Modular Ratio:

Let the composite bar illustrated in Figure in which an aluminum bar is encased just snug in a copper tube in which itself is encased just snug in a steel tube. Let us analyze how the three different components of the composite bar share the load applied axially on the composite bar.

     Figure

The fundamental requirement in such a case is that all of the three components of the bar must undergo the similar amount of deformation when carrying the load. Or else, the bar which shortens the least alone shall be in contact with the load that is physically impossible, as a component which loses its contact shall not be carrying any load and therefore there might be no shortening of that component that contradicts the assumption that it shortens more. Therefore, it is logically essential that all of the three bars must undergo the similar amount of deformation. This condition is known as the compatibility condition or condition of consistent deformation. Satisfaction of this condition is the basis on which the problem of composite bars is analysed.