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**Tall Buildings Initiative Summary of Case Studies**

Farzin Zareian University of California, Irvine Quake Summit 2010 San Francisco, Oct 8, 2010

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Collaborators Jack Moehle, Yousef Bozorgnia. UCB John Wallace, Zeynep Tuna. UCLA Tony Yang. UBC Pierson Jones. UCI Nilesh Shome. RMS Paul Somerville. URS

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Sponsors California Seismic Safety Commission California Office of Emergency Services (CalEMA) FEMA City of Los Angeles

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Objective and Scope Assess the performance of designed tall buildings using latest technology Development of earthquake ground motions for design studies. Development of building analytical models Conduct a large number of earthquake simulations of tall buildings to develop statistics of engineering demand parameters Perform loss estimation for designed buildings Few side studies: simulated vs recorded motions, effect of vertical component of ground motion, etc.

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**1.5Km, Puente Hills 7.3Km, Hollywood 8.8Km, Raymond**

Sierra Madre (San Fernando) San Andreas Sierra Madre (Cucamonga) Verdugo Raymond Santa Monica Hollywood 1.5Km, Puente Hills 7.3Km, Hollywood 8.8Km, Raymond Elsinore (Whittier) Elsinore (Chino) Newport-Inglewood-Rose Canyon 11.5Km, Santa Monica 24.5Km, Elsinore 40.0Km, Sierra Madre 56Km, San Andreas

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**Challenges in Ground Motion Selection**

Significance of several modes of vibration in response of the building. Similar ground motions for all structures. Five hazard levels needs to be looked at: (SLE- 25, SLE-43, DBE, MCE, OVE) A large number of motions are required (we used 15) to have a reasonable estimate of the dispersion in EDP.

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**Record Selection and Scaling**

Used a subset of NGA database (no aftershocks & etc.) Only two recordings from any single event was selected No restriction on Magnitude Rmin&Rmax at 0.0 and Km Min and Max shear wave velocity = and m/s Low pass filter cutoff frequency of the selected motions are less than 0.1

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**Record Selection and Scaling**

Maximum acceptable scale factor = 5.0 The scale factor, by which the smallest weighted error between the target spectrum and the geometric mean spectrum of a single recording is acquired, is computed. Records are matched between Tmin&Tmax at 0.5 & 10.0 sec. Largest T = 6.47 sec. (Bldg. IIIB) X1.5 = 9.7 sec. Smallest T = 4.28 sec. (Bldg IIB) X0.2 = 0.86 sec.

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**Record Selection and Scaling**

Maximum acceptable scale factor = 5.0 The scale factor, by which the smallest weighted error between the target spectrum and the geometric mean spectrum of a single recording is acquired, is computed. Records are matched between Tmin&Tmax at 0.5 & 10.0 sec. Uniform Error Weight Variable 26% % % 10% % % 0.5 3.0 7.0 Period

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**Response Spectra SLE25 (25 year)**

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**Response Spectra SLE43 (43 year)**

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**Response Spectra DBE (475 year)**

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**Response Spectra MCE (2475 year)**

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**Response Spectra OVE (4975 year)**

7 unscaled pairs are from simulated motions (URS/SCEC)

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**Response Spectra OVE (4975 year)**

Rec Sim Med Target Sa(T) Period

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**Building Design and Modeling**

42-story reinforced concrete core wall 42-story reinforced concrete dual system 40-story steel special moment-frame Three Building Systems After: Zeynep Tuna

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**Building Design and Modeling**

