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

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Question: What is the relationship between the stiffness (k) of a beam and its deflection (δ) under a load (P)?

Options:

Correct Answer: k = P / δ

Solution:

The stiffness (k) of a beam is defined as the ratio of the load (P) applied to the deflection (δ) produced, thus k = P / δ.

What is the relationship between the stiffness (k) of a beam and its deflection (δ) under a load (P)?

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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