1
INTRODUCTION................................................................................................................3
1.1
OBJECTIVES ....................................................................................................................3
1.2
METHODOLOGY ..............................................................................................................3
1.3
BUILDING MODELS FOR RESPONSE COMPARISON ...........................................................4
1.3.1
Acquire Structural Plans, Earthquake Ground Motions and Damage Reports ....4
1.3.2
Development of 3-D Models of Buildings ..............................................................6
1.3.3
Run Elastic Time History Analysis ........................................................................7
1.3.4
Comparison of Responses ......................................................................................7
1.3.5
Model 3 Elastic Analysis........................................................................................8
1.3.6
Model 3; Inelastic Analysis....................................................................................8
1.3.7
Summary of Responses...........................................................................................8
1.4
BUILDING EVALUATION USING PREVAILING PRACTICE UBC-97 AND FEMA-273..........9
1.4.1
UBC-97 ..................................................................................................................9
1.4.2
Evaluation Using FEMA 273...............................................................................16
2
ANALYSIS OF AN EIGHT STORY OFFICE BUILDING, NORTH HOLLYWOOD,
CALIFORNIA............................................................................................................................25
2.1
BUILDING DESCRIPTION ................................................................................................25
2.2
THE SAP2000 COMPUTER MODELS..............................................................................28
2.3
MASS CALCULATIONS ...................................................................................................29
2.4
MODAL PERIODS ...........................................................................................................31
2.5
EARTHQUAKE GROUND MOTIONS .................................................................................34
2.6
TIME HISTORY ANALYSES.............................................................................................34
2.6.1
Model 1 and Model 2 ...........................................................................................34
2.6.2
Model 3 ................................................................................................................38
2.6.3
Elastic Demand Ratios and Demand Capacity Ratios ........................................40
2.7
COMPARISON OF ACTUAL DAMAGE WITH PREDICTED DAMAGE ...................................40
2.8
EVALUATION WITH PREVAILING PRACTICE – UBC-97 AND FEMA-273.......................43
2.8.1
Analysis Using UBC-97 .......................................................................................43
2.8.2
Analysis Using FEMA 273...................................................................................47
2.9
SUMMARY .....................................................................................................................57
3
ANALYSIS OF A TEN STORY OFFICE BUILDING, TARZANA, CALIFORNIA 58
3.1
BUILDING DESCRIPTION ................................................................................................58
3.2
THE SAP2000 COMPUTER MODEL ...............................................................................61
3.3
THE IDARC2D-V.5 COMPUTER MODEL .......................................................................61
3.4
MASS CALCULATIONS ...................................................................................................64
3.5
MODAL PERIODS ...........................................................................................................65
3.6
EARTHQUAKE GROUND MOTIONS .................................................................................67
3.7
TIME HISTORY ANALYSES.............................................................................................69
3.7.1
Model 1 and Model 2. ..........................................................................................70
3.7.2
Model 3 ................................................................................................................73
3.7.3
Demand Capacity Ratios .....................................................................................76
3.8
COMPARISON OF ACTUAL DAMAGE WITH PREDICTED DAMAGE. ..................................76
3.9
EVALUATION USING PREVAILING PRACTICE UBC-97 AND FEMA-273 ........................79
1
3.9.1
Analysis Using UBC-97 .......................................................................................79
3.9.2
Analysis Using FEMA 273...................................................................................83
3.9.3
Acceptance Criteria .............................................................................................88
3.10 SUMMARY .....................................................................................................................92
4
ANALYSIS OF A SIXTEEN STORY BUILDING, SHERMAN OAKS, CALIFORNIA
93
4.1
BUILDING DESCRIPTION ................................................................................................93
4.2
THE SAP2000 COMPUTER MODELS..............................................................................97
4.3
MASS CALCULATIONS ...................................................................................................99
4.4
MODAL PERIODS .........................................................................................................101
4.5
EARTHQUAKE GROUND MOTIONS ...............................................................................102
4.6
TIME HISTORY ANALYSES...........................................................................................103
4.6.1
Model 1 and Model 2 .........................................................................................103
4.6.2
Model 3 ..............................................................................................................107
4.6.3
Elastic Demand Ratios.......................................................................................109
4.7
COMPARISON OF OBSERVED AND PREDICTED DAMAGE .............................................110
4.8
EVALUATION WITH PREVAILING PRACTICE – UBC-97 AND FEMA-273.....................111
4.8.1
Analysis Using UBC-97 .....................................................................................111
4.8.2
Analysis Using FEMA 273.................................................................................116
4.9
SUMMARY ...................................................................................................................125
5
ANALYSIS OF A TWENTY STORY BUILDING, ENCINO, CALIFORNIA ........126
5.1
BUILDING DESCRIPTION ..............................................................................................126
5.2
THE SAP2000 COMPUTER MODELS............................................................................128
5.3
MASS CALCULATIONS .................................................................................................131
5.4
MODAL PERIODS .........................................................................................................133
5.5
EARTHQUAKE GROUND MOTIONS ...............................................................................134
5.6
OBSERVED DAMAGE ...................................................................................................135
5.7
TIME HISTORY ANALYSIS ...........................................................................................138
5.7.1
Model 1 and Model 2 .........................................................................................138
5.7.2
Model 3 ..............................................................................................................139
5.7.3
Elastic Demand Ratios.......................................................................................145
5.7.4
Demand/Plastic-Moment Ratios ........................................................................146
5.8
EVALUATION WITH PREVAILING PRACTICE – UBC-97 AND FEMA-273.....................146
5.8.1
Analysis Using UBC-97 .....................................................................................146
5.8.2
Analysis Using FEMA-273 ................................................................................150
5.9
SUMMARY ...................................................................................................................156
6
SUMMARY AND RECOMMENDATIONS.................................................................158
6.1
6.2
6.3
6.4
6.5
GENERAL MODELING ASSUMPTIONS ...........................................................................158
COMPARISON OF MAXIMUM ROOF DISPLACEMENTS ...................................................159
COMPARISON OF INTER-STORY DRIFTS .......................................................................161
COMPARISON OF BASE SHEARS ...................................................................................163
DAMAGE STRESS RATIOS ............................................................................................164
2
1
1.1
INTRODUCTION
Objectives
The purpose of this study is to evaluate the seismic performance of four instrumented steel
buildings during the 1994 Northridge earthquake. Based on the findings from the analysis,
modifications to the conventional analysis and code design procedures are to be suggested to
enhance the reliability of current analysis and design techniques. For this study, the code design
methods of UBC-97 according to LRFD and FEMA-273 were used.
1.2
Methodology
The methodology adopted for this study was as follows:
•
The four buildings used in this study were chosen by CSMIP, they are the a) North
Hollywood Building, b) Tarzana Building, c) Sherman Oaks Building, and d) Encino
Building. The description of each building is given in each building’s individual chapter.
•
The buildings were inspected after the earthquake for potential damage using the procedures
outlined by SAC in its interim guidelines (FEMA 267, 1995). The investigators who worked
on the respective buildings were consulted with and through them structural plans and repair
drawings were acquired. Their observations were documented giving valuable information
on the building and damaged observed after the earthquake.
•
The strong-motion records from the Northridge Earthquake for the buildings were made
available by CSMIP.
•
Analytical models for each building were created and analyzed using elastic/linear and/or
inelastic/nonlinear analysis techniques. The models were calibrated based on the
comparisons with the recorded building response and the actual building performance. The
comparisons included, but were not limited to, building periods, drifts, higher-mode
response, time histories and location of damaged joints if any.
3
•
Conclusions were made based on the extent of damage and modeling techniques adopted for
each building which included damping, higher mode effects and panel zone effectiveness.
•
The buildings were evaluated against current building design guidelines and practices,
namely the UBC-97 code and the FEMA-273 rehabilitation guidelines. The model which
best simulated the actual response observed in the field was used for this evaluation.
1.3
Building Models for Response Comparison
The outline of the procedure adopted for the building response comparison is shown in the
flowchart in Figure 1-1. The actual procedures used for each building are described in the
following chapters. Each of these chapters describes in detail a particular building as well as the
steps taken to construct, calibrate and study the analytical models used in this study.
1.3.1 Acquire Structural Plans, Earthquake Ground Motions and Damage Reports
The North Hollywood building was inspected by Myers Nelson Houghton Inc. The Sherman
Oaks building was inspected and repaired by Englekirk and Sabol Consulting Structural
Engineers. The Encino building was evaluated and repaired by Kariotis & Associates Structural
Engineers. The Tarzana building was inspected and repaired by John A. Martin and Associates.
Interviews were setup with the respective firms where their observations and type of damage to
each building was documented. Structural plans and damage reports were obtained.
The strong-motion records were given by CSMIP for each building. The motions included
displacements, velocities and accelerations in the North-South, East-West, and Vertical
directions. The motions were recorded by accelerometers located on the ground, at mid level,
and on the roof of each building.
4
Building Response Comparison
Acquire Model Plans, Time History Records,
Damage Reports and Repair Drawings
Develop 3-D Models
Model 1 (No rigid-end zones)
Model 2 (Full rigid End Zones)
Run Elastic Time-History Analysis
Is Actual Response bounded by the
Model 1 and Model 2 Responses?
Adjust Rigid End Zones and
Re-Run Time-History Analysis
NO
Develop Inelastic Model
Run Inelastic
Time-History Analysis
YES
YES
Elastic Analysis?
NO
Does the existing model time-trace
correlate well with the actual recording?
Adjust Hysteretic Parameters
NO
YES
Does the existing model amplitudes
correlate well with the actual recording?
NO
Adjust Modal Damping and
Re-Run Time-History Analysis
YES
Model 3
- Check Story Drifts
- Compare Stresses with Actual Damage
- Summarize Findings and Modeling Assumptions
- Evaluate with Prevailing Practice
Figure 1-1: Procedure used for the Comparison Building Response.
5
1.3.2 Development of 3-D Models of Buildings
Three-dimensional models of the lateral resisting system for all four buildings were constructed
for use with the computer program SAP2000. Two models were created for the elastic timehistory analysis that had different rigid end zone assignments. The first model (Model 1) utilized
all of the rigid end zones and the second model (Model 2) assumed no rigid end zones.
The primary lateral resisting system for all the buildings consisted of Special Moment Resisting
Frames (SMRF). One of the buildings had shear walls and cross braces at the lower levels and
were modeled as a part of the lateral resisting system. Gravity framing was excluded in the
model, as it was proven (Chapter 2) that it did not contribute significantly to the lateral
resistance. The mass and gravity loads from the gravity framing however were included. It was
verified for the North Hollywood building that their contribution to the lateral stiffness of the
building was minimal (the difference in the responses was between 2 and 5%). The response
comparisons for the other buildings looked good and did not warrant further investigation of the
influence of the gravity framing.
The influence of vertical ground motion was investigated for the Tarzana building (Chapter 3).
Again, the added modeling requirements necessary to include the effects of vertical ground
motion in the analysis, proved insignificant in terms of stress increases or displacement
responses. Thus, the effects of vertical ground motion were ignored in the analysis.
For the SAP2000 models, columns and beams were modeled as FRAME elements while the
shear walls were modeled as SHELL elements. Each member was assigned gravity loads. The
gravity loads consisted of the self-weight of the member and any supported dead load that
corresponded to the weight of the structure distributed to that member.
The mass, mass moment of inertia and center of mass were calculated and included for each of
the 3-D models. The calculations were made by the computer program JAMA-SDS (MMI). The
mass included the weight of the floor slab, framing member, partition loads, ceiling loads and
mechanical loads. The mass of the building was lumped at the center of mass on each floor. The
6
mass moments of inertia were applied at the center of mass for rotational inertia forces about the
vertical axis. The floor slab system was modeled using a rigid diaphragm formulation.
1.3.3
Run Elastic Time History Analysis
Model 1 and Model 2 were analyzed for the elastic time-history analysis that had different rigid
end zone assignments. The accelerations recorded at the ground level during the 1994
Northridge Earthquake were used as the input ground accelerations for the time-history analyses
These accelerations included components in the three principal axes of the buildings. The effects
of vertical excitation were investigated and it was concluded to be insignificant. Therefore, the
vertical component of the ground motion was not used in the analyses. Details on this
investigation are given for the Tarzana building (Chapter 3). Thus only the two horizontal
components were used in the time-history-analysis. Throughout this report, the North-South
direction is also referred to as “180” and the East-West direction is also referred to as “90”
The results from time-history analysis of Models 1 and 2 were compared against the actual
recorded responses from the Northridge earthquake. For three of the four buildings (Tarzana,
North Hollywood, and Sherman Oaks) the precise location of the seismographs/accelerometers
was unavailable therefore they were assumed to be located at the center of mass of the respective
floors. . The torsional response from the analyses were checked and found to be insignificant.
The actual torsion from the earthquake could not be determined, as there was only one sensor at a
particular floor, and the torsional component of the response was not recorded.
1.3.4 Comparison of Responses
A comparison between the acceleration, velocity and displacement responses for Model 1 and
Model 2 and the actual recorded responses was performed. When the actual recorded timehistory was bounded from the analysis results for Model 1 and Model 2 then the response was
identified as elastic and the required calibration was made by modifying the length of the rigid
zones. On the contrary, when the actual time-history appeared to be more flexible than Model 2,
this was a clear indication of inelastic behavior. Therefore, inelastic analysis had to be
performed calibrating both the rigid zone length and the structural hysteretic characteristics.
7
1.3.5
Model 3 Elastic Analysis
Model 3 was calibrated to match the earthquake response by an iterative process that consisted of
three basic steps: a) run the elastic analysis, b) compare the results, and c) adjust the rigid zones
and modal damping until the results matched the recorded response.
1.3.6 Model 3; Inelastic Analysis.
Inelastic models were developed only for those buildings that did not fall in the elastic range, as
described earlier. For this study it was the Tarzana building. The computer program used for the
inelastic analysis was IDARC2D-v.5. The details of the inelastic analysis setup are given in
Chapter 3. Since this program has limited 3D capabilities, a combination of two 2D models, one
for each direction, was prepared.
The iterative process used to calibrate Model 3 consisted of following three basic steps: a) run the
inelastic analysis, b) compare the results and c) adjust the hysteretic parameters and modal
damping until the results matched the recorded response.
1.3.7 Summary of Responses
The responses from Model 3 were examined to determine the accuracy of predicting zones of
high stress, draw conclusions on the validity of modeling techniques and to illustrate the ease or
difficulties in calibrating procedure. The methods used to determine areas of overstress in the
buildings are described in this section, however the conclusions on the modeling techniques are
discussed in the main conclusions of this report.
Elastic Demand Ratios (EDR) were calculated for each member, to determine any overstressed
areas within the buildings. The equations used to calculate the EDR are described in Section
1.4.1.5.1. The Elastic Demand Ratios are ratios of the recorded forces in each member divided
by the capacity of each member. These checks were used to correlate the overstressed areas
(ratios above unity) with the damaged areas from the Northridge earthquake. The Elastic
Demand Ratios were calculated for the load combination that actually existed in the building at
the time of the earthquake. This is the dead load of the building, with partition loads and the
maximum earthquake loads from the time history analysis. Moment and axial member capacities
8
were calculated according to the Load and Resistant Factor Design (LRFD) method [3]. The
expected yield strengths were used in the calculation of the member capacities.
The demand/plastic-moment ratios were an additional calculation performed to determine any
overstresses in the building members. The demand/plastic ratios are the maximum moments
from the combination of earthquake and gravity loads divided by the plastic moment capacity of
the element and should not be confused with the LRFD elastic demand ratios. The expected
yield strengths were used in the calculation of the member capacities.
1.4
Building Evaluation using Prevailing Practice UBC-97 and FEMA-273
All four buildings were analyzed according to UBC-97 [1] and FEMA-273 [2], to check for
compliance with current design standards. The results are used as a guide to identify the
potential for damage. The actual results will be presented later when each building is discussed
in detail.
1.4.1 UBC-97
Reference to Tables, and Equation numbers in italics correspond to those in UBC-97.
The UBC-97 design method used in this study is described in this section. The topics discussed
are the lateral forces applied to the buildings, the calculation of elastic demand ratios, the drift
limit calculations and the seismic special provisions required for structural steel moment
connections. A summary of the steps taken for the UBC-97 analysis is shown in the flow chart in
Figure 1-2.
1.4.1.1 Static Base Shear
The Design Static Base Shear was calculated for all four buildings according to Section 1630.2
formula 30-4:
V=
CV I
W,
RT
9
where I is the Importance Factor according to Table 16-K, Cv is the seismic coefficient
according to Table 16-R, R (Table 16-N) is a coefficient representing the inherent over strength
and global ductility capacity, and T is the period of the structure. The following values were used
for all four buildings.
a) An R value of 8.5 as the lateral resistance is provided from a steel moment-resisting
structural system.
b) An importance factor (I) of 1.0 because of regular occupancy
c) A seismic coefficient (Cv) of 0.77, that corresponds to a near source distance of 5 km
and a stiff soil profile SD for three of the buildings. The fourth building (Encino),
used a seismic coefficient (Cv) of 1.024, that corresponds to a near source distance of
2 km or less and a stiff soil profile SD.
d) The period calculated according to Section 1630.2.2 Item 2 Method B was used as the
period of the building (T).
In addition to the equation above, the UBC-97 set limits that this Static Design Base Shear
should not exceed. The Maximum Design Base Shear is set equal to
V=
2.5 C a I
W
R
where Ca is a seismic coefficient corresponding to a seismic factor and soil profile type SE and
V = 0.11 C a I W .
Only for buildings located at Seismic Zone 4 the Maximum Design Base Shear is set equal to
V=
0.8 Z N V I
W.
R
10
Compliance with UBC-97
Calculate Static Base Shear
Is # of Stories ≤5
and H≤
≤65 ft?
YES
YES
Is
BuildingIrr
l ?
NO
NO
NO
Is Building>
240 ft Tall?
YES
Dynamic Analysis
(Response Spectrum)
Static Analysis
Distribute Forces on
to Masses on Each
N-S and E-W
Construct Response Spectrum
Scale Response Spectrum
so that the Base Shear agrees
with the code specifications
Run Static Analysis
Perform
1. Check Drift Limits at Each
Run Dynamic Analysis
Floor Height (h)
∆M ≤ 0.2 h
∆M = 0
2. Create Elastic Force Demand
Ratios and Check ≤ 1.0
3. Check Special and Seismic
Provisions for Steel
Figure 1-2: Flowchart Showing Steps Taken for UBC-97 Analysis
11
1.4.1.2 Static Analysis
For the Tarzana and North Hollywood buildings that were less than 240 feet tall, static analysis
procedures were used and the member forces were calculated by vertically distributing the static
base shears along the height of the buildings. The vertical distribution of the static base shear
applied at each floor was calculated for the static analysis according to Section 1630.5. The
formula (30-15) is shown here:
FX =
(V − Ft ) w X h X
n
∑w
i
hi
i =1
where Ft = 0.07 T V and is applied at the roof.
1.4.1.3 Dynamic Analysis
Dynamic analysis procedures were used for the Encino and Sherman Oaks buildings. The
distribution of the earthquake loads were determined using the Response Spectrum Analysis
method. The design response spectra used for the two buildings were not the same because the
seismic coefficients (Cv) used, described in Section 1.4.1.1 Item C, were different. The design
response spectrum used for the North Hollywood, Tarzana, and Sherman Oaks buildings, is
shown in Figure 1-3 and the design response spectrum used for the Encino building in Figure 14. Both the Encino and Sherman Oaks building had weight irregularities and therefore the
response spectrum was scaled according to Section 1631.5.4 Item 3 so that the calculated base
shear was equal to 100% of the static base shear.
1.4.1.4 Static and Dynamic Analysis Load Combinations
Load combinations that take into consideration the earthquake loading were used in the static and
dynamic analysis. The equations, according to Section 1612.2.1, were:
•
1.2D+1.0E+0.5L
•
0.9D+1.0E
•
0.9D-1.0E
where D stands for Dead Load, E stands for earthquake load, and L stands for live load. The live
load used for the analyses was 50 psf, as UBC-97 requires for office buildings.
12
The earthquake loads were calculated as:
E = ρE h + E v
Where E h is the earthquake force due to the vertical distribution of the static base shear for the
static analysis or the forces from the dynamic response spectra analysis. The
reliability/redundancy factor ρ is described from Equation 30-3 in section 1630.1.1 and E v is the
load effect resulting from the vertical component of the earthquake ground motion and is equal to
0.5CaID.
All four buildings considered the effects of accidental torsion by shifting the center of mass by
5% of the dimension of the buildings for each direction, according to Section 1630.6.
1.4.1.5 Calculations of Member Demand Ratios
The Elastic Demand Ratios (EDR) were calculated to determine any overstressed areas within
each building for the load combinations mentioned earlier. Moment and axial member capacities
were calculated according to the Load and Resistant Factor Design (LRFD) methods [3]. The
specified yield strengths of steel were used in the EDR calculations. Elastic force demand ratios
were calculated according to LRFD Equations H1-1a and H1-1b and are shown here:
a) For
Pu
≥ 0.2
ϕPn
M uy
Pu 8  M u x
+
+
ϕPn 9  ϕM nx ϕM n y

 ≥ 1.0


13
DESIGN RESPONSE SPECTRUM
1.60
Control Periods
T S =C V /(2.5 C V )
T 0 =0.2 T S
Spectral Accelerations (g)
1.40
T0=
0.14
sec
TS=
0.70
sec
PEAK ACCELERATION
2.5 Cα=
1.20
1.10
g
1.00
Damping Ratio ξ= 0.05
0.80
0.60
0.40
0.20
0.14
0.00
0.00
0.70
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
Period (sec)
Figure 1-3: UBC-97 Design Response Spectrum (North Hollywood, Tarzana, Sherman Oaks)
DESIGN RESPONSE SPECTRUM
1.60
Control Periods
T S =C V /(2.5 C V )
T 0 =0.2 T S
Spectral Accelerations (g)
1.40
TS=
0.72
sec
T0=
0.14
sec
PEAK ACCELERATION
2.5 Cα=
1.20
1.43
g
1.00
Damping Ratio ξ= 0.05
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
Period (sec)
Figure 1-4: UBC-97 Design Response Spectrum (Encino)
14
5.00
5.50
6.00
b) For
Pu
≤ 0.2
ϕPn
 M
M uy
Pu
+  ux +
2ϕPn  ϕM nx ϕM n y

 ≥ 1.0


1.4.1.6 Check for Drift Limitations
The story drift limits were calculated according to the Section 1630.10. The maximum
experienced inter-story drift was calculated as the Maximum Inelastic Response Displacement
(∆M) for each floor, and is given in the following equation:
∆ M = 0.7 R ∆ S
where ∆S is the Design Level Response Displacement, which is the total story drift that
corresponds to the design seismic forces as described in Section 1630.2.1. The maximum
Inelastic Response Displacement can not be greater than 2% of the story height.
1.4.1.7 Check for Special Seismic Provisions
To determine if the four buildings met the special seismic provisions in UBC-97 the panel zone
thickness, the need for continuity plates, and the column-beam moment ratio checks were
investigated.
1. The required panel zone thickness was calculated according to the following formula (Chapter
22 Division IV 8.3b Formula 8-2)
t z ≥ (d z + wz ) / 90
2. The equation used to determine if continuity plates were required was calculated from the
following formula (Chapter 22 Division IV 8.5)
Rn = 6.25(t cf ) 2 Fyf and Rn = 1.8Fyf b f tbf
15
3. The Column-Beam Moment ratios were calculated from the equation shown below. One of the
following equations must be satisfied: (Chapter 22 Division IV 8.6)
∑ ( Fyc
− Puc / Ag )
∑ Z b Fyb
≥ 1.0
or
∑ ( F yc − Puc / Ag )
Vn d b H /( H − d b )
≥ 1.0
1.4.2 Evaluation Using FEMA 273
The buildings were checked for the Basic Safety Objective (BSO), as outlined in the FEMA-273.
The BSO requires the building to satisfy two criteria, Life Safety for the BSE-1 level earthquake,
and Collapse Prevention for the BSE-2 level earthquake. A non-linear static procedure was
adopted for all four buildings since the building heights exceeded 100 ft (page 2-31 guidelines).
A summary of the steps taken for the FEMA-273 analysis is shown in the flow chart in Figure 15. The development of the Response Spectrum for each earthquake, the Pushover analysis, and
the acceptance criteria is discussed in this section.
1.4.2.1 Non-linear Static Pushover Analysis
The pushover analysis requires the building to be displaced to a specified target displacement
depending on the magnitude of the earthquake for prescribed load patterns. The target
displacements are calculated from Equation 3-11 of FEMA-273.
1.4.2.2 Mathematical Model
The mathematical model used for the analysis is the best fit model or Model 3. Hinges are
applied to the beams and columns, with force deformation parameters adopted from Table 5-4 of
FEMA-273.
1.4.2.3 Lateral Load Patterns
The following load patterns were used on the buildings for the pushover analysis:
16
a) Uniform Pattern with forces distributed based on the mass at each floor
b) “A lateral load pattern proportional to the story inertia forces consistent with the story
shear distribution calculated by combination of modal responses using Response
Spectrum Analysis of the building including a sufficient number of modes to capture
90% of the total mass”
c) Force (linear) pattern used for the linear static procedure given by the equation:
FX =
w X h Xk
n
∑w h
i
V,
K
i
i =1
where:
k is between 1 and 2, depending on the fundamental period of the building
wi - hi are the floor weights – heights, and
V is the Design Base Shear
Generally FEMA-273 requires at least two of the following combinations for dynamic analysis
(the Uniform Pattern and one of the other two, depending on the building requirements) or just
Linear Distribution Pattern for static analysis. In this project, all patterns were used for a more
complete picture (expect for the Encino building -‘Chapter 5’- where pattern “c” was not used).
17
Design Risk/Performance Category
1.1
Analysis Options
a. Elastic-Static or Dynamic
b. Non-Linear Static (Pushover)
Pushover analysis was used
c. Non-Linear dynamic because Buildings were > 100 feet tall
1.1.1.1 Mathematical Model
•
Modeled Lateral Resisting System of Buildings
(Model 3)
1.1.1.3 Lateral Load Patterns Applied
1. Uniform Distribution FX =
mX
V
∑ mi
m X h Xk
2. Linear Distribution
FX =
3. Modal Distribution
Response Spectra, Modal Analysis/Forces
k
∑ mi h X
V
1.1.1.2 Push to Target Displacement
δ t = C 0 C1C 2 C3 S a (Te2 / 4π 2 ) g for BSE-1 and BSE-2
1.1.1.4 Acceptance Criteria
All Hinges must Meet BSO, Which is
Life Safety for BSE-1 and Collapse
Prevention for BSE-2
YES
NO
Building Meets Fema-273 Criteria
and no Changes to the Building is
Needed
Building Does Not Meet
FEMA-273 Criteria and Must
be Retrofitted
Figure 1-5: Flowchart Showing Steps Taken for FEMA-273 Analysis
18
1.4.2.4 Push to Target Displacement
The target displacement calculated from Equation 3-11 of FEMA-273 as:
2
T
δ t = C0C1C2C3 S a e 2 g
4π
where
C0 is the modification factor to relate spectral displacement and likely roof displacement.
C1 is the modification factor to relate expected maximum inelastic displacements to
displacements calculated for linear elastic responses.
C2 is the modification factor to represent the effect of hysteresis shape on the maximum
displacement response.
C3 is the modification factor to represent increased displacements due to second order
effects.
Sa (g) is the Response spectrum acceleration at the fundamental period and damping ratio
of the building.
The response spectra corresponding to the BSE-1 and BSE-2 level earthquakes were generated
from the corresponding spectral acceleration Sa values for each level earthquake and are shown in
Figure 1-6. The spectral acceleration is derived from the mapped short period response
acceleration parameter SS and the modified mapped response acceleration parameter at “one
second” period S1 for the given site. For the BSE-1 level earthquake, it is taken as the smaller of
the 10% probability of exceedance in 50 years (5% of Critical Damping) and two thirds of the
value for the 2% probability of exceedance in 50 years (section 2.6.1.2). In general, the BSE-1
and the BSE-2 earthquakes are typically taken as 10/50 and 2/50 year events
The Spectral Response Acceleration parameters for the Los Angeles area, for which all four
buildings were located, were taken from maps 29 and 30. The parameter values are:
19
BSE-1
SS = 1.25g , and S1 = 0.50g.
BSE-2
SS = 1.75 g, and S1 = 0.75g.
FEMA 273 guidelines require that since we had insufficient or no soil data available, Site Class
E (SE) that corresponds to soft clays should be used. The spectral response acceleration
parameters adjusted for Site Class E from Tables 2-13 and 2-14 (FEMA-273) were set to be Fa=1
and Fv=2. From these values the design short period spectral response acceleration parameter,
SXS and design spectral response acceleration parameter SX1 were calculated as
SXS = 1.17g, and SX1 = 1.0g for BSE-1 and
SXS = 1.75g, and SX1 = 1.5g for BSE-2
The period T0 of the general response spectrum curve in Figure 2-1 of FEMA-273 at an effective
damping of 5% is:
T0 = (SX1BS) / (SXSBS) = 1.0/1.17 = 0.86 seconds for BSE-1 and
T0 = (SX1BS) / (SXSBS) = 1.5/1.75 = 0.86 seconds for BSE-2
The fundamental periods of all four buildings fell in the constant velocity portion of the
spectrum. The response spectra for the site for the BSE-1 and BSE-2 level earthquakes at 5%
damping are given in Figure 1-6. The spectral acceleration Sa from Figure 1-3 is:
Sa = 1.17g, for BSE-1 and
Sa = 1.75g, for BSE-2
1.4.2.5 Acceptance Criteria
The acceptance criteria for the beams and columns assumed as fully restrained are taken
from Table 5-4 of FEMA-273. The maximum plastic rotations corresponding to the LifeSafety (LS) and Collapse Prevention (CP) requirements as well as the hinge properties are
calculated depending on the Width-Thickness ratio (b/t) of each section under the guideline
specifications.
20
Acceleration Response Spectrum for BSE-1
1.40
T0 =
S
S
X 1
BS
T0= 0.86 sec
XS
B1
0.2T0= 0.17 sec
1.20
Sa= 1.17 g
PGA= 0.47 g
Sα (g's)
1.00
Response Spectrum
0.2 T0
T0
Response at T=1 sec
S XS
Sa =
BS

