The material is graphite for which Eg=800ksi and νg=0.23 . The magnitudes of the stresses are σx=8ksi , σy=14ksi , and σz=26ksi .
PART A
Determine the principal strains.
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The material is graphite for which Eg=800ksi and νg=0.23 . The
magnitudes of the stresses are...
Learning Goal: To be able to identify the initial stresses and the angle of rotation, including t...
Learning Goal: To be able to identify the initial stresses and
the angle of rotation, including the correct signs, and use these
in the stress-transformation equations to find the stress on a
plane or element at a different angle than the original. The method
of calculating the state of stress on an inclined plane is tedious,
prone to error, and incomplete—if we calculate σx′ and τx′y′, we
have to do a separate calculation to determine σy′. Consider the
stress element...
The principal plane stresses and associated strains in a plane at a point are 01 =...
The principal plane stresses and associated strains in a plane at a point are 01 = 37 ksi , 02 = 16 ksi , €1 = 1.02(10-3), €2 = 0.180(10-3). Part A Determine the modulus of elasticity. Express your answer using three significant figures and include the appropriate units. ? I MÅ E = Value O a Units Submit Request Answer Part B Determine the Poisson's ratio. Express your answer using three significant figures. V ALQ vec R o 2...
The principal plane stresses and associated strains in a plane at a point are 91 =...
The principal plane stresses and associated strains in a plane at a point are 91 = 37 ksi, 02 = 18 ksi, 61 = 1.02(10-3). C2 = 0.180(10-3). Part A Determine the modulus of elasticity. Express your answer using three significant figures and include the appropriate units. E = Value Units Submit Request Answer Part B Determine the Poisson's ratio. Express your answer using three significant figures. VALOT vec o 2 ? Submit Request Answer
The cylinder consists of spirally wrapped steel plates that are welded at the seams in the...
The cylinder consists of spirally wrapped steel plates that are
welded at the seams in the orientation shown. Assume β = 30 ∘ . The
cylinder has an inside diameter of 31 in. and a wall thickness of
0.3125 in. The end of the cylinder is capped by a rigid end plate.
The cylinder is subjected to a compressive load of P = 115
kips and a torque of T = 255 kip-ft, which are applied to
the rigid end...
An element in plane stress is subjected to stresses Ox, Oy, and Txy (see figure). The...
An element in plane stress is subjected to stresses Ox, Oy, and Txy (see figure). The material is aluminum with modulus of elasticity E:= 10 (10%) psi and Poisson's ratio v:=0.25. Hint: start with Hooke's Law for Plane Stress (Eq. 7-35 and 36) and the relationship between G and E! (a) Determine the strains for an element oriented at an angle e. (b) Determine the principal strains. (c) Determine the maximum shear strains. 0x := 3000 psi , := 600...
The strain rosette shown was used to obtain normal strain data at a point on the free surface of a machine component. Given the values εa= -185 με, εb= -150 με, εc= 55 με, E = 10,800 ksi, and v = 0.33...
The strain rosette shown was
used to obtain normal strain data at a point on the free surface of
a machine component. Given the values εa= -185 με, εb= -150 με, εc=
55 με, E = 10,800 ksi, and v = 0.33,
determine
(a) the stress components σx, σy, and τxy at the point.
(b) the principal stresses and the maximum in-plane shear stress at
the point; on paper, show these stresses on an appropriate sketch
that indicates the orientation...
Orthotropic Material 3. (20 pts) Suppose we have a thin composite material comprised of unidirectional graphite...
Orthotropic Material 3. (20 pts) Suppose we have a thin composite material comprised of unidirectional graphite fibers in an epoxy matrix. The ply is loaded in uniaxial tension in the x direction. Plane stress conditions can be assumed. The ply is oriented at an angle 0 from the x axis as shown. Material properties for this material (which may be assumed to be orthotropic) are given in the following figure. T300/934 ET= 9.65 GPa a) (8 pts) Given θ-200, find...
Part 7 To determine the normal and shear stresses on the indicated plane, we must first...
Part 7
To determine the normal and shear stresses on the indicated
plane, we must first determine the orientation of the inclined
plane relative to the x face of the stress element.
Determine the magnitude of the clockwise angle θ between the
x face and the inclined plane.
Assume Sx = 80 ksi, Sy = 10
ksi, and Sxy = 12 ksi.
Part 8
For Mohr’s circle, all angular measures are doubled; therefore,
point n (which represents the state of...
A strain gauge rosette attached to an aircraft component fabricated from thin sheet material recorded the...
A strain gauge rosette attached to an aircraft component fabricated from thin sheet material recorded the following strains: E = 550 JE E45 = -450 ME €90 = -150 ue The thin sheet material properties are: E = 70 GPS v = 0.3 (a) Determine the state of stress in the 0°-90° axis system at the strain gauge location. [11 marks) (b) Determine the principal stresses at the strain gauge location and the maximum shear stress. [6 marks) (c) With...
