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.
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Perform transformation of stress for a point in a body, for
which σxx = 90 MPa;...
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:...
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...
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...
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 plane stress at a point on a body is represented by the element...
The state of plane stress at a point on a body is represented by the element below. 16 MPa 24 MPa V Determine the equivalent state of plane stress on an element at the same point that is rotated by 0= -30°. Remember that a negative sign indicates a clockwise rotation and a positive sign indicates a counter-clockwise rotation. 0 = number (rtol=0.01, atol=1e-05) MPa ? Ty number (rtol=0.01, atol=1e-05) MPa ? Ta'y = number (rtol=0.01, atol=1e-05) MPa
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...
1. Given a plane element in a body is subjected to a normal tensile stress in the x-direction of 120 MPa, a normal stre...
1. Given a plane element in a body is subjected to a normal tensile stress in the x-direction of 120 MPa, a normal stress in the y-direction of-75 MPa and shear stresses of 50 MPa, as shown. Determing a. What is the maximum principal stress? b. What is the minimum principal stress? 75 MPa What is the maximum shear stress? 50 MPa c. d. what is the angle to the principal plane, θ e. What is the angle to the...
6. The components of stress within a structure are oxx 90 MPa, oxy -30 MPa, oxz...
6. The components of stress within a structure are oxx 90 MPa, oxy -30 MPa, oxz = ayz = 0 50 MPa, oyy -60 MPa, ozz (4 poin Draw 3D Mohr's circle and locate the principal stresses 01, 02 and a3 as well as the maximum shear stress a. b. Calculate the angle required to rotate the x-y plane to the principal frame and locate that angle on the cirlce (4 poir c. Draw the rotated 3D stress element
2. Let the components of a stress matrix at a point P in a body be...
2. Let the components of a stress matrix at a point P in a body be given by (in MPa) σ11 = 63 MPa; σ12 =-63 MPa; 013 = 42 MPa ơ33-:-21 MPa (a) Show these stresses on a cubic element enclosing the point P (b) Calculate the traction vector on a plane passing through the point P and oriented at n- 2e1 3e2 +6e3)
Question 2 20 pts For the stress element above, O, has a magnitude of 12 MPa."...
Question 2 20 pts For the stress element above, O, has a magnitude of 12 MPa." has a magnitude of 40 MPa, and Try has a magnitude of 19 MPa. 1. Find the stresses on the stress element shown above if it is rotated 36° counter clockwise. 2. Find the direction of the principal stresses (as measured from the original stress element above). Glve magnitude and direction! (direction is either clockwise or counter clockwise). NOTE: This answer is an angle....
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:...
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 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 plane stress at a point on a body is represented by the element below. 16 MPa 24 MPa V Determine the equivalent state of plane stress on an element at the same point that is rotated by 0= -30°. Remember that a negative sign indicates a clockwise rotation and a positive sign indicates a counter-clockwise rotation. 0 = number (rtol=0.01, atol=1e-05) MPa ? Ty number (rtol=0.01, atol=1e-05) MPa ? Ta'y = number (rtol=0.01, atol=1e-05) MPa
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...
1. Given a plane element in a body is subjected to a normal tensile stress in the x-direction of 120 MPa, a normal stress in the y-direction of-75 MPa and shear stresses of 50 MPa, as shown. Determing a. What is the maximum principal stress? b. What is the minimum principal stress? 75 MPa What is the maximum shear stress? 50 MPa c. d. what is the angle to the principal plane, θ e. What is the angle to the...
6. The components of stress within a structure are oxx 90 MPa, oxy -30 MPa, oxz = ayz = 0 50 MPa, oyy -60 MPa, ozz (4 poin Draw 3D Mohr's circle and locate the principal stresses 01, 02 and a3 as well as the maximum shear stress a. b. Calculate the angle required to rotate the x-y plane to the principal frame and locate that angle on the cirlce (4 poir c. Draw the rotated 3D stress element
2. Let the components of a stress matrix at a point P in a body be given by (in MPa) σ11 = 63 MPa; σ12 =-63 MPa; 013 = 42 MPa ơ33-:-21 MPa (a) Show these stresses on a cubic element enclosing the point P (b) Calculate the traction vector on a plane passing through the point P and oriented at n- 2e1 3e2 +6e3)
Question 2 20 pts For the stress element above, O, has a magnitude of 12 MPa." has a magnitude of 40 MPa, and Try has a magnitude of 19 MPa. 1. Find the stresses on the stress element shown above if it is rotated 36° counter clockwise. 2. Find the direction of the principal stresses (as measured from the original stress element above). Glve magnitude and direction! (direction is either clockwise or counter clockwise). NOTE: This answer is an angle....
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