408
10 Dynamic Direct Stiffness Method
mp
2
E I
=
2.313
6.1
4
or
p =
2.313
6.1
4 8.28 × 10
7
95.8
1/2
= 133.67 rad/s.
10.5 Dynamic Stiffness Matrix for Flexure and Rigid Axial
Displacements
For the analysis of the framed structures which are of moderate height, it is the usual
practice to ignore the axial deformation. But certain members of the structure may
undergo axial displacement as a rigid body, such as in a one-bay portal, where the
frame undergoes sidesway movement involving the horizontal member to move as a
rigid body in that direction. There is no contribution to the stiffness matrix due to the
axial deformation of the member. As such, the element in the stiffness matrix due to
the rigid axial displacement is represented by the inertial effect associated with its
rigid body axial accelerations.
Referring to Fig. 10.7
N i = −m Lp
2 u i
(10.50)
Fig. 10.7 A beam segment