Stiffness EI of Composite Beam (Steel W Shape Encased in Conc) 1

[tipsabc]

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.

 

[JAE]

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.

 

[tipsabc]

Thank you, JAE. I appreciate it.