UCSD/NEES/PCA BLIND PREDICTION CONTEST: ENTRY FROM NATIONAL UNIVERSITY OF MEXICO, MEXICO
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Transcript of UCSD/NEES/PCA BLIND PREDICTION CONTEST: ENTRY FROM NATIONAL UNIVERSITY OF MEXICO, MEXICO
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UCSD/NEES/PCA BLIND PREDICTION CONTEST: ENTRYFROM NATIONAL UNIVERSITY OF MEXICO, MEXICO
Mario E. Rodriguez1; Miguel Torres2; and Roque Sanchez3
Abstract: This paper describes analysis procedures and results from the National University of Mexicoentry to the Blind Prediction Contest. The model implemented to simulate the response of the building
used the two-dimensional computer platform RUAUMOKO, with only 42 nodes and 126 degrees of
freedom. Predicted peak base shear and overturning base moments matched well with test results, but not
so well for peak displacements and accelerations. Peak base shear and overturning base moments were
overestimated in most earthquakes in less than 12 %. Lateral displacements and floor accelerations were
underestimated up to 40% and 62%, respectively.
Introduction
Between late 2005 and early 2006, a full-scale
vertical slice of a seven-story RC wall building
was tested at the new shake table of the University
of California at San Diego (UCSD). The building
was subjected to several ground motions in the
shake table. The largest ground motion was one
recorded during the 1994 Northridge Earthquake.
To improve the analytical modeling of wall
buildings, a blind prediction contest was
sponsored by the School of Engineering at UCSD,
the Portland Cement Association (PCA) of
Skokie, Illinois, and the NEES Consortium Inc.
(NEESinc). A team from the Universidad
Nacional Autonoma de Mexico (UNAM) entered
to this contest under the academic/research
category.
This paper describes the modeling of the
building for nonlinear analysis conducted by the
UNAM team and compares predicted results with
test results.
1Professor, National University of MexicoAp Postal 70-290, Coyocan, CP 04510, Mexico City,
Mexico
[email protected] 2PhD Candidate, National University of MexicoAp Postal 70-472, Coyocan, CP 04510, Mexico City,
Mexico
[email protected] 3PhD Candidate, National University of Mexico
Ap Postal 70-472, Coyocan, CP 04510, Mexico City,Mexico
Building description
A plan and elevation of the building under study
are shown in Fig 1. As seen there, the lateral force
resisting system of the building was constructed
with cast-in-place walls (identified in Fig 1 as web
wall and flange wall), and a post-tensioned precast
wall of the segmental type. The gravity resisting
system consisted in gravity columns. Cast-in-place
slabs were connected to the walls using a bracing
system shown in Fig. 1.
a) Elevation
Fig. 1.. Typical plan and elevation of the building
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b) Plan
Fig. 1.. Typical plan and elevation of the building
(Cont.)
Analytical Model
The model implemented to simulate the response
of the building was analyzed using the two-
dimensional computer program platform
Ruaumoko (Carr, 1998). The modeling
assumptions are described below.
Material and Mass Properties
Material strengths used for the computer analysis
were those provided by the contest organizers.Assumed material properties for unconfined
concrete are shown in Table 1. The different
types of concrete correspond to the concrete cast
sequence shown in Fig 2. The concrete properties
are concrete strength, f’c, modulus of elasticity, Ec
and ultimate strain, εcu, shown also in Fig 3.
Table 1. Concrete Properties
Concrete
placement
f‘ c
(ksi)
Ec
(ksi)
εcu
C2 7.87 3349 0.00281
C3 5.43 3549 0.00269C5 5.70 3771 0.00229
C7 6.11 5053 0.00214
C9 6.03 4380 0.00236
C11 5.80 4191 0.00225
C13 5.78 4661 0.00233
C15 6.25 4864 0.00210
C17 5.62 4194 0.00234
C18 5.45 4398 0.00220
Fig. 2. Concrete cast sequence
Fig. 3. Unconfined concrete stress-strain curve
Material data were also provided for the
reinforcing steel of the building. Table 2 shows
values used in the computer analysis. These values
correspond to stress at yielding, f y, ultimate stress
and strain, f su and εsu, respectively, and strain at
the starting of strain hardening, εsh. These
parameters are also shown in Fig 4.
Fig. 4. Reinforcing steel stress-strain curve
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Table 2. Reinforcing steel properties
Bar
id.
