Given:

$a$:$=40*mm$

$M_{\text{t}\text{o}\text{n}\text{g}\text{u}\text{e}}$:$=100*kg{F}_{\text{p}\text{u}\text{l}\text{l}}$:$=4\mathrm{.}905*kN$

$,$

The trailer hitch shown in Figure P$4-2$ and Figure $1-1$ has loads applied as defined in Problem

$3-4.$ The tongue weight of $100$ kg acts downward and the pull force of $4905$ N acts horizontally.

Using the dimensions of the ball bracket shown in Figure $1-5,$ determine:

$($a$)$ The principal stresses in the shank of the ball where it joins the ball bracket.

$($b$)$ The bearing stress in the ball bracket hole.

$c$:$=70*mm,d$:$=20*mm$

$d_{sh}$:$=26*mm$

$t$:$=19*mm$

The internal bending moment at $A$ on the FBD of the ball

$M$:$=F_{\text{p}\text{u}\text{l}\text{l}}*a$

Distance to neutral axis

$c_{sh}$:$=0\mathrm{.}5*d_{sh}$

Moment of inertia of shank $,I_{sh}$:$=\frac{*(d_{sh}{)}^4}{64}$

Bending stress at $A,{}_x$:$=\frac{M*c_{sh}}{I_{sh}}$

${}_1$:$={}_x$

$A_{\text{b}\text{e}\text{a}\text{r}\text{n}\text{g}}$:$=d_{sh*t}$

${}_{\text{b}\text{e}\text{a}\text{n}\text{n}\text{g}}$:$=\frac{F_{\text{p}\text{u}\text{l}\text{l}}}{A_{\text{b}\text{e}\text{a}\text{n}\text{n}\text{g}}}$