The magnitude relation between the longitudinal (σ_l), radial (σ_r) and circumferential (σ_c) stresses is (being

Question

BlackTom AI · Accepted Answer

When comparing stresses in a pressurized cylinder or vessel, several relative magnitudes are commonly observed due to how forces distribute around the geometry.
Option 1: 'σ_c > σ_r > σ_l' claims the circumferential (hoop) stress is largest, followed by radial, then longitudinal. This ordering misplaces the axial stress, which, for internal pressure scenarios, typically sits between hoop and radial but not below radial in magnitude; thus this sequence is inconsistent with standard stress distributions.
Option 2: 'σ_c > σ_l > σ_r' states that the circumferential (hoop) stress is the largest, the longitudinal (axial) stress is second, and the radial stress is the smallest. This aligns with the conventional pattern in many pressure-loaded cylinders (especially thin-walled approximations), where hoop stress dominates due to the continuous tension around the circumference, axial stress arises from the ends, and radial stress remains smallest and is often limited to the inner boundary where the pressure acts.
Option 3: 'σ_l > σ_r > σ_c' asserts that axial stress is the largest and hoop stress is the smallest. This contradicts the fundamental behavior under internal pressure, where the hoop stress generally exceeds the axial stress, so this ordering is incorrect.
Option 4: 'σ_r > σ_l > σ_c' claims radial stress is the largest, which is not typical in standard pressure-supported configurations, since radial stress is usually the smallest component (often near zero on the outer surface) and hoop stress dominates. Therefore this choice is inaccurate.
Overall, the second option matches the well-established hierarchy of stresses in many pressure-acted cylindrical structures, with hoop stress being the greatest, followed by axial, and radial being the smallest.

The magnitude relation between the longitudinal (σ_l), radial (σ_r) and circumferential (σ_c) stresses is (being单项选择题

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