Enter symmetric I-beam dimensions
All dimensions must use the same unit. Equal top and bottom flanges are assumed.
Example data
| Dimension | Symbol | Example value | Unit |
|---|---|---|---|
| Overall depth | D | 300 | mm |
| Flange width | B | 150 | mm |
| Flange thickness | tf | 12 | mm |
| Web thickness | tw | 8 | mm |
This example gives Jp of approximately 95,470,960 mm4.
Formula used
The calculator divides the section into two flanges and one web. It assumes equal flanges and a centroid at mid-depth.
Clear web depth: hw = D − 2tf
Strong-axis inertia: Ix = 2[(Btf3 / 12) + (Btf)(D/2 − tf/2)2] + twhw3 / 12
Weak-axis inertia: Iy = 2(tfB3 / 12) + hwtw3 / 12
Geometric polar moment: Jp = Ix + Iy
How to use this calculator
- Measure the outside depth and equal flange width.
- Enter the thickness of one flange and the web.
- Select the unit used for every dimension.
- Confirm the clear web depth remains positive.
- Press Calculate properties to view the result above.
- Use CSV or PDF downloads for project records.
- Verify final design decisions against governing standards.
I-beam geometry and section behavior
How the section works
An I-beam concentrates material near the top and bottom edges. This shape creates high bending efficiency. This makes efficient use of material during common bending load demands. The web connects both flanges. It also carries much of the shear force. The calculator treats the profile as a symmetric built-up section. It uses rectangular components. Two flange rectangles sit above and below one web rectangle.
Centroidal properties
The centroid lies at mid-depth for equal flanges. That assumption keeps the method direct. The strong axis runs horizontally through the centroid. The weak axis runs vertically through the centroid. The calculator finds both second moments of area. It then adds them. The sum is the geometric polar moment about the centroid.
Consistent dimensions matter
Use consistent dimensions for every input. Millimetres produce fourth-power millimetre outputs. Inches produce fourth-power inch outputs. Never mix systems inside one calculation. Check the overall depth first. It must exceed twice the flange thickness. The resulting clear web depth must remain positive. Review dimensions against the drawing. Nominal beam labels can differ from actual sizes.
Reading the values
The strong-axis inertia usually controls vertical bending behavior. Deep flanges increase this value greatly. Weak-axis inertia reacts strongly to flange width. A narrow flange reduces lateral stiffness. The polar result describes how area spreads around both centroidal axes. It is useful for comparing section geometry. It is not automatically the torsional constant for an open I-beam.
Torsion needs separate care
Open sections can twist differently from closed tubes. Their Saint-Venant torsional constant is often much smaller. Warping can also affect long members. Do not calculate torsional stress from the displayed polar moment alone. Use an approved torsion method when torque is important. Consider lateral restraint and load paths. Examine local flange and web slenderness. Include connections in the final design.
Using preliminary results
The calculator also reports section modulus. Section modulus supports elastic bending checks. Radius of gyration supports stability reviews. Area helps with material quantity estimates. These values are geometric properties only. They do not confirm capacity. Material grade, load combinations, connection design, deflection limits, and governing codes remain essential.
Final review
Use the result as a transparent preliminary check. Compare it with manufacturer tables when available. Recheck unusual sections by hand. Model unsymmetrical sections using a suitable method. Ask a qualified structural engineer to verify final member selection. Careful geometry creates better decisions before fabrication starts.
Frequently asked questions
1. What does this calculator measure?
It calculates geometric properties for a symmetric I-beam. Outputs include Ix, Iy, polar moment, area, radii of gyration, and elastic section modulus.
2. What is the polar moment in this calculator?
It is the geometric polar moment about centroidal axes. The calculator uses Jp = Ix + Iy. It describes how area is distributed around both axes.
3. Is the result the torsional constant?
No. An open I-beam has a torsional constant that differs from its geometric polar moment. Use dedicated torsion calculations when applied torque or twist controls the design.
4. Which beam shape does the calculator assume?
It assumes a symmetric I-section. Both flanges have the same width and thickness. The web has one constant thickness. The section centroid therefore lies at mid-depth.
5. Can I enter inch dimensions?
Yes. Select inches and enter every dimension in inches. The calculator then reports area in in², inertia in in⁴, section modulus in in³, and radii in inches.
6. Why must depth exceed twice flange thickness?
The web must have a positive clear depth. If depth is not greater than two flange thicknesses, the assumed I-beam geometry cannot exist.
7. What is the strong axis?
For the usual upright I-beam, the strong axis is horizontal through the centroid. It generally has the larger inertia and commonly governs vertical bending behavior.
8. What is section modulus used for?
Elastic section modulus links bending moment and extreme-fiber stress in elastic analysis. It is a geometric value. Capacity still depends on material properties, restraints, code rules, and loading.
9. Can this tool calculate unequal flanges?
No. This version uses equal flanges for a clear centroidal method. Unequal flanges require a separate centroid calculation before the parallel-axis terms are evaluated.
10. Are fillets included?
No. The calculator uses sharp rectangular flange and web components. Manufacturer sections often include root fillets. Use published section tables for final comparisons when fillets matter.
11. Does this result prove a beam is safe?
No. It provides section geometry only. Final safety checks need loads, spans, supports, material grade, lateral restraint, deflection limits, connections, and applicable design standards.