## Elastic deformations, stresses and forces

Strength theory is a classic area of mechanical engineering. It examines how components are affected by loading, the stresses and deformations that occur and the extent to which those components are able to withstand them. Loading might, for example, involve pressure, tension or torsion. Application of the theory to specific cases is often a complex matter. It requires sound knowledge of the elastic properties of a given material, i.e. the effect exerted by elastic modulus, Poisson’s ratio, bulk modulus and shear modulus. Furthermore, we repeatedly encounter differential equations, the solution of which requires in-depth mathematical knowledge.

### Example

A slotted annulus is opened up by being pushed onto a conical drive shaft, the outer diameter of which is larger than the inner diameter of the annulus. Knowledge of the elastic properties of the ring allows us to determine the exact shape that the annulus will assume on the shaft.

Internal stresses in the ring exert varying forces along the contact surface of the shaft. From this, we can determine the braking effect of the ring on the shaft.