Round Tube Beams Deflection Calculator
The Formula
The formula for calculating the deflection of a round tube beam is:
\[Deflection = \frac{P L^3}{48 E I}\]
Where:
- P: Applied load (in pounds)
- L: Beam length (in inches)
- E: Elastic modulus of the material (in psi)
- I: Moment of inertia of the cross-section (in in⁴)
For a round tube, the moment of inertia is calculated as:
\[I = \frac{\pi}{64}(OD^4 - ID^4)\]
Where:
- OD: Outer diameter of the tube
- ID: Inner diameter of the tube
Calculation Steps
- Calculate the inner diameter: ID = OD - (2 × Wall Thickness)
- Calculate the moment of inertia using the formula above
- Use the deflection formula to determine the beam's deflection
Example Calculation
Let's calculate the deflection for a round tube beam with the following properties:
- Outer Diameter: 2 inches
- Wall Thickness: 0.125 inches
- Beam Length: 10 feet (120 inches)
- Load: 500 lbs
- Elastic Modulus: 29,000,000 psi (for steel)
- Inner Diameter = 2 - (2 × 0.125) = 1.75 inches
- I = (π / 64) × (2⁴ - 1.75⁴) = 0.3436 in⁴
- Deflection = (500 × 120³) / (48 × 29,000,000 × 0.3436) = 0.3629 inches
Visual Representation
This visual shows the deflection of a round tube beam based on our example calculation.