seismic design of conventional structures

Seismic Design of Seismic Design of Conventional StructuresConventional Structures

Prof. Dr.Prof. Dr.--Ing. Uwe E. Ing. Uwe E. DorkaDorka

Earthquake EngineeringEarthquake EngineeringProf. Dr.Prof. Dr.--Ing. Uwe E. Ing. Uwe E. DorkaDorka Stand: 11.07.2006

22

Basic Design Requirements

No Collapse Requirement:

EC 8 - 2

ultimate limit state

10 % in 50 years ⇒ return Period: 475 years

Damage Limitation Requirement:

serviceability limit state

10 % in 10 years ⇒ return Period: 95 years


33

Basic Design Requirements

EC 8 - 2

Importance Categories:

I

II

III

IV

γ1

1,4

1,2

1,0

0,8

Recommendedimportance factors


44Stahlbau Grundlagen – EinführungProf. Dr.-Ing. Uwe E. Dorka 4

UdineUdine

aagRgR= 0.275 g= 0.275 g

aagg= 0.275x1.2=0.33 g= 0.275x1.2=0.33 g

Representation of Seismic Action

Seismic Zones

Importance factor building category III

Reference peak-groundacceleration:


55

Representation of Seismic ActionClassification of Subsoil Classes

EC 8 - 3


66

Inertia Efects

Representation of Seismic Action

EC 8 - 3


77

viscously damped SDOF oscillator

( )⋅ + ⋅ + ⋅ = − ⋅ ⋅&& & &&F1m u d u k u m y tm( )⋅ + ⋅ + ⋅ = − ⋅&& & &&Fm u d u k u m y t

( )+ ⋅ω⋅ ς ⋅ + ω ⋅ = −&& & &&2Fu 2 u u y t

where: Eigenfrequency:

Damping ratio:

ω =km

ς =⋅ ⋅ωd

2 m

-solving this equation for various ω and ζ, butonly for one specific accelerogramm

-the maximum absolute acceleration of this solution gives us the abzissa for the following diagramm

From Petersen (2)

From Meskouris (5)

Representation of Seismic ActionElastic „Responce“ Spectra


88

Representation of Seismic ActionHorizontal Elastic Design Spectra

EC 8 - 3

( ) ( ) ≤ ≤ = ⋅ ⋅ ⋅ + ⋅ η ⋅ −

B e g

B

T0 T T : S T a k S 1 2,5 1T

( )≤ ≤ = ⋅ ⋅ ⋅ η ⋅B C e gT T T : S T a k S 2,5

( ) ≤ ≤ = ⋅ ⋅ ⋅ η ⋅ C

c D e gTT T T : S T a k S 2,5T

( ) ⋅ ≤ ≤ = ⋅ ⋅ ⋅ η ⋅ C D

D e g 2T TT T 4sec : S T a k S 2,5

T


99

Representation of Seismic ActionVertical Elastic Design Spectra

( ) ( ) ≤ ≤ = ⋅ + ⋅ η ⋅ −

B ve v,g

B

T0 T T : S T a k 1 3,0 1T

( )≤ ≤ = ⋅ ⋅ η ⋅B C ve v,gT T T : S T a k 3,0

( ) ≤ ≤ = ⋅ ⋅ η ⋅ ⋅ C

c D ve v,gTT T T : S T a k 3,0T

( ) ⋅ ≤ ≤ = ⋅ ⋅ η ⋅ ⋅ C D

D ve v,g 2T TT T 4sec : S T a k 3,0

T

Vertical Elastic Spectrum

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

0,0 0,5 1,0 1,5

T (s)

k*et

a*av

g/ag

EC 8 - 3


1010

Time-History RepresentationRepresentation of Seismic Action

General: • representation of seismic motion in terms of ground acceleration time-history isallowed

Artificial accelerograms:

• Artfificial accelerograms shall be generated to match the elastic response spectragiven by EC 8

