Dynamic Responses - Mechanics of Structures: Variational and Computational Methods - page 641

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Problems

Structural Matrices
10.1 Find the element stiffness and consistent mass matrices and the global stiffness and
mass matrices for the frame of Fig. P10.1.

FIGURE P10.1
L-shaped frame.

Answer: The global stiffness and mass matrices, after invoking the boundary
conditions, are

[ U Xb U Zb U Xc U Zc

c ] b

. −

1216 8 0 60 12 0 60

. − − .

0 1216 8 60 0 1204 80

60 − 60 800 − 60 0 200

=

K 830

− 12 0 − 60 12 0 − 60

0 − 1204 . 8 0 0 1204 . 8 0

60 0 200 − 60 0 800

296 0 220 54 0 − 130

0 296 220 0 70 0

= ρ
420

220 220 800 130 0 − 300

M

54 0 130 156 0 − 220

0 70 0 0 140 0

− 130 0 − 300 − 220 0 400