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The gas tank shown in Figure 4 is made from A-36 steel and has an inner diameter of 1.50 m The tank should withstand a gauge pressure of p-5 MPa. Apply a F.S.=1.5 against yielding. a. Express the hoop stress and the longitudinal stress as functions of the thickness t. Assume that the vessel is thin-walled. b. Determine the required minimum wall thickness to the nearest mm using the maximum-shear-stress theory. Neglect the radial stress, assuming that the vessel is subjected to a biaxial stress. c. Prove that the designed by the maximum-shear-stress theory vessel is thin-walled.

The gas tank shown in Figure 4 is made from A-36 steel and has an inner diameter of 1.50 m The tank should withstand a gauge pressure of p-5 MPa. Apply a F.S.=1.5 against yielding. a. Express the hoop stress and the longitudinal stress as functions of the thickness t. Assume that the vessel is thin-walled. b. Determine the required minimum wall thickness to the nearest mm using the maximum-shear-stress theory. Neglect the radial stress, assuming that the vessel is subjected to a biaxial stress. c. Prove that the designed by the maximum-shear-stress theory vessel is thin-walled.

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
Problem 1.1MA
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Figure 4 The gas tank shown in Figure 4 is made from A-36 steel and has an inner diameter of 1.50 m. The tank should withstand a gauge pressure of p-5 MPa. Apply a F.S.=1.5 against yielding. a. Express the hoop stress and the longitudinal stress as functions of the thickness t. Assume that the vessel is thin-walled. b. Determine the required minimum wall thickness to the nearest mm using the maximum-shear-stress theory. Neglect the radial stress, assuming that the vessel is subjected to a biaxial stress. c. Prove that the designed by the maximum-shear-stress theory vessel is thin-walled. d. Determine the required minimum wall thickness to the nearest mm using the maximum-distortion-energy theory. Neglect the radial stress, assuming that the vessel is subjected to a biaxial stress. e. Prove that the designed by maximum- distortion-energy theory vessel is thin-walled. f. Assume that the vessel has thickness t designed by maximum-distortion-energy theory. Take an infinitely small volume element centered at a point on the interior wall of the vessel. Denote that point as A. Calculate and depict all stresses acting on the walls of that element including the radial stress. Classify the state of stress at 4.
Transcribed Image Text:Figure 4 The gas tank shown in Figure 4 is made from A-36 steel and has an inner diameter of 1.50 m. The tank should withstand a gauge pressure of p-5 MPa. Apply a F.S.=1.5 against yielding. a. Express the hoop stress and the longitudinal stress as functions of the thickness t. Assume that the vessel is thin-walled. b. Determine the required minimum wall thickness to the nearest mm using the maximum-shear-stress theory. Neglect the radial stress, assuming that the vessel is subjected to a biaxial stress. c. Prove that the designed by the maximum-shear-stress theory vessel is thin-walled. d. Determine the required minimum wall thickness to the nearest mm using the maximum-distortion-energy theory. Neglect the radial stress, assuming that the vessel is subjected to a biaxial stress. e. Prove that the designed by maximum- distortion-energy theory vessel is thin-walled. f. Assume that the vessel has thickness t designed by maximum-distortion-energy theory. Take an infinitely small volume element centered at a point on the interior wall of the vessel. Denote that point as A. Calculate and depict all stresses acting on the walls of that element including the radial stress. Classify the state of stress at 4.
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