3T
⋅  0 .4 +

T0

0.80
Sa =
β = 5.0 %
S XS
Sa =
0.60




BS
S X1
B1 T
0.40
0.20
0.00
0.00
1.00
2.00
3.00
4.00
5.00
6.00
Period (sec)
Acceleration Response Spectrum for BSE-2
2.00
T0 =
1.80
T0= 0.86 sec
S
X 1
B
S
XS
B1
S
0.2T0= 0.17 sec
Sa= 1.75 g
PGA= 0.70 g
1.60
Response Spectrum
0.2 T0
T0
Response at T=1 sec
Sa =
1.40
S XS
BS

3T
⋅  0.4 +

T0

Sα (g's)
1.20
Sa =
β = 5.0 %
1.00
Sa =
0.80
S XS




BS
S X1
B1 T
0.60
0.40
0.20
0.00
0.00
1.00
2.00
3.00
4.00
5.00
Period (sec)
Figure 1-6: FEMA 273 Design Spectra for BSE-1 and BSE-2 Earthquakes
21
6.00
1.4.2.6 Response Comparisons using Demand-Capacity Spectra Response Method
The Demand-Capacity Spectra method for seismic evaluation and retrofit of buildings as outlined
in ATC-40 and the FEMA-273 guidelines, is based on comparing the seismic demand spectrum
with the capacity spectrum of a building. The structural performance or maximum displacement
during a specific seismic event can be well approximated, as the intersection of the pushover
curve (capacity spectrum) with the inelastic demand spectra for a specified damping value,
plotted in Acceleration Displacement Response Spectrum (ADRS) format. The ADRS plot is a
representation of the spectral displacements and the corresponding spectral accelerations for a
specific damping ratio. Using modal analysis it is possible to modify this cure to give the elastic
composite spectrum that represents the BS of the building for different values of roof
displacement. Assuming an elastic structure with well-defined mode shapes (taken as mass
normalized φ Tj [M ]φ j = 1 , where T represents transposition and [M] the mass matrix), the
Maximum Base Shear (BS) can be represented in terms of Spectral Acceleration (Sa(ωj, ξj)) as:
 S (ω ξ )
BS = g Γ j2  α j j 
g


where:
g is the acceleration due to gravity
Γ j = φ Tj [M ][r ] is the modal participation factor and
[r ]T = {1,1,...,1}
is a unit vector.
Using the same concept the maximum roof displacement (uij) can be represented in terms of
spectral displacement (Sd(ωj, ξj)) as follows:
uij = φij Γ j S d (ω j , ξ j ).
22
Assuming that the first mode is dominant (which is true for all the structures analyzed for this
project) a single mode can be used to define the response and the equations above can be
modified as:
 S (ω ξ )
BS = g Γ12  α j j  and u1 j = φ1 j Γ1 S d (ω j , ξ j )
g


It is worth mentioning that ( φ1 j Γ1 ) represents the C0 coefficient as defined in FEMA 273
guidelines or the modal story participation factor (PFim) in ATC-40.
In this study, as demonstrated later, three of the four buildings behaved elastically. Thus,for
these buildings there was no need to define the inelastic demand spectrum, since it coincides
with the elastic one. For the case where inelasticity was detected, an inelastic demand spectrum
was necessary.
A rigorous procedure to define an inelastic spectrum, requires multiple time history analyses for a
variety of structures in order to obtain the maximum deformation under the already specified
ground motion. This procedure is analytically described by Reinhorn (1996). Instead, there are
other methods developed to approximate the inelastic spectra from the elastic spectra without the
requirement of the additional time history analyses. Such a method is used for this project and is
described below.
The inelastic spectra is derived from the elastic response spectra through the factor Rµ , which is
defined as
Rµ =
S AE W
Qy g
where:
S AE is the point defined by the pushover curve and the elastic demand spectrum,
W is the weight of the structure,
23
Qy is the yield Base Shear and
g is the acceleration due to gravity
This factor reduces the elastic spectral accelerations to account for the inelasticity in the
structure. The inelastic displacement spectrum can be now defined from the elastic displacement
spectrum as:
S dI =
S dE
Rµ
E
 1 c
 Sd
(
)
1
+
R
−
1
≥


µ
 c
 Rµ
where:
S dI is the inelastic spectral displacement,
S dE is the inelastic spectral displacement and
T0a
b
c=
+
is a factor suggested from Krawinkler and Nasser (1992).
a
1 + T0 T0
The factors a, b are specified in the same publication and are functions of the structural post
yielding stiffness of the building as shown in the pushover curves. T0 is the fundamental period
of the structure.
The inelastic acceleration spectrum is also defined from the elastic acceleration spectrum by
using the following equation:




E
 SI
S 
S aI = a 1 + a  d
E
Rµ
  S d

R

 µ




− 1 ,
 


 
 
