Page 196 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Sec. 6.5 Static Condensation for Pinned Joints 183

In like manner, the third column of the stiffness matrix is found from the
configuration of Fig. 6.4-4(c) (see Fig. 6.4-7).

E l
0 0 6^
M, = 0 0 2-^
M, 0 0 8^ 1
V /

By superpositioning the preceding three configurations, the stiffness matrix for the
square frame with fixed legs is
/ ^ i \
" 24 6 6 "
/2 / / ^'1
El 6
A/, <
T * -
M 2 0.
V ) \ /

6.5 STATIC CONDENSATION FOR PINNED JOINTS
For pinned joints where the moment is zero, the size of the stiffness matrix can be
reduced by a procedure called static condensation.^ The procedure can also be
used in discrete mass systems where the mass moment of inertia is small enough to
be ignored. We here illustrate the procedure by applying it to previous Example
6.4-1 of the square frame when the fixed support of the lower right leg is replaced
by a pinned support.
Example 6.5-1
Determine the stiffness matrix of the square frame shown in Fig. 6.5-1, where the
lower right support is pinned.

(1) (2)

Figure 6.5-1

,. Meirovitch, Computational Methods in Structural Dynamics (Rockville, MD: Sidthoff &
Noordhoff, 1990), p. 369.