One characteristic of thick cylinders is that the circumferential stress is constant throughout their thickness.

Question

BlackTom AI · Accepted Answer

Re-stating the question: The statement claims that in thick cylinders, the circumferential (hoop) stress is constant throughout the thickness of the cylinder.
Option 1: True. The claim that the hoop stress remains constant across the thickness is not accurate for thick-walled cylinders. In thick-walled pressure vessels, the radial and hoop stresses vary with the radial position r within the wall, with the hoop stress typically being highest at the inner surface and decreasing toward the outer surface according to the Lamé equations. Therefore, the assertion in this option is incorrect.
Option 2: False. Saying the hoop stress is constant throughout the thickness contradicts the classic thick-wall theory. The exact solution shows that stress is a function of radius, reflecting the redistribution of stress across the wall to balance internal pressure. This variability is a key feature distinguishing thick-walled from thin-walled behavior.
Additional nuance: In thin-walled assumptions, hoop stress is often approximated as uniform across the thickness, but this approximation breaks down for thick cylinders where the wall thickness is not small compared to the radius. The precise distribution requires solving the Lamé problem for thick cylinders, yielding a non-constant hoop stress profile.
In summary, the statement alleging a constant circumferential stress through thickness does not hold for thick cylinders, making the true classification of the option as incorrect and the overall assertion false.

BK10A6500 Engineering Mechanics 3 - Blended teaching 6.1.2025-20.4.2025 Quiz 9.2

One characteristic of thick cylinders is that the circumferential stress is constant throughout their thickness.

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