Input data
Define the tube and applied loads
Use consistent project assumptions. The calculator combines a free-end load and a full-span uniform load.
Formula Used
The calculator uses linear elastic beam equations. It combines a free-end point load and a full-span uniform load.
δ = P L³ / (3 E I) + w L⁴ / (8 E I)
θ = P L² / (2 E I) + w L³ / (6 E I)
V = P + w L
M = P L + w L² / 2
σ = M c / I
For round tube, I = π(D⁴ − d⁴) / 64. For rectangular hollow tube, I = [b h³ − bᵢ hᵢ³] / 12 about the selected axis.
How to Use This Calculator
- Choose the unit system and tube shape.
- Enter the external dimensions and wall thickness.
- Measure the unsupported cantilever length.
- Enter the end load and full-span uniform load.
- Set elastic modulus, yield strength, and density.
- Select self-weight when it is part of the load.
- Choose a project deflection ratio such as L/180.
- Review deflection, stress, reactions, and the warnings.
Example Data Table
| Input | Example value | Purpose |
|---|---|---|
| Tube section | 60 mm outside diameter × 3 mm wall | Defines area and bending stiffness. |
| Cantilever length | 1,200 mm | Measured from the fixed face. |
| End load | 1,000 N | Represents a free-end equipment load. |
| Uniform load | 0 N/m | Adds continuous load when required. |
| Elastic modulus | 200 GPa | Typical stiffness input for steel. |
| Deflection limit | L/180 | Sets the selected serviceability check. |
Cantilever Tube Behavior
A cantilever tube is fixed at one end. The other end remains free. Loads create bending, shear, and rotation. The free end often shows the greatest movement. That movement is called deflection.
Tube members are efficient because material sits away from the center. This improves the second moment of area. A larger outside diameter can reduce deflection strongly. Wall thickness also matters. However, increasing thickness adds weight and cost.
Why Deflection Matters
Excessive movement can damage finishes, seals, pipes, glazing, or equipment. It can also create poor alignment. A member may remain below yield stress but still deflect too much. Serviceability checks are therefore important.
The selected span-to-deflection limit depends on the use. Decorative work may tolerate more movement. Supports for sensitive equipment may need stricter limits. Project specifications can also govern. Always use the required limit when one exists.
Load Placement and Direction
A tip load produces a high bending moment at the fixed support. A distributed load acts along the entire span. Self-weight behaves like a distributed load. The calculator combines these effects using linear elastic superposition.
Load direction must match the intended bending axis. A rectangular tube is stiffer when its larger outside dimension is vertical. Rotating that tube can greatly increase deflection. Round tubes have equal bending stiffness in every direction.
Material and Connection Checks
Elastic modulus controls stiffness. Steel is usually stiffer than aluminum. Yield strength controls the onset of permanent material deformation. Neither value alone proves a safe installation.
The fixed connection is critical. Bolts, welds, plates, anchors, and supporting members must resist the calculated shear and moment. Local wall crushing may also occur near attachments. Check these conditions separately.
Good Design Practice
Use realistic service loads for deflection checks. Include equipment, finishes, wind, and self-weight where relevant. Do not apply code load combinations unless the selected criterion requires them. Confirm units before reviewing results.
Measure the unsupported length from the true fixed face. Avoid assuming a short bracket is rigid. Small connection flexibility can materially increase actual field deflection under working loads.
This tool assumes a straight, prismatic tube and a fully fixed support. It uses small-deflection elastic theory. Large movement, vibration, buckling, impact, corrosion, holes, and welded details need additional review. A qualified engineer should verify final construction decisions.
Frequently Asked Questions
1. What does this calculator determine?
It estimates free-end deflection, slope, support shear, support moment, bending stress, and selected serviceability checks for a hollow cantilever tube.
2. Which load cases are included?
The calculation combines one point load at the free end and one uniform load over the complete cantilever span. Tube self-weight can be included as additional uniform load.
3. Can I use a rectangular hollow section?
Yes. Select rectangular hollow tube, enter outside width and height, then choose the strong or weak bending axis. The selected axis changes the second moment of area.
4. Why is the fixed support so important?
A cantilever depends on rotation restraint at the fixed end. A flexible plate, loose anchor group, or deforming support increases movement beyond the ideal calculation.
5. Does a lower stress guarantee an acceptable tube?
No. A member can remain below yield strength while exceeding a deflection limit. Strength and serviceability should be reviewed separately.
6. What is the purpose of elastic modulus?
Elastic modulus measures stiffness. A higher modulus reduces deflection for the same section and load. It does not directly set the material yield strength.
7. Should I include tube self-weight?
Include it when the tube is horizontal or when its own gravity load contributes to bending. It matters more for long, heavy, or thick-wall members.
8. What does L/180 mean?
L/180 is a deflection limit equal to the unsupported length divided by 180. The correct limit depends on the project, finishes, occupancy, and governing requirements.
9. Is this suitable for large deflection?
No. The equations assume small elastic deflection. Large movement changes geometry and may need nonlinear structural analysis.
10. Does the calculator check local tube wall failure?
No. Check local yielding, wall crushing, bolt bearing, weld capacity, connection plates, and support members separately where they apply.
11. Can these results be used for final construction approval?
Use the output for preliminary assessment. Final construction design should be checked against project requirements by a qualified structural professional.