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.
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$\begingroup$ Try this: bu.edu/moss/mechanics-of-materials-bending-normal-stress $\endgroup$– GertCommented Dec 23, 2015 at 22:56
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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: $$ F = E \times {u \over L} \times \pi \times d^2/4 $$
That gives positive force for a positive displacement. If you want the restoring force applied to the thing that causes the displacement, negate it.
The force is the same at any distance along the bar.
