ucsd/nees/pca blind prediction contest: entry from national university of mexico, mexico

8/2/2019 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

[email protected]

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



2

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



3

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


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


c) Input Ground motion EQ3

Fig. 8. Comparison of Displacement Profiles



7

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.



8

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.

ucsd/nees/pca blind prediction contest: entry from national university of mexico, mexico

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