Problem $5$

A solid cylinder of diameter $d=80mm$ is fixed at

A$.$ A rigid bar is welded at the other end as

shown. A force $F$ is applied in the z$-$direction and

a force $10F$ is applied in the $x-$direction.

For the most critical location $($highest stresses$)$ at

$A(x=0,y=0,z=r)$ :

a$)$ Draw a cube showing the stress components

on each coordinate face.

b$)$ Find the principal stresses.

c$)$ Draw the $3$D Mohr circle and indicate the

principal stresses location and the magnitude

of the maximum shear stress.

d$)$ Find the highest force $F$ so that the maximum

normal stress is less than $120$MPa and the

maximum shear stress is less than $60$MPa.

e$)$ Calculate the maximum allowable force $F$ if a

groove of radius $r=1\mathrm{.}9mm$ is machined at $x=0.$

Stresses equations: $r=$ radius

Bending

$=\frac{Mc}{\text{I}},I=\frac{r^4}{4}$

Torsion

$=\frac{Tr}{J},J=\frac{r^4}{2}$