How is stess and strain related?

Question

A steel cable on a crane has a diameter of 13mm. What force is necessary to produce a strain of 0.1% in the wire?

Answer 1

Stress / Strain = Young's Modulus which is a material property.

Load / area of cross section gives you stress.

0.1% strain simply means that the length of the cable increases by 0.1%

Change in length / original length = Strain.

We need Young's modulus to solve the problem.

Answer 2

young modulus,E=stress/strain
where, stress=force/area
strain=extension/length

E =(F/A)/(e/l )
= Fl/Ae
F=(Ae/l)E

where, e=extension
l=length


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