In the below diagram the components of σy and τxy are shown alone for clarity...the opposing shears and stresses are present but not drawn on the diagram. Using the coordinate axes and sign conventions of the text for a plane at -40 degrees to the horizontal axis (as shown) what is the magnitude of the shear τx'y' in MPa? [x] Give your answer to three significant digits.
Homework Answers
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In the below diagram the components of σy and τxy are shown
alone for clarity...the opposing...
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...
your Consider the element in plane stress as shown below. () (2 points) Draw corresponding Mohr's...
your Consider the element in plane stress as shown below. () (2 points) Draw corresponding Mohr's circle coordinate axes with appropriate labels, center point A. radius of the circle (1) (3 points) Using the Mohir's circle, find the magnitude of the principal stresses and principal directions. Show them on a sketch of a properly oriented clement (c) (3 points) Using the Mohr's circle, find the magnitude of the maximun shear stress and associated normal stresses Show them on a sketch...
Part A - Normal Stresses, Shear, and Angles The stress element shown in the figure below...
Part A - Normal Stresses, Shear, and Angles The stress element shown in the figure below is subjected to the indicated stresses of magnitude 0,1 = 35 MPa, oyl = 57 MPa, and Tryl = 41 MPa Oy Txy Determine the principal normal stresses 01 and 02, the maximum in-plane shear stress Tmax,in-plane, and the angles at which they occur relative to the given stress element. Follow the sign convention. Suppose that when the element is oriented at an angle...
cratonic region. The shear and normal stress components associated with these directions are shown in the...
cratonic region. The shear and normal stress components
associated with these directions are shown in the diagram.
Assume that the stress field is homogeneous over the field of
view.
Assume that the intermediate principal stress ( ) is
vertical.
Using the information provided above and a Mohr diagram or
diagrams (with a scale of 2 cm = 100 bars):
(a) determine the magnitudes and orientations of the principal
stresses ( and );
b) plot and label the orientations of the...
A 3-m diameter roller gate retains water on both sides of a dam crest as shown below. Axes (x,y) are given in the diagram to indicate the convention for positive values. The origin of your coordinate...
A 3-m diameter roller gate retains water on both sides of a dam crest as shown below. Axes (x,y) are given in the diagram to indicate the convention for positive values. The origin of your coordinate system (O) is at the base of the roller gate where it contacts the dam. Indicate direction of Forces either with an arrow, writing the direction (ie. Right/left or up/down) or +/- sign indicating what way is positive based on the axes definition given....
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...
Problem 1 (a) (b) For the 3D stress state represented in part (a), draw a labeled...
Problem 1 (a) (b) For the 3D stress state represented in part (a), draw a labeled 3D Mohr's circle diagram and find the (c) Represent the critical stress components determined for the beam in Problem 1(b) of Homework #3 on a neatly drawn 3D element with properly labeled coordinate axes. principal normal stresses q, ơ2, ơ3 and the principal shear stresses โ1/2, 2/3, t1/3. Determine the angle фр from the x axis to ơ1 and sketch the plane stress elements...
The cantilever beam shown in the figure is subjected to a concentrated load at point B....
The cantilever beam shown in the figure is subjected to a concentrated load at point B. The stresses acting at point Hon the beam are to be determined Ques! Text- Quest Text Ent T Quest Text End Cross section Viewir Text-Ent For this analysis, use the following values Beam and Load. Questi Muitstep a. 1.75 m b-0.30 m 0.63 degrees P.49 KN Questid Text Entry Questio Text Entry Cross-sectional Dimensions d - 275 mm by - 150 mm - 13...
The figure on the left below shows a stress block (plane strain condition is assumed, z...
