Introductory notes

1. 1
CE 412: Introduction to Structural Dynamics and
Earthquake Engineering
MODULE 1

2. Static Vs Dynamic Force
Examples of dynamic forces are: forces
caused by rotating machines, wind forces,
impulsive forces, seismic forces, suddenly
applied gravity loads e.t.c.
A dynamic force is one which produces nonuniform velocity (non zero
acceleration) in the acting body i.e dv/dt ≠ 0. where v = velocity of the
body
A dynamic force always varies with time
2
v
t
dv/dt (slope of v-t diagram) ≠0

3. Static Vs Dynamic Force
A static force is one which produces no acceleration in the acting body.
A static force may or may not vary with time
A force, even if it varies with time, is still static if its variation with the
time is too low to produce significant acceleration in the acting body. e.g.,
slowly applied load on a specimen tested in a UTM .
3
A static force can be considered as
special case of dynamic force in which
dv/dt =0
v
t
dv/dt = 0
dv/dt = 0

4. Why inertial force in the beam is maximum at
the point of application of dynamic force, p(t) ?
Static Vs Dynamic Force

5. 5
Why we need dynamic analysis ?
Concepts discussed in courses that were studied till now are based on the
assumption that the loads are either already present or applied very slowly on
the structure/system.
The above mentioned assumption work well as long no/ insignificant
acceleration is produced in structure/system due to external loads.
In case of structures/ systems subjected to dynamics loads (rotating
machines, winds, suddenly applied gravity load, blasts, earthquakes…..) the
afore mentioned assumption may lead to non-conservative results.
This course is designed to provide fundamental knowledge regarding the
response of the structures/systems subjected to dynamic loading

6. Causes of Dynamic Loading
Impact
6
Machine vibration
Blast

7. Causes of Dynamic Loading
Wind
Ground motion
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Does earthquake always govern design of structures ?

8. 8
Which type of force is produced by truck on bridge (structure)?, when Truck is:
1) Standing (engine off) on bridge
2) Standing (engine on) on bridge
3) Moving on the bridge with a constant velocity assuming perfectly smooth road
4) Moving on the bridge with a constant velocity assuming rough road
5) Moving on the bridge with a variable velocity assuming perfectly smooth road
6) Moving on the bridge (condition 3) with a speed breaker some where in the
bridge
Question. 1.1

9. Classification of dynamic loads
Dynamic loads may be classified as ‘deterministic’ and ‘non-deterministic’.
If the magnitude, point of application of the load and the variation of the
load with respect to time are known, the loading is said to be deterministic
and the analysis of a system to such loads is defined as deterministic analysis.
On the other hand, if the variation of load with respect to time is not
known, the loading is referred to as random or stochastic loading and the
corresponding analysis is termed as non-deterministic analysis.

10. Periodic loads

11. Non-Periodic loads

12. Effect of dynamic forces on structural
response
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13. A common type of dynamic forces is a harmonic force due to unbalance
in a rotating machines (such as turbines, electric motors and electric
generators, rotating shafts, etc).
When the wheels of a car are not balanced, harmonic forces are
developed in the rotating wheels. If the rotational speed of the wheels is
close to the natural frequency of the car’s suspension system in vertical
direction , amplitude of vertical displacement in the car’s suspension system
increases many fold and violent shaking occur in car.
Dynamic forces exerted by rotating machines
(Harmonic loading)
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14. 14
Random dynamic forces, Blast (Impulsive) loading
Variation of blast loading w.r.t time and its effect
1
1
2
1
3
1
4
1
5
1
1
1
2
1
3
1
4
1
5
1

15. 15
Random dynamic forces, Earthquake loading
ag
t
Ground acceleration (ag) variation during earthquake (EQ). ag can
easily be converted to EQ force acting on a SDOF structure ?

