PROBLEMS

$1\mathrm{.}1$ Two solid cylindrical rods $AB$ and $BC$ are welded together at $B$ and loaded as shown. Knowing that the average normal stress must not exceed $175$ MPa in rod $AB$ and $150$ MPa in rod $BC,$ determine the smallest allowable values of $d_1$ and $d_2.$

$1\mathrm{.}2$ Two solid cylindrical rods $AB$ and $BC$ are welded together at $B$ and loaded as shown. Knowing that $d_1=50mm$ and $d_2=30mm,$ find the average normal stress at the midsection of $(a)rodAB,($b$)$ rodBC.

$1\mathrm{.}3$ 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 $BC.$