Bulb Flat Section Modulus Calculator Form
Example Data Table
| Case | Bulb Position | Flat Width (mm) | Flat Thickness (mm) | Bulb Width (mm) | Bulb Height (mm) | Cap Radius (mm) | Area (mm²) | Centroid from Bottom (mm) | Ix (mm⁴) | Min Section Modulus (mm³) |
|---|---|---|---|---|---|---|---|---|---|---|
| Sample 1 | Top | 180.00 | 12.00 | 80.00 | 35.00 | 40.00 | 7,473.27 | 34.30 | 4,600,596.66 | 87,301.67 |
| Sample 2 | Top | 150.00 | 10.00 | 60.00 | 30.00 | 30.00 | 4,713.72 | 26.95 | 1,905,693.95 | 44,270.05 |
| Sample 3 | Bottom | 200.00 | 14.00 | 90.00 | 45.00 | 45.00 | 10,030.86 | 62.54 | 8,873,802.81 | 141,882.42 |
These examples use a composite model with a plate rectangle, a bulb stem rectangle, and a semicircular cap.
Formula Used
This calculator models the bulb flat as three aligned components: a flat plate rectangle, a bulb stem rectangle, and a semicircular cap.
1) Component areas
Rectangle area:
A = b × h
Semicircle area:
A = 0.5 × π × r²
2) Composite centroid
ȳ = Σ(Aᵢ × yᵢ) / ΣAᵢ
3) Moment of inertia about the composite centroid
Iₓ = Σ(Icᵢ + Aᵢ × dᵢ²)
where dᵢ = yᵢ - ȳ.
4) Rectangle and semicircle inertia terms
Rectangle:
Ic = b × h³ / 12
Semicircle about its own centroidal axis:
Ic = r⁴ × (π/8 - 8/(9π))
5) Elastic section modulus
Ztop = Iₓ / ctop
Zbottom = Iₓ / cbottom
6) Bending stress and elastic moment capacity
σ = M / Z
Melastic = Fy × Zmin
Use consistent force and length units. For example, if length is mm and force is N, enter moment in N·mm and yield stress in N/mm².
How to Use This Calculator
- Enter the flat width and flat thickness of the base plate.
- Enter the bulb stem width and height.
- Leave cap radius blank to automatically set it to half the bulb width.
- Choose whether the bulb sits on the top or bottom side.
- Select consistent force and length units before entering moment or yield strength.
- Click the calculate button to show results below the header and above the form.
- Review centroid, inertia, and top or bottom section modulus values.
- Use the CSV or PDF buttons to export the final summary.
FAQs
1) What is bulb flat section modulus?
It is the elastic bending capacity indicator for a bulb flat shape. A larger section modulus means the section resists bending stress more effectively for the same applied moment.
2) Why are top and bottom section modulus values different?
Bulb flats are usually unsymmetrical through depth. Because the neutral axis is not centered, the distance to the top and bottom fibers differs, giving different elastic section modulus values.
3) Why does the calculator show centroid and moment of inertia?
The centroid locates the neutral axis. The moment of inertia measures how the area is distributed about that axis. Both quantities are required before section modulus and bending stress can be calculated.
4) Can I leave the cap radius empty?
Yes. The calculator then uses bulb width divided by two. That assumption produces a semicircular cap matching the bulb width and usually gives the smoothest plotted shape.
5) Which units should I use for moment and stress?
Use a consistent set. If length is mm and force is N, enter moment in N·mm and yield strength in N/mm². The displayed stress and moment capacity follow the same chosen unit system.
6) What changes when the bulb is placed at the bottom?
The geometry is mirrored vertically. That changes centroid location, top and bottom distances, and the controlling section modulus. The inertia magnitude can also shift because area moves relative to the neutral axis.
7) Is this suitable for stiffener or plating checks?
It is useful for preliminary section-property work, comparison studies, and education. Final design should still follow the relevant structural code, fabrication tolerances, and any exact manufacturer profile dimensions.
8) Does the calculator compute plastic section modulus?
No. This version computes elastic section modulus, bending stress, and elastic moment capacity only. Plastic modulus requires a separate plastic neutral axis calculation and different compression-tension area balancing.