Section Inputs
Choose geometry, units, materials, design factors, and accuracy.
Saved Comparisons
Store calculated sections inside this browser.
| Section | Zpx | Zpy | Capacity | Utilization | Remove |
|---|---|---|---|---|---|
| No comparison entries exist. | |||||
Formula Used
The calculator integrates every occupied area cell numerically.
Zp = ∫A |y − yp| dAMp = ∫A Fy |y − yp| dAS = I ÷ cShape factor = Zp ÷ SZrequired = Mu ÷ (φFy)The force-balanced axis equalizes tensile and compressive yield forces.
Mixed custom components may use different yield strengths.
How to Use This Calculator
- Select the required section shape.
- Choose consistent length, stress, and moment units.
- Enter every visible section dimension carefully.
- Set material strengths and design factors.
- Select the bending axis and direction.
- Enter the applied design moment.
- Increase resolution for curved or thin sections.
- Press the calculation button.
- Review plastic axes and shape factors.
- Read every warning before using capacity.
- Download the preferred calculation report.
Example Data Table
| Example | Shape | Dimensions | Yield strength | Suggested resolution |
|---|---|---|---|---|
| 1 | Rectangle | 200 × 300 mm | 250 MPa | 260 |
| 2 | I-section | 400 × 200 × 20 × 12 mm | 355 MPa | 380 |
| 3 | Hollow circle | 200 mm outside, 140 mm inside | 250 MPa | 520 |
| 4 | Channel | 300 × 100 × 15 × 10 mm | 275 MPa | 420 |
| 5 | Custom polygon | Six coordinate points | 300 MPa | 550 |
Understanding Plastic Section Properties
Plastic Modulus Purpose
Plastic section modulus describes fully yielded bending resistance.
It depends only on section geometry.
Material strength converts modulus into plastic moment.
Larger values generally provide stronger bending resistance.
Plastic Neutral Axis
The plastic neutral axis balances yielded internal forces.
Homogeneous sections usually require equal areas.
Mixed materials require equal yield-force resultants instead.
The axis may differ from the centroid.
Elastic and Plastic Behavior
Elastic bending keeps stresses below initial yielding.
The elastic modulus uses inertia and extreme distance.
Plastic bending assumes extensive yielding across the section.
The plastic modulus therefore exceeds common elastic values.
Shape Factor Meaning
Shape factor compares plastic and elastic section moduli.
It indicates reserve capacity after first yielding.
Different shapes provide different redistribution potential.
Numerical errors can distort unusually low ratios.
Positive and Negative Bending
Symmetric materials often give equal directional capacities.
Unequal strengths can create different directional results.
Custom components may also use different strengths.
Review both directions for unsymmetrical built-up sections.
Numerical Integration
This calculator divides geometry into many small cells.
Each occupied cell contributes area and first moment.
Curved edges need finer grids for accuracy.
Thin walls also benefit from higher resolution.
Custom Component Workflow
Add rectangles, circles, or ellipses as solids.
Use subtract components for holes and cutouts.
Coordinates position each component around the origin.
Rotation angles change rectangles and ellipses directly.
Section Classification
Full plastic resistance needs suitable local slenderness.
Thin plates may buckle before complete yielding.
Classification rules depend on the chosen design standard.
Always verify compactness outside this calculator.
Member Stability
Section capacity differs from complete member capacity.
Lateral torsional buckling can reduce bending strength.
Overall buckling can also control combined actions.
Connection behavior may further limit usable resistance.
Interaction Options
Optional reductions provide preliminary sensitivity checks.
They are not complete design-standard equations.
Use verified interaction rules for final design.
Document every assumption inside the generated report.
Accuracy Checks
Compare simple shapes against trusted closed formulas.
Increase resolution until important results stabilize.
Inspect the canvas before accepting custom geometry.
Review balance errors near the plastic axes.
Reporting Practice
Reports should include inputs, assumptions, and warnings.
Project names improve calculation traceability.
Saved comparisons support early section selection.
Independent checking remains essential for structural work.
Supported Capabilities
Major-axis bending Minor-axis bending Positive bending Negative bending Hollow sections Built-up sections Custom polygons Mixed strengths Principal inertias Shape factors Required modulus CSV reports PDF reports Canvas exports Local comparisonsFrequently Asked Questions
What does plastic section modulus measure?
It measures fully yielded geometric bending resistance.
Does yield strength change plastic section modulus?
No. Yield strength changes plastic moment capacity.
Why can the plastic axis differ?
Unsymmetrical geometry shifts the equal-area division.
Can custom materials use different strengths?
Yes. Each custom component accepts a strength.
Why does resolution affect results?
The method approximates geometry using small cells.
Which resolution should I choose?
Use higher values for curves and thin walls.
Does the calculator check local buckling?
No. Local buckling requires separate classification checks.
Does it check lateral torsional buckling?
No. Member stability requires separate design verification.
How are holes created?
Add subtractive components after the surrounding solids.
Can I export calculation data?
Yes. CSV, PDF, JSON, and images are available.
Are interaction reductions code compliant?
No. They provide preliminary sensitivity estimates only.