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15.3 (B). Show that the strain energy per unit volume of a material under a single direct stress is given by (stress x strain). Hence show that for a material under the action of the principal stresses o1,02 and o3 the strain energy per unit volume becomes 1 2E A thin cylinder 1m diameter and 3 m long is filled with a liquid to a pressure of 2 MN/m². Assuming a yield stress for the material of 240 MN/m2 in simple tension and a safety factor of 4, determine the necessary wall thickness of the cylinder, taking the maximum shear strain energy as the criterion of failure. For the cylinder material, E = 207 GN/m² and v 0.286. [14.4 mm.]

15.3 (B). Show that the strain energy per unit volume of a material under a single direct stress is given by (stress x strain). Hence show that for a material under the action of the principal stresses o1,02 and o3 the strain energy per unit volume becomes 1 2E A thin cylinder 1m diameter and 3 m long is filled with a liquid to a pressure of 2 MN/m². Assuming a yield stress for the material of 240 MN/m2 in simple tension and a safety factor of 4, determine the necessary wall thickness of the cylinder, taking the maximum shear strain energy as the criterion of failure. For the cylinder material, E = 207 GN/m² and v 0.286. [14.4 mm.]

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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15.3 (B). Show that the strain energy per unit volume of a material under a single direct stress is given by (stress x strain). Hence show that for a material under the action of the principal stresseso,,02 and o, the strain energy per unit volume becomes 1 Toi+o +o3 - 2v(0,02+0,03+0203)] 2E A thin cylinder 1m diameter and 3 m long is filled with a liquid to a pressure of 2 MN/m?. Assuming a yield stress for the material of 240 MN/m2 in simple tension and a safety factor of 4, determine the necessary wall thickness of the cylinder, taking the maximum shear strain energy as the criterion of failure. For the cylinder material, E = 207 GN/m2 and v 0.286. [14.4 mm.]
Transcribed Image Text:15.3 (B). Show that the strain energy per unit volume of a material under a single direct stress is given by (stress x strain). Hence show that for a material under the action of the principal stresseso,,02 and o, the strain energy per unit volume becomes 1 Toi+o +o3 - 2v(0,02+0,03+0203)] 2E A thin cylinder 1m diameter and 3 m long is filled with a liquid to a pressure of 2 MN/m?. Assuming a yield stress for the material of 240 MN/m2 in simple tension and a safety factor of 4, determine the necessary wall thickness of the cylinder, taking the maximum shear strain energy as the criterion of failure. For the cylinder material, E = 207 GN/m2 and v 0.286. [14.4 mm.]
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