Problem #$1(100$ pts$)$:

Given:

A pressurized pipe experiences combined loading due to unaccounted thermal expansion

The four locations $($A$,$ B$,$ C$,$ and D$)$ are identified as areas of concern

You are tasked with finding the stresses present at each element, the principal stresses, and the FoS with respect to yielding at each point

$P_x=2\mathrm{.}5kN,P_y=1kN,P_z=3\mathrm{.}5kN,P_i=2\mathrm{.}0$MPa $($internal gage pressure$)$

Outside diameter $=200mm,$ wall thickness $=10mm$

$Y_1=0\mathrm{.}63m,Y_2=1\mathrm{.}72m,Z_1=1\mathrm{.}22m,Z_2=1m$

Yield strength $=350$MPa

Find:

List which forces $(Px,Py,Pz)$ induce non$-$zero stresses at the four locations

Note that thin$-$walled pressure stresses from $P_i$ are not included in this table

$\backslash$table$[[$Stress Type,A$,$B$,$C$,$D$],[$Axial $($Normal$),,,,],[$Bending$,,,,],[$Torsional Shear,,,,$],[$Transverse Shear,,,,$]]$