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Dynamic Response of Single Degree of Freedom Systems (SDOF) toDynamic Response of Single-Degree of Freedom Systems (SDOF) to

Ground Motion

Dynamic of structure Dynamic load

Degree of freedom

) (

- -

--

kuf =

)(ff &

--

kufs),( uuff ss &=

Damping Friction Viscous Building

)

ucf &= ucfD =

(Response) ): ( ( )

Displacement Velocity Acceleration

.

. .

Classic Duhamel Integral Numerical techniques St t State space

)

.

Elastic Response Spectra )(

.

Elastic Response Spectra

:

Spectral pseudo - velocity - Spectral pseudo velocity

Strain energy Strain energy

- Spectral pseudo acceleration

ADRS -

Elastic design spectra

.

) ( -- .

FEMA356 -

Newmark-Hall Elastic Design Spectrum(1982)

FEMA-356 Elastic Design Spectrum

:

1) 2) 3)4) 4)

Source factors

a. Inter-Plate Earthquakes b. Shallow inland Earthquakes c. Intra-Plate Earthquakes

Directivity effect

Travel path effects :

:

:

Local site effects :

basin effects -- --

Topographical effects --

-- --

Soil-structure interaction - :

:

)( --

) radiation(

) ( --

hysteresis

hysteresis . . )hysteresis( :

. . )hysteresis( :

Structural stiffness

Yield Displacement

Structural material

Structural system

Structural material

Connection configuration

elasto-plastic bilinear

curvilinear Ramberg-Osgood

elastoplastic bilinear trilinear trilinear multilinear RambergOsgood degrading stiffness pinched loops slackness developing

: .

Reduction factor

Nonlinear behavior Nonlinear behavior

Multi degree of freedom

Structural over strength


:

)()(

iy

y

non

e

FF

VVR

=

===

1

)( iynon FV

-

-

)exp()(

TR 161 +=

R R

F

yMDOF

ySDOFMDOF

SDOF

MDOFM F

FR

RRRR ===

121501 += )]ln(..[ TRM )]([ M

R R

SSSEM RRRRR ...=

SER

SSR

: .

Reduction factor


Multi degree of freedom

Structural over strength

11 FMSa =.


:

)()(

iy

y

non

e

FF

VVR

=

===

1

)( iynon FV

-

)exp()( TR 161 +=

- )exp()(

R 1+

) R m Rm m . m

Rm .

R R

F

yMDOF

ySDOFMDOF

SDOF

MDOFM F

FR

RRRR ===

121501 += )]ln(..[ TRM )]([ M

R R

SSSEM

RRR

RRRRR ...=

SM RRR .. =

SER

SSR

) ( SR

(Redundancy)

(T) ) )T

.

Ct 0.08 0.07............. 0.05

d 2

=dxmy

dxdx

ydEIT

2

2

2

2)(

(T)

-

(T) T

.

Ct 0.08 0.07............. 0.05

-

dxdxydEI

T2

2

2)(

=

dxmydxT

22

-

equivalent-static force analysis d i l i dynamic analysis

o o o o

Low dissipative structural behaviour

dissipative structural behaviour

Buckling Connection failure

Load

Deformation

Elasticbehaviour

Load

Deformation

%20>mU%51.>yU

%20>yu ff

Load

Deformation

PlastificationPlastification

%20>mU%51.>yU

%20>yu ff

Plastification Load

Deformation

Plastification

Plastificationdissipatedenergy

%20>mU%51.>yU

%20>yu ff

=

.

Bending (Frame) Normal Force (Bracings) Shear (ecc. Bracings)

MN

QM

NQ

) ( .

.

.

:

-1

-2

LRFD - . LRFD

.

.

1,2

: LRFD -1-2 -3

.

-1.

-1.

. -2

-3 .

.

: -1 -2 -3 -4

Primary lateral load -1 resisting systemSecondary lateral load -2 resisting system

demand .

.

. .

:

)1.

)2 .

)3. 75 + -1 -2) + ( -3

) ( + -1

-) . ( ) ( . . .

