Question 1. For each of the plane-stress conditions given below, construct a Mohr’s circle of stress,...
Question 1.
For each of the plane-stress conditions given below, construct a
Mohr’s circle of stress, find the principal stresses and the
orientation of the principal axes relative to the x,y axes and
determine the stresses on an element, rotated in the x-y plane 60°
counterclockwise from its original position:
(a) σx = 200 MPa
σy = 300 MPa
τxy = - 40 MPa
(b) σx = 500 MPa
σy = -80 MPa
τxy = 400 MPa
Question 2.
For each of the plane-stress conditions given in Question 1, using
the matrix transformation law, determine the state of stress at the
same point for an element rotated in the x-y plane 60°
counterclockwise from its original position.
Homework Answers
Add Answer to:
Question 1.
For each of the plane-stress conditions given below, construct a
Mohr’s circle of stress,...
hello guys can u help me :) Question 1. For each of the plane-stress conditions given...
hello guys can u help me :)
Question 1. For each of the plane-stress conditions given below, using the matrix transformation law, determine the state of stress at the same point for an element rotated in the x-y plane 30° clockwise from its original position: (a) Ox = 200 MPa Oy = 400 MPa Txy = - 60 MPa (b) Ox = 300 MPa Oy = -180 MPa Txy = 320 MPa Question 2 my x2 The state of stress...
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...
3. The state of plane stress at a point is shown on the element below. Construct...
3. The state of plane stress at a point is shown on the element below. Construct Mohr's circle. Determine the principal stresses acting at this point and their orientation D,. Also determine the maximum in-plane shear stresses and the orientation of the element upon which they act. What is the state of stress if it is rotated 20° counterclockwise? (20 points) 90 MPa 60 MPa -20 MPa
Q4. (a) Plot a Mohr circle for the plane stress element which has been rotated 40...
Q4. (a) Plot a Mohr circle for the plane stress element which has been rotated 40 degrees in the anti-clockwise direction as shown in Figure Q4(a). (8 marks) (b) By using Mohr Circle, determine and sketch; all the stresses (Ox, O, and tyy) of the same element in the orientation as shown in Figure Q4(b). (4 marks) (i) the principal stress and its orientation. (4 marks) (i) the maximum shear stress, the corresponding normal stress, and its orientation. (4 marks)...
3. Figure shows a state of plane stress consists of normal stresses 60 MPa and Ly-40MPa;...
3. Figure shows a state of plane stress consists of normal stresses 60 MPa and Ly-40MPa; and unknown shear stress, The maximum principal stress was determined to be 104.34 MPa. Using Mohr's cirdle, determine a. the magnitude of the shear stress, b. the principal plane and the minimum principal stress. Then, sketch the element showing all stresses in its proper orientation, c. the maximum shear stress, associated normal stress and the orientation of the element. Then, sketch the element showing...
Problem 6 (15 points) The state of plane stress at a point is shown on the...
Problem 6 (15 points) The state of plane stress at a point is shown on the element in Figure 6. a. Using Mohr's circle, determine the principal stresses and the maximum in-plane shear stress and average normal stress. Specify the orientation of the element in each case. b. Represent the state of stress on an element oriented 30° counterclockwise from the position shown in Figure 6. 20 MPa 100 MPa 40 MPa Figure 6 (plot Mohr's circle on the next...
The 3D state of stress in a point of an elastic solid is given in the...
The 3D state of stress in a point of an elastic solid is given in the x-y-z coordinates by: 「200 200 01 [o] 1 200 300 01 Using the matrix transformation law, determine the state of stress at the same point for an element rotated in the x-y plane 30° anticlockwise about the z-axis from its original position. a. b. Calculate the stress invariants and write the characteristic equation for the original state of stress Calculate the deviatoric invariants for...
For the stress state shown, use Mohr's Circle to determine the following:
For the stress state shown, use Mohr's Circle to determine the following: (a) Principal stresses σ1 and σ2, the associated shear stress τx'y', and the element orientation θp. Clearly indicate magnitude and direction. (b) Maximum in-plane shear stress τmax,in plane , the associated normal stresses σx' and σy', and the element orientation θs. Clearly indicate magnitude and direction. (c) Absolute maximum shear stress τmax,absolute · Show all work using Mohr's Circle. If your drawings do not indicate that you used Mohr's Circle appropriately, you...
Must draw Mohr’s circle in this question 3) For the stress state shown to the right,...
