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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
50 mm expansion joints
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
50 mm expansion joints
Lead-rubber bearings
50 mm expansion joints
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
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
Lava rock, 8-10 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).
4/3
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.