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# HW8 - AE 321 Homework#8 Due Monday Chapter 7 Failure NOTE...

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AE 321 – Homework #8 Due: Monday November 17, 2008 Chapter 7: Failure NOTE: All questions in this homework have previously appeared in exams. 1. A linear, elastic, isotropic and homogeneous solid circular cylinder of length L and radius R (no restriction on L and R ), Young’s modulus E , Poisson’s ratio ± and uniaxial yield strength ² y , is subjected to an applied pressure P on its lateral surface. The end faces are traction free (a) Find the stress and strain state in the bar. Hint: In-plane, i.e. looking down the cylinder axis, the loading appears hydrostatic. (b) What is the maximum value of pressure before yield occurs if the material subscribes to a Von Mises yield condition? (c) What would the Von Mises criterion predict if the pressure P were applied on the end faces as well as the lateral surface? x 3 P P

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2. Bending moments M y and M z are applied to the rectangular bar shown below. The bar is made up of a brittle linear elastic isotropic and homogeneous material with elastic properties E , ± and
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