For a simply supported beam, what is the deflection at the center due to a point

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Question: For a simply supported beam, what is the deflection at the center due to a point load at the center?

Options:

Correct Answer: WL^3/48EI

Solution:

The deflection at the center of a simply supported beam due to a point load at the center is given by δ = WL^3/48EI.

For a simply supported beam, what is the deflection at the center due to a point load at the center?

For a simply supported beam, what is the deflection at the center due to a point load at the center?

Step 1: Identify the parameters needed for the formula. You need the load (W), the length of the beam (L), the modulus of elasticity (E), and the moment of inertia (I).
Step 2: Understand the formula for deflection at the center of the beam, which is δ = WL^3/48EI.
Step 3: Plug in the values for W, L, E, and I into the formula.
Step 4: Calculate L^3 (length cubed).
Step 5: Multiply the result from Step 4 by W (the load).
Step 6: Multiply the result from Step 5 by 1/48.
Step 7: Divide the result from Step 6 by the product of E and I (modulus of elasticity times moment of inertia).
Step 8: The final result is the deflection (δ) at the center of the beam.

Beam Deflection – Understanding how a simply supported beam behaves under a point load, specifically calculating the deflection at the center.
Material Properties – Knowledge of the modulus of elasticity (E) and moment of inertia (I) as they relate to beam deflection.
Load and Span Relationship – Recognizing the relationship between the load (W), span length (L), and the resulting deflection.