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For a cantilever beam with a point load at the free end, what is the deflection

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Question: For a cantilever beam with a point load at the free end, what is the deflection at the free end?

Options:

  1. WL^3/(3EI)
  2. WL^3/(12EI)
  3. WL^2/(2EI)
  4. WL^4/(8EI)

Correct Answer: WL^3/(3EI)

Solution: 

The deflection (δ) at the free end of a cantilever beam with a point load (W) at the end is given by δ = WL^3/(3EI), where E is the modulus of elasticity and I is the moment of inertia.

For a cantilever beam with a point load at the free end, what is the deflection

Practice Questions

Q1
For a cantilever beam with a point load at the free end, what is the deflection at the free end?
  1. WL^3/(3EI)
  2. WL^3/(12EI)
  3. WL^2/(2EI)
  4. WL^4/(8EI)

Questions & Step-by-Step Solutions

For a cantilever beam with a point load at the free end, what is the deflection at the free end?
  • Step 1: Identify the cantilever beam. A cantilever beam is fixed at one end and free at the other end.
  • Step 2: Recognize the point load. A point load (W) is applied at the free end of the beam.
  • Step 3: Understand the variables. You need to know the length of the beam (L), the modulus of elasticity (E), and the moment of inertia (I) of the beam's cross-section.
  • Step 4: Use the deflection formula. The formula to calculate the deflection (δ) at the free end is δ = WL^3 / (3EI).
  • Step 5: Plug in the values. Substitute the values of W, L, E, and I into the formula to find the deflection at the free end.
  • Cantilever Beam Deflection – The deflection of a cantilever beam under a point load is determined by the relationship between the load, the length of the beam, the material properties, and the beam's cross-sectional geometry.
  • Beam Theory – Understanding the basic principles of beam theory, including how loads affect deflection and the significance of the modulus of elasticity and moment of inertia.
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