PSG-Civil 22.03.2014 02

Indian Institute of Technology Delhi (IIT)
New Delhi, INDIA
Prepared for:
[COMPANY NAME]
Prof. T. K. Datta
Department of Civil Engineering,
Indian Institute of Technology
Delhi
Saturday, 22nd
, March 2014
IIT DelhiIIT Delhi
1

IIT DelhiIIT Delhi Structural Dynamics for Practicing Civil Engineers
2
o Eart hquakes
o Wind
o Wave
o Land Slides/ Avalanches
o Caving in of Eart h
o Volcanic Erupt ions
Nat ure Sources of Dynamic Loads
o Blast / Terrorist at t ack
o Collisions
o Vehicular Movement / rack
Train Dynamics
o Machines/ I mpact /
Accident s
Man made Sources
o Eart hquakes
o Land Slides/ Avalanches
o Caving in of Eart h
o Blast of longer durat ions
Short Durat ion
(T< 1 mt s)
o Oceanic Waves
o Cyclones
o Machine Vibrat ions
o Vehicular Movement s
o Volcanic Erupt ions
Long Durat ion
(T > 5 min - 10 min)
o Missile I mpact
o Falling mass/ Collision
o Sudden blast of short durat ion
I mpact t ype
(T<1 sec)
Classifying different
dynamic loads
Classifying different
dynamic loads We shall focus us
on earthquake,
blast and wind
loads

3
Idealization of
Loads
Amplit ude
Phase
T
y = a sin (ωt +
φ)
Harmo
nic
Period
ic

4
Irregul
ar
Rando
m
T T T T
Impa
ct
Idealization of
Loads

5
II
Fourier Synthesis of
Dynamic Loads
∑
∑∑
∞
=
∞
=
∞
=
φ+ω=
ω+ω+=
0
11
0
)cos(
sincos
2
)(
n
nnn
n
nn
n
nn
tA
tbta
a
tf
dtttf
T
a
T
T
nn ∫−
ω=
2
2
cos)(
2
dtttf
T
b
T
T
nn ∫−
ω=
2
2
sin)(
2 22
nnn baA +=






=φ −
n
n
n
a
b1
tan
where

6
Raw and Smoothed FAS

7
EarthquakeEarthquake
ss

8
Ground Motion Records-
Acceleration time history
Recorded at
discrete
intervals

9
ω(t )
u(t )
v(t )
vertical
W
ave propagat ion
maj or principal
direct ion
v(t ) , ω(t ) = n u (t )
nis gener ally < 1
Ground Motion- Propagation

10
Ground Motion Records-
Acceleration, Velocity and
Displacement time history

11
Response Spectrum- El Centro 1940
Earthquake
Displacement Response
Spect rum
Velocit y Response Spect rum
Accelerat ion Response
Spect rum

12
Combined D- V –A Response spectrum for EI Centro Ground motion

13
Construction of elastic design
spectrum
Const ruct ion of elast ic design
spect rum f or ground mot ions wit h
ugo = 1g, ugo = 48 in./ sec. and ugo =
36 in.; ζ=5%

14
Salient
Points
No correlat ion bet ween principal direct ions
Plot of [ ] Vs T is called energy
spect rum.
Fourier spect rum is a measure of t ot al energy of
SDOF at t he end of t ime t .
Energy spect rum is generally great er t han
Fourier amplit ude spect rum.
)(2
1)(2
1)( 22
tkxtxmtE += 
( )max
)(2 mtE

15
Shape of the Kanai – Tajimi
power spectral density
function
)(ωG
Gω
ω

16
0.0
0 10 20 30 40 50 60 70 80
0.04
0.12
0.24
0.36
0.28
0.32
0.08
0.16
0.20
Spect rum
(5)ω (5)=24.6
Spect rum
(4)ω (4)=12.85
Spect rum
(3)ω (3)=9.30
Spect rum
(2)ω (2)=5.61
Spect rum (1)
ω (1)=2.87
Frequency ω (rad/Sec)
Spectrum ωg
1 π 0.3
2 2π 0.4
3 3.5π 0.5
4 5π 0.6
5 10π 0.8
For all spectra ωf = 0.1ωg &
f= g
guNormalised Spectra of Ground
Acceleration

17
BlastBlast

18
BED ROCKBED ROCK
Force = Pressure ×
Influence area
St ruct ural
Members
Blast
Pressure
Wave
Blast
Pressure
Wave, Pa
Ground
Mot ion
Pg
Pa> Pg
How do air pressure and
ground motion induce forces in
the building?
The result ant f orce will be
lumped at t he j oint , if only
columns are considered in
t he analysis
P = Equivalent lat eral Load (St at ic)
Obt ained From Response spect rum f or ground
accelerat ion.
Mass × PGA (amplif ied) is t he f orce at each
f loor level.

0
19
How do air pressure and
ground motion induce forces in
the building?
p0
p0
p0
4(td/T
n)π(td/Tn)
2
1
0
1 2 3 4
t d
t d
t d
( )0
0
st
d
u
u
R =
2π(td/Tn)

20
WindWind

21
Fluct uat ing component of t he wind is assumed as
a st at ionary random process.
For predict ive/ analysis purposes, it is
represent ed by a spect rum and a co-spect rum of
wind velocit y.
Spect rum denot es t he dist ribut ion of energy of
t he wind velocit y wit h f requency.
Co-spect rum denot es t he degree of co-relat ion
bet ween t he wind velocit ies at t wo point s.
I n a similar way, eart hquake when modeled as a
st at ionary random process, is described by
spect rum and co-spect rum.
Salient
Points

22
Sampled and averaged at some int erval
Δt
; ;
U(t ) is in along wind direct ion ; v(t ) and
w(t )
)()( tuUtU += )(tv )(tω
Gust iness (f luct uat ing
part ) Mean
Velocit yU
)(tU t
Wind Record

23
Terrain roughness is t he key paramet er.
α, u*, Z0, Zd are some import ant paramet ers f or
det ermining mean wind velocit y and gust iness at
any height .
St andard Measurement
10 m
Hg
Vg
U10
Mean wind variat ion wit h
height
( ) ( )Zu
Z
Z
Zu 2
2
1
1
α






=
Wind Measurement

24
Longitudinal turbulence
spectra

25
Simulat ion of art if icial t ime hist ories of
eart hquake/ wind velocit y is quit e of t en done.
From spect rum and co-spect rum, t ime hist ories
are simulat ed.
Basis of simulat ion f rom spect rum is again t he
concept of Fourier series expansion.
Simulat ion of eart hquake f rom response
spect rum is also possible.
The basis is an it erat ive process involving
Fourier t ransf orm t o improve an init ially
generat ed Gaussion t ime hist ory.
Salient
Points

26
Si
ωdiω ω
( )ωS
2
Area σ=
ω= dSA ii 2 )sin()( ii tAtx φ+ωΣ=

27
τd
τ
dt
t
)(tp
τd
)(τp
t
τ−t
ττ= dpxm )(
m
dp
x
ττ
=
)(


28
Thank YouThank You

29
F1= T
a1
+
+
a2

PSG-Civil 22.03.2014 02

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