G W Housner was instrumental in the widespread acceptance of the concept of earthquake response spectrum introduced by M A Biot in 1932.
Response spectrum concept
G W Housner was instrumental in the widespread acceptance of
the concept of earthquake response spectrum introduced by M A Biot in 1932.
This is a
practical way of characterizing the ground motions and their
effects with structure. It provides a convenient means of summarizing peak
response of all possible SDOF systems to a particular component of ground
motion. It also provides a practical approach to apply knowledge of dynamics to
design of structure and development of lateral force requirements in loads. We
have already seen that
In typical engineering structure the percentage of critical
damping is relatively small. It is approximately 2–8% for steel buildings and
5–10% for concrete structures.
One can plot deformation with
respect to natural period for the El Centro earthquake as shown in Fig. 17.12.
The pseudo-velocity and pseudo-acceleration are also plotted in Fig. 17.13a.
Pseudo-velocity
spectrum
Consider spectral velocity related to deformation as
V =
velocity = ω_{n}D Let peak
deformation
D ≡ u_{0} 17.19b
Then elastic force is obtained from the strain energy or kinetic energy of
the mass.
The right-hand side is the
kinetic energy of mass with velocity V and is called peak
pseudo-velocity.
A pseudo-spectral velocity response spectrum is a plot of V
in terms of natural period T_{n}.
S_{pv} = ωS_{d --- --- }17.20