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. uyuy ueue uiui FyFy F max

3. Basic Approach Uses peak displacement response of an elastic-perfectly plastic oscillator as the primary intensity measure used for record scaling and selection. uyuy ueue uiui FyFy F max R = F max FyFy ueue uyuy =  uiui uyuy

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,  is selected so that after scaling, the yield force is consistent with the pushover curve. ( i.e.  = D target / u yield ) 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 2 nd mode elastic displacements.

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

11. 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 Motivation for normalization: elimination of (M, r) dependence

12. Determining Target Displacement Surface A very convenient form is … The ‘ in C  reflects that constant strength is imposed with the reference strength defined for C a =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. Case 2: What is the distribution of peak displacement response given M, r, F y, and  (or a specified Sa)? Determining Target Displacement Surface  (or S a ) can easily be related to C a. Both terms in NIDD have C a dependence.

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

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

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