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Physics, 13.03.2020 18:27 sabrinamarie391

A heavy weight eagle is wandering around and suddenly decides to land at the tip of a branch of an old tree. As a vibration expert you are called upon to analyze the following problem for the Forest Trees Protection Society of San Luis Obispo. The mass of a typical heavy weight eagle is 10 Kg and the branch is modeled as a cantilever beam with E=100MPa, l=10-4 m4, L=2m and assumed to be massless, and having a damping ratio of 1%. Find the maximum bending stress developed at the point of connection of the branch with the trunk of the tree. If assuming the distance from the centroid of the cross section of the branch to the top or bottom fiber of the cross section of the branch is 5 cm and the mother nature has limited the tolerable bending stress of the branch to 150 kPa, will this branch tolerate the drop weight of the monkey? Hint: Draw the shear-moment diagram of the branch.

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