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STRUCTURAL DYNAMICSWITH REFERENCE TO EQ

S. K. Bhattacharyya

Central Building Research Institute

Roorkee

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Earthquake Forces

Earthquake forces are caused by the inertiaof the structure, which tries to resist ground

motions. The movement between the two parts of the

building creates a force equal to the groundacceleration times the mass of the structure.

The ground acceleration depends on themagnitude of the seismic event.

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In addition to the earthquakemagnitude, the value of the seismic

force also depends on the type of soilunder the building.

Some soils tend to amplify seismicwaves and can even turn to a liquid likeconsistency during an earthquake.

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Seismic Response of Soil-Structure systems

To evaluate the seismic response of astructure at a given site, the dynamic

properties of the combined soil-structure system must be considered.

The nature of the sub-soil mayinfluence the response of the structurein the following ways:

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The seismic excitation at bedrock is modifiedduring transmission through the overlyingsoils to the foundation. This may cause

attenuation or amplification effects.

The fixed base dynamic properties of the

structure may be significantly modified bythe presence of soils overlying bedrock. Thiswill include changes in the mode shape andperiods of vibration.

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A significant part of the vibrational energy ofthe flexibly supported structure may bedissipated by material damping and radiationdamping in the supporting medium.

The increase in the fundamental period of

moderately flexible structures due to soil-structure interaction may have detrimentaleffects on the imposed seismic demand.

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Structures sited on soft alluvium maybe damaged by differential vertical

displacements occurring before and/orduring earthquakes. It appears logicalthat structures with relatively low

horizontal strength will suffer worstfrom this phenomenon i.e low risestructures will be most vulnerable.

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Analysis Steps

Subsoil

Substructure

Superstructure

Non-structure

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Equation of Motion

It is clear that for given groundacceleration the deformation responsedepends only on the natural frequency ornatural period.

Two systems with same natural period &damping ratio same displacement

)(22

tuuuugnn

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Response Quantities

Deformation of the system displacement

of the mass

Internal forces

Shears & bending arelinearly dependent on u.

Total displacement

helpful in providingseparation between buildings.

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Response History

Refer Figure

Longer the vibration period, the greater

the peak deformation.

Pseudo-acceleration response

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Response History

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Pseudo-Acceleration Response

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Deformation Response Spectrum

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Deformation response;

Pseudo-velocity &Pseudo-acceleration

Spectrum

Damping ratio2%

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Combined D-V-A Spectrum

Deformation spectrum provides the peakdeformation of a system

The Pseudo-velocity spectrum is relateddirectly to the peak strain energy stored inthe system during the earthquake.

Pseudo-acceleration spectrum is relateddirectly to the peak value of the equivalentstatic force and base shear.

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Secondly the shape of the spectrum can

be approximated more readily for design

purposes with the aid of all three spectralquantities.

D V A R S t

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D-V-A Response Spectrum

C bi d D V A S f El C d i

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Combined D-V-A Spectrum for El-Centro ground motion

Damping ratio

0, 2, 5, 10 & 20%

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Response Spectrum

Damping

ratio2%

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5%

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Construction of Design Spectrum

Plot corresponding to the peak values of

ground acceleration, velocity and

deformation for design ground motion. For damping ratio selected obtain

amplification factors

Plot after multiplying the factors to theresponse quantities.

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Codal Provisions

Equivalent Static Analysis

Dynamic Analysis

Modal technique

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