MODULE_1.pdf

University of Engineering and Technology
Peshawar, Pakistan
CE-412: Introduction to Structural Dynamics and
Earthquake Engineering
MODULE 1:
FUNDAMENTAL CONCEPTS RELATED TO DYNAMIC
ANALSYSIS & EARTHQUAKE ENGINEERING
Prof. Dr. Akhtar Naeem Khan & Prof. Dr. Mohammad Javed
drakhtarnaeem@nwfpuet.edu.pk mjaved@nwfpuet.edu.pk
1

CE-412: MODULE 1 ( Fall 2015)
Why to carry out dynamic analysis ?
2

CE-412: MODULE 1 ( Fall 2015) 3
Importance of dynamic analysis
Concepts discussed in courses related to structural engineering that
you have studied till now is based on the basic assumption that the
either the load (mainly gravity) is either already present or applied very
slowly on the structures.
This assumption work well most of the time as long no acceleration
is produced due to applied forces. However, in case of structures/
systems subjected to dynamics loads due to rotating machines, winds,
suddenly applied gravity load, blasts, earthquakes, using the afore
mentioned assumption provide misleading results and may result in
structures/ systems with poor performance that can sometime fail.
This course is designed to provide you fundamental knowledge about
how the dynamic forces influences the structural/systems response

Sources of Dynamic Excitation
Impact? (Slide12)
4
Machine vibration
(always negative effect?
Blast ?(11)

Sources of Dynamic Excitation
Wind
Ground motion
5
Difference in transfer of external force in wind and earthquake ? (16)
Is earthquake always govern design of structure or wind is also in some cases??

Static Vs Dynamic Force
v
t
dv/dt≠0
Examples of dynamic
forces are: forces caused by
rotating machines, wind
forces, seismic forces,
suddenly applied gravity
loads e.t.c.
A dynamic force is one which produces acceleration in a body.
i.e dv/dt ≠ 0. where v = velocity of body subjected to force
A dynamic force always varies with time
6

v
t
dv/dt = 0
A static force is one which produces no acceleration in the acting
body.
A static force usually does not vary with time
A force, even if it varies with time, is still considered static
provided the variation with time is so slow that no acceleration is
produced in the acting body. e.g.,
7
slowly applied load on a
specimen tested in a UTM .
A static force can be
considered as special case of
dynamic force in which dv/dt =0

CE-412: MODULE 1 ( Fall 2015) 8
What will be the effect of truck (load) on bridge and response of 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 (perfectly smooth road)
4) Moving on the bridge with a constant velocity (rough road )
5) Moving on the bridge with a variable velocity (rough road )
6) Moving on the bridge (condition 3) with a speed breaker in the middle of the
bridge
7) A truck with a capacity of 100 tonnes crosses the bridges half a million times while
carrying a load which is 60% of its capacity
H.A. M 1.1

Implications of dynamic forces
9

A common source of dynamic forces is harmonic forces due to
unbalance in a rotating machines (such as turbines, electric motors and
electric generators, as well as fans, or rotating shafts).
Unbalance cloth in a rotating drum of a washing machine is also an
harmonic force.
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 and violent shaking occur in car.
A Single degree of freedom system?(SDOF) respond harmonically till
motion cease after the removal of force (irrespective of the type of
dynamic load).
Dynamic forces exerted by rotating machines
(Harmonic loading)
10

CE-412: MODULE 1 ( Fall 2015) 11
Random dynamic forces, Blast 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

CE-412: MODULE 1 ( Fall 2015) 12
Random dynamic forces, impulsive loading
Typical force–time curve for an impulsive force

CE-412: MODULE 1 ( Fall 2015) 13
H. Assignment M1.2
Estimate the average impact force between an airliner traveling at
600 mi/hr and a 1 pound duck whose length is 1 foot.
Random dynamic forces, impulsive loading
Problem hint

CE-412: MODULE 1 ( Fall 2015) 14
Random dynamic forces, earthquake loading
ag
t
Ground acceleration (ag) during earthquake (EQ) vs time. ag can
easily be converted to EQ force acting on a SDOF structure ?

