$$ \begin{array}{l}{\text { Data: } \mathrm{L}=6 \mathrm{m}, \mathrm{W}_{1}=18 \mathrm{kN}, \mathrm{W}_{2}=18 \mathrm{kN}, \sigma_{\mathrm{b}}=10 \mathrm{N} / \mathrm{mm}^{2}, \mathrm{b}=\mathrm{d}} \ {\text { Find: } \mathrm{b}, \mathrm{d}}\end{array} $$ $$ \begin{array}{l}{\mathrm{RA}=\mathrm{RB}=18 \mathrm{kN} \text { (Due to symmetry) }} \ {\mathrm{M}_{\max }=\mathrm{M}_{\mathrm{C}}=\mathrm{M}_{\mathrm{D}}=18 \times 2=36 \mathrm{kN}-\mathrm{m}=36 \times 10^{6} \mathrm{N}-\mathrm{mm}} \ {\mathrm{I}=\frac{\mathrm{bd}^{3}}{12}=\frac{\mathrm{b}^{4}}{12}} \ {\mathrm{Y}=\frac{\mathrm{d}}{2}=\frac{\mathrm{b}}{2}}\end{array} $$ $$ \begin{array}{l}{\frac{\mathrm{M}}{\mathrm{I}}=\frac{\sigma}{\mathrm{Y}}} \ {\sigma=\frac{\mathrm{M}}{\mathrm{I}} \times \mathrm{Y}} \ {10=\frac{\left(36 \times 10^{6}\right)}{\frac{\mathrm{b}^{4}}{12}} \times \frac{\mathrm{b}}{2}} \ {10=\frac{\left(36 \times 10^{6}\right)}{10} \times 6} \ {\mathrm{b}^{3}=216 \times 10^{5}}\ b= 278.495 mm \d= 278.495 mm\end{array} $$