Question

Help with solid mechanics X)

Answer 1

Two solid cylindrical rods AB and BC are welded together at B and loaded shown below. Knowing that \(d_1=30 \text{mm}\) and \(d_2=50\text{mm}\), find the average normal stress at the midsection of
(a). Rod AB
(b). Rod BC


\[\large \mathbf{My~Solution:}\](a).\[\text{P}= 60\text{kN}=60,000 \text{N}\]\[\text{Area}_\text{AB}=\frac{\pi (0.03\text{m})^2}{4}=0.000707\text{m}^2\]\[\sigma_\text{AB}=\frac{\text{P}}{\text{A}_\text{AB}}=\frac{60,000\text{N}}{0.000707\text{m}^2}=85~\text{kPa}\]

(b).\[\text{P}= 60-2(125)=-190\text{kN}=-190,000 \text{N}\]\[\text{Area}_\text{BC}=\frac{\pi (0.05\text{m})^2}{4}=0.00196\text{m}^2\]\[\sigma_\text{BC}=\frac{\text{P}}{\text{A}_\text{BC}}=\frac{-190,000\text{N}}{0.00196\text{m}^2}=-97~\text{MPa}\]