Selection of round cross-section beams

Maximal bending moment Mmax = kNm
Allowable stress [σ] = MPa

Resistance moment $$W = \frac{M_{max}}{[\sigma]} = \frac{40000}{160} = 250cm^3$$
For round section $$W=\frac{\pi \cdot d^3}{32}$$  so diameter $$d = \sqrt[3]{\frac{32\cdot W}{\pi}} = \sqrt[3]{\frac{32\cdot 250}{\pi}} = 13.7 см$$ Section area $$A = \frac{\pi \cdot d^2}{4} = \frac{\pi \cdot 13.7^2}{4} = 147cm^2$$


Selection of rectangular beam section

Maximal bending moment Mmax = kNm
Allowable stress [σ] = MPa
h / b =

Minimal resistance moment $$W = \frac{M_{max}}{[\sigma]} = \frac{40000}{160} = 250cm^3$$
For rectangle section $$W=\frac{b \cdot h^2}{6} = \frac{b \cdot (2.5b)^2}{6} = \frac{b^3 \cdot 2.5^2}{6}$$ Section width $$b = \sqrt[3]{\frac{6\cdot W}{2.5^2}} = \sqrt[3]{\frac{6\cdot 250}{2.5^2}} = 6.21 см$$ Section height $$h=6.21\cdot 2.5 = 15.5 cm$$ Section area $$A = h \cdot b = 15.5\cdot 6.21 = 96.3cm^2$$