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MechanicsSimply Supported Beam (Uniformly Distributed Load) Calculator: Roof Support Beam
Diagram of the simply supported beam with load applied at the center.
You're designing a roof where beams support the weight of the roof and any potential snow load. The beam is simply supported at both ends, and you want to calculate the deflection under a uniformly distributed load.
Calculation:
For a simply supported beam with a uniformly distributed load, the deflection at the center is given by:
Deflection (δ) = (5 × w × L⁴) / (384 × E × I)
Where:
- w = Uniform load per unit length
- L = Length of the beam
- E = Modulus of Elasticity of the beam material
- I = Moment of Inertia of the beam's cross-section
Example-3 : Practical Use of Beam Deflection Calculator: Roof Support Beam
Diagram of the simply supported beam with load applied at the center.
You're designing a roof where beams support the weight of the roof and any potential snow load. The beam is simply supported at both ends, and you want to calculate the deflection under a uniformly distributed load.
Calculation:
For a simply supported beam with a uniformly distributed load, the deflection at the center is given by:
Deflection (δ) = (5 × w × L⁴) / (384 × E × I)
Where:
- w = Uniform load per unit length
- 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:
- w = 2000 N/m (load due to roof weight and snow)
- L = 6 meters
- E = 200 GPa (Steel)
- I = 6 × 10⁻⁶ m⁴ (Rectangular cross-section)
Using these values in the formula:
δ = (5 × 2000 × 6⁴) / (384 × 200 × 10⁹ × 6 × 10⁻⁶) = 0.010 m (10 mm)
So, the deflection at the center of the beam is 10 mm, which should be checked to ensure it's within the allowable deflection limits.
