Numerical - Maximum shear stress, given given torque & bending moment

Q.  What is the maximum shear stress induced in a solid shaft of 50 mm diameter which is subjected to both bending moment and torque of 300 kN.mm and 200 kN.mm respectively?
- Published on 23 Sep 15

a. 9.11 N/mm2
b. 14.69 N/mm2
c. 16.22 N/mm2
d. 20.98 N/mm2

ANSWER: 14.69 N/mm2

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    Discussion

  • Sravanthi   -Posted on 25 Nov 15
    Given: Shaft diameter = 50 mm, bending moment = 300 kN.mm, torque = 200 kN.mm

    Formula: 1) Polar sectional modulus (Zp )= (J / R)

    2) Maximum shear stress = (√ M2 + T2 ) / (Zp )

    Solution:

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

    J = (π 504) / (25) = 613592.31 mm3

    R = d / 2 = 50 / 2 = 25 mm

    (Zp )= 24543.69 mm3

    2) Maximum shear stress = (√ M2 + T2 ) / (Zp)

    = [√ (300 x 103)2 + (200 x 103)2 ] / ( 24543.69)

    = 14.69 N/mm2

    Maximum shear stress induced in a solid shaft is 14.69 N/mm2

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