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, on model
building assuming that most
model’s weight is located at
roof level. Depending upon
magnitude of FI, building can
overturn in the direction of FI
15
Random dynamic forces, earthquake loading
FI

Random dynamic forces, wind loading
 Dynamic actions are caused on buildings by both wind and
earthquakes. But, design for wind forces and for earthquake
effects are distinctly different.
 The intuitive philosophy of structural design uses force as the
basis, which is consistent in wind design, wherein the building
is subjected to a pressure on its exposed surface area; this is
force-type loading.
 However, in earthquake design, the building is subjected to
random motion of the ground at its base (Figure on next slide),
which induces inertia forces in the building that in turn cause
stresses; this is displacement-type loading
16

Figure : Difference in the design effects on a building during natural
actions of (a) Earthquake Ground Movement at base, and (b) Wind
Pressure on exposed area
17

 Wind force on the building has a non-zero mean component
superposed with a relatively small oscillating component (Figure
on next slide).
 Thus, under wind forces, the building may experience small
fluctuations in the stress field, but reversal of stresses occurs only
when the direction of wind reverses, which happens only over a
large duration of time.
 On the other hand, the motion of the ground during the earthquake
is cyclic about the neutral position of the structure.
 Thus, the stresses in the building due to seismic actions undergo
many complete reversals and that too over the small duration of
earthquake.
18

CE-412: MODULE 1 ( Fall 2015) 19
Figure: Nature of temporal variations of design actions:
(a) Earthquake Ground Motion – zero mean, cyclic, and (b) Wind
Pressure – non-zero mean, oscillatory

What happens during an earthquake?
Waves of different types and
velocities travel different paths
before reaching a building’s site
and subjecting the local ground to
various motions.
The ground moves rapidly back
and forth in all directions, usually
mainly horizontally, but also
vertically.
20
During an earthquake, seismic waves arise from sudden
movements in a rupture zone (active fault) in the earth's crust.

CE-412: MODULE 1 ( Fall 2015) 21

CE-412: MODULE 1 ( Fall 2015) 22
Two different types of seismic waves are generated by the sudden movement
on a fault: P-waves (primary waves) and S-waves (secondary waves).
A third type of seismic wave (Surface waves) is generated by the interaction
of the P- and S-waves with the surface and internal layers of the Earth.

CE-412: MODULE 1 ( Fall 2015) 23
Various types of waves

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.
24

The structure response to earthquake shaking occurs over the
time of a few seconds.
During this time, the several types of seismic waves are
combining to shake the structure in ways that are different in detail
for each earthquake.
In addition, as the result of variations in fault slippage, differing
rock through which the waves pass, and the different geological
and geotechnical nature of each site, the resultant shaking at each
site is different ( see details on next slide).
25

In comparison with rock, softer soils are particularly prone to
substantial local amplification of the seismic waves. Response of
two plate with one containing steel block and other jelly )?
Picture?
26
Note that the ground
displacement amplifies
with decrease in soil
stiffness
E values of various soil type s?

CE-412: MODULE 1 ( Fall 2015) 27
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. 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.
What happens to the structures? (case study)

CE-412: MODULE 1 ( Fall 2015) 28
A portion of the Cypress Freeway after the 1989 Loma Prieta earthquake
What happens to the structures? (case study)

The characteristics of each structure are different, whether in
size, configuration, material, structural system, age, or quality of
construction: each of these characteristics affects the structural
response.
In spite of the complexity of the interactions between the
structures and the ground during the few seconds of shaking there is
broad understanding of how different building types will perform
under different shaking conditions.
29
(Additional aspects affecting response)

Variation of horizontal displacement at various story levels in San Francisco’s
Transamerica Pyramid due to 1989 Loma Prieta E.quake 30
What about building response?
Is harmonic or pulse ?
Any idea on random response
What happens to the structures (Ground and
building displacements?)
Difference in peak response
encircled? Time difference?

CE-412: MODULE 1 ( Fall 2015) 31
Variation of horizontal acceleration at various story levels in San Francisco’s
Transamerica Pyramid due to 1989 Loma Prieta Equake
What happens to the structures (Ground and
building acceleration?)
Consider building
shown in video
1. consequences of
variation in acceleration
along height?
2. Inertial forces vary along
height ?
3. Structure will fail at
story with maximum
inertial force or ground
story?

Higher inertial forces in structural system with inadeqequate
detailing or inferior quality of material or both can cause substantial
damage with local failures and, in extreme cases, collapse. Is the
video answers question asked on previous slide?
The ground motion parameters and other characteristic values at a
location due to an earthquake of a given magnitude may vary
strongly. They depend on numerous factors, such as the distance,
direction, depth, and mechanism of the fault zone in the earth's crust
(epicenter), as well as, in particular, the local soil characteristics
(layer thickness, shear wave velocity).
32

The Mexico City earthquake (MS = 8.1) occurred in 1985.
Mexico City itself lies in a broad basin formed approximately
30 million years ago by faulting of an uplifted plateau.
Volcanic activity closed the basin and resulted in the formation
of Lake Texcoco. The Aztecs chose an island in this lake as an
easily defended location for their capital.
The expansion of the capitol (Mexico City) and the gradual
draining of the lake left the world's largest population center
located largely on unconsolidated lake-bed sediments.
The Mexico 1985 Earthquake: Effects of Local
Site Conditions on Ground Motion
33

