$9-81-$mod$)$ For the state of plane stress shown below:

$($a$)$ Draw the Mohr's circle and determine the

magnitudes and orientations of the

principal stress state, and maximum in$-$

plane shear stress state using the Mohr's

circle

$($b$)$ Draw the principal stress state and

maximum in$-$plane shear stress state on

appropriately oriented elements

$($c$)$ Using the Mohr's circle, determine the state

of stress on an element oriented $75^($@$)$CW

from the given state of stress and draw this

state of stress on an appropriately oriented

element

$($d$)$ Determine the magnitude of the absolute

maximum shear stress

ANS: sigma x $=20$ ksi ; sigma y $=10$ ksi ; R$=9\mathrm{.}434$ ksi ; Center$=(15,0)$; sigma x$\text{'}=6\mathrm{.}67$ ksi ; sigma y$\text{'}=23\mathrm{.}33$ ksi $,$ Tx$\text{'}$y$\text{'}=-4\mathrm{.}429$ ksi ; a $=28$ degrees