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HW2 - σ xx = 4MPa σ yy = 3MPa σ zz = 0MPa τ xy = 2MPa...

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EAS4200C Aerospace Structures Homework #2 (Due: Sep. 11th) 1. Consider a unit cube of a solid occupying the region 0 x 1 , 0 y 1 , 0 z 1 . After loads are applied, the displacements are given by u = α x , v = β y , w = 0 . (a) Sketch the deformed shape for α = 0.03, β = 0.01 . (b) Calculate the six strain components. (c) Find the volume change Δ V [ Δ V = V (the volume after deformation) V 0 (the original volume ) ] for this unit cube. Show that ε xx + ε yy + ε zz Δ V . 2. The state of stress in a body is uniform and is given by
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Unformatted text preview: σ xx = 4MPa, σ yy = 3MPa, σ zz = 0MPa, τ xy = 2MPa, τ yz = 0MPa, τ xz = 0MPa . (a) Find the three components of the stress vector t on the surface ABCD as shown in the figure. (b) Find the normal component σ n of the stress vector. 3. Find the principal stresses and corresponding principal directions for the stresses given in Problem 2. Check the result with other methods such as Mohr’s circle....
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