# Earth quake forces 2009.06.04

Document Sample

```					Calculation of of earth quake loads in
acc. with Eurocode 8/NS-EN1998-1

Course: June 4th 2009, Norwegian Steel Association
CONTENTS

–   Shear Force at Ground Level
–   Seismic Class
–   Effect of Soil Type
–   Natural periods
–   Design Spectrum
–   Seismic mass
–   Distribution of forces within building.
–   Capacity control
–   Exemption Criteria
Earth quake in structures

•   Essentials giving
greatest contribution
to Fb:
•   Natural period of
structure (T).
•   Energy dissipation in
structure, (q).
•   Soil Type (S).
• Earth quakes are dynamic fenomenons
and are solved in accordance with this.

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

• F = ms*Sd(T)*λ (Eurocode + NA, 2008)
Load factors for earth quakes: Accident Limit State

Permanente    Dominerende      Andre variable       Jordskjelv last
laster        variabel last    laster

1,0          0,0 – 0,8         0,0 – 0,8              1,0          For krefter i
konstruksjonen
(se nedenfor)     (se nedenfor)

1,0             1,0               1,0                 1,0          For brudd i
grunnen.

(valid for seismic mass)

Boliger        Kontorer     Forsamlingslokale        Butikker           Lager

0,3             0,3              0,6                  0,6              0,8
Material factor, Steel
• γm = 1,1

(NA.6.1.3.(1))
pkt 4.3.3.2.2:

Shear forces at ground level or at the top of a rigid
basement.
•   F = ms*Sd(T)*λ

•   ms = the seismic mass of the structure

•    Sd(T) = design spectrum
•    λ = correction factor
(0,85 for T < 2*TC and more than 2 storeys, otherwise 1,0)
ref pkt 3.2.2.5 (4)P
Design Spectrum – principal shape

Most buildings
are within:
(Tb+Tc)/2
and
(Tc+Td)/2
Sd(T) = Design Spectrum
ag , S ,T

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

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

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

T > TD       Sd(T) =   ag*S*2,5*(TC*TD/T)/q
Parameters that must be determined:
•   q = construction factor < 1,5 – 4>

•   ag40hz = peak value of ground acceleration < 0 – 3,0 m/s²>

•   γ1 = Factor for seismic class < 0,7 – 2,0>

•   ag = 0,8* ag40hz* γ1 = 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 factor S

•   2 orthogonal directions is considered.
Earth quake
in Norway the
last 110 years.

The map indicates automatic
registrations performed by av
NORSAR of earth quakes and other
seismic activities (explosions etc.) the
last 110 years. ILL: NORSAR
ag40hz = peak value
for ground
acceleration
ag40hz = peak value for
ground acseleration
γ1 = Factor for seismic class
(≈ ’pålitelighetsklasse’)
Then calculate design ground
acceleration:
• ag = 0,8* ag40hz* γ1
Effect of Soil under and around
building:
• Illustrated by a case in Iceland.
Example of increase of earthquake actions
Case study in Iceland, Thjorsa Bru

Reykjavik

M6.5, June 21 - 2000
Hveragerði
Keflavík
M6.5 - June 17 - 2000
Selfoss      Thjorsa-bridge
Hella
Þorlákshöfn
Hvolsvöllur
0      10       20     30         40   50
Scale in Kilometers
Thjorsa Bru – Different type of soil on each side.

Accelerometer
WEST SIDE                                                                       EAST SIDE

50 mm expansion joints                                     50 mm expansion joints

Lava rock, 8-10 m thick
Thjorsa-River
Pier              Back wall with wing
walls
Alluvial deposits, 18-20 m thick
Approach
Bedrock               span

Bedrock on the east side
Lava rock on alluvial
deposits on west side
Accelerations measured in 2000 for the
same quake.
