Earth quake forces 2009.06.04

Document Sample
Earth quake forces 2009.06.04 Powered By Docstoc
					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
–   Load factors and combinations
–   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).
   Let’s start with the ’basics’
• 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.




       Load factors for permanent variable loads:
       (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
    = dead load + permanent loads + % of live loads.

•    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




                                         Lead-rubber bearings
   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 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.
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
    seismic load in question.
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
     additional requirements. (Only if q≤1,5)

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

DCL is a straight forward first attemt to design for earthquakes.