

Allowable Bending Stress (Fb) for Common Structural Materials
Material	Grade / Spec	Fy or Fb (psi)	ASD Fb (psi)	E (psi)	Standard
Structural Steel	ASTM A36	36,000	23,760	29,000,000	AISC 360-22 Chapter F
Structural Steel	ASTM A992	50,000	33,000	29,000,000	AISC 360-22 Chapter F
Douglas Fir-Larch	No. 2, 2-3" thick	875	875	1,600,000	NDS 2018 Supp. Table 4A
Southern Pine	No. 2, 2-3" thick	1,000	1,000	1,400,000	NDS 2018 Supp. Table 4B
Hem-Fir	No. 2, 2-3" thick	850	850	1,300,000	NDS 2018 Supp. Table 4A
Glulam	24F-V4 (Douglas Fir)	2,400	2,400	1,800,000	NDS 2018 Supp. Table 5A
LVL	1.9E Grade	2,600	2,600	1,900,000	NDS 2018 Supp. Table N1

Source: AISC Steel Construction Manual, 16th Ed. Table 1-1; NDS 2018 Supplement Tables 4A-4B. ASD Fb for compact steel = 0.66 × Fy, assuming full lateral bracing per AISC 360-22 Section F2.

Bending Moment and Shear Formulas Used

This calculator uses the standard structural beam formulas from AISC Steel Construction Manual Table 3-22 and Roark's Formulas for Stress and Strain, 8th Edition. For combined bending and axial load scenarios, refer to the concrete stress calculator.

Simply Supported — Center Point Load

M_max = PL / 4

V_max = P / 2

P_allow = 4 × Fb × S / L

AISC Table 3-22a, Case 1

Simply Supported — Uniform Distributed Load

M_max = wL² / 8

V_max = wL / 2

w_allow = 8 × Fb × S / L²

AISC Table 3-22a, Case 2

Cantilever — Point Load at Free End

M_max = PL

V_max = P

P_allow = Fb × S / L

Roark's 8th Ed., Table 8.1

Cantilever — Uniform Distributed Load

M_max = wL² / 2

V_max = wL

w_allow = 2 × Fb × S / L²

Roark's 8th Ed., Table 8.1

Fixed-Fixed — Center Point Load

M_max = PL / 8

V_max = P / 2

P_allow = 8 × Fb × S / L

Roark's 8th Ed., Table 8.2

Fixed-Fixed — Uniform Distributed Load

M_max = wL² / 12

V_max = wL / 2

w_allow = 12 × Fb × S / L²

Roark's 8th Ed., Table 8.2

Where: M_max = maximum bending moment (lb-in), P = point load (lb), w = distributed load (lb/in), L = span (in), Fb = allowable bending stress (psi), S = section modulus (in³), V = maximum shear force (lb).

Understanding Beam Load Capacity

Beam load capacity is the maximum load a beam can carry before the internal bending stress exceeds the material's allowable limit. It is controlled by three variables: span length, section modulus, and allowable bending stress. Doubling the span cuts the point load capacity in half, while doubling the section depth increases capacity by roughly four times because section modulus scales with the square of depth.

Two separate limits must be satisfied. The strength limit checks that the actual bending stress (M/S) does not exceed Fb from AISC 360-22 or NDS 2018. The serviceability limit checks that deflection does not exceed L/360, L/240, or L/480 per IBC 2024 Table 1604.3. A beam can pass the strength check and still fail the deflection check, particularly on long spans. For combined loading scenarios, the concrete load-bearing capacity calculator covers axial plus bending interaction.

Maximum shear force controls design at support points and governs for short, heavily loaded beams. For simply supported beams under UDL, maximum shear equals wL/2 and occurs directly at each support. For steel beams, allowable shear stress is 0.4 × Fy per AISC 360-22 Section G2.1. For wood, allowable horizontal shear stress (Fv) from NDS 2018 ranges from 135 psi for Douglas Fir to 175 psi for Southern Pine.

Span-to-Depth Ratio Guidelines

Typical Span-to-Depth Ratios for Preliminary Beam Sizing
Beam Type	Material	Span/Depth Ratio	Source
Simply Supported Floor Beam	Steel	20–24	AISC Design Guide 3
Simply Supported Floor Beam	Wood	12–18	NDS Commentary 2018
Cantilever	Steel	8–12	AISC Design Guide 3
Roof Beam (light)	Steel	24–30	AISC Design Guide 3
Glulam Roof Beam	Glulam	14–20	APA EWS Data File E20W

Sample Load Capacity Calculations

These worked examples follow AISC 360-22 and NDS 2018 formulas. For rebar sizing in the supporting concrete structure, the rebar spacing calculator handles that step separately.

Example 1 — Steel Floor Beam, Simply Supported

Span	18 ft (216 in)
Section	W12x35 (Sx = 46.8 in³)
Material	A36 Steel (Fb = 23,760 psi)
Load Type	UDL
Application	Floor Live Load (L/360)

w_allow = 2,285 lb/ft

Calculation: w = 8 × 23,760 × 46.8 / 216² = 189.7 lb/in = 2,275 lb/ft. Deflection check: I = 285 in⁴; δ_allow = 216/360 = 0.600 in; governs at ~1,600 lb/ft for a deflection-controlled result.

