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15 July, 01:55

A 21-mm-diameter steel bar is to be used as a torsion spring. If the torsional stress in the bar is not to exceed 109 MPa when one end is twisted through an angle of 15°, what must be the length of the bar?

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  1. 15 July, 05:35
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    2m

    Explanation:

    The modulus of rigidity was omitted in the question and I'm using the modulus of rigidity of structural steel (G=79 GPa)

    For the shaft, the maximum moment

    T=π*rho*d³/16

    Where π=3.14

    Rho = torsional stress=109MPa

    d=diameter of of shaft = 21mm

    Inserting values of π, rho and d

    T = 198,230.54Nmm

    Polar moment of the shaft is given by

    J = π D⁴ / 32

    Also torsional moment (in radian) of the shaft is given as

    α = L * T / (J * G)

    α = 32 * L*T / (G * π * D⁴)

    And in degrees,

    αdegrees = 584 * L*T / (G*D⁴)

    Where L=length of shaft and G is modulus of rigidity

    L=α*d⁴*G/584*T

    Where α=15⁰, d=0.021m, G=79*10⁹Pa, T=198.23Nm

    Substituting values for α, d, G and T

    L=1.99m approximately 2m
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