. - UBC 0.7R R demand . . 0.4R

. -ERPDL .. 0850 +

: 2 o.4R

. ancher bolt --. --

-1. -2. -3. -4. -5 P-Delta -6. Overturning, uplift -7. -8. -9

. Anchor Bolt -15. -11 -12

.

) ( -2

)1) ( ) 2 ) 3 ) 4 ) 5

. .

. . ) 6

. ,Overturning ) 7 uplift .. ) 8 ) 9

. ) 10

P

P

:

) ( -1

: ) (

. --

. --

) ( --

-2

. .

H/B . .

H/B >5 H/B

-3

.

) (

= + +

dMM 21 +

. ) (

: :

. )( .

+

. H/B

+ . e .

.

. . )(

. .

( )

)(

( ) . )(.

)( . . .

. A

.

23 )10( 2 .

2 . R . .

,(b) (a)

.

AB B CD D

. .Coupling Beam ..

B A B,A.

SMF

- -

: )SEAOC( - 1 -2

-3

200 60 1999 - 7 : : 7.

.

. . %33 03/0

.

:

. 03/0 .

:2

. 03/0 - 1. -2

. - 3. - 4

1 /3 . 03/0-1. - 2. - 3 -4

forced control.

Panel zone

.

.

(M2+M1) .

32

2

1

1

950950V

dM

dMV

bbpz += ..

wcycb

p

bpz AFd

Md

MMV 55021 .

) . tpz

90zz

pzwdt +

: twc < tpz

pzdpwc ttt >+2

.

- :

)AISC LAFD (

=

++

etcSBF.

MRFE

E

-0.9D.L )

0.5LL.2D.L )

0

0

0

252

32

11

1>

*

*

pb

pc

MM

:

Mv : (

)

= )(*g

ucycpcpc A

PFZM

aLM

aVM

MZFRM

pbpv

vpbybypb

==

+=2

11

)(

).(*

c

g

ucyepc

pc hAPFZ

V)(

=2

. (d/2 (a -d/3 - (b)2 .. -. -. -displacement Forced control - control

:

. -

. g

uc

AP

120cm .

.

.

: 3

04/0 -1 04/0 . (

).

04/0 % 80 -2 % 20 04/0 (. ) .

-3

. ( 04/0 . )

LZFR

VV pbybyLbp +=

).()(

112

. - Bone Dog -

. . -

) ( :

1>

*

*

pb

pc

MM

ycg

uc FAP 30. j

u

vj

u

v

RR

RR )(.)(

)Intermediate(

. 02/0

)Ordinary(

.

. -. SMF .IMF PR FR -

)FR (: -

pby MR11.min .

(Back Plate)

. ) (

: )1 )2

(CBF)

. .

Force Displacement Controlled Controlled .

. Dual System

- -7 -8 -

Members) (Displacement Control.

.

: - - Plate Gusset - Gusset Plate - -

: - -

:

(Kl/r) + ) Kl/r (

. .

:

. -- Gusset --

( gyy AFR

: .

t2 --

. Gusset --

:

.

SCBF

. - -

.

: -1 -2 -3 -4 -5

. 8 7 --. 8 7 --. --

. 7 8 -- Fybftbf 0.02 .

.

EBF

)1

--- ---

)2 --- ---

. .

EBF . ) (

B A :: Vp e

p

p

wfyp

yP

VM

e

ttdFVZFM

2

260

0 =

=

=

)(.

. e>e0 e

Mp Vp

.

=

=

> )

)

21

1181

150

y

uppa

y

uppa

y

u

PPVV

PPMM

PP

(

(.

.

: e0 Vpa Mpa

p

p

y

w

VM

AAe

61501510

.)..( =

. )1

>

>

),.max( cmtttorbb

ws

wfs

1750

22

0900600302938565

.,.,.,, ==

=

forC

dtCa

s

ws

. )2

: )3

p

p

p

p

p

p

fp

p

p

p

wsp

p

VM

e

VM

eV

M

baV

Me

VM

dtCaVM

e

54

21562

3

516261

2

561

1

>

): (EBF

.

: RyVn

),(eM

VMinV ppn2

=

.

.

) (

EBF

) (

e Proportioning .

. 0

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