Recorded or simulated accelerograms:

• The use of recorded or simulated accelerograms is allowed if the used samples areadequately qualified with regard to the seismogenic features of the sources and to the soil conditions for the site of question

• for spatial models the same accelerogram should not be used simultaneously alongboth horizontal directions

• the description of seismic action may be made by using artificialaccelerograms

• the number of accelerograms to be used shall be such as to give a stable statisticmeasure of the response quantities of interest

• the duration of the generated accelerogram shall be consistent with the relevant features of the seismic event underlying the establishment of ag

EC 8 - 3


1111

Combination With Other ActionsCombination Coefficients for Variable Actions

EC 8 - 4


1212

Structural Requirements

• masses regular

• stiffness irregular• stiffness regular

• masses irregular

Regularity


1313

Regularity

EC 8 - 4

Structural RequirementsRegularity


1414z

y

x

M

M

Müg,z(t)üg,y(t)

Displacements in z-direction

Displacements in y-directioncoupled with torsional effects

Structural RequirementsTorsional Effects


1515

• The accidental torsional effects may be accounted for by multiplying the action effectsresulting in the individual load resisting elements from above with the following factor:

δ = + ⋅e

x1 0,6L

y

z

Stiffness axis

mlmk

m1

Direction of seismic action Considering mass m1

Le

x

Structural RequirementsAccidental Torsional Effects


1616

Definition of the q – Faktor

ü

ulinear equivalent

non-linear

üd

ud

q·üd

q·ud

Linear Methods of Analysis

to account for non-linear dissipative effects


1717

Linear Methods of Analysisq-Factors According to EC-8


1818

Linear Methods of AnalysisNon-Linear Design Spectrum

EC 8 - 3

( )

ββ =

dS T : ordinate of the design spectrumq : behaviour factor

: lower bound factor for the spectrumrecommended value : 0,2


1919

Linear Methods of AnalysisLateral Force Method

General: • structure could be analyse by a planar model for both horizontal direction• higher modes do not have a significant influence on the structural response.

These requirements deemed to be satisfied in buildings which fulfil both of the following conditions

⋅≤

c1

4 TT

2,0 sec1where T is the highest natural Period

for oneof the both main direction

Base shear force:The seismic base shear force Fb for each maindirection is determined as follows ( )= ⋅ ⋅ λb d 1F S T m

( )

λλ = ≤ ⋅ λ =

d 1 1

1

1 C

S T ordinate of the chosen design spectrum at period TT highest natural Period of the structure in the direction consideredm total mass of the building in regard to other actions

correction factor0,85 if T 2 T , or 1,0 otherwise


2020

Linear Methods of AnalysisLateral Force Method

Distribution of the horizontal seismic forces:• The seismic action effects shall be determined by

applying horizontal forces Fi to all storey masses mi

⋅= ⋅

⋅∑i i

i bj j

s mF Fs m

m1

m2

s1

s2

2 22 b

1 1 2 2

s mF Fs m s m

⋅= ⋅

⋅ + ⋅

1 11 b

1 1 2 2

s mF Fs m s m

⋅= ⋅

⋅ + ⋅

h2

h1

Mode 1distribution

Simplified analysis of 1st mode period T1:For structures lower than 40 m: • Ct = 0,085 for steel frames

• Ct = 0,075 for rc- frames and excentricaly braced steel frames• Ct = 0,05 for all other structures


2121

Linear Methods of AnalysisResponse Spectrum Analysis

General: • the structures have to comply with the criteria for regularity in plan• in some cases the structure shall be analysed using a spatial model• the response of all modes of vibration contributing significantly to the global

response shall be taken into accountdemonstrating that the sum of the effektive modal masses for the modestaken into account amounts to at least 90% of total mass of the structuredemonstrating that all modes with effective modal masses greater than 5% of the total mass are considered

