Pneumatic-Hydraulic 
Materials-Weight
Miscellaneous Cal's
MechanicsRight Ad Content
Beam Deflection Calculator - Simply Supported Beam with Center Load
Deflection (δ) = (F × L³) / (48 × E × I)
Where:
- F = Force applied at the center of the beam
- L = Length of the beam
- E = Modulus of Elasticity of the beam material
- I = Moment of Inertia of the beam's cross-section
Result:
Left Ad Content
Bottom Ad Content
Example-1 : Practical Use of Beam Deflection Calculator: Bridge Beam
Diagram of the simply supported beam with load applied at the center.
You're designing a bridge where the beam is simply supported at both ends. You need to calculate the maximum deflection in the middle of the beam when a load (e.g., a vehicle) is placed on it.
Calculation:
For a simply supported beam with a point load in the center, the deflection is given by:
Deflection (δ) = (F × L³) / (48 × E × I)
Where:
- F = Load applied at the center
- L = Length of the beam
- E = Modulus of Elasticity of the beam material
- I = Moment of Inertia of the beam's cross-section
Example Values:
- F = 10000 N (1000 kg vehicle weight)
- L = 10 meters
- E = 210 GPa (Steel)
- I = 5 × 10⁻⁶ m⁴ (Rectangular cross-section)
Using these values in the formula:
δ = (10000 × 10³) / (48 × 210 × 10⁹ × 5 × 10⁻⁶) = 0.019 m (19 mm)
So, the maximum deflection in the middle of the beam is 19 mm, which should be within acceptable limits for bridge design.
