Data : b = 100mm, d = 50 mm, P = 40kN

$\mathrm{A}=\mathrm{b} \times \mathrm{d}=50 \times 100=5000 \mathrm{mm}^{2}$

$\mathrm{I}=\frac{\mathrm{b} \times \mathrm{d}^{3}}{12}=\frac{50 \times 100^{3}}{12}=4.17 \times 10^{6} \mathrm{mm}^{4}$

$\mathrm{Y}=\frac{\mathrm{b}}{2}=\frac{100}{2}=50 \mathrm{mm}$

$\mathrm{M}=\mathrm{P} \times \mathrm{e}=40 \times 10^{3} \times 300=12 \times 10^{6} \mathrm{N}-\mathrm{mm}$

$\sigma_{\mathrm{o}}=\frac{\mathrm{P}}{\mathrm{A}}=\frac{40 \times 10^{3}}{5000}=8 \mathrm{N} / \mathrm{mm}^{2}$

$\sigma_{\mathrm{b}}=\frac{\mathrm{M}}{\mathrm{I}} \times Y=\frac{12 \times 10^{6}}{4.17 \times 10^{6}} \times 50=143.88 \mathrm{N} / \mathrm{mm}^{2}$

$\sigma_{\max }=\sigma_{0}+\sigma_{\mathrm{b}}$

$\sigma_{\max }=8+143.88=151.88 \mathrm{N} / \mathrm{mm}^{2}$

$\sigma_{\max }=\sigma_{0}-\sigma_{\mathrm{b}}$

$\sigma_{\min }=8-143.88=135.88 \mathrm{N} / \mathrm{mm}^{2}$