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Inelastic Displacement Surface Method. Tom Shantz CALTRANS- Division of Research and Innovation. Basic Approach. Uses peak displacement response of an elastic-perfectly plastic oscillator as the primary intensity measure used for record scaling and selection. F max. F y. u y. u e. u i. - PowerPoint PPT Presentation
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Inelastic Displacement Surface Method
Tom Shantz CALTRANS- Division of Research and Innovation
Basic Approach Uses peak displacement response of an elastic-perfectly plastic
oscillator as the primary intensity measure used for record scaling and selection.
uy ue ui
Fy
Fmax
Basic Approach Uses peak displacement response of an elastic-perfectly plastic
oscillator as the primary intensity measure used for record scaling and selection.
uy ue ui
Fy
Fmax
R = Fmax
Fy
ue
uy
=
ui
uy
Basic Approach Evaluate displacement surface for a record (precalculated)
0 1 2 3 4 5Periods 2
4
6
8
0
2
4
6
8
Dmaxcm
0 1 2 3 4 5Periods
Basic Approach Evaluate displacement surface for a record (precalculated)
Basic Approach Evaluate displacement surface for a record (precalculated) Define target displacement surface (will discuss details in a minute)
0 1 2 34 5
Periods 2
4
6
8
0
2
4
6
8
Dmaxcm
0 1 2 34 5
Periods
Basic Approach Evaluate displacement surface for a record (precalculated) Define target displacement surface (will discuss details in a minute) Define region for comparison
0 1 2 34 5
Periods 2
4
6
8
0
2
4
6
8
Dmaxcm
0 1 2 34 5
Periods
Basic Approach Evaluate displacement surface for a record (precalculated) Define target displacement surface (will discuss details in a minute) Define region for comparison Determine optimum scale factor
0 1 2 34 5
Periods 2
4
6
8
0
2
4
6
8
Dmaxcm
0 1 2 34 5
Periods
Basic Approach A record’s displacement surface scales uniformly with scale factor as long as the yield force of the oscillator is scaled as
well. Thus, is selected so that after scaling, the yield force is consistent with the pushover curve. ( i.e. = Dtarget / uyield ) Select records for nonlinear analysis by the quality of their fit to the target region
0 1 2 34 5
Periods 2
4
6
8
0
2
4
6
8
Dmaxcm
0 1 2 34 5
Periods
Can also impose secondary criteria such as how close the scaled record matches 2nd mode elastic displacements.
Determining Target Displacement Surface Case 1: What is the distribution of peak displacement response
given M, r, and Fy?
(M, r) San Andre
as
Determining Target Displacement Surface
Calculate the response of the oscillator for a grid of and T for each of over 1800 records of the NGA dataset.
Define the response in terms of “Normalized Inelastic Displacement Demand” (NIDD) where
NIDD(, T) j = ui, jSd, j
and Sd , j
is the median spectral displacement as estimated
using A&S97 and M , rjMotivation for normalization: elimination of (M, r) dependence
Determining Target Displacement Surface
A very convenient form is …
NIDD(, T) = uiSd =
uiSd
* SdSd
= C' Ca
The ‘ in C reflects that constant strength is imposed with the reference strength defined for Ca =1.
Determining Target Displacement Surface
Statistics on NIDD response:
Since NIDD is a function of Ca, and since Ca is influenced by earthquake event terms, a 2-step regression procedure is required determine the median.
The median Target Displacement Surface is then calculated as..
DTarget (, T) = NIDDMedian (, T) * Sd
(T) D84Target (, T) = NIDDMedian (, T) * Sd
(T) *e NIDD
Determining Target Displacement Surface
An approximate functional form looks something like…:
N ID D (T , ) = 1 .374 - 0 .787 T + 0.326 T2
- 0 .0526 T3 +0 .00365 T
4
- 0 .000142 T5 + 0 .0165
Ln(T , ) = 0 .808 - 0 .425 T + 0 .297 T2
- 0 .0912 T
3 + 0 .0128 T4 - 0 .000679 T
5
+ 0 .0336 - 0 .00231 2
0 1 2 3 4 5P e rio d (s)
0.7
0.8
0.9
1
1.1
1.2
Me
dian
NID
D
0 1 2 3 4 5Period (s)
0.6
0.64
0.68
0.72
0.76
0.8
Ln
(NID
D)
Case 2: What is the distribution of peak displacement response given M, r, Fy, and (or a specified Sa)?
Determining Target Displacement Surface
(or Sa) can easily be related to Ca. Both terms in NIDD have Ca dependence.
NIDD(, T) = C', TCa (T)
Determining Target Displacement Surface
-3 -2 -1 1 2LogCa
-3
-2
-1
1
2
LogNIDD
One can plot NIDD vs Ca (in this example for =4 and T=1s)…
Take median and from a data bin centered on the desired Ca
Determining Target Displacement Surface
-3 -2 -1 1 2LogCa
-3
-2
-1
1
2
LogNIDD
One can plot NIDD vs Ca (in this example for =4 and T=1s)…
Take median and from a data bin centered on the desired Ca
One can plot NIDD vs Ca (in this example for =4 and T=1s)…
Take median and from a data bin centered on the desired Ca
Determining Target Displacement Surface
-3 -2 -1 1 2LogCa
-3
-2
-1
1
2
LogNIDD