For example if concrete have E= 200 Mpa and Rebars have 500Mpa then how to find the Modulus (E) and other properties of the re- in forced concrete?
Not sure this is what you are looking for but it is common practice to establish compatibility of materials.
The material of the concrete reinforced section can be considered to be homogeneous if the area of steel is transformed into area of concrete - or vice versa. The transformation of areas can be simply done by doing for instance Ast = As * Es/Ec, where the subscript indicates steel (s) or concrete (c) whilst Ast can be read as transformed area of steel (into concrete).
Not sure this is what you are looking for but it is common practice to establish compatibility of materials.
The material of the concrete reinforced section can be considered to be homogeneous if the area of steel is transformed into area of concrete - or vice versa. The transformation of areas can be simply done by doing for instance Ast = As * Es/Ec, where the subscript indicates steel (s) or concrete (c) whilst Ast can be read as transformed area of steel (into concrete).
You need to reduce the the modulus if the member is cracked. The standards usually have a formula (either in the standard or in the commentary). AS5100.5 and commentary have such a formula.
I guess that the discussion refers to the normal cross-section of the bar member and its behaviour under longitudinal tension/compression and/or bending. According to my understanding of the things there is no specific value of the modulus of elasticity (E) for the reinforced concrete. In the cross-section area there is usually the level of around 1% of steel and 99% of concrete area. So, there are two materials: concrete with usually larger area but lower modulus and steel with lower area and higher modulus. If the property you search for is the so called "modulus" of the whole cross-section, you have to select one reference material (usually concrete) and to substitute the area of the whole cross-section with the transformed area which accounts for the "rigidifying" effect of steel. The modulus of the cross-section will be then equal to the modulus of concrete. The whole expression for the rectangular cross-section which depth is h and width is b will be: Acs=bxh+(1-(Es/Ec))xAs. Please remember that always two parameters must be considered: area and modulus, never the only one of them.
I guess that the Modulus of Elasticity of Reinforced concrete might be higher than the modulus of elasticity of concrete and lower than the modulus of elasticity of steel. But I never see any equation or anything to calculate that. Just my Guess.
The true value of Modulus of elasticity of reinforced concrete might be obtained in lab experiments or with numerical analysis using softwares.
These steps might be followed to calculate the modulus of elasticity of reinforced concrete:
After performing many experiments may be you can develop an equation to calculate the modulus of elasticity of reinforced concrete. This will be an interesting project.
One way to calculate mechanical properties, such as young modulus, of reinforced materials is to use the "Rule of Mixtures":
"Rule of Mixtures is a method of approach to approximate estimation of composite material properties, based on an assumption that a composite property is the volume weighed average of the phases (matrix and dispersed phase) properties."
Long align fibers
Modulus of Elasticity in longitudinal direction (El)
El = Ec* Vc + Es* Vs
Modulus of Elasticity in transverse direction (Et)
1/ Et = Vc / Ec + Vs / Es
Where
Ec =Modulus of elasticity of concrete
Es = modulus of elasticity of steel
Vc = volume of concrete
Vs = volume of steel.
But remember that you have to allow for cracking, and crack spacing, So the rule of mixtures does not quite work.
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