Advanced Methods of Structural Analysis

Problems 547

14.4.Symmetrical statically indeterminate frame carried one lumped mass. Deter-
mine the frequency of free horizontal and vertical vibrations.

EI 2

EI 1

M

h

l/ 2

Fig. P14.4

Ans.!horD

s

12 EI 2

h^3 M.2ˇCk/

;ˇD

I 2

I 1

;kD

l

h

I !vertD

s

48 EI 2

l^3 M



12kC8ˇ

3kC8ˇ

14.5.Calculate the frequency of free vertical vibration of symmetrical truss pre-
sented in Fig.P14.5. Axial rigidity for diagonals and vertical elementsEA,forlower
and top chords is 2EA. A lumped massMis placed at joint 6.

h=3

1

d=4m

3795

(^2468)
2 EA
2 EA
EA
M^10
Fig. P14.5
Ans.!D
s
1
mı 11
D
r
EA
24:555M

s^1

:
14.6.A massless beam carried two lumped mass (Fig.P14.6). Calculate the fre-
quency of free vibration, find the modal matrix and show the shapes of vibrations.
M
EI
2 M
aaa
Fig. P14.6
Ans.! 1 D0:8909
r
EI
a^3 M
,! 2 D3:6887
r
EI
a^3 M
,ˆD

11
1:04830:4769