(Solved): [3]. A hook of triangular cross-section as shown below has a base of 50mm and altitude of 75 mm. ...

[3]. A hook of triangular cross-section as shown below has a base of $50\mathrm{mm}$ and altitude of 75 $\mathrm{mm}$. If the radius of curvature is $50\mathrm{mm}$ at the inner curved surface, what is the allowable safe load on the hook if permissible tensile and compressive yield strength limits are $105\mathrm{MPa}$ and $84\mathrm{MPa}$ respectively. The load line is $75\mathrm{mm}$ from the edge of the inner surface. Note that the centroidal axis passes through point $\mathrm{G}$ on the right sketch. Also, the center of curvature is at point $\mathrm{C}$ and the base of the triangle is towards the center of curvature. Neutra axis is marked by line NA ( $\underline{3}$ marks) 2 Hint: For the determination of ${\mathrm{r}}_{\mathrm{n}}$ value, one will need to solve for the integral $?\frac{dA}{v}$ where $dA=$ $bdv$. where $b$ is width of the strip. Also, for integration, one would need to come up with a geometric relationship between $v$ and $b$ parameter that should satisfy the boundary conditions of $b$ $=0$ when $v=125\mathrm{mm}$, and $b=50\mathrm{mm}$ when $\mathrm{v}=50\mathrm{mm}$, for the triangular cross-section.