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Wood Beam Span Screening Calculator — result sheet
Screen a simply supported rectangular beam under a uniform load using entered elastic modulus, allowable bending stress, and deflection ratio.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: I = bh³/12; Mmax = wL²/8; σ = Mmax(h/2)/I; δmax = 5wL⁴/(384EI). Stress-limited L = √(4σ_allow bh²/(3w)); deflection-limited L = ∛(384EI/(5wn)); governing span = min of both.
This bounded screen compares two elastic limits for a simply supported rectangular beam carrying a uniform line load: an entered bending-stress limit and an entered L/n deflection limit. The governing span is the smaller of the two, with the assumptions kept visible.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Beam width — mm; minimum 1.0E-6; maximum 1000000
- Beam depth — mm; minimum 1.0E-6; maximum 1000000
- Uniform service load — N/m; minimum 1.0E-6; maximum 1000000000
- Entered allowable bending stress — MPa; minimum 1.0E-6; maximum 1000000
- Young's modulus — GPa; minimum 1.0E-6; maximum 1000000
- Deflection limit ratio L/n — minimum 1; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Beam width | 90 |
| Beam depth | 190 |
| Uniform service load | 2000 |
| Entered allowable bending stress | 8 |
| Young's modulus | 10 |
| Deflection limit ratio L/n | 360 |
The screen reports separate stress- and deflection-limited spans and uses the smaller one as the governing idealized span.
Assumptions and limits
- The beam is prismatic, simply supported, rectangular, and loaded uniformly over the full span.
- The entered allowable stress and Young's modulus describe the selected material and design context; no wood species or code table is guessed.
- Small-deflection Euler–Bernoulli bending is used; self-weight, shear deformation, lateral stability, connections, bearing, vibration, creep, fire, and load combinations are excluded.
- The result is an educational screening estimate, not a structural design, permit document, or safety approval.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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