3.12 Response to SDF Systems to a General Type of Forcing Function
97
x =
F 0
k
[ cos p (t − t d ) − cos pt ]
3.13 Dynamic Load Factor and Response Spectrum
The dynamic load factor (DLF) is defined as the ratio of dynamic displacement at any
instant of time to the static displacement. It is non-dimensional and independent of
the magnitude of the load. In many structural problems, maximum value of dynamic
load factor is of importance.
For the Example 3.12, the dynamic load factor is given by
DLF = 1 − cos pt = 1 − cos 2π
t
T
for t ≤ t d
DLF = cos p (t − t d ) − cos pt
= cos 2π
t
T
−
t d
T
− cos 2π
t
T
for t > t d
(3.94)
where T is the time period.
For the rectangular pulse, two responses corresponding to
t d
T
=
1
10
and
t d
T
=
5
4
are
shown in Fig. 3.25. It can be seen that the response increases with the increase of
t d /T . Maximum response for varying t d /T has been plotted for a rectangular pulse in
Fig. 3.26. The ratio of the duration of the pulse to the natural period is the important
parameter. So, to read the maximum response for a given load function, one needs to
know the natural period of the system. However, the chart does not include damping.
Maximum dynamic load factor usually corresponds to the first peak response, where
the damping existing in structures does not decrease it appreciably. As such, damping
in the system will not have any significant effect.
Fig. 3.25 Time variation of DLF for a rectangular pulse