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25 December, 04:56

A 100 ft long steel wire has a cross-sectional area of 0.0144 in. 2. When a force of 270 lb is applied to the wire, its length increases by 0.75 in. Determine: a. The stress (precision of 1000) b. The strain (precision of 0.00000) c. The modulus of elasticity of the steel (precision of 1,000,000)

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  1. 25 December, 06:35
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    (a) The stress on the steel wire is 19,000 Psi

    (b) The strain on the steel wire is 0.00063

    (c) The modulus of elasticity of the steel is 30,000,000 Psi

    Explanation:

    Given;

    length of steel wire, L = 100 ft

    cross-sectional area, A = 0.0144 in²

    applied force, F = 270 lb

    extension of the wire, e = 0.75 in

    Part (A) The stress on the steel wire;

    δ = F/A

    = 270 / 0.0144

    δ = 18750 lb/in² = 19,000 Psi

    Part (B) The strain on the steel wire;

    σ = e / L

    L = 100 ft = 1200 in

    σ = 0.75 / 1200

    σ = 0.00063

    Part (C) The modulus of elasticity of the steel

    E = δ/σ

    = 19,000 / 0.00063

    E = 30,000,000 Psi
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