Problem $1(30$ points$)$

A hollow circular pipe supports a load P that is uniformly distributed around a cap plate at the top

of the lower pipe. The inner and outer diameters of the upper and lower parts of the pipe are $d_1=50$

$mm,d_2=60mm,d_3=57mm$ and $d_4=64mm,$ respectively. Pipe lengths are $L_1=2m$ and $L_2=3m.$

Neglect the self$-$weight of the pipes. Assume that cap plate thickness is small compared to $L_1$ and

$L_2($which means you don't need to consider the thickness in the analysis$).$ Let $E=110$MPa.

a$)$ If the tensile stress in the upper part is ${}_1=10\mathrm{.}5$MPa, what is load P $?$ Also, what are reactions, $R_1$

in the upper support and $R_2$ at the lower support? What is the stress ${}_2(MPa)$ in the lower part?

b$)$ Find displacement $(mm)$ at the cap plate. Plot the axial force diagram $($AFD$)N(x)$ and axial

displacement diagram $($ADD$)(x).$

c$)$ Add the uniformly distributed load q along the centroidal axis of pipe segment $2.$ Find $q(k\frac{N}{m})$

so that $R_2=0.$ Assume that load $P$ from part $($a$)$ is also applied.

PLEASE ANSWER ALL PARTS AND SHOW ALL WORK. NEED HELP WITH PART C THE MOST.