where a is the structural post yielding stiffness of the building as shown in the pushover curves.
24
2
2.1
ANALYSIS OF AN EIGHT STORY OFFICE BUILDING,
NORTH HOLLYWOOD, CALIFORNIA
Building Description
This building is an eight-story Steel Moment Resisting Frame (SMRF) office building located at
North Hollywood, California. It is rectangular in plan, with approximate dimensions 71’ X 192’.
The lateral resistance in the North-South direction comprises of four single bay moment resisting
frames along the centerline, while that in the East-West direction comprises of two bay moment
resisting frames at the North and South edges of the building. A floor plan of the lateral resisting
system as well as the column orientations is shown in Figure 2-1. The member sizes and story
heights for the moment resisting frames in the North-South and East-West directions are shown
in Figure 2-2. Beam column connections are typical pre-Northridge SMRF connections with the
beam complete penetration field welded to the column flange. The panel zones have doubler
plates welded to each side of the column web and continuity plates at the levels of the top and
bottom beam flanges. The moment frame connection detail is shown in Figure 2-3.
The structural steel used is either Grade A36 or Grade A572 (Grade 50) as specified on the
construction drawings. The floor system at all floors except the roof is composed of QL-99-20
steel deck overlaid with 3¼” lightweight concrete. The roof is a combination of a QL-99-20 steel
deck overlaid with 3¼” lightweight concrete and a TUFCOR 24 GA. metal deck with 2¼’’
zonolite.
Seismic sensors are located at the base, the fifth floor and the roof.
25
20’
19’
38’
19’
20’
19’
19’
19’
19’
N
35’ 2’’
35’ 2’’
Figure 2-1: Model Dimensions and Column Orientations.
26
7 X 12’ 6’’=87’ 6’’
17’
17’
7 X 12’ 6’’=87’ 6’’
NS Frames
EW Frame
Figure 2-2: Frame Elevation and Member Sizes.
27
Figure 2-3: Moment Frame Connection Detail
2.2
The SAP2000 Computer Models
The SAP2000 models were created as outlined in the introduction. The additional modeling
assumptions made for this building are:
The columns were assumed fixed at the base because they were supported at the foundation
by individual pile footings. The actual fixity could not be determined, because the base-plate
connection details were not available. This assumption is justified because the response of
the model with its base model showed much better comparisons with the actual recordings
than the model on which the columns were assumed to be pinned at the base.
The unit weight of the penthouse was assumed to be the same as the unit weight of the roof.
The lateral resistance between the 8th floor and the roof in the East-West direction was
provided by diagonal bracing, but the brace sizes were not available in the plans. The braces
due to modeling considerations were replaced with an equivalent 2-bay moment frame, as
seen in Figure 2-1. The relative lateral stiffness at this level was assumed proportional to the
28
stiffness of the 8th floor with proportionality constant equal to the ratio of the mass at the roof
and the 8th floor.
The splice locations were not discretely modeled and the column sections were assumed to
remain constant between two adjacent floors.
The effectiveness of the rigid zones for Model 3 was calibrated at 80% of the full rigid zone
length for the East-West direction frames, and 85% for the North-South direction frames. The
damping ratios used for the fundamental periods of Model 3 were set at 5% for the East-West
direction and 4% for the North-South direction. All higher modes were damped at 10% so that
the contribution of the high frequency response in the acceleration time histories would be
minimal. A summary of the modeling assumptions is presented in Table 2-1.
Table 2-1: Modeling Differences Between the Various Models.
Model
Rigid Zones
Analysis
Model 1
Model 2
All Elements
None
80 % EW
85% NS
Elastic 3D
Elastic 3D
Yield Stress
(ksi)
-
Elastic 3D
-
Model 3
Modal Damping
EW: 5% 1st, all others 10% damped
NS: 4% 1st, all others 10% damped
A visual representation of the three-dimensional SAP2000 model used is shown in Figure 2-4.
2.3
Mass Calculations
The loading criteria used to calculate the masses from the plans or the manufacturer
specifications are given in Table 2-2. Any contribution from the live loads was assumed to be
included in the partition loading. An additional 30-psf skin loading along the perimeter was
considered where applicable. A summary of the results is presented in Table 2-3.
29
Figure 2-4: 3D Model of the Building.
Table 2-2: Dead Loads Considered for the Mass Calculations
Story / Area
Structural Weight
(psf)
Roof Below
Penthouse Floor
47.4
Roof Area
10.4
Typical Floors
46+(8.545…13.4 )
Additional Vertical Loads
(psf)
Partition
20
Ceiling and Mechanical
5
Roofing and Insulating
6
Ceiling and Mechanical
5
Partition
20
Ceiling and Mechanical
5
30
Total
(psf)
72.39
21.4
(79.5…84.4)
Table 2-3: Center of Mass, Mass and Mass Moment of Inertia for Different Levels.
Typical Floor (2-6, avg.)
Level 7
Level 8
Roof
Mass Moment of
Inertia
(kips sec2 in)
1842490
1788245
1853151
962017
Mass
(kips sec2/in)
3.30
3.21
3.33
2.08
Center of Mass
X coord.
Y coord.
(in)
(in)
1165.5
420.24
1165.5
420.24
1165.5
420.24
1092.09
424.09
The floor plan layout showing the center of mass locations, plan openings, and perimeter line
loads is shown in Figure 2-5.
2.4
Modal Periods
The modal periods of the building for the three different models along with their mass
participation factors are given in Table 2-4. Model 3, had a fundamental period of 2.57 seconds
in the East-West and 2.19 in the North-South direction. The natural frequencies of the building
were obtained from the actual recorded responses using the transfer functions of the story
accelerations normalized by the superimposed input base motion in the frequency domain (Figure
2-6). The Mode 8 (3rd mode in the NS direction) could not be identified. A possible reason
might be the relatively high damping (see method requirements as described in the Tarzana
building). The modal periods calculated using this method matched well with the periods
obtained from the modal analysis of Model 3. The maximum difference was 7.3% on the third
mode in the East-West direction. The analytical results of this study are shown in Table 2-5.
31
4th Floor
Typical Floor
8th Floor
Roof
Figure 2-5: JAMA-SDS (MMI) calculations.
Table 2-4: Modal Periods for the Selected Computer Models.
Model
1
Model
2
Model
3
Mode
Period
1
(sec)
2.513
4
7
1
4
7
1
4
7
1.008
0.570
2.790
1.114
0.638
2.565
1.028
0.583
East-West
Modal
Cumulative Modal
Participation
Participation
Factor
Factor
(%)
(%)
76.39
76.39
12.86
5.39
75.74
12.74
5.46
76.26
12.84
5.41
89.28
94.80
75.74
88.50
94.12
76.26
89.13
94.67
32
Mode
Period
2
(sec)
2.145
5
8
2
5
8
2
5
8
0.728
0.399
2.427
0.829
0.464
2.185
0.742
0.408
North-South
Modal
Cumulative Modal
Participation
Participation
Factor
Factor
(%)
79.52
79.52
13.85
3.79
78.91
13.53
4.10
79.44
13.80
3.84
93.37
97.16
78.91
92.44
96.54
79.44
93.24
97.08
Table 2-5: Comparison of the Modal Periods for Model 3 and the Period Obtained from the
Recorded Response Using the FFT Method.
Mode
1
4
7
East-West
Modal
Modal Periods
Periods
(FFT Analysis)
(SAP2000)
(sec)
(sec)
2.565
2.6
1.028
1.039
0.583
0.540
Diff.
Mode
(%)
1.3
1.1
7.3
2
5
8
North-South
Modal
Modal Periods
Periods
(FFT Analysis)
(SAP2000)
(sec)
(sec)
2.189
2.111
0.746
0.771
0.412
Not Identified
Torsional Modes
Figure 2-6: FFT Analyses.
33
Diff.
(%)
3.6
3.2
2.5
Earthquake Ground Motions
The earthquake ground motions used in this study are the actual ground motions recorded at the
base of the building during the 1994 Northridge Earthquake. These motions include components
in the North-South, East-West and Vertical directions shown in Figure 2-7.
Acceleration Record at Level 0 (ground - 90)
Acceleration Record at Level 0 (ground - UP)
700
500
500
500
300
300
300
-100
-300
-500
2
2
100
Acceleration (cm/sec )
700
Acceleration (cm/sec )
2
Acceleration (cm/sec )
Acceleration Record at Level 0 (ground - 180)
700
100
-100
-300
-500
-700
10
20
30
40
50
60
-300
-500
-700
0
100
-100
-700
0
10
20
30
40
50
Time (sec)
Time (sec)
North-South Component
East-West Component
60
0
5
10
15
20
25
30
35
40
45
50
Time (sec)
Vertical Component
Figure 2-7: Ground Motion Components.
2.6
Time History Analyses
Linear dynamic time history analyses were performed on all the three models (see Table 2-1).
The time histories of the acceleration, velocity and displacement responses for the individual
models are presented in Figures 2-8 through 2-16.
2.6.1 Model 1 and Model 2
By comparing the time-history responses for Model 2 with the actual structural responses
(Figures 2-11 through 2-13), it is clear that this model is more flexible than the actual structure.
This is also evident by the fact that the fundamental periods calculated from the transfer function
method were 2.60 seconds for the East-West direction and 2.11 seconds for the North-South
direction, while from the modal analysis of Model 2 these values were 2.79 seconds and 2.43
seconds respectively. Thus, the assumption of no rigid zones is clearly inaccurate for this
building.
The model assuming full rigid zones (Model 1) gave much better results (Figures 2-8 through 210). There is however a sharp spike in the acceleration responses at the roof both in the NorthSouth and the East-West directions. This difference in amplitude also appears in the
34
displacement response at the roof shown in Figure 2-10, but to a much lesser degree. The
acceleration, velocity, and displacement responses also show a slight difference in the period of
vibration toward the tail end of the response. The fundamental periods from the transfer function
method compared better with those calculated from the modal analysis of Model 1, which were
2.51 seconds in the East-West direction and 2.14 seconds in the North-South direction.
Acceleration Record at Level 5 (90)
700
500
500
300
300
2
Acceleration (cm/sec )
2
Acceleration (cm/sec )
Acceleration Record at Level 5 (180)
700
100
-100
-300
100
-100
-300
Recorded History
Recorded History
-500
-500
Model 1
Model 1
-700
-700
0
10
20
30
40
50
60
0
10
20
Time (sec)
50
60
Acceleration Record at Roof (90)
700
700
500
500
300
300
2
Acceleration (cm/sec )
2
40
Time (sec)
Acceleration Record at Roof (180)
Acceleration (cm/sec )
30
100
-100
-300
100
-100
-300
Recorded History
Recorded history
-500
-500
Model 1
Model 1
-700
-700
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
Time (sec)
Figure 2-8: Acceleration Records for Model 1.
35
40
50
60
Relative Velocity Record at Level 5 (90)
100
80
80
60
60
40
40
Velocity (cm/sec)
Velocity (cm/sec)
Relative Velocity Record at Level 5 (180)
100
20
0
-20
-40
20
0
-20
-40
-60
-60
Recorded History
-80
Recorded History
-80
Model 1
Model 1
-100
-100
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Relative Velocity Record at Roof (180)
Relative Velocity Record at Roof (90)
100
100
80
80
60
60
40
40
Velocity (cm/sec)
Velocity (cm/sec)
30
20
0
-20
-40
20
0
-20
-40
-60
-60
Recorded History
-80
Recorded history
-80
Model 1
Model 1
-100
-100
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
40
50
60
Time (sec)
Figure 2-9: Velocity Records for Model 1.
Relative Displacement Record at Level 5 (90)
25
20
20
15
15
10
10
Displacement (cm )
Displacement (cm )
Relative Displacement Record at Level 5 (180)
25
5
0
-5
-10
5
0
-5
-10
-15
-15
Recorded History
Recorded History
-20
-20
Model 1
Model 1
-25
-25
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Relative Displacement Record at Roof (180)
Relative Displacement Record at Roof (90)
25
25
20
20
15
15
10
10
Displacement (cm )
Displacement (cm )
30
5
0
-5
-10
5
0
-5
-10
-15
-15
Recorded History
Recorded history
-20
-20
Model 1
Model 1
-25
-25
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
Time (sec)
Figure 2-10: Displacement Records for Model 1.
36
40
50
60
Acceleration Record at Level 5 (90)
700
500
500
300
300
2
Acceleration (cm/sec )
2
Acceleration (cm/sec )
Acceleration Record at Level 5 (180)
700
100
-100
-300
100
-100
-300
Recorded History
Recorded History
-500
-500
Model 2
Model 2
-700
-700
0
10
20
30
40
50
60
0
10
20
Time (sec)
Acceleration Record at Roof (180)
40
50
60
Acceleration Record at Roof (90)
700
700
500
500
300
300
2
Acceleration (cm/sec )
2
Acceleration (cm/sec )
30
Time (sec)
100
-100
-300
100
-100
-300
Recorded History
Recorded history
-500
-500
Model 2
Model 2
-700
-700
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
40
50
60
Time (sec)
Figure 2-11: Acceleration Records for Model 2.
Relative Velocity Record at Level 5 (90)
100
80
80
60
60
40
40
Velocity (cm/sec)
Velocity (cm/sec)
Relative Velocity Record at Level 5 (180)
100
20
0
-20
-40
20
0
-20
-40
-60
-60
Recorded History
-80
Recorded History
-80
Model 2
Model 2
-100
-100
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Relative Velocity Record at Roof (180)
Relative Velocity Record at Roof (90)
100
100
80
80
60
60
40
40
Velocity (cm/sec)
Velocity (cm/sec)
30
20
0
-20
-40
20
0
-20
-40
-60
-60
Recorded History
-80
Recorded history
-80
Model 2
Model 2
-100
-100
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
Time (sec)
Figure 2-12: Velocity Records for Model 2.
37
40
50
60
Relative Displacement Record at Level 5 (90)
25
20
20
15
15
10
10
Displacement (cm )
Displacement (cm )
Relative Displacement Record at Level 5 (180)
25
5
0
-5
-10
5
0
-5
-10
-15
-15
Recorded History
Recorded History
-20
-20
Model 2
Model 2
-25
-25
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Relative Displacement Record at Roof (180)
Relative Displacement Record at Roof (90)
25
25
20
20
15
15
10
10
Displacement (cm )
Displacement (cm )
30
5
0
-5
-10
5
0
-5
-10
-15
-15
Recorded History
Recorded history
-20
-20
Model 2
Model 2
-25
-25
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
40
50
60
Time (sec)
Figure 2-13: Displacement Records for Model 2.
2.6.2 Model 3
The results for the best fit model (Model 3) are shown in Figures 2-14 to 2-16. The fundamental
periods calculated from modal analysis were 2.56 seconds for the East-West direction and 2.18
seconds for the North-South direction. These periods had 1.3% and 3.6% difference respectively
from the periods calculated from the transfer function method. The time history responses also
closely match the recorded responses. Thus from the results of the time history analysis, the
building appears to have behaved elastically.
38
Acceleration Record at Level 5 (90)
700
500
500
300
300
2
Acceleration (cm/sec )
2
Acceleration (cm/sec )
Acceleration Record at Level 5 (180)
700
100
-100
-300
100
-100
-300
Recorded History
Recorded History
-500
-500
Model 3
Model 3
-700
-700
0
10
20
30
40
50
60
0
10
20
Time (sec)
Acceleration Record at Roof (180)
40
50
60
Acceleration Record at Roof (90)
700
700
500
500
300
300
2
Acceleration (cm/sec )
2
Acceleration (cm/sec )
30
Time (sec)
100
-100
-300
100
-100
-300
Recorded History
Recorded history
-500
-500
Model 3
Model 3
-700
-700
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
40
50
60
Time (sec)
Figure 2-14: Acceleration Records for Model 3.
Relative Velocity Record at Level 5 (90)
100
80
80
60
60
40
40
Velocity (cm/sec)
Velocity (cm/sec )
Relative Velocity Record at Level 5 (180)
100
20
0
-20
-40
20
0
-20
-40
-60
-60
Recorded History
-80
Recorded History
-80
Model 3
Model 3
-100
-100
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Relative Velocity Record at Roof (180)
Relative Velocity Record at Roof (90)
100
100
80
80
60
60
40
40
Velocity (cm/sec)
Velocity (cm/sec)
30
20
0
-20
-40
20
0
-20
-40
-60
-60
Recorded History
-80
Recorded history
-80
Model 3
Model 3
-100
-100
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
Time (sec)
Figure 2-15: Velocity Records for Model 3.
39
40
50
60
Relative Displacement Record at Level 5 (90)
25
20
20
15
15
10
10
Displacement (cm )
Displacement (cm )
Relative Displacement Record at Level 5 (180)
25
5
0
-5
-10
5
0
-5
-10
-15
-15
Recorded History
Recorded History
-20
-20
Model 3
Model 3
-25
-25
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Relative Displacement Record at Roof (180)
Relative Displacement Record at Roof (90)
25
25
20
20
15
15
10
10
Displacement (cm )
Displacement (cm )
30
5
0
-5
-10
5
0
-5
-10
-15
-15
Recorded History
Recorded history
-20
-20
Model 3
Model 3
-25
-25
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
40
50
60
Time (sec)
Figure 2-16: Displacement Records for Model 3.
2.6.3 Elastic Demand Ratios and Demand Capacity Ratios
The Elastic Demand Ratios (EDR) were calculated for this building using the load combination
of the time history and the dead load. The expected yield strengths for the different types of
structural steel were used. The analysis showed a number of locations where potential damage
could occur, since there were a large number of beam sections with the EDR exceeding 1 (Table
2-6). In addition, there are also yielding in several column elements (Figure 2-17).
The demand capacity ratios which is the moment demand for the load combination described
above to moment capacity based on expected yield strengths also showed a number of locations
where potential damage could have occurred.
2.7
Comparison of Actual Damage with Predicted Damage
In this building there are 92 moment resisting frame connections, 64 of which are in the NorthSouth and 28 in the East-West direction of the building. The building was inspected for damage
40
after the earthquake with 11 connections tested in the North-South direction and 6 in the EastWest direction using visual and ultrasonic examination. The inspection results showed no
detectable defects or damage caused by the earthquake. The same conclusion is drawn from the
displacement responses (Figure 2-16) where the elastic SAP2000 analysis coincides with the real
recordings.
This is however contrary to the results from the EDR and Demand/Capacity ratios. The only
logical conclusion that can be drawn at this time for this building is that the quality of the welds
was good and inelastic yielding did occur at some of the beam column connections but was
slight. The inelasticity was probably absorbed in the damping that was used, which was 5% in
the 1st mode for the East-West direction, and 4% in the 1st mode for the North-South direction.
41
Table 2-6: SAP2000 Stress Checks for Beam Elements after Time History Analysis
Element Stress Ratio
15
16
17
18
19
20
21
22
103
104
105
106
107
108
109
110
2nd Story
0.693
0.68
0.918
0.916
0.916
0.917
0.703
0.699
6th story
1.059
1.081
0.991
0.984
0.984
0.988
1.052
1.074
Demand /
Demand /
Demand /
Demand /
Element Stress Ratio
Element Stress Ratio
Element Stress Ratio
Capacity
Capacity
Capacity
Capacity
4th story
3rd story
5th story
0.72
37
0.795
0.83
59
0.836
0.88
81
1.088
1.06
0.70
38
0.788
0.83
60
0.86
0.90
82
1.107
1.08
0.94
39
0.892
0.92
61
0.723
0.75
83
0.849
0.88
0.94
40
0.889
0.92
62
0.727
0.75
84
0.844
0.88
0.94
41
0.889
0.92
63
0.727
0.75
85
0.844
0.88
0.94
42
0.89
0.92
64
0.725
0.75
86
0.847
0.88
0.73
43
0.806
0.85
65
0.807
0.84
87
1.08
1.01
0.72
44
0.804
0.84
66
0.825
0.86
88
1.098
1.04
7th story
8th story
Roof
1.04
125
1.383
1.23
147
1.55
1.37
169
0.198
0.04
1.07
126
1.391
1.25
148
1.477
1.32
170
0.198
0.04
1.03
127
1.071
1.10
149
0.796
0.82
171
0.358
0.37
1.02
128
1.061
1.09
150
0.783
0.81
172
0.348
0.36
1.02
129
1.061
1.09
151
0.783
0.81
173
0.348
0.36
1.03
130
1.066
1.10
152
0.79
0.81
174
0.353
0.36
0.99
131
1.371
1.17
153
1.543
1.32
175
0.198
0.04
1.02
132
1.378
1.19
154
1.47
1.27
176
0.198
0.04
Figure 2-17 Stress Ratios calculated from SAP2000 after time history analysis.
42
2.8
2.8.1
Evaluation with Prevailing Practice – UBC-97 and FEMA-273
Analysis Using UBC-97
In order to investigate how current methods for analysis and design meet the seismic demands,
the building was examined for compliance with the UBC-97 code. Design Static Analysis
procedures were used because the building was categorized as regular and its height was less
than 240 ft.
The Design Base Shear was calculated by the method outlined in the introduction and verified to
be within the acceptable range specified in UBC-97 as described in section 1630.2.1. The values
used for all the above parameters are reported in Table 2.7.
The distribution of the static base shear applied at each level is calculated according to the static
procedure and given in Table 2-7. These loads amplified by the appropriate redundancy factors
give the lateral earthquake forces applied to this building and are given in Table 2-7.
Table 2-7: UBC-97 Summary Table, Parameters and Forces
Site Parameters
Z
0.4
Ca
0.44
Cv
0.77
SEISMIC ZONE: 4
OCCUPANCY CATEGORY: Standard Occupancy
REGULAR STRUCTURE
BUILDING HEIGHT: 104.5 feet
BASE SHEAR VEW= 589.83 kips
BASE SHEAR VNS= 589.83 kips
I
Nv
Structural Parameters
R
8.5
TEW (sec)
1.49
TNS (sec)
1.49
1.00
W (kips)
9708.06
1.20
-- STATIC ANALYSIS -Base Shear Distribution, Earthquake Loads and Overturning Moments
applied to the structure
Lateral Loads
(kips)
Redundancy
Factors
Earthquake Forces
OTM
(kips)
(kips-feet)
FNS
FEW
ρNS
ρEW
NS
EW
NS
EW
Level
139.58
110.18
91.78
78.56
63.90
50.00
35.22
20.60
139.58
110.18
91.78
78.56
63.90
50.00
35.22
20.60
1.31
1.50
183.06
144.51
120.38
103.03
83.81
65.58
46.20
27.02
209.36
165.28
137.67
117.83
95.85
75.00
52.84
30.91
1744.70
4866.70
9135.99
14387.24
20437.24
27112.23
34227.54
44254.63
1744.70
4866.70
9135.99
14387.24
20437.24
27112.23
34227.54
44254.63
Roof
7
6
5
4
3
2
1
43
From Table 2-7, the influence of the redundancy factors in this building is evident. Although the
same base shear is distributed in both directions from the UBC-97 Static Analysis, the final
lateral distribution of the equivalent seismic forces are higher in the East-West Direction (ρ=1.5)
of the building than in the North-South Direction (ρ=1.31). It is important to note that UBC-97
suggests redundancy factors less than 1.25. Therefore, this building does not satisfy the
redundancy checks as recommended in the UBC-97.
2.8.1.1 Check for Drift Limitations
UBC-97 story drift limitations are not satisfied for any of the stories. Analytically, the results for
all stories are presented in Table 2-8.
Table 2-8: UBC-97 Summary Displacements and Drift Limit Checks.
Maximum Inelastic
Response Displacements
INTERSTORY DRIFT RATIO
∆M
(% of story height)
(in)
Level
NS
EW
Roof
7
6
5
4
3
2
1
40.75
37.18
32.35
26.81
21.12
15.26
9.99
5.06
73.19
60.31
50.11
40.44
31.72
22.89
14.63
6.93
NS
2.38
3.22
3.69
3.79
3.91
3.51
3.29
2.48
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
EW
8.59
6.80
6.44
5.82
5.88
5.51
5.13
3.40
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
From the table above it is obvious that the drift ratios in the East-West direction were
significantly higher than in the North-South direction. The reasons behind that are:
a) The lateral stiffness of the building is less in the East-West direction than in the North-South
direction and
b) The UBC-97 earthquake lateral forces applied in the East-West direction are higher due to a
higher redundancy factor.
44
2.8.1.2 Elastic Demand Ratios
The Elastic Demand Ratios were calculated from SAP2000 for the UBC-97 load combinations
with yielding calculated from the nominal yield stresses for the structural steel. The EDR were
in many cases larger than 1 (see Table 2-9). In addition, there is yielding in column elements
(see Figures 2-18, 2-19). The EDR from the UBC-97 design forces clearly show that the
building is not compliant with the code, and there is a high potential for damage to this building.
Table 2-9: Elastic Demand Ratios for Beam Elements from UBC-97
Response Spectrum Analysis
Element
15
16
17
18
19
20
21
22
103
104
105
106
107
108
109
110
EW
2nd Story
0.938
1.14
0.005
0.005
0.005
0.004
0.968
1.169
6th story
1.209
1.439
0.011
0.009
0.009
0.006
1.224
1.454
NS
Element
0.052
0.062
0.663
0.66
0.66
0.664
0.063
0.052
37
38
39
40
41
42
43
44
0.053
0.095
0.582
0.588
0.588
0.582
0.095
0.053
125
126
127
128
129
130
131
132
EW
3rd story
1.075
1.3
0.008
0.007
0.007
0.006
1.111
1.337
7th story
1.398
1.636
0.014
0.011
0.011
0.007
1.419
1.657
NS
Element
0.052
0.077
0.734
0.738
0.738
0.736
0.077
0.052
59
60
61
62
63
64
65
66
0.062
0.117
0.524
0.53
0.53
0.523
0.116
0.062
147
148
149
150
151
152
153
154
EW
4th story
1.067
1.288
0.008
0.007
0.007
0.006
1.104
1.324
8th story
1.358
1.549
0.017
0.013
0.013
0.008
1.373
1.564
NS
Element
0.046
0.08
0.689
0.694
0.694
0.691
0.08
0.046
81
82
83
84
85
86
87
88
0.062
0.112
0.366
0.373
0.373
0.364
0.112
0.061
169
170
171
172
173
174
175
176
EW
5th story
1.278
1.534
0.01
0.008
0.008
0.006
1.293
1.549
Roof
0.577
0.577
0.013
0.01
0.01
0.007
0.577
0.577
NS
0.054
0.095
0.66
0.668
0.668
0.664
0.095
0.054
0.577
0.577
0.169
0.173
0.173
0.166
0.577
0.577
2.8.1.3 Seismic Special Provision Checks
The steel section of UBC-97 (Chapter 22) requires a number of additional checks to be
performed for Special Moment Resisting Frames. Three of these checks were performed, namely.
a) panel zone thickness, b) continuity plates, and c) column-beam moment ratios. A summary of
the individual checks is shown in Table 2-10. All the panel zones met the thickness requirement
although no doubler plates were provided. Continuity plates were required on the top 5 floors of
the North-South frame. Continuity plates were provided so this requirement was satisfied. The
Column-Beam moment ratio checks did not pass for top two floors.
45
Figure 2-18 Stress Ratios calculated from SAP2000 in the East-West Direction after
UBC-97 Static Analysis Procedure.
Figure 2-19 Stress Ratios calculated from SAP2000 in the North-South Direction after
UBC-97 Static Analysis Procedure.
46
Table 2-10: UBC-97 Seismic Provisions for Structural Steel
Check
Results
UBC-97 Special Seismic Provisions Checks
Continuity
Panel Thickness
Col-Bm Moment Ratios
plates?
Passed (Top 5
The top two floors of
floors need
North-South frame did not
Passed
Continuity
satisfy the code
Plates)
requirements
2.8.2 Analysis Using FEMA 273
2.8.2.1 Non-linear Static Pushover Analysis
The calculated target displacements for the BSE-1 and BSE-2 level earthquake and the factors
used to calculate these target displacements for both principle directions of the building are
presented in Table 2.11. The spectral acceleration of the building for the BSE-1 level earthquake
is 0.46g for the East-West direction and 0.39g in the North-South direction. For the BSE-2 level
earthquake, these values are 0.49g and 0.58g respectively. The roof target displacements for the
East-West and the North-South directions for the BSE-1 earthquake are 32.18 inches and 37.78
inches. This corresponds to an overall drift ratio of 2.57% in the North-South direction and
3.01% in the East-West direction. The corresponding drift ratios for the BSE-2 level earthquake
are 3.37% and 4.52% respectively.
It is worth mentioning that these results are for Site Class E, which is the default for FEMA-273
if the soil type is unavailable. From experience we can approximate that the soil in the building
location is better described by using Site Class D (Stiff Soil). By using this Site Class the roof
target displacements for the BSE-1 Earthquake reduce at 24.14 inches (or 1.92% drift ratio) and
28.34 inches (or 2.25% drift ratio) for the East-West and the North-South directions respectively.
The same values for BSE-2 earthquake are 36.21 inches (2.89%) and 42.50 inches (3.39%). In
this document the roof target displacements corresponds to the values for Site class E which is
the default for FEMA-273.
47
Table 2-11: FEMA 273 Summary Target Displacement Calculation.
Non-Linear Static Procedure
1) Period Determination:
T e = Ti
Ke is determined at 60% of Vy
Ki
Ke
BSE-1
BSE-2
EW
2.19
NS
2.56
2) Vertical Distribution of Seismic Forces
Uniform Pattern
Lateral Forces Proportional to the Total Mass at Each Floor Level
AND AT LEAST ONE OF THE FOLLOWING:
i) Lateral load distribution as described in the Linear Static Procedure if more than 75% of the total mass
participates in the fundamental mode in the direction under consideration
ii) Lateral load pattern proportional to the story inertia forces consistent with the story shear distribution
calculated by combination of modal responses using (a) Response Spectrum Analysis using sufficient number
of modes to capture the 90% of the total mass or (b) the appropriate ground motion spectrum
δ t = C0 C1 C2 C3 Sa
Te2
g
4π 2
3) Target Displacement δt (in)
EW
32.18
48.28
NS
37.78
56.67
C0 : Modification Factor to Relate Spectral Displacement and likely building Roof
Displacement (TABLE 3-2)
1.50
C1 : Modification Factor to Relate Expected Maximum Displacements to
Displacements Calculated for Linear Elastic Response
EW
1
1
NS
1
1
C2 : Modification Factor to Represent the effect of Stiffness Degradation and
Strength Deterioration on Maximum Displacement Response (TABLE 3-1)
EW
1
1
NS
1
1
C3 : Modification Factor to Represent Increased Displacements due to Dynamic
P-∆ Effects (positive post-yielding stiffness assumed)
EW
1
1
