Calculator Inputs
Enter each rectangular solid or opening. Use x and y as the lower-left corner coordinates. Material factor lets you transform areas for composite sections.
Example Data Table
This sample represents a T-like section with a small opening.
| Label | Type | Width | Height | x from Left | y from Bottom | Material Factor |
|---|---|---|---|---|---|---|
| Flange | Solid | 300 | 100 | 0 | 300 | 1 |
| Web | Solid | 100 | 300 | 100 | 0 | 1 |
| Opening | Void | 40 | 60 | 130 | 120 | 1 |
Formula Used
For each rectangular component, area is: A = b × h
Equivalent transformed area is: A′ = s × n × A
Here, s = +1 for solids and s = -1 for voids. n is the material factor.
Component centroid coordinates are: cx = x + b/2 and cy = y + h/2
Composite centroid, or neutral axis location, is: x̄ = Σ(A′cx) / ΣA′ and ȳ = Σ(A′cy) / ΣA′
Local second moments for a rectangle are: Ix,cg = b h³ / 12 and Iy,cg = h b³ / 12
Using the parallel-axis theorem: Ix = Σ(Ix,cg′ + A′dy²) and Iy = Σ(Iy,cg′ + A′dx²)
Section modulus is: S = I / c
How to Use This Calculator
- Enter one row for each rectangular solid or rectangular opening.
- Use width and height in a consistent unit system.
- Set x and y as the lower-left corner of each rectangle.
- Choose Solid for material and Void for holes.
- Keep material factor as 1 unless transformed sections are required.
- Click Calculate Neutral Axis to view centroid, inertia, and section modulus.
- Use the Plotly diagram to visually verify the section geometry.
- Export the output using the CSV or PDF buttons.
Frequently Asked Questions
1. What is the neutral axis?
The neutral axis is the line in a section where bending stress becomes zero. For symmetric and homogeneous sections, it passes through the centroid. For composite or irregular sections, its location depends on transformed areas and geometry.
2. Can I include openings or ducts?
Yes. Mark any rectangular opening as a void. The calculator subtracts its equivalent area and inertia contribution from the overall section properties.
3. What does material factor mean?
Material factor is the transformed-area multiplier. Use 1 for same-material sections. For composite sections, enter the modular ratio or chosen transformed-section factor for each component.
4. Which units should I use?
Use any consistent unit system. If dimensions are entered in millimeters, the centroid will be in millimeters, area in square millimeters, and inertia in millimeters to the fourth power.
5. Does this work for steel, wood, and concrete?
Yes, for rectangular subcomponents. The method is geometric and transformed-section based, so it can support many construction materials when you use proper dimensions and factors.
6. Why are x̄ and ȳ both shown?
Many real sections are not symmetric in both directions. Showing both centroid coordinates helps with bending, stability, and combined-axis design checks.
7. Why might my result look unusual?
Check coordinates, units, and whether a component should be solid or void. Also verify that material factors are positive and that the equivalent transformed area is not near zero.
8. Does the plot affect the calculation?
No. The plot is only a visual aid. All section properties are computed on the server before the graph is drawn.