Building 1A (Code design) Building 1B (PBEE design) Building 1C (PBEE+ design) Designed using IBC 2006. Designed using 2008 LATBSDC procedure. Designed using PEER TBI draft guideline. Building 1A (Code design) Building 1B (PBEE design) Building 1C (PBEE+ design) Designed using IBC 2006. Designed using 2008 LATBSDC procedure. Designed using PEER TBI guideline. All provisions were followed except the height limit. All provisions were followed. Except: 1) Vmin was waived. 2) SLE was checked using 25-yr EQ (w z = 2.5%) instead of 43-yr EQ (w z = 5%). No more than 20% of the elements are allowed to reach 150% of the code specified capacity. Similar to 1B design Except: 1) SLE was check 43-yr EQ (w z = 2.5%). 2) All ductile elements such as the coupling beams and flexural yielding of the concrete walls are allowed to reach 150% of the code specified capacity. Performance-based design guideline for tall buildings After: Tony Yang

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**42-Story Concrete Core Wall**

General Modeling Assumptions 3D nonlinear dynamic finite element model (Perform3D). Ignored the gravity system. Basement walls below grade were modeled using elastic shear wall elements (Eeff = 0.8 E) Slabs below grade were modeled using elastic shear shell element (Eeff = 0.25 E)

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**42-Story Concrete Core Wall**

Shear wall flexural behavior: Nonlinear fiber wall element with expected material property. After: Tony Yang

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**42-Story Concrete Core Wall**

Building Design Comparison 1A: Code 1B: PBEE 1C: PBEE+ 24” 24” 28” 28” 32” 32” Wall: Strong Stronger Strongest Coupling beam: Stronger Stronger Strong T1EW = 5.2 sec T1EW = 4.8 sec T1EW = 4.6 sec 1st mode Period: T1NS = 4.0 sec T1NS = 3.6 sec T1NS = 3.5 sec After: Tony Yang

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**42-Story Concrete Core Wall**

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**42-Story Concrete Core Wall**

Structural design: Wall thickness: Wall vertical reinforcement: Coupling beam reinforcement: Structural period: Structural response: Wall stress safety index: Coupling beam demand: Inter-story drift and wall edge strain: 1A < 1B < 1C 1A < 1B < 1C 1C < 1A ~ 1B 1C < 1B < 1A 1B < 1A < 1C 1A < 1B < 1C 1C < 1B < 1A After: Tony Yang

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**Building Design and Modeling**

42-story reinforced concrete core wall 42-story reinforced concrete dual system 40-story steel special moment-frame Three Building Systems After: Zeynep Tuna

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**42-Story Concrete Dual System**

General Modeling Assumptions 3D nonlinear dynamic finite element model (Perform3D). Ignored the gravity system. Basement walls below grade were modeled using elastic shear wall elements (Eeff = 0.8 E) Slabs below grade were modeled using elastic shear shell element (Eeff = 0.25 E)

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**42-Story Concrete Dual System**

General Modeling Assumptions Rigid end zone Beam M P Axial Force Moment Strength EIeff=0.7*EIg M θ Column Effective Stiffness Nonlinear Rotation Hinges The moment frame columns are defined as elastic column elements with plastic hinges and rigid end zones at each end, as summarized in Figure 3-8. The elastic portion of the column is modeled with the cross-section dimensions and the stiffness modification factors of EIeff= 0.7*EIg (flexural), GA=1.0*GAg (shear). To define a column plastic hinge, a moment-axial capacity interaction curve is calculated using the expected material properties of column. The backbone curve is elastic-perfectly plastic, neglecting strength loss and cyclic degradation.

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**42-Story Concrete Dual System**

Building Design Comparison 2A: Code 2B: PBEE 1C: PBEE+ Columns: Columns: 16” 18” 36 X 36 36 X 36 18” 42 X 42 42 X 42 24” 24” 46 X 46 46 X 46 Wall: Strongest Strong Coupling beam: Strong Strong T1EW = 4.5 sec T1EW = 4.3 sec 1st mode Period: T1NS = 4.0 sec T1NS = 3.9sec

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**42-Story Concrete Dual System**

Building 2A – Inter-story drifts in H1 direction

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**42-Story Concrete Dual System**

Building 2B – Inter-story drifts in H1 direction

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**42-Story Concrete Dual System**

