Torsion: solid vs. hollow shaft with identical length, weight, and material Two shafts A (solid) and B (hollow) have the same length, weight, and material; both are under pure torsion. State the correct comparative statement about their torsional strength/stiffness.
-
ABoth transmit the same torque at the same allowable shear stress
-
BThe solid shaft is stronger and stiffer
-
CThe hollow shaft is stronger and stiffer for the same weight
-
DThe hollow shaft is weaker but stiffer
Answer
Correct Answer: The hollow shaft is stronger and stiffer for the same weight
Explanation
Given• Same material ⇒ same allowable shear stress (τallow) and shear modulus G.• Same length and weight ⇒ for the hollow shaft, material is distributed farther from the center.
ConceptTorque capacity at a given τ scales with the polar section modulus Zp; torsional stiffness scales with the polar moment of inertia J:Tmax = τallow · Zp, θ = T L / (G J)For a given mass, moving material outward (hollowing) increases both J and Zp, hence higher torque capacity and lower twist.
ResultA hollow shaft of equal weight/length is stronger in torsion and has greater torsional rigidity than a solid shaft.
Final AnswerThe hollow shaft is stronger and stiffer for the same weight