Thin cylindrical/spherical shells: if thickness-to-diameter ratio is less than 0.1 (thin shell), which stress effect is neglected in membrane-stress calculations?

Introduction / Context:Thin-shell theory simplifies stress analysis of pressurized vessels and domes by assuming membrane action dominates. This is common for tanks, pipelines, and vessels with small thickness compared to radius/diameter.

Given Data / Assumptions:

• Thickness-to-diameter ratio t/D < 0.1, qualifying as “thin.”
• Uniform internal pressure, away from edges/discontinuities.
• Material behaves elastically within service conditions.

Concept / Approach:Membrane theory assumes forces act in the shell surface producing primarily in-plane (membrane) stresses. Bending moments and transverse shear are neglected in regions far from boundaries or local loads, enabling simple closed-form expressions for hoop and meridional stresses.

Step-by-Step Solution:Identify dominant stresses: hoop and longitudinal (membrane) due to pressure.Recognize that bending moments are small for thin shells under uniform pressure.Therefore, bending is neglected in membrane-stress calculations.

Verification / Alternative check:Edge effects and nozzles require refined analysis (e.g., bending present locally). Away from discontinuities, membrane assumptions accurately predict stresses and deformations.

Why Other Options Are Wrong:

• Deformation/elongation: These occur and are part of the membrane response.
• Shear: Transverse shear is small but the primary neglected effect emphasized in theory is bending.
• Internal pressure: This is the loading cause, not something neglected.

Common Pitfalls:Applying membrane formulas near supports/nozzles where bending cannot be ignored; using thin-shell equations for thick shells.

Final Answer:Bending