3. The state of stress throughout a body is given by the stress tensor 0 Cx2...
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3. The state of stress throughout a body is given by the stress tensor 0 Cx2 0 Cx2 CX3 -CX 0 -CX1 0 ij = where C is an arbitrary constant. (a) At the point P(1,1,1), calculate the traction vectors on the plane X + x - x3 =1, and on the sphere X + x + x3 = 3. (10%) (b) Determine the principal stress at point at point P. (5%) (c) According to the results of question (b), find the corresponding principal axes. Please satisfy the following relationship. (5%) 01>02>03, ||)|=|()|=|()|=1, (d) Use the principal directions to define a new coordinate system. Determine the stress tensor in the new coordinate system by tensor transformation. (5%) (e) Suppose the traction vectors calculated in problem (a) are denoted t and t2, respectively. What are the components of t and t in the new coordinate system? (10%) (1). n () ;(3) 3. The state of stress throughout a body is given by the stress tensor 0 Cx2 0 Cx2 CX3 -CX 0 -CX1 0 ij = where C is an arbitrary constant. (a) At the point P(1,1,1), calculate the traction vectors on the plane X + x - x3 =1, and on the sphere X + x + x3 = 3. (10%) (b) Determine the principal stress at point at point P. (5%) (c) According to the results of question (b), find the corresponding principal axes. Please satisfy the following relationship. (5%) 01>02>03, ||)|=|()|=|()|=1, (d) Use the principal directions to define a new coordinate system. Determine the stress tensor in the new coordinate system by tensor transformation. (5%) (e) Suppose the traction vectors calculated in problem (a) are denoted t and t2, respectively. What are the components of t and t in the new coordinate system? (10%) (1). n () ;(3)
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a To calculate the traction vectors on the plane x x x 1 and on the sphere x x x 3 at the point P111 we need to substitute the coordinates of the poin... View the full answer
Related Book For
Shigleys Mechanical Engineering Design
ISBN: 978-1121345317
9th edition
Authors: Richard G. Budynas, J. Keith Nisbett
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