Homework$-3-$DUE DATE: January ${31}^{st},2024$ at the beginning of the class. NO LATE SUBMISSIONS! Solve these problems on separate sheets of paper.

Staple them together and use this page as a cover page with your name on it$.$

P$1$ Ans: a$)833\mathrm{.}6$MPa, b$)324\mathrm{.}1$MPa

A thick$-$walled cylinder made of Steel $4340$ is subjected to an internal pressure $p_i.$ It has an outside diameter $d_o=8\mathrm{.}0cm$ and wall thickness $t=1\mathrm{.}0cm.$ During the inspection it was discovered that the cylinder has a through thickness radial crack in the longitudinal direction with a depth of $a=0\mathrm{.}25cm.$ Determine: a$)$ the fracture stress, b$)$ the internal pressure that will cause crack to grow.

$\frac{a}{r_s}-r_j$