![]() ![]() Compute the first-order, mean-centered estimates for the mean and standard deviation of the modulus of elasticity. Furthermore, the density and compressive strength are positively correlated with ρ = 0.30. The uncertainty in the compressive strength f c ′ is also modeled with a gamma distribution but with parameters k = 16 and λ = 0.004 in 2 / lb. For a particular type of concrete, the density, γ c , has a gamma distribution (see Section 8 of Lecture notes) with parameters k = 210.25 and λ = 1.45 ft 3 / lb. Because the density and compressive strength of concrete are uncertain quantities, we treat them as random variables. The Canadian Concrete Design Handbook provides the following formula for predicting the modulus of elasticity of reinforced concrete (the American Concrete Institute has a similar formula) E c = 0.033 γ c 1.5 f c ′ where E c is the modulus of elasticity in kips / in 2, γ c is the density of the concrete in lb / ft 3 and f c ′ is the compressive strength of concrete in l b / in 2. Reinforced concrete beam design includes serviceability, ultimate limit state design in bending and design for shear according to AS3600-2018.
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