Sa : Response Spectrum Acceleration at the Fundamental Period and Damping
Ratio of the Building in the Direction Under Consideration (g)
EW
0.46
0.69
NS
0.39
0.58
NS
The base shears and corresponding yield displacements for the three loading patterns used for the
pushover analysis to achieve the target roof displacement are presented in Tables 2-12 through 215. Clearly the Uniform pattern showed the highest yield shear and required displacement
ductility. The displacement ductility for the BSE-1 earthquake was 2.81 for the North-South and
2.24 for the East-West direction, and that for the BSE-2 earthquake was 4.22 and 3.10
respectively.
The actual recorded maximum relative roof displacement in the North-South direction was 6.86
inches (0.5% drift ratio) and in the East-West direction 7.24 inches (0.6% drift ratio). This
corresponds to 18% for the North-South and 22% for the East-West, of the roof target
displacement for the BSE-1 earthquake. The maximum recorded displacements in both
directions were significantly lower than the corresponding yield displacements, calculated from
48
the pushover curves. From the results of the acceptance criteria, it is clear that the plastic
rotations definitely meet the Life Safety requirement. The actual displacement is slightly greater
than the yield displacement, as seen in the demand capacity spectra graphs of the building
(Figures 2-20 to 2-23), which indicates that there could be some yielding or damage. According
to this analysis the building should satisfy the life safety requirements, which it did.
49
Table 2-12: Nonlinear Static results for BSE-1 in the North-South Direction.
East-West
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
1306
Target
Displacement
(inches)
0.13
Yield
Displacement
(inches)
12.86
1524
0.16
12.86
32.18
1778
0.18
11.43
Yield Base
Shear Coefficient
Displacement
Ductility
2.50
2.50
2.81
Table 2-13: Nonlinear Static results for BSE-1 in the East-West Direction
North-South
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
1180
Target
Displacement
(inches)
0.12
Yield
Displacement
(inches)
17.71
1330
0.14
18.29
37.78
1780
0.18
16.86
Yield Base
Shear Coefficient
Displacement
Ductility
2.13
2.06
2.24
Table 2-14: Nonlinear Static results for BSE-2 in the North-South Direction.
North-South
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
1366
Target
Displacement
(inches)
0.14
Yield
Displacement
(inches)
13.14
1585
0.16
13.71
48.28
1805
0.19
11.43
Yield Base
Shear Coefficient
Displacement
Ductility
3.67
3.52
4.22
Table 2-15: Nonlinear Static results for BSE-2 in the East-West Direction.
East-West
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
1207
Target
Displacement
(inches)
0.12
Yield
Displacement
(inches)
17.71
1341
0.14
18.86
56.67
1976
0.20
18.28
Yield Base
Shear Coefficient
50
Displacement
Ductility
3.10
3.00
3.10
1.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
1.20
Base Shear Coefficient (BS/W)
Target Displacement BSE-1
Target Displacement BSE-2
1.00
Elastic Demand Spectrum, Damping Ratio 4%
BSE-1 Demand Spectrum
Inelastic Demand Spectrum, Damping Ratio 4%, R=1
0.80
Maximum Equivalent Response
0.60
0.40
BSE-1 δ t =
BSE-2 δ t =
37.78 in
56.67 in
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
Roof Drift (%)
Figure 2-20 Demand-Capacity Spectra for the East-West Direction.
1.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
1.20
Base Shear Coefficient (BS/W)
Target Displacement BSE-1
Target Displacement BSE-2
1.00
Elastic Demand Spectrum, Damping Ratio 5%
BSE-1 Demand Spectrum
Inelastic Demand Spectrum, Damping Ratio 5%, R=1
0.80
Maximum Equivalent Response
0.60
0.40
BSE-1 δ t =
32.18 in
BSE-2 δ t =
48.28 in
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
Roof Drift (%)
Figure 2-21 Demand-Capacity Spectra for the North-South Direction.
51
5.00
0.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
0.35
Target Displacement BSE-1
Target Displacement BSE-2
Base Shear Coefficient (BS/W)
Elastic Demand Spectrum, Damping Ratio 5%
BSE-1 Demand Spectrum
0.30
Inelastic Demand Spectrum, Damping Ratio 5%, R=1
Maximum Equivalent Response
0.25
0.20
0.15
0.10
BSE-1 δ t =
BSE-2 δ t =
32.18 in
48.28 in
0.05
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
Roof Drift (%)
Figure 2-22 Demand-Capacity Spectra for the East-West Direction - Detail.
0.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
0.35
Target Displacement BSE-1
Target Displacement BSE-2
Base Shear Coefficient (BS/W)
Elastic Demand Spectrum, Damping Ratio 4%
BSE-1 Demand Spectrum
0.30
Inelastic Demand Spectrum, Damping Ratio 4%, R=1
Maximum Equivalent Response
0.25
0.20
0.15
0.10
BSE-1 δ t =
BSE-2 δ t =
37.78 in
56.67 in
0.05
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
Roof Drift (%)
Figure 2-23 Demand-Capacity Spectra for the North-South Direction – Detail.
52
2.8.2.2 Acceptance Criteria
The yield pattern of the hinges for the North-South direction at the BSE-1 roof target
displacement for uniform distribution of the earthquake forces is given in Figure 2-24. The yield
pattern at the BSE-2 roof target displacement is given in Figure 2-25. For the East-West
direction, the hinge patterns for the two earthquake levels are given in Figures 2-26 and 2-27.
The summary of the acceptance criteria is presented in Table 2-16. For the BSE-1 earthquake
there were no hinges that failed to satisfy the required Life Safety (LS) acceptance criterion. For
the BSE-2 earthquake however there were 16 hinges with plastic rotations that exceeded the
required Collapse Prevention (CP) criterion in the North-South direction. Therefore, although
the building meets the first requirement (LS for BSE-1 earthquake) of the Basic Safety Objective
(BSO) does not satisfy the second (CP for BSE-2 earthquake) and further improvement of the
design is required.
53
Figure 2-24 Hinge Yield Pattern at the BSE-1 Level Target Displacement for the Uniform
Distribution Pushover Analysis in the North-South Direction.
Figure 2-25 Hinge Yield Pattern at the BSE-2 fLevel Target Displacement for the
Uniform Distribution Pushover Analysis in the North-South Direction
54
Figure 2-26 Hinge Yield Pattern at the BSE-1 Level Target Displacement for the Uniform
Distribution Pushover Analysis in the East-West Direction.
Figure 2-27 Hinge Yield Pattern at the BSE-2 Level Target Displacement for the Uniform
Distribution Pushover Analysis in the East-West Direction.
55
Table 2-16: Plastic Hinges at the Building Formed for BSE1 and BSE2 after performing
Pushover Analysis in both Directions
Type and Number of Hinges formed at BSE-1 Target Displacement in the
East-West Direction for the Uniform Pattern
Step
0
1
2
3
4
5
6
7
8
9
Displacement Base Shear
-0.15
0.00
7.35
889.15
8.18
987.63
13.87
1434.73
21.43
1695.13
32.03
1885.02
39.72
1995.54
53.84
2174.29
58.16
2226.41
58.16
2124.96
at Target Displacement
A-B
B-IO
816
816
810
756
722
695
686
676
674
674
676
0
0
6
60
62
41
38
20
20
20
20
IO-LS LS-CP
0
0
0
0
32
80
92
86
76
74
86
0
0
0
0
0
0
0
34
42
44
34
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
816
816
816
816
816
816
816
816
816
816
Type and Number of Hinges formed at BSE1 Target Displacement in the
North-South Direction for the Uniform Pattern
Step
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Displacement Base Shear
-0.01
0.00
5.01
783.23
9.44
1476.28
9.54
1488.35
11.15
1616.27
18.65
1940.65
27.97
2169.09
32.99
2278.44
38.11
2389.01
40.78
2437.56
40.78
2105.87
43.09
2208.18
43.09
1856.14
44.01
1908.43
49.05
2059.03
50.15
2080.09
at Target Displacement
A-B
B-IO
352
352
344
336
328
312
304
304
296
282
282
280
280
280
272
272
304
0
0
8
16
24
16
16
16
16
22
22
24
24
24
16
16
16
IO-LS LS-CP
0
0
0
0
0
24
32
28
16
24
24
24
24
24
40
40
32
0
0
0
0
0
0
0
4
24
16
16
8
8
8
8
8
0
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
8
16
16
16
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
352
352
352
352
352
352
352
352
352
352
352
352
352
352
352
352
Type and Number of Hinges formed at BSE-2 Target Displacement in the
East-West Direction for the Uniform Pattern
Step
0
1
2
3
4
5
6
7
8
9
10
11
Displacement Base Shear
0.00
0.00
10.00
1079.69
13.31
1437.02
16.03
1635.60
23.92
1854.45
40.30
2061.23
50.46
2156.20
61.86
2227.64
71.86
2289.32
81.86
2350.99
91.86
2412.66
97.20
2445.58
at Target Displacement
A-B
B-IO
352
352
350
329
308
292
279
276
276
276
276
276
276
0
0
2
23
44
28
29
24
18
8
8
8
24
IO-LS LS-CP
0
0
0
0
0
32
44
52
58
48
42
40
52
0
0
0
0
0
0
0
0
0
20
26
24
0
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
352
352
352
352
352
352
352
352
352
352
352
352
Type and Number of Hinges formed at BSE-2 Target Displacement in the
North-South Direction for the Uniform Pattern
Step
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Displacement Base Shear
-0.01
0.00
9.45
1476.52
9.55
1488.56
11.15
1616.53
18.65
1940.82
32.72
2272.72
40.88
2439.10
40.88
2107.41
43.17
2209.26
43.17
1857.42
44.09
1909.61
49.15
2060.33
53.46
2127.33
53.46
1810.63
55.25
1902.93
59.12
2000.42
68.35
2143.51
68.35
1746.89
68.52
1763.47
71.56
1923.80
75.28
2012.42
91.09
2183.34
99.99
2268.38
at Target Displacement
A-B
B-IO
352
344
336
328
312
304
282
282
280
280
280
272
272
272
272
272
272
272
272
272
264
264
264
272
0
8
16
24
16
16
22
22
24
24
24
16
16
16
16
16
8
8
8
8
16
16
8
16
56
IO-LS LS-CP
0
0
0
0
24
32
24
24
24
24
24
40
32
32
32
32
40
40
40
40
40
40
40
40
0
0
0
0
0
0
16
16
8
8
8
8
8
8
8
8
0
0
0
0
0
0
8
8
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
8
0
0
0
8
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
8
16
16
16
16
24
24
24
24
32
32
32
32
32
32
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
352
352
352
352
352
352
352
352
352
352
352
352
352
352
352
352
352
352
352
352
352
352
352
2.9
Summary
Table 2-17: Summary of Building Performance
Northridge Earthquake
Elastic Demand Ratios
(Model 3)
Damage
Remarks
No
–Elastic Response--
Ratios >1 in Beams and
Columns
Retrofit
Strategy
Design/Capacity
Ratios (Model 3)
Ratios >1 in Beam and
Column
Structural Elements
None
UBC-97
EDR
Compliance
No
EDR>1
in
Several
Elements
Special Provisions
ColumnDrift
Redundancy
Panel Continuity
Beam
Limits
Factors
zones
Plates
Moment
Ratios
No
No
OK
Limit
Failed to
>1.25
Provided
Exceeded Exceed Code OK
pass the
where
at all
Limitations
test on the
needed
Levels
top 2 floors
Retrofit
Strategy
Compliance
Increase Lateral Resisting Moment Frames
Life SafetyBSE-1
FEMA-273
Collapse PreventionBSE-2
Demand-Capacity
Spectra
OK
Failed in NS Direction
Elastic Behavior.
Retrofit
Strategy
57
3
3.1
ANALYSIS OF A TEN STORY OFFICE BUILDING,
TARZANA, CALIFORNIA
Building Description
This building is a ten-story Steel Moment Resisting Frame (SMRF) office building located at
Tarzana, California. The lateral resistance comprises of three moment resisting frames acting in
the North-South direction, and six in the East-West direction, with all connections being moment
resisting. The floor plan of the lateral resisting system and the column orientations is shown in
Figure 3-1.
The building has a taller first story, which is 192” in height. The remaining stories are 156” in
height. All member sizes and story heights for the moment resisting frames in the North-South
and East-West directions are shown in Figure 3-2. The columns typically have continuity plates
but no doubler plates. Beam-column connections for the North-South moment frames are
typically SMRF connections with the beam flanges complete penetration field welded directly to
the column flange or continuity plate. The East-West moment frame connections incorporated
flange plates complete penetration shop or field welded to the columns and fillet welded in the
field to the beam flanges. The moment frame connection detail is shown in Figure 3-3.
The structural steel is Grade A36 for the beams and Grade A572 (Grade 50) for the columns.
The floor system comprises of a 6¼” thick composite metal deck, with a 3”, 24-gauge metal
deck, overlaid by 3¼” lightweight concrete.
The seismic sensors for this building are located at the base the fifth floor and the roof.
58
30’
30’
30’
N
30’
30’
36’
30’
Figure 3-1: Model Dimensions and Column Orientations.
59
10’ x 13’=130’
60
10’ x 13’=130’
Figure 3-2: Frame Elevation and Member Sizes
16’
X=360
X=0
16’
X=792
Figure 3-3: Moment Frame Connection Detail
3.2
The SAP2000 Computer Model
SAP2000 models were created for Model 1 and Model 2 as outlined in the introduction. The
additional modeling assumptions for this building were:
Columns were assumed fixed at the base.
Splice locations were not discretely modeled and the column sections were assumed to
remain constant between two adjacent floors.
3.3
The IDARC2D-v.5 Computer Model
The computer program IDARC2D-v.5 is a two-dimensional analysis computer program for the
inelastic analysis of structures. It has two built-in hysteretic models (multi-linear or smooth) to
capture the behavior of both major structural materials – concrete and steel, by proper choice of
values for the parameters governing the three different types of deterioration (stiffness, strength
and slip). Since the computer program can analyze only two-dimensional frames, individual
models were created for the North-South and East-West directions. Additionally in the inelastic
models the penthouse was not explicitly modeled as in the elastic model, but its mass was added
at the roof level.
61
The hysteretic model chosen for this study was the multi-linear model, similar to that referred to
in previous versions of IDARC2D (as the three-parameter model). The member capacity was
defined by a moment-curvature envelope with equal positive and negative moment capacities
equal to the plastic moment of the section. The post yield stiffness was set at 3% of the original
elastic stiffness. Moderate stiffness degradation was used, with values of a varying between 1.7
in the East-West model and 3.0 in the North-South model. No strength degradation (β=0) or slip
(γ=1) were the hysteretic values chosen because they best simulate the behavior of steel. A
visual representation of the hysteretic model with the assumed hysteretic parameters is shown in
Figure 3-4.
M
K3 = a K1
K1
φ
Modeling of the Bauschinger
effect (slip parameter γ=1)
Pivot Point
a My
Figure 3-4: Hysteretic Model Used for this Study
For Model 3 full rigid zones were used in the North-South direction and no rigid zones in the
East-West direction. Rayleigh damping was used on the first and second modes in order to
eliminate the overshoots in the acceleration time histories. This is equivalent to the higher
damping used in the elastic models. The damping ratios used were 3% in the East-West
direction and 7% in the North-South direction. A summary of the modeling differences between
the various models is presented in Table 3-1.
62
Table 3-1: Summary of Modeling Differences.
Model
Rigid Zones
Analysis
Model 1
Model 2
All Elements
None
EW: No Rigid Zones
NS: Full Rigid Zones
Elastic 3D
Elastic 3D
Model 3
Inelastic 2D
Yield Stress
(ksi)
Beams 36
Columns 55
The visual representation of the model is shown in Figure 3-5.
Figure 3-5: Three Dimensional Model of the Building.
63
Modal Damping
7%
7%
EW: 3% Rayleigh
NS: 7% Rayleigh
3.4
Mass Calculations
The loading criteria used to calculate the masses from the plans or the manufacturer
specifications were:
•
•
•
•
8 psf for mechanical equipment.
20 psf for partition loading.
60 psf for the weight of the concrete slab with the steel panels.
30 psf for skin loading along the perimeter of the building, where applicable.
No additional live load was included.
The floor masses, mass moment of inertia and center of gravity, calculated using the computer
program JAMA-SDS (MMI) are presented in Table 3-2.
The floor plan layout showing the center of mass locations, plan openings, and perimeter line
loads is shown in Figure 3-6.
Table 3-2: Center of Mass, Mass and Mass Moment Of Inertia for Different Levels.
Level 2
Levels 3-10
Roof
Penthouse
Mass Moment of Inertia
(kips sec2 in)
Mass
(kips sec2/in)
530541
521028
431312
25042
1.99
1.97
1.61
0.39
64
Center of Gravity
X coord.
Y coord.
(in)
(in)
360.1
900
358.77
900
361.69
900
587.24
1080
1st Floor
Typical Floor
Roof
Penthouse
Figure 3-6: JAMA-SDS (MMI) calculations.
3.5
Modal Periods
The modal periods of the building for the three different models along with their mass
participation are given in Tables 3-3 and 3-4 for the SAP2000 and IDARC2D models. Model 3
had a fundamental period of 2.35 seconds in the East-West and a period of 2.15 seconds in the
North-South direction. The natural frequencies of the building were obtained from the actual
recorded responses using the transfer functions of the story accelerations normalized by the
superimposed input base motion in the frequency domain (see Figure 3-7). The third mode in the
North-South direction from the transfer function was unable to be identified probably because of
the high damping in the structure. The FFT method requires the structure to be lightly damped
with well-separated modes. A comparison of the frequencies from the transfer function and the
analytical models for the first three modes of vibration are given in Table 3-5. These frequencies
differ from the frequencies for Model 3, the best-fit model, in the range of 3%.
65
Table 3-3: Modal Periods for the SAP2000 Computer Models.
East-West
Model
1
Model
2
North-South
Mode
Period
Modal
Participation
Factor
Cumulative Modal
Participation Factor
1
4
7
1
4
8
(sec)
2.164
0.724
0.413
2.374
0.801
0.462
(%)
82.02
10.13
3.30
81.11
10.22
3.41
(%)
82.02
92.48
95.88
81.11
91.79
95.54
Mode
Period
Modal
Participation
Factor
Cumulative Modal
Participation Factor
2
5
8
2
5
7
(sec)
2.119
0.713
0.411
2.345
0.795
0.463
(%)
81.88
9.87
3.28
81.36
10.06
3.40
(%)
81.88
92.67
96.08
81.36
92.00
95.43
Table 3-4: Modal Periods for the IDARC Computer Models.
East-West
Model
3
Mode
Period
Modal
Participation
Factor
1
2
3
2.349
0.796
0.458
82.14
10.10
3.53
North-South
Cumulative
Modal
Participation
Factor
82.14
92.24
95.77
Mode
Period
Modal
Participation
Factor
1
2
3
2.153
0.721
0.412
83.03
9.84
3.37
Cumulative
Modal
Participation
Factor
83.03
92.87
96.24
Table 3-5: Comparison of the Modal Periods for Model 3 with the Periods from the Recorded
Response using the FFT Method.
East-West
North-South
Modal Periods
(IDARC2D)
Modal Periods
(FFT Analysis)
Diff.
(sec)
(sec)
(%)
1
2.349
2.272
3.24
2
3
0.796
0.458
0.833
0.602
4.48
1.07
Mode
66
Modal Periods
(IDARC2D)
Modal Periods
(FFT Analysis)
Diff.
(sec)
(sec)
(%)
1
2.153
2.222
3.11
2
3
0.721
0.412
0.75
Not identified
3.87
Mode
Torsional Mode
Figure 3-7: FFT Analyses.
3.6
Earthquake Ground Motions
The earthquake ground motions used in this study were the actual ground motions recorded at the
base of the building during the 1994 Northridge Earthquake. These motions include components
in the North-South, East-West and Vertical directions shown in Figure 3-8. Traditionally vertical
dynamic effects are ignored in a lateral analysis as the building is very stiff vertically and is
designed to take the gravity dead and live loads. The effects of vertical excitation were
investigated for this building for the following reasons:
a) All the frames were moment resisting.
b) The total mass of the building being vertically supported by the lateral frames would
put the maximum stresses from vertical excitation on these frames.
c) The vertical component of the ground motion appeared to be severe enough to
influence the response, which was characteristic of the Northridge Earthquake.
67
Acceleration Record at Level 0 (ground - 90)
Acceleration Record at Level 0 (ground - UP)
500
400
400
300
300
300
100
0
-100
-200
200
100
0
-100
-200
-300
-300
-400
-400
-500
-500
0
5
10
15
20
25
30
35
40
45
50
2
2
200
Acceleration (cm/sec )
500
400
Acceleration (cm/sec )
2
Acceleration (cm/sec )
Acceleration Record at Level 0 (ground - 180)
500
200
100
0
-100
-200
-300
-400
-500
0
5
10
15
20
Time (sec)
25
30
35
40
45
50
0
5
10
15
20
Time (sec)
North-South Component
East-West Component
25
30
35
40
45
Time (sec)
Vertical Component
Figure 3-8: Ground Motion Components
To investigate the effects of the vertical ground motion, a new model was created. The floor
slabs were divided into individual panel elements with the masses assigned per unit volume.
Each floor slab supported between frame grids was subdivided into a four by four grid system to
ensure sufficient vertical degrees of freedom to capture the vertical effects of the ground motion.
The effective thickness of the floor slab was 5” with a modulus of elasticity equal to that of the
concrete. The rigid diaphragm assumption was maintained for each floor in order to obtain
approximately the same period and modes of response as Model 3. This modeling procedure
results in a structure with a very large number of degrees of freedom, driving up the
computational time of the analysis significantly. A visual presentation of the model is shown in
Figure 3-9.
The following response parameters were checked in the study of the vertical effects.
1)
Maximum horizontal displacements.
2)
Change in beam moments.
The change in the peak displacements due to vertical effects were found to be insignificant. In
addition, the time history responses using the vertical excitation overlaid almost perfectly with
those that include only the horizontal excitation. The change in beam moments when compared
to its capacity showed a maximum increase of 6% at the mid-span, with an average difference of
only 0.18%. At the beam-ends, the difference was only 2% of the member capacity with an
average difference of 0.17%.
68
50
The added advantages of including the vertical effects of ground motion are far outweighed by
the additional effort in modeling and computational time. Therefore, no vertical effects on the
response and stresses calculations were taken into consideration for further analysis and for the
other three buildings.
Figure 3-9: 3D Model of the Building Used for the Vertical Excitation Checks.
3.7
Time History Analyses
Linear dynamic time history analyses were performed on Model 1 and Model 2 (see Table 3-1).
The time histories of the acceleration, velocity and displacement responses for the individual
models are presented in Figures 3-10 through 3-15. Clearly, the analytical model is much stiffer
than the actual building as observed from the responses in both directions. The analytical
comparisons look much better for Model 2, as seen in Figures 3-13 through 3-15.
69
3.7.1 Model 1 and Model 2.
From the displacement responses for Model 1 and Model 2, shown respectively in Figures 3-12
and 3-15, it is clear that there was an elongation of the period in the actual response, which was
an indication of significant inelasticity in the building response. Therefore, an inelastic analysis
was required to capture this behavior.
Acceleration Record at Level 5 (90)
700
500
500
300
300
2
Acceleration (cm/sec )
2
Acceleration (cm/sec )
Acceleration Record at Level 5 (180)
700
100
-100
-300
100
-100
-300
Recorded History
Recorded History
-500
-500
Model 1
Model 1
-700
-700
0
10
20
30
40
50
60
0
10
20
Time (sec)
50
60
Acceleration Record at Roof (90)
700
700
500
500
300
300
2
Acceleration (cm/sec )
2
40
Time (sec)
Acceleration Record at Roof (180)
Acceleration (cm/sec )
30
100
-100
-300
100
-100
-300
Recorded History
Recorded history
-500
-500
Model 1
Model 1
-700
-700
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
Time (sec)
Figure 3-10: Acceleration Records for Model 1.
70
40
50
60
Relative Velocity Record at Level 5 (90)
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
Relative Velocity Record at Level 5 (180)
200
50
0
-50
-100
50
0
-50
-100
Recorded History
Recorded History
-150
-150
Model 1
Model 1
-200
-200
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
24
26
28
30
32
34
36
38
40
42
44
46
48
50
Time (sec)
Relative Velocity Record at Roof (180)
Relative Velocity Record at Roof (90)
200
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
22
50
0
-50
-100
50
0
-50
-100
Recorded History
Recorded history
-150
-150
Model 1
Model 1
-200
-200
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
Time (sec)
Figure 3-11: Velocity Records for Model 1.
Relative Displacement Record at Level 5 (90)
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
Relative Displacement Record at Level 5 (180)
50
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded History
Recorded History
-40
-40
Model 1
Model 1
-50
-50
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
Relative Displacement Record at Roof (180)
Time (sec)
36
38
40
42
44
46
48
50
0
50
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
0
10
0
-10
-20
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
Relative Displacement Record at Roof (90)
Time (sec)
36
38
40
42
44
46
48
50
10
0
-10
-20
-30
-30
Recorded History
Recorded history
-40
-40
Model 1
Model 1
-50
-50
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
22
24
26
28
Time (sec)
Figure 3-12: Displacement Records for Model 1.
71
30
32
34
36
38
40
42
44
46
48
50
Acceleration Record at Level 5 (90)
750
750
2
Acceleration (cm/sec )
1250
2
Acceleration (cm/sec )
Acceleration Record at Level 5 (180)
1250
250
-250
-250
Recorded History
Recorded History
-750
250
-750
Model 2
Model 2
-1250
-1250
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
24
26
28
30
32
34
36
38
40
42
44
46
48
50
Time (sec)
Acceleration Record at Roof (180)
Acceleration Record at Roof (90)
1250
750
750
Acceleration (cm/sec )
1250
2
2
Acceleration (cm/sec )
22
250
-250
Recorded History
-750
250
-250
Recorded history
-750
Model 2
Model 2
-1250
-1250
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
Time (sec)
Figure 3-13: Acceleration Records for Model 2.
Relative Velocity Record at Level 5 (90)
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
Relative Velocity Record at Level 5 (180)
200
50
0
-50
50
0
-50
-100
-100
Recorded History
Recorded History
-150
-150
Model 2
Model 2
-200
-200
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
Relative Velocity Record at Roof (180)
Time (sec)
34
36
38
40
42
44
46
48
0
50
200
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
0
50
0
-50
-100
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
Relative Velocity Record at Roof (90)
Time (sec)
34
36
38
40
42
44
46
48
50
50
0
-50
-100
Recorded History
Recorded history
-150
-150
Model 2
Model 2
-200
-200
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
Time (sec)
18
20
22
24
26
28
Time (sec)
Figure 3-14: Velocity Records for Model 2.
72
30
32
34
36
38
40
42
44
46
48
50
Relative Displacement Record at Level 5 (90)
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
Relative Displacement Record at Level 5 (180)
50
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded History
Recorded History
-40
-40
Model 2
Model 2
-50
-50
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
24
26
28
30
32
34
36
38
40
42
44
46
48
50
Time (sec)
Relative Displacement Record at Roof (180)
Relative Displacement Record at Roof (90)
50
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
22
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded History
Recorded history
-40
-40
Model 2
Model 2
-50
-50
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
Time (sec)
Figure 3-15: Displacement Records for Model 2.
3.7.2 Model 3
Numerous checks were performed in order to ensure that the two-dimensional IDARC2D-v.5
model and the three-dimensional SAP2000 models give essentially the same results. An elastic
time-history response comparison between the IDARC2D-v.5 and SAP2000, with 7% mass
proportional damping is shown in Figure 3-16. There is a slight overshoot in the displacement
responses from IDARC2D-v.5 for the first twenty seconds of analysis, after which the responses
reverse with IDARC2D-v.5 under-predicting the amplitudes. This is attributed to the different
techniques used for integration and damping formulation between the two programs. The
analysis time step was set as half of the input time step (0.01 seconds). Smaller time steps did
not change the response. Static checks gave identical results for the two programs.
73
Comparison (Linear Analysis) between IDARC and SAP2000
-roof 18050
40
30
Displacement (cm)
20
10
0
-10
-20
-30
-40
-50
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
Time (sec)
Figure 3-16: Comparison between SAP2000 and IDARC2D-v.5 linear analysis results.
The responses from the inelastic time history analysis showed excellent agreement with the
recorded data see Figures 3-17 to 3-19.
Acceleration Record at Level 5 (90)
750
750
2
Acceleration (cm/sec )
1250
2
Acceleration (cm/sec )
Acceleration Record at Level 5 (180)
1250
250
-250
Recorded History
-750
250
-250
Recorded History
-750
Model 5
Model 5
-1250
-1250
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
24
26
28
30
32
34
36
38
40
42
44
46
48
50
Time (sec)
Acceleration Record at Roof (180)
Acceleration Record at Roof (90)
1250
750
750
2
Acceleration (cm/sec )
1250
2
Acceleration (cm/sec )
22
250
-250
Recorded History
-750
250
-250
Recorded history
-750
Model 5
Model 5
-1250
-1250
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
22
24
26
28
Time (sec)
