Contact of two cylinders with their axes parallel to the y-coordinate:

For a change, let us assume that an elastic half space is being contacted by a distributed uniform load which acts between and throughout the axis. Then the vertical displacement at a location on the surface ( ) of the layer have the following forms within and outside the contact area respectively.

	(10.4a)

	(10.4b)

Here is a constant, which is determined arbitrarily by considering that the displacement is zero at a distance .

At the vertical displacement varies logarithmically. In other word, it is just not possible to estimate the displacement at a point without arbitrarily choosing a datum for these problems, i.e. can not be determined absolutely. So it is not possible to determine the pressure distribution within the contact area as was done for three dimensional problems. Therefore, for two dimensional problems, the contact between two parallel cylinders is solved in the manner discussed in the next slide..