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2. (10pts) How to describe the components of stress of a point in a body which...
Problem 1 (10pts) The components of stress at a point are given as right. Compute the...
Problem 1 (10pts) The components of stress at a point are given as right. Compute the effective/von Mises stress o Also determine the components of stress vector T( σ/) if this stress acts on the plane 2x+ 3y-52-5 0. (Note, first find the unit normal vector to this surface.) σ- ,=13-2-31 MPa 1-32丿 Extra Credit (5pts) Find the three principal stresses for this state of stress. Also determine the "principal direction/vector' of the largest tensile principal stress.
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)
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...
16. The stress state in a two dimensional body, in which the only non-vanishing stress components...
16. The stress state in a two dimensional body, in which the only non-vanishing stress components are a single pair of shearing stresses is called simple shear. Take σ12 σ21 and all other components of σ equal to zero. (a) Find the principal values and principal directions of this stress state. (b) Find the maximum shearing stress and planes on which it acts.
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.
0 The state of stress at a point in a body is specified by the following...
0 The state of stress at a point in a body is specified by the following stress components: = 110MPa = 60MPa , = -86 MPa 0 = 55 MPa Determine the principal stresses, direction cosines of the principal stress directions and the maximum shearing stress.
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:...
Problem 1 (10pts) For each figure shown below, sketch the smallestw w geometry which can be model...
Problem 1 (10pts) For each figure shown below, sketch the smallestw w geometry which can be modeled in a finite element analysis. Clearly show the boundary/restraint conditions with 'rollers' and 'pins', and the loading conditions with 'arrows' and labelmagnitude. Remember to suppress the rigid body translation displacement. Note a symmetry line does not have to be parallel to ' the x or y axis (can be inclined Same plates
Problem 1 (10pts) For each figure shown below, sketch the smallestw...
Question 5 (1 mark) Attempt 1 In a solid body, the six components of the stress at a point P, are given by: σ,-90 M...
Question 5 (1 mark) Attempt 1 In a solid body, the six components of the stress at a point P, are given by: σ,-90 MPa, ơy-85 MPa, σ,--80 MPa. Tyz 26 MPa, Txz74 MPa, Txy50 MPa If the normal vector to the body at point P is determine the normal stress at the point P (in MPA) Enter your answer in decimal form. For example: 50.1175345 You can round your answer to five decimal places. For example: 50.11753
Question 5...
describe the effects of stress on the body.
describe the effects of stress on the body.
Problem 1 (10pts) The components of stress at a point are given as right. Compute the effective/von Mises stress o Also determine the components of stress vector T( σ/) if this stress acts on the plane 2x+ 3y-52-5 0. (Note, first find the unit normal vector to this surface.) σ- ,=13-2-31 MPa 1-32丿 Extra Credit (5pts) Find the three principal stresses for this state of stress. Also determine the "principal direction/vector' of the largest tensile principal stress.
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)
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...
16. The stress state in a two dimensional body, in which the only non-vanishing stress components are a single pair of shearing stresses is called simple shear. Take σ12 σ21 and all other components of σ equal to zero. (a) Find the principal values and principal directions of this stress state. (b) Find the maximum shearing stress and planes on which it acts.
0 The state of stress at a point in a body is specified by the following stress components: = 110MPa = 60MPa , = -86 MPa 0 = 55 MPa Determine the principal stresses, direction cosines of the principal stress directions and the maximum shearing 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:...
Problem 1 (10pts) For each figure shown below, sketch the smallestw w geometry which can be modeled in a finite element analysis. Clearly show the boundary/restraint conditions with 'rollers' and 'pins', and the loading conditions with 'arrows' and labelmagnitude. Remember to suppress the rigid body translation displacement. Note a symmetry line does not have to be parallel to ' the x or y axis (can be inclined Same plates
Problem 1 (10pts) For each figure shown below, sketch the smallestw...
Question 5 (1 mark) Attempt 1 In a solid body, the six components of the stress at a point P, are given by: σ,-90 MPa, ơy-85 MPa, σ,--80 MPa. Tyz 26 MPa, Txz74 MPa, Txy50 MPa If the normal vector to the body at point P is determine the normal stress at the point P (in MPA) Enter your answer in decimal form. For example: 50.1175345 You can round your answer to five decimal places. For example: 50.11753
Question 5...
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