Example 2 — Wood Cantilever Beam

Span	6 ft (72 in)
Section	4x12 Lumber (S = 73.8 in³)
Material	Douglas Fir No. 2 (Fb = 875 psi)
Load Type	Point Load at Free End
Application	Cantilever L/180

P_allow = 895 lb

Calculation: P = Fb × S / L = 875 × 73.8 / 72 = 895 lb. Deflection: δ = PL³/(3EI) = 895 × 72³ / (3 × 1,700,000 × 415) = 0.298 in; L/180 = 0.400 in. PASS.

Example 3 — Steel A992 Fixed-Fixed Beam

Span	24 ft (288 in)
Section	W16x36 (Sx = 56.5 in³)
Material	A992 Steel (Fb = 33,000 psi)
Load Type	UDL
Application	Floor Total Load (L/240)

w_allow = 2,701 lb/ft

Calculation: w = 12 × 33,000 × 56.5 / 288² = 270.1 lb/in = 3,241 lb/ft. Deflection check I = 448 in⁴; δ_allow = 288/240 = 1.200 in governs at 2,700 lb/ft. PASS at 2,700 lb/ft.

Common Beam Load Calculation Mistakes

❌ Using the wrong bending moment formula for the support condition

A cantilever with a point load at the free end has M = PL, while a simply supported beam under the same load has M = PL/4. Using the wrong formula overstates capacity by a factor of 4 for cantilevers. Per AISC Steel Construction Manual Table 3-22, each support condition and load pattern produces a distinct moment coefficient.

❌ Confusing section modulus (S) with moment of inertia (I)

Section modulus S = I/c controls bending strength: M_allow = Fb × S. Moment of inertia I controls deflection: δ = PL³/(48EI). Using I in place of S in the bending formula overstates capacity dramatically. For a W12x35, S = 46.8 in³ but I = 285 in⁴, a factor of 6 difference.

❌ Applying beam span in feet instead of inches in formulas

The bending moment formula M = PL/4 requires L in inches when P is in pounds and Fb is in psi. Using L = 20 ft instead of 240 in understates the moment by a factor of 12 and falsely overstates the safe load. This calculator handles unit conversion automatically.

❌ Ignoring deflection as a secondary limit

Many calculations stop after the bending stress check. Per IBC 2024 Table 1604.3, deflection governs most real-world floor beams. A W14x22 over 20 ft will pass the bending stress check at 2,000 lb total UDL but deflect 0.82 in under that load, exceeding the L/360 limit of 0.667 in. Deflection, not stress, is the binding constraint on long-span beams.

❌ Using Fb without checking lateral bracing requirements

AISC 360-22 Section F2 allows Fb = 0.66Fy only when the compression flange is fully braced against lateral-torsional buckling. If the beam has no mid-span bracing, the allowable stress must be reduced using the lateral-torsional buckling provisions in AISC 360-22 Section F2.2. Unbraced compact beams can see Fb reductions of 30 to 50 percent on spans over 15 feet.

Sizing tip: For steel floor beams, target a span-to-depth ratio of 20-24. A 20-foot beam wants a depth of approximately 10-12 inches, pointing to a W10 or W12 series. This rule often produces a deflection-controlled design that passes both the strength and serviceability checks simultaneously. See AISC Design Guide 3 for full guidance on serviceability-controlled steel beam design.

IBC 2024 Deflection Limits — Quick Reference

Both the strength check and the deflection check must pass independently. The slab load calculator applies the same L/360 and L/240 limits for two-way concrete slabs.

IBC 2024 Table 1604.3 Maximum Allowable Deflection
Element	Load Case	Limit	20 ft Span Example
Floor beams	Live load (L)	L/360	0.667 in
Floor beams	Total load (D+L)	L/240	1.000 in
Roof beams	Live load (L)	L/360	0.667 in
Roof beams	Total load (D+L)	L/240	1.000 in
Brittle finishes (tile, plaster)	Live load (L)	L/480	0.500 in
Cantilevers	Live load (L)	L/180	1.333 in (10 ft cant.)

Source: IBC 2024 Table 1604.3. L is the clear span in inches. For steel members, dead-load deflection may be set to zero per Table 1604.3 footnote (g).

Frequently Asked Questions

What is the maximum safe load for a W12x35 steel beam over 20 feet? +

For a simply supported W12x35 (Sx = 46.8 in³) in A36 steel (Fb = 23,760 psi) under UDL over a 20-foot span: w_allow = 8 × 23,760 × 46.8 / 240² = 154.9 lb/in = 1,859 lb/ft for bending strength alone. The deflection check using I = 285 in⁴ reduces this to roughly 1,400 lb/ft for the L/360 floor limit. Use this calculator to confirm both checks simultaneously.