Figure 3-17: Acceleration Records for Model 3.
74
30
32
34
36
38
40
42
44
46
48
50
Relative Velocity Record at Level 5 (90)
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
Relative Velocity Record at Level 5 (180)
200
50
0
-50
-100
50
0
-50
-100
Recorded History
-150
Recorded History
-150
Model 5
Model 5
-200
-200
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
24
26
28
30
32
34
36
38
40
42
44
46
48
50
Time (sec)
Relative Velocity Record at Roof (180)
Relative Velocity Record at Roof (90)
200
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
22
50
0
-50
-100
50
0
-50
-100
Recorded History
Recorded history
-150
-150
Model 5
Model 5
-200
-200
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
Time (sec)
Figure 3-18: Velocity Records for Model 3.
Relative Displacement Record at Level 5 (90)
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
Relative Displacement Record at Level 5 (180)
50
10
0
-10
-20
0
-10
-20
Recorded History
-30
-40
Recorded History
-30
-40
Model 5
-50
Model 5
-50
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
Relative Displacement Record at Roof (180)
Time (sec)
36
38
40
42
44
46
48
50
0
50
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
10
10
0
-10
-20
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
Relative Displacement Record at Roof (90)
Time (sec)
36
38
40
42
44
46
48
50
10
0
-10
-20
Recorded History
-30
-40
Recorded history
-30
-40
Model 5
-50
Model 5
-50
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
22
24
26
28
Time (sec)
Figure 3-19: Displacement Records for Model 3.
75
30
32
34
36
38
40
42
44
46
48
50
3.7.3 Demand Capacity Ratios
Table 3-6 shows a comparison of the demand/capacity ratios for all the beams in the model. It
should be noted that these demand capacity ratios are the inelastic demand capacity ratios. A
visual representation is shown in Figure 3-20. No stress calculations were performed for this
model since the best-fit model was inelastic.
Table 3-6: Inelastic Demand/Capacity Ratios for Beam Elements
Element Stress Ratio
2nd story
1
2
3
4
5
51
52
53
54
55
101
102
103
7th story
26
27
28
29
30
76
77
78
79
80
116
117
118
3.8
Demand /
Demand /
Demand /
Demand /
Demand /
Element Stress Ratio
Element Stress Ratio
Element Stress Ratio
Element Stress Ratio
Capacity
Capacity
Capacity
Capacity
Capacity
4th story
3rd story
5th story
6th story
1.14
6
1.16
11
1.10
16
1.13
21
1.14
1.12
7
1.13
12
1.11
17
1.13
22
1.14
1.13
8
1.13
13
1.11
18
1.13
23
1.14
1.13
9
1.14
14
1.11
19
1.13
24
1.15
1.12
10
1.14
15
1.11
20
1.13
25
1.16
1.15
56
1.15
61
1.15
66
1.15
71
1.17
1.18
57
1.17
62
1.17
67
1.18
72
1.19
1.19
58
1.17
63
1.16
68
1.18
73
1.19
1.19
59
1.18
64
1.18
69
1.18
74
1.19
1.16
60
1.15
65
1.15
70
1.16
75
1.17
1.14
104
1.14
107
1.13
110
1.16
113
1.16
1.14
105
1.17
108
1.11
111
1.14
114
1.16
1.14
106
1.16
109
1.12
112
1.14
115
1.15
8th story
9th story
10th story
11th story
1.10
31
1.05
36
0.89
41
0.65
46
0.37
1.07
32
1.02
37
0.71
42
0.49
47
0.32
1.09
33
1.02
38
0.73
43
0.44
48
0.22
1.08
34
1.02
39
0.71
44
0.43
49
0.22
1.14
35
1.07
40
0.82
45
0.56
50
0.34
1.14
81
1.12
86
1.07
91
0.77
96
0.37
1.16
82
1.14
87
1.08
92
0.81
97
0.43
1.16
83
1.13
88
1.08
93
0.84
98
0.45
1.16
84
1.16
89
1.07
94
0.83
99
0.45
1.15
85
1.11
90
1.06
95
0.75
100
0.37
1.12
119
1.11
122
1.00
125
0.69
128
0.32
1.13
120
1.10
123
0.90
126
0.60
129
0.29
1.14
121
1.13
124
1.01
127
0.68
130
0.33
Comparison of Actual Damage with Predicted Damage.
This building had 460 moment resisting frame connections, 260 of which were in the NorthSouth and 200 in the East-West direction of the building. The building was inspected for
damage after the earthquake with 33 connections tested in the North-South direction and 28 in
the East-West direction using visual and ultrasonic examination at 30 different randomly selected
locations. No damage was found at any of these connections except at location B6 for the 3rd
level as shown in Figure 3-21, which suffered a fracture in the bottom flange (SAC, type G4).
Minor damage was found in location B6 for the 4th level (probable slab and lack of fusion
identified -SAC, type W1-), which suffered of a minor weld root defect.
76
Figure 3-20: Locations where the Demand/Capacity Ratio is Larger than 1 after IDARC
Dynamic Inelastic Analysis.
77
Figure 3-21: Locations where Damage was Detected.
78
3.9
3.9.1
Evaluation using Prevailing Practice UBC-97 and FEMA-273
Analysis Using UBC-97
In order to investigate how current methods for analysis and design meet the seismic demands,
the building was examined for compliance with the UBC-97 code. Design Static Analysis
procedures were used because the building was categorized as regular and its height was less
than 240 ft.
The calculated Design Base Shear was also verified to be within the acceptable range specified in
UBC-97 as described in section 1630.2.1. The values used for all the above parameters are
reported in Table 3.7.
The distribution of the static base shear as well as the earthquake loads applied at each level were
calculated according to the code provisions as defined in detail in the introduction. Here the
lateral loads are equal with the earthquake forces since the redundancy factors for this building
are equal to 1 as shown in Table 3-7.
Table 3-7: UBC-97 Summary Table, Parameters and Forces
Site Parameters
Z
0.4
Ca
0.44
Cv
0.77
SEISMIC ZONE: 4
OCCUPANCY CATEGORY: Standard Occupancy
REGULAR STRUCTURE
BUILDING HEIGHT: 133 feet
BASE SHEAR VX=
386.70
kips
BASE SHEAR Vy=
386.70
kips
I
Nv
Structural Parameters
R
8.5
TX (sec)
1.78
Ty (sec)
1.78
1.00
W (kips)
7626.66
1.20
-- STATIC ANALYSIS -Base Shear Distribution, Earthquake Loads and Overturning Moments
applied to the structure
Lateral Loads
(kips)
Redundancy
Factors
Earthquake Forces
OTM
(kips)
(kips-feet)
FEW
FNS
ρEW
ρNS
EW
NS
EW
NS
Level
109.40
54.36
48.47
42.58
36.69
30.80
24.91
19.03
13.14
7.32
109.40
54.36
48.47
42.58
36.69
30.80
24.91
19.03
13.14
7.32
1.00
1.00
109.40
54.36
48.47
42.58
36.69
30.80
24.91
19.03
13.14
7.32
109.40
54.36
48.47
42.58
36.69
30.80
24.91
19.03
13.14
7.32
1422.21
3551.08
6310.06
9622.58
13412.10
17602.06
22115.91
26877.08
31809.03
37996.26
1422.21
3551.08
6310.06
9622.58
13412.10
17602.06
22115.91
26877.08
31809.03
37996.26
Roof
9
8
7
6
5
4
3
2
1
79
3.9.1.1 Check for Drift Limitations
For this building, it was found that the UBC-97 story drift limitations were satisfied in most
floors. Analytically, the results for all stories are presented in Table 3-8. The maximum interstory drift being 2.14% at the third floor in the East-West (X) Direction.
Table 3-8: UBC-97 Summary Displacements and Drift Limit Checks.
Maximum Inelastic
Response Displacements
INTERSTORY DRIFT RATIO
∆M
(% of story height)
(in)
Level
EW
NS
Roof
9
8
7
6
5
4
3
2
1
26.12
25.05
23.26
21.06
18.45
15.53
12.55
9.40
6.07
2.92
25.41
24.28
22.43
20.35
17.79
14.93
12.08
9.04
5.89
2.80
EW
0.69
1.14
1.41
1.68
1.87
1.91
2.02
2.14
2.02
1.52
OK
OK
OK
OK
OK
OK
Limit Exceeded
Limit Exceeded
Limit Exceeded
OK
NS
0.72
1.18
1.33
1.64
1.83
1.83
1.95
2.02
1.98
1.46
OK
OK
OK
OK
OK
OK
OK
Limit Exceeded
OK
OK
3.9.1.2 Elastic Demand Ratios
The Elastic Demand Ratios calculated for the beam elements from SAP2000 following the UBC97 requirement using the nominal yield stresses for the structural steel were all less than 1 (Table
3-9). All EDR are shown in Figures 3-22 and 3-23. In general, the conclusion after the stress
ratio analysis for UBC-97 is that the building will behave elastically and will suffer no damage,
which was not in agreement on what happened in reality.
80
Table 3-9: UBC-97 Elastic Demand Capacity Ratios.
Element
1
2
3
4
5
51
52
53
54
55
101
102
103
26
27
28
29
30
76
77
78
79
80
116
117
118
EW
2nd story
0.24
0.38
0.38
0.48
0.49
0.20
0.46
0.36
0.21
0.40
0.03
0.06
0.78
7th story
0.72
0.03
0.02
0.05
0.82
0.04
0.02
0.67
0.15
0.23
0.03
0.65
0.15
NS
Element
0.27
0.31
0.48
0.53
0.41
0.46
0.34
0.35
0.39
0.31
0.51
0.39
0.44
6
7
8
9
10
56
57
58
59
60
104
105
106
0.46
0.25
0.50
0.33
0.46
0.30
0.51
0.25
0.22
0.19
0.50
0.25
0.21
31
32
33
34
35
81
82
83
84
85
119
120
121
EW
3rd story
0.40
0.56
0.55
0.41
0.58
0.49
0.03
0.02
0.75
0.61
0.74
0.03
0.02
8th story
0.75
0.03
0.02
0.05
0.82
0.17
0.38
0.36
0.18
0.42
0.22
0.16
0.35
NS
Element
0.48
0.60
0.51
0.49
0.61
0.24
0.30
0.49
0.45
0.34
0.46
0.26
0.51
11
12
13
14
15
61
62
63
64
65
107
108
109
0.47
0.24
0.51
0.38
0.44
0.43
0.34
0.24
0.43
0.43
0.18
0.33
0.30
36
37
38
39
40
86
87
88
89
90
122
123
124
EW
4th story
0.57
0.42
0.53
0.54
0.35
0.04
0.03
0.06
0.80
0.75
0.05
0.81
0.77
9th story
0.57
0.04
0.02
0.63
0.16
0.39
0.19
0.43
0.40
0.20
0.31
0.17
0.37
NS
Element
0.49
0.50
0.51
0.45
0.47
0.27
0.52
0.40
0.44
0.46
0.35
0.43
0.47
16
17
18
19
20
66
67
68
69
70
110
111
112
0.28
0.28
0.48
0.26
0.22
0.42
0.44
0.44
0.42
0.44
0.22
0.33
0.38
41
42
43
44
45
91
92
93
94
95
125
126
127
EW
5th story
0.47
0.46
0.04
0.02
0.72
0.04
0.02
0.05
0.83
0.78
0.03
0.03
0.05
10th story
0.26
0.18
0.42
0.35
0.18
0.42
0.37
0.21
0.29
0.48
0.35
0.18
0.38
NS
Element
0.43
0.25
0.29
0.46
0.46
0.27
0.52
0.36
0.43
0.47
0.26
0.53
0.39
21
22
23
24
25
71
72
73
74
75
113
114
115
0.21
0.45
0.37
0.31
0.45
0.35
0.36
0.37
0.21
0.25
0.39
0.34
0.39
46
47
48
49
50
96
97
98
99
100
128
129
130
EW
6th story
0.48
0.03
0.02
0.06
0.79
0.03
0.03
0.05
0.86
0.71
0.83
0.70
0.05
11th story
0.44
0.41
0.19
0.45
0.41
0.03
0.03
0.74
0.60
0.04
0.36
0.19
0.39
NS
0.24
0.24
0.49
0.38
0.47
0.27
0.53
0.40
0.43
0.33
0.43
0.33
0.29
0.44
0.45
0.46
0.45
0.44
0.29
0.48
0.45
0.33
0.26
0.31
0.34
0.31
3.9.1.3 Seismic Special Provision Checks
A summary of the individual special seismic checks performed is shown in Table 3-10. All the
panel zones met the thickness requirement. Continuity plates were needed on the top 3 floors
and were provided, so this requirement was satisfied. The Column-Beam moment ratio checks
were satisfied for all connections.
Table 3-10: UBC-97 Seismic Provisions for Structural Steel
Check
Results
UBC-97 Special Seismic Provisions Checks
Panel Zone
Continuity
Column-Beam Moment
Thickness
Plates
Ratios
Passed (Top 3
floors needed
Passed
Passed
Continuity
Plates)
81
Figure 3-22 Stress Ratios calculated from SAP2000 in the East-West Direction for UBC97 Static Analysis Procedure.
Figure 3-23 Stress Ratios calculated from SAP2000 in the North-South Direction for
UBC-97 Static Analysis Procedure.
82
3.9.2 Analysis Using FEMA 273
3.9.2.1 Non-linear Static Pushover Analysis
The calculated target displacements for the BSE-1 and BSE-2 level earthquake and the important
factors used for both principle directions of the building are presented in Table 3-11. The
spectral acceleration of the building for BSE-1 level earthquake was 0.43g for the East-West
direction and 0.47g in the North-South direction. For the BSE-2 level earthquake, these values
were 0.64g and 0.70g respectively. The roof target displacements for the East-West and the
North-South directions for the BSE-1 earthquake were 29.89 inches and 27.35 inches. This
corresponds to an overall drift ratio of 1.87% in the East-West direction and 1.70% in the NorthSouth direction. The roof target displacements for the East-West and the North-South directions
for the BSE-2 earthquake were 44.83 inches and 41.02 inches. The corresponding drift ratios for
the BSE-2 level earthquake were 2.80% and 2.57% respectively.
It is worth mentioning that these results were for Site Class E, which is the default for FEMA273 if the soil type is unavailable. From experience we can approximate that the soil profile at
the building location is better described by using Site Class D (Stiff Soil). By using this Site
Class the roof target displacements for the BSE-1 earthquake reduce to 22.42 inches (or 1.40%
drift ratio) and 20.51 inches (or 1.28% drift ratio) for the East-West and the North-South
directions respectively. The same values for BSE-2 earthquake are 33.63 inches (2.1%) and
30.76 inches (1.93%). In this document, the roof target displacements correspond to the values
for Site Class E.
The base shears and corresponding yield displacements for the three loading patterns used for the
pushover analysis to achieve the target roof displacement are presented in Tables 3-12 through 315. Clearly the Uniform pattern showed the highest yield shear and required displacement
ductility. The displacement ductility for the BSE-1 earthquake was 2.16 for the North-South and
2.30 for the East-West direction, and that for the BSE-2 earthquake was 3.24 and 3.30
respectively.
The actual recorded maximum relative roof displacement in the North-South direction was 15.43
inches (1% drift ratio) and in the East-West direction 10.01 inches (0.6% drift ratio). This
83
corresponds to 75% for the North-South and 45% for the East-West of the roof target
displacement for the BSE-1 earthquake. The maximum recorded displacements in both
directions were approximately equal to the yield displacements, as observed from the demand
capacity spectrum curves (Figures 2-24 to 2-27). From this analysis, the building should behave
inelastically in the North-South direction and is very close to inelastic behavior in the East-West
direction. Similar conclusions were drawn from the time-history analyses.
Table 3-11: FEMA 273 Summary Displacements and Drift Limit Checks.
Non-Linear Static Procedure
1) Period Determination:
Ki
Ke
T e = Ti
Ke is determined at 60% of Vy
BSE-1
BSE-2
EW
2.35
NS
2.15
2) Vertical Distribution of Seismic Forces
Uniform Pattern
Lateral Forces Proportional to the Total Mass at Each Floor Level
AND AT LEAST ONE OF THE FOLLOWING:
i) Lateral load distribution as described in the Linear Static Procedure if more than 75% of the total mass
participates in the fundamental mode in the direction under consideration
ii) Lateral load pattern proportional to the story inertia forces consistent with the story shear distribution
calculated by combination of modal responses using (a) Response Spectrum Analysis using sufficient #
of modes to capture the 90% of the total mass or (b) the appropriate ground motion spectrum
δ t = C0 C1 C2 C3 Sa
Te2
g
4π 2
3) Target Displacement δt (in)
EW
29.89
44.83
NS
27.35
41.02
C0 : Modification Factor to Relate Spectral Displacement and likely building Roof
Displacement (TABLE 3-2)
1.30
C1 : Modification Factor to Relate Expected Maximum Displacements to
Displacements Calculated for Linear Elastic Response
EW
1
1
NS
1
1
C2 : Modification Factor to Represent the effect of Stiffness Degradation and
Strength Deterioration on Maximum Displacement Response (TABLE 3-1)
EW
1
1
NS
1
1
C3 : Modification Factor to Represent Increased Displacements due to Dynamic
P-∆ Effects (positive post-yielding stiffness assumed)
EW
Sa : Response Spectrum Acceleration at the Fundamental Period and Damping
Ratio of the Building in the Direction Under Consideration (g)
EW
0.43
0.64
NS
0.47
0.70
84
1
1
NS
Table 3-12: Nonlinear Static results for BSE-1 in the North-South Direction.
East-West
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
1236
Target
Displacement
(inches)
0.16
Yield
Displacement
(inches)
14.83
1419
0.19
14.67
27.35
1581
0.21
12.67
Yield Base
Shear Coefficient
Displacement
Ductility
1.84
1.86
2.16
Table 3-13: Nonlinear Static results for BSE-1 in the East-West Direction
North-South
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
1216
Target
Displacement
(inches)
0.16
Yield
Displacement
(inches)
15.09
1419
0.19
15.09
29.89
1581
0.21
13.02
Yield Base
Shear Coefficient
Displacement
Ductility
1.98
1.98
2.30
Table 3-14: Nonlinear Static results for BSE-2 in the North-South Direction.
North-South
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
1277
Target
Displacement
(inches)
0.17
Yield
Displacement
(inches)
15.33
1419
0.19
15.33
41.02
1581
0.21
12.67
Yield Base
Shear Coefficient
Displacement
Ductility
2.67
2.67
3.24
Table 3-15: Nonlinear Static results for BSE-2 in the East-West Direction.
East-West
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
1236
Target
Displacement
(inches)
0.16
Yield
Displacement
(inches)
15.77
1419
0.19
15.77
44.83
1662
0.22
13.6
Yield Base
Shear Coefficient
85
Displacement
Ductility
2.84
2.84
3.30
1.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
1.20
Base Shear Coefficient (BS/W)
Target Displacement BSE-1
Target Displacement BSE-2
1.00
Elastic Demand Spectrum, Damping Ratio 3%
BSE-1 Demand Spectrum
Inelastic Demand Spectrum, Damping Ratio 3%, R=1
0.80
Maximum Equivalent Response
0.60
0.40
BSE-1 δ t =
BSE-2 δ t =
29.89 in
44.83 in
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
Roof Drift (%)
Figure 3-24: Demand-Capacity Spectra for the East-West Direction.
1.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
1.20
Base Shear Coefficient (BS/W)
Target Displacement BSE-1
Target Displacement BSE-2
1.00
Elastic Demand Spectrum, Damping Ratio 7%
BSE-1 Demand Spectrum
Inelastic Demand Spectrum, Damping Ratio 7%, R=1.22
0.80
Maximum Equivalent Response
0.60
0.40
BSE-1 δ t =
27.35 in
BSE-2 δ t =
41.02 in
0.20
0.00
0.00
0.50
1.00
1.50
Roof Drift (%)
2.00
2.50
Figure 3-25: Demand-Capacity Spectra for the North-South Direction.
86
3.00
0.50
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
0.45
Non-linear Static Procedure - "Modal Analysis" Pattern
Target Displacement BSE-1
Base Shear Coefficient (BS/W)
0.40
Target Displacement BSE-2
Elastic Demand Spectrum, Damping Ratio 3%
BSE-1 Demand Spectrum
0.35
Inelastic Demand Spectrum, Damping Ratio 3%, R=1
Maximum Equivalent Response
0.30
0.25
0.20
0.15
BSE-1 δ t =
0.10
BSE-2 δ t =
29.89 in
44.83 in
0.05
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
Roof Drift (%)
Figure 3-26: Demand-Capacity Spectra for the East-West Direction – Detail.
0.50
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
0.45
Non-linear Static Procedure - "Modal Analysis" Pattern
Target Displacement BSE-1
Base Shear Coefficient (BS/W)
0.40
Target Displacement BSE-2
Elastic Demand Spectrum, Damping Ratio 7%
BSE-1 Demand Spectrum
0.35
Inelastic Demand Spectrum, Damping Ratio 7%, R=1.22
Maximum Equivalent Response
0.30
0.25
0.20
0.15
BSE-1 δ t =
27.35 in
BSE-2 δ t =
41.02 in
0.10
0.05
0.00
0.00
0.50
1.00
1.50
Roof Drift (%)
2.00
2.50
Figure 3-27: Demand-Capacity Spectra for the North-South Direction - Detail.
87
3.00
3.9.3 Acceptance Criteria
The yield pattern of the hinges for the North-South direction at the BSE-1 level target
displacement for the uniform push pattern is given in Figure 3-28. The yield pattern at the BSE-2
level target displacement in Figure 3-29. For the East-West direction, the hinge patterns for the
two earthquakes are given in Figures 3-30 and 3-31.
The summary of the acceptance criteria is presented in Table 3-16. For both the BSE-1 and the
BSE-2 earthquakes there were no hinges that exceeded the Life Safety (LS) acceptance criterion.
Thus, the building meets both the requirements (LS for BSE-1 earthquake and CP for BSE-2
earthquake) of the Basic Safety Objective (BSO) and therefore no further improvement of the
design is required.
88
Figure 3-28: Hinge Yield Pattern at the BSE-1 Level Target Displacement for the Uniform
Distribution Pushover Analysis in the North-South Direction.
Figure 3-29: Hinge Yield Pattern at the BSE-2 Level Target Displacement for the Uniform
Distribution Pushover Analysis in the North-South Direction
89
Figure 3-30: Hinge Yield Pattern at the BSE-1 Level Target Displacement for the Uniform
Distribution Pushover Analysis in the East-West Direction.
Figure 3-31: Hinge Yield Pattern at the BSE-2 Level Target Displacement for the Uniform
Distribution Pushover Analysis in the East-West Direction.
90
Table 3-16: Plastic Hinges at the Building Formed for BSE1 and BSE2 after performing
Pushover Analysis in both Directions
Type and Number of Hinges formed at Target Displacement in the
East-West Direction, the Uniform Pattern and BSE1
Step
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Displacement Base Shear
-0.15
0.00
7.35
889.15
8.18
987.63
13.87
1434.73
21.43
1695.13
32.03
1885.02
39.72
1995.54
53.84
2174.29
58.16
2226.41
58.16
2124.96
58.55
2157.64
58.55
2130.31
58.55
2112.29
58.96
2142.63
58.96
2118.73
58.96
2118.73
at Target Displacement
A-B
B-IO
816
816
810
756
722
695
686
676
674
674
674
674
674
674
674
674
674
0
0
6
60
62
41
38
20
20
20
20
20
20
20
20
20
20
IO-LS LS-CP
0
0
0
0
32
80
92
86
76
74
72
72
72
72
71
71
72
0
0
0
0
0
0
0
34
42
44
45
44
44
43
43
42
0
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
4
5
6
6
6
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
816
816
816
816
816
816
816
816
816
816
816
816
816
816
816
816
Type and Number of Hinges formed at Target Displacement in the
North-South Direction, the Uniform Pattern and BSE1
Step
0
1
2
3
4
5
6
7
8
9
10
11
12
Displacement Base Shear
0.00
0.00
7.50
923.31
7.89
970.74
14.10
1460.83
22.63
1732.49
34.81
1941.65
48.60
2141.83
54.72
2222.81
54.72
2121.22
55.16
2151.11
55.88
2178.23
56.61
2195.31
56.61
2195.31
at Target Displacement
A-B
B-IO
816
816
815
738
682
666
652
642
642
642
642
642
642
642
0
0
1
78
84
34
27
26
26
26
26
26
26
26
IO-LS LS-CP
0
0
0
0
50
116
109
82
82
74
72
70
70
70
0
0
0
0
0
0
28
60
60
68
70
65
65
0
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
7
7
0
0
0
0
0
0
0
0
0
6
6
6
6
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
816
816
816
816
816
816
816
816
816
816
816
816
816
Type and Number of Hinges formed at Target Displacement in the
East-West Direction, the Uniform Pattern and BSE2
Step
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Displacement Base Shear
-0.15
0.00
7.35
889.17
8.18
987.63
13.87
1434.40
21.43
1694.85
32.03
1884.83
39.72
1995.40
53.84
2174.14
58.16
2226.27
58.16
2124.82
58.55
2157.50
58.55
2130.17
58.55
2112.15
58.96
2142.49
58.96
2118.59
58.96
2118.59
at Target Displacement
A-B
B-IO
816
816
810
756
722
695
686
676
674
674
674
674
674
674
674
674
674
0
0
6
60
62
41
38
20
20
20
20
20
20
20
20
20
20
IO-LS LS-CP
0
0
0
0
32
80
92
86
76
74
72
72
72
72
71
71
72
0
0
0
0
0
0
0
34
42
44
45
44
44
43
43
42
34
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
4
5
6
6
6
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
816
816
816
816
816
816
816
816
816
816
816
816
816
816
816
816
Type and Number of Hinges formed at Target Displacement in the
North-South Direction, the Uniform Pattern and BSE2
Step
0
1
2
3
4
5
6
7
8
9
10
11
12
Displacement Base Shear
0.00
0.00
7.50
923.30
7.89
970.74
14.10
1460.85
22.63
1732.49
34.81
1941.64
48.60
2141.82
54.72
2222.82
54.72
2121.22
55.16
2151.12
55.88
2178.23
56.61
2195.32
56.61
2195.32
at Target Displacement
A-B
B-IO
816
816
815
738
682
666
652
642
642
642
642
642
642
642
0
0
1
78
84
34
27
26
26
26
26
26
26
26
91
IO-LS LS-CP
0
0
0
0
50
116
109
82
82
74
72
70
70
70
0
0
0
0
0
0
28
60
60
68
70
65
65
28
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
7
7
0
0
0
0
0
0
0
0
0
6
6
6
6
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
816
816
816
816
816
816
816
816
816
816
816
816
816
3.10 Summary
Table 3-17: Summary of Building Performance
Northridge Earthquake
Elastic Demand Ratios
(EDR)
Damage
Design/Capacity
Ratios
Remarks
Yes
–Figure 3-21--
N/A
Ratios >1 in Beams and
Columns
Retrofit
Strategy
None
N/A
None
UBC-97
Compliance
EDR
Drift
Limits
Redundancy
Factors
Yes
No
Table
3-8
OK
Retrofit
Strategy
Compliance
Special Provisions
ColumnPanel Continuity
Beam
Zones
Plates
Moment
Ratios
OK
Provided
OK
OK
where
needed
None
Life SafetyBSE-1
FEMA-273
Collapse PreventionBSE-2
OK
OK
Retrofit
Strategy
None
92
Demand-Capacity
Spectra
Actual response indicates
inelastic behavior.
4
4.1
ANALYSIS OF A SIXTEEN STORY BUILDING,
SHERMAN OAKS, CALIFORNIA
Building Description
This building is a sixteen-story Steel Moment Resisting Frame (SMRF) office building located at
Sherman Oaks, California. It is rectangular in plan, with approximate dimensions 129’ X 152’.
The lateral resistance of the structure comprises of two pairs of identical multiple bay moment
resisting frames, one acting in the North-South and one in the East-West direction. All moment
frames were located along the perimeter of the building. A floor plan of the lateral resisting
system and the column orientations is shown in Figure 4-1. The member sizes and story heights
for the moment resisting frames in the North-South and East-West directions are shown in Figure
4-2. The top and bottom beam flanges are fully welded to the columns using complete
penetration welds, and the beam web is attached to the column through a steel shear tab and
A325 high strength bolts. The moment frame connection detail is shown in Figure 4-3.
The structural steel is either Grade A36 or Grade A572 (Grade 50) as specified on the
construction drawings. The floor system at all floors except the roof is composed of QL-3-20
GA 1½” steel deck overlaid with 2½” lightweight concrete. For the roof, a QL-3-18 GA 1½”
steel deck overlaid with 4½” lightweight concrete was used.
The seismic sensors for this building are located at the base, the eighth floor and the roof.
93
30’
29’ 5’’
Y
30’
30’
30’
N
X
31’
32’
32’
31’ 6’’
Figure 4-1: Model Dimensions and Column Orientations.
94
16’ 8’’
12 X 12’ 10’’=154’
Figure 4-2 Frame Elevation and Member Sizes
95
22’
17’
EW Frame
NS Frame
Figure 4-3: Moment Frame Connection Details
4.2
The SAP2000 Computer Models
The SAP2000 models were created as outlined in the introduction. The additional modeling
assumptions made for this building are:
The base of the model was taken at the ground level, with the two levels of parking below
grade ignored. This is because the presence of basement shear walls all around, made the
stiffness of the two levels of parking many times stiffer than the flexible superstructure. The
columns were assumed fixed at the base.
The splice locations were not discretely modeled and the column sections were assumed to
remain constant between two adjacent floors.
97
The effectiveness of the rigid zones for Model 3 was calibrated at 80% of the full rigid zone
length for the East-West direction frames, and 34% for the North-South direction frames. The
damping ratios used for the first two modes of Model 3 in the East-West direction were set at 2%
and 3% while in the North-South direction at 1% and 3%. All higher modes were damped at 6%,
so that the contribution of the high frequency response in the acceleration time histories would be
minimal. A summary of the modeling differences between the models is presented in Table 4-1.
Table 4-1: Modeling Differences Between the Various Models.
Model
Rigid Zones
Analysis
Model 1
Model 2
All Elements
None
80 % EW
34% NS
Elastic 3D
Elastic 3D
Yield Stress
(ksi)
-
Elastic 3D
-
Model 3
Modal Damping
1%EW, 2% NS
1%EW, 2% NS
EW: 2% 1st, 3% 2nd, 6% all others
NS: 1% 1st, 3% 2nd , 6% all others
The visual representation of the three-dimensional SAP2000 model used is shown in Figure 4-4.
Figure 4-4: 3D Model of the Building.
98
4.3
Mass Calculations
The loading criteria used to calculate the masses from the plans or the manufacturer
specifications are given in Table 4-2. Any contribution from live load was assumed to be
included in the partition loads. An additional 30-psf skin loading along the perimeter was
considered where applicable. A summary of the results is presented in Table 4-3.
The floor plan layout showing the center of mass locations, plan openings, and perimeter line
loads is shown in Figure 4-5.
Table 4-2: Dead Loads Considered for the Mass Calculations
Story / Area
Structural Weight
(psf)
Helistop Area (Pent. Roof)
44.2
Roof Area
49.7+31.9
Penthouse Floor
49.7
Office Floors
30.4+(10.8…18.0)
Upper and Lower Plaza
30.4+26.4
99
Additional Vertical Loads
(psf)
Wearing Slab
3
Mechanical / Misc.
83
Roofing and Insulating
6
Fill for Drainage
57
Ceiling and Mechanical
5
Fill for Acoustic
96
Ceiling and Mechanical
5
Partition
20
Ceiling and Mechanical
5
Finish
60
Ceiling and Mechanical
5
Total
(psf)
130.2
149.6
150.7
(66.2…73.4)
121.8
Table 4-3: Center of Mass, Mass and Mass Moment of Inertia for Different Levels.
Mass Moment of
Inertia
(kips sec2 in)
3585427
2143969
2050000
2153977
7448494
Upper Plaza
Level 3
Typical Floor (4-14, avg.)
Level 15
Roof
Center of Gravity
X coord.
Y coord.
(in)
(in)
760.50
899.50
760.51
760.51
760.50
899.47
760.46
899.37
763.13
858.19
Mass
(kips sec2/in)
6.60
3.96
3.67
3.83
16.38
Upper Plaza
Third Floor
Typical Floor
Roof
Figure 4-5: JAMA-SDS (MMI) calculations.
100
4.4
Modal Periods
The modal periods of the building for the three different models along with their mass
participation are given in Table 4-4. Model 3 had a fundamental period of 3.27 seconds in the
East-West and 3.61 seconds in the North-South direction. The natural frequencies of the
building were obtained from the actual recorded responses using the transfer functions of the
story accelerations normalized by the superimposed input base motion in the frequency domain
(Figure 4-6). In the East-West direction, the identification of the natural frequencies is not clear;
if time-history responses from more levels were recorded, a better modal period identification
would be possible. The modal periods calculated using this method matched well with the
periods obtained from the modal analysis of Model 3. The maximum difference was 9.2% in the