Inter-story drifts in H1 direction

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**Building 2A –Peak Floor Acc. in H1 direction**

42-Story Concrete Dual System Building 2A –Peak Floor Acc. in H1 direction Building 2A – Peak Floor Accelerations in H1

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**Building 2B –Peak Floor Acc. in H1 direction**

42-Story Concrete Dual System Building 2B –Peak Floor Acc. in H1 direction Building 2B – Peak Floor Accelerations in H1 Structural and Earthquake Engineering

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**42-Story Concrete Dual System Summary of findings**

Overall behaviors of the two building designs are quite similar. Median inter-story drift ratios (max ≈ 2%), median core wall strains (max ≈ tension; compression), median coupling beam rotations (max ≈ 0.02 rad) are all well below established limits. Wall shear stresses and strains are slightly higher in the code-based design. Column axial forces in the code-based design are twice as high as those in the PBD. Wall design for shear appears conservative. (Requires further study)

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**42-Story Concrete Dual System Summary of findings**

Overall behaviors of the two building designs are quite similar. Median inter-story drift ratios (max ≈ 2%) are all well below established limits. Wall shear stresses and strains are slightly higher in the code-based design. Column axial forces in the code-based design are twice as high as those in the PBD.

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**Building Design and Modeling**

42-story reinforced concrete core wall 42-story reinforced concrete dual system 40-story steel special moment-frame Three Building Systems After: Zeynep Tuna

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**40-Story Buckling Restrained B.F.**

General View Bldg. 3A Bldg. 3B Bldg. 3C

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**40-Story Buckling Restrained B.F.**

General Modeling Assumptions PERFORM3D (version 4.03) structural analysis software by Computers and Structures Inc. was used for the nonlinear time history analysis. The only nonlinear element employed in the model is the Buckling Restrained Brace element. (Ry = 1.1, ω = 1.25, and β = 1.1.) The brace components in the model have a maximum deformation capacity of (20εy) Gusset plate will have full ductility capacity. No cyclic deterioration was modeled

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**40-Story Buckling Restrained B.F.**

General Modeling Assumptions Rigid panel zone BRBF “brace” element, nonlinear. Connections modeled as pins. BRBF “stiff endzone” 30% length linear elastic bar Elastic Column element, equivalent steel cross section used (axial, torsional, and bending stiffness modified to account for concrete) Elastic Beam Element with pinned connections to columns

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**40-Story Buckling Restrained B.F.**

Building Design Comparison Bldg. 3A Bldg. 3C 300K-500K 501K-800K 801K-1200K KEY: BRB strength [Kips] Bldg. 3B NOTE: GRID LINE 2&7 N-S DIRECTION T1NS = 5.3sec T1NS = 6.5 sec T1NS= 5.7 sec T1EW = 3.8 sec T1EW= 4.5 sec T1EW = 4.2 sec

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**Building 3A MAXIMUM IDR N-S E-W 4975 (years) Return Period OVE MCE DBE**

median %16th and %84th Individual earthquake Building 3A 4975 (years) Return Period OVE MCE DBE SLE43 SLE25 GM set 2475 (years) 475 (years) 43 (years) 25 (years)

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**Building 3B MAXIMUM IDR 4975 (years) Return Period OVE MCE DBE SLE43**

median Individual earthquake 4975 (years) Return Period OVE MCE DBE SLE43 SLE25 GM set 2475 (years) 475 (years) 43 (years) 25 (years) %16th and %84th N-S E-W Building 3B

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**Building 3C MAXIMUM IDR 4975 (years) Return Period OVE MCE DBE SLE43**

median Individual earthquake 4975 (years) Return Period OVE MCE DBE SLE43 SLE25 GM set 2475 (years) 475 (years) 43 (years) 25 (years) %16th and %84th N-S E-W Building 3C

