I am doing a comparative analysis of steel and reinforced concrete sections. I need transformed RC section of beams and columns (rectangular) for exactly same I of steel sections which I have already completed works for. I will be glad if any one give me an idea, and thank you in advance.
For example, I need RC section (rectangular) for beam having equivalent I with W 12 x 79 steel beam. Actually, I am worried about the type and numbers of Rebars, and the slab above the beam as they contribute to the I of transformed section.
Dear Prabodh:
It is not possible to transform a steel section into a reinforced concrete section. However, you can simulate the properties of a steel section using a reinforced concrete section. You have to decide if the simulation is for the linear range (i.e. pre-yielding) or the strength (i.e. plastic) range. In the case of the former, you can use an iterative process as follows:
1) determine the moment of inertia for the steel section,
2) estimate gross section dimensions for the concrete section,
3) select a trial reinforcing scheme for the concrete section,
4) determine the moment of inertia of the trial concrete section,
5) compare moments of inertia for steel and concrete sections, and
6) if the I values do not match, revise the concrete section and return to 4).
For step 2), you can assume initially that the cracked section moment of inertia for the concrete section is one-third that of the uncracked section, and that the cracked section moment of inertia for a T-section is twice that of the web alone (assuming that the slab is in compression).
If you are simulating the plastic response, then you can use moment-curvature relations for trial concrete sections that match that of the steel section. Response2000 (http://www.ecf.utoronto.ca/~bentz/r2k.htm) is a good (and free) option for the moment-curvature calculations.
I hope that this helps.
Art
In the earlier reinforced concrete practices based on working stress design (WSD), an approach called transformed area method was used for cracked section analysis. I have attached two files that will give you an idea, I hope it can serve the purpose
Dear Prabodh:
What I am suggesting in step 4) in my suggested procedure is calculation using the cracked and transformed section concept. However, that procedure alone is not sufficient because it requires numerical values for the concrete section dimensions as well as the steel reinforcement. The other steps in my suggested procedure define an iterative procedure that will allow you to determine the concrete section depth and width, and the amount of reinforcement.
Arturo
Hello Prabodh
You must resolve the equation
Es * Is = 6 Ec * Ic
Es is the Young modulus of steel, and Ec is the modulus of concrete; Is and Ic are the moments of inertia.
Why 6 times?, because the cracked section must be taken into account.
Maybe you need to fix the base and resolve depth for a rectangular shape.
Good look
Hello Prabodh, you can follow Nasir Shafiq answer, or you can also refer to the Steel Design book by William T. Segui (pages 552-559), which provides a straightforward analysis of the problem.
Dear Prabodh:
Attached please find an example that implements the simple procedure that I suggested.
Arturo
it is very interesting question. however, they are two different materials having different elasticity modulus.
Just a small remark from my side: to be sure, you should probably add which moment of inertia you are trying to fit. For instance, if you are working in the field of explosive loading of structures, different moments of inertia come into play.
Je vous suggère d'utiliser la notion de section équivalente. Si les deux matériaux ont la même inertie, ils subiront la même déformation sous même charge.
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