Module 1 ( (CE-409: Introduction to Structural Dynamics and Earthquake Engineering))

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]

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CE-409: MODULE 1 ( Fall 2013)

Why to carry out dynamic analysis ?

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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

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Machine vibration

Blast


Sources of Dynamic Excitation

Wind Ground motion

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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

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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.,

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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

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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


Implications of dynamic forces

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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)

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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

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The Effects of Vibration on the Human Body


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?


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The Effects of Vibration on the Human Body

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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

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Vibration frequency sensitivity of different parts of human body.

The Effects of Vibration on the Human Body (contd…)


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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

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Random dynamic forces, impulsive loading

Typical force–time curve for an impulsive force

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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

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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

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Random dynamic forces, earthquake loading

FI


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.

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During an earthquake,

seismic waves arise from sudden movements in a rupture zone

(active fault) in the earth's crust.

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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.


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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.

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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).

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In comparison with rock, softer soils are particularly prone to substantial local amplification of the seismic waves

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Note that the ground displacement amplifies with decrease in soil stiffness


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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.


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A portion of the Cypress Freeway after the 1989 Loma Prieta earthquake



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.

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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


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Variation of horizontal acceleration at various story levels in San Francisco’s Transamerica Pyramid due to 1989 Loma Prieta Equake


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).

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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

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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)


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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.


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CE-409: MODULE 1 ( Fall 2013) 36



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


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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.

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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.


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The Mexico 1985 Earthquake: Effects of Local Site conditions on Ground Motion

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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

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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.

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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).


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Magnitude of earthquake and acceleration of seismic waves

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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 ?

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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

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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

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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.

Cornell et al. (1979)

Ground motion model is:

Ln(PGA) = a + b ML + c ln(R + 25)



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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)



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Comment on the statement (generally made) that Tarbela dam is designed for Mw= 12 ?

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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.

Module 1 ( (CE-409: Introduction to Structural Dynamics and Earthquake Engineering))

Technology

effect of dynamic forces

random dynamic forces

applied forces

harmonic forces

static force

type of dynamic load

special case of dynamic

seismic forces