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**MAXIMUM ACCELERATION [g]**

median Individual earthquake MAXIMUM ACCELERATION [g] 4975 (years) Return Period OVE MCE DBE SLE43 SLE25 GM set 2475 (years) 475 (years) 43 (years) 25 (years) %16th and %84th N-S E-W Building III–A

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**MAXIMUM ACCELERATION [g]**

median Individual earthquake MAXIMUM ACCELERATION [g] 4975 (years) Return Period OVE MCE DBE SLE43 SLE25 GM set 2475 (years) 475 (years) 43 (years) 25 (years) %16th and %84th N-S E-W Building III–B

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**MAXIMUM ACCELERATION [g]**

median Individual earthquake MAXIMUM ACCELERATION [g] 4975 (years) Return Period OVE MCE DBE SLE43 SLE25 GM set 2475 (years) 475 (years) 43 (years) 25 (years) %16th and %84th N-S E-W Building III–C

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**%Exceedance Of 3% Drift Ratio**

40-Story Buckling Restrained B.F. %Exceedance Of 3% Drift Ratio 25% 20% 15% 10% 5% 0% Safe maximum IDR considered to be IDR=.03 There were no component failures for the BRBF lateral load system $249/SF $256/SF $245/SF OVE MCE DBE SLE43 SLE25 Building 3C did not exceed the safe IDR in any of the ground motions, was considered to perform the best. Building 3A generally performed better than the performance based design (Building 3B)

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**40-Story Buckling Restrained B.F. Summary of findings**

Behavior of Building 3C is different from Buildings 3A and 3B (different structural system) Stiffer building (3A) observes larger acceleration and smaller deformation compared to other two buildings. No collapse was indicated Building 3B appeared to be the one with higher probability of exceeding the drift limit of 3% in MCE and OVE hazard levels. Building 3A exceeded the limit only at the OVE level.

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**Comparison of Results for Simulated and Recorded Motions in OVE set for BRBF40-CBD**

direction h1 target response spectrum (4975 yr) recorded ground motion - median recorded ground motion - individual simulated ground motion - median simulated ground motion - individual T1 * T2 * T3 * T4 * direction h2 Key *The periods and mode shapes correspond to deformation parallel to the direction of analysis. h2 h1 A detailed comparison of the results due to the simulated and recorded motions in the OVE set.The results are divided into component directions with h1 on the right and h2 on the left. The uppermost plots show the response spectra for the OVE set and the 4 highest periods of the structure being analyzed. These periods are for modes of deformation along the h1 or h2 axis of the building as specified. The two central plots show the mode shapes and the mode drifts (normalized to their maximum values) which correspond to the periods. The lower plots show the max. IDR on the left and the res. IDR on the right. Results for recorded motions are shown in dashed red lines and simulated ones are shown in solid blue lines. Thin, light lines indicate individual earthquake results while the thick, heavy lines indicate the median values.

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**A.) B.) Comparison of IDR time histories simulated vs recorded:**

How was the IDR envelope developed? A.) An example of typical IDR time histories for the BRBF40-CBD structure in the h2 direction.The three-dimensional plots (on the left hand side of the figures) show time and IDR on the two horizontal axes and story number on the vertical axis. Time histories for the individual stories are stacked from the bottom, with the 1st, 10th, 20th, 30th, and 40th stories shown in black and all other stories shown in grey. The Instances where maxima occur are emphasized. Blue circles indicate the maximum in each stories’ time history and the entire drift profile at that instant is shown in pink. The res. IDR, representative of the permanent strain that remains in the braces of a story, is shown at the end of the time history with a green profile. Keys (on the right side of the figures) show a comparison of the response spectra and IDR plots. For the simulated motion, the earthquake under consideration is shown in dark blue and the simulated set, including the median, is shown in light blue. For the recorded motion, the earthquake under consideration is shown in dark red and the rest of the recorded set, including the median, is shown in light red. A.) simulated motion: notice the higher drift demands in stories 25-40 B.) recordedmotion: notice the higher drift demands in stories 1-20 B.)

