Solid Round Beams Deflection Calculator
The Formula
The formula for calculating the deflection of a solid round beam (cantilever with point load at free end) is:
\[\delta = \frac{F L^3}{3 E I}\]
Where:
- δ: Deflection at the free end (in meters)
- F: Applied force (in Newtons)
- L: Length of the beam (in meters)
- E: Young's modulus of the material (in Pascals)
- I: Moment of inertia of the beam cross-section (in m⁴)
For a solid round beam, the moment of inertia is:
\[I = \frac{\pi D^4}{64}\]
Where D is the diameter of the beam (in meters).
Calculation Steps
- Calculate the moment of inertia (I) using the beam diameter
- Use the deflection formula to calculate the deflection at the free end
- Convert the result to millimeters for easier interpretation
Example Calculation
Let's calculate the deflection for a solid round beam with the following properties:
- Length (L) = 2 m
- Diameter (D) = 50 mm = 0.05 m
- Load Force (F) = 1000 N
- Young's Modulus (E) = 200 GPa = 200 × 10⁹ Pa
- I = (π × 0.05⁴) / 64 = 3.068 × 10⁻⁷ m⁴
- δ = (1000 × 2³) / (3 × 200 × 10⁹ × 3.068 × 10⁻⁷) = 0.0087 m
- δ = 0.0087 m × 1000 = 8.7 mm
Therefore, the deflection at the free end of the beam is approximately 8.7 mm.
Visual Representation
This visual shows the deflection of a solid round beam based on our example calculation.