Consider the indeterminate, axially loaded rod system shown below.

$P_1=20,000lb$

$A=2i{n}^2$

$P_2=12,000lb$

$E=15,000,000$ psi

Determine the reactions at $c$ and $d,$ and the displacements at a and $b$ using:

Provide detailed analytical model with all DOFS$/$Forces$/$Displacements shown Label nodes$/$elements

a$.$ Mechanics of materials methods PL$/$AE$)$;