:A member whose material properties remain unchanged under rotation of 90° about axes (x, y, z) is called a cubic material relative to axes (x, y, z) and has three independent elastic coefficients (Cı, C2, C3). It's stress-strain relationships relative to axes (x, y, z) are: Ozx = C;Ɛgx + C2Eyy + C2Ezz Iyy = C,Ez + C;Eyy + CzEz Oz = C2Ezx + C2Eyy + C,Ezz Ozy = C3Yxy C3Yxz Gyz = C,Yyz Although in practice, aluminum is often assumed to be an isotropic material, it is actually a cubic material with C1=103GP,, C2=55GPA, and C3=27.6GPA. At a point in an airplane wing, the strain components are ɛxz = 0.0003, ɛy = 0.0002, En = 0.0001, €xy = 0.00005, and ɛx = Eyz = 0. a) Determine all three principal strains and corresponding unit vectors of the axes of principal strains., b) Determine a and o,y. c) Use the consideration of aluminum being an isotropic material with E=72 GPa, and v=0.33 to estimate the C, C2, and C3. What would be the value for them?
:A member whose material properties remain unchanged under rotation of 90° about axes (x, y, z) is called a cubic material relative to axes (x, y, z) and has three independent elastic coefficients (Cı, C2, C3). It's stress-strain relationships relative to axes (x, y, z) are: Ozx = C;Ɛgx + C2Eyy + C2Ezz Iyy = C,Ez + C;Eyy + CzEz Oz = C2Ezx + C2Eyy + C,Ezz Ozy = C3Yxy C3Yxz Gyz = C,Yyz Although in practice, aluminum is often assumed to be an isotropic material, it is actually a cubic material with C1=103GP,, C2=55GPA, and C3=27.6GPA. At a point in an airplane wing, the strain components are ɛxz = 0.0003, ɛy = 0.0002, En = 0.0001, €xy = 0.00005, and ɛx = Eyz = 0. a) Determine all three principal strains and corresponding unit vectors of the axes of principal strains., b) Determine a and o,y. c) Use the consideration of aluminum being an isotropic material with E=72 GPa, and v=0.33 to estimate the C, C2, and C3. What would be the value for them?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text::A member whose material properties remain unchanged under rotation
of 90° about axes (x, y, z) is called a cubic material relative to axes (x, y, z) and has
three independent elastic coefficients (Cı, C2, C3). It's stress-strain relationships relative
to axes (x, y, z) are:
Ozx = C;Ɛgx + C2Eyy + C2Ezz
Iyy = C,Ez + C;Eyy + CzEz
Oz = C2Ezx + C2Eyy + C,Ezz
Ozy = C3Yxy
C3Yxz
Gyz = C,Yyz
Although in practice, aluminum is often assumed to be an isotropic material, it is
actually a cubic material with C1=103GP,, C2=55GPA, and C3=27.6GPA.
At a point in an airplane wing, the strain components are ɛxz = 0.0003, ɛy = 0.0002,
En = 0.0001, €xy = 0.00005, and ɛx = Eyz = 0.
a) Determine all three principal strains and corresponding unit vectors of the axes of
principal strains.,
b) Determine a and o,y.
c) Use the consideration of aluminum being an isotropic material with E=72 GPa,
and v=0.33 to estimate the C, C2, and C3. What would be the value for them?
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