LSR PPT

Characterization of earthquakes Characterization of earthquakes Response spectra & Design Response spectraResponse spectra & Design Response spectra

L.S. RamachandraAssociate ProfessorDepartment of Civil Engineering, I.I.T.,Kharagpur

UNDP training Programme on Earthquake-Resistant Design of buildings, July 1-3, 2004

UNDP training Programme on Earthquake-Resistant Design of buildings, July 1-3 2004

Earth’s InteriorEarth’s Interior

Source: USGS


CrustCrustThe earth’s crust is a dynamic assembly of moving plates whose interactions explain the occurrence of earthquake

MantleMantleIt contains high concentration of magnesium and iron.It is in semi molten condition. Temperature is 5000 C which causes convection currents.

CoreCore

The outer core is semi molten where as the inner core is solid due to high pressure


Plate TectonicsPlate Tectonics

Plate tectonics is the continual slow movement of the tectonic plates, the outermost part of the earth.

Source: USGS


EarthquakesEarthquakes

• Plate tectonicstectonics action introduce stresses in rock present in earths crust. These rocks are elastic and brittle in nature

• When the stresses reach a critical value, the rocks break along weak section (faultfault) and release enormous energy

• The sudden release of energy, results in shaking of earth which is known as earthquake earthquake

• The earthquake commonly occurs along plate boundaries

Some past earthquakesSome past earthquakes


Seismic Zone map of India: IS 1893-1984Seismic Zone map of India: IS 1893-1984



Revised Indian Seismic Zone MapRevised Indian Seismic Zone Map

Source: IS 1893-2002


Source: IIT, Kanpur


FaultsFaults

Rocks deform along faults.

Source: UC Berkeley


Seismic WavesSeismic Waves• The sudden displacement of rocks generate seismic Waves

Body waves and surface wavesBody waves and surface waves

Primary-Waves:Primary-Waves:Short Wavelength and high frequency.Velocity: 5-7 Kms/sec.

Shear Wave or S-WaveShear Wave or S-Wave

• S-waves travel at a speed of 3.5 Kms/sec.


Surface WavesSurface Waves

• Long Wavelengths and low frequency. Slower than Body waves

• Damaging to foundation of Structures

Love WaveLove Wave

Sideways motion of particles in the horizontal planeSideways motion of particles in the horizontal plane


Rayleigh WavesRayleigh Waves

Elliptic motion of particles in the vertical planeElliptic motion of particles in the vertical plane


FocusFocus

Seismic wavesSeismic waves

FaultFault

EpicentreEpicentre

Focus and EpicentreFocus and Epicentre


Strong Ground motionStrong Ground motion


Accelerogram from El Centro earthquake, May 18, 1940 (NS component)

Amplitude,frequency content and durationAmplitude,frequency content and duration


Seismograph (Source: ://www.thetech.org/)


Characteristics of strong ground motionCharacteristics of strong ground motion

Peak amplitude (Peak ground acceleration, PGA)

Magnitude of EarthquakeMagnitude of Earthquake

• Magnitude is measured using Richter’s scale. It accounts for the amplitude of waves with the distance from the epicentre

• In the Richter’s scale the logarithm of the amplitude of waves recorded by seismographs is measured.

As, the scale is logarithmic; each increase of 1 on the scale indicates tenfoldtenfold increase in the motion of the ground and corresponds to the release of about 3131 times more energy.


MagnitudeApproximate Equivalent TNT Energy

4.0 1010 tons

5.0 31800 tons

6.0 1,010,000 tons

7.0 31,800,000 tons

8.0 1,010,000,000 tons

9.0 31,800,000,000 tons

Amount of Energy released during a earthquake

I Ton of TNT = 4.2 x 109 Joules

Descriptor Magnitude Average Annually

Great 8 and higher 1

Major 7 - 7.9 18

Strong 6 - 6.9 120

Moderate 5 - 5.9 800

Light 4 - 4.9 6,200 (estimated)

Minor 3 - 3.9 49,000 (estimated)

Very Minor < 3.0 Magnitude 2 - 3: about 1,000 /day Magnitude 1 - 2: about 8,000 /day

