khinz -
You indicated familiarity with [Δ] = PL/AE.
For concrete - E is defined in the ACI 318 code as 57,000(sqrt(f'c)). If you have 5000 psi concrete then f'c = 5,000 psi and E = 57,000(sqrt(5000)) = 4,030,508 psi or 4,031 ksi.
The compressive strength f'c = 5,000 psi and the resulting E = 4,031 ksi are properties of your fully cured concrete.
The 5,000 psi strength (at 28 days) is verified by taking concrete cylinders and testing them to failure in a machine per an ASTM specification.
The tested cylinder strength, in actuality, might end up being a bit higher or lower than the target 5,000 psi strength. Say the test reveals that your concrete is 5,100 psi.
If so your E = 4,071 ksi.
So with that concrete your [Δ] would equal your PL/AE based on the E = 4,071 ksi.
If you had 3,000 psi specified concrete then E = 57,000(sqrt(3000)) and so on.
With weaker concrete (strength-wise) you would have smaller values of E and more deflection under load.
The value of E for steel is 29,000 ksi. No matter what maximum yield strength you have in the steel, the E is basically constant at 29,000 ksi.
You asked about a dual cylinder of steel and concrete.
I'm assuming you are talking about a cylinder where looking down on it you would see a half-circle of steel and a half-circle of concrete.
With that condition - if you tried to apply load to the cylinder, the two would compress equally under the testing machine - (same [Δ] - since the machine would probably be two heavy plates applying uniform load to the circular surface.
With a common delta you can then back calculate the load the steel takes and the load the concrete takes. Rearrange the [Δ]=PL/AE equation to get:
P(concrete) = ([Δ] x A(concrete) x E(concrete)) / L
P(steel) = ([Δ] x A(steel) x E(steel)) / L
The concrete force would be much smaller since it is "softer" than the steel. Think of compressing a cylinder with half of it steel and the other half of sponge or foam. The foam would take some load - but very very little....just enough to compress it by [Δ].
Does that answer your questions? I sure hope so.