written 6.8 years ago by | • modified 6.6 years ago |
$\sum M_A=0\ (\circlearrowright +ve)$
$-V_D\times5+(\frac{1}{2}\times6\times5)(\frac{2}{3}\times6)+10\times1.5$
$+(2\times2)(3+1)+(\frac{1}{2}\times2\times2)\times(3+\frac{2}{3}\times2)=0$
$\boxed{V_D=19.934\ kN}\ (\uparrow)$
$\sum F_Y=0(\uparrow+ve)$
$V_A+19.934-10-(2\times2)-\frac{1}{2}\times2\times2=0$
$\boxed{V_A=-3.934\ kN}\ (\downarrow)$
$\sum F_X=0(\rightarrow+ve)$
$-H_A+\frac{1}{2}\times6\times5=0$
$\boxed{H_A=15\ kN}\ (\leftarrow)$
1. Consider part AB:
$BM_A=0\\BM_B=15\times6-\frac{1}{2}\times6\times5\times\frac{1}{3}\times6\\ BM_B=\underline{60\ kNm} $
2. Consider part BC:
$\textbf{1. Shear force calculation: }(\uparrow|\downarrow+ve)$
$SF_{BL}=0$
$SF_{BR}=-3.434\ kN$
$SF_{EL}=-3.434\ kN$
$SF_{ER}=-3.934-10=13.934\ kN$
$SF_F=13.934\ kN$
$SF_C=-19.934\ kN$
$\textbf{2. Bending moment calculation: }(\circlearrowright|\circlearrowleft+ve)$
$BM_{B}=\underline{60\ kNm}\ \text{\{obtained already\}}$
$BM_{E}\ \text{\{considering part EBA\}}$
$=15\times6-\frac{1}{2}\times5\times6\times\frac{1}{3}\times6-3.934\times1.5$
$\phantom{BM_{E}\ \text{\{considering part EBA\}}}=\underline{54.01\ kNm}$
$BM_F\ \text{\{considering part FEBA\}}$
$=15\times6-3.934\times3-\frac{1}{2}\times5\times6\times\frac{1}{3}\times6-10\times1.5$
$\phantom{BM_{E}\ \text{\{considering part FEBA\}}}=\underline{33.198\ kNm}$
$BM_{F}\ \text{\{considering part CD\}}=0$
$\therefore \text{part CD does not bend at all.}$
$\underline{BM_C=0}$
3. Consider part CD: