Beam Load Capacity Calculator

Maximum beam load from section modulus, span and allowable bending stress for common simply-supported and cantilever load cases. Metric and imperial. Free, no signup.

Inputs

View results

Load case

Support and loading case used for maximum bending moment.

Span length (L)

Clear span or cantilever length for the selected case.

Section modulus (S)

Elastic section modulus about the bending axis.

cm³

Allowable bending stress (sigma_allow)

Material allowable or design bending stress before applying the safety factor.

MPa

Safety factor (N)

Design stress = allowable stress / safety factor.

Applied load to check (F or W)

Total point load or total uniform load to compare against the allowable load.

Results

Default result

Edit inputs

Allowable total load(F_allow)

8,000N

Pass

8 kN · 1,798 lbf

Derived from M_allow = (allowable stress / safety factor) * S.

Load that reaches design bending stress.

Also computed

Applied utilization(U)0.25

Applied bending stress(sigma)25MPa

Required section modulus(S_req)5cm³

Allowable moment(M_allow)2,000N·m

Applied moment(M)500N·m

Allowable load / span(w_eq)8N/mm

Method notes 3 notes

This is an elastic bending-stress capacity check using sigma = M/S. It does not check deflection, shear, bearing, web crippling, local buckling or lateral-torsional buckling.
Uniform-load cases use total load W across the span. The load/span output is the equivalent uniform line load for quick comparison.
Use the section modulus about the actual bending axis and apply code-specific resistance factors where required.

Beam load capacity starts with elastic bending stress, sigma = M/S. The calculator reduces allowable stress by your safety factor, computes M_allow = sigma_design·S, then converts that moment into total load for simply supported or cantilever point/uniform load cases. It also checks an applied load utilization.

How to use this calculator

Choose load case. Select the support condition and whether the load is point or uniform.
Enter span. Use the clear span or cantilever length.
Enter section modulus. Use S about the actual bending axis.
Set allowable stress. Enter allowable bending stress and safety factor.
Check applied load. Compare the applied load utilization with the allowable load.

How it works

Elastic bending stress is moment divided by section modulus: sigma = M / S The calculator first reduces allowable stress by the safety factor, then computes M_allow = sigma_design x S.

The selected load case converts allowable moment to load. For a simply supported center point load, M = F x L / 4. For a simply supported total uniform load, M = W x L / 8.

Worked example

Verified against the live calculator

A beam with S = 20 cm^3 (20,000 mm^3), allowable bending stress 150 MPa and safety factor 1.5 uses design stress 100 MPa.

The allowable moment is 100 x 20,000 = 2,000,000 N*mm. On a 1,000 mm simply supported span with center load, allowable load is 4 x 2,000,000 / 1,000 = 8,000 N.

Frequently asked questions

How do you calculate allowable beam load from section modulus?

First find allowable moment from M_allow = sigma_design * S, where sigma_design is allowable stress divided by safety factor. Then convert moment to load using the selected beam case.

What moment formula is used for a simply supported center load?

For a simply supported beam with a center point load, maximum moment is M = F*L/4, so allowable load is F = 4*M_allow/L.

What moment formula is used for a uniform load?

For a simply supported beam with total uniform load W, maximum moment is M = W*L/8, so allowable total load is W = 8*M_allow/L.

Does this check deflection?

No. It is a bending-stress capacity check. Use the beam deflection calculator to check deflection and span/deflection ratio.

Can this be used for square tube or I-beams?

Yes if you enter the correct elastic section modulus about the bending axis. Use the section modulus calculator first if you do not have S.

Is this a code design calculator?

No. It does not include code resistance factors, lateral-torsional buckling, local buckling, shear, web crippling or connection checks.

Method & assumptions

Elastic bending only: sigma = M / S.
Uniform-load inputs are total load over the span, not load per unit length.
Section modulus must match the bending axis and section orientation.
For LVL span checks with plies, live/dead line loads and deflection limits, use the LVL beam calculator.
Deflection, shear, local buckling, lateral-torsional buckling, bearing, web crippling, fatigue and code factors are not included.

Beam Load Capacity Calculator

Calculator