that long cylinders, e.g. those used in pipelines, are subject to a state of the longitudinal strain is neglected in comparison with other strain state of strain at material point of a long cylinder in a pipeline, described in where the pipeline is extended in the y-direction, is given by: -200 0 -180 yx yy E *10-6
that long cylinders, e.g. those used in pipelines, are subject to a state of the longitudinal strain is neglected in comparison with other strain state of strain at material point of a long cylinder in a pipeline, described in where the pipeline is extended in the y-direction, is given by: -200 0 -180 yx yy E *10-6
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![It can be assumed that long cylinders, e.g. those used in pipelines, are subject to a state of
plane strain, where the longitudinal strain is neglected in comparison with other strain
components.
The 3-dimensional state of strain at material point of a long cylinder in a pipeline, described in
X, y, z coordinates, where the pipeline is extended in the y-direction, is given by:
E.
xx
E yx
-200 0 -180
[e ]= E,
E, E =
*10-6
ху
yy
Ezy
[Ex E E=
-180 0
50
yz
a. Calculate the volumetric strain and the deviatoric strain invariants
b. Calculate the mean stress and the deviatoric stress tensor.
c. Calculate the characteristic equation of strain.
d. Calculate the characteristic equation of stress.
The material is linear elastic (E=200GPA, v=0.3).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b1c1b32-0e75-405b-870f-c7d4f0ae8ea0%2Fc427c1fc-9b9e-4af7-99c6-73e87435ca37%2Fqij9rq2_processed.png&w=3840&q=75)
Transcribed Image Text:It can be assumed that long cylinders, e.g. those used in pipelines, are subject to a state of
plane strain, where the longitudinal strain is neglected in comparison with other strain
components.
The 3-dimensional state of strain at material point of a long cylinder in a pipeline, described in
X, y, z coordinates, where the pipeline is extended in the y-direction, is given by:
E.
xx
E yx
-200 0 -180
[e ]= E,
E, E =
*10-6
ху
yy
Ezy
[Ex E E=
-180 0
50
yz
a. Calculate the volumetric strain and the deviatoric strain invariants
b. Calculate the mean stress and the deviatoric stress tensor.
c. Calculate the characteristic equation of strain.
d. Calculate the characteristic equation of stress.
The material is linear elastic (E=200GPA, v=0.3).
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