Selected Final Exam Questions - p i r i r o 1 Specify the boundary condition for each of the following cases in terms of the chosen x-y frame i.e xx \uf073

# Selected Final Exam Questions - p i r i r o 1 Specify the...

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p i r i r o 1. Specify the boundary condition for each of the following cases in terms of the chosen x - y frame, i.e. xx , yy , xy , u x , u y . 2. The stress state at a point with respect to the coordinate system, x 1 , x 2 , x 3 , is 1 11 , 2 22 , 3 33 , the other stress components being zero. Consider a plane having unit normal vector 3 2 1 e e e s n m l . ( a ) Find the shear stress on this plane. ( b ) Find the values of l , m , and n such that the shear stress at that plane is extremum. Answer: a ) 2 2 3 2 2 2 1 2 2 3 2 2 2 2 2 1 n m n m , b ) Six solutions: (1) 1 , 0 n m , (2) 2 1 , 2 1 , 0 n m , (3) 2 1 , 0 , 2 1 n m , (4) 0 , 1 n m , (5) 0 , 2 1 , 2 1 n m , (6) 0 , 1 , 0 n m 3. Consider a composite beam subject to pure bending moment. The beam is made of two layers each with a thickness of h .