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What is the relationship between the moment of inertia and the stiffness of a be
What is the relationship between the moment of inertia and the stiffness 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 stiffness of a beam?
Directly proportional
Inversely proportional
No relationship
Exponential relationship
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The stiffness of a beam is directly proportional to its moment of inertia (I); a larger I results in greater stiffness.
Questions & Step-by-step Solutions
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Q
Q: What is the relationship between the moment of inertia and the stiffness of a beam?
Solution:
The stiffness of a beam is directly proportional to its moment of inertia (I); a larger I results in greater stiffness.
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 affects how easily it can bend.
Step 2: Know what stiffness means. Stiffness is how resistant a beam is to bending when a force is applied.
Step 3: Learn that a larger moment of inertia (I) means the mass is distributed further from the center of the beam.
Step 4: Realize that when the moment of inertia (I) is larger, the beam becomes stiffer and bends less under the same force.
Step 5: Conclude that the stiffness of a beam is directly proportional to its moment of inertia (I); as I increases, stiffness increases.
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