Page 68 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

1.7 sprinG elements 65
equivalent k of a Crane
example 1.8
The boom AB of the crane shown in Fig. 1.32(a) is a uniform steel bar of length 10 m and area of
2
cross section 2500 mm . A weight W is suspended while the crane is stationary. The cable CDEBF
2
is made of steel and has a cross-sectional area of 100 mm . Neglecting the effect of the cable CDEB,
find the equivalent spring constant of the system in the vertical direction.
Solution: The equivalent spring constant can be found using the equivalence of potential energies
of the two systems. Since the base of the crane is rigid, the cable and the boom can be considered to
be fixed at points F and A, respectively. Also, the effect of the cable CDEB is negligible; hence the
weight W can be assumed to act through point B as shown in Fig. 1.32(b).

C B

D E

10 m W

1.5 m 45
1.5 m
F A

(a)

B
90 u
x
45
k eq
, k
l 1 1 W
l 10 m, k 2
2
W
45
F u A
3 m
(b) (c)

FiGure 1.32 Crane lifting a load.