ME $323$ MACHINE DESIGN I

HOMEWORK

$1-$For the bolted assembly, two plates of cast iron are clamped together. The top plate has a thickness of $\frac{3}{8}$ inch and the bottom plate has $\frac{1}{2}$ inch thickness. The bolt material is steel. The bolt specification is $\frac{7}{16}in-14$UNC$1\frac{1}{4}$inSAE grade $8.$ A fluctuating external load is applied to the entire joint with $P_{\text{m}\text{a}\text{x}}=88$ kips and $P_{\text{m}\text{i}\text{n}}=60$ kips. $(80$ POINTS$)$

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

b$)$ In the same bolted assembly, assume $11$ 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 $1\mathrm{.}25$ inch and the washer has $0\mathrm{.}01$ inch thickness. $($standard washer face diameter is $1\mathrm{.}5$ d $,$ d is bolt diameter$)$

d$)$ 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 steel top plate is $1\mathrm{.}25$ inch and the thickness of cast iron bottom plate is $1\mathrm{.}75.$ The washer has $0\mathrm{.}01$ inch thickness. $($standard washer face diameter is $1\mathrm{.}5d,d$ is bolt diameter$)$

Given Data:

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

$-$Applied preload is $75$ percent of the proof load