$1-$For a bolted assembly, two plates of cast iron are clamped together. Each cast iron assembly part

has $0\mathrm{.}75$ inch thickness. The bolt is $\frac{3}{4}in-16$UNF$2\frac{1}{2}$inSAE grade $5.($UNF$-$Fine Series$).$ The bolt

material is steel. A fluctuating external load is applied to the entire joint with $P_{\text{m}\text{a}\text{x}}=120$ kips and $P_{\text{m}\text{i}\text{n}}=60$

kips. $(70$ POINTS$)$

a$)$ Calculate the minimum number of bolts necessary to avoid joint seperation.

b$)$ In the same bolted assembly, assume $15$ bolts are used and calculate the fatigue factor of

safety using the Goodman theory.

c$)$ Using the Frustum Method, determine the member spring rate $km$ if the top plate is steel and

the bottom plate is cast iron. Assume that a steel washer is used under the bolt head. The

thickness of each assembly plate is $0\mathrm{.}75$ inch and the washer has $0\mathrm{.}01$ inch thickness. $($standard

washer face diameter is $1\mathrm{.}5d,d$ is bolt diameter$)$

Given Data:

$-E_{\text{s}\text{t}\text{e}\text{e}\text{l}}$:$30M,E_{\text{c}\text{a}\text{s}\text{t}\text{i}\text{r}\text{o}\text{n}\text{:}}14M$

$-$Applied preload is $75$ percent of the proof load $(F_i=0\mathrm{.}75F_p)$ and $F_p=A_t*S_p,$

$-$Endurance strength of bolt is $18\mathrm{.}6k$

$S_{ut}($ultimate tensile strength$),A_t($tensile stress area$)$ and $S_p($proof strength$)$ of bolt should be found

from the corresponding tables in your textbook.

$2-$Explain self$-$locking condition and determine the roles of lead angle and friction coefficient in self

locking. $(30$ POINTS$)$