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What is the relationship between the moment of inertia and the deflection of a b
What is the relationship between the moment of inertia and the deflection of a beam?
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Practice Questions
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Q1
What is the relationship between the moment of inertia and the deflection of a beam?
Directly proportional
Inversely proportional
No relationship
Exponential relationship
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The deflection of a beam is inversely proportional to the moment of inertia (I); as I increases, deflection decreases.
Questions & Step-by-step Solutions
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Q
Q: What is the relationship between the moment of inertia and the deflection of a beam?
Solution:
The deflection of a beam is inversely proportional to the moment of inertia (I); as I increases, deflection decreases.
Steps: 5
Show Steps
Step 1: Understand what moment of inertia (I) is. It is a measure of how mass is distributed in a beam and how resistant it is to bending.
Step 2: Know what deflection is. Deflection is how much a beam bends or moves under a load.
Step 3: Learn the relationship: As the moment of inertia (I) increases, the beam becomes stiffer.
Step 4: Realize that a stiffer beam will bend less under the same load, meaning less deflection.
Step 5: Conclude that deflection is inversely proportional to the moment of inertia: if I goes up, deflection goes down.
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