The stress state of a point is defined by σxx =−30MPa, σyy =60MPa, and σxy =−40MPa...
The stress state of a point is defined by σxx =−30MPa, σyy =60MPa, and σxy =−40MPa
Using the Mohr’s circle, determine the range of values of θ defined as the inclined angle of a random point on the circle with respect to the positive σx’y’ axis, for which the normal stress is tensile. Do this analytically rather than graphically.
Homework Answers
so this is range of angle from x face for
which stress is tensile.
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The stress state of a point is defined by σxx =−30MPa, σyy
=60MPa, and σxy =−40MPa...
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...
Problem 2 (25 points) SMR For the state of stress at a point, P, as shown....
Problem 2 (25 points) SMR For the state of stress at a point, P, as shown. JUNY Plot the state of stress on a Mohr's circle. Also determine (either graphically or by equation, the principal stresses and the maximum shear stress. What angle would the original X-axis of the unit square need to be rotated to face the direction of maximum normal stress? What angle would the original X-axis of the unit square need to be rotated to face the...
The state of plane stress at a point on a body can be depicted by the...
The state of plane stress at a point on a body can be depicted by the Mohr's circle below. Point X has coordinates(-18, 12) MPa and point Y has coordinates (-14,-12) MPa Determine the normal and shear stresses associated with a rotation of the stress element θ--26 Remember that a negative sign indicates a clockwise rotation and a positive sign indicates a counter-clockwise rotation. Note that you can use the Mohr's circle to obtain your answers graphically or you can...
The state of stress at a point on a body is given by the following stress...
The state of stress at a point on a body is given by the following stress components: 0 = 15 MPa, Oy = -22 MPa and Try = 9 MPa Matlab input: sx = 15; sy = -22; txy = 9; 1) Determine the principal stresses 01 and 02. 1 = MPa 02= MPa 2) Sketch the principal stress element, defined by the rotation @pl. y Enter the rotation @pi (-360º < Opl < 360°): Opl = Add stress components:...
Perform transformation of stress for a point in a body, for which σxx = 90 MPa;...
Perform transformation of stress for a point in a body, for which σxx = 90 MPa; σyy = -10 MPa; τxy = 40 MPa. a. Find tensor components for a point P on a cutting plane Q with normal vector n = 1/sqrt(2)i - 1/sqrt(2)j b. Find the state of stress for an element rotated by θ = π/6 clockwise (negative direction) from x-axis.
16 QUESTION 3: At Point A on a concrete wall, the state of stress duc to...
16 QUESTION 3: At Point A on a concrete wall, the state of stress duc to the indicated loading condition is shown below on the right. Using the Mohr's Circle method, determine the following stresses and illustrate the orientation and direction of the stresses on a sketch: a) The principal normal stresses; and b) The normal and shear stresses on a plane defined by Line b-b. Note: The stress transformation equations, rather than Mohr's circle, can be used, however there...
The state of plane stress at a point under the surface of the ANKA airplane wing...
The state of plane stress at a point under the surface of the ANKA airplane wing is represented on the element oriented as shown in the Figure. Deternine principal Stresses Calculate the maximum in-plane shear stress and associated average normal stress by using the analytical method and Mohr's circle. For each case, determine the corresponding orientation of the element with respect to the element shown and sketch the state of stress on the element. Determine the absolute maximum shear stress...
Please draw each point PROBLEM 4 (25%) Given the following state of stress, 20 ksi 16...
Please draw each point
PROBLEM 4 (25%) Given the following state of stress, 20 ksi 16 ksi 8 ksi Given the following state of stress, using the Mohr's circle: Determine the principal normal stresses and show their sense on a properly oriented element, “PRINCIPAL STRESS”. Show stress invariance with the original stress condition. Find the maximum shear stress with their associate normal stresses and show the results on a properly oriented element, "MAX SHEAR STRESS”. Show stress invariance with the...
The rectangular plate shown in the figure below has the given loads uniformly distributed over the...
