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

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

Options:

  1. 5wL^4 / 384EI
  2. wL^4 / 8EI
  3. wL^3 / 3EI
  4. wL^3 / 48EI

Correct Answer: 5wL^4 / 384EI

Solution: 

The maximum deflection (δ) at the free end of a cantilever beam with a uniform distributed load (w) is given by δ = 5wL^4 / 384EI, where E is the modulus of elasticity and I is the moment of inertia.

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

Practice Questions

Q1
For a cantilever beam with a uniform distributed load, what is the formula for the maximum deflection at the free end?
  1. 5wL^4 / 384EI
  2. wL^4 / 8EI
  3. wL^3 / 3EI
  4. wL^3 / 48EI

Questions & Step-by-Step Solutions

For a cantilever beam with a uniform distributed load, what is the formula for the maximum deflection at the free end?
  • Step 1: Identify the type of beam. In this case, it is a cantilever beam, which is fixed at one end and free at the other.
  • Step 2: Understand the load applied. The beam has a uniform distributed load, meaning the load is spread evenly along the length of the beam.
  • Step 3: Know the variables involved in the formula. The variables are: δ (maximum deflection), w (uniform load per unit length), L (length of the beam), E (modulus of elasticity), and I (moment of inertia).
  • Step 4: Write down the formula for maximum deflection at the free end of the cantilever beam. The formula is δ = 5wL^4 / 384EI.
  • Step 5: Recognize that this formula helps calculate how much the beam will bend at the free end due to the load.
  • Cantilever Beam Deflection – The maximum deflection of a cantilever beam under a uniform distributed load is determined by the beam's length, load intensity, material properties, and cross-sectional geometry.
  • Material Properties – Understanding the significance of the modulus of elasticity (E) and moment of inertia (I) in calculating deflection.
  • Load Types – Differentiating between uniform distributed loads and point loads, and their effects on beam deflection.
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