How it works
Check the arithmetic of an idealized simple beam with a specified section and uniformly distributed total load.
This is the Canada planning view, with monetary inputs and outputs in CAD. A currency label does not establish that a tax rate, construction price, coverage rule or legal limit has been verified locally. The inputs and limitations below describe the actual scope.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
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?unitSystem=Measurement systemChoice · Optional · Default: metric · Accepted values: imperial, metric
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?span=Simply supported clear spanNumber · Required · Default: 4
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?uniformLoad=Specified total uniform loadNumber · Required · Default: 10
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?elasticModulus=Material elastic modulusNumber · Required · Default: 200
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?sectionModulus=Section modulus about bending axisNumber · Required · Default: 500
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?secondMoment=Second moment of area about bending axisNumber · Required · Default: 10,000
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?unitRate=Material price per length unitMoney · Required · Default: 0
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?laborCost=Total labor allowanceMoney · Required · Default: 0
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?deliveryCost=Delivery allowanceMoney · Required · Default: 0
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?otherCost=Other fixed costsMoney · Required · Default: 0
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?costMultiplier=Material/labor multiplierNumber · Required · Default: 1
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?spreadPercent=Low/high sensitivity around the entered totalPercentage · Required · Default: 15
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?taxRate=Explicit tax allowancePercentage · Required · Default: 0
Outputs
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momentMaximum bending momentNumber
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reactionReaction at each simple supportNumber
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stressElastic bending stressNumber
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deflectionElastic midspan deflectionNumber
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materialCostMaterial costCurrency · Currency: CAD
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laborCostLabor allowanceCurrency · Currency: CAD
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deliveryCostDelivery allowanceCurrency · Currency: CAD
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otherCostOther specified costsCurrency · Currency: CAD
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taxEntered tax allowanceCurrency · Currency: CAD
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lowLow cost scenarioCurrency · Currency: CAD
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midMiddle cost scenarioCurrency · Primary output · Currency: CAD
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highHigh cost scenarioCurrency · Currency: CAD
Formula
M = wL²/8; V = wL/2; elastic stress = M/Z; deflection = 5wL⁴/(384EI).
Calculations retain numeric precision internally. Displayed values are rounded for readability. Quantities that must be purchased as whole units are rounded up only where the formula explicitly requires it.
Read the inputs before calculating
- Simply supported clear span: Enter the quantity described by the label. The measurement selector converts this physical quantity; it does not change the underlying scenario.
- Specified total uniform load: Enter the quantity described by the label. The measurement selector converts this physical quantity; it does not change the underlying scenario.
- Material elastic modulus: Enter the quantity described by the label. The measurement selector converts this physical quantity; it does not change the underlying scenario.
- Section modulus about bending axis: Enter the quantity described by the label. The measurement selector converts this physical quantity; it does not change the underlying scenario.
- Second moment of area about bending axis: Enter the quantity described by the label. The measurement selector converts this physical quantity; it does not change the underlying scenario.
- Material price per length unit: Zero means unpriced, not free. Enter a current, scoped supplier quote. This is a price per displayed unit, so the price converts inversely to the physical quantity.
- Total labor allowance: Enter the quantity described by the label.
- Delivery allowance: Enter the quantity described by the label.
- Other fixed costs: Enter the quantity described by the label.
- Material/labor multiplier: Use a verified regional index only when supplied. 1 is an unadjusted scenario, not a researched index.
- Low/high sensitivity around the entered total: Enter the quantity described by the label.
- Explicit tax allowance: Enter the quantity described by the label.
Reproducible worked example
The following is a fictional arithmetic example, not a local quote, a verified claimant or a market forecast. Its values are included so the formula can be checked. The form does not automatically confirm any verification checkbox.
| Input | Example value |
|---|---|
| Simply supported clear span (m) | 4 |
| Specified total uniform load (kN/m) | 10 |
| Material elastic modulus (GPa) | 200 |
| Section modulus about bending axis (cm³) | 500 |
| Second moment of area about bending axis (cm⁴) | 10,000 |
| Material price per length unit (/m) | 0 |
| Total labor allowance | 0 |
| Delivery allowance | 0 |
| Other fixed costs | 0 |
| Material/labor multiplier | 1 |
| Low/high sensitivity around the entered total | 15 |
| Explicit tax allowance | 0 |
| Output | Calculated result |
|---|---|
| Maximum bending moment | 20 kN·m |
| Reaction at each simple support | 20 kN |
| Elastic bending stress | 40 MPa |
| Elastic midspan deflection | 1.6667 mm |
| Material cost | CAD 0 |
| Labor allowance | CAD 0 |
| Delivery allowance | CAD 0 |
| Other specified costs | CAD 0 |
| Entered tax allowance | CAD 0 |
| Low cost scenario | CAD 0 |
| Middle cost scenario | CAD 0 |
| High cost scenario | CAD 0 |
Interpreting a changed assumption
Start with one complete scenario and change only one input when diagnosing a difference. Recheck units, the period of every rate, whether an amount is recurring or one-off, and whether a cost is already included elsewhere. A larger calculated benefit is not evidence that an assumption is more likely to occur.
Limitations
- Quantities and user-entered costs are planning estimates. Drawings, manufacturer instructions, local permits and qualified site-specific design take precedence.
- Material is unpriced. A zero material price is not evidence that the material is free.
- Prices and the tax allowance are user-entered planning assumptions, not a verified local quote. Low/high outputs are sensitivity scenarios, not market confidence limits.
- The multiplier applies only to material and labor; delivery and fixed costs are not multiplied.
- Not a beam-selection, structural approval or safety result. Buckling, shear, connections, lateral restraint, load combinations, vibration, fire and local code checks are omitted. Include self-weight in the entered load.
Frequently asked questions
What does this Simply Supported Steel Beam Screening result represent?
Check the arithmetic of an idealized simple beam with a specified section and uniformly distributed total load. It applies the displayed formula to your inputs; it does not infer omitted facts.
Are the starting amounts verified Canada prices or legal rules?
No. Numeric defaults are illustrative unless an input or dated reference explicitly identifies a researched component. Currency is CAD; local quotes, eligibility and unsupported rules must be entered and verified separately.
What must I check before relying on the result?
Quantities and user-entered costs are planning estimates. Drawings, manufacturer instructions, local permits and qualified site-specific design take precedence.
Can I compare or share different assumptions?
Change one assumption at a time and use the browser-local project or share controls. A shared URL contains the encoded input values; do not include information you do not wish to disclose.
Sources and reference scope
- NIST unit conversion guidance — retrieved 2026-09-24. Unit definitions; geometry and financial arithmetic in these worksheets are explicitly stated.
- DOE insulation overview — retrieved 2026-09-24. Insulation and thermal resistance concepts; not structural or code approval.
These references support only their stated scope. They are not evidence that every local rule or price needed by the master expansion has been loaded.