Effective Elastic Properties

In order to simplify calculations it is possible to determine affective elastic properties of a section. The simplest of these is the area. Consider a section with both concrete and steel with areas and respectively. The axial stiffnesses are

And the total stiffness is then

To simply calculation we can choose a reference material. So for concrete as a reference material

or

More generally for a collection of components with a reference section

For a section made of multiple components the effective centroid is defined as

As for axial properties effective bending properties can be defined (allowing for the different centroids) as