# Introduction to Elasticity/Sample final6

## Sample Final Exam Problem 6[edit | edit source]

Two long cylinders are in contact as shown in the figure below. Both cylinders are made of the same material which has a Young's modulus of 10 GPa and a Poisson's ratio 0.20. The smaller cylinder has a radius of 4 cm while the outer one has a radius of 10 cm. What is the width of the region of contact of the two cylinders under the action of a force of 1 kN per unit length of the cylinders.

## Solution[edit | edit source]

The area of contact per unit length is given by

For plane strain

Therefore, for the material of the cylinders

Since the outer cylinder contains the inner one, the radius of curvature can be considered to be negative. Therefore,

The area of contact per unit length of the cylinders is

The width of the region of contact is