(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

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!)

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

Selected Mechanism at Target Drift

DESIGN BASE SHEAR

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)

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

Effect of Target Inelastic Drift

Comparison of the Design Base Shear Coefficients at Ultimate Strength Level

Comparison of Base shear-Roof drift curves of two frames

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

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

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.

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

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

4. Higher Mode Effect Accentuated by Inelastic Behavior

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

2. Maximum Interstory Drift Distributions

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

Interior column Exterior column (Lee and Goel, 2001)

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

SOME RESULTS

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

Plastic Hinge Distribution in 20-Story SMRF

Maximum Story Drift due to Selected Earthquake Records

(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