Global Occurrence of earthquakes



Intensity of earthquakeIntensity of earthquake

Modified Mercalli Intensity scale is used. It is a qualitative scale. It is marked from I to XII. It is based on:

• Human Perception• Building Response• Changes in Natural Surroundings


Effect of Earthquake on StructuresEffect of Earthquake on Structures

Building natural frequencyBuilding natural frequency

Building Height Typical Natural Period

2 story .2 seconds

5 story .5 seconds

10 story 1.0 seconds



Period=1/Natural frequency

Representative values of periods of buildings


Ground motion

Height, Stiffness and PeriodHeight, Stiffness and Period


Natural Period of VibrationNatural Period of Vibration

The approximate natural period of vibration (Ta) in seconds of a moment Resisting frame building without brick infill panels is

Ta=0.075 h0.75 For RC frame building

=0.085 h0.75 For steel frame building

h=height of the building in m.


ResonanceResonance

Buildings suffer the greatest damage from ground motion at a frequency close or equal to their own natural frequency.

Inertial force F=Ma Inertial force F=Ma


Response of a simple Rigid blockResponse of a simple Rigid block

Ground Motion


Ground motion

Lateral forced induced in a multistoried building


B

A

C

D

k/2k/2

m

Section of a building Mathematical model


The transverse vibration of the buildingThe transverse vibration of the building


Few Mathematical PreliminariesFew Mathematical Preliminaries

xg = ground displacement; xt =total motion of the building; x = column distortion

0)( )( )( txktxctxm t

The equation of motion of this SDOF system is

effg ptxmtxktxctxm )()( )( )(

Or,


The response of the frame to specified ground acceleration may be obtained by Duhamel’s integral

dtextx Dt

t

gD

)( sin )(1

)( )(

0

Where cc

c

max0

)( sin)(exp[)(

t

gv dtttxS

Let

The maximum value of response is vSx max

and 21 D


Response Spectrum ConceptResponse Spectrum Concept

• Different buildings respond in widely different manners to the same earthquake ground motion

• The same building would respond differently for different earthquake

• To represent different building’s response to the same earthquake a graphical representation known as Response SpectrumResponse Spectrum is used.


• A response spectrum is a graph which plots the maximum response values of acceleration, velocity and displacement against period for various damping values.

• SSdd, SSvv and SSdd are the displacement, velocity and acceleration response spectra. They are related by

v

d

SS dva SSS 2 and


Simplified Response Spectra


Psuedovelocity response spectrum, El Centro earthquake, 1940


Response Spectra for El Centro Earthquake, 1940


If T=0.3 Sec. and %5

Then Sa=0.5g

Inertial force F=Ma Inertial force F=Ma

m


• For structures with relatively long periods above 15 sec. the maximum displacement response Sd is practically equal to the maximum ground displacement for all damping values and maximum acceleration response Sa is very small.

Flexible Structure


• A system with short periods less than 0.035 sec. the maximum acceleration Sa approaches the maximum ground acceleration and Sd is very small.

Stiff structure


The maximum force developed in a SDOF system

adds mSmSkSf 2

• The jagged response spectrum is a plot of maximum response of different oscillators to a given accelerogram and hence is a description of a particular ground motion.


The earthquake-resistant design depends on

• Site seismological data concerning the earthquake

• Return periods of earthquakes

• The response spectrum for different earthquakes would be different


Design Response SpectrumDesign Response Spectrum

• The design spectrum should be representative of ground motions recorded at the site during past earthquakes

• If no past earthquake histories are recorded at a site then, the design spectrum for that site should be based on ground motions recorded at other sites under similar conditions


• The same design spectrum has to reflect the potential shaking from different earthquakes

• The shape of the design spectra is determined averaging several comparable several response spectra.



Construction of elastic design spectrum



• The jagged response spectrum is a plot of the maximum response (acceleration, velocity and displacement) of all SDOF systems to a particular earthquake and hence it is a description of the particular earthquake.

• The smooth design spectrum is a specification of the level of seismic design force for which the structure is being designed.

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