ha4 - 0.30. Using the stress function approach: 16.20 Home...

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16.20 Handed Out: Lecture 16 Due: Lecture 20 HOME ASSIGNMENT #4 Warm-Up Exercises Let’s consider the stress field around the hole in an isotropic 2a σ o y 1 y 2 r θ plate loaded in uniaxial compression (no buckling occurs): 1. Derive expressions for the stress components at the hole boundary (r = a) as a function of θ in the y 1 - y 2 - y 3 coordinate system. 2. Plot these values, normalized by the applied far-field stress, σ o , as a function of θ . 3. Plot the “polar coordinate” stresses at the hole boundary as a function of θ . 4. Compare the plots of #2 and #3. Discuss any similarities/differences/noteworthy points. Practice Problems 5. A pressurized aluminum vessel results in a state of plane stress in the skin of 100 MPa in one direction and 250 MPa perpendicular to this direction. Aluminum has a modulus of approximately 70 GPa and a Poissons’s ratio of
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Unformatted text preview: 0.30. Using the stress function approach: 16.20 Home Assignment #4 Page 2 Fall, 2002 (a) Construct a solution for this configuration. (b) Determine the full strain state. (c) Determine the entire deformation field. Application Tasks 6. Use appropriate combinations of the Airy stress functions provided to: (a) Construct a solution for the case of an isotropic cantilevered beam loaded by an end load as pictured. (b) Compare these results (for xx and xz ) with those from simple beam theory. (c) Where in this problem is it necessary to apply St. Venants principle? P l h x 100 MPa 250 MPa z 16.20 Home Assignment #4 Page 3 Fall, 2002 C 30 x 3 C 03 y 3 16.20 Home Assignment #4 Page 4 Fall, 2002 C 31 x 3 y...
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ha4 - 0.30. Using the stress function approach: 16.20 Home...

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