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Inelastic Displacement Surface Method

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.

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Inelastic Displacement Surface Method

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  1. Inelastic Displacement Surface Method Tom Shantz CALTRANS- Division of Research and Innovation

  2. Basic Approach • Uses peak displacement response of an elastic-perfectly plastic oscillator as the primary intensity measure used for record scaling and selection. Fmax Fy uy ue ui

  3. Fmax ue Fy uy Basic Approach • Uses peak displacement response of an elastic-perfectly plastic oscillator as the primary intensity measure used for record scaling and selection. R = = Fmax ui m= Fy uy uy ue ui

  4. Basic Approach • Evaluate displacement surface for a record (precalculated)

  5. Basic Approach • Evaluate displacement surface for a record (precalculated)

  6. Basic Approach • Evaluate displacement surface for a record (precalculated) • Define target displacement surface (will discuss details in a minute)

  7. Basic Approach • Evaluate displacement surface for a record (precalculated) • Define target displacement surface (will discuss details in a minute) • Define region for comparison

  8. 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

  9. 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, m is selected so that after scaling, the yield force is consistent with the pushover curve. ( i.e. m = Dtarget / uyield ) • Select records for nonlinear analysis by the quality of their fit to the target region • Can also impose secondary criteria such as how close the scaled record matches 2nd mode elastic displacements.

  10. Determining Target Displacement Surface • Case 1: What is the distribution of peak displacement response given M, r, and Fy? San Andreas (M, r)

  11. Determining Target Displacement Surface • Calculate the response of the oscillator for a grid of m and T for each of over 1800 records of the NGA dataset. • Define the response in terms of “Normalized Inelastic Displacement Demand” (NIDD) where Motivation for normalization: elimination of (M, r) dependence

  12. Determining Target Displacement Surface • A very convenient form is … The ‘ in Cm reflects that constant strength is imposed with the reference strength defined for Ca =1.

  13. 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..

  14. Determining Target Displacement Surface • An approximate functional form looks something like…:

  15. Determining Target Displacement Surface • Case 2: What is the distribution of peak displacement response given M, r, Fy, ande(or a specified Sa)? e(or Sa) can easily be related to Ca. Both terms in NIDD have Ca dependence.

  16. Determining Target Displacement Surface • One can plot NIDD vs Ca (in this example for m=4 and T=1s)… • Take median and s from a data bin centered on the desired Ca

  17. Determining Target Displacement Surface • One can plot NIDD vs Ca (in this example for m=4 and T=1s)… • Take median and s from a data bin centered on the desired Ca

  18. Determining Target Displacement Surface • One can plot NIDD vs Ca (in this example for m=4 and T=1s)… • Take median and s from a data bin centered on the desired Ca

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