Formula Used
The section is treated as three non-overlapping rectangles: one base plate and two side walls.
Area: A = ΣAi
Centroid: x̄ = Σ(Aixi) / A, and ȳ = Σ(Aiyi) / A
Centroidal inertia: Ix = Σ[(bihi3 / 12) + Ai(yi - ȳ)2]
Centroidal inertia: Iy = Σ[(hibi3 / 12) + Ai(xi - x̄)2]
Section modulus: S = I / c. Radius of gyration: r = √(I / A). Bending stress: σ = Mc / I.
How to Use This Calculator
Choose the unit first. Enter the full outside width and height. Add the side wall thickness and base thickness. The calculator assumes a square-cornered U section with no lips or fillets. Add member length and density when weight is needed. Add bending moments when quick stress estimates are needed. Press calculate. The result appears above the form. Use CSV or PDF buttons to save the output.
Example Data Table
| B |
H |
Side thickness |
Base thickness |
Area |
Approx Ix |
Approx Iy |
| 80 mm |
120 mm |
6 mm |
8 mm |
1,984 mm² |
4.37E+6 mm⁴ |
1.46E+6 mm⁴ |
| 120 mm |
180 mm |
10 mm |
12 mm |
4,800 mm² |
2.07E+7 mm⁴ |
7.56E+6 mm⁴ |
| 160 mm |
220 mm |
12 mm |
16 mm |
7,456 mm² |
5.46E+7 mm⁴ |
1.94E+7 mm⁴ |
U Beam Moment of Inertia Guide
A U beam is a channel shaped section. It has one base plate and two side plates. This shape is common in frames, rails, brackets, machine beds, and light supports. Its moment of inertia shows how strongly the section resists bending about a chosen centroidal axis. A larger value means less bending deflection under the same load.
Why Centroid Matters
The centroid is the balance point of the area. For a symmetric U beam, the horizontal centroid stays at mid width. The vertical centroid moves toward the heavier base or taller side plates. The calculator first divides the channel into three rectangles. It then finds each area and local centroid. The weighted average gives the final section centroid.
Formula Method
Each rectangle has its own second moment of area. For a rectangle, Ix equals width times height cubed divided by twelve. Iy equals height times width cubed divided by twelve. These values apply about each rectangle centroid. The parallel axis theorem then shifts every rectangle value to the combined centroid. The shifted values are added together. This gives Ix and Iy for the complete U beam.
Useful Design Outputs
Section modulus helps estimate bending stress. It divides inertia by the farthest distance to an edge. Radius of gyration compares inertia with area. It is useful for column checks and section efficiency. The tool also estimates weight per length from density. Optional moments provide quick stress values in MPa.
Practical Notes
Use consistent dimensions. Do not mix inches with millimeters in one run. Select the input unit before submitting. Measure the full outside width, full outside height, side thickness, and base thickness. The side thickness must leave an inside opening. The base thickness must be less than the total height. Fillets, lips, welds, holes, and tapered walls are not included. Use refined section software for final certified design.
Best Use
This calculator is ideal for early sizing and comparison. Try several thickness values. Watch how Ix changes with height and how Iy changes with width. Export results for records. Share the table with team members during review. Use the stress estimate as a screen. Confirm final members with code checks and professional judgment before fabrication.
FAQs
What is a U beam moment of inertia?
It is the second moment of area for a channel shaped beam. It shows how the area is distributed around a bending axis and helps estimate stiffness.
Does this calculator include rounded corners?
No. It uses three rectangular parts. Fillets, lips, holes, welds, and curved transitions should be added with a more detailed section model.
Which axis is usually stronger?
The horizontal centroidal axis is often stronger when the section height is large. The exact answer depends on width, height, and wall thickness.
Can I use inches?
Yes. Select inches before entering values. Keep every geometric input in the same selected unit to avoid incorrect area and inertia values.
What does section modulus mean?
Section modulus equals inertia divided by distance to the farthest fiber. It is used with bending moment to estimate normal bending stress.
Why is the centroid not at half height?
The base plate adds extra area near the bottom. This pulls the vertical centroid downward, especially when the base is thick.
Is polar area moment torsional strength?
No. Ix plus Iy is a polar area value for the plane. Open channel torsion needs specialized torsion constants and warping checks.
Can this replace engineering design?
No. It supports early checks and comparisons. Final member selection should follow the correct code, load cases, supports, and professional review.