The figure on the left below shows a stress block (plane strain condition is assumed, z axis is not shown here). Its components as well as the material properties are, • 0,= 10 MPa . O, is currently unknown • Txy = 30 MPa • Young's Modulus E = 150 GPa • Poisson's Ratio V=-0.25 • Note: Poisson's Ratio is negative Rotate the x-y axes in the anticlockwise direction by 45° (as shown in the figure on the right below),...
tyles 3. For the body shown below a) Find the magnitude and orientation of the minor...
tyles 3. For the body shown below a) Find the magnitude and orientation of the minor and major principal stresses relative to the base directions provided b) Find the maximum shear stress magnitude and orientation relative the x y axis c) Find the normal and shear stress state on the horizontal plane d) Find the normal and shear stress state on plane AB For a) through d) find the solution using I) the stress transform equations as determined from the...
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...
your Consider the element in plane stress as shown below. () (2 points) Draw corresponding Mohr's circle coordinate axes with appropriate labels, center point A. radius of the circle (1) (3 points) Using the Mohir's circle, find the magnitude of the principal stresses and principal directions. Show them on a sketch of a properly oriented clement (c) (3 points) Using the Mohr's circle, find the magnitude of the maximun shear stress and associated normal stresses Show them on a sketch...
Part A - Normal Stresses, Shear, and Angles The stress element shown in the figure below is subjected to the indicated stresses of magnitude 0,1 = 35 MPa, oyl = 57 MPa, and Tryl = 41 MPa Oy Txy Determine the principal normal stresses 01 and 02, the maximum in-plane shear stress Tmax,in-plane, and the angles at which they occur relative to the given stress element. Follow the sign convention. Suppose that when the element is oriented at an angle...
cratonic region. The shear and normal stress components
associated with these directions are shown in the diagram.
Assume that the stress field is homogeneous over the field of
view.
Assume that the intermediate principal stress ( ) is
vertical.
Using the information provided above and a Mohr diagram or
diagrams (with a scale of 2 cm = 100 bars):
(a) determine the magnitudes and orientations of the principal
stresses ( and );
b) plot and label the orientations of the...
A 3-m diameter roller gate retains water on both sides of a dam crest as shown below. Axes (x,y) are given in the diagram to indicate the convention for positive values. The origin of your coordinate system (O) is at the base of the roller gate where it contacts the dam. Indicate direction of Forces either with an arrow, writing the direction (ie. Right/left or up/down) or +/- sign indicating what way is positive based on the axes definition given....
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...
Problem 1 (a) (b) For the 3D stress state represented in part (a), draw a labeled 3D Mohr's circle diagram and find the (c) Represent the critical stress components determined for the beam in Problem 1(b) of Homework #3 on a neatly drawn 3D element with properly labeled coordinate axes. principal normal stresses q, ơ2, ơ3 and the principal shear stresses โ1/2, 2/3, t1/3. Determine the angle фр from the x axis to ơ1 and sketch the plane stress elements...
The cantilever beam shown in the figure is subjected to a concentrated load at point B. The stresses acting at point Hon the beam are to be determined Ques! Text- Quest Text Ent T Quest Text End Cross section Viewir Text-Ent For this analysis, use the following values Beam and Load. Questi Muitstep a. 1.75 m b-0.30 m 0.63 degrees P.49 KN Questid Text Entry Questio Text Entry Cross-sectional Dimensions d - 275 mm by - 150 mm - 13...
The figure on the left below shows a stress block (plane strain condition is assumed, z axis is not shown here). Its components as well as the material properties are, • 0,= 10 MPa . O, is currently unknown • Txy = 30 MPa • Young's Modulus E = 150 GPa • Poisson's Ratio V=-0.25 • Note: Poisson's Ratio is negative Rotate the x-y axes in the anticlockwise direction by 45° (as shown in the figure on the right below),...
tyles 3. For the body shown below a) Find the magnitude and orientation of the minor and major principal stresses relative to the base directions provided b) Find the maximum shear stress magnitude and orientation relative the x y axis c) Find the normal and shear stress state on the horizontal plane d) Find the normal and shear stress state on plane AB For a) through d) find the solution using I) the stress transform equations as determined from the...
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