prob_08_05_05 - = ⎪ ⎭ ⎪ ⎬ ⎪ ⎩ ⎪ ⎨ ...

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Problem 8.5-5 Given: Element ij shown is a 2D beam element that has both axial and bending stiffness. At each of nodes i , j , 1, and 2, d.o.f. are u , v , and counterclockwise rotation θ . Imagine that the d.o.f. at nodes i and j are to be made slave to d.o.f. at nodes 1 and 2 via rigid links i 1 and j 2. Write the 6 by 6 transformaito matrix [T] Solution: Using the following equations from our class notes:
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Unformatted text preview: ⎧ = ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − = ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ i i i ij i i i i j j i j j j v u v u x x y y v u θ ] [ θ 1 1 1 θ T We can get: T 1 1 b 1 a 1 − 1 1 1 b 2 a 2 − 1 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ =...
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This note was uploaded on 01/11/2011 for the course MAE 5020 taught by Professor Folkman during the Fall '10 term at Utah State University.

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