16. Earthquakes cause ground shaking. Ground shaking induces inertial loads
in building elements. stronger ground shaking or heavier building elements
result in greater loads
Force exerted by
truck’s engine
Inertia force , FI , in the model building are
produced in leftward direction when the
truck move in the right ward direction
with certain acceleration.
Resultant FI act at the roof level if the
greater portion of mass is lumped there.
Model will overturn , if the destabilizing
moment due to FI at the bottom of model
exceeds stabilizing moment due to
resultant weight of model
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Random dynamic forces, earthquake loading
FI
a≠0

17. Random dynamic forces, Earthquake loading
17
Flow of seismic inertia forces through all structural
components.
Effect of Inertia in a building when shaken at
its base

18. What happens during an earthquake?
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During an earthquake, seismic waves arise from sudden movements in
a rupture zone (active fault) in the earth's crust.
Waves of different types and velocities travel different paths
before reaching a building’s site.
What does the blue curves indicate?

19. 19
What happens during an earthquake?

20. 20
Various types of waves
What happens during an earthquake?

21. What happens to the structures?
Inertia force and relative motion within a building
The upper part of the structure
however ‘would prefer’ to remain
where it is because of its mass of
inertia.
If the ground moves rapidly back and forth, then the foundations of the
structures are forced to follow these movements due to the friction at the base.
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Resultant Inertia force
Foundation movement

22. The structural response during an earthquake mainly depends:
1. Natural time period
2. Configuration, material, structural system, age, or quality of construction.
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What happens to the structures?

23. 23
Variation of horizontal acceleration at various story levels in San Francisco’s
Transamerica Pyramid during to 1989 Loma Prieta Equake
Consider building shown in video
1. Why floor acceleration increases
along the height?
2. Will structure fail at story with
maximum inertial force (top
floor) or ground story?
Amplification of accelerations along height of a
structure

24. In comparison with rock, softer soils are particularly prone to
substantial local amplification of the seismic waves.
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Note the amplification of
ground displacement with
decrease in soil stiffness
Influence of local soil conditions on structures

25. 25
The 1.6 mile ling cypress freeway structure in Oakland, USA, was built in the
1950s. Part of the structure standing on soft mud (dashed red line) collapsed in
the 1989 magnitude 6.9 Loma Prieta earthquake.
Influence of local soil conditions on structures
Adjacent parts of the structure
(solid red) that were built on firmer
ground remained standing.
Seismograms (upper right) show that
the shaking was especially severe in
the soft mud.

26. 26
A portion of the Cypress Freeway (located along dashed redline, previous
slide) after the 1989 Loma Prieta earthquake
Influence of local soil conditions on
structures

27. The Mexico City earthquake (MS = 8.1) occurred in 1985.
The interesting phenomenon about this earthquake, which generated
worldwide interest, is that it caused only moderate damage in the vicinity of
its epicenter (near the Pacific coast) but resulted in extensive damage further
afield, some 350–360 km from the epicenter, in Mexico City.
The Mexico 1985 Earthquake: Effects of
Local Site Conditions on Ground Motion
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28. For the seismic studies that ensued, the city
has often been subdivided into three zones
 The Foothill Zone is characterized by
deposits of granular soil and volcanic fall-off.
 In the Lake Zone there are thick deposits
of very soft soil formed over the years.
 Between the Foothill Zone and Lake Zone is
the Transition Zone where the soft soil
deposits do not extend to great depths.
The Mexico 1985 Earthquake: Effects of
Local Site Conditions on Ground Motion
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Geologic zones of Mexico city
Section a-a
FOOTHILL
ZONE
FOOTHILL ZONE
TRANSITION ZONE
LAKE ZONE

29. 29
The Mexico 1985 Earthquake: Effects of Local Site
Conditions on Ground Motion
(Stiff soil)
(Soft soil)

30. The UNAM site was on basaltic (Oceanic) rock. The SCT site was on
soft soil.
The time histories recorded at the two sites are shown in figure
The Mexico 1985 Earthquake: Effects of Local Site
Conditions on Ground Motion
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31. 0.12/0.03= 4 times
amplification in
ground accelerations
10 times amplification of
structural acceleration in
buildings with natural time
period of around 2 second
The Mexico 1985 Earthquake: Resonance
phenomena
The computations of response spectra
at the two sites from the time histories
are shown in figure
The response spectrum is a reflection of
the frequency content and the
predominant period is around 2 seconds.

