module 1, introduction to structural dynamics & earthquake engineering,fall 2015

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

[email protected] [email protected]

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CE-412: MODULE 1 ( Fall 2015)

Why to carry out dynamic analysis ?

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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)

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Machine vibration

(always negative effect?

Blast ?(11)


Sources of Dynamic Excitation

Wind Ground motion

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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

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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

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

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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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Vibration due to rotating machine.flv




ROTATING UNBALANCE Simulation.flv










MIT Physics Demo -- Spray Paint Oscillator.flv




CE-412: MODULE 1 ( Fall 2015) 11

Random dynamic forces, Blast loading

Variation of blast loading w.r.t time and its effect

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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

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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

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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

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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.


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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.

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During an earthquake, seismic waves arise from sudden

movements in a rupture zone (active fault) in the earth's crust.

fault rupture.flv

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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


The paths of seismic waves from an earthquake are recorded by UPOR seismic station in Portland.flv


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. Response of

two plate with one containing steel block and other jelly )?

Picture?

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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.

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(Additional aspects affecting response)

SDOF Resonance Vibration Test.flv





















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?

Japanese skyscrapers swaying.flv

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).

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../../2012 Spring/MODULE 1/6 Story Building by NIED.wmv












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-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


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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 → 0.4

from other scales

For Mw = 6.0, extreme difference

of Mw from other scales reduces

( as compared to Mw= 7.5)

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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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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)



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

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

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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

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Discuss the implications of vibrations

(specially noise) to common peoples and

those working in various industries?

H.A. M 1.3

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