For a cantilever beam with a uniform distributed load, what is the formula for the maximum deflection at the free end?
Practice Questions
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Q1
For a cantilever beam with a uniform distributed load, what is the formula for the maximum deflection at the free end?
5wL^4 / 384EI
wL^4 / 8EI
wL^3 / 3EI
wL^3 / 48EI
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.
Questions & Step-by-step Solutions
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Q
Q: For a cantilever beam with a uniform distributed load, what is the formula for the maximum deflection at the free end?
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.
Steps: 5
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.
