A close end tube of thin-walled circular section may be subjected to torque Tand internal pressure P, as shown in Figure Q3. The shear stress in the wall caused by the torque can be calculated as T = T/(2πR²t), where the mean radius of the cross section is R(i.e., the radius of the centreline of the wall) and the wall thickness is t. The internal radius of the tube can be calculated as (R-t/2). However, as R>>t, you can approximately assume that the internal radius of the tube is equal to Rin the subsequent calculation. The tube is made from a material with Young's modulus E, Poisson's ratio v. T Centreline of the wall R P Ozz бөө Orr Z бут бее Ozz Figure Q3 (a) If the change of the diameter cannot exceed 0.1 m under elastic deformation, calculate the minimum allowable wall thickness of the cylindrical pressure vessel if P=23.6 MPa, T=0 KN.m, R = 2 m, Young's modulus E = 246 GPa, and Poisson's ratio v = 0.21. Step-1 the functional relationships between hoop stress σ and wall thickness (units: mm), and the longitudinal stress σ, and wall thickness t(units: mm) can be most accurately expressed as (Please note that " X = L/2" is the same as "X = L÷2".) Select one: O 1. Hoop stress = 31466.667/t (MPa); Longitudinal stress = 31466.667/t (MPa) O 2. Hoop stress = 23600.000/t (MPa); Longitudinal stress = 23600.000/t (MPa) ○ 3. Hoop stress = 47200.000/t (MPa); Longitudinal stress = 18880.000/t (MPa) O 4. Hoop stress = 47200.000/t (MPa); Longitudinal stress = 23600.000/t (MPa) O 5. Hoop stress 15733.333/t (MPa); Longitudinal stress = 7866.667/t (MPa) ○ 6. Hoop stress = 31466.667/t (MPa); Longitudinal stress = 23600.000/t (MPa) 7. Hoop stress = 23600.000/t (MPa); Longitudinal stress = 11800.000/t (MPa) ○ 8. Hoop stress =94400.000/t (MPa); Longitudinal stress = 47200.000/t (MPa)
A close end tube of thin-walled circular section may be subjected to torque Tand internal pressure P, as shown in Figure Q3. The shear stress in the wall caused by the torque can be calculated as T = T/(2πR²t), where the mean radius of the cross section is R(i.e., the radius of the centreline of the wall) and the wall thickness is t. The internal radius of the tube can be calculated as (R-t/2). However, as R>>t, you can approximately assume that the internal radius of the tube is equal to Rin the subsequent calculation. The tube is made from a material with Young's modulus E, Poisson's ratio v. T Centreline of the wall R P Ozz бөө Orr Z бут бее Ozz Figure Q3 (a) If the change of the diameter cannot exceed 0.1 m under elastic deformation, calculate the minimum allowable wall thickness of the cylindrical pressure vessel if P=23.6 MPa, T=0 KN.m, R = 2 m, Young's modulus E = 246 GPa, and Poisson's ratio v = 0.21. Step-1 the functional relationships between hoop stress σ and wall thickness (units: mm), and the longitudinal stress σ, and wall thickness t(units: mm) can be most accurately expressed as (Please note that " X = L/2" is the same as "X = L÷2".) Select one: O 1. Hoop stress = 31466.667/t (MPa); Longitudinal stress = 31466.667/t (MPa) O 2. Hoop stress = 23600.000/t (MPa); Longitudinal stress = 23600.000/t (MPa) ○ 3. Hoop stress = 47200.000/t (MPa); Longitudinal stress = 18880.000/t (MPa) O 4. Hoop stress = 47200.000/t (MPa); Longitudinal stress = 23600.000/t (MPa) O 5. Hoop stress 15733.333/t (MPa); Longitudinal stress = 7866.667/t (MPa) ○ 6. Hoop stress = 31466.667/t (MPa); Longitudinal stress = 23600.000/t (MPa) 7. Hoop stress = 23600.000/t (MPa); Longitudinal stress = 11800.000/t (MPa) ○ 8. Hoop stress =94400.000/t (MPa); Longitudinal stress = 47200.000/t (MPa)
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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Transcribed Image Text:A close end tube of thin-walled circular section may be subjected to torque Tand internal pressure P, as shown in Figure Q3. The shear stress in the wall caused by
the torque can be calculated as T = T/(2πR²t), where the mean radius of the cross section is R(i.e., the radius of the centreline of the wall) and the wall thickness
is t. The internal radius of the tube can be calculated as (R-t/2). However, as R>>t, you can approximately assume that the internal radius of the tube is equal to Rin
the subsequent calculation. The tube is made from a material with Young's modulus E, Poisson's ratio v.
T
Centreline of
the wall
R
P
Ozz
бөө
Orr
Z
бут
бее
Ozz
Figure Q3
(a) If the change of the diameter cannot exceed 0.1 m under elastic deformation, calculate the minimum allowable wall thickness of the cylindrical pressure vessel if
P=23.6 MPa, T=0 KN.m, R = 2 m, Young's modulus E = 246 GPa, and Poisson's ratio v = 0.21.
Step-1
the functional relationships between hoop stress σ and wall thickness (units: mm), and the longitudinal stress σ, and wall thickness t(units: mm) can be
most accurately expressed as
(Please note that " X = L/2" is the same as "X = L÷2".)
Select one:
O 1. Hoop stress = 31466.667/t (MPa); Longitudinal stress = 31466.667/t (MPa)
O 2. Hoop stress = 23600.000/t (MPa); Longitudinal stress = 23600.000/t (MPa)
○ 3. Hoop stress = 47200.000/t (MPa); Longitudinal stress = 18880.000/t (MPa)
O 4. Hoop stress = 47200.000/t (MPa); Longitudinal stress = 23600.000/t (MPa)
O 5. Hoop stress 15733.333/t (MPa); Longitudinal stress = 7866.667/t (MPa)
○ 6. Hoop stress = 31466.667/t (MPa); Longitudinal stress = 23600.000/t (MPa)
7. Hoop stress = 23600.000/t (MPa); Longitudinal stress = 11800.000/t (MPa)
○ 8. Hoop stress =94400.000/t (MPa); Longitudinal stress = 47200.000/t (MPa)
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