Bar
number
f y
(ksi)
f su
(ksi) ε sh ε su
b1 #4 65.2 108.9 0.0054 0.1009
b2 #4 63.1 103.0 0.0074 0.1096
b3 #5 65.9 101.0 0.0078 0.1128
b4 #7 69.1 111.1 0.0079 0.1117 b5 #7 65.7 112.5 0.0070 0.1053
b6 #6 71.6 113.7 0.0052 0.1046
b7 #6 66.4 104.4 0.0054 0.0836
b8 #3 66.0 105.1 0.0086 0.1169
b9 #3 63.5 102.1 0.0087 0.1098
Seismic floor weights were calculated assuming a
volumetric weight equal to 0.15 kips/ft3 and
considering all elements. Resulting values are
shown in Table 3.
Table 3. Seismic weights in the buildingLevel Weight
(kips)
1 65.0
2 to 6 62.0
7 50.5
Element Types
Fig 5 shows the geometry of the analytical model
used in the computer analysis and the numbering
of nodes and elements. Plain numbers and
numbers in a circle correspond to nodes andelements, respectively. The web wall and flange
wall were modeled using the nonlinear FRAME
element of the Ruaumoko program. Properties
assumed for these walls are shown in Tables 4 and
5 for the web and flange wall, respectively. Shown
in these tables are assumed values for the cross
section area, A, reinforcing steel area, A s, moment
of inertia , I , yielding moment, M y, parameter r that
defines the inelastic stiffness measured as a
fraction r of the initial stiffness, and plastic length
l p measured as a fraction of the wall depth, l w.
The post-tensioned wall was modeled using the
FRAME element. Since the post-tensioned wall
had an asymmetric section, different response of
the section would be expected depending on
whether the flange is in tension or compression.
The FRAME element in the Ruaumoko program
uses only one elastic stiffness for these two cases
of flange response, which led to define a unique
value for this property using the average of calculated values for these two responses. Fig 6
shows a typical calculated moment-curvature
curve for post-tensioned walls in levels 1 to 5 and
a bilinear representation of this curve.
SPRING rotational elements were used for representing sections between precast wall
segments and are numbered as elements 64 and 65
in Fig 5. Assumed properties for these elements
were obtained from section analysis of the
interfaces between precast wall elements.
Gravity columns were modeled using a
longitudinal elastic spring. Floors were assumed
rigid for in-plane forces and were modeled using a
FRAME element with a flexural stiffness
calculated assuming a full slab width contribution
without rigid ends. Slabs were connected tocolumn lines using the rigid link elements shown
in Fig 5.
9 .
0 0
f t
9 .
0 0
f t
9 .
0 0
f t
9 .
0 0
f t
9 .
0 0
f t
9 .
0 0
f t
9 .
0 0
f t
0 5 1 2 1 9 2 6 3 3
L e v e l 4
L e v e l 3
L e v e l 2
L e v e l 1
5 .0 0 ft
0 1 0 9 1 7
3 . 2 8 f t 5 . 0 0 f t
5 0
0 1
0 2
1 50 8
1 0
3 6
1 8
2 5 3 3
3 .2 8 ft
5 7
2 2
4 3
2 6
2 9
3 4
5 2 3 86 4
5 1
0 2
0 3
0 3
1 91 1
0 9 1 6
3 7
1 0 1 7
5 3
0 4
0 4
0 5
1 2
1 1
2 0
1 8
1 3 2 1
3 9
5 94 5
5 8
2 7
4 4
2 3
2 4
3 0
3 5
3 1
6 0
2 8
2 5
4 6
2 9
3 6
3 2
3 7
L e v e l 7
L e v e l 5
L e v e l 6
W e b w a ll
0 7
5 5
5 46 5
0 6
0 6
1 4
4 0
2 2
1 3 2 0
4 1
P T w a ll
5 6
0 7
0 8
1 5
1 4
2 3
2 1
1 6
4 2
3 9
6 2
6 14 7
3 0
4 8
2 7
3 8
3 4
6 3
F la n g e w a ll
3 1
2 8
2 4
4 9
3 2
3 5
4 0
G r a v i t y c o l u m n G r a v i t y C o l u m n
Fig. 5. Geometry of the building analytical model
The assumed hysteresis rule for the FRAME
elements was the Modified Takeda Degrading
stiffness rule (Carr, 1998). The SPRING element
that modeled the interfaces of post-tensioned walls
was assumed that followed the Linear Elastic rule.
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This assumption was not validated. This SPRINGelement would have been better modeled using a
Bilinear-Elastic hysteresis rule that is also in the
library of the Ruaumoko program.
