This calculator estimates the small elastic tip deflection and maximum fixed-end bending stress of a hollow round cantilever with a point load at its free end. Lengths are in inches, force is in pounds, and the material list supplies an elastic modulus in pounds per square inch. The formulas are useful for an early check under a narrow set of assumptions. They do not establish load capacity, fatigue life, buckling resistance or a safe structural design.
Round tube beam deflection Calculator
Form
Results
Deflection (Inches)
0
Bending Stress (PSI)
0
Table of Contents
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What is Round tube beam deflection?
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How to Use This Calculator
- Enter cantilever length, outside diameter and wall thickness in inches. Wall thickness must be less than half the outside diameter so the tube has a positive inside diameter.
- Enter the transverse end force in pounds and choose the material preset. The preset supplies Young’s modulus for the elastic deflection calculation.
- Select Calculate. The page finds inside diameter, section moment of inertia, tip deflection and bending stress. Deflection is returned directly in inches; no extra display scale is applied.
The model assumes a prismatic tube, a perfectly fixed support, a point load perpendicular to the beam at its free end, linear elastic material and small deflection. Real joints and load spread can behave differently.
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Formula Used
Inside diameter: d = D − 2t.
Second moment of area: I = π(D⁴ − d⁴) ÷ 64.
Tip deflection: δ = PL³ ÷ (3EI).
Fixed-end bending stress: σ = PL(D ÷ 2) ÷ I.
With inches, pounds and psi, I is in in⁴, deflection is in inches and stress is in psi.
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Variables Explained
| Symbol | Meaning |
|---|---|
| L | Distance in inches from the fixed support to the point load. |
| D and d | Outside and calculated inside tube diameters in inches. |
| t | Uniform tube wall thickness in inches. |
| P | Transverse point force at the free end in pounds. |
| E | Selected elastic modulus in pounds per square inch. |
| I | Area moment of inertia about a centroidal bending axis, in in⁴. |
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Worked Example
Take a 48 in cantilever with 2 in outside diameter, 0.125 in wall, 100 lb end load and aluminum preset E = 10,500,000 psi. Inside diameter is 1.75 in. I = π(2⁴ − 1.75⁴) ÷ 64 ≈ 0.325 in⁴. Tip deflection is about 1.080 in, and fixed-end stress is about 14,770 psi. Small differences come from retaining more digits.
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Why Use This Calculator?
Deflection rises in direct proportion to force and with the cube of length. Doubling length while holding everything else fixed multiplies the predicted deflection by eight and doubles bending stress. A larger diameter or thicker wall increases I, generally reducing both values. The fourth-power diameter terms explain why modest section changes can have a large stiffness effect.
The stress result is nominal elastic bending stress at the outer surface near the fixed end. Compare it only with an appropriate allowable value after considering material grade, temperature, stress concentrations, holes, welds, local tube behavior, fatigue, load factors and applicable standards. The generic modulus presets do not identify strength or guarantee that a specific product matches the listed value.
NASA’s cantilever reference gives δ = PL³/(3EI) for an end load. The former page display multiplied that physical result by 100,000,000; that scaling has been removed. Large deflection, nonuniform material, flexible supports and loads at other positions need a different analysis. Ask a qualified engineer to review safety-critical work.
A useful sensitivity check is to change one input at a time. Doubling force doubles both predicted deflection and stress. Doubling elastic modulus halves deflection but leaves the stress formula unchanged. Changing diameter or thickness affects the section property and therefore changes both outputs. These relationships help catch typing errors: if a change produces the opposite trend, recheck units and dimensions. Measure actual tube dimensions when tolerances matter, because the fourth-power section calculation can magnify diameter differences. Keep more than the displayed digits when comparing nearby options.
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Common Mistakes
- Entering millimetres or newtons even though this form requires inches and pounds.
- Using wall thickness equal to or greater than half the outside diameter.
- Selecting a generic material label without checking the actual product’s modulus and grade.
- Applying the cantilever end-load formula to a simply supported beam or distributed load.
- Treating calculated bending stress as an allowable load or complete safety check.
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Frequently Asked Questions
What support condition does the formula assume?
It assumes one end is perfectly fixed and the other end is free, with a transverse point load applied at the free end.
Why must wall thickness be below half the diameter?
Inside diameter equals outside diameter minus twice the wall. A larger thickness would produce a zero or negative opening and no valid hollow tube.
Why does length affect deflection so strongly?
The end-load deflection formula contains length cubed. Doubling length therefore multiplies predicted deflection by eight when the other inputs stay fixed.
Does the material selection determine strength?
No. It supplies an elastic modulus for stiffness. Yield strength and allowable stress depend on grade, condition and design requirements.
Can I enter metric measurements?
Not directly. Convert length to inches and force to pounds before using this page, and keep the material modulus in psi.
Is the result valid for large bending?
The equation is a small-deflection linear elastic model. Large rotations or material yielding require a more suitable analysis.
Can this value approve a structural member?
No. Connections, stability, fatigue, load combinations, material data and governing standards need professional review for safety-critical use.
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Sources & References
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