1. (PERFORMANCE-BASED PLASTIC DESIGN)  
A SEISMIC DESIGN APPROACH USING TARGET DRIFT AND YIELD MECHANISM AS PERFORMANCE OBJECTIVES
(PERFORMANCE-BASED PLASTIC DESIGN)
DESIGN BASE SHEAR & VERTICAL DISTRIBUTION
Subhash C. Goel
Sutat Leelataviwat
Bozidar Stojadinovic
Soon-Sik Lee
Prabuddha Dasgupta
Shih-Ho Chao
Department of Civil and Environmental Engineering
The University of Michigan
Ann Arbor, MI

2. CURRENT DESIGN PRACTICE
Design Base Shear
V = Ce W/R
Elastic Design/Analysis
Drift Check
Cd Δ < Δlimit
Prescribed Ductility Detailing
(Works most of the time – But not always!)

3. CONCEPT Base Shear Ve Vu = ΩoV V = Ve /R Δ CdΔ ≤ Δu
Displacement (Story Drift)

8. Selected Mechanism at Target Drift

9. DESIGN BASE SHEAR

10. Using Newmark-Hall Inelastic Spectra (Rµ-µs-T) for E-P SDOF,
For the given system,
Solution of Work-Energy Equation gives Design Base Shear
Ref: Housner (1956, 1960)

11. Ductility Reduction Factors Proposed by Newmark and Hall [1973]
Acceleration Region
Velocity, Displacement Region
Modification Factor for Energy Equation versus Period
Acceleration Region
Velocity, Displacement Region

12. Effect of Target Inelastic Drift

13. Comparison of the Design Base Shear Coefficients at Ultimate Strength Level

14. Comparison of Base shear-Roof drift curves of two frames

15. Design Lateral Force Distribution Based on Inelastic Response  
 Design Lateral Force Distribution Based on Inelastic Response

16. First-Mode Dynamic Solution of Lumped MDOF System Elastic Response
  Lateral Force Distributions in Current Building Codes :
First-Mode Dynamic Solution of Lumped MDOF System
Elastic Response
(Clough and Penzien 1993; Chopra 2000; NEHRP 2001)
IBC 2003
Close to a straight line (k =1) when the T is 0.5 second or less;
Close to a parabola (k = 2) when T period is 2.5 seconds or more

17. A New Lateral Force Distribution Based on Inelastic Response of Structures (Lee and Goel, 2001; Chao and Goel, 2005):
Lateral Force at level i
Lateral Force at Top level n
Story Shear Distribution Factor
was originally proposed as 0.5, which was revised to 0.75 based on more extensive nonlinear dynamic analyses on EBFs, CBFs, and STMFs.

18. 1. Relative Story Shear Distributions
 Justification of the New Lateral Force Distribution
1. Relative Story Shear Distributions

21. Relative Story Shear Distributions (comparison between elastic and inelastic responses):

22. 4. Higher Mode Effect Accentuated by Inelastic Behavior

23. Beams impose no restraint on joint rotations
Beams impose complete restraint on joint rotations
(Chopra, 2005)

24. 2. Maximum Interstory Drift Distributions

25. 3. Column Design Moments
Free body diagram of an exterior “column tree”

26. Interior column
Exterior column
(Lee and Goel, 2001)

27. (a) Exterior
(b) Interior
(Lee and Goel, 2001)

28. SOME RESULTS

29. Plastic Hinge Distribution in 3-Story SMRF and 9-Story SMRF

30. Plastic Hinge Distribution in 20-Story SMRF

31. Maximum Story Drift due to Selected Earthquake Records

32. (a) 1.5% Target Drift
(b) 2.0% Target Drift
(c) 2.5% Target Drift
(d) 3.0% Target Drift
Maximum Story Drifts of Four 20-Story Frames Designed with (a) 1.5% Target Drift, (b) 2.0% Target Drift, (c) 2.5% Target Drift, and (d) 3.0% Target Drift under Four Earthquakes