second mode for the North-South direction. The analytical results of this study are given in
Table 4-5.
Table 4-4: Modal Periods for the Selected Computer Models.
Mode
Period
(sec)
Model
1
Model
2
Model
3
1
4
7
1
4
7
1
4
7
3.313
1.133
0.632
3.828
1.310
0.736
3.610
1.234
0.689
North-South
Modal
Cumulative Modal
Participation
Participation
Factor
Factor
(%)
(%)
78.11
11.57
3.56
77.48
11.46
3.65
77.70
11.51
3.50
78.11
89.68
93.24
77.48
88.94
92.59
77.70
89.25
92.88
101
Mode
Period
(sec)
2
5
8
2
5
8
2
5
8
3.172
1.072
0.610
3.676
1.243
0.711
3.267
1.104
0.629
East-West
Modal
Cumulative Modal
Participation
Participation
Factor
Factor
(%)
78.16
11.51
3.67
77.63
11.33
3.74
78.05
11.48
3.68
78.16
89.68
93.34
77.63
88.96
92.70
78.05
89.53
93.21
Table 4-5: Comparison of the Modal Periods as Calculated from Modal Analysis and the Real
Records Using the FFT Method.
Mode
1
4
7
North-South
Modal
Modal Periods
Periods
(FFT Analysis)
(SAP2000)
(sec)
(sec)
3.610
3.55
1.234
1.13
0.689
0.66
Diff.
Mode
(%)
1.8
9.2
4.2
2
5
8
East-West
Modal
Modal Periods
Periods
(FFT Analysis)
(SAP2000)
(sec)
(sec)
3.267
3.0
1.104
1.083
0.629
0.66
Diff.
(%)
9.0
1.9
5.1
Figure 4-6: FFT Analyses.
4.5
Earthquake Ground Motions
The earthquake ground motions used in this study are the actual ground motions recorded at the
base of the building during the 1994 Northridge Earthquake. These motions include components
in the North-South, East-West and Vertical directions shown in Figure 4-7.
102
Acceleration Record at Level 0 (ground - 180)
Acceleration Record at Level 0 (ground - UP)
500
400
400
400
300
300
300
100
0
-100
-200
200
100
0
-100
-200
-300
-300
-400
-400
-500
2
2
200
Acceleration (cm/sec )
500
Acceleration (cm/sec )
2
Acceleration (cm/sec )
Acceleration Record at Level 0 (ground - 90)
500
10
20
30
40
50
60
100
0
-100
-200
-300
-400
-500
0
200
-500
0
10
20
Time (sec)
30
40
50
60
Time (sec)
North-South Component
East-West Component
0
5
10
15
20
25
30
35
40
45
50
Time (sec)
Vertical Component
Figure 4-7: Ground Motion Components.
4.6
Time History Analyses
Linear dynamic time history analyses were performed on all the three models (see Table 4-1).
The time histories of the acceleration, velocity and displacement responses for the individual
models are shown in Figures 4-8 through 4-16.
4.6.1 Model 1 and Model 2
The responses for Model 2 (see Figures 4-11 through 4-13), show that this model is unable to
capture the response in the latter portion of the analysis, even though the initial portion seems to
follow closely the initial response. This phenomenon is attributed to some sort of resonance
effect occurring in the structure. This is observed from the acceleration response of the actual
structure (Figure 4-11), where the frequency of the acceleration time history closely matches the
frequency of the actual response. This is 3.26 seconds for the East-West and 3.6 seconds for the
North-South directions from Model 3. The periods from Model 2 were 3.68 seconds and 3.83
seconds in the East-West and North-South directions respectively. Thus this model is unable to
capture the amplified responses caused by the resonance effect for the actual structure.
The responses for Model 1 Figures 4-8 through 4-10 show that the actual structure is definitely
more flexible than predicted by this model, from the initial portion of the response. Obviously the
response at the latter half does not come anywhere close to the actual response. The periods from
Model 1 were 3.17 seconds and 3.30 seconds in the East-West and North-South directions
respectively.
103
Acceleration Record at Level 8 (90)
750
750
2
Acceleration (cm/sec )
1250
2
Acceleration (cm/sec )
Acceleration Record at Level 8 (180)
1250
250
-250
-250
Recorded History
Recorded History
-750
250
-750
Model 1
Model 1
-1250
-1250
0
10
20
30
40
50
60
0
10
20
30
Time (sec)
50
60
Time (sec)
Acceleration Record at Roof (180)
Acceleration Record at Roof (90)
1250
750
750
2
Acceleration (cm/sec )
1250
2
Acceleration (cm/sec )
40
250
-250
Recorded History
-750
250
-250
Recorded history
-750
Model 1
Model 1
-1250
-1250
0
10
20
30
40
50
60
0
10
20
30
Time (sec)
40
50
60
Time (sec)
Figure 4-8: Acceleration Records for Model 1.
Relative Velocity Record at Level 8 (90)
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
Relative Velocity Record at Level 8 (180)
200
50
0
-50
-100
50
0
-50
-100
Recorded History
Recorded History
-150
-150
Model 1
Model 1
-200
-200
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Relative Velocity Record at Roof (180)
Relative Velocity Record at Roof (90)
200
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
30
50
0
-50
-100
50
0
-50
-100
Recorded History
Recorded history
-150
-150
Model 1
Model 1
-200
-200
0
10
20
30
40
50
60
0
10
Time (sec)
20
30
Time (sec)
Figure 4-9: Velocity Records for Model 1.
104
40
50
60
Relative Displacement Record at Level 8 (90)
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
Relative Displacement Record at Level 8 (180)
50
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded History
Recorded History
-40
-40
Model 1
Model 1
-50
-50
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Relative Displacement Record at Roof (180)
Relative Displacement Record at Roof (90)
50
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
30
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded History
Recorded history
-40
-40
Model 1
Model 1
-50
-50
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
40
50
60
Time (sec)
Figure 4-10: Displacement Records for Model 1.
Acceleration Record at Level 8 (90)
750
750
2
Acceleration (cm/sec )
1250
2
Acceleration (cm/sec )
Acceleration Record at Level 8 (180)
1250
250
-250
-250
Recorded History
Recorded History
-750
250
-750
Model 2
Model 2
-1250
-1250
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Acceleration Record at Roof (180)
Acceleration Record at Roof (90)
1250
750
750
2
Acceleration (cm/sec )
1250
2
Acceleration (cm/sec )
30
250
-250
Recorded History
-750
250
-250
Recorded history
-750
Model 2
Model 2
-1250
-1250
0
10
20
30
40
50
60
0
Time (sec)
10
20
Figure 4-11: Acceleration Records for Model 2.
105
30
Time (sec)
40
50
60
Relative Velocity Record at Level 8 (90)
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
Relative Velocity Record at Level 8 (180)
200
50
0
-50
-100
50
0
-50
-100
Recorded History
Recorded History
-150
-150
Model 2
Model 2
-200
-200
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Relative Velocity Record at Roof (180)
Relative Velocity Record at Roof (90)
200
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
30
50
0
-50
-100
50
0
-50
-100
Recorded History
Recorded history
-150
-150
Model 2
Model 2
-200
-200
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
40
50
60
Time (sec)
Figure 4-12: Velocity Records for Model 2.
Relative Displacement Record at Level 8 (90)
50
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
Relative Displacement Record at Level 8 (180)
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded History
Recorded History
-40
-40
Model 2
Model 2
-50
-50
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Relative Displacement Record at Roof (180)
Relative Displacement Record at Roof (90)
50
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
30
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded History
Recorded history
-40
-40
Model 2
Model 2
-50
-50
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
Time (sec)
Figure 4-13: Displacement Records for Model 2.
106
40
50
60
4.6.2 Model 3
The results for the best fit model (Model 3) are shown in Figures 4-14 to 4-16. The fundamental
periods calculated from modal analysis were 3.27 seconds for the East-West direction and 3.61
seconds for the North-South direction. These periods are very close to the period obtained from
the transfer function method. The time history responses also closely match the recorded
responses. Again, the theory of resonant response rather than inelastic behavior is clear. The
effectiveness of the rigid zones and the damping had to be carefully adjusted to achieve the
desired comparisons. As a conclusion from the time history analysis, the building appears to
have behaved elastically with the building going into resonance with the input motion.
Acceleration Record at Level 8 (180)
750
750
2
Acceleration (cm/sec )
1250
2
Acceleration (cm/sec )
Acceleration Record at Level 8 (90)
1250
250
-250
250
-250
Recorded History
-750
Recorded History
-750
Model 3
Model 3
-1250
-1250
0
10
20
30
40
50
60
0
10
20
Time (sec)
40
50
60
Time (sec)
Acceleration Record at Roof (90)
Acceleration Record at Roof (180)
1250
750
750
2
Acceleration (cm/sec )
1250
2
Acceleration (cm/sec )
30
250
-250
Recorded history
-750
250
-250
Recorded History
-750
Model 3
Model 3
-1250
-1250
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
Time (sec)
Figure 4-14: Acceleration Records for Model 3.
107
40
50
60
Relative Velocity Record at Level 8 (180)
Relative Velocity Record at Level 8 (90)
200
200
150
150
100
100
50
50
0
0
-50
-50
-100
-100
Recorded History
Recorded History
-150
-150
Model 3
Model 3
-200
-200
0
10
20
30
40
50
60
0
10
30
40
50
60
Relative Velocity Record at Roof (90)
200
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
Relative Velocity Record at Roof (180)
20
50
0
-50
-100
50
0
-50
-100
Recorded History
Recorded history
-150
-150
Model 3
Model 3
-200
-200
0
10
20
30
40
50
60
0
10
20
30
Time (sec)
40
50
60
Time (sec)
Figure 4-15: Velocity Records for Model 3.
Relative Displacement Record at Level 8 (90)
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
Relative Displacement Record at Level 8 (180)
50
10
0
-10
10
0
-10
-20
-20
-30
-30
Recorded History
Recorded History
-40
-40
Model 3
Model 3
-50
-50
0
10
20
30
40
50
0
60
10
20
40
50
60
Time (sec)
Time (sec)
Relative Displacement Record at Roof (180)
Relative Displacement Record at Roof (90)
50
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
30
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded History
Recorded history
-40
-40
Model 3
Model 3
-50
-50
0
10
20
30
40
50
60
0
10
20
Time (sec)
30
Time (sec)
Figure 4-16: Displacement Records for Model 3.
108
40
50
60
4.6.3 Elastic Demand Ratios
The Elastic Demand Ratios (EDR) were calculated for this building using the load combination
of the time history and the dead load. The expected yield strengths for the different types of
structural steel were used. The analysis showed a number of locations where potential damage
could occur since a large number of beam elements between the floors 11 to 15 have exceeded
the EDR of 1 (see Table 4-6). In addition, there was yielding in the corner columns on the
ground floor and at the top floors of the building (Figure 4-17). It is also important to notice that
by comparing the demand/capacity ratio (see Table 4-6) only two beams exceeded the critical
point, where all columns have adequate capacity.
From all the analyses performed, it is safe to conclude that the magnitude of the overstress that
the code suggests is very conservative when applied to this type of analysis.
Figure 4-17 Stress Ratios calculated from SAP2000 for the Time-History Analysis.
109
Table 4-6 SAP2000 Stress Checks for Beam Elements from Time History Analysis
Demand /
Demand /
Demand /
Demand /
Demand /
Element Stress Ratio
Element Stress Ratio
Element Stress Ratio
Element Stress Ratio
Capacity
Capacity
Capacity
Capacity
Capacity
4th story
Upper Plaza
3rd story
5th story
6th story
0.76
0.69
55
0.75
0.67
91
0.75
0.67
127
0.64
0.57
163
0.59
0.53
0.70
0.63
56
0.65
0.58
92
0.63
0.56
128
0.55
0.49
164
0.48
0.42
0.70
0.63
57
0.65
0.59
93
0.63
0.57
129
0.55
0.50
165
0.48
0.43
0.73
0.66
58
0.74
0.66
94
0.74
0.66
130
0.64
0.57
166
0.58
0.51
0.52
0.46
59
0.52
0.46
95
0.59
0.53
131
0.58
0.52
167
0.63
0.54
0.51
0.46
60
0.50
0.45
96
0.57
0.51
132
0.55
0.50
168
0.64
0.54
0.46
0.41
61
0.45
0.40
97
0.53
0.47
133
0.52
0.47
169
0.61
0.53
0.47
0.42
62
0.45
0.41
98
0.53
0.47
134
0.51
0.46
170
0.61
0.54
0.46
0.42
63
0.45
0.41
99
0.53
0.47
135
0.52
0.47
171
0.61
0.53
0.47
0.42
64
0.46
0.41
100
0.53
0.48
136
0.51
0.46
172
0.61
0.53
0.46
0.41
65
0.45
0.40
101
0.53
0.47
137
0.52
0.47
173
0.61
0.54
0.47
0.42
66
0.45
0.41
102
0.53
0.48
138
0.51
0.46
174
0.61
0.53
0.48
0.43
67
0.49
0.44
103
0.56
0.50
139
0.56
0.50
175
0.63
0.57
0.49
0.44
68
0.49
0.44
104
0.56
0.50
140
0.56
0.50
176
0.62
0.56
0.72
0.65
69
0.72
0.65
105
0.73
0.66
141
0.63
0.57
177
0.54
0.49
0.65
0.58
70
0.60
0.54
106
0.58
0.52
142
0.50
0.45
178
0.46
0.40
0.65
0.59
71
0.61
0.55
107
0.58
0.52
143
0.50
0.45
179
0.46
0.40
0.67
0.61
72
0.68
0.61
108
0.69
0.62
144
0.58
0.53
180
0.53
0.46
7th story
8th story
9th story
10th story
11th story
0.54
0.49
235
0.52
0.47
271
0.63
0.57
307
0.90
0.71
343
1.00
0.77
0.47
0.42
236
0.51
0.43
272
0.63
0.53
308
0.90
0.69
344
1.00
0.77
0.47
0.43
237
0.50
0.43
273
0.63
0.53
309
0.90
0.70
345
1.00
0.77
0.54
0.46
238
0.55
0.44
274
0.63
0.56
310
0.91
0.75
346
1.03
0.84
0.65
0.54
239
0.66
0.54
275
0.65
0.53
311
0.62
0.51
347
0.57
0.46
0.67
0.54
240
0.69
0.58
276
0.71
0.60
312
0.70
0.59
348
0.66
0.56
0.62
0.55
241
0.65
0.58
277
0.65
0.59
313
0.64
0.57
349
0.61
0.55
0.63
0.56
242
0.66
0.59
278
0.67
0.60
314
0.66
0.59
350
0.63
0.57
0.63
0.56
243
0.65
0.59
279
0.66
0.59
315
0.65
0.58
351
0.62
0.55
0.63
0.56
244
0.66
0.59
280
0.67
0.60
316
0.65
0.59
352
0.63
0.56
0.63
0.56
245
0.66
0.59
281
0.67
0.60
317
0.65
0.58
353
0.62
0.56
0.63
0.56
246
0.66
0.59
282
0.67
0.60
318
0.65
0.59
354
0.63
0.57
0.67
0.60
247
0.71
0.64
283
0.73
0.66
319
0.72
0.65
355
0.69
0.62
0.64
0.58
248
0.67
0.60
284
0.67
0.60
320
0.64
0.58
356
0.59
0.53
0.55
0.49
249
0.53
0.48
285
0.62
0.55
321
0.90
0.69
357
1.01
0.78
0.45
0.40
250
0.51
0.44
286
0.64
0.54
322
0.90
0.69
358
0.99
0.77
0.45
0.41
251
0.51
0.43
287
0.63
0.53
323
0.89
0.69
359
0.99
0.77
0.49
0.41
252
0.51
0.42
288
0.66
0.55
324
0.91
0.73
360
1.01
0.82
Element Stress Ratio
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
Element Stress Ratio
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
4.7
12th story
1.11
1.09
1.09
1.15
0.49
0.60
0.56
0.58
0.57
0.58
0.57
0.59
0.62
0.51
1.13
1.09
1.09
1.12
Demand /
Demand /
Demand /
Demand /
Demand /
Element Stress Ratio
Element Stress Ratio
Element Stress Ratio
Element Stress Ratio
Capacity
Capacity
Capacity
Capacity
Capacity
13th story
14th story
15th story
Roof
0.86
415
1.17
0.91
451
1.17
0.92
487
1.17
0.92
523
0.82
0.62
0.84
416
1.15
0.88
452
1.17
0.92
488
1.17
0.92
524
0.73
0.59
0.84
417
1.15
0.88
453
1.17
0.92
489
1.17
0.92
525
0.73
0.59
0.92
418
1.22
0.98
454
1.22
1.01
490
1.23
1.01
526
0.83
0.68
0.42
419
0.45
0.39
455
0.51
0.44
491
0.58
0.51
527
0.42
0.38
0.51
420
0.54
0.46
456
0.55
0.45
492
0.64
0.53
528
0.50
0.40
0.50
421
0.50
0.45
457
0.51
0.43
493
0.53
0.45
529
0.36
0.32
0.52
422
0.53
0.47
458
0.54
0.45
494
0.54
0.45
530
0.38
0.33
0.51
423
0.51
0.46
459
0.52
0.43
495
0.54
0.45
531
0.38
0.32
0.52
424
0.52
0.47
460
0.54
0.45
496
0.54
0.44
532
0.38
0.32
0.52
425
0.52
0.46
461
0.52
0.44
497
0.53
0.44
533
0.36
0.32
0.53
426
0.53
0.48
462
0.54
0.45
498
0.54
0.44
534
0.37
0.32
0.56
427
0.56
0.50
463
0.53
0.48
499
0.63
0.57
535
0.46
0.42
0.46
428
0.45
0.41
464
0.50
0.43
500
0.56
0.45
536
0.43
0.33
0.87
429
1.20
0.92
465
1.19
0.94
501
1.18
0.93
537
0.83
0.62
0.83
430
1.14
0.87
466
1.16
0.91
502
1.15
0.91
538
0.71
0.57
0.84
431
1.14
0.88
467
1.16
0.91
503
1.15
0.91
539
0.72
0.59
0.89
432
1.18
0.94
468
1.17
0.95
504
1.17
0.96
540
0.78
0.65
Comparison Of Observed and Predicted Damage
There are 133 out of a total of 576 moment resisting frame connections of the building that were
tested using visual and ultrasonic examination. The inspection results showed no detectable
defects or damage caused by the earthquake. From the inspected connections though, there were
eight connections with defective welds. These damages were considered to be just a result of the
construction process.
110
The conclusion that there should not be any earthquake related damages in the lateral resistance
system of the building is also drawn from the displacement responses (see Figure 4-16) where the
elastic SAP2000 analysis coincides with the real recordings.
4.8
4.8.1
Evaluation with Prevailing Practice – UBC-97 and FEMA-273
Analysis Using UBC-97
In order to investigate how current methods for analysis and design meet the seismic demands,
the building was examined for compliance with the UBC-97 code. Design Dynamic Analysis
Procedures were used, because the building was categorized as irregular (with weight
irregularity) and its height was more than 65 ft.
The calculated Design Base Shear from the equation given in the introduction was verified to be
within the acceptable range specified in UBC-97 as described in section 1630.2.1. The values
used for all the parameters used in the calculation of the Base Shear are reported in Table 4.7.
The earthquake forces are applied to the structure based on a Response Spectrum Analysis with
the response spectra scaled to give a base shear equal to the design base shear. The design base
shears were amplified by the appropriate redundancy factors giving the resulting lateral
earthquake forces. The three first modes in each direction were considered in the response
spectrum analysis. The summary of the forces and overturning moments from the analysis is
given in Table 4-7.
UBC-97 suggests that the redundancy factors should be less than 1.25. In this case these factors
are 1.42 and 1.27. Therefore, this building does not satisfy the redundancy checks as
recommended in UBC-97.
4.8.1.1 Check for Drift Limitations
UBC-97 story drift limitations are satisfied only for the first and the three top and the ground
stories in East-West direction. In all other stories the story drift limits were exceeded.
Analytically, the results are presented in Table 4-8.
111
Table 4-7: UBC-97 Summary Table, Parameters and Forces
Site Parameters
Z
0.4
Ca
0.44
Cv
0.77
SEISMIC ZONE: 4
OCCUPANCY CATEGORY: Standard Occupancy
IRREGULAR 15 STORY STRUCTURE: Weight/Mass Ir
BUILDING HEIGHT: 209.83 feet
BASE SHEAR VX=
1331.54 kips
BASE SHEAR Vy=
1331.54 kips
I
Nv
Structural Parameters
R
8.5
TX (sec)
2.51
Ty (sec)
2.51
1.00
W (kips)
27511.14
1.20
-- DYNAMIC ANALYSIS -Base Shear Distribution, Earthquake Loads and Overturning Moments
applied to the structure
Lateral Loads
(kips)
Redundancy
Factors
Earthquake Forces
OTM
(kips)
(kips-feet)
FNS
FEW
ρNS
ρEW
NS
EW
NS
EW
Level
647.81
84.18
51.29
43.11
48.21
53.33
52.09
45.13
38.67
37.10
41.92
49.68
54.20
53.01
31.80
639.48
88.05
56.10
45.27
46.69
50.31
50.05
45.01
39.93
39.03
43.51
50.04
53.45
52.34
32.27
1.42
1.27
918.67
119.37
72.74
61.13
68.37
75.63
73.87
64.00
54.84
52.61
59.44
70.46
76.87
75.17
45.09
813.82
112.06
71.39
57.61
59.42
64.02
63.70
57.28
50.82
49.67
55.37
63.68
68.02
66.61
41.07
10796.91
20190.79
30242.93
40848.29
52072.39
63980.89
76557.85
89714.03
103366.51
117495.14
132161.69
147465.84
163465.62
192059.99
214696.16
10658.05
19994.75
30051.39
40689.00
51925.84
63808.27
76333.02
89435.41
103050.27
117166.05
131840.20
147156.51
163158.72
191742.55
214378.71
Roof
14
13
12
11
10
9
8
7
6
5
4
3
2
1
4.8.1.2 Elastic Demand Ratios
The Elastic Demand Ratios were calculated from SAP2000 for the UBC-97 load combinations
with yielding calculated from the nominal yield stresses for the structural. The EDR for the
beams were all less than 1 (see Table 4-9). There were however, four corner columns in the
North-South direction (2 on the ground and 2 on the third floor), that had stress ratios exceeding
unity (see Figures 4-18, 4-19). In general, the conclusion after the stress ratio analysis for UBC97 is that the building will behave well but special attention should be paid for those four column
elements.
112
Table 4-8: UBC-97 Summary Displacements and Drift Limit Checks.
Maximum Inelastic
Response Displacements
INTERSTORY DRIFT RATIO
∆M
(% of story height)
(in)
Level
NS
EW
Roof
14
13
12
11
10
9
8
7
6
5
4
3
2
1
75.35
70.05
65.89
61.61
57.28
52.67
47.96
43.16
38.41
33.56
28.71
23.76
18.84
13.85
4.27
55.69
51.82
48.91
45.93
42.84
39.57
36.12
32.37
28.62
24.87
21.24
17.55
14.04
10.53
3.33
NS
2.65
2.70
2.78
2.81
2.99
3.06
3.12
3.08
3.15
3.15
3.21
3.19
3.24
3.63
2.09
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
EW
1.93
1.89
1.93
2.01
2.13
2.24
2.43
2.43
2.43
2.36
2.40
2.28
2.28
2.73
1.63
OK
OK
OK
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
OK
4.8.1.3 Seismic Special Provision Checks
The three topics investigated for the seismic special provisions checks were the panel zone
thickness, the need for continuity plates, and the column-beam moment ratios checks. All checks
performed satisfied the code requirements. A summary of the individual checks is given in Table
2-10.
113
Table 4-9 SAP2000 Stress Checks for Beam Elements from UBC-97
Response Spectrum Analysis
Element
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
EW
Upper Plaza
0.12
0.12
0.12
0.14
0.57
0.66
0.53
0.61
0.53
0.61
0.53
0.61
0.57
0.67
0.13
0.13
0.13
0.15
7th story
0.11
0.13
0.13
0.18
0.67
0.78
0.64
0.73
0.64
0.73
0.64
0.73
0.67
0.78
0.11
0.14
0.14
0.20
Element
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
12th story
0.13
0.14
0.14
0.22
0.57
0.66
0.58
0.66
0.58
0.66
0.58
0.66
0.57
0.66
0.13
0.14
0.15
0.23
NS
Element
0.69
0.66
0.66
0.69
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.13
0.13
0.78
0.74
0.74
0.78
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
0.76
0.71
0.71
0.76
0.14
0.13
0.12
0.12
0.12
0.12
0.13
0.13
0.23
0.23
0.87
0.79
0.79
0.86
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
NS
Element
0.74
0.73
0.73
0.74
0.19
0.19
0.13
0.13
0.14
0.14
0.14
0.15
0.27
0.27
0.83
0.81
0.80
0.83
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
EW
3rd story
0.10
0.11
0.11
0.13
0.57
0.67
0.52
0.60
0.52
0.60
0.52
0.60
0.58
0.67
0.10
0.12
0.12
0.14
8th story
0.12
0.13
0.14
0.20
0.68
0.78
0.65
0.74
0.65
0.74
0.65
0.74
0.68
0.79
0.12
0.14
0.15
0.21
13th story
0.14
0.13
0.14
0.21
0.55
0.64
0.56
0.64
0.56
0.63
0.56
0.64
0.54
0.64
0.13
0.14
0.15
0.23
NS
Element
0.74
0.66
0.66
0.74
0.09
0.09
0.10
0.10
0.10
0.10
0.10
0.10
0.13
0.13
0.83
0.73
0.74
0.82
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
0.77
0.73
0.73
0.77
0.15
0.15
0.12
0.12
0.12
0.13
0.13
0.13
0.24
0.24
0.87
0.82
0.82
0.87
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
NS
Element
0.70
0.70
0.70
0.70
0.20
0.20
0.14
0.14
0.14
0.14
0.15
0.15
0.27
0.27
0.80
0.78
0.78
0.80
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
EW
4th story
0.10
0.12
0.12
0.16
0.65
0.75
0.60
0.69
0.60
0.69
0.60
0.69
0.65
0.76
0.11
0.13
0.13
0.17
9th story
0.12
0.13
0.13
0.20
0.67
0.77
0.64
0.73
0.64
0.73
0.64
0.73
0.67
0.77
0.12
0.14
0.14
0.22
14th story
0.14
0.14
0.15
0.21
0.56
0.65
0.58
0.67
0.58
0.66
0.58
0.67
0.56
0.65
0.14
0.15
0.15
0.22
NS
Element
0.81
0.72
0.72
0.81
0.11
0.10
0.12
0.12
0.12
0.12
0.12
0.12
0.18
0.18
0.91
0.80
0.80
0.91
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
0.76
0.72
0.72
0.76
0.16
0.16
0.12
0.12
0.12
0.13
0.13
0.13
0.25
0.25
0.85
0.80
0.80
0.85
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
NS
Element
0.69
0.70
0.70
0.69
0.21
0.21
0.15
0.15
0.15
0.15
0.16
0.16
0.28
0.28
0.80
0.79
0.79
0.80
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
EW
5th story
0.10
0.12
0.12
0.16
0.64
0.74
0.59
0.68
0.59
0.68
0.59
0.68
0.64
0.74
0.10
0.13
0.13
0.18
10th story
0.13
0.14
0.14
0.22
0.64
0.74
0.62
0.70
0.62
0.70
0.62
0.70
0.64
0.74
0.13
0.15
0.16
0.23
15th story
0.15
0.14
0.15
0.22
0.58
0.67
0.58
0.66
0.58
0.66
0.58
0.66
0.57
0.67
0.14
0.14
0.15
0.23
NS
Element
0.78
0.70
0.70
0.77
0.11
0.11
0.12
0.12
0.12
0.12
0.12
0.12
0.19
0.19
0.88
0.78
0.78
0.87
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
0.80
0.78
0.78
0.80
0.17
0.17
0.12
0.12
0.13
0.13
0.14
0.14
0.26
0.26
0.89
0.86
0.86
0.89
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
NS
Element
0.70
0.70
0.70
0.70
0.23
0.22
0.15
0.15
0.16
0.16
0.16
0.16
0.29
0.28
0.82
0.79
0.79
0.82
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
EW
6th story
0.11
0.13
0.13
0.18
0.67
0.78
0.64
0.73
0.64
0.73
0.64
0.73
0.68
0.79
0.11
0.14
0.14
0.19
11th story
0.13
0.14
0.14
0.22
0.61
0.71
0.60
0.68
0.60
0.68
0.60
0.68
0.60
0.71
0.13
0.15
0.15
0.23
UBC-97 Special Seismic Provisions Checks
Continuity
Column-Beam Moment
Panel Thickness
plates?
Ratios
Passed
Passed
114
Passed
0.77
0.76
0.76
0.77
0.18
0.18
0.13
0.13
0.13
0.13
0.14
0.14
0.26
0.26
0.86
0.83
0.83
0.86
NS
Roof
0.18
0.17
0.15
0.22
0.39
0.45
0.42
0.47
0.41
0.46
0.42
0.47
0.39
0.45
0.18
0.17
0.16
0.22
Table 4-10: UBC-97 Seismic Provisions for Structural Steel
Check
Results
NS
0.78
0.72
0.72
0.78
0.13
0.12
0.12
0.12
0.12
0.12
0.13
0.13
0.22
0.22
0.89
0.81
0.81
0.89
0.47
0.50
0.50
0.47
0.21
0.21
0.17
0.18
0.16
0.16
0.16
0.16
0.24
0.24
0.55
0.55
0.55
0.55
Figure 4-18 Stress Ratios calculated from SAP2000 in the East-West Direction for UBC97 Response Spectrum Analysis.
Figure 4-19 Stress Ratios calculated from SAP2000 in the North-South Direction for
UBC-97 Response Spectrum Analysis.
115
4.8.2 Analysis Using FEMA 273
4.8.2.1 Non-linear Static Pushover Analysis
The calculated target displacements for the BSE-1 and BSE-2 level earthquake and the important
factors used for both principle directions of the building are presented in Table 4.11. The
spectral acceleration of the building for BSE-1 level earthquake is 0.31g for the East-West
direction and 0.28g in the North-South direction. For the BSE-2 level earthquake, these values
are 0.46g and 0.42g respectively. The roof target displacements for the East-West and the NorthSouth directions for the BSE-1 earthquake are 41.02 inches and 45.34 inches. This corresponds
to an overall drift ratio of 1.63% in the East-West direction and 1.80% in the North-South
direction. The corresponding drift ratios for the BSE-2 level earthquake are 2.45% and 2.70%
respectively.
It is worth mentioning that these results are for Site Class E, which is the default for FEMA-273
if the soil type is unavailable. From experience we can approximate that the soil in the building
location is better described by using Site Class D (Stiff Soil). By using this Site Class the roof
target displacements for the BSE-1 Earthquake reduce to 30.77 inches (or 1.22% drift ratio) and
34 inches (or 1.35% drift ratio) for the East-West and the North-South directions respectively.
The same values for BSE-2 earthquake are 46.27 inches (1.84%) and 51.1 inches (2.03%). In
this document, the roof target displacements correspond to the values for a Site class E.
The base shears and corresponding yield displacements for the three loading patterns pushed to
the target roof displacement are presented in Tables 4-12 through 4-15. Clearly the Uniform
pattern showed the highest yield shear and required displacement ductility. The displacement
ductility for the BSE-1 earthquake was 1.53 for the North-South and 1.26 for the East-West
direction, and that for the BSE-2 earthquake was 2.29 and 2.20 respectively.
The actual recorded maximum relative roof displacement in the North-South direction was 16.19
inches (0.6% drift ratio) and in the East-West direction was 14.35 inches (0.6% drift ratio). This
corresponds to 42% for the North-South and 53% for the East-West of the roof target
displacement for the BSE-1 earthquake. The maximum recorded displacements in both
directions were significantly lower than the corresponding yield displacements, calculated from
116
the pushover curves of the building. From the results of the acceptance criteria, it is clear that the
plastic rotations definitely meet the Life Safety requirement. The actual displacements were
slightly greater than the yield displacements as seen in the demand capacity spectra graphs of the
building (Figures 4-20 to 4-23). This indicates that there could be some minor yielding or
damage. According to this analysis, the building satisfied the life safety requirements.
Table 4-11: FEMA 273 Summary Displacements and Drift Limit Checks.
Non-Linear Static Procedure
1) Period Determination:
T e = Ti
Ke is determined at 60% of Vy
Ki
Ke
BSE-1
BSE-2
NS
3.61
EW
3.27
2) Vertical Distribution of Seismic Forces
Uniform Pattern
Lateral Forces Proportional to the Total Mass at Each Floor Level
AND AT LEAST ONE OF THE FOLLOWING:
i) Lateral load distribution as described in the Linear Static Procedure if more than 75% of the total mass
participates in the fundamental mode in the direction under consideration
ii) Lateral load pattern proportional to the story inertia forces consistent with the story shear distribution
calculated by combination of modal responses using (a) Response Spectrum Analysis using sufficient number
of modes to capture the 90% of the total mass or (b) the appropriate ground motion spectrum
δ t = C0 C1 C2 C3 Sa
3) Target Displacement δt (in)
NS
45.34
68.01
EW
41.02
61.54
C0 : Modification Factor to Relate Spectral Displacement and likely building Roof
Displacement (TABLE 3-2)
C1 : Modification Factor to Relate Expected Maximum Displacements to
Displacements Calculated for Linear Elastic Response
C2 : Modification Factor to Represent the effect of Stiffness Degradation and
