Prob. $1$ Combined Loadings $(50$ pts$.)$

Two forces $P1$ and $P2,$ of magnitude $P1=15kN$ and $P2=18kN,$ are applied as shown to the end

A of bar AB$,$ which is welded to a solid cylindrical member BD of radius $c=20mm($Fig$.1\mathrm{.}1).$

Knowing that the distance from $A$ to the axis of member $BD$ is $a=50mm$ and assuming that all

stresses remain below the proportional limit of the material, determine the resulting normal $$ and

shearing stresses $$ at points $h,$I,$j$ and $k.$ The location of interest for analysis is at distance $b=$

$60mm$ from end B $($Fig$.1\mathrm{.}2).$ Show all calculations to get full credit. Draw the axial, bending,

shear and torsional stress diagrams to substantiate your results. Ignore the self$-$weight of the bar.

Fig $1\mathrm{.}2$ Cross$-$Section