What is the deflection at the midpoint of a simply supported beam subjected to a uniform load w?
Practice Questions
1 question
Q1
What is the deflection at the midpoint of a simply supported beam subjected to a uniform load w?
5wL^4/384EI
wL^3/3EI
wL^4/8EI
wL^3/48EI
The deflection at the midpoint of a simply supported beam subjected to a uniform load w is given by δ = wL^4/8EI.
Questions & Step-by-step Solutions
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Q
Q: What is the deflection at the midpoint of a simply supported beam subjected to a uniform load w?
Solution: The deflection at the midpoint of a simply supported beam subjected to a uniform load w is given by δ = wL^4/8EI.
Steps: 5
Step 1: Understand the problem. We have a simply supported beam, which means it is supported at both ends and can bend in the middle.
Step 2: Identify the load. The beam is subjected to a uniform load 'w', which means the same weight is applied evenly across the entire length of the beam.
Step 3: Know the variables. 'L' is the length of the beam, 'E' is the modulus of elasticity (a measure of how stiff the material is), and 'I' is the moment of inertia (a measure of how the beam's cross-section resists bending).
Step 4: Use the formula for deflection. The formula to calculate the deflection (how much the beam bends) at the midpoint is δ = wL^4 / (8EI).
Step 5: Plug in the values. If you know the values for 'w', 'L', 'E', and 'I', you can substitute them into the formula to find the deflection at the midpoint.