Strength Deterioration on Maximum Displacement Response (TABLE 3-1)
Te2
g
4π 2
1.28
NS
1
EW
1
1
NS
1
1
EW
1
1
1
1
NS
1
C3 : Modification Factor to Represent Increased Displacements due to Dynamic
P-∆ Effects (positive post-yielding stiffness assumed)
EW
Sa : Response Spectrum Acceleration at the Fundamental Period and Damping
Ratio of the Building in the Direction Under Consideration (g)
NS
0.28
0.42
EW
0.31
0.46
117
Table 4-12: Nonlinear Static results for BSE-1 in the North-South Direction.
East-West
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
4258
Target
Displacement
(inches)
0.15
Yield
Displacement
(inches)
29.14
4935
0.18
30.29
41.02
5804
0.21
26.86
Yield Base
Shear Coefficient
Displacement
Ductility
1.41
1.35
1.53
Table 4-13: Nonlinear Static results for BSE-1 in the East-West Direction
North-South
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
3806
Target
Displacement
(inches)
0.14
Yield
Displacement
(inches)
38.67
4452
0.16
40
45.34
5390
0.20
36
Yield Base
Shear Coefficient
Displacement
Ductility
1.17
1.13
1.26
Table 4-14: Nonlinear Static results for BSE-2 in the North-South Direction.
North-South
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
4193
Target
Displacement
(inches)
0.15
Yield
Displacement
(inches)
28.57
4935
0.18
30
61.54
5742
0.21
26.86
Yield Base
Shear Coefficient
Displacement
Ductility
2.15
2.05
2.29
Table 4-15: Nonlinear Static results for BSE-2 in the East-West Direction.
North-South
Linear Static
Modal
Analysis
Uniform
Yield Base
Shear
(kips)
3871
Target
Displacement
(inches)
0.14
Yield
Displacement
(inches)
33.14
4516
0.16
34.29
68.01
5390
0.20
30.86
Yield Base
Shear Coefficient
118
Displacement
Ductility
2.05
1.98
2.20
1.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
1.20
Base Shear Coefficient (BS/W)
Target Displacement BSE-1
Target Displacement BSE-2
1.00
Elastic Demand Spectrum, Damping Ratio 2%
BSE-1 Demand Spectrum
Inelastic Demand Spectrum, Damping Ratio 2%, R=1
0.80
Maximum Equivalent Response
0.60
0.40
BSE-1 δ t =
41.02 in
BSE-2 δ t =
61.54 in
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
Roof Drift (%)
Figure 4-20: Demand-Capacity Spectra for the East-West Direction.
2.50
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
Target Displacement BSE-1
Base Shear Coefficient (BS/W)
2.00
Target Displacement BSE-2
Elastic Demand Spectrum, Damping Ratio 1%
BSE-1 Demand Spectrum
1.50
Inelastic Demand Spectrum, Damping Ratio 1%, R=1
Maximum Equivalent Response
1.00
0.50
BSE-1 δ t =
45.34 in
BSE-2 δ t =
68.01 in
0.00
0.00
0.50
1.00
1.50
2.00
2.50
Roof Drift (%)
Figure 4-21: Demand-Capacity Spectra for the North-South Direction.
119
3.00
0.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
0.35
Target Displacement BSE-1
Base Shear Coefficient (BS/W)
Target Displacement BSE-2
Elastic Demand Spectrum, Damping Ratio 2%
0.30
BSE-1 Demand Spectrum
Inelastic Demand Spectrum, Damping Ratio 2%, R=1
Maximum Equivalent Response
0.25
0.20
0.15
0.10
BSE-1 δ t =
0.05
BSE-2 δ t =
41.02 in
61.54 in
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
Roof Drift (%)
Figure 4-22: Demand-Capacity Spectra for the East-West Direction - Detail.
0.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
0.35
Target Displacement BSE-1
Base Shear Coefficient (BS/W)
Target Displacement BSE-2
Elastic Demand Spectrum, Damping Ratio 1%
0.30
BSE-1 Demand Spectrum
Inelastic Demand Spectrum, Damping Ratio 1%, R=1
Maximum Equivalent Response
0.25
0.20
0.15
0.10
BSE-1 δ t =
0.05
45.34 in
BSE-2 δ t =
68.01 in
0.00
0.00
0.50
1.00
1.50
2.00
2.50
Roof Drift (%)
Figure 4-23: Demand-Capacity Spectra for the North-South Direction - Detail.
120
3.00
4.8.2.2 Acceptance Criteria
The yield pattern of the hinges for the East-West direction at the BSE-1 level target displacement
for the uniform push pattern is given in Figure 4-24. The yield pattern at the BSE-2 roof target
displacement is given in Figure 4-25. For the North-South direction, the hinge patterns for the
two earthquake levels are given in Figures 4-26 and 4-27.
The summary of the acceptance criteria is presented in Table 4-16. For both the BSE-1 and the
BSE-2 earthquakes there were no hinges that exceeded the Life Safety (LS) acceptance criterion.
Thus the building meets the both requirements (LS for BSE-1 earthquake and CP for BSE-2
earthquake) of the Basic Safety Objective (BSO) and therefore no further improvement of the
design is required.
121
Figure 4-24 Hinge Yield Pattern at the BSE-1 for the Level Target Displacement for the
Uniform Distribution Pushover Analysis in the East-West Direction.
Figure 4-25 Hinge Yield Pattern at the BSE-2 for the Level Target Displacement for the
Uniform Distribution Pushover Analysis in the East-West Direction
122
Figure 4-26 Hinge Yield Pattern at the BSE-1 for the Level Target Displacement for the
Uniform Distribution Pushover Analysis in the North-South Direction.
Figure 4-27 Hinge Yield Pattern at the BSE-2 for the Level Target Displacement for the
Uniform Distribution Pushover Analysis in the North-South Direction.
123
Table 4-16: Plastic Hinges at the Building Formed for BSE-1 and BSE-2 after performing
Pushover Analysis in both Directions
Type and Number of Hinges formed at BSE-1 Target Displacement in the
North-South Direction for the Uniform Pattern
Step
0
1
2
3
4
5
6
7
8
9
10
11
12
Displacement Base Shear
0.00
0.00
10.07
1754.25
20.13
3508.50
24.26
4227.87
28.56
4902.31
30.27
5051.77
40.53
5447.73
50.67
5685.25
63.90
5943.49
77.80
6185.66
88.27
6350.86
98.81
6509.89
100.64
6536.94
at Target Displacement
A-B
B-IO
1080
1080
1080
1078
1032
1002
956
931
916
902
890
885
884
931
0
0
0
2
48
78
120
80
50
46
38
41
42
80
IO-LS LS-CP
0
0
0
0
0
0
4
69
114
132
150
112
100
69
0
0
0
0
0
0
0
0
0
0
2
42
54
0
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
Type and Number of Hinges formed at BSE1 Target Displacement in the
East-West Direction for the Uniform Pattern
Step
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Displacement Base Shear
0.00
0.00
10.06
2162.80
20.13
4325.60
22.04
4736.83
25.09
5324.80
27.26
5516.76
38.22
5896.49
49.57
6192.59
62.64
6474.55
80.90
6819.37
95.61
7081.39
96.68
7099.85
96.68
6947.63
96.90
6973.49
at Target Displacement
A-B
B-IO
1080
1080
1080
1078
1014
968
918
892
866
840
818
818
814
814
892
0
0
0
2
66
112
146
78
58
76
82
82
86
86
78
IO-LS LS-CP
0
0
0
0
0
0
16
110
156
158
96
96
96
96
110
0
0
0
0
0
0
0
0
0
6
84
82
82
80
0
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
Type and Number of Hinges formed at BSE-2 Target Displacement in the
North-South Direction for the Uniform Pattern
Step
0
1
2
3
4
5
6
7
8
9
10
11
12
Displacement Base Shear
0.00
0.00
10.07
1754.25
20.13
3508.50
24.27
4230.38
28.57
4903.57
30.25
5050.03
40.80
5453.59
51.19
5694.55
63.90
5942.10
77.93
6186.59
88.11
6346.96
98.72
6507.11
100.64
6535.50
at Target Displacement
A-B
B-IO
1080
1080
1080
1078
1033
1002
955
929
916
902
890
885
884
902
0
0
0
2
47
78
120
81
50
46
38
41
42
46
IO-LS LS-CP
0
0
0
0
0
0
5
70
114
132
150
113
104
132
0
0
0
0
0
0
0
0
0
0
2
41
50
0
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
Type and Number of Hinges formed at BSE-2 Target Displacement in the
East-West Direction for the Uniform Pattern
Step
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Displacement Base Shear
0.00
0.00
10.06
2162.80
20.13
4325.60
22.05
4739.44
25.12
5328.26
27.24
5516.73
38.27
5898.68
49.49
6191.48
62.65
6475.49
80.98
6821.48
95.53
7080.63
96.80
7102.54
96.80
6948.92
97.36
7011.70
at Target Displacement
A-B
B-IO
1080
1080
1080
1078
1014
969
918
892
866
840
818
818
814
812
866
0
0
0
2
66
111
147
78
58
76
82
82
86
88
58
124
IO-LS LS-CP
0
0
0
0
0
0
15
110
156
158
96
96
96
96
156
0
0
0
0
0
0
0
0
0
6
84
82
82
80
0
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
1080
4.9
Summary
Table 4-16: Summary of Building Performance
Actual Damage
Remarks
No
–Elastic Response--
Retrofit
Strategy
Ratios >1 in Beams and
Columns
OK
Compliance with UBC-97
Special Provisions
ColumnDrift
Redundancy
Panel Continuity
Beam
Limits
Factors
zones
Plates
Moment
Ratios
>1.25
No
Exceed Code
OK
OK
OK
Table 4-8
Limitations
Retrofit
Strategy
Increase Lateral Resisting Moment Frames
Life SafetyBSE-1
Compliance
Ratios >1 in Beams and
Columns
Design/Capacity
Ratios (Model 3)
None
EDR
Compliance
Northridge Earthquake
Elastic Demand Ratios
(Model 3)
OK
Evaluation with FEMA-273
Collapse PreventionDemand-Capacity
BSE-2
Spectra
OK
Retrofit
Strategy
125
OK
5
5.1
ANALYSIS OF A TWENTY STORY BUILDING,
ENCINO, CALIFORNIA
Building Description
This building is located in Encino California, and comprises of a twenty-story tower with a fourstory parking garage. The structure is over 249 feet tall and rectangular in plan. The lateral
resisting system of the building is provided by Steel Moment Resisting Frames (SMRF)
connected by a floor slab which acts a rigid diaphragm at each floor. The four story parking
structure is offset to the east of the main tower, but shares a continuous floor diaphragm with the
main tower. The lateral resistance of the parking structure is also provided by SMRF, which are
independent from the frames in the main tower of the building. The parking structure is
comprised of two four-bay frames in the North-South and East-West directions. The main tower
has four four-bay frames in the North-South direction and two seven-bay frames in the East-West
direction for the first four floors. The frames on the remaining floors are cutback by one bay in
the North-South direction. There is a bank vault in the Southwest corner of the tower with four
concrete shear walls at the first floor and two X-braces on the second floor. A three-dimensional
model showing the lateral resisting system of the building is shown in Figure 5–1.
A plan view of the building showing the lateral frames, corresponding gridlines, and column
orientations are shown in Figure 5-2. The beam-column connections are typical pre-Northridge
SMRF connections. Figure 5-3 shows the connection detail for beams that frame into column
flanges. The beam flanges are connected to the column flanges by complete penetration field
welds. The detail in Figure 5-3 shows the presence of continuity plates. These continuity plates
are however provided only on the upper five floors from floors 16 to 20. Figure 5-3 shows the
detail for beams that frame into column webs. The beam flange is welded to the end of the
continuity plate and the continuity plate is welded to the inside of the column flanges. Both
details have shear tabs that are bolted to the beam webs.
There are four non-prismatic girders per floor that are located on gridlines 4 and 7 and span from
lines A to D and E to G. The rolled steel sections are Grade A572 (grade 50) steel and the plate
126
girders, used for the non-prismatic members, are grade 36. The floor slabs are 5 inches thick
lightweight concrete.
Seismic sensors are located in the basement (arcade) level, 10th floor, and roof. These sensors
recorded the displacement, velocity, and acceleration responses in the North-South, East-West,
and vertical directions during the Northridge earthquake.
Figure 5-1. Three-dimensional Model of the Building
127
Figure 5-2: Plan View of Seismic Frames and Gridlines.
5.2
The SAP2000 Computer Models
The SAP2000 program was used to model the lateral resisting system of the building, as
mentioned in the introduction. Beams and columns were modeled as frame elements. The shear
walls at the southwest corner of the first floor were modeled as shell elements. The level between
the basement (arcade level) and first floor was very stiff with basement walls running along the
entire perimeter of the building and parking structure. Compared to the levels above, this level
was very stiff, and was modeled with a diaphragm restraint in the two horizontal directions, and
the walls were not explicitly modeled. The columns are supported by piles with rigid pile caps.
The boundary conditions at the base were therefore assumed as fixed. The splice locations at the
mid-height of the floors were included in the model.
Initially for the best fit model (Model 3), rigid end zone factors were assigned to the beams and
columns that best represented the connections details of the actual structure. All the beams were
assigned full rigid zones because the beam-ends were connected to the face of the column and
did not extend into the column centerline (see Figure 5-3). Corner columns and columns that had
three or more beams framing into it, were assigned full rigid zones. The full rigid zone was used
128
because these columns had its panel zone stiffened by the beams that framed into the column
web (see Figure 5-3 Section B). Columns with beams only on either side of the column flanges
had no rigid zone assignment.
Column rigid zone factors were adjusted by no more than 5% for the final best-fit model (Model
3), which very closely simulated the responses of the building with the recorded data. The rigid
zone factors for all three models are shown in Table 5-1. The rigid zone factors for columns with
corner connections was reduced by 5%, while columns with 3 and 4 way connections was
unchanged. The rigid end zone factors, for columns with beams only on either side of the column
flanges, with continuity and without continuity plates were increased by 5% and 2.5%
respectively. The small adjustment to the rigid zone factors indicated that the initial assumptions
of the rigid zone factors were representative of the actual building.
The damping was adjusted for each mode to correlate the modal response amplitudes with the
measured response. The best results were obtained using 3% damping for the North-South
direction (modes one, three, and six) and 2.5% damping for the East-West direction (modes one
and five). Higher modes were damped at 10% to reduce the high frequency response in the
acceleration time histories.
Table 5-1: Rigid End Zone Factors and Modal Damping in the Models.
Model
Model 1
Model 2
Model 3
Rigid End Zone Factors
All Elements=100%
All Elements=0%
All Beams
100 %
Columns
Moment connection in 2 directions
3 and 4 way=100%
Corner=95%
Moment connection in 1 direction
With Continuity Plates=5%
Without Continuity Plates=2.5%
129
Analysis
Elastic 3D
Elastic 3D
Modal Damping
NS: 3% 1st ,3rd ,and 6th,
all others 10% damped
Elastic 3D
EW: 2.5% 1st and 5th, all
others 10% damped
Figure 5-3: Moment Connection Details.
130
5.3
Mass Calculations
In the calculation of the masses, in addition to the self-weight of the structure, there was an
additional line load of 30-psf for the perimeter curtain wall, 20-psf for partitions, and 8-psf for
ceiling. Live loads were not included in the mass calculations and any contribution of live load
is included in the 20 psf added for partitions. The mass, center of mass, mass moment of inertia,
and loads used to calculate mass for each floor are presented in Table 5-2.
Table 5-2: Center of Mass, Mass, and Mass Moment of Inertia for Different Levels Loads
Story / Area
Level 2
Level 3
Level 4
Typ. Floor (5-19)
Roof/
Penthouse Floor
Structural Weight
(kips)
97.5
103.5
78
102.4
For Area 1=92
For Area 2=136
For Area 3=64.7
For Area 4=138
Mass
Moment
of Inertia
(kips sec2
in)
8233490
26861450
20856650
3334724
4255367
Mass
(kips
sec2/in)
6.11
13.25
11.75
5.26
8.57
Center of Mass
X coord.
(in)
Y coord.
(in)
63.71
356.71
219.32
1214.46
1228.89
1188.28
722.72
775.17
525.48
549.05
Figure 5-4 shows the results/floor plan layouts, from the JAMA-SDS (MMI) program, that
includes the center of mass locations, distributed loads, and perimeter line loads.
131
2nd Floor
3rd Floor
4th Floor
Typical Floor
Roof
Figure 5-4: JAMA-SDS (MMI) calculations
132
5.4
Modal Periods
The modal periods and participation factors of the building for Models 1, 2, and 3 are given in
Table 5-3. From actual recordings, the natural frequencies were calculated using the transfer
functions of the story acceleration responses normalized by the superimposed input base motion
in the frequency domain. This is a well-known identification procedure used extensively in lab
experiments. However, this method is valid only when the structure is lightly damped with wellseparated modes. Table 5-4 summarizes the analytical results of this study and Figure 5-5 shows
the results of the FFT analysis. The largest percent difference was only 11.3%. This closeness
indicated that the modal periods of the computer model correlated well with the periods of the
actual building.
Table 5-3: Modal Periods for the Selected Computer Models
North-South
Model
1
Model
2
Model
3
Mode
Period
Modal
Participation
Factor
1
(sec)
2.483
(%)
62.28
4
7
1
5
8
1
4
7
0.863
0.509
2.951
1.041
0.621
2.754
0.967
0.573
11.52
7.67
61.19
12.05
7.62
61.90
12.55
7.52
East-West
Cumulative
Modal
Participation
Factor
Cumulati
ve
Modal
Participat
ion
Factor
Mode
Period
Modal
Participation
Factor
(%)
62.28
2
(sec)
2.331
(%)
65.59
66.04
74.42
83.97
61.19
75.33
83.39
61.90
74.81
82.91
5
8
2
4
7
2
5
8
0.849
0.507
2.865
1.055
0.632
2.530
0.930
0.558
11.53
6.98
64.51
11.69
7.00
65.98
12.48
7.09
78.80
85.90
65.78
77.54
85.38
66.18
78.90
86.02
133
Table 5-4: Comparison of Modal Periods for Model 3 and the Actual Records-FFT Method
North-South
Mode
1
4
7
Modal
Periods
(SAP2000)
Modal Periods
(FFT Analysis)
Diff.
(sec)
2.754
0.967
0.573
(sec)
2.596
0.937
0.531
(%)
5.7
3.1
7.3
Mode
2
5
8
East-West
Modal
Modal
Periods
Periods
(FFT
(SAP2000)
Analysis)
(sec)
(sec)
2.530
2.242
0.930
0.931
0.558
0.538
North-South
Diff.
(%)
11.3
1.1
3.6
East-West
Figure 5-5: FFT Analyses
5.5
Earthquake Ground Motions
As described in the introduction, accelerations recorded at the arcade (basement) level during the
1994 Northridge Earthquake were used as the input ground accelerations for the time-history
analysis. These accelerations included components in the North-South, East-West and vertical
directions (Figure 5-6). Only the two horizontal components were used in the time-historyanalysis. The effects of vertical excitation were investigated for the Tarzana building (Chapter 3)
and it was concluded to be insignificant. Therefore, the vertical motion was ignored from this
analysis.
134
Acceleration Record at Base Level (ground - UP)
Acceleration Record at Base Level (ground - 90)
500
400
400
400
300
300
300
100
0
-100
-200
200
100
0
-100
-200
-300
-300
-400
-400
-500
2
2
200
Acceleration (cm/sec )
500
Acceleration (cm/sec )
2
Acceleration (cm/sec )
Acceleration Record at Base Level (ground - 180)
500
5
10
15
20
25
30
35
40
45
50
55
60
Time (sec)
100
0
-100
-200
-300
-400
-500
0
200
-500
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
Time (sec)
North-South Component
East-West Component
20
25
30
35
40
45
50
Time (sec)
Vertical Component
Figure 5-6: Ground Motion Components
5.6
Observed Damage
After the Northridge earthquake, the connections in the building were inspected for damage. A
summary of the different types of damage found and the corresponding (SAC) identifications are
given in Table 5-5. The type 1D damage was small enough that it was not repaired. Therefore,
the 1D type damage will be excluded from any of the comparisons made in this study. The
locations of the different types of damages on the seismic frames are very important to
understand, in order to compare the actual damage with the predicted damage. Figures 5-7A
through 5-7D show the different locations of damage on the moment resisting frames. The most
severe damage was experienced in the columns on the North-South seismic frame along line 2,
see Figure 5-7A, where the crack propagated all the way into the column web.
135
Table 5-5: Identification of Damage
ID
Name
1D-W4
C2
C3
P5
W4
SAC Identification Definitions
Light beam flange weld cracking
Column flange damage:
Complete flange tear out from beam flange weld
Column flange damage:
Partial cross-flange crack in HAZ
Column Web Damage:
Partial depth cracking originating from cracked col. Flange
Beam Flange Damage: Crack at column interface (in weld)
Figure 5-7A: Damage on Gridline 2 and Damage on Gridline 9
136
Figure 5-7B: Damage on Gridline 4 and Damage on Gridline 7
Figure 5-7C: Damage on Gridline A
137
Figure 5-7D: Damage on Gridline G
5.7
Time History Analysis
Linear dynamic time history analyses were performed on all the three models (see Table 5-1).
The displacement, velocity, and acceleration time history responses are compared with the actual
recorded responses from the earthquake and shown in Figures 5-8 through 5-16. . The NorthSouth direction is defined by a “180” and the East-West, by a “90”. Elastic Demand Ratios and
Demand/Plastic-Moment Ratios were calculated from the Time History analysis in order to
determine if overstressed areas compare with the observed damage to the building.
5.7.1 Model 1 and Model 2
Observation of the displacement responses for Model 1, which is the full rigid zone model,
clearly shows that the Model is stiffer than the actual structure see Figure 5-9. From the
description of the building, the absence of continuity plates in the frame columns for most of the
height of the building indicate that the response is probably closer to the no rigid zone
assumption in Model 2. However, there are a number of frame columns that have beams on three
138
sides that would be closer to the full rigid zone scenario. From Figure 5-13, the responses look
better, but the model is softer than the actual structure. The zero crossings of the analytical
response have a wider separation than that from the actual response. The actual response is
therefore somewhere between the full rigid zone and no rigid zone models. Acceleration and
velocity responses are shown for completeness.
5.7.2 Model 3
The responses from “the best-fit model” (Model 3) with its rigid zone assumptions as stated
earlier are shown in Figures 5-14 through 5-16. The displacement velocity and acceleration
responses correlated very well with the recorded response. There were some spikes in the
acceleration responses that were probably due to higher modes responses. These higher modes
were very highly damped in the actual structure. The displacement response amplitudes in the
North-South direction show some departure from the actual response from about 15 to 25
seconds. This is probably due to some inelastic response in this range but did not significantly
affect the overall stiffness of the structure. The inelastic response could be attributed to both
structural and non-structural elements. Additional damping by yielding of some of the nonstructural elements could also be the result in the differences in the responses
The locations and types of damages on the building were discussed in Section 5-6. The severity
of damage in the North-South direction (180) was much greater than in the East-West direction
(90), as described in Section 5-6. That is why there is a noticeable change in stiffness or the
inelastic behavior of the building responses in the North-South direction. This difference is best
seen from the roof displacement response in the North-South direction (Figure 5-16). Around 15
seconds, the first offset (shift) appeared in the time history record. This change in stiffness of the
actual building time-history response was a direct result of damage caused by the earthquake.
The elastic time-history analysis was unable to capture this change.
Although the North-South direction experienced some inelastic behavior, the difference in the
elastic response of the computer model to the inelastic behavior of the building was very small.
Also, there was no noticeable difference in the East-West direction response although there was
damage. This small or no change in the time history responses indicated that the amount of
139
damage was not large enough to greatly affect the overall performance of the building. The extent
of damage, in each direction, is summarized in Table 5-6 as the ratio of the number of damaged
connections to the total number of connections. The ratios were very small which indicated that
there was a large amount of redundancy in the building. These ratios were only calculated from
the fifth floor up, because there was no damage to the seismic frame below that floor. It should
be pointed out that only the areas that were repaired were considered in the ratios. Thus, the
actual ratio of damage could be slightly higher.
Table 5-6: Summary of Damaged Connections
East-West
North-South
Columns
Total Number
of
Connections
512
Number of
Damaged
Connections
0
Beams
448
11
Member
Columns
Total Number
of
Connections
256
Number of
Damaged
Connections
5
Beams
384
19
Ratio
(%)
Member
0
2.5
140
Ratio
(%)
1.9
5
Acceleration Record at Level 10 (90)
600
600
400
400
2
Acceleration (cm/sec )
800
2
Acceleration (cm/sec )
Acceleration Record at Level 10 (180)
800
200
0
-200
-400
200
0
-200
-400
R ecorded H istory
Recorded History
-600
-600
M odel1
Model 1
-800
-800
0
5
10
15
20
25
30
35
40
45
50
55
0
60
5
10
15
20
25
35
40
45
50
55
60
Time (sec)
Time (sec)
Acceleration Record at Roof (180)
Acceleration Record at Roof (90)
800
600
600
400
400
2
Acceleration (cm/sec )
800
2
Acceleration (cm/sec )
30
200
0
-200
-400
200
0
-200
-400
Recorded History
-600
Recorded history
-600
Model 1
Model 1
-800
-800
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
20
25
Time (sec)
30
35
40
45
50
55
60
Time (sec)
Figure 5-8: Acceleration Records for Model 1
Relative Velocity Record at Level 10 (90)
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
Relative Velocity Record at Level 10 (180)
200
50
0
-50
-100
50
0
-50
-100
Recorded History
Recorded History
-150
-150
Model 1
Model 1
-200
-200
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
20
25
Time (sec)
35
40
45
50
55
60
Time (sec)
Relative Velocity Record at Roof (180)
Relative Velocity Record at Roof (90)
200
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
30
50
0
-50
-100
50
0
-50
-100
Recorded History
Recorded history
-150
-150
Model 1
Model 1
-200
-200
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
Time (sec)
20
25
30
Time (sec)
Figure 5-9: Velocity Records for Model 1
141
35
40
45
50
55
60
Relative Displacement Record at Level 10 (90)
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
Relative Displacement Record at Level 10 (180)
50
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded History
Recorded History
-40
-40
Model 1
Model 1
-50
-50
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
20
25
Time (sec)
35
40
45
50
55
60
Time (sec)
Relative Displacement Record at Roof (180)
Relative Displacement Record at Roof (90)
50
40
40
30
30
20
20
Displacement (cm )
50
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded history
Recorded History
-40
-40
Model 1
Model 1
-50
-50
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
20
25
Time (sec)
30
35
40
45
50
55
60
Time (sec)
Figure 5-10: Displacement Records for Model 1
Acceleration Record at Level 10 (90)
800
600
600
400
400
2
Acceleration (cm/sec )
800
2
Acceleration (cm/sec )
Acceleration Record at Level 10 (180)
200
0
-200
-400
200
0
-200
-400
Recorded History
-600
Recorded History
-600
Model 2
Model 2
-800
-800
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
20
25
Time (sec)
30
35
40
45
50
55
60
Time (sec)
Acceleration Record at Roof (180)
Acceleration Record at Roof (90)
800
600
600
400
400
2
Acceleration (cm/sec )
800
2
Acceleration (cm/sec )
Displacement (cm )
30
200
0
-200
-400
200
0
-200
-400
Recorded History
-600
Recorded history
-600
Model 2
Model 2
-800
-800
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
20
Time (sec)
25
30
Time (sec)
Figure 5-11: Acceleration Records for Model 2
142
35
40
45
50
55
60
Relative Velocity Record at Level 10 (90)
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
Relative Velocity Record at Level 10 (180)
200
50
0
-50
50
0
-50
-100
-100
Recorded History
Recorded History
-150
-150
Model 2
Model 2
-200
-200
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
20
25
Time (sec)
35
40
45
50
55
60
Time (sec)
Relative Velocity Record at Roof (180)
Relative Velocity Record at Roof (90)
200
200
150
150
100
100
Velocity (cm/sec)
Velocity (cm/sec)
30
50
0
-50
50
0
-50
-100
-100
Recorded History
Recorded history
-150
-150
Model 2
Model 2
-200
-200
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
20
25
Time (sec)
30
35
40
45
50
55
60
Time (sec)
Figure 5-12: Velocity Records for Model 2
Relative Displacement Record at Level 10 (90)
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
Relative Displacement Record at Level 10 (180)
50
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded History
Recorded History
-40
-40
Model 2
Model 2
-50
-50
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
20
25
Time (sec)
35
40
45
50
55
60
Time (sec)
Relative Displacement Record at Roof (180)
Relative Displacement Record at Roof (90)
50
50
40
40
30
30
20
20
Displacement (cm )
Displacement (cm )
30
10
0
-10
-20
10
0
-10
-20
-30
-30
Recorded history
Recorded History
-40
-40
Model 2
Model 2
-50
-50
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
20
Time (sec)
25
30
Time (sec)
Figure 5-13: Displacement Records for Model 2
143
35
40
45
50
55
60
Acceleration Record at Level 10 (90)
