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29 September, 17:23

A gear motor can develop 2 hp when it turns at 450rpm. If the motor turns a solid shaft with a diameter of 1 in., determine the maximum shear stress developed in the shaft. (30 pts)

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  1. 29 September, 17:37
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    Maximum shear stress is;

    τ_max = 1427.12 psi

    Explanation:

    We are given;

    Power = 2 HP = 2 * 746 Watts = 1492 W

    Angular speed; ω = 450 rev/min = 450 * 2π/60 rad/s = 47.124 rad/s

    Diameter; d = 1 in

    We know that; power = shear stress * angular speed

    So,

    P = τω

    τ = P/ω

    τ = 1492/47.124

    τ = 31.66 N. m

    Converting this to lb. in, we have;

    τ = 280.2146 lb. in

    Maximum shear stress is given by the formula;

    τ_max = (τ•d/2) / J

    J is polar moment of inertia given by the formula; J = πd⁴/32

    So,

    τ_max = (τ•d/2) / (πd⁴/32)

    This reduces to;

    τ_max = (16τ) / (πd³)

    Plugging in values;

    τ_max = (16 * 280.2146) / ((π*1³)

    τ_max = 1427.12 psi
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