Structural engineers often need to calculate the deflection of beams to ensure their stability and efficiency. In this guide, we’ll walk through a detailed calculation for the deflection of a simply supported beam subjected to a triangular distributed load.
Given Parameters
- Applied Triangular Load (w): 10,000 Nm⁻¹
- Beam Length (L): 1.8 meters
- Material Modulus of Elasticity (E): 207 × 10⁹ Nm⁻² (Steel)
- Moment of Inertia (I): 1098 cm⁴
Step 1: Calculate the Distance (x)
The midpoint of the beam is crucial for calculating deflection accurately.
Step 2: Compute Stiffness (EI)
The stiffness of the beam is obtained by multiplying the elastic modulus and the moment of inertia:
Step 3: Deflection Formula for Triangular Load
The deflection at the midpoint can be calculated using the formula:
Calculation Breakdown
After simplification:
Final Deflection Value
Converting the result to centimeters:
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