Can I Transform Multiple Steel Beams into a Single Piece of Concrete?

[pj33]

When I convert the steel beams to concrete, do I transform the several different beams into a single piece of concrete in order to do the calculations to find the second moment of area of the beam or do I transform each beam separately into a concrete piece?
Intuitively, t seems reasonable to just convert all the beams into a single piece of concrete as the the cross-sectional area is usually small, but if it is true is it always valid?

 

[Lnewqban]

I believe that we will need some kind of schematic, or more information at least.

 

[pj33]

In a simple case like this.

 

[jrmichler]

My copy of Reinforced Concrete Design, by Spiegel and Limbrunner, has 18 pages on the design of rectangular beams with only tension steel. I recommend that you find a similar book because there is more to the analysis than what is implied in your question.

Hint: Read carefully the part about balanced vs underreinforced vs overreinforced beams.

 

[Lnewqban]

In a simple case like this.

What is the material within the rest of the rectangular cross section?
Does that concrete contain steel in any shape?

 

[pj33]

What is the material within the rest of the rectangular cross section?
Does that concrete contain steel in any shape?

It is a rectangular shaped concrete which has 3 beams of steal in order to reinforce it. When I transforme the 3 beams, I have converted all 3 of them to a single piece of concrete with area mA.
A is the total area of the 3 beams of steal and m is the ratio of the steal's Young's Modulus to the concrete's Young's Modulus