hw2 - ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ 150 750 900 750 300...

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MAE 3250 Analysis of Mechanical and Aerospace Structures Fall 2009 HW# 2, Due: 11:10 am, Monday, Sep. 14th 1. A member has the following non-zero strains: ε xx = a 0 + a 1 y 2 + y 4 ε yy = b 0 + b 1 x 2 + x 4 ε xy = c 0 + c 1 xy(x 2 + y 2 + c 2 ) Is there a relationship between the constants that make the foregoing expressions possible? If so, state the relationships. 2. The displacement field in a body is given by: u = c(x 2 + 10) v = 2cyz w = c(-xy + z 2 ) Where c = 10 -4 . Determine the state of strain at the point (0, 2, 1). 3. The following describes the state of strain at a point in a structural member:
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Unformatted text preview: ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 150 750 900 750 300 600 900 600 450 μ Find the magnitudes and directions of the principal strains. 4. For a given steel with E = 200 GPa and G = 80 GPa, if the state of strain is given by ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 400 400 300 100 100 200 μ Determine the corresponding components of the stress tensor. 5. For a steel plate (E = 200 GPa, G = 80 GPa), determine the strain tensor for a state of stress given by: ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − 15 10 5 10 4 5 4 20 MPa...
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