600
600
400
400
2
Acceleration (cm/sec )
800
2
Acceleration (cm/sec )
Acceleration Record at Level 10 (180)
800
200
0
-200
-400
200
0
-200
-400
Recorded History
-600
Recorded History
-600
Model 3
Model 3
-800
-800
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
20
25
30
Time (sec)
35
40
45
50
55
60
Time (sec)
Acceleration Record at Roof (180)
Acceleration Record at Roof (90)
800
800
600
600
2
Acceleration (cm/sec )
400
Acceleration (cm/sec )
400
2
200
0
-200
-400
Recorded History
200
0
-200
-400
Recorded history
-600
Model 3
-600
-800
Model 3
0
5
10
15
20
25
30
35
40
45
50
55
60
-800
Time (sec)
0
5
10
15
20
25
30
45
200
150
150
100
100
Velocity (cm/sec)
200
50
0
-50
50
0
-50
-150
Model 3
Model 3
-200
-200
0
5
10
15
20
25
30
35
40
45
50
55
0
60
5
10
15
20
25
30
35
40
45
50
Relative Velocity Record at Roof (180)
150
150
100
100
Velocity (cm/sec)
200
50
0
-50
-100
50
0
-50
-100
Recorded History
Recorded history
-150
-150
Model 3
Model 3
-200
-200
0
5
10
15
20
25
30
35
40
45
50
55
60
0
5
10
15
Time (sec)
20
25
30
35
40
Time (sec)
Figure 5-15: Velocity Records for Model 3
Relative Displacement Record at Level 10 (180)
50
40
40
144
30
isplacement (cm )
isplacement (cm )
Relative Displacement Record at Level 10 (90)
50
-10
60
Relative Velocity Record at Roof (90)
200
0
55
Time (sec)
Time (sec)
10
60
Recorded History
Recorded History
-150
20
55
-100
-100
30
50
Relative Velocity Record at Level 10 (90)
Relative Velocity Record at Level 10 (180)
Velocity (cm/sec)
40
Time (sec)
Figure 5-14: Acceleration Records for Model 3
Velocity (cm/sec)
35
20
10
0
-10
45
50
55
60
Figure 5-16: Displacement Records for Model 3
5.7.3 Elastic Demand Ratios
Checks on the Elastic Force Demand Ratios were performed using the Load and Resistant Factor
Design (LRFD) method. The expected yield strengths were used to calculate the capacities for the
Elastic Demand Ratios, which are 1.5 times that for A36 steel and 1.15 times that for A50 steel.
Columns on lines 2, 4, 7, 9, and that are common to seismic frames in each direction were the
only members that had elastic demand ratios greater than unity. No damage was observed in
these columns. These columns had to resist biaxial moments, driving up the demands on these
columns. The possible reason no damaged occurred was caused by the added strength from the
perpendicular beam.
The damaged members had ratios below unity and were no higher than the undamaged members.
For example, the elastic demand ratio that corresponded to the severely damaged column (F-2 on
the 16th floor) had a ratio of 0.67 and the undamaged column (F-9 on the 16th floor) on the
opposite side of the building had a ratio of 0.64. There was only a 4% difference between the
145
ratios of the damaged and undamaged columns. This difference was too small to indicate that an
overstress would occur in column F-9 on the 16th floor. The elastic demand ratios were unable to
predict, with any degree of certainty, damage to the building. All the ratios for the damaged
members are summarized in Table 5-8. The SAP2000 program does not calculate Elastic force
demand ratios according to the LRFD method for non-prismatic members. Therefore, the force
demand ratios for the non-prismatic plate girder beams, that suffered damage, are not reported.
5.7.4 Demand/Plastic-Moment Ratios
Table 5-8 shows the demand/plastic-moment ratios for all the damaged members. None of the
demand/plastic-moment ratios exceeded unity, which implied that there was no damage. This
contradicts the actual state of the members after the earthquake.
5.8
5.8.1
Evaluation with Prevailing Practice – UBC-97 and FEMA-273
Analysis Using UBC-97
As described in the introduction, a dynamic response-spectra analysis was used to calculate the
forces in the building members because the building was over 240 feet tall. The design base
shear was 2706 kips which corresponded to the minimum code value. This is about one-half the
base shear from the time history analysis, which was 6249 kips and 5006 kips for North-South
and East-West directions, respectively
A summary of the forces and overturning moments from the analysis is given in Table 5-7.
The following sections discuss the results of individual checks made for this building. The three
checks include the elastic demand ratios or overstress checks on the building members calculated
from the UBC-97 loading, building drifts compared to the UBC-97 drift limitations, and the
results of the seismic provisions for SMF.
146
Table 5-7: UBC-97 Summary Table, Parameters and Forces
Site Parameters
Z
0.4
Ca
0.57
Cv
1.02
SEISMIC ZONE: 4
OCCUPANCY CATEGORY: Standard Occupancy
IRREGULAR 19 STORY STRUCTURE: Weight/Mass Ir
BUILDING HEIGHT: 249.125 feet
BASE SHEAR VX= 3173.42 kips
BASE SHEAR Vy=
I
Nv
3244.83 kips
Structural Parameters
R
8.5
TX (sec)
2.54
Ty (sec)
2.72
1.00
W (kips)
43010.50
1.60
-- DYNAMIC ANALYSIS -Base Shear Distribution, Earthquake Loads and Overturning Moments
applied to the structure
Lateral Loads
(kips)
Redundancy
Factors
Earthquake Forces
OTM
(kips)
(kips-feet)
FEW
FNS
ρEW
ρNS
EW
NS
EW
NS
Level
748.86
361.87
249.99
160.97
115.75
110.34
121.51
124.26
113.05
97.02
86.89
87.50
97.97
111.56
118.70
108.82
173.39
154.34
30.64
795.95
376.94
248.70
142.03
88.63
89.37
114.66
126.42
112.40
88.00
74.19
81.96
105.47
127.63
133.85
118.25
198.52
180.47
41.37
1.00
1.00
748.86
361.87
249.99
160.97
115.75
110.34
121.51
124.26
113.05
97.02
86.89
87.50
97.97
111.56
118.70
108.82
173.39
154.34
30.64
795.95
376.94
248.70
142.03
88.63
89.37
114.66
126.42
112.40
88.00
74.19
81.96
105.47
127.63
133.85
118.25
198.52
180.47
41.37
9676.85
23007.02
39032.68
56711.69
75549.41
95545.54
116890.53
139647.26
163679.36
188771.12
214772.04
241670.26
269590.96
298715.85
329160.83
360842.80
390701.79
422359.18
499856.81
10322.88
24458.94
41278.97
59519.88
78573.76
98508.90
119693.08
142304.20
166172.91
190980.61
216532.64
242909.17
270404.84
299318.69
329763.68
361584.76
391923.28
424417.43
504275.40
Roof
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
5.8.1.1 Elastic Force Demand Capacity Ratios
The Elastic Force Demand Capacity Ratios for the damaged members are given in Table 5-8.
The yield strengths, as designated on the plans, were used for the calculation of these checks.
147
Table 5-8: Elastic Demand Ratios for Damaged Members
Elastic Demand
Ratios
(Time-History)
Demand-Plastic
Moment Ratio
(Time-History)
Elastic Demand Ratios
(UBC-97 Spectral
Analysis)
C2
C3
.944
.976
.550
Column G-2/16th
.663
.230
.363
Column E-7/19th
C3
.400
.211
.268
Column G-6/18th
P5
.672
.264
.294
Column F-2/17th
P5
.665
.279
.303
Column F-2/16th
P5
.711
.297
.390
Column C-2/15th
P5
.734
.310
.405
Column F-2/15th
W4
.542
.416
.390
Beam C-2/15th
W4
.634
.466
.352
Beam A-2/17th
W4
.616
.466
.351
Beam F-2/12th
W4
.279
.192
.232
Beam D-4/19th
W4
.364
.246
.262
Beam D-4/16th
W4
N/A
.579
N/A
Beam G-4/14th
W4
N/A
.469
N/A
Beam D-4/10th
W4
.569
.420
.452
Beam F-9/18th
W4
.684
.506
.598
Beam F-9/16th
W4
.617
.457
.395
Beam C-9/15th
W4
.497
.368
.520
Beam C-9/15th
W4
.525
.389
.428
Beam C-9/14th
W4
.661
.484
.547
Beam F-9/10th
W4
.455
.272
.526
Beam A-7/18th
W4
.449
.332
.504
Beam A-8/16th
W4
W4
W4
W4
W4
.384
.524
.414
N/A
N/A
.339
.388
.392
.580
.611
.287
.522
.320
N/A
N/A
Beam A-3/15th
Beam A-5/12th
Beam A-9/14th
Beam A-7/18th
Beam D-7/16th
W4
N/A
.622
N/A
Beam D-7/15th
W4
W4
W4
W4
W4
W4
N/A
.324
.330
.495
.446
.530
.668
.226
.320
.366
.330
.392
N/A
.343
.338
.536
.441
.552
Beam D-7/12th
Beam G-8/18th
Beam G-9/16th
Beam G-6/16th
Beam G-6/15th
Beam G-5/14th
Damage
ID
148
Member
Location
Grid #/Floor
None of the ratios shown in Table 5-8 for the UBC-97 analysis was above unity. The UBC-97
method was, therefore, unsuccessful in predicting the damage to this 20-story building.
5.8.1.2 Check for Drift Limitations
For this building, it was found that the UBC-97 story drift limitations were satisfied only for a
small number of the stories. Analytically, the results are presented in Table 5-9. The largest drift
percentage was 3.61%, which occurred in the East-West direction on the 4th level.
Table 5-9: UBC-97 Summary Displacements and Drift Limit Checks
Maximum Inelastic
Response Displacements
INTERSTORY DRIFT RATIO
∆M
(% of story height)
(in)
Level
EW
NS
Roof
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
67.65
65.39
62.53
59.20
55.57
51.88
48.20
44.33
40.28
36.35
32.49
28.50
24.51
20.47
16.36
11.96
6.55
4.34
1.73
75.98
73.66
70.51
66.82
62.71
58.25
53.55
48.61
43.55
38.56
33.62
28.74
23.92
19.04
14.40
10.12
5.77
3.93
1.84
EW
1.45
1.90
2.22
2.42
2.46
2.46
2.58
2.70
2.62
2.58
2.66
2.66
2.70
2.74
2.94
3.61
1.67
1.98
0.54
OK
OK
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
OK
OK
OK
NS
1.49
2.10
2.46
2.74
2.98
3.13
3.29
3.37
3.33
3.29
3.25
3.21
3.25
3.09
2.86
2.90
1.40
1.58
0.58
OK
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
Limit Exceeded
OK
OK
OK
5.8.1.3 Seismic Provision Checks
The three topics investigated were the panel zone thickness, the need for continuity plates, and
the column-beam moment ratios checks. A summary of the individual checks is shown on Table
5-10. All the panel zones met the thickness requirement although no doubler plates were
provided. Continuity plates were provided on the building where needed and therefore the
149
building connections were compliant. The Column-Beam moment ratio checks did not pass for
all the connections on the roof level.
Table 5-10: UBC-97 Seismic Provisions for Structural Steel
Check
Panel Thickness
Passed/Failed
Passed
UBC-97
Continuity
plates?
Passed
Column-Beam Moment
Ratios
Did Not Pass
5.8.2 Analysis Using FEMA-273
5.8.2.1 Non-linear Static Pushover Analysis
The resulting base shears and corresponding yield displacements from the two loading patterns
pushed to the target displacement are presented in Tables 5-11 through 5-14.
Table 5-11: Nonlinear Static results for BSE-1 in the North-South Direction
North-South
Uniform
Modal
Analysis
Yield Base
Shear
(kips)
16775
15800
Yield Base
Shear Coefficient
0.39
Yield
Displacement
(inches)
35
0.37
43.5
Target
Displacement
(inches)
Displacement
Ductility
1.10
37.66
0.87
Table 5-12: Nonlinear Static results for BSE-1 in the East-West Direction
East-West
Uniform
Modal
Analysis
Yield Base
Shear
(kips)
18871
13911
0.44
Yield
Displacement
(inches)
33.51
0.32
38.92
Yield Base
Shear Coefficient
150
Target
Displacement
(inches)
Displacement
Ductility
1.02
34.29
0.88
Table 5-13: Nonlinear Static results for BSE-2 in the North-South Direction
North-South
Uniform
Modal
Analysis
Yield Base
Shear
(kips)
16936
0.40
Yield
Displacement
(inches)
35.5
0.37
39
Yield Base
Shear Coefficient
15800
Target
Displacement
(inches)
Displacement
Ductility
1.59
56.49
1.45
Table 5-14: Nonlinear Static results for BSE-2 in the East-West Direction
East-West
Uniform
Modal
Analysis
Yield Base
Shear
(kips)
18710
Yield Base
Shear Coefficient
13911
0.43
Yield
Displacement
(inches)
33
0.32
38
Target
Displacement
(inches)
Displacement
Ductility
1.56
51.43
1.53
The required displacement ductility and the yield base shear for the building had maximum
values for the uniform load pattern. Therefore, only the results from the uniform load pattern
will be discussed. The required displacement ductility for the BSE-1 earthquake was 1.1 for the
North-South and 1.02 for the East-West direction. The required displacement ductility for the
BSE-2 earthquake was 1.59 and 1.56 for the North-South and East-West direction, respectively.
These values were close to unity. This indicated that the target displacement occurred close to
the yield displacement and there was still some strength left in the building after the target
displacement was reached. All the target displacements were based on the soil type SE because
the soil profile was unavailable. A comparison of the target displacements for the SE soil type
and the SD soil types are presented in Table 5-15. The table shows that all the target
displacements increased by 33%.
151
Table 5-15: Comparison of Target Displacements for SE and SD Soil Types
Soil Type
North-South
East-West
BSE-1
Target Displacement
SE
SD
37.66 in
28.25 in
34.29 in
25.72 in
%
Difference
33%
33%
BSE-2
Target Displacement
SE
SD
56.49 in
42.37 in
51.43 in
38.57 in
%
Difference
33%
33%
5.8.2.2 Acceptance Criteria
Table 5-16 shows the displacement, base shear, and number of hinges that exceed the different
acceptance criteria for each step during the static push over analysis. The BSE-1 target
displacements satisfied the code requirements since all hinges performed below the Life Safety
criterion. All the BSE-2 target displacements satisfied the code requirements since all hinges
performed below the Collapse Prevention criterion.
It was observed that the initial hinges, formed during the pushover analysis, did not occur where
the earthquake damage occurred. In addition, the hinges that eventually formed at the ends of
damaged members did not have higher levels of plastic rotation compared to the hinges in the
undamaged members. This shows that the static non-linear pushover analysis was unable to
predict the damage that was caused by the Northridge earthquake.
5.8.2.3 Response Comparisons using Demand-Capacity Spectra Response Method
The Response Comparisons from the FEMA-273 method are summarized Figures 5-17 and 5-18.
A close up of the demand and capacity curve crossings are shown in Figures 5-19 and 5-20. The
elastic demand spectrum curve intersected the linear portion of the capacity spectrum curve
(pushover curve) in both directions. This confirmed that the building behaved elastically, in both
directions, under the Northridge earthquake motion although there was small damage to the
building. It is also interesting to note that the intersection of the BSE-1 demand spectrum and the
capacity spectrum (pushover curve) from the modal distribution was at the same roof drift
152
Table 5-16: Plastic Hinges from Pushover Analysis for BSE-1 and BSE-2
Type and Number of Hinges formed at Target Displacement in the
East-West Direction, the Uniform Pattern and BSE1
Step
0
1
2
3
4
5
6
7
8
Displacement Base Shear
-0.03
0
11.92
6768
14.56
8260
26.76
14854
34.63
17665
47.70
19629
60.13
20943
72.69
21918
72.69
21918
at Target Displacement
A-B
B-IO
2406
2406
2405
2376
2284
2180
2100
2039
2039
2284
0
0
1
29
99
134
154
187
187
99
IO-LS LS-CP
0
0
0
1
23
92
150
151
151
23
0
0
0
0
0
0
0
0
0
0
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2406
2406
2406
2406
2406
2406
2406
2406
2406
Type and Number of Hinges formed at Target Displacement in the
North-South Direction, the Uniform Pattern and BSE1
Step
0
1
2
3
4
5
6
7
8
9
Displacement Base Shear
0.05
0
12.00
5710
21.33
10161
33.58
15375
45.72
18308
58.23
20294
59.06
20414
59.06
20207
59.40
20298
59.40
20298
at Target Displacement
A-B
B-IO
2406
2406
2405
2333
2194
2125
2123
2119
2118
2118
2194
0
0
1
73
167
146
144
147
147
147
167
IO-LS LS-CP
0
0
0
0
45
127
129
130
130
129
45
0
0
0
0
0
8
8
8
8
9
0
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2406
2406
2406
2406
2406
2406
2406
2406
2406
2406
Type and Number of Hinges formed at Target Displacement in the
East-West Direction, the Uniform Pattern and BSE2
Step
0
1
2
3
4
5
6
7
8
Displacement Base Shear
-0.03
0
11.92
6768
14.56
8260
26.76
14854
34.63
17665
47.70
19629
60.13
20943
72.69
21918
72.69
21918
at Target Displacement
A-B
B-IO
2406
2406
2405
2376
2284
2180
2100
2039
2039
2100
0
0
1
29
99
134
154
187
187
154
IO-LS LS-CP
0
0
0
1
23
92
150
151
151
150
0
0
0
0
0
0
2
28
28
2
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2406
2406
2406
2406
2406
2406
2406
2406
2406
Type and Number of Hinges formed at Target Displacement in the
North-South Direction, the Uniform Pattern and BSE2
Step
0
1
2
3
4
5
6
7
8
9
Displacement Base Shear
0.05
0
12.00
5710
21.33
10161
33.58
15375
45.72
18308
58.23
20294
59.06
20414
59.06
20213
59.35
20291
59.35
20291
at Target Displacement
A-B
B-IO
2406
2406
2405
2333
2194
2125
2123
2119
2119
2119
2125
0
0
1
73
167
146
144
147
146
146
146
IO-LS LS-CP
0
0
0
0
45
127
129
130
131
129
127
153
0
0
0
0
0
8
8
8
7
9
8
CP-C
C-D
D-E
>E
TOTAL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2406
2406
2406
2406
2406
2406
2406
2406
2406
2406
1.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
1.20
Base Shear Coefficient (BS/W)
Target Displacement BSE-1
Target Displacement BSE-2
1.00
Elastic Demand Spectrum, Damping Ratio 2.5%
BSE-1 Demand Spectrum
Inelastic Demand Spectrum, Damping Ratio 2.5%, R=1
0.80
Maximum Equivalent Response
0.60
BSE-1 δ t =
BSE-2 δ t =
37.68 in
56.52 in
0.40
0.20
0.00
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
Roof Drift (%)
Figure 5-17: Demand-Capacity Spectrum for the N-S Dir.
1.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
1.20
Base Shear Coefficient (BS/W)
Target Displacement BSE-1
Target Displacement BSE-2
1.00
Elastic Demand Spectrum, Damping Ratio 3%
BSE-1 Demand Spectrum
Inelastic Demand Spectrum, Damping Ratio 3%, R=1
0.80
Maximum Recorded Roof Displacement
0.60
BSE-1 δ t =
34.30 in
BSE-2 δ t =
51.46 in
0.40
0.20
0.00
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
Roof Drift (%)
Figure 5-18: Demand-Capacity Spectrum for the E-W Dir.
1.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
S/W)
1.20
154
Non-linear Static Procedure - "Modal Analysis" Pattern
Target Displacement BSE-1
Target Displacement BSE-2
1.00
Elastic Demand Spectrum, Damping Ratio 5%
2.00
Figure 5-19: Close up View of Demand-Capacity Spectrum for the N-S Dir.
1.40
Linear Static Procedure
Non-linear Static Procedure - Uniform Pattern
Non-linear Static Procedure - "Modal Analysis" Pattern
1.20
Base Shear Coefficient (BS/W)
Target Displacement BSE-1
Target Displacement BSE-2
1.00
Elastic Demand Spectrum, Damping Ratio 5%
BSE-1 Demand Spectrum
Inelastic Demand Spectrum, Damping Ratio 5%, R=1
0.80
Maximum Equivalent Response
0.60
BSE-1 δ t =
34.30 in
BSE-2 δ t =
51.46 in
0.40
0.20
0.00
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
Roof Drift (%)
Figure 5-20: Close up View of Demand-Capacity Spectrum for the E-W Dir.
155
2.00
percentage as the BSE-1 target displacement. This shows that the modal load pattern the most
realistic of the load patterns.
5.9
Summary
A summary of the performance of the building from the time history, UBC-97, and FEMA-273
analyses are given in Table 5-17.
Table 5-17: Summary of Building Performance
Northridge Earthquake
Elastic Demand Ratios
(Model 3)
Ratios >1 in Corner
Columns.
Damaged members had
ratios <1.
Actual Damage
Remarks
Yes
Damage caused by
Earthquake, Figure
5-7.
Retrofit
Strategy
Design/Capacity
Ratios (Model 3)
Ratios <1 in All
Members
Damaged connections repaired.
UBC-97
Compliance
EDR
Drift
Limits
OK
EDR<1
No
Table 5-8.
Retrofit
Strategy
Compliance
Special Provisions
ColumnRedundancy
Panel Continuity
Beam
Factors
zones
Plates
Moment
Ratios
OK
No
Provided
Roof level
OK
OK
where
failed the
needed
test
Increase Lateral Resisting Moment Frames
Life SafetyBSE-1
FEMA-273
Collapse PreventionBSE-2
Demand-Capacity
Spectra
OK
OK
Elastic Behavior.
Retrofit
Strategy
None
156
Model 3 was able to match the response of the actual earthquake very well. Although the NorthSouth direction experienced some inelastic behavior, the difference between the elastic response
of the computer model to the inelastic behavior of the building was very small. Also, there was
no noticeable difference in the East-West direction though there was damage. This small change
in the time history responses indicated that there was a large amount of redundancy in the
building and the overall performance of the building was not greatly affected by the damaged
members. Thus, the modeling assumptions are realistic and if high stress ratios can be an
indication of greater damage potential technically it should be able to be predicted. This proved
not to be the case for the following reasons:
•
The demand/plastic-moment ratios and elastic demand ratios, calculated from the
elastic time-history analysis, did not exceed unity in the damaged members.
•
The elastic demand checks from the analysis according to UBC-97 did not show
higher ratios in the damaged members compared to the undamaged members.
•
The initial hinges that formed during the pushover analysis did not occur in the
damaged members and the hinges that eventually formed at the ends of damaged
members did not have higher levels of plastic rotation compared to the undamaged
members.
This leads to the conclusion that damage caused in this building by the Northridge earthquake
was more of a random nature and possibly correlated with construction defects rather than the
earthquake itself. This conclusion is consistent with the findings of other researchers
[reference?].
157
6
6.1
SUMMARY AND RECOMMENDATIONS
General Modeling Assumptions
The effectiveness of the rigid end zones, and damping for the four buildings are summarized in
Table 6-1.
Table 6-1: Summary of Modeling Assumptions.
Building
North Hollywood
Building
Tarzana Building
Sherman Oaks
Building
Encino Building
Beams
Columns
Frames 3 or 4 sides
Frames 1 side
Corner
Rigid Zone
Effectiveness
EastNorthWest
South
Doubler
Plates
Continuity
Plates
1st Mode
Damping
EastNorthWest
South
80%
85%
Yes
Yes
5%
4%
0%
100%
Yes
Yes
3%
7%
34%
80%
Yes
Yes
1%
2%
2.5%
3%
100%
100%
100%
2.5%
95%
100%
2.5%
Yes
No
Yes
No
From Table 6-1 the following observations and modeling recommendations are made:
•
If no doubler or continuity plates are added, the effectiveness of the rigid end zones is
close to zero. Recommendation: No rigid end zones should be considered if no
doubler or continuity plates are added.
•
If douber plates and continuity plates are present, the effectiveness of the rigid end
zones is between 80-100%. Recommendation: Full rigid end zones should be
considered if doubler and continuity plates present.
158
•
The Sherman Oaks and Encino buildings experienced high resonant response, and
lower damping was used for these two buildings. This kind of response is difficult to
anticipate and accounts for general modeling assumptions. Although the comparisons
for Model 3 look good for both buildings, the difference in the peak response is
substantial. For the Sherman Oaks building the East-West direction response from
Model 3 gave a peak displacement of 31.55 inches, while the recorded response at the
same instance in time was 41.12 inches. This is 23% difference in the response. For
the North-South direction for the same building it was 26%. For the Encino building
the responses compared well in the North-South direction but were off by 24% in the
East-West direction.
•
Except for the Tarzana building, which had 7% damping in the North-South
direction, the damping for all the buildings was within 5%. Recommendation: As a
conservative estimate, a damping of 2-3% is suggested.
•
A damping of 10% should be used for modes beyond the first three modes of
vibration in a particular direction.
6.2
Comparison of Maximum Roof Displacements
The maximum roof displacements recorded from the earthquake for the four buildings were
compared with the maximum inelastic displacement from UBC-97 and the target displacement
from FEMA-273 in Table 6-2.
159
Table 6-2. Comparison of Roof Displacements
Comparison of Recorded Roof Displacement with Prevailing Practice
UBC-97
FEMA-273
Recorded
Soil Type SD
Soil Type SD
Building
East-West North-South East-West North-South East-West North-South
(in)
(in)
(in)
(in)
(in)
(in)
6.86
7.24
40.76
73.19
28.34
24.14
North Hollywood Building
Percent of Recorded
594.17% 1010.94% 413.12% 333.43%
Tarzana Building
11.43
15.43
26.12
25.41
22.42
20.51
Percent of Recorded
Sherman Oaks Building
Percent of Recorded
Encino Building
16.19
13.51
228.58%
164.68%
196.20%
132.92%
14.35
55.69
75.35
30.77
34.00
18.11
343.98%
67.65
525.11%
75.98
190.06%
28.26
236.93%
25.73
500.75%
419.56%
209.18%
142.08%
Percent of Recorded
The following observations are made:
•
The drift limits for all buildings at some floors were exceeded in the UBC-97 check.
•
The UBC-97 estimate of the maximum roof displacement is several orders of
magnitude higher than the maximum displacements recorded at the roof.
•
Except for the Tarzana building where Static Analysis Procedures with redundancy
factors of 1 were used and all the frames in the building were special moment
resisting frames, the estimated maximum inelastic displacements from UBC-97 were
significantly greater than the calculated target displacements from FEMA-273.
•
In light of the maximum recorded displacements from the Northridge Earthquake, the
target displacements from FEMA-273 seem reasonable for the Life Safety Acceptance
criteria for a BSE-1 earthquake.
160
•
The calculation of the maximum inelastic displacements from UBC-97 seems overly
conservative for steel buildings.
6.3
Comparison of Inter-Story Drifts
A summary of the inter-story drifts for the four buildings is given in Table 6-3. The inter-story
drifts for the North Hollywood building from the UBC-97 calculations are significantly higher
than the inter-story drifts obtained from Model 3 for the Northridge earthquake. This is more
pronounced in the East-West direction, where there are only two, two-bay lateral resisting frames
in this direction. The forces and the redundancy factors from the UBC-97 are therefore higher in
this direction for this building. This again goes with the philosophy of the UBC-97 to penalize
buildings with low redundancy. Nevertheless the penalty here seems too high and the
displacements from the earthquake again suggest a lower factor to be used in the computation of
the maximum inelastic displacement from UBC-97. It is recommended that this factor be revised
for steel moment resisting frame buildings. In may not be universally applicable for other
buildings, namely concrete buildings or steel buildings with braced frame systems.
161
Table 6-3: Summary of Inter-Story Drifts
Building
Story
North Hollywood Building
Roof
7
6
5
4
3
2
1
Roof
9
8
7
6
5
4
3
2
1
Roof
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Roof
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
Tarzana Building
Sherman Oaks Building
Encino Building
Inter-Story Drift as Percent of Story Height
UBC-97
Northridge Earthquake
East-West North-South East-West
North-South
1.14
0.69
8.59
2.38
0.65
0.76
6.80
3.22
0.67
0.65
6.44
3.69
0.63
0.42
5.82
3.79
0.65
0.47
5.88
3.91
0.61
0.60
5.51
3.51
0.57
0.68
5.13
3.29
0.37
0.58
3.40
2.48
0.37
0.35
0.69
0.72
0.35
0.71
1.14
1.18
0.42
0.87
1.41
1.33
0.51
1.01
1.68
1.64
0.68
0.81
1.87
1.83
0.78
1.02
1.91
1.83
0.97
1.31
2.02
1.95
1.23
1.60
2.14
2.02
1.31
1.66
2.02
1.98
0.89
1.11
1.52
1.46
0.43
1.20
1.93
2.65
0.47
0.53
1.89
2.70
0.55
0.45
1.93
2.78
0.58
0.48
2.01
2.81
0.64
0.51
2.13
2.99
0.67
0.30
2.24
3.06
0.57
0.01
2.43
3.12
0.57
0.16
2.43
3.08
0.57
0.31
2.43
3.15
0.49
0.46
2.36
3.15
0.49
0.58
2.40
3.21
0.48
0.66
2.28
3.19
0.47
0.73
2.28
3.24
0.58
0.91
2.73
3.63
0.36
0.57
1.63
2.09
0.36
0.47
0.99
0.95
0.48
0.59
1.43
1.31
0.47
0.73
1.63
1.51
0.47
0.79
1.82
1.63
0.49
0.80
1.98
1.67
0.52
0.85
2.14
1.67
0.57
0.88
2.18
1.75
0.60
0.85
2.22
1.82
0.56
0.72
2.22
1.79
0.51
0.58
2.22
1.75
0.53
0.63
2.18
1.79
0.53
0.67
2.14
1.79
0.52
0.71
2.18
1.82
0.51
0.65
2.06
1.86
0.50
0.59
1.90
1.98
0.63
0.74
1.90
2.46
0.28
0.30
0.95
1.08
0.35
0.34
1.04
1.35
0.23
0.27
0.39
0.37
162
6.4
Comparison of Base Shears
The maximum base shears from the earthquake for the four buildings are compared with the
maximum base shears from UBC-97 and FEMA-273 at the target displacement in Table 6-4.
Table 6-4: Comparison of Base Shears
Comparison of Base Shears from the Earthquake with Prevailing Practice
Northridge Earthquake UBC-97 Soil Type SD FEMA-273 Soil Type SD
Building
East-West North-South East-West North-South East-West North-South
(kips)
(kips)
(kips)
(kips)
(kips)
(kips)
North Hollywood
565.00
1137.00
884.74
773.59
2035.00
2250.00
Building
Percent of Earthquake
156.59%
68.04%
360.18%
197.89%
1295.19
1568.82
386.70
386.70
1850.00
1800.00
Tarzana Building
Percent of Earthquake
29.86%
24.65%
142.84%
114.74%
3154.00
1694.55
1888.26
6000.00
5700.00
Sherman Oaks Building 2252.00
Percent of Earthquake
75.25%
59.87%
266.43%
180.72%
5006.00
6249.00
3173.42
3244.83
18125.00
14503.00
Encino Building
Percent of Earthquake
63.39%
51.93%
362.07%
232.09%
The following observations are made:
•
The design base shears from UBC-97 are less than the actual recorded base shears
because inelastic behavior is assumed.
•
The base shears at the target displacement for the Uniform pattern from FEMA-273
are significantly higher than the base shears from the Northridge Earthquake and
UBC-97. In the case of the Tarzana building though where inelastic behavior took
place, the results compare very well (difference 14% in the North-South direction
where inelasticity is certain)
•
The base shears from the Tarzana building (which experienced inelastic behavior)
from UBC-97 was the lowest for the four buildings compared with the Northridge
163
Earthquake. This was because the analysis in this building only, was performed using
before of the Static Analysis procedures with redundancy factors of 1.
6.5
Damage Stress Ratios
164