33. The dynamic response of structural systems, facilities and soil is very
sensitive to the frequency content of the ground motions.
The frequency content describes how the amplitude of a ground motion
is distributed among different frequencies.
The frequency content strongly influences the effects of the motion. Thus,
the characterization of the ground motion cannot be complete without
considering its frequency content.
Using Fourier transformation (mathematical technique) we can find the
frequency content of seismic waves by shifting from time domain to
frequency domain
Frequency content parameter
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34. The plot of Fourier amplitude versus frequency is known as a
Fourier amplitude spectrum
Frequency content parameter
Fourier amplitude spectrum of a
strong ground motion expresses
the frequency content of a motion
very clearly.
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35. Frequency content parameter
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Ground motions can be expressed as a
sum of harmonic (sinusoidal) waves
with different frequencies and arrivals.
The Fourier amplitude spectrum (FAS)
is capable of displaying these
frequencies (i.e. the frequency content
of the ground motion).

36. Relation between Magnitude of earthquake
& acceleration of seismic waves
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37. Earthquake Magnitude Scales
Several magnitude scales are widely used and each is based on measuring
of a specific type of seismic wave, in a specified frequency range, with a
certain instrument.
The scales commonly used in western countries, in chronological order
of development, are:
1. local (or Richter) magnitude (ML),
2. surface-wave magnitude (Ms),
3. body-wave magnitude (mb for short period, mB for long period), and
4. moment magnitude (Mw or M)
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38. Attenuation Relationships
Strong-motion attenuation equations are empirical equations that can be used to
estimate the values of strong-motion parameters (PGA, PGV, PGD, duration of EQ,
intensity, Peak spectral acceleration, etc.) as functions of independent parameters (like
magnitude, distance from the fault to the site, local geology of the site, etc.) that
characterise the earthquake and the site of interest.
Y = f(M, R, site)
Y = ground motion parameter
M = magnitude
R = is a measure of distance
from the fault to the site ( to take into account the path effect
Site = local site conditions near the ground surface like soft, stiff, hard soil
Attenuation relationships developed for a particular region cannot be used for other
regions unless they have similar seismo-tectonic environment.
Ground Motion Evaluation
Source + Path + Site
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39. Ground Motion Prediction Equations (GMPE’s)
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“Attenuation Equations” is a poor term. We should call them “Ground-
Motion Prediction Equations”. They describe the CHANGE of amplitude
with distance for a given magnitude (usually, but not necessarily, a
DECREASE of amplitude with increasing distance).
Following is short description attenuation relationships. Here emphasis is
given on spectral acceleration attenuation relationships based on world-
wide data base in active shallow tectonic regions with a broad range of
applicability.

40. Ground Motion Prediction Equations (GMPE’s)
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Cornell et al. (1979)
Ground motion model is:
ln(PGA) = a + b M + c ln(R + 25)
where, PGA is in cm/s2 (gals), a = 6.74, b = 0.859, c = −1.80 and σ = 0.57.
ln(PHA)(gals)=6.74 + 0.859M-1.8ln(R+25)
Developed for Western US. No more than 7 records from one earthquake to
avoid biasing results.
Records from basements of buildings or free-field.

41. Ground Motion Prediction Equations (GMPE’s)
Example: A building is to be constructed at 25 km distance away from a
fault which can generate an earthquake of magnitude 7.7. Using Cornell
equation ,determine the PHA that the building would experience.
ln(PHA)= 6.74 + 0.859 x 7.7 – 1.8 ln(25+25)
Ln(PHA) = 6.312
PHA=exp(6.312)
PHA=551 gal
PHA = 551/981=0.57g
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