Page 187 - Dynamics of Mechanical Systems

0593_C06_fm Page 168 Monday, May 6, 2002 2:28 PM

168 Dynamics of Mechanical Systems

The forces F and F may be expressed in terms of n , n , and n by first expressing them
6
3
7
1
2
in terms of unit vectors µµ µµ and νν νν along the box diagonals as:
F = 26µµ and F = 20νν (6.3.9)
6 7
where µµ µµ and νν νν are directed along OQ and GQ, respectively. Then, µµ µµ and νν νν are:

µµ= OQ OQ = (3n + 12n + 4n ) 13 (6.3.10)
1 2 3

and

νν= GQ GQ = (3n + 4n ) 5 (6.3.11)
1 3
Hence, F and F are:
6
7
F = 6 n + 24 n + 8 n lb (6.3.12)
6 1 2 3

and

F = 12 n + 16 n lb (6.3.13)
7 1 3

These results may be tabulated as in Table 6.3.1.
The components of the resultant R are then obtained by adding the columns in Table
6.3.1. That is,

R = 3 n + 24 n + 24 n lb (6.3.14)
1 2 3

The moment of the system about O may be calculated using Eq. (6.3.2): using convenient
position vectors M becomes:
O
M = OO × F + OC × F + OB × F + F + OC × F
O 1 2 3 3 4
+ OB × F + OO × F + OG × F
5 6 7
0
=+ 3 n × − ( 10 n ) + 4 n × − ( 15 n ) + 3 n × − ( 8 n )
1 3 3 1 1 2
0
+ 4 n ×(8 n ) ++ 12 n ×(12 n + 16 n )
3 2 2 1 3
= 30 n = 60 n − 24 n − 32 n − 144n + 192n
2 2 3 1 1 3 1
or:

M = 160 n − 30 n − 168 n ftlb (6.3.15)
O 1 2 3