6. If the stresses and strains at a point in a linear elastic material are given...
6. If the stresses and strains at a point in a linear elastic
material are given by
σij = ε
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
=
885 154 0
154 1038 615
0 615 577
0 002 0 001 0
0 001 0 003 0 004
0 0 004 0
MPa; and ij
. .
. . .
.
respectively, determine (i) the total strain energy density in the
material, (ii) the hydrostatic...
Learning Goal: To be able to identify the initial stresses and
the angle of rotation, including the correct signs, and use these
in the stress-transformation equations to find the stress on a
plane or element at a different angle than the original. The method
of calculating the state of stress on an inclined plane is tedious,
prone to error, and incomplete—if we calculate σx′ and τx′y′, we
have to do a separate calculation to determine σy′. Consider the
stress element...
The principal plane stresses and associated strains in a plane at a point are 01 = 37 ksi , 02 = 16 ksi , €1 = 1.02(10-3), €2 = 0.180(10-3). Part A Determine the modulus of elasticity. Express your answer using three significant figures and include the appropriate units. ? I MÅ E = Value O a Units Submit Request Answer Part B Determine the Poisson's ratio. Express your answer using three significant figures. V ALQ vec R o 2...
The principal plane stresses and associated strains in a plane at a point are 91 = 37 ksi, 02 = 18 ksi, 61 = 1.02(10-3). C2 = 0.180(10-3). Part A Determine the modulus of elasticity. Express your answer using three significant figures and include the appropriate units. E = Value Units Submit Request Answer Part B Determine the Poisson's ratio. Express your answer using three significant figures. VALOT vec o 2 ? Submit Request Answer
The cylinder consists of spirally wrapped steel plates that are
welded at the seams in the orientation shown. Assume β = 30 ∘ . The
cylinder has an inside diameter of 31 in. and a wall thickness of
0.3125 in. The end of the cylinder is capped by a rigid end plate.
The cylinder is subjected to a compressive load of P = 115
kips and a torque of T = 255 kip-ft, which are applied to
the rigid end...
An element in plane stress is subjected to stresses Ox, Oy, and Txy (see figure). The material is aluminum with modulus of elasticity E:= 10 (10%) psi and Poisson's ratio v:=0.25. Hint: start with Hooke's Law for Plane Stress (Eq. 7-35 and 36) and the relationship between G and E! (a) Determine the strains for an element oriented at an angle e. (b) Determine the principal strains. (c) Determine the maximum shear strains. 0x := 3000 psi , := 600...
The strain rosette shown was
used to obtain normal strain data at a point on the free surface of
a machine component. Given the values εa= -185 με, εb= -150 με, εc=
55 με, E = 10,800 ksi, and v = 0.33,
determine
(a) the stress components σx, σy, and τxy at the point.
(b) the principal stresses and the maximum in-plane shear stress at
the point; on paper, show these stresses on an appropriate sketch
that indicates the orientation...
Orthotropic Material 3. (20 pts) Suppose we have a thin composite material comprised of unidirectional graphite fibers in an epoxy matrix. The ply is loaded in uniaxial tension in the x direction. Plane stress conditions can be assumed. The ply is oriented at an angle 0 from the x axis as shown. Material properties for this material (which may be assumed to be orthotropic) are given in the following figure. T300/934 ET= 9.65 GPa a) (8 pts) Given θ-200, find...
Part 7
To determine the normal and shear stresses on the indicated
plane, we must first determine the orientation of the inclined
plane relative to the x face of the stress element.
Determine the magnitude of the clockwise angle θ between the
x face and the inclined plane.
Assume Sx = 80 ksi, Sy = 10
ksi, and Sxy = 12 ksi.
Part 8
For Mohr’s circle, all angular measures are doubled; therefore,
point n (which represents the state of...
A strain gauge rosette attached to an aircraft component fabricated from thin sheet material recorded the following strains: E = 550 JE E45 = -450 ME €90 = -150 ue The thin sheet material properties are: E = 70 GPS v = 0.3 (a) Determine the state of stress in the 0°-90° axis system at the strain gauge location. [11 marks) (b) Determine the principal stresses at the strain gauge location and the maximum shear stress. [6 marks) (c) With...
6. If the stresses and strains at a point in a linear elastic
material are given by
σij = ε
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
=
885 154 0
154 1038 615
0 615 577
0 002 0 001 0
0 001 0 003 0 004
0 0 004 0
MPa; and ij
. .
. . .
.
respectively, determine (i) the total strain energy density in the
material, (ii) the hydrostatic...
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