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:

$$\Delta =0.301\text{cm}$$

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