Características geométricas

\begin{aligned} &A_1=20\cdot 80=1600\ mm^2 \\ &A_2=20\cdot 100=2000\ mm^2 \\ &z_1=40\ mm \\ &z_2=90\ mm \\ &z_c=\frac{Sy}{A}=\frac{z_1\cdot A_1+z_2\cdot A_2}{A_1+A_2} \\ &z_c=67,78\ mm\\ &I_{yc}=I_{y1}+A_1\cdot (z_1-z_c)^2+I_{y2}+A_2\cdot (z_2-z_c)^2\\ &I_{yc}=\frac{20\cdot 80^3}{12}+1600\cdot (40-67,78)^2+\frac{100\cdot 20^3}{12}+2000\cdot (90-67,78)^2=3083888,9\ mm^4=3,08\cdot 10^{-6}\ m^4\\ \end{aligned}

Tensiones normales

\begin{aligned} &\sigma =\frac{M}{I_{yc}}\cdot z\\ &\sigma_5 =\frac{5000}{3,08\cdot 10^{-6}}\cdot 32,22\cdot 10^{-3}=52,31\ MPa\\ &\sigma_1 =110,03\ MPa\\ \end{aligned}

Tensiones cortantes

\begin{aligned} &S_1=S_5=0\\ \end{aligned}

\begin{aligned} &S_3=S_4=100\cdot 20\cdot 22,22=44440\ mm^3=4,44\cdot 10^{-5}\ m^3\\ \end{aligned}

\begin{aligned} &S_2=S_4+12,22\cdot 20\cdot 6,11=4,59\cdot 10^{-5}\ m^3\\ \end{aligned} \begin{aligned} &\tau=\frac{T\cdot S}{b\cdot I_{xc}}=\frac{100\cdot 10^3}{3,08\cdot 10^{-6}}\cdot \frac{S}{b}=3,25\cdot 10^{10}\cdot \frac{S}{b} &\tau_1=\tau_5=0\\ &\tau_4=3,25\cdot 10^{10}\cdot \frac{4,44\cdot 10^{-5}}{0,1}=14,43\ MPa\\ &\tau_3=3,25\cdot 10^{10}\cdot \frac{4,44\cdot 10^{-5}}{0,02}=72,15\ MPa\\ &\tau_2=3,25\cdot 10^{10}\cdot \frac{4,59\cdot 10^{-5}}{0,02}=74,59\ MPa\\ \end{aligned}

Gráfico de tensiones normales y cortantes

Flexión

Resistencia de materiales - Flexión - Ejemplo 9

Ejemplo 9