The proposed analytical model had 42 nodes, 65
members and 126 degrees of freedom, which is asmall number comparing with that needed in a
typical analysis of the finite element type. The
members had only 21 different section types.
-1.5
-1
-0.5
0
0.5
1
1.5
2
-40 -30 -20 -10 0 10 20
ϕ / ϕy
M
/ M
y
Calculated
Bilinear
My=234.6 kip-ft
ϕy=0.00017 rad/in
r=0.023
r=0.011
Fig. 6. Monotonic moment-curvature for typical
sections of post-tensioned walls in levels 1 to 5
Damping Properties
Structural damping properties were assumed
following a general approach proposed by
Caughey (Chopra, 1995), in which a required
amount of damping at various modes of response
is provided. This approach is implemented in theRuaumoko program. It was found in previous
research (Rodriguez et. al, 2006) that this
approach leads to a reasonable correlation
between measured and predicted response,
especially in the evaluation of inertial forces and
accelerations since these parameters can be largely
influenced by higher modes of response. The
assumed damping ratio for the Ruaumoko analysis
was equal to 0.03 for all modes of response.
Additional Analysis Procedures
P-Delta effects were considered in the analyses by
using the small displacement formulation and the
corresponding P-Delta option in Ruaumoko. This
option assumes that the nodal coordinates remain
unchanged during the analysis but allows the
lateral softening of the stiffness of the columns
due to gravity loads (Carr, 1998).
Table 4. Web Wall Properties
Level
A
(in2)
As
(in2)
I
(in4)
M y
(kip-ft) r lp / lw
1 1152 960 824409 5016.5 0.009 0.03
2 864 720 872658 4179.2 0.018 0.02
3 864 720 601733 3861.6 0.022 0.02
4 864 720 778474 3609.0 0.016 0.02
5 864 720 724085 3212.0 0.021 0.02
6 864 720 390211 2887.2 0.039 0.02
7 1536 960 327775 2699.5 0.037 0.02
Table 5 Flange Wall Properties
Level A
(in2) As (in2)
I (in4)
M y (kip-ft) r lp / lw
1 1536 1280 989 126.3 0.040 0.5
2 1152 960 539 107.5 0.027 0.5
3 1152 960 386 103.2 0.028 0.5
4 1152 960 430 99.6 0.028 0.5
5 1152 960 407 93.8 0.033 0.5
6 1152 960 338 86.6 0.039 0.5
7 1152 960 318 85.2 0.035 0.5
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Newmark’s Constant Average Acceleration
method ( β = 0.25) was used to solve the dynamic
equation of equilibrium. According to Bathe
and Wilson (1976) the Newmark method is
accurate when the time-step is smaller than
about 0.01 T p, where T p is the smallest period of
the system, which for the building under study isequal to 0.014 seconds. The time-step for
running Ruaumoko was set constant and equal to
0.0001 seconds. This value was defined based
on a trial-and-error procedure in which the
absolute floor accelerations and lateral
displacements at each floor level relative to the
base were evaluated with several runs of the
program using decreasing time-steps until results
from the last and previous analysis were
considered similar. Rodriguez et al (2006) have
shown that while convergence of displacements
could be achieved with a time step of only 0.01seconds, a much smaller time step of 0.0001
seconds might be required for achieving
convergence of accelerations.
Input Ground Motions
Four input ground motions were used in the test
program, namely EQ1, EQ2, EQ3 and EQ4.
Elastic response spectra for these ground
motions using a critical damping ratio equal to
0.05 are shown in Fig 7. As shown in the performed analysis of the building, record EQ1
led to almost elastic response, while the others
took the building into inelastic response.
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0
T (sec)
S a ( g ) EQ1
EQ2
EQ3
EQ4
ζ = 5%
Fig. 7. Pseudoacceleration elastic response spectra
for earthquake records EQ1, EQ2, EQ3 and EQ4.
Modal Analysis
Periods (T) and modal masses calculated by the
Ruaumoko program before the analysis using
record EQ1 are shown in Table 6.
Table 6. Periods and Modal MassesMode T
(s)
Cumulative
Mass (%)
1 0.751 66
2 0.135 86
3 0.055 93
7 0.014 100
Processing Results from the Ruaumoko
Analysis
Displacement, absolute floor acceleration, andshear at each level were extracted from results
envelopes given by the Ruaumoko analysis for
each earthquake and were compared with
measured values. Shear (V) at each level was
obtained as summation of element shears.
