a concrete has a height of 5m and has unit area 3m² supports a mass of 30000kg. Determine the stress, strain and change in height ​

Question

a concrete has a height of 5m and has unit area 3m² supports a mass of 30000kg.
Determine the stress, strain and change in height ​

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Thành Đạt 5 years 2021-07-15T14:22:12+00:00 1 Answers 13 views 0

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  1. Philomena
    0
    2021-07-15T14:24:00+00:00
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    Answer:

    stress = 98000 N/m^2

    strain = 3.92 x 10^-6

    change in height = 0.0196 mm

    Explanation:

    Height, h = 5 m

    Area, A = 3 m²

    mass, m = 30000 kg

    Stress is defined as the force per  unit area.

    stress = \frac{mg}{A}\\\\stress = \frac{30000\times 9.8}{3}\\\\stress = 98000 N/m^2

    Young’s modulus of concrete is Y = 2.5 x 10^10 N/m^2

    Young’s modulus is defined as the ratio of stress to the strain.

    Y = \frac{stress}{strain}\\\\2.5\times 10^{10}= \frac{98000}{strain}\\\\strain = 3.92\times 10^{-6}

    let the change in height is h’.

    Strain is defined as the ratio of change in height to the original height.

    3.92\times 10^{-6} = \frac{h'}{5}\\\\h' = 1.96\times 10^{-5}m = 0.0196 mm

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