Given: $=-1000$ psi, $3000$ psi, and $3000$ psi$($ccW$).$

Determine:

a$.$ Draw and label the cartesian stress element

b$.$ Calculate the principal stresses.

c$.$ Von Mises effective stress

d$.$ Maximumabsolute shear stress

$1,2$

; $1,3$

; $2,3$

; ${?}^{\frac{?}{abs}}$

$q,$

$q,$

e$.$ If the part is made from ductile AISI $1030$ hot rolled steel under static loading and assuming $Sy=38$ kisi, determine if the part will fail for a design factor of $2,$ using:

f$)$ Distortion Energy Theory $($DE$)$

g$)$ Maximum Shear Stress Theory $($MSS$)$