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University of Engineering and Technology Peshawar, Pakistan
CE-409: Introduction to Structural Dynamics and Earthquake Engineering
MODULE 1: FUNDAMENTAL CONCEPTS RELATED TO THE
EARTHQUAKE ENGINEERING
Prof. Dr. Akhtar Naeem Khan & Prof. Dr. Mohammad Javed [email protected] [email protected]
1
CE-409: MODULE 1 ( Fall 2013)
Why to carry out dynamic analysis ?
2
CE-409: MODULE 1 ( Fall 2013) 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
CE-409: MODULE 1 ( Fall 2013)
Sources of Dynamic Excitation
Impact
4
Machine vibration
Blast
CE-409: MODULE 1 ( Fall 2013)
Sources of Dynamic Excitation
Wind Ground motion
5
CE-409: MODULE 1 ( Fall 2013)
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
CE-409: MODULE 1 ( Fall 2013)
Static Vs Dynamic Force
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-409: MODULE 1 ( Fall 2013) 8
Static Vs Dynamic Force
What will be the effect of truck (load) on bridge and response of bridge (structure)?, when:1)Truck is not moving and present on bridge all the times2)Moving on the bridge3) Truck entering in to the bridge through a speed breaker4)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. 1
CE-409: MODULE 1 ( Fall 2013)
Implications of dynamic forces
9
CE-409: MODULE 1 ( Fall 2013)
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-409: MODULE 1 ( Fall 2013)
Vibrations influence the human body in many different ways. The response to a vibration exposure is primarily dependent on the frequency, amplitude, and duration of exposure.
Other factors may include the direction of vibration input, location and mass of different body segments, level of fatigue and the presence of external support.
The human response to vibration can be both mechanical and psychological.
Mechanical damage to human tissue can occur, which are caused by resonance within various organ systems.
Effect of dynamic forces exerted on humans
11
The Effects of Vibration on the Human Body
CE-409: MODULE 1 ( Fall 2013)
From an exposure point of view, the low frequency range of vibration is the most interesting. Exposure to vertical vibrations in the 5-10 Hz range generally causes resonance in the thoracic-abdominal system, at 20-30 Hz in the head-neck-shoulder system, and at 60-90 Hz in the eyeball.
Driver fatigue?
Effect of dynamic forces exerted on humans
12
The Effects of Vibration on the Human Body
CE-409: MODULE 1 ( Fall 2013) 13
Table: Symptoms Due to Whole-Body Vibration and the Frequency Range at which they Usually Occur
Effect of dynamic forces exerted on humansThe Effects of Vibration on the Human Body
CE-409: MODULE 1 ( Fall 2013) 14
Vibration frequency sensitivity of different parts of human body.
The Effects of Vibration on the Human Body (contd…)
Effect of dynamic forces exerted on humans
CE-409: MODULE 1 ( Fall 2013) 15
Random dynamic forces, Blast loading
Variation of blast loading wr.t time and its effect
1
1
2
1
3
1
4
1
5
1
11
21
31
41
51
CE-409: MODULE 1 ( Fall 2013) 16
Random dynamic forces, impulsive loading
Typical force–time curve for an impulsive force
CE-409: MODULE 1 ( Fall 2013) 17
H.Assignment 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-409: MODULE 1 ( Fall 2013) 18
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 ?
CE-409: MODULE 1 ( Fall 2013)
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
19
Random dynamic forces, earthquake loading
FI
CE-409: MODULE 1 ( Fall 2013)
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-409: MODULE 1 ( Fall 2013) 21
What happens during an earthquake?
CE-409: MODULE 1 ( Fall 2013) 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.
What happens during an earthquake?
CE-409: MODULE 1 ( Fall 2013) 23
Various types of waves
What happens during an earthquake?
CE-409: MODULE 1 ( Fall 2013)
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
CE-409: MODULE 1 ( Fall 2013)
What happens to the structures?
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
CE-409: MODULE 1 ( Fall 2013)
In comparison with rock, softer soils are particularly prone to substantial local amplification of the seismic waves
26
Note that the ground displacement amplifies with decrease in soil stiffness
What happens to the structures?
CE-409: MODULE 1 ( Fall 2013) 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?
CE-409: MODULE 1 ( Fall 2013) 28
A portion of the Cypress Freeway after the 1989 Loma Prieta earthquake
What happens to the structures?
CE-409: MODULE 1 ( Fall 2013)
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
What happens to the structures?
CE-409: MODULE 1 ( Fall 2013)
Variation of horizontal displacement at various story levels in San Francisco’s Transamerica Pyramid due to 1989 Loma Prieta Equake 30
Structure vibrate in fundamental mode ? due to specific geometry of building. What about building response? Is it random, harmonic , pulse
What happens to the structures?
CE-409: MODULE 1 ( Fall 2013) 31
What happens to the structures?
Variation of horizontal acceleration at various story levels in San Francisco’s Transamerica Pyramid due to 1989 Loma Prieta Equake
CE-409: MODULE 1 ( Fall 2013)
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.
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
What happens to the structures?
CE-409: MODULE 1 ( Fall 2013)
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
CE-409: MODULE 1 ( Fall 2013)
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)
The Mexico 1985 Earthquake: Effects of Local Site Conditions on Ground Motion
34
CE-409: MODULE 1 ( Fall 2013)
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.
The Mexico 1985 Earthquake: Effects of Local Site Conditions on Ground Motion
35
CE-409: MODULE 1 ( Fall 2013) 36
The Mexico 1985 Earthquake: Effects of Local Site Conditions on Ground Motion
CE-409: MODULE 1 ( Fall 2013)
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
The Mexico 1985 Earthquake: Effects of Local Site Conditions on Ground Motion
37
CE-409: MODULE 1 ( Fall 2013)
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 Mexico 1985 Earthquake: Effects of Local Site Conditions on Ground Motion
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
CE-409: MODULE 1 ( Fall 2013)
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.
The Mexico 1985 Earthquake: Effects of Local Site Conditions on Ground Motion
39
CE-409: MODULE 1 ( Fall 2013)
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
CE-409: MODULE 1 ( Fall 2013)
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
CE-409: MODULE 1 ( Fall 2013)
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.
42
CE-409: MODULE 1 ( Fall 2013)
Frequency content parameter
43
CE-409: MODULE 1 ( Fall 2013)
Frequency content parameter
44
CE-409: MODULE 1 ( Fall 2013)
Frequency content parameter
45
CE-409: MODULE 1 ( Fall 2013)
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).
Frequency content parameter
46
CE-409: MODULE 1 ( Fall 2013)
Magnitude of earthquake and acceleration of seismic waves
47
CE-409: MODULE 1 ( Fall 2013)
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
CE-409: MODULE 1 ( Fall 2013)
Relation of Mw with other magnitude Scales
For Mw = 7.5, extreme difference of Mw → 0.5 from other scales
For Mw = 6.0, extreme difference of Mw from other scales ia insignificant
49
CE-409: MODULE 1 ( Fall 2013)
Attenuation RelationshipsStrong-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 parameterM = magnitudeR = 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 EvaluationSource + Path + Site
50
CE-409: MODULE 1 ( Fall 2013)
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 ML + c ln(R + 25)
CE-409: MODULE 1 ( Fall 2013)
Ground Motion Prediction Equations (GMPE’s)
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)
CE-409: MODULE 1 ( Fall 2013)
Ground Motion Prediction Equations (GMPE’s)
53
CE-409: MODULE 1 ( Fall 2013)
Comment on the statement (generally made) that Tarbela dam is designed for Mw= 12 ?
54
The statement 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 distance of 350–360 km from the epicenter.