earthquake forces calculation

7/29/2019 earthquake forces calculation

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Calculation of of earth quake loads inacc. with Eurocode 8/NS-EN1998-1

Course: June 4th 2009, Norwegian Steel Association


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CONTENTS

Shear Force at Ground Level

Seismic Class Effect of Soil Type

Natural periods

Design Spectrum

Load factors and combinations

Seismic mass

Distribution of forces within building.

Capacity control

Exemption Criteria


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Earth quake in structures

Essentials giving

greatest contributionto Fb:

Natural period of

structure (T).

Energy dissipation instructure, (q).

Soil Type (S).


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Lets start with the basics

Earth quakes are dynamic fenomenonsand are solved in accordance with this.

F = m*a > 0 (Sir Isac Newton, 1666).

F = ms*Sd(T)* (Eurocode + NA, 2008)


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Load factors for earth quakes: Accident Limit State

Permanentelaster

Dominerendevariabel last

Andre variablelaster

Jordskjelv last

1,0 0,0 0,8

(se nedenfor)

0,0 0,8

(se nedenfor)

1,0 For krefter ikonstruksjonen

1,0 1,0 1,0 1,0 For brudd i

grunnen.

Boliger Kontorer Forsamlingslokale Butikker Lager

0,3 0,3 0,6 0,6 0,8

LoadLoadfactorsfactorsfor permanent variablefor permanent variable loadsloads::

(valid for(valid for seismicseismic massmass))


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Material factor, Steel

m = 1,1

(NA.6.1.3.(1))


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pkt 4.3.3.2.2:

Shear forces at ground level or at the top of a rigidbasement.

F = ms*Sd(T)*

ms = the seismic mass of the structure

= dead load + permanent loads + % of live loads.

Sd(T) = design spectrum = correction factor

(0,85 for T < 2*TC and more than 2 storeys, otherwise 1,0)


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ref pkt 3.2.2.5 (4)P

Design Spectrum principal shape

Most buildingsare within:

(Tb+Tc)/2

and

(Tc+Td)/2


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Sd(T) = Design Spectrumag , S ,T

ag*

S*2,5

*(T

C*T

D/T)/qS

d(T) =T > T

D

ag*S*2,5*(TC/T)/qSd(T) =TC < T < TD

ag*

S*2,5/qS

d(T) =T

B< T < T

C

ag*S*(2/3 +(T/TB)*(2,5/q 2/3))Sd(T) =0 < T < TB


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Parameters that must be determined:

q = construction factor < 1,5 4>

ag40hz = peak value of ground acceleration < 0 3,0 m/s>

1 = Factor for seismic class < 0,7 2,0>

ag = 0,8* ag40hz* 1 = design ground acceleration

S = Soil factor, dependent on the ground conditions< 1,0 1,7 and greater>

T = Natural period of the structure, usually < 0,5 s 1,5 s>

TB, TC og TD in the design spectrum (Sd(T)), governed by soil factorS

2 orthogonal directions is considered.


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Earth quake

in Norway the

last 110 years.


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ag40hz = peak valuefor groundacceleration


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ag40hz = peak value forground acseleration


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1 = Factor for seismic class( plitelighetsklasse)


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Then calculate design groundacceleration:

ag = 0,8* ag40hz* 1


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Effect of Soil under and aroundbuilding:

Illustrated by a case in Iceland.


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Example of increase of earthquake actions

Case study in Iceland, Thjorsa Bru

0 10 20 30 40 50

Scale in Kilometers

Reykjavik

Hella

Selfoss

Keflavk

Thjorsa-bridgeM6.5 - June 17 - 2000

M6.5, June 21 - 2000

Hvolsvllur

Hverageri

orlkshfn


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Thjorsa Bru Different type of soil on each side.

