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# ha3 - 16.20 Handed Out Lecture 12 Due Lecture 16 HOME...

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16.20 Handed Out: Lecture 12 Due: Lecture 16 HOME ASSIGNMENT #3 Warm-Up Exercises Let’s explore the use of Mohr’s circle for strains in the case of plane stress. Use geometrical arguments/considerations to: 1. Show that the transformation of an arbitrary state of in-plane strain ( ε 11 , ε 22 , ~ ~ ε 12 ) to another in-plane system ( ε ~ 11 , ε 22 , ε 12 ) yields the three equations represented by: ε αβ = l ~ βλ ε σλ ασ l ~ 2. Look at the circle diameter. The circle diameter is some combination of the strains that is invariant. Determine what this is (in terms of ε αβ and the transformation angle θ ). 3. Does the combination of strains that coincides to the circle diameter have any physical significance? If so, what is it; if not, is there another geometric item with physical significance? Practice Problems 4. A 2-meter long aluminum bar has a square cross-section (35 cm to a side) and is subjected to uniform side pressures of p 1 and p 2 . The modulus of aluminum is 70.8 GPa and the Poisson’s ratio is 0.3.

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ha3 - 16.20 Handed Out Lecture 12 Due Lecture 16 HOME...

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