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Methods for Evaluating Inelastic Displacement Surfaces in Structural Analysis

This document presents a comprehensive approach for assessing inelastic displacement surfaces using the peak displacement response of an elastic-perfectly plastic oscillator as a primary intensity measure. It outlines methods for scaling records, defining target displacement surfaces, and selecting appropriate records for nonlinear analysis based on their fit within defined regions. The study calculates the Normalized Inelastic Displacement Demand (NIDD) while eliminating dependence on magnitude and distance by employing a two-step regression procedure for median calculation. This work serves as a practical guideline for seismic performance evaluation in engineering.

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Methods for Evaluating Inelastic Displacement Surfaces in Structural Analysis

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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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