Overturning moment (M) at each level was
obtained as the summation of the moment of the
calculated inertia forces about the base level.
Time-histories of roof displacements, roof
absolute floor accelerations, base shear (V b) and
base overturning moment (M b) were also
obtained from the analysis for each earthquake.
Earthquakes EQ1, EQ2, EQ3 and EQ4 were
analyzed sequentially. The structure’s state at
the end of each earthquake defined the initial
state for the subsequent earthquake.
Comparison of Measured and Predicted
Response
Displacements and horizontal floor
accelerations
Table 7 compares peak response parameters
obtained from the Ruaumoko analysis with
measured results from the shaking table test.
These parameters are roof floor lateral
displacements and roof absolute accelerations.
An acceptable correlation was obtained for
analytical and test results for peak displacements
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Table 7. Peak Response Results. Displacements and accelerations
ParameterType of
ResultEQ1 EQ2 EQ3 EQ4
Average
Ruaumoko
....Test
Test 2.05 5.75 6.29 15.55
Ruaumoko 2.92 4.49 5.91 9.36Roof Displacement (inches)
Ruaumoko
....Test1.42 0.78 0.94 0.60
0.94
Test 0.42 0.59 0.73 1.08
Ruaumoko 0.63 0.95 0.97 1.75Roof Absolute Accelerations(g)
Ruaumoko
....Test1.50 1.61 1.33 1.62
1.51
for EQ2 and EQ3, where response was
underestimated by less than 22%, but for EQ1 and
EQ4 response was overestimated and
underestimated by 42% and 40%, respectively, see
Table 7. Regarding absolute horizontal floor
accelerations at the roof level, response was
overestimated by 50%, 61%, 33%, and 62% for
EQ1, EQ2, EQ3 and EQ4, respectively, see Table
7.Fig 8 compares displacement profiles for
predicted and measured response for EQ1, EQ2,
EQ3 and EQ4. In Fig 8 hi and H are the floor
height at level i and building height, respectively.
Results are normalized against the predictedmaximum roof floor displacement. As seen there,
the larger differences correspond to input ground
motion EQ4.
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1 1.2
d / dTOP PREDICTED
h i / H
Predicted
Measured
dTOP PREDICTED=2.9 in
a) Input Ground motion EQ1
0
0.2
0.4
0.60.8
1
0 0.2 0.4 0.6 0.8 1 1.2 1 .4
d / dTOP PREDICTED
h i / H
Predicted
Measured
dTOP PREDICTED=4.5 in
b) Input Ground motion EQ2
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1 1.2
d / dTOP PREDICTED
h i / H
Calculated
Measured
dTOP PREDICTED=5.9 in
c) Input Ground motion EQ3
Fig. 8. Comparison of Displacement Profiles
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0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
d / dTOP PREDICTED
h i / H
CalculatedMeasured
dTOP CPREDICTED=9.4 in
d) Input Ground motion EQ4
Fig. 8. Comparison of Displacement Profiles(Cont.)
Envelopes of horizontal floor accelerationsalong the building height from test and analysis
are shown in Fig 9 for input ground motions
EQ1, EQ2, EQ3 and EQ4. Results arenormalized with the predicted maximum roof
floor acceleration.
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1 1.2
ü / üRoof, max
h i / H
Predicted
Measured
Ü Roof, max =0.63g
a) Input Ground motion EQ1
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1 1.2
ü / ÜRoof, max
h i / H
Predicted
Measured
ÜRoof, max =0.95g
b) Input Ground motion EQ2
Fig. 9. Envelopes of horizontal floor accelerationsfrom test and analysis
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1 1.2ü / üRoof, max
h i / H
Predicted
Measured
ÜRoof, max=0.97g
c) Input Ground motion EQ3
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1 1.2
ü / üRoof, max
h i / H
Predicted
Measured
ÜRoof, max=1.75g
d) Input Ground motion EQ4
Fig. 9. Envelopes of horizontal floor accelerations
from test and analysis (Cont.)
Figures 10 and 11 show predicted and
measured roof absolute acceleration time
histories for the strong part of the input ground
motion EQ4 and floor response spectra
(calculated with ζ = 3 %) for the measured and predicted roof absolute acceleration for the full
input ground motion, respectively. As seen in
Figs 10 and 11 the match between predicted and
measured accelerations is not very good.
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
43 45 47 49 51 53
t(s)
Ü ( g )
MeasuredPredicted
Ü max measured = 1.1 g
Ü max predicted = 1.8 g
Fig. 10. Measured and predicted roof absolute floor
acceleration time histories for the strong part of EQ4.