Lava rock on alluvial

deposits on west side

Approach

spanBedrock

50 mm expansion joints

Lead-rubber bearings


Alluvial deposits, 18-20 m thick

Lava rock, 8-10 m thick

Thjorsa-River

WEST SIDE EAST SIDE

Back wall with wing

walls

Pier

Accelerometer

Approach

spanBedrock


Lead-rubber bearings


Alluvial deposits, 18-20 m thick


Thjorsa-River

WEST SIDE EAST SIDE

Back wall with wing

walls

Pier

Accelerometer

Bedrock on the east side


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Accelerations measured in 2000 for the

same quake.

Sand and fine gravel, 18-20 m thick


West side East side

Thjorsa River

Dolerite (bedrock)

83 m

-0.50

0.00

0.50

-0.50

0.00

0.50

Acceleration

-(g)

0 5 10 15Time- (s)

-0.50

0.00

0.50

0 5 10 15Time- (s)

N-S N-S

E-W E-W

Vertical Vertical

WEST SIDE EAST SIDE

0,29 hz,

greater Sd(T) 0,21 hz,

less Sd(T)

InsignificantSd(t)

Insignificant

Sd(t)


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Geotechnical advice needed when:

Geotechnical advice or values not given by Eurocode.

Possibility for lique-faction (Soil type S2)

Plastified and soft clay and silts (Soil type S1)

Mix of several Soil Types A - E

Possibility of great pore overpressures

Lateral forces on Piles

Partly freestanding piles.

Structural interaction soil and building

Foundation flexibility in analyses.


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The basic equation:

T = *


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Approximate equations for the first naturalperiod:

point 4.3.3.2.2.(3), (4) og (5).

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1 HCT t =

dT = 21


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Natural period, T,flexibility of foundation

T1= 2 (M

1/K

1) T

1= C

t

H3/4 T1= 2

d


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--


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Non Regular buildings

Buildings designed in DCM ( 2 < q < 4)

Buildings with foundations partly on rock and deposits.

Buildings in seismic class


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Calculate the following :

Sd(T) = Design Spectrum

ag*

S*2,5/q

*(T

C*T

D/T)Sd(T) =T > TD

ag*S*2,5/q*(TC/T)Sd(T) =TC < T < TD

ag*

S*2,5/qSd(T) =TB < T < TC

ag*

S*

(2/3 +(T/TB

)*

(2,5/q 2/3))Sd(T) =0 < T < TB


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Point 3.2.2.5 (4)P

Respons Spectrum (in principle)


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Udesired eccentricity (Torsion)

point 4.3.3.2.4 Reinforcement factor

= 1+x/ Le

x = the distance of the structure in question from the masscentre of the overall structure in the level measred at rightangles to the relevant seismic load.

Le = the distance between the outer strucural parts withstandingapplied loasds, measured at right angles to the direction of theseismic load in question.


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Shear force at foundation level or at the roof level of a rigidbasement

F= m*Sd(T)*


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point 4.3.3.2.3

The distribution of shear forces on the floors ofthe building.


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The distribution of shear forces on thefloors of the building.

Will also be given by a 2D or 3Ddynamic analysis


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Low seismicity:

Condition: - ag S = I * agR * S < 0.1 g = 0.98 m/s2

- q 1.5

=> Simplified design rules may be used

Condition: - Sd(T)< 0.05 g = 0.49 m/s2

- q 1.5

Very low seismiscty:

=> Do not require earth quake design


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ref NA.3.2.1 (5)P

Excemption criteria.

Not necessary to determine sufficient capacity for seismic loads:

Structures in seismic class I (i.e. 1 = 0,7)

Light timber structures

when ag*S


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Structures with small energy dissipation, DCL:

1,5 q 2,0

Elstic analyses without accounting for nonlinearities.

Carry out design and sizing acc to Gjennomfredimensjonering iht NS-EN Steel Standardwithoutadditional requirements. (Only if q1,5)

Ved ikke-regularitet i oppriss reduseres q til 0,8*q < 1,5.(pkt 4.2.3.1)

DCL is a straight forward firstattemt to design for earthquakes.

earthquake forces calculation

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