Question

An aluminium rod with semi-circular cross-section of radius r = 12 mm is bent into the shape of circular arc of mean radius, R = 2.5 m. Knowing that the flat face of the rod is turned towards the centre of curvature of the arc, the ratio of maximum tensile and compressive bending stress in rod is

• A. 0.74
• B. 1.78
• C. 2.35
• D. 1.36

Answer 1

The correct option is D 1.36


$y_1=\frac{4r}{3\pi }$

$y_2=r-\frac{4r}{3\pi }$

$\frac{{\sigma }_T}{y_2}=\frac{{\sigma }_C}{y_1}$

$\Rightarrow \frac{{\sigma }_T}{{\sigma }_C}=\frac{y_2}{y_1}=\frac{(r-\frac{4r}{3\pi })}{\frac{4r}{3\pi }}=1.36$