ProblemSet2 - internal angles might be different from the...

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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 2 Distributed: Tuesday, February 21, 2006 Due: Monday, February 27, 2006 Reading Assignment: Hibbeler Sections 3.1, 3.2, 3.4, 3.5, 3.6, 3.7, 4.1, 4.2 Problem 1: Hibbeler 1-47 (10 pts) Problem 2: Hibbeler 1-42 &1-44 (15 pts) Problem 3: Hibbeler 1-64 &1-65 (15 pts) Problem 4: Hibbeler 2.8 (10 pts) Problem 5: (10 pts) Plate ABCD is a square of side length L when it is undeformed. When the plate is subjected to a state of homogeneous deformation ( same strain at all points of the plate ) the plate becomes a parallelogram and the opposite sides remain parallel, but the
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Unformatted text preview: internal angles might be different from the original π /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: ε xx , ε yy , ε xy , ε yx and for the engineering shear strain γ xy for each case. (i) (iii) (ii) (iv) A B C D A B C D x y L L A B C D x y 2 h 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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