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

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

Interesting question

Kindly follow Nasir Shafik answer.

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

Informative

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.