PROBLEM $3.$ Two solid cylindrical rods $AB$ and $BC$ are welded together at $B$ and loaded as shown. Determine the magnitude of the force $P$ for which the tensile stress in rod $AB$ has the same magnitude as the compressive stress in rod BC$.$

Solution:

${}_{AB}={}_{BC}$

$\frac{P}{\frac{}{4}(2in{)}^2}=\frac{60-P}{\frac{}{4}(3in{)}^2}$

$90=4(60-P)$

$P=18\mathrm{.}46kN$

Determine the deformation of $AB,BC$ and total deformation $(mm)$ from A to C $.$

E$=200$ Gpa