Question

Using the compressive stress-strain data provided in fig below and the Australian standard AS 1012.17 test method for determining the modulus of elasticity of concrete, determine the modulus of elasticity of concrete for the following two scenarios: a. concrete requiring complete hydration f the Portland cement and minimal porosity b. Concrete that will simulate equivalent workability to the concrete mix listed in bullet point (a) but with HWR added to the mix to maximize the plasticising effect

Answer 1

Answer)

We know, for complete hydration of cement and minimum porosity required water cement ratio is 0.50. Also, modulus of elasticity (E) is slope of stress strain curve within elastic limit so. according to 0.5 w/c ratio curve

=> E = (\sigma2 - \sigma 1) / (\varepsilon2 - \varepsilon 1)

Let \sigma 1 and \sigma2 be two stress within elastic limit so,

\sigma1 = 20 MPa and \sigma 2 = 10 MPa

Strain corresponding to 20 MPa is 900 x10^(-6)

Strain corresponding to 10 MPa is 400 x 10^(-6)

=> E = (20 - 10) / [(900 - 400) x 10^(-6)]

=> E = 10 / [500 x 10^(-6)]

=> E = 20000 MPa or 20 GPa

So, option C is correct

Ans) Now, since workability of concrete is same as in part (a) but water retarder (HWR) is added to the mix so w/c ratio will be more that as it in part (a) . Therefore w/c ratio can be either 0.67 or 1. But since, w/c ratio cannot be more than 1 as it will result in bleeding so only option left for w/c ratio is 0.67 .

Also, modulus of elasticity (E) is slope of stress strain curve within elastic limit so. according to 0.67 w/c ratio curve

=> E = (\sigma2 - \sigma 1) / (\varepsilon2 - \varepsilon 1)

Let \sigma 1 and \sigma2 be two stress within elastic limit so,

\sigma1 = 10 MPa and \sigma 2 = 5 MPa

Strain corresponding to 10 MPa is 500 x10^(-6)

Strain corresponding to 5 MPa is 250 x 10^(-6)

=> E = (10 - 5) / [(500 - 250) x 10^(-6)]

=> E = 5 / [250 x 10^(-6)]

=> E = 20000 MPa or 20 GPa