HW1_solution

HW1_solution - UNIVERSITY OF CALIFORNIA College of...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science and Engineering Fall 2011 MSE 113 Professor Ritchie Mechanical Behavior of Materials 1 PROBLEM SET 1 Problem 1 (20 points) Assuming a linear elastic pressure vessel pressurized to & in static equilibrium, with wall thickness and inner radius , such that . Force Balance: 0 0 0 2 ! 2 Since , we can drop all terms as approximation 2 & & 2 UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science and Engineering Fall 2011 MSE 113 Professor Ritchie Mechanical Behavior of Materials 2 & 0 ## 0 ## 2$ 2 $ 0 ## 2$ 2 $ ## & 0 % 2 ( )% )% 0 Since , the area difference between inside, middle and exterior is small and can be ignored. Therefore: )% 2 * 0 Since both hoop and longitudinal stress has an extra factor of + % , which is expected to be large, radial stress is much smaller in comparison, and therefore can be generally ignored. Furthermore, the thin wall assumption guarantees no shear stress due to pressurization....
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HW1_solution - UNIVERSITY OF CALIFORNIA College of...

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