Numerical - Maximum principle stress, given torque & bending moment

Q.  What is the maximum principle stress induced in a solid shaft of 40 mm diameter which is subjected to both bending moment and torque of 300 kN.mm and 150 kN.mm respectively?
- Published on 23 Sep 15

a. 21.69 N/mm2
b. 28.1 N/mm2
c. 50.57 N/mm2
d. 52.32 N/mm2

ANSWER: 50.57 N/mm2

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    Discussion

  • Sravanthi   -Posted on 25 Nov 15
    Given: Diameter of shaft = 40 mm, bending moment = 300 kNmm, torque = 150 kNmm

    Formula: 1) Maximum principle stress = (1 / Zp) x [ M + √M2 + T2]

    here, Zp is the polar sectional modulus, M is the bending moment, T is the torque

    2) Polar sectional modulus (Zp )= (J / R)


    Solution:

    1) Polar sectional modulus = (J / R)

    J = (πd4) / 32 = (π 404) / 32 = 251327.41 mm4

    R = d / 2 = 40 / 2 = 20 mm

    Polar sectional modulus = 251327.41 mm4 / 20 mm = 12566.37 mm3

    2) Maximum principle stress = (1 / Zp) x [ M + √M2 + T2]

    Substituting the given values,

    = (1 / 12566.37) x [300 x 103 +√ (300 x 103)2 + (150 x 103)2

    = 50.57 N/mm2

    The maximum principle stress induced in a solid shaft is 50.57 N/mm2

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