6.6a Selected Problem Answers

Question 1

$ILM_B=\frac{3}{8}x$ for $0 \leqslant x \leqslant \SI{5}{m}$
$ILM_B=5-\frac{5}{8}x$ for $\SI{5}{m} \leqslant x \leqslant \SI{8}{m}$
$A_y=\SI{178}{kN}\uparrow$

Question 2

$ILV_C=\frac{1}{2}-\frac{1}{6}x$ for $0 \leqslant x \leqslant \SI{6}{m}$
$ILV_C=\frac{3}{2}-\frac{1}{6}x$ for $\SI{6}{m} \leqslant x \leqslant \SI{12}{m}$
$M_{C,max}=\SI{219}{kNm}$

Question 3

$ILM_B=0$ for $0 \leqslant x \leqslant \SI{6}{m}$
$ILM_B=6-x$ for $\SI{6}{m} \leqslant x \leqslant \SI{11}{m}$
$M_{A,max}=\SI{2490}{kNm}$

Question 4

[ERROR: $ILC_y=0.167x$ for $0 \leqslant x \leqslant \SI{8.5}{m}$
$ILC_y=6.23-0.567x$ for $\SI{8.5}{m} \leqslant x \leqslant \SI{15}{m}$
$V_{D,max}=\SI{258}{kN}$]

Question 5

[ERROR: $ILV_C=-0.429-0.143x$ for $0 \leqslant x \leqslant \SI{6}{m}$
$ILV_C=0.571-0.143x$ for $\SI{6}{m} \leqslant x \leqslant \SI{10}{m}$]

Question 6

$ILM_D=-x$ for $0 \leqslant x \leqslant \SI{6}{m}$
$ILM_D=\frac{3}{2}x-15$ for $\SI{6}{m} \leqslant x \leqslant \SI{10}{m}$

Question 7

$ILM_A(\SI{4}{m})=-4.0$, $ILM_A(\SI{12}{m})=2.4$,
$ILV_B(\SI{4}{m}left)=0$, $ILV_B(\SI{4}{m}right)=1.0$, $ILV_B(\SI{12}{m})=-0.6$

Question 8

$ILM_B(\SI{4}{m})=1.333$, $ILM_B(\SI{8}{m})=-1.333$,
$ILV_B(\SI{4}{m}left)=-0.667$, $ILV_B(\SI{4}{m}right)=0.333$, $ILV_B(\SI{8}{m})=-0.333$

Question 9

$ILM_C(\SI{5}{m})=-4.0$, $ILM_C(\SI{9}{m})=0$,
$ILV_B(\SI{5}{m}left)=1.0$, $ILV_B(\SI{5}{m}right)=0$

Question 10

$ILM_B(\SI{8}{m})=2.18$, $ILM_B(\SI{11}{m})=0$,
$ILV_B(\SI{8}{m}left)=-0.727$, $ILV_B(\SI{8}{m}right)=0.273$, $ILV_B(\SI{11}{m})=0$

Question 11

$ILF_{AH}(\SI{5}{m})=-0.975$, $ILF_{AH}(\SI{10}{m})=-0.651$,
$ILF_{BC}(\SI{5}{m})=0.625$, $ILF_{BC}(\SI{10}{m})=0.417$

Question 12

[Error: $ILF_{FH}(\SI{4}{m})=-0.0452$, $ILF_{FH}(\SI{8}{m})=-0.864$,
$ILF_{BH}(\SI{4}{m})=-0.268$, $ILF_{BH}(\SI{8}{m})=-0.0459$
$F_{AF,max}=\SI{112}{kN}$]