For a system with longer period Sd with approach to ug0, Spa is very small.

**Response spectrum characteristics**

Let *u***˙˙**_{g}_{0} , *u***˙** _{g}_{0} , *u _{g}*

We identify the effects of
damping on systems with short period *T _{n}* <

For a system with longer period *S _{d}* with
approach to

For short period system *T _{n}T_{a}*
<

For a long period *T _{d}*
<

Based on the observation of
response spectrum, it is logical to divide the spectrum into three ranges:

• **Long
period range ***T _{n}*

• **Short
period range ***T _{n}*

• **Intermediate
range ***T _{c}*

The periods *T _{a}*,

Idealizing a spectrum by a series
of straight lines *a*, *b*, *c*, *d*, *e*, *f* in
the four-way logarithmic plot is obviously not a precise process. The period
values at *a*–*f *and amplification factors are judgemental. The
advantages of an idealized* *spectrum are that we can very easily
construct a design spectrum. These values vary from one ground motion with
others.

Example 17.7

Consider an elastic design
spectrum, 84.1% for ground motion *u***˙˙**_{g}_{0}
= 1 *g* ; *u***˙**_{g}_{0} = 121.92 cm/s; *u _{g}*

Solution

From Fig. 17.23, we can construct
a pseudo-acceleration spectrum in terms of *g* plotted in log scale in
Fig. 17.24 for ground acceleration of 1*g* and damping factor 5%.
Similarly for various values of *ρ* an elastic pseudo-acceleration spectrum can be plotted in log
scale as shown in Fig. 17.25 and a design spectrum in Fig. 17.26. If
pseudo-acceleration is plotted at a normal scale, the diagram is as shown in
Fig. 17.26.

Example 17.8

Estimate the maximum sensitive response for the industrial
building of Example 17.1 using Newmark–Hall design spectra for an anticipated
ground acceleration

of 0.308*g* and for a
damping factor of 0.05. Compare the results with the maximum response obtained
from time history analysis.

Solution

Damping = 5%

(i) NS
direction, *T* = 0.567 s

From chart (see Fig. 17.23), spectra value *S _{d}*
= 6.35 cm;

Maximum
base shear = *mS _{pa}*

= 131 697.2
× 7.843

1032.9 kN

(ii)
EW direction *S _{d} *= 20 mm

*S _{pv} *= 393.7 mm/s

*T *= 0.313* *

Maximum base shear = *mS _{pa}*

= 1032.9 kN

Comparison of the maximum
response obtained from time history analysis response spectra and design
spectrum analysis is presented in Table 17.4 for NS direction. There is a
considerable discrepancy between the results of response spectrum and design
spectrum. The former represents the response to a specific earthquake while the
latter represents predicted response to any earthquake.

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Civil : Structural dynamics of earthquake engineering : Response spectrum characteristics |

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