Question

Q1 (10/35) A thin skewed plate is subjected to a uniform distribution of stress along its sides as shown in Figure 1. (a) Calculate ?x, ?y, and ?xy. (b) Determine the principal stresses. Q2 (12.5/35) At a point P in a body and in the given coordinate system, the stress element in Figure 2 has determined. (a) Write the matrix representing the stress tensor. (b) Calculate the stress invariants. (c) Determine the magnitude of the principal stresses. (d) Determine the directional cosines of the maximum principal stress ?1. Q3. (12.5/35) The block shown in Figure 3 has dimensions a = 1.0mm, b = 1.0mm, and c = 2.0mm. It is subjected to triaxial stresses ?x = 20MPa, ?y = -10MPa, and ?z = 15MPa (all the shear stress components are zero) acting on the x, y, and z faces, respectively. Use E = 50GPa and ? = 0.25. (a) Calculate the strain components ?x, ?y, ?z, ?xy, ?yz, and ?zx. (b) Calculate the change ?V in volume. (c) Determine the normal strain in the direction of line OA. (d) Determine the strain energy stored in the block.

          Q1 (10/35) A thin skewed plate is subjected to a uniform distribution of stress along its sides as shown in Figure 1.
(a) Calculate ?x, ?y, and ?xy.
(b) Determine the principal stresses.

Q2 (12.5/35) At a point P in a body and in the given coordinate system, the stress element in Figure 2 has determined.
(a) Write the matrix representing the stress tensor.
(b) Calculate the stress invariants.
(c) Determine the magnitude of the principal stresses.
(d) Determine the directional cosines of the maximum principal stress ?1.

Q3. (12.5/35) The block shown in Figure 3 has dimensions a = 1.0mm, b = 1.0mm, and c = 2.0mm. It is subjected to triaxial stresses ?x = 20MPa, ?y = -10MPa, and ?z = 15MPa (all the shear stress components are zero) acting on the x, y, and z faces, respectively. Use E = 50GPa and ? = 0.25.
(a) Calculate the strain components ?x, ?y, ?z, ?xy, ?yz, and ?zx.
(b) Calculate the change ?V in volume.
(c) Determine the normal strain in the direction of line OA.
(d) Determine the strain energy stored in the block.

Q1 (10/35) A thin skewed plate is subjected to a uniform distribution of stress along its sides as shown in Figure 1.
(a) Calculate ?x, ?y, and ?xy.
(b) Determine the principal stresses.

Q2 (12.5/35) At a point P in a body and in the given coordinate system, the stress element in Figure 2 has determined.
(a) Write the matrix representing the stress tensor.
(b) Calculate the stress invariants.
(c) Determine the magnitude of the principal stresses.
(d) Determine the directional cosines of the maximum principal stress ?1.

Q3. (12.5/35) The block shown in Figure 3 has dimensions a = 1.0mm, b = 1.0mm, and c = 2.0mm. It is subjected to triaxial stresses ?x = 20MPa, ?y = -10MPa, and ?z = 15MPa (all the shear stress components are zero) acting on the x, y, and z faces, respectively. Use E = 50GPa and ? = 0.25.
(a) Calculate the strain components ?x, ?y, ?z, ?xy, ?yz, and ?zx.
(b) Calculate the change ?V in volume.
(c) Determine the normal strain in the direction of line OA.
(d) Determine the strain energy stored in the block.

Added by Elena G.

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