Neutral Axis Calculator

Calculator Inputs

Example data table

Example I‑section modeled with three rectangles (two flanges and one web), using millimeters.

Formula used

The neutral axis for bending about a horizontal axis passes through the centroid of the cross‑section. For a composite section split into parts:

Where A_i is the area of part i and y_i is its centroid location from the reference axis. In transformed‑section mode, the effective area becomes A′_i = n_i A_i.

To compute the second moment of area about the neutral axis (optional output):

How to use this calculator

1. Choose a datum for y = 0, typically the bottom edge.
2. Split the cross‑section into rectangles (flanges, web, slab, plates).
3. For each rectangle, enter width b, height h, and centroid y.
4. If using different materials, switch to transformed mode and set n for each part.
5. Press Calculate to see ȳ, depth checks, and I about the neutral axis.
6. Use the download buttons to export CSV or PDF summaries.

Professional article

1) Neutral axis as a design reference

The neutral axis is the line in a bending member where longitudinal strain is zero. Above it, fibers shorten in compression; below it, fibers lengthen in tension. Locating this line helps engineers and builders place reinforcement, choose plate locations, and judge whether extreme fibers exceed allowable stress under service loads.

2) What the calculator actually delivers

This calculator reports the centroid-based neutral axis ȳ for a built-up cross-section. It also provides effective area and a second moment about the neutral axis using the parallel axis theorem. The “from top” and “from bottom” distances support quick depth checks before detailed bending calculations.

3) Rectangles are a practical site model

Many construction members can be decomposed into rectangles: flanges, webs, haunches, added plates, and slab strips. Each rectangle contributes an area A and a centroid location y. By summing A·y and dividing by ΣA, you capture how geometry shifts the neutral axis in a transparent, auditable way.

4) Centroid location and common input errors

Centroid y must be measured from a consistent datum, usually the bottom edge. A frequent mistake is entering a top-fiber distance for some parts and a bottom-fiber distance for others. Another error is overlapping rectangles, which double-counts area and pushes ȳ toward the overlapped zone.

5) Transformed sections for mixed materials

When materials differ, stiffness matters, not just geometry. The transformed section method converts each part to a reference material using the modular ratio n = E/Eref. The calculator multiplies area and the rectangle’s own second moment by n, so stiffer components attract more effective contribution, matching standard elastic compatibility assumptions.

6) Why second moment output is useful

With I about the neutral axis, elastic bending stress can be estimated as σ = M·y/I. This supports quick checks on steel plates, timber laminations, or slab compression zones. For deflection screening, the product E·I is central; transformed mode helps approximate E·I for composite members during preliminary sizing.

7) Interpreting results in construction context

If the neutral axis is closer to one face, that face will experience lower stress at the same moment. For asymmetric built-up members, this can influence weld sizing, bolt line placement, and stiffener detailing. Always confirm the modeled rectangles match as-built thicknesses, openings, and any fire protection layers.

8) Documentation and review workflow

Record the datum, units, and any modular ratios used, then export the report for design files. A good review step is to compare ȳ with a quick hand estimate for symmetry and proportion. When values look off, re-check centroid y inputs, rectangle boundaries, and whether transformed mode is appropriate for your loading case and staging.

FAQs

1) What is the neutral axis in simple terms?
It is the line inside a bending member where longitudinal strain is zero. Material above it is in compression and material below it is in tension, for typical sagging bending.

2) How do I choose a good datum for y = 0?
Use a physical edge that is easy to measure on drawings, commonly the bottom of the section. Any datum works if every centroid y value is measured from the same reference.

3) What shapes can I model with this tool?
Any shape that can be approximated with rectangles, including I, T, channel, box variants, and built-up plates. Increase rectangle count when geometry changes, and avoid overlaps to keep areas correct.

4) When should I use transformed section mode?
Use it for mixed materials with different elastic modulus, such as steel–concrete composites or timber with steel plates. Enter n = E/Eref so stiffer parts contribute proportionally in elastic analysis.

5) Does the calculator include holes or notches?
Not directly. You can subtract a hole by entering it as a rectangle with negative area is not supported here. Instead, split the section into rectangles that exclude the void, or adjust the geometry to represent net area.

6) Why is my neutral axis outside the section depth?
It usually indicates inconsistent centroid y references, wrong sign, overlapping rectangles, or missing components. Verify each rectangle’s centroid location from the same datum and confirm heights match the intended depth direction.

7) Are the CSV and PDF exports identical?
They contain the same core results and component list. CSV is best for spreadsheets and checking formulas, while PDF is a quick attachment for submittals and field records.