For a cantilever beam with a uniformly distributed load, what is the formula for

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Question: For a cantilever beam with a uniformly distributed load, what is the formula for the maximum deflection at the free end?

Options:

Correct Answer: 5wL^4/384EI

Solution:

The maximum deflection δ for a cantilever beam with a uniformly distributed load w is given by δ = 5wL^4/384EI.

For a cantilever beam with a uniformly distributed load, what is the formula for the maximum deflection at the free end?

For a cantilever beam with a uniformly distributed load, what is the formula for the maximum deflection at the free end?

Step 1: Understand what a cantilever beam is. A cantilever beam is fixed at one end and free at the other end.
Step 2: Know that a uniformly distributed load (w) means the load is spread evenly along the length of the beam.
Step 3: Identify the length of the beam (L) from the fixed end to the free end.
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.
Step 6: Use the formula for maximum deflection (δ) at the free end of the cantilever beam, which is δ = 5wL^4 / 384EI.

Cantilever Beam Deflection – The maximum deflection of a cantilever beam under a uniformly distributed load is derived from beam theory, specifically using the relationship between load, material properties, and geometry.
Uniformly Distributed Load – Understanding how a uniformly distributed load affects the bending and deflection of beams is crucial for structural analysis.
Material Properties – The formula incorporates the modulus of elasticity (E) and the moment of inertia (I), which are essential for determining how materials respond to loads.