Concrete has a tensile strength of 3×106 Pa and an elastic modulus of 30×109 Pa. Because the concrete fractures in a brittle manner, it is to be reinforced with 10 vol % uniaxial 1020 steel rebar that has a yield strength of 205×106 Pa, and the steel rods have an elastic modulus of 211×109 Pa.
(a) What is the maximum strain that this composite can withstand without the concrete cracking or the rebar yielding?
(b) What is the maximum tensile stress applied parallel to the rebar axis that can be withstood by this reinforced concrete before the concrete cracks or the rebar yields? Assume that there is good bonding between the concrete and the rebar.
(a) Assume that the concrete is linear elastic to the tensile fracture stress (?cu). Then the strain in the concrete when it begins to fracture is
(b) Calculate the stress in the rebar (?r) when the concrete begins to fracture assuming the isostrain model; thus the strain in the concrete and steel are the same
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