83 m
West side                                                                                                     East side

Lava rock, 8-10 m thick
Thjorsa River

Sand and fine gravel, 18-20 m thick

Dolerite (bedrock)

WEST SIDE                                        EAST SIDE
0.50
N-S                                                   N-S

0.00
0,29 hz,
greater Sd(T) -0.50
0.50
0,21 hz,
Acceleration - (g)

E-W                                                   E-W        less Sd(T)
0.00

-0.50
0.50
Vertical                                            Vertical

Insignificant                     0.00
Insignificant
Sd(t)                                                                                                                                           Sd(t)
-0.50
0          5                10              15 0            5                10                 15
Time - (s)                                       Time - (s)
Effect of ground types (S-faktor)

•   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.
Natural periods of the structure, T
Natural periods of the structure, T
The basic equation:

T = α * √(M/K)
•   M = Seismic mass:
•   Masses from permanent loads + % variable
•   K = stiffness:
•   Some contribution from the load bearing structure
and some from the ”non load bearing” structure
Approximate equations for the first natural
period:
point 4.3.3.2.2.(3), (4) og (5).

T1 = Ct ⋅ H 3 / 4
where

C = 0,085 for steel frames
C = 0,075 for concrete frames
C = 0,050 for other systems

d is the horizontal displacement in
Second approximate equation:       meter on the top floor when the forces
of gravity are applied as horizontal

T1 = 2 ⋅ d                 forces

THE EQUATIONS USUALLY
DETERMINE FOR A SHORT
PERIOD, T (CONSERVATIVELY)
Natural period, T,
flexibility of foundation
T1 = 2 . π . √(M1/K1)   T1 = Ct . H3/4   T1 = 2 . √   d
Which modes shall be calculated?
X-direction
Y-direction
Rotation

Several periods are calculated when:
-   The sum of the swing mode masses < 90% of total mass
-   The swing form has mass > 5% of total masse
2D or 3D analyses to calculate T
required for:

• Non Regular buildings

•Buildings designed in DCM ( 2 < q < 4)

• Buildings with foundations partly on rock and deposits.

• Buildings in seismic class
Natural periods for
non-regular structures:

•   Use computer programmes (2D or 3D)

•   Calculate all required swing modes (90 %- and 5 % - rule)

•   Accurately determine the T-values

•   Test against the excemption criteria
Calculate the following :
Sd(T) = Design Spectrum

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

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

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

T > TD         Sd(T) =    ag*S*2,5/q*(TC*TD/T)
Point 3.2.2.5 (4)P
Respons Spectrum (in principle)
Udesired eccentricity (Torsion)

point 4.3.3.2.4 – Reinforcement factor δ

•   δ = 1+x/ Le

•   x = the distance of the structure in question from the mass
centre of the overall structure in the level measred at right
angles to the relevant seismic load.

•   Le = the distance between the outer strucural parts withstanding
applied loasds, measured at right angles to the direction of the
Shear force at foundation level or at the roof level of a rigid
basement

F= m*Sd(T)*λ
point 4.3.3.2.3
The distribution of shear forces on the floors of
the building.
The distribution of shear forces on the
floors of the building.

• Will also be given by a 2D or 3D
dynamic analysis
Limiting conditions
How and when do we design for earth quakes?
Low seismicity:
Condition:     - ag S = γI * agR * S < 0.1 g = 0.98 m/s2
- q ≤ 1.5

=> Simplified design rules may be used

Very low seismiscty:
Condition:     - Sd(T)< 0.05 g = 0.49 m/s2
- q ≤ 1.5

=> Do not require earth quake design
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. γ1 = 0,7)

• Light timber structures

r
• when ag*S <0,05g = 0,49 m/s²                                                          nted fo
accou
n   ’ are
• when Sd(T) < 0,05g = 0,49 m/s² with q < 1,5.                  rd esig
iples fo
ic   princ
•Very low seimicity.                     ’bas
at
in   g th
Assum
Structures with small energy dissipation, DCL:
•   1,5 ≤ q ≤ 2,0

•   Elstic analyses without accounting for nonlinearities.

•   Carry out design and sizing acc to Gjennomføre
dimensjonering iht NS-EN Steel Standard without