A Beginner's Guide to Structural Mechanics/Analysis Transformed Moments of Interia (c) 2007, T. Bartlett Quimby 

Section ITR.1 Overview Last Revised: 11/04/2014 Transformed Moment of Inertia are used for computing stress and deflection in composite members (i.e. member that consist of materials with different Modulus of Elasticity, E). The need for using transformed sections results from the fact that most elastic stress and deflection equations assume homogeneous materials. When materials have different stiffnesses (i.e. different E) then the equations for stress and deflection need to be modified to account for the difference. One way of modifying the equations is to modify the section property terms by "transforming" all the materials in the section into a single material. To get a section in one material that has the same stiffness as the composite material requires that you change the cross sectional dimensions to account for the change in material stiffness. The following sections show how this is done. 