Problem $(1)$

$(15$ marks$)$

Assume that you work as a design engineer in an engineering company, and you are given a task by your

manager to select an appropriate ductile material for the machine element shown below in the figure.

$D=45mm$

$d_2=40mm$

$d=30mm,$

From an earlier analysis, it is known that the critical section of the machine member is at the shoulder

$80$ mm from the left end support. The state of stress at the critical point is: