Bulb flat geometry and options
Enter dimensions, choose units, then calculate section modulus and inertia.
Formula used
This calculator models a bulb flat as a composite section: a rectangle (the flat) plus a semicircle (the bulb) attached to the rectangle edge. Composite centroid and second moments of area are found using the parallel-axis theorem.
| Step | Expression | Meaning |
|---|---|---|
| Areas | A = A₁ + A₂ | Rectangle area plus bulb area. |
| Centroid | x̄ = Σ(Aᵢ xᵢ)/A, ȳ = Σ(Aᵢ yᵢ)/A | Weighted average of component centroids. |
| Inertia | I = Σ(Iᵢ + Aᵢ dᵢ²) | Parallel-axis theorem for composite sections. |
| Section modulus | Z = I / c | c is distance to extreme fiber. |
| Elastic moment capacity | M = Zmin · Fy | Uses minimum modulus for conservative bending. |
- The bulb is a semicircle with radius R.
- The semicircle is attached at x = w and can be vertically offset by Δy.
- Results are elastic properties; no plastic redistribution is included.
How to use this calculator
- Select your preferred unit system.
- Enter the flat width w and thickness t.
- Enter the bulb radius R. Use a vertical offset only if needed.
- Optionally add yield strength and a safety factor for allowable moment.
- Press Calculate. Results appear above the form.
- Use Download CSV or Download PDF for reporting.
Example data table
Sample dimensions and typical outputs (elastic properties). These examples help you sanity-check your entries.
| Units | w | t | R | Δy | Approx. Zx(min) | Approx. Zy(min) |
|---|---|---|---|---|---|---|
| mm | 120 | 10 | 18 | 0 | ~ 18,000 mm³ | ~ 62,000 mm³ |
| mm | 160 | 12 | 22 | 0 | ~ 34,000 mm³ | ~ 130,000 mm³ |
| in | 6.0 | 0.5 | 0.9 | 0 | ~ 2.3 in³ | ~ 9.0 in³ |
Technical article
1) Bulb flats as efficient stiffeners
Bulb flats are widely used as stiffeners because the bulb places material away from the neutral axis. Compared with a plain flat bar of similar mass, bending stiffness can increase noticeably. This tool models a bulb flat as a rectangle plus a semicircular bulb for fast, repeatable property estimates.
2) Section modulus and bending stress
Elastic section modulus links geometry to stress: σ = M/Z. The calculator reports Z about x–x (strong axis) and y–y (weak axis). When the shape is not symmetric, top and bottom (or left and right) moduli differ, so the minimum value is the safe choice for checks.
3) Inertia values used for deflection
Second moments Ixx and Iyy govern deflection through formulas such as δ ∝ 1/EI. Even if strength is adequate, low inertia can cause serviceability issues. Reporting both Ixx and Iyy helps you evaluate stiffness in the primary bending direction and the lateral direction.
4) Typical unit expectations
Modulus has length³ units (mm³, in³). Many medium stiffeners fall in the 10,000–100,000 mm³ range for Zx(min), while imperial work may show a few in³ to a few tens of in³. Always keep your stress units consistent with your modulus units when computing capacity.
5) Geometry sensitivity: w, t, and R
Increasing thickness t boosts the rectangle’s Ixx strongly because the term contains t³. Increasing width w boosts Iyy strongly because it contains w³. A larger bulb radius R adds area on the bulb side and increases distances to extreme fibers, which can lift both Zx and Zy.
6) Centroid shift and extreme fibers
The centroid is the area-weighted average of the rectangle and bulb centroids. As R grows, x̄ shifts toward the bulb. If you set a vertical offset Δy, ȳ shifts too. These shifts change the extreme-fiber distances c used in Z = I/c, so asymmetry should not be ignored.
7) Elastic moment capacity with Fy
With yield strength Fy in MPa (N/mm²), elastic moment capacity is estimated as M = Zmin · Fy and shown in kN·m. The allowable moment divides by your safety factor. This is a simplified elastic check; design standards may require buckling and connection verification beyond section properties.
8) Using examples to validate inputs
Use the example table as a reasonableness check. If your result is far off, confirm the selected units, verify that w and t are entered correctly, and ensure Δy is not accidentally set. For final design, compare against rolled-section tables or CAD section-property reports.
FAQs
1) Is this a plastic section modulus calculator?
No. It returns elastic section modulus using Z = I/c. Plastic modulus depends on the full stress block and needs a different method.
2) What does Δy do?
Δy shifts the bulb center vertically relative to the flat midline. It changes the composite centroid and the top/bottom extreme-fiber distances.
3) Which modulus should I use for design?
Use the minimum modulus for the bending direction you are checking. That conservative value limits stress when the section is asymmetric.
4) Why are top and bottom moduli different?
If the centroid is not centered between extremes, c-top differs from c-bottom. Since Z = I/c, different c values produce different moduli.
5) Can I use different materials?
Yes. Geometry is unchanged. For capacity, enter the correct yield strength and apply the requirements of your governing design code.
6) Is the semicircle bulb exact for rolled shapes?
It is an approximation. Real rolled bulb flats may include fillets and specific contours. Use mill tables for final sign-off.
7) My capacity looks high. What should I check?
Confirm units and Fy in MPa, and confirm the axis selection. Remember elastic capacity ignores buckling and connection effects.