Must draw Mohr’s circle in this question
3) For the stress state shown to the right, determine (a) the three principal stresses, and (b) the maximum shear stress. (Hint: consider this as a 3D problem, similar to in-class 3D example problem.) Ans: (a) Onui = 220 MPa, Ontermediate = 60 MPa, Onlin-0, (b)T,nax = 1 10 MPa 140 MPa 80 MPa 140 MPa 140 MPa 140 MPa
with drawings Question 4 (CLO5) (6 points) The state of the stress at a point is...
with drawings
Question 4 (CLO5) (6 points) The state of the stress at a point is shown on the element. Determine the following: (a) The principal stresses, and the corresponding orientation of the element (b) The maximum in-plane shear stress and the associated average normal stress at the point. Show the corresponding orientation of the element. (c) Using Mohr's circle (only), determine the stress components at the same point on another element oriented 30° counterclockwise from the position shown. Draw...
hello guys can u help me :)
Question 1. For each of the plane-stress conditions given below, using the matrix transformation law, determine the state of stress at the same point for an element rotated in the x-y plane 30° clockwise from its original position: (a) Ox = 200 MPa Oy = 400 MPa Txy = - 60 MPa (b) Ox = 300 MPa Oy = -180 MPa Txy = 320 MPa Question 2 my x2 The state of stress...
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...
3. The state of plane stress at a point is shown on the element below. Construct Mohr's circle. Determine the principal stresses acting at this point and their orientation D,. Also determine the maximum in-plane shear stresses and the orientation of the element upon which they act. What is the state of stress if it is rotated 20° counterclockwise? (20 points) 90 MPa 60 MPa -20 MPa
Q4. (a) Plot a Mohr circle for the plane stress element which has been rotated 40 degrees in the anti-clockwise direction as shown in Figure Q4(a). (8 marks) (b) By using Mohr Circle, determine and sketch; all the stresses (Ox, O, and tyy) of the same element in the orientation as shown in Figure Q4(b). (4 marks) (i) the principal stress and its orientation. (4 marks) (i) the maximum shear stress, the corresponding normal stress, and its orientation. (4 marks)...
3. Figure shows a state of plane stress consists of normal stresses 60 MPa and Ly-40MPa; and unknown shear stress, The maximum principal stress was determined to be 104.34 MPa. Using Mohr's cirdle, determine a. the magnitude of the shear stress, b. the principal plane and the minimum principal stress. Then, sketch the element showing all stresses in its proper orientation, c. the maximum shear stress, associated normal stress and the orientation of the element. Then, sketch the element showing...
Problem 6 (15 points) The state of plane stress at a point is shown on the element in Figure 6. a. Using Mohr's circle, determine the principal stresses and the maximum in-plane shear stress and average normal stress. Specify the orientation of the element in each case. b. Represent the state of stress on an element oriented 30° counterclockwise from the position shown in Figure 6. 20 MPa 100 MPa 40 MPa Figure 6 (plot Mohr's circle on the next...
The 3D state of stress in a point of an elastic solid is given in the x-y-z coordinates by: 「200 200 01 [o] 1 200 300 01 Using the matrix transformation law, determine the state of stress at the same point for an element rotated in the x-y plane 30° anticlockwise about the z-axis from its original position. a. b. Calculate the stress invariants and write the characteristic equation for the original state of stress Calculate the deviatoric invariants for...
For the stress state shown, use Mohr's Circle to determine the following: (a) Principal stresses σ1 and σ2, the associated shear stress τx'y', and the element orientation θp. Clearly indicate magnitude and direction. (b) Maximum in-plane shear stress τmax,in plane , the associated normal stresses σx' and σy', and the element orientation θs. Clearly indicate magnitude and direction. (c) Absolute maximum shear stress τmax,absolute · Show all work using Mohr's Circle. If your drawings do not indicate that you used Mohr's Circle appropriately, you...
Must draw Mohr’s circle in this question
3) For the stress state shown to the right, determine (a) the three principal stresses, and (b) the maximum shear stress. (Hint: consider this as a 3D problem, similar to in-class 3D example problem.) Ans: (a) Onui = 220 MPa, Ontermediate = 60 MPa, Onlin-0, (b)T,nax = 1 10 MPa 140 MPa 80 MPa 140 MPa 140 MPa 140 MPa
with drawings
Question 4 (CLO5) (6 points) The state of the stress at a point is shown on the element. Determine the following: (a) The principal stresses, and the corresponding orientation of the element (b) The maximum in-plane shear stress and the associated average normal stress at the point. Show the corresponding orientation of the element. (c) Using Mohr's circle (only), determine the stress components at the same point on another element oriented 30° counterclockwise from the position shown. Draw...
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