ProblemSet3 - homogeneous deformation ( same strain at all...

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M ASSACHUSETTS I NSTITUTE OF T ECHNOLOGY Department of Mechanical Engineering 2.001-Mechanics and Materials I Spring, 2006 Problem Set 3 Distributed: Tuesday, February 27, 2006 Due: Monday, March 6, 2006 Reading Assignment: Hibbeler Sections 10.6 (+examples 10.10&10.11), 4.3, 4.4, 4.5, 4.6, 8.1 Solve all the following problems assuming that the material is linear, isotropic, elastic Problem 1: Hibbeler 3-16 ( E Steel =200 GPa) Problem 2: Hibbeler 3-26 Problem 3: Hibbeler 3-33 Problem 4: Hibbeler 3-37 ( E Al =70 GPa) Problem 5: Hibbeler 4-10 Problem 6: Hibbeler 4-27 (The plate has properties E , ν )
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Plate ABCD is a square of side length L when it is undeformed. When the plate is subjected to a state of
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Unformatted text preview: homogeneous deformation ( same strain at all points of the plate ) the plate becomes a parallelogram and the opposite sides remain parallel, but the internal angles might be different from the original /2. Consider the four deformed (dashed) shapes for the plate depicted below. Assume that the deformations are small (small strain, the deformations in the pictures have been magnified for clarity). Give expressions for the in-plane components of the strain tensor: xx , yy , xy , yx and for the engineering shear strain xy for each case. A B C D L L 2 h (i) (iii) (ii) (iv) A B C D x y A B C D x y h A B C D x y h h A B C D x y h h/2 h/2 h...
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ProblemSet3 - homogeneous deformation ( same strain at all...

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