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**Combination of drift demand due to the two highest modes of vibration:**

Mode combinations at peak IDR demand for T1 and T2 Key h1 simulated match, a = -1 h1 recorded match, a = -0.5 h2 simulated match, a = 1 h2 recorded match, a = -1 direction h1 direction h2 Key target response spectrum (4975 yr) recorded ground motion - median recorded ground motion - individual simulated ground motion - median simulated ground motion - individual T1 * T2 * T3 * T4 * Combination of drift demand due to the two highest modes of vibration: IDR=[ Mode1 + a*mode2 ] Mode1 = IDR from 1st mode shape Mode2 = IDR from 2nd mode shape assumptions: For simplicity the mode combinations do not consider modes of vibration higher than the second mode, although they certainly contribute to the analysis IDR response is treated as completely elastic, which is certainly not the case. First mode IDR, mode1, is not factored so the value of IDR on the x-axis does not correspond to IDR values in the results. *The periods and mode shapes correspond to deformation parallel to the direction of analysis. Approximate combinations of mode drifts for all three structures to qualitatively match the median drifts of the max. IDR plots.The value of alpha was varied to obtain mode combinations that match the bulges in the median of the response spectra. For in-phase combinations, the value of alpha is positive while for out of phase combinations it is negative.The purpose is not to quantify the exact combinations of modal vibrations, but rather, to qualitatively identify the primary shape of the in-phase and out-of-phase responses which cause stories with high drift demands. h2 h1

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**For h2, when response is in phase, a bulge occurs in stories 25-40**

Mode combinations at peak IDR demand for T1 and T2 Key a =1 For h2, when response is in phase, a bulge occurs in stories 25-40 [ Mode1 + a*mode2 ] h1 simulated match, a = -1 [ Mode1 + a*mode2 ] h1 recorded match, a = -0.5 [ Mode1 + a*mode2 ] h2 simulated match, a = 1 [ Mode1 + a*mode2 ] h2 recorded match, a = -1 a = -1 For h2, when response is out of phase, a bulge occurs in stories 1-20 Approximate combinations of mode drifts for all three structures to qualitatively match the median drifts of the max. IDR plots. Mode1 and Mode2 correspond to the mode plots in figures Higher modes were ignored for simplicity. Alpha is positive for in phase combinations and negative for out of phase combinations. For the CBD structure: H1 recorded: the smaller bulge in stories 1-20 the result of slightly out of phase energy content. (alpha = -0.5) H1 simulated: the larger bulge in stories 1-20 the result of out of phase energy content. (alpha = -1) H2 recorded: bulge in stories 1-20 the result of slightly out of phase energy content. (alpha = -0.5) H2 simulated: bulge in stories the result of out of phase energy content. (alpha = 1) Results are similar for all three buildings. recorded ground motion - median recorded ground motion - individual simulated ground motion - median simulated ground motion – individual

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**Basic Assumptions for Loss Calculations**

Based on inter-story drift and floor acceleration results only. Similar components in all buildings. The EDPs from nonlinear time-history analysis are used directly for loss calculations without any fitting as done commonly for loss estimations.

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**Limitations for Loss Calculations**

Residual drift ratio was not used in the loss estimation process. Variability of EDPs given the ground motion intensity is not accurately modeled. However, for the purpose of loss estimation this shortcoming has been adjusted. Ground motion selection and scaling is mostly focused on matching spectral acceleration at long periods. This can underrepresent accelerations at short periods

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After: Nilesh Shome

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After: Nilesh Shome

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After: Nilesh Shome

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General Summary Performance of 9 tall buildings at five hazard levels were evaluated: Three lateral load resisting systems X Three design guidelines. The progress in reduction in estimated loss from CBD to PBD+ designs shows the a general success in proposed design guidelines for tall buildings. On going efforts: Loss estimation methodology

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Thank You

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