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16 May, 17:31

On a day that the temperature is 21.0°C, a concrete walk is poured in such a way that the ends of the walk are unable to move. Take Young's modulus for concrete to be 7.00 109 N/m2 and the compressive strength to be 2.00 109 N/m2. (The coefficient of linear expansion of concrete is 1.2 10-5 (°C-1).) (a) What is the stress in the cement on a hot day of 33.0°C? N/m2

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  1. 16 May, 17:52
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    1*10^6 N/m^2

    Explanation:

    Coefficient of Linear Expansion for Concrete = α = 1.2 x 10^-5 (°C) ^-1

    Change in temperature = ΔT

    ΔT = T2 - T1

    ΔT = 33 - 21

    ΔT = 12°C

    ΔL = α * L (i) * ΔT

    ΔL = (1.2 x 10^-5 (°C) ^-1) * L (i) * (12°C)

    ΔL = 1.44 x 10^-4

    Stress = F / A

    Strain = ΔL / L

    Strain = (1.44*10^-4) * (L) / L

    Strain = 1.44*10^-4

    Y = Stress / Strain

    Stress = Y * Strain

    Stress = (7.00*10^9 N/m^2) * (1.44*10^-4)

    Stress = 1*10^6 N/m^2

    Thus, the stress in the cement on a hot day of 33° is 1*10^6 N/m^2
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