What is the relationship between the moment of inertia (I) and the deflection of a beam?
Practice Questions
1 question
Q1
What is the relationship between the moment of inertia (I) and the deflection of a beam?
Directly proportional
Inversely proportional
No relationship
Exponential relationship
The deflection of a beam is inversely proportional to the moment of inertia (I); as I increases, deflection decreases.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the relationship between the moment of inertia (I) 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: 4
Step 1: Understand what moment of inertia (I) means. It is a measure of how much a beam resists bending. A higher moment of inertia means the beam is stiffer.
Step 2: Know what deflection means. Deflection is how much a beam bends or moves under a load.
Step 3: Learn the relationship. When the moment of inertia (I) increases, the beam becomes stiffer and bends less, which means the deflection decreases.
Step 4: Remember the key idea: If I goes up, deflection goes down. This is called being inversely proportional.
