# Restoring force in circular rod

Can somebody explain how to calculate the restoring force in a uniform circular rod with known Young's modulus and diameter. I would need the restoring force in a specified distance from the origin with also a specified deviance.

• – Gert Dec 23 '15 at 22:56

The force of a stress uniformly distributed over an area A is $$F = \sigma \times A$$
Stress = Young's modulus * strain $$\sigma = E \times \epsilon$$
Strain = displacement / Length $$\epsilon = {u \over L}$$
so putting it together, along with the area of a circle: $$F = E \times {u \over L} \times \pi \times d^2/4$$