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0593_C06_fm Page 169 Monday, May 6, 2002 2:28 PM

Forces and Force Systems 169

TABLE 6.3.1
A Component Listing of the Forces of Figure 6.3.6
F (lb)
F i n 1 n 2 n 3
i
10 0 0 10
F 1
10 0 0 –10
F 2
15 –15 0 0
F 3
8 0 –8 0
F 4
8 0 8 0
F 5
26 6 24 8
F 6
20 12 0 16
F 7
Similarly, this moment about Q is:
M = QO × F + QA × F + QB × F + QH × F
Q 1 2 3 4
+ QQ × F + QD × F + QD × F
5 6 7
n )
=− ( 4 n − 12 n ) ×(10 n ) +− ( 12 n + 3 n ) ×− ( 10
3 2 3 2 1 3
+− ( 12 n ) ×− ( 15 n ) +(3 n − 4 n ) ×− ( 8 n )
2 1 1 3 2
×
+ O + 3 n × 6 ( n + 24 n + 8n 3) + 3n 1 ( 12n + 16n 3)
1 1 2 2 3
=− 120n + 120n + 30n − 180n − 24n − 32n
1 1 2 3 3 1
+ 72n − 24n − 48n
3 2 2

or

M =−32 n − 42 n − 132 n ftlb (6.3.16)
Q 1 2 3

According to Eq. (6.3.6), M and M are related by the expression:
O
Q
×
M = M + OQ R (6.3.17)
O Q
By substituting from Eqs. (6.3.14), (6.3.15), and (6.3.16), we can check the validity of
Eq. (6.3.17):

160n − 30n − 168n = − 32n − 42n − 132n
?
1 2 3 1 2 3
+( 12n + 4n ) ×( 3n + 24n + 24n )
2 3 1 2 3
=− 32n − 42n − 132n − 36n + 288n + 12n − 96n
1 2 3 3 1 2 1
= 160n − 30n − 168n
1 2 3
Equation (6.3.17) is thus verified.