For a cantilever beam with a point load at the free end, what is the deflection at the free end?
Practice Questions
1 question
Q1
For a cantilever beam with a point load at the free end, what is the deflection at the free end?
WL^3/(3EI)
WL^3/(12EI)
WL^2/(2EI)
WL^4/(8EI)
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.
Questions & Step-by-step Solutions
1 item
Q
Q: For a cantilever beam with a point load at the free end, what is the deflection at the free end?
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.
Steps: 5
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.