The rectangular plate shown in the figure below has the given loads uniformly distributed over the edges. The plate is 50 mm thick, AB is 500 mm and BC is 400 mm (a) (b) (c) (d) (e) Determine the shear forces which must operate on the edges BC and DA to maintain the equilibrium of the plate Relative to the x,y reference axes, determine the state of stress at any point P in the interior of the plate For the...
2. (35pts) For a 3D combined loading, please determine the 3D stress state at point A...
2. (35pts) For a 3D combined loading, please determine the 3D stress state at point A and B in the circular cross-section of a-a. The radius of the cross-section is R. The end of the structure is clamped. We are interested in the stress state on the cross-section that is cut by a-a plane. Please go through the following steps: 2.1) (5pts) List the contributions (axial force, bending moment, or twisting torque) from F2. Clearly indicate what kind of contribution...
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...
Problem 2 (25 points) SMR For the state of stress at a point, P, as shown. JUNY Plot the state of stress on a Mohr's circle. Also determine (either graphically or by equation, the principal stresses and the maximum shear stress. What angle would the original X-axis of the unit square need to be rotated to face the direction of maximum normal stress? What angle would the original X-axis of the unit square need to be rotated to face the...
The state of plane stress at a point on a body can be depicted by the Mohr's circle below. Point X has coordinates(-18, 12) MPa and point Y has coordinates (-14,-12) MPa Determine the normal and shear stresses associated with a rotation of the stress element θ--26 Remember that a negative sign indicates a clockwise rotation and a positive sign indicates a counter-clockwise rotation. Note that you can use the Mohr's circle to obtain your answers graphically or you can...
The state of stress at a point on a body is given by the following stress components: 0 = 15 MPa, Oy = -22 MPa and Try = 9 MPa Matlab input: sx = 15; sy = -22; txy = 9; 1) Determine the principal stresses 01 and 02. 1 = MPa 02= MPa 2) Sketch the principal stress element, defined by the rotation @pl. y Enter the rotation @pi (-360º < Opl < 360°): Opl = Add stress components:...
16 QUESTION 3: At Point A on a concrete wall, the state of stress duc to the indicated loading condition is shown below on the right. Using the Mohr's Circle method, determine the following stresses and illustrate the orientation and direction of the stresses on a sketch: a) The principal normal stresses; and b) The normal and shear stresses on a plane defined by Line b-b. Note: The stress transformation equations, rather than Mohr's circle, can be used, however there...
The state of plane stress at a point under the surface of the ANKA airplane wing is represented on the element oriented as shown in the Figure. Deternine principal Stresses Calculate the maximum in-plane shear stress and associated average normal stress by using the analytical method and Mohr's circle. For each case, determine the corresponding orientation of the element with respect to the element shown and sketch the state of stress on the element. Determine the absolute maximum shear stress...
Please draw each point
PROBLEM 4 (25%) Given the following state of stress, 20 ksi 16 ksi 8 ksi Given the following state of stress, using the Mohr's circle: Determine the principal normal stresses and show their sense on a properly oriented element, “PRINCIPAL STRESS”. Show stress invariance with the original stress condition. Find the maximum shear stress with their associate normal stresses and show the results on a properly oriented element, "MAX SHEAR STRESS”. Show stress invariance with the...
The rectangular plate shown in the figure below has the given loads uniformly distributed over the edges. The plate is 50 mm thick, AB is 500 mm and BC is 400 mm (a) (b) (c) (d) (e) Determine the shear forces which must operate on the edges BC and DA to maintain the equilibrium of the plate Relative to the x,y reference axes, determine the state of stress at any point P in the interior of the plate For the...
2. (35pts) For a 3D combined loading, please determine the 3D stress state at point A and B in the circular cross-section of a-a. The radius of the cross-section is R. The end of the structure is clamped. We are interested in the stress state on the cross-section that is cut by a-a plane. Please go through the following steps: 2.1) (5pts) List the contributions (axial force, bending moment, or twisting torque) from F2. Clearly indicate what kind of contribution...
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