Problem $1$

The beam with a circular cross$-$section is subjected to combined loads as shown in the figure below.

$($a$)$ Draw the $3$D stress element and $2$D stress element $($plane stress condition$)$ at locations A$,$ B$,$

$C,D,$ and E on the cross$-$section at the wall.

Include all non$-$zero stress components acting on the element.

Clearly show the coordinate system used for each of your stress elements.

See L$3$ class notes for a similar example.

$($b$)$ Evaluate the maximum shear stress $({}_{\text{m}\text{a}\text{x}})$ at points $A,B,C,D,$ and E $.$ Which of these is the

critical location?

The dimensions and forces are as below:

$d=20mm$

$l=100mm$

$F=550N(+Z$ direction $)$

$P=15,000N(+x$ direction $)$

$T=20,000N-mm(-x$ direction $)$