Ejercicios propuestos - Capítulo IV

Centroides

1. xˉ=∫xdA∫dA=12∫01  my2/3dy∫01  my1/3dy=0.4  m\={x} = \frac{\displaystyle\int xdA}{\displaystyle\int dA} = \frac{\displaystyle\frac12\int_0^{1\;m} y^{2/3}dy}{\displaystyle\int_0^{1\;m} y^{1/3}dy} = 0.4\;m
yˉ=∫ydA∫dA=∫01  my4/3dy∫01  my1/3dy=0.57  m\={y} = \frac{\displaystyle\int ydA}{\displaystyle\int dA} = \frac{\displaystyle\int_0^{1\;m} y^{4/3}dy}{\displaystyle\int_0^{1\;m} y^{1/3}dy} = 0.57\;m

3. xˉ=19.28  cm\={x} = 19.28\;cm, yˉ=6.94  cm\={y} = 6.94\;cm

5. yˉ=237.5  mm\={y}= 237.5\;mm

Fuerzas distribuidas en vigas

7. RA=32  kNR_A = 32\;kN, MA=124  kN⋅mM_A = 124\;kN\cdot m

9. FR=∫04w(x)dx=∫042.5x3dx=160  NF_R= \displaystyle\int_0^4 w(x)dx = \displaystyle\int_0^4 2.5x^3 dx = 160\;N
xˉ=∫xw(x)dx∫w(x)dx=∫042.5x4dx160=3.2m\={x} = \frac{\displaystyle\int xw(x)dx}{\displaystyle\int w(x)dx} = \frac{\displaystyle\int_0^4 2.5x^4 dx}{160} = 3.2 m

Momentos de inercia

11. Iy=2.67  m4I_y = 2.67\;m^4

13. 20a420a^4