Combination of modal responses:• the response in two vibration modes i and j may be considered as independent of

each other, if their Periods Ti and Tj satisfy the following condition: ≤ ⋅i jT 0,9 T

• whenever all relevant modal responses may be regardedas independent of each other, the maximum value of theglobal response may be taken as:

=

= ∑n

2j

j 1S S


2222

Non-Linear Methods of Analysis

General: • a nonlinear static analysis under constant gravity loads and monotonically increasinghorizontal loads

• it is possible to analyse the structure in two planar models

• EC 8 gives two vertical distributions of lateral forces:1. a ‚uniform‘ pattern with lateral forces that a proportional to masses2. a ‚modal‘ pattern, proportional to lateral forces consisting with the

lateral force distribution determined in elastic analysis

Static Push-Over Analysis

Lateral loads:


2323

Non-Linear Methods of AnalysisStatic Push-Over Analysis - Example

q=60 kN/m

q=60 kN/m

q=60 kN/m

q=60 kN/m

all Columns HEB 300, S 235

all Beams HEA 320, S 235

3500

3500

3500

3500

6000

q=60 kN/m

q=60 kN/m

q=60 kN/m

q=60 kN/m

nodal masses M=18 t

=1T 1,2sec

1f 1,0=

2f 0,82362=

3f 0,54236=

4f 0,21149=


2424

• Soil A• Response Spectrum type 1• ag~0,2g=1,962 m/s2

• η=1,0• k=1,0• m~150t

base shear force: Fb=245 kN

vertical Distribution derived with‚lateral force method‘

1F 95,14kN=

2F 78,36kN=

3F 51,60kN=

4F 20,12 kN=

pushover analysis- monotonically increasing Fi

- constant q

d

q=60 kN/m

q=60 kN/m

q=60 kN/m

q=60 kN/m

q=60 kN/m

q=60 kN/m

Fb=245 kN

Non-Linear Methods of AnalysisStatic Push-Over Analysis - Example


2525

Non-Linear Methods of AnalysisDesign Limits

CAPACITY CURVE

0

50

100

150

200

250

300

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

DISPLACEMENT ON TOP [m]

BA

SE S

HEA

R F

OR

CE

[kN

]

plastic mechanism

as limit displacement

*md

=*yd 0,124

*yF

*mE


2626

non-linear cyclic behavior of frames

From Müller, Keintzel (2)Failure in soft storey

Non-Linear Methods of AnalysisDesign Limits

w

Fplastic stability

limit dipl.

elasto-plastic capacity


2727

elastic energy ~ plastic energy

= ⋅ ⋅ π &&

2Tu u2

Assuming an elastic system, therelationship between accelerationsand displacements is given by:

Non-Linear Methods of AnalysisStatic Push-Over Analysis - Verification

control displacement

limit displacement

elastic displ. ~ plastic displ.

control displacement


2828

• Non-linear structural models under a number of (generated) esarthquakes

• using less than 7, peak non-linear displacements must be used for design

• with 7 or more, average displacements can be used

Non-Linear Methods of AnalysisTime History

Design limits may be:

• ultimate deformation capacity of a member (e.g. rotational capacity of a plastic hinge

• overall plastic instability due to vertical loads


2929

References

(1) Wakabayashi –Design of EarthquakeDesign of Earthquake--Resistant BuildingsResistant BuildingsMcGraw-Hill Book Company

(2) Müller, Keintzel –ErdbebensicherungErdbebensicherung von von HochbautenHochbautenVerlag Ernst & Sohn

(3) Petersen –DynamikDynamik derder BaukonstruktionenBaukonstruktionenVieweg

(4) Clough, Penzien –Dynamics of StructuresDynamics of StructuresMcGraw-Hill

(5) Chopra –Dynamics of StructuresDynamics of StructuresPrentice Hall

(6) Meskouris–BaudynamikBaudynamikErnst & Sohn

seismic design of conventional structures

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