What is the deflection formula for a simply supported beam under a uniform load?

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Question: What is the deflection formula for a simply supported beam under a uniform load?

Options:

Correct Answer: 5wL^4/384EI

Solution:

The deflection (δ) at the center of a simply supported beam under a uniform load (w) is given by δ = 5wL^4/384EI.

What is the deflection formula for a simply supported beam under a uniform load?

What is the deflection formula for a simply supported beam under a uniform load?

Step 1: Understand what a simply supported beam is. It is a beam that is supported at both ends and can freely deflect under load.
Step 2: Know that a uniform load (w) means the weight is evenly distributed along the length of the beam.
Step 3: Identify the length of the beam (L), which is the distance between the two supports.
Step 4: Recognize that E is the modulus of elasticity of the material, which measures how stiff the material is.
Step 5: Understand that I is the moment of inertia, which depends on the shape of the beam's cross-section and affects how it bends.
Step 6: Use the deflection formula: δ = 5wL^4 / 384EI. This formula calculates how much the beam will bend (deflect) at its center under the uniform load.

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