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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
Nonlinear behavior Nonlinear behavior
:
)()(
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
Nonlinear behavior Nonlinear behavior
Multi degree of freedom
Structural over strength
11 FMSa =.
Nonlinear behavior Nonlinear behavior
:
)()(
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