6. A stubborn glass jar has seemingly glued itself shut and refuses to be opened. The person trying to open it is twisting and pulling with all their might (definitely not from personal experience). These torques and tensions generate an axial stress σxx = 6 MPa and a shear stress σxy = 4 MPa as shown in the figure. The glass has mechanical properties of E = 70 GPa, v = 0.23 and σy = 7 MPa. a. What are the principal stresses and their directions? b. What are the strains in the axial, circumferential and radial directions? Hint: these correspond to the x-, y- and z-directions respectively in the coordinate system shown. C. Given that the material is brittle, does it fail? d. If it did fail, what would the orientation of the failure plane be relative to the horizontal (y-z) plane (sketch this)? F T Oxy бху 10xx Оху

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter2: Axially Loaded Members
Section: Chapter Questions
Problem 2.5.25P: A capped cast-iron pipe is compressed by a brass rod, as shown. The mil is turned until it is just...
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6. A stubborn glass jar has seemingly glued itself shut and refuses to be opened. The person trying to open
it is twisting and pulling with all their might (definitely not from personal experience). These torques
and tensions generate an axial stress σxx = 6 MPa and a shear stress σxy = 4 MPa as shown in the
figure. The glass has mechanical properties of E = 70 GPa, v = 0.23 and σy = 7 MPa.
a. What are the principal stresses and their directions?
b. What are the strains in the axial, circumferential and radial directions? Hint: these correspond to
the x-, y- and z-directions respectively in the coordinate system shown.
C.
Given that the material is brittle, does it fail?
d. If it did fail, what would the orientation of the failure plane be relative to the horizontal (y-z) plane
(sketch this)?
F
T
Oxy
бху
10xx
Оху
Transcribed Image Text:6. A stubborn glass jar has seemingly glued itself shut and refuses to be opened. The person trying to open it is twisting and pulling with all their might (definitely not from personal experience). These torques and tensions generate an axial stress σxx = 6 MPa and a shear stress σxy = 4 MPa as shown in the figure. The glass has mechanical properties of E = 70 GPa, v = 0.23 and σy = 7 MPa. a. What are the principal stresses and their directions? b. What are the strains in the axial, circumferential and radial directions? Hint: these correspond to the x-, y- and z-directions respectively in the coordinate system shown. C. Given that the material is brittle, does it fail? d. If it did fail, what would the orientation of the failure plane be relative to the horizontal (y-z) plane (sketch this)? F T Oxy бху 10xx Оху
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