| Span (m) | Spacing (mm) | Section (mm) | DL (kN/m²) | LL (kN/m²) | Point (kN) | Typical note |
|---|---|---|---|---|---|---|
| 3.6 | 400 | 50×200 | 0.75 | 2.0 | 0 | Residential floor baseline |
| 4.2 | 450 | 50×225 | 1.00 | 2.0 | 1.5 | Heavier finishes plus small point load |
| 5.0 | 400 | 63×250 | 0.90 | 3.0 | 0 | Higher live load assumption |
| 3.0 | 600 | 38×184 | 0.60 | 1.5 | 0 | Short span, wider spacing |
| 6.0 | 400 | 75×300 | 1.20 | 4.0 | 2.0 | Long span with demanding loads |
- Tributary width = spacing (m).
- Uniform line load on one joist: w = (DL + LL) × trib + line (kN/m).
- Max moment: M = wL²/8 + PL/4.
- Max shear: V = wL/2 + P/2.
- Section modulus (rectangular): S = b h²/6.
- Second moment (rectangular): I = b h³/12.
- Bending stress: fb = M/S; allowable Fb′ = Fb × factors.
- Shear stress (rectangular): fv = 1.5V/(b h); allowable Fv′ similar.
- Deflection: δ = 5wL⁴/(384EI) + PL³/(48EI), checked against L/ratio.
- Enter span, spacing, and joist breadth and depth.
- Set dead and live loads that match your project.
- Add any line load or midspan point load if needed.
- Input material properties and adjustment factors from your reference.
- Choose a deflection limit that suits the floor performance target.
- Press calculate and review bending, shear, and deflection checks.
- Use CSV or PDF exports to document the run.
Load components and tributary width
Area loads are entered as dead load and live load in kN/m². The calculator converts them to a line load on one joist using tributary width equal to spacing (m). Add any extra line load for partitions, nib walls, or supported edges.
Bending demand and section capacity
Maximum moment for a simply supported joist is M = wL²/8, plus PL/4 when a midspan point load is present. Required bending stress is fb = M/S, where S = b h²/6 for a rectangular section. Allowable Fb′ applies adjustment factors to the reference Fb value.
Shear check at supports
Support reaction governs shear: V = wL/2 plus P/2. The rectangular shear stress approximation fv = 1.5V/(b h) is commonly used for quick checks. If shear utilization controls, increasing breadth b or reducing loads typically improves results.
Service deflection and comfort limits
Floor serviceability is driven by deflection. The calculator uses δ = 5wL⁴/(384EI) + PL³/(48EI) and compares it to a chosen limit such as L/360 or L/480. Stiffness grows rapidly with depth because I scales with h³, so modest depth changes can be meaningful.
Worked example snapshot
The example below highlights typical magnitudes for uniform load, moment, shear, bending stress, and deflection. Use it as a reasonableness check before exporting a report or adjusting joist spacing for constructability.
For preliminary sizing, keep utilizations below about 0.90 to allow for detailing, notching, and construction tolerances.
| Span (m) | Spacing (mm) | Section (mm) | DL | LL | Point | w (kN/m) | M (kN·m) | V (kN) | fb (MPa) | δ (mm) |
|---|---|---|---|---|---|---|---|---|---|---|
| 4.0 | 400 | 50×200 | 0.75 | 2.0 | 0.0 | 1.10 | 2.20 | 2.20 | 6.60 | 11.0 |
| 4.8 | 400 | 50×225 | 0.75 | 2.0 | 1.5 | 1.10 | 4.97 | 3.39 | 11.78 | 23.3 |
FAQs
1) What does “tributary width” mean here?
It is the floor width assigned to one joist. This tool uses joist spacing as tributary width, converting area loads (kN/m²) into a line load (kN/m) on that joist.
2) Should I include the joist self-weight in dead load?
Yes, if it is not already covered. Many projects include self-weight within the dead load allowance. Add a small margin when finishes, ceilings, or services are uncertain.
3) Why does depth change results so much?
Bending and deflection depend strongly on depth. Section modulus scales with h² and stiffness with h³, so even a modest increase in depth can significantly reduce stress and deflection.
4) How do I pick Fb, Fv, and E?
Use graded timber values from your supplier data, code tables, or project specification. Apply adjustment factors consistent with your design standard and service conditions.
5) What if I have a point load that is not at midspan?
This version assumes a midspan point load for a conservative, simple check. For off-center loads, moments and deflections change; consider a more detailed analysis or an engineer review.
6) What deflection limit is typical?
L/360 is commonly used for general floors, while L/480 can suit stiffer performance targets. Always follow the requirement for your occupancy, finishes, and local practice.
7) Does “PASS” mean it is code-compliant?
No. “PASS” only indicates these simplified checks meet the chosen allowables and deflection ratio. You must still confirm load combinations, detailing, bearing, vibration, and local code rules.