For a simply supported beam subjected to a uniformly distributed load, what is t

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Question: For a simply supported beam subjected to a uniformly distributed load, what is the deflection at the center?

Options:

Correct Answer: 5WL^3/48EI

Solution:

The deflection (δ) at the center of a simply supported beam subjected to a uniformly distributed load (w) is given by δ = 5WL^3/48EI.

For a simply supported beam subjected to a uniformly distributed load, what is the deflection at the center?

For a simply supported beam subjected to a uniformly distributed load, what is the deflection at the center?

Step 1: Identify the type of beam. In this case, it is a simply supported beam.
Step 2: Understand the load applied. Here, it is a uniformly distributed load (w) across the length of the beam.
Step 3: Know the variables involved: W is the total load, L is the length of the beam, E is the modulus of elasticity of the material, and I is the moment of inertia of the beam's cross-section.
Step 4: Use the formula for deflection at the center of the beam: δ = 5WL^3 / 48EI.
Step 5: Plug in the values for W, L, E, and I into the formula to calculate the deflection (δ).

Beam Deflection – Understanding how beams deform under load, specifically the calculation of deflection for simply supported beams with uniformly distributed loads.
Material Properties – Knowledge of the modulus of elasticity (E) and moment of inertia (I) as they relate to beam deflection.
Load Distribution – Recognizing the effects of uniformly distributed loads on structural elements.