How to evaluate the stiffness EI of a composite beam (like W24 encased inside a 36 in diameter 4000 psi concrete) considering the craking effect in concrete? Thank you very much.
Probably much like ACI does to develop their Ie value in Chapter 9.
I would look at the unfactored load stress condition and discount any concrete that was in a tension zone. You could include rebar in the tension and compression zones as well - just transform the concrete in compression to steel - with a circular cross section that is much more difficult - you'd end up with an ellipse when factoring the width down by n=Es/Ec.
You could perhaps take segments of the compresssion portion of the circular concrete section and transform each one down. Then just calculate your properties.
ACI treats a concrete section for determination of moment of inertia using a transition between the non-cracked and fully cracked conditions. This is their Ie formula where they discount some of the stiffness before the section reaches the cracking moment. I presume you could do something like that here...just not sure of the step-by-step process.
AISC has a nice section in their LRFD manual (second edition) on page 5-67 where they deal with composite columns - check that out and see if it helps you.