How much stronger is a fixed-fixed beam than a simply supported beam? +

A fixed-fixed beam carries 2 to 3 times more load than a simply supported beam of the same span and section. Under a center point load, the bending moment coefficient changes from PL/4 to PL/8, meaning the same beam can carry twice the point load at the same stress. Under UDL, the coefficient changes from wL²/8 to wL²/12, a 50% increase in capacity. Deflection also decreases 4x. These advantages require the end connections to be designed as moment connections, which adds fabrication cost.

Can I use this calculator for a composite steel-concrete beam? +

This calculator applies to non-composite beams, where the steel section alone resists all bending. For composite beams (steel beam acting together with a concrete slab via shear studs), the effective section modulus is higher and must be calculated using the transformed section method per AISC 360-22 Chapter I. Composite floor beams can achieve 30 to 50 percent more capacity than the steel section alone. For the concrete component, refer to the concrete flexural strength calculator.

How do I calculate shear capacity for a steel beam? +

Per AISC 360-22 Section G2.1, nominal shear capacity is Vn = 0.6 × Fy × Aw × Cv1, where Aw = d × tw (web area) and Cv1 = 1.0 for most standard W-shapes with h/tw ≤ 2.24√(E/Fy). For A36 steel, h/tw must not exceed 53.9 for Cv1 = 1.0. For ASD, allowable shear Va = Vn / Ωv = Vn / 1.67. A W12x35 with Aw = 12.5 × 0.30 = 3.75 in² has Va = 0.6 × 36,000 × 3.75 / 1.67 = 48,500 lb, which rarely governs on spans over 10 feet under normal floor loads.

What is the difference between ASD and LRFD for beam design? +

Allowable Stress Design (ASD) limits the actual bending stress (M/S) to an allowable value (Fb = 0.66Fy for compact sections with full bracing). Load and Resistance Factor Design (LRFD) amplifies loads using factors (1.2D + 1.6L) and checks the beam against its full nominal capacity reduced by a resistance factor (φb = 0.90). Both are permitted under AISC 360-22. ASD is common for simple projects because it uses unfactored service loads directly. LRFD is more efficient on complex projects where dead and live loads differ significantly. For equivalent spans and loads, ASD typically gives a slightly more conservative result than LRFD by about 10 to 15 percent.

How does wood beam load capacity compare to steel? +

Steel has a significantly higher strength-to-weight ratio. An A36 W12x35 weighing 35 lb/ft can carry roughly 25 to 30 times the bending moment of a 2x12 Douglas Fir board at 3 lb/ft. However, wood is more practical for residential spans under 20 feet because it is easier to cut, fasten, and frame on site. For long residential spans (over 16 feet), LVL and glulam bridge the gap, with Fb values of 2,400 to 2,600 psi versus 875 psi for dimension lumber. The concrete beam calculator covers reinforced concrete beam options.

Does beam self-weight affect the safe load capacity? +

Yes. Self-weight acts as an additional UDL that consumes part of the beam's bending capacity. A W14x48 beam weighing 48 lb/ft over a 24-foot span generates a self-weight moment of 48 × 288² / 8 = 497,664 lb-in, which must be subtracted from the total allowable moment before calculating safe applied load. For steel beams, self-weight typically consumes 5 to 15 percent of total capacity on spans under 30 feet. Use the self-weight field in Advanced Options to include this in the calculation.

Sources and Methodology

AISC Steel Construction Manual, 16th Edition (2022) — Table 1-1 W-shape section properties, Table 3-22 beam diagrams and formulas, Chapter F allowable bending stress. aisc.org/manual
AISC 360-22 Specification for Structural Steel Buildings — Section F2 flexural capacity of compact sections; Section G2.1 shear capacity. aisc.org/360-22
IBC 2024 International Building Code — Table 1604.3 allowable deflections for structural members. iccsafe.org
NDS 2018 National Design Specification for Wood Construction — Supplement Tables 4A-4B reference design values for sawn lumber; Table 5A for glulam. awc.org
Roark's Formulas for Stress and Strain, 8th Edition (2012) — Table 8.1 cantilever beams; Table 8.2 fixed-fixed beams. Warren Young, Richard Budynas, Ali Sadegh.
APA EWS Data File E20W — Span-to-depth ratios and design values for structural glulam beams. apawood.org

Last reviewed May 2026. Built by Muhammad Ramzan Babar, physics researcher (PhD candidate). Reviewed by site author.

⚠ Engineering Disclaimer

This calculator provides estimates for planning purposes. For permitted structural work, foundations, multi-story construction, retaining walls over 4 feet, and commercial projects, calculations must be verified by a licensed structural engineer per IBC 2024 Section 1604. ConcreteCalculate.com is not liable for structural decisions made from these estimates.

Allowable bending stress values assume compact sections with full lateral bracing of the compression flange per AISC 360-22 Section F2. Unbraced beams require lateral-torsional buckling checks that reduce allowable stress. Wood beam values assume dry service conditions, normal load duration, and no size factor adjustments per NDS 2018 Section 4.3.

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Beam Load Calculator 2026 Simply Supported, Cantilever & Fixed Beams