Problem $1$

For the pure bending and shear loading on the circular beam shown below, determine the bending stress distributions on the cross$-$section at BC using both the Strength of Material and Theory of Elasticity formulations. Draw diagrams to compare the distributions from the two methods. The cross$-$section of the circular beam is square, $\backslash (50\backslash$mathrm$\{$~mm$\}\backslash$times $50\backslash$mathrm$\{$~mm$\}\backslash ),$ and a $\backslash (=30\backslash$mathrm$\{$~mm$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$b$\}=80\backslash$mathrm$\{$~mm$\}\backslash ).$