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Table 8 Peak Response Results. Base shear and Overturning Base Moment
ParameterType of
ResultEQ1 EQ2 EQ3 EQ4
Average
Ruaumoko
....Test
Test 95.6 141.2 158.3 266.3Ruaumoko 100.6 175.2 166.6 276.7
Base Shear (kips)Ruaumoko
....Test1.05 1.24 1.05 1.04
1.10
Test 4135 5970 6262 8733
Ruaumoko 4728 6432 7021 8737Base Moment (kips-ft)
Ruaumoko
....Test1.14 1.08 1.12 1.00
1.09
0
1
2
3
4
5
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
T(s)
S a ( g )
measured
predicted
ζ =3%
Fig. 11. Roof floor response spectra
Base shear and overturning base moment
Table 8 compares computed peak base shears
and peak base moments with test results for
input ground motions EQ1, EQ2, EQ3 and EQ4.
An acceptable correlation was obtained for
analytical and test results. Base shear was
overestimated in less than about 5% for input
motions EQ1, EQ3 and EQ4, and by less than
25% for EQ2. A good prediction of overturning
base moment was also obtained for all input
ground motions since response was
overestimated in less than 15% for all input
ground motions, see Table 8.
Base shear and overturning base moment time
histories for measured and predicted response
for the strong part of EQ4 are shown in Fig 12
and 13, respectively. Results are normalized
against maximum predicted base shear and base
moment. As seen in Figs 12 and 13, amplitude
response is reasonably captured by analysis, and
some predicted frequency content captures the
frequency content of the measured response.
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
43 45 47 49 51 53
t(s)
V / V * b , m a x
Measured
Predicted
V*b, max = 276.7 kips
Fig. 12. Base shear time histories for a strong
part of EQ4 (V* b,max = predicted maximum base
shear)
-1
-0.5
0
0.5
1
1.5
43 45 47 49 51 53
t(s)
M / M * b m a x
Measured
PredictedM*b ,max= 8737.2 kips-ft
Fig. 13. Overturning base moment time histories
for a strong part of EQ4 (M* b,max = predicted
maximum overturning moment)
Figures 14 and 15 show measured and calculated
plots of base shear-roof drift ratio and
overturning moment-roof drift ratio of the
building when subjected to the input ground
motion EQ4, where the roof drift ratio Dr is
defined as the ratio of roof lateral displacement
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Table 10. Maximum measured and predictedtensile strains in reinforcing bars in web wall
Max
tensile
strain in
reinforcingsteel
EQ1 EQ2 EQ3 EQ4
Measured - - - 0.0263
Predicted 0.0075 0.0210 0.0201 0.0328
Conclusions
A simple two-dimensional model and the
Ruaumoko computer program were used for
predicting the seismic response of the building
during the shaking table tests. Only 42 nodes
were used, with a total of 126 degrees of freedom. Predicted peak base shear and
overturning base moment matched reasonably
well with test results, both in amplitude and
frequency content, but not so well for peak
lateral displacements, horizontal floor
accelerations and residual displacements. Base
shear and overturning base moment were
overestimated in most earthquakes in less than
12%. Lateral displacements were underestimated
in 22%, 6% and 40% for earthquakes EQ2, EQ3,
and EQ4, respectively, whereas for the same
earthquakes floor accelerations wereoverestimated in 61%, 31% and 62%.
The shaking table tests of the slice building
proved to be a very useful tool for structuralanalysis calibration in earthquake engineering.
References
Bathe, K. and Wilson, E.L. (1976). “Numerical
Methods in Finite Element Analysis”, Prentice-
Hall, New Jersey, USA
Carr A.J. (1998). “RUAUMOKO user manual”,A Computer Program Library, University of
Canterbury, Department of Civil Engineering.
(Also
http://www.civil.canterbury.ac.nz/ruaumoko/),
New Zealand.
Chopra, A., (1995). “Dynamics of Structures.
Theory and Applications to Earthquake
Engineering.” Second Edition. Prentice Hall,Inc, Upper Saddle River, New Jersey, USA.
Mander, J.B. (1984). “Seismic Design of Bridge
Piers”, Report 84-2, Department of Civil
Engineering, University of Canterbury, New
Zealand.
Rodriguez, M. E., Restrepo, J. I., and Blandon,J.J. (2006). “Shaking Table Tests of a Four-
Story Miniature Steel Building - Model
Validation”, Earthquake Spectra Journal,
August.