Exam ii

$14$:$650$:$291$ Introduction to Mechanics of Materials

Rutgers University, $11/19/24$

Please be sure to turn in your two sheets $({8\mathrm{.}5}^{\text{'}\text{'}}11"$ or A$4)$ of notes with your name on them, along with the questions for the exam and all the answer sheets $($even the blank ones$).$ Once the exam begins, please separate the answer sheets from the questions and write your name on at least one side of each page. Please show all work on the included answer sheets. Writing on the questions themselves will not be graded. You may use a standard calculator without emailing, texting, or internet$-$cnabled access. Finally, please ensure you give numerical answers using the appropriate units. Good luck and do the best you can!

Question $1(5$ points$)$

You are pondering the states of stress in thin$-$walled pressure vessels on a Saturday night. A thin$-$walled cylindrical pressure vessel has a radius of $20$ cm $,$ a thickness of $1$ mm $,$ and a gauge pressure of $800$ kPa $.$

a$)(1$ pt$.)$ What are the hoop stress and longitudinal$/$axial stress in the wall of this cylinder?

b$)(3$ pt$.)$ If the hoop stress is ${}_x$ and the longitudinal$/$axial stress is ${}_y,$ please use method of slices on a material element to calculate ${}_{z^{\text{'}}}$ and ${}_{x^{\text{'}}{y}^{\text{'}}}$ for an angle of rotation about the $z-$axis of $30.$

c$)(1$ pt$.)$ Use Mohr's circle to determine the angle of rotation necessary to get to a state of maximum, in$-$plane shear stress. What is the value of this max, in$-$plane shear stress?