Page 186 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Sec. 6.1 Flexibility Influence Coefficients 173

The complete flexibility matrix is now the sum of the three prior matrices:
( 1 1 1 ( \
/,
1 1 1 1 1

^= <
^2
1 1 1 1 1 1
k l ^2 ^ ^3 V ;

Note the symmetry of the matrix about the diagonal.
Example 6.1-2
Determine the flexibility matrix for the system shown in Fig. 6.1-2.

Figure 6.1-2.
and ^3 = k, and the flexibility matrix from
Example 6.1-1 becomes
0.5 0.5 0.5'
0.5 1.5 1.5
0.5 1.5 2.5
Example 6.1-3
Determine the flexibility influence coefficients for stations (1), (2), and (3) of the
uniform cantilever beam shown in Fig. 6.1-3.
Solution: The influence coefficients can be determined by placing unit loads at (1), (2), and
(3) as shown, and calculating the deflections at these points. By using the area

7 ni2 ^3
- o
(1) (2) (3)

<^I3 i^23 i^33

Figure 6.1-3.