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.
Fortunately ground motions were recorded at two sites, UNAM
(Universidad Nacional Autonoma de Mexico) and SCT (Secretary of
Communications and Transportation)
34

For the seismic studies that ensued, the city has often been
subdivided into three zones (see figure on next slide)
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. These are deposits due to accompanying rainfall of
airborne silt, clay and ash from nearby volcanoes. The soft clay
deposits extend to considerable depths.
Between the Foothill Zone and Lake Zone is the Transition Zone
where the soft soil deposits do not extend to great depths.
35

CE-412: MODULE 1 ( Fall 2015) 36
Distance b/w SCT
and UNAM

The UNAM site was on basaltic (Oceanic) rock. Oceanic crust is
younger, thinner and heavier than Continental crust (granite). The
SCT site was on soft soil.
The time histories recorded at the two sites are shown in figure
37

From the site measurements of the soil depth and the average shear
wave velocity, the natural period of the site was estimated at 2 sec.
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 again around 2 seconds.
38

The following items coincided at the SCT (soft soil) site:
1. The underlying soft soils had a natural period of about 2 sec;
2. The predominant period of site acceleration was about 2 sec.
As a result of this, structural damage in Mexico City was mixed.
Most parts of the Foot Hill Zone (rock) suffered hardly any damage.
In the Lake Zone damage to buildings with a natural period of around
2 seconds (not unusual for medium-sized buildings of 10–20 storeys)
was severe, whereas damage to taller buildings (more than 30 storeys)
and buildings of lesser height (less than 5 storeys) was not major.
This was a tragic case of resonance, which produced the widespread
damage.
39

The Mexico 1985 Earthquake:
Effects of Local Site conditions
on Ground Motion
40
Dynamic soil response in
damaged areas
Soil site period, Ts ~ 2 s
Ts = 4 H / Vs = 4(35 m)/70 m/s
= 2 s
Damaged Buildings Soft Soil
Mostly taller buildings
Tbldg ~ 2 s
Areas east with deeper soil, Ts
>> Tbldg

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
41

The plot of Fourier amplitude versus frequency is known as a Fourier
amplitude spectrum
Fourier amplitude
spectrum of a strong
ground motion expresses
the frequency content of
a motion very clearly.
42

43

44

45

It can be concluded that the 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).
46

Magnitude of earthquake and
acceleration of seismic waves
47

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)
What does it mean when a statement is generally made that an x
structural system has been designed for Mw= 10 ?
48

Relation of Mw with other magnitude Scales
For Mw = 7.5, extreme
difference of Mw → 0.4
from other scales
For Mw = 6.0, extreme difference
of Mw from other scales reduces
( as compared to Mw= 7.5)
49

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
50

Ground Motion Prediction Equations (GMPE’s)
51
“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.
Cornell et al. (1979)
Ground motion model is:
Ln(PGA) = a + b M + c ln(R + 25)

52
Cornell et al. (1979) [Contd…]
where, PGA is in cms−2 (gals), a = 6.74, b = 0.859, c = −1.80 and
σ = 0.57.
Developed for Western US.
No more than 7 records from one earthquake to avoid biasing
results.
Records from basements of buildings or free-ﬁeld.
Attenuation relationship developed by Cornell et al. (1979) for
Western US.
Ln(PHA)(gals)=6.74 + 0.859M-1.8ln(R+25)

Cornell et al. (1979) [Contd…]
Example: A building is to be constructed at 25 Km distance away
from a fault which can generate an earthquake of magnitude 7.7. What
is 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
53

Comment on the statement (generally made) that
Tarbela dam is designed for say Mw= 12 ?
54
The title statement mentioned above is technically incorrect due to a
number of reasons:
1. Occurrence of Magnitude 12 scale has never been considered in
Seismology
2. Location of epicenter shall be explicitly mentioned while talking about
magnitude of earthquake since it is the horizontal ground acceleration
(ag) that has a direct damaging effect on structures. ag recorded in
Peshawar due to 2005 Kashmir earthquake (Mw=7.6) was around 0.07g,
however, one may expect higher ag, if, God forbid, an earthquake with
Mw= 6.0 occur at Cherat fault which is very near to Peshawar.
3. Soil condition is yet another important parameter that influence the
damaging effect of an earthquake. Reconsider the example of 1985
Mexico earthquake that caused only moderate damage in the vicinity of
its epicenter but resulted in extensive damage in Mexico city located a

 Discuss the implications of vibrations
(specially noise) to common peoples and
those working in various industries?
H.A. M 1.3
55

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