Civil Engineering MCQAE Level Civil Engineering
For a solid circular shaft of diameter D, the polar moment of inertia J is:
Engineering MechanicsPolar Moment of Inertia ShaftMEDIUM
Choose the correct answer
A
J = pi D^4 / 64
B
J = pi D^4 / 32
C
J = pi D^3 / 16
D
J = D^4 / 16
Correct Answer
B. J = pi D^4 / 32
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Polar moment: J = Ixx + Iyy = 2 Ixx (by symmetry for circular sections) = 2 x piD^4/64 = piD^4/32. For hollow shaft (D_o, D_i): J = pi(D_o^4 - D_i^4)/32. Torsion formula: tau_max = T x (D/2) / J = T D / (pi D^3 / 16) = 16T / pi D^3. Angle of twist theta = TL / (GJ).
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