Introduction to structural dynamics and earthquake engineering

Table: Symptoms Due to Whole-Body Vibration and the Frequency Range at which they Usually Occur Effect of dynamic forces exerted on humans The Effects of Vibration on the Human Body... T

University of Engineering and Technology

Why to carry out dynamic analysis ?

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

Sources of Dynamic Excitation

Impact

Machine vibration Blast

Sources of Dynamic Excitation

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

Static Vs Dynamic Force

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.,

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

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 times

2)Moving on the bridge

3) Truck entering in to the bridge through a speed breaker

4)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

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 forces exerted by rotating machines

(Harmonic loading)

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

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?

Effect of dynamic forces exerted on humans

The Effects of Vibration on the Human Body

Table: Symptoms Due to Whole-Body Vibration and the Frequency

Range at which they Usually Occur

Effect of dynamic forces exerted on humans

The Effects of Vibration on the Human Body

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

Random dynamic forces, Blast loading

Random dynamic forces, impulsive loading

Typical force–time curve for an impulsive force

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

Random dynamic forces, earthquake loading

ag

t

Ground acceleration (a g ) during earthquake (EQ) vs time a g 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 , F I , on model

building assuming that most

model’s weight is located at

roof level Depending upon

magnitude of F I , building can

overturn in the direction of F I

Random dynamic forces, earthquake loading

F I

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.

During an earthquake, seismic waves arise from sudden movements in a rupture zone

(active fault) in the earth's crust

What happens during an

earthquake?

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?

Various types of waves

What happens during an

earthquake?

What happens to the structures?

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

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)

In comparison with rock, softer soils are particularly prone to

substantial local amplification of the seismic waves

Note that the ground displacement amplifies with decrease in soil

What happens to the structures?

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?

A portion of the Cypress Freeway after the 1989 Loma Prieta

earthquake

What happens to the structures?

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

What happens to the structures?

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?

What happens to the structures?

Variation of horizontal acceleration at various story levels in San Francisco’s

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)

What happens to the structures?

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

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

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

The Mexico 1985 Earthquake: Effects of

Local Site Conditions on Ground Motion

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

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

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

The Mexico 1985 Earthquake: Effects of

Local Site Conditions on Ground Motion

The Mexico 1985 Earthquake:

Effects of Local Site conditions

Damaged Buildings Soft Soil

Mostly taller buildings

Tbldg ~ 2 s

Areas east with deeper soil, Ts

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

spectrum of a strong

ground motion expresses

the frequency content of

a motion very clearly

Frequency content parameter

Frequency content parameter

Frequency content parameter

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

Magnitude of earthquake and acceleration of seismic waves

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),

Relation of Mw with other magnitude Scales

For M w = 7.5, extreme

difference of M w → 0.5

from other scales

For M w = 6.0, extreme difference

of M w from other scales ia

insignificant

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

Ground Motion Evaluation

Source + Path + Site