Concrete can be pre-stressed in structural applications using steel wires stretched in tension prior to the curing of the concrete and upon

Question

Concrete can be pre-stressed in structural applications using steel wires stretched in tension prior to the curing of the concrete and upon curing, the tension can be released, compressing the concrete. If steel wires comprising 40% of the composite volume are pulled with 500kN of force and then released once the concrete has cured. What is the amount of force transferred to the concrete?

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Ben Gia 6 months 2021-08-05T17:11:32+00:00 2 Answers 5 views 0

Answers ( )

    0
    2021-08-05T17:12:48+00:00

    Answer: 500kN

    Explanation: the total force transfered to the concrete is 500kN force with which it was prestressed.

    0
    2021-08-05T17:13:23+00:00

    Here is the full question

    Concrete can be pre-stressed in structural applications using steel wires stretched in tension prior to the curing of the concrete and upon curing, the tension can be released, compressing the concrete. If steel wires comprising 40% of the composite volume are pulled with 500kN of force and then released once the concrete has cured. What is the amount of force transferred to the concrete?

    (moduli of concrete and wires are 50 and 100 GPa respectively.)

    Answer:

    375 kN

    Explanation:

    Given that:

    A steel wire A_s = 40 % ; if we consider the width of the steel to be =40%;

    Then , the concrete A_c = 60%

    Load (P) = 500 kN

    Moduli of concrete E_c = 50 GPa

    Moduli of steel wire E_s = 100 GPa

    A_T = A_s + A_c

    (\frac{stress}{strain})_s = 100 \ GPa

    \frac{500*1000N/Ast}{Strain_s} =100 GPa

    Strain_s = \frac{500*1000\ N\ mm^2}{100*10^9\ N \ A_st }

    Strain_s = \frac{5*10^{-6}}{0.4A_t}

    Strain_s = \frac{1.25*10^{-5}}{A_t}

    Since;

    Strain_{steel} = Strain_ {concrete}

    Then:

    \frac{1.25*10^{-5}}{A_t} = \frac {Stress_s}{E_c}

    Stress in the concrete = \frac{1.25*10^{-5}*E_c}{A_t}

    Stress in the concrete = \frac{1.25*10^{-5}* 50*10^9}{A_t}

    Stress in the concrete = \frac{625 \ kN}{A_t}

    However,0.6 A_t = A_c

    ∴ Force transferred to  the concrete = \frac{625 \ kN}{A_t} * \ 0.6 \ A_t

    Force  transferred to the concrete = 375 kN

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