Answered: Analyze the stress developed in…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Analyze the stress developed in thin-walled pressure vessels?

Expert Solution

Step 1

Thin-walled pressure vessels are the vessels whose thickness may be considered very small compared to their diameter.

Criteria for thin vessels,

$(\frac{Inner dia of the cylinder (d_{i})}{wall thickness (t)}) > (15 or 20)$

Stresses in the thin cylindrical pressure vessels, considering both ends are closed.

1) Longitudinal stress $(σ_{L})$ : These are tensile in nature due to internal pressure (P_i) and compressive in nature if an external pressure is applied to it. In the case of thin cylindrical, these are uniform across the thickness of the shell.

$(σ_{L}) = (\frac{P_{i} \times D_{i}}{4 \times t})$

2) Hoop or circumferential stress $(σ_{h})$ : These are tensile in nature due to internal pressure (P_i) is applied to it. In the case of thin cylindrical, these are uniform across the thickness of the shell.

$(σ_{h}) = (\frac{P_{i} \times D_{i}}{2 \times t})$

3) Radial stresses: These are neglected in the case of thin cylindrical pressure vessels as their magnitudes are negligible as compared to the other two stresses in it.

And $(σ_{L}) a n d (σ_{h})$ are the principal stresses as no shear stress acts on in the plane.

4) Absolute maximum shear stresses,

$(τ_{\max, absolute}) = (\frac{σ_{h} - 0}{2}) = (\frac{P_{i} \times D_{i}}{4 \times t})$

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