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What is the relationship between the stiffness (k) of a beam and its deflection

Practice Questions

Q1
What is the relationship between the stiffness (k) of a beam and its deflection (δ) under a load (P)?
  1. k = P / δ
  2. k = δ / P
  3. k = P * δ
  4. k = P + δ

Questions & Step-by-Step Solutions

What is the relationship between the stiffness (k) of a beam and its deflection (δ) under a load (P)?
  • Step 1: Understand that stiffness (k) is a measure of how much a beam resists bending when a load is applied.
  • Step 2: Know that deflection (δ) is how much the beam bends or moves from its original position when the load (P) is applied.
  • Step 3: Remember the formula that relates stiffness, load, and deflection: k = P / δ.
  • Step 4: This formula means that if you increase the load (P), the deflection (δ) will also increase if the stiffness (k) remains the same.
  • Step 5: Conversely, if the stiffness (k) of the beam is higher, the deflection (δ) will be smaller for the same load (P).
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