Page 354 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 10 Problems 341

10-21 Determine the deflection and slope at the load for the frames of Fig. PlO-21.
Consider the corners to be rigid.

(b)

( d )

10-22 The pinned-free beam of Prob. 10-17 is restrained by a spring of torsional stiffness K
lb • in./rad at the pin, as shown in Fig. PlO-22. Choose the numerical value of K so
that under its static weight, the beam rotates 1/10 rad, and make the calculations as
in Prob. 10-18. (Use one and two elements and let 5mgP/EI = 1.0.)

t
El Figure PlO-22.
10-23 Figure PlO-23 shows a pin-ended beam with a linear spring k at midspan and a
torsional spring K at the right end. Determine the stiffness matrix for a two-element
analysis.

i / z l/Z
Figure PlO-23.

10-24 Determine the mass matrix for the beam of Prob. 10-23 and find all its natural
frequencies and mode shapes when
kP _ \ ^ _ I 2
El ~ 2 El ~ 4^
Check the solution of Prob. 10-23 by letting k = K = 0. The eigenvalues should agree
with those of a pinned-pinned beam.