Teacher Manual.pdf - College of Engineering, Purdue University

***Teacher’s Manual ***

SMALL-SCALE S HAKE TABLE EXPERIMENTS AND COMPARISON TO ANALYTICAL PREDICTIONS A PROJECT DEVELOPED FOR THE UNIVERSITY CONSORTIUM ON INSTRUCTIONAL SHAKE TABLES

http://ucist.cive.wustl.edu/

Developed by:

Brenda E. Shonkwiler Thomas H. Miller Oregon State University

This project is supported in part by the National Science Foundation Grant No. DUE9950340.

1.0 Overview This teacher’s manual contains a sample set of data for the experiments in the Student Manual. The ultimate goal for these experiments is to compare results from an earthquake simulation done on the UCIST Shake Table to analytical results using SAP 2000 software.

1.1 Introduction The UCIST Shake Table was designed for experimental use and for demonstrations. It can be used in undergraduate and graduate level earthquake engineering and structural dynamics classes. The table is also appropriate for outreach programs at high schools and middle schools. The experiments outlined in this manual and the corresponding Student Manual would be appropriate for use in introductory level earthquake engineering and structural dynamics classes.

1.2 Teacher’s Manual Contents 1.0 Overview .......................................................................................................................2 1.1 Introduction...............................................................................................................2 1.2 Teacher’s Manual Contents ......................................................................................2 2.0 3D Model Specifications ...............................................................................................3 2.1 3D Model Properties Experiment Results ................................................................3 2.2 Stiffness Calculation for 3D Model..........................................................................5 2.2.1 3D Model Stiffness Hand Calculation............................................................. 5 2.2.2 Stiffness Experiment Results and Comparison to Hand Calculation............... 6 2.3 Damping Experiment Results ...................................................................................9 2.4 3D Model Schematic .............................................................................................12 3.0 El Centro Earthquake Scale Results ...........................................................................13 4.0 UCIST Shake Table Experiments ...............................................................................16 4.1 Shake Table Experimental Results (Accelerations) ...............................................16 4.2 Displacement Experiment Results ..........................................................................22 5.0 SAP 2000 Results .......................................................................................................24 6.0 Comparison of SAP 2000 and UCIST Shake Table Results ......................................34 7.0 Other Uses...................................................................................................................39

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Oregon State University

2.0 3D Model Specifications This section includes the necessary steps to quantify pertinent characteristics of the 3D model. These characteristics include mass, dimensions, stiffness, and damping.

2.1 3D Model Properties Experiment Results The tables below contain the results of the 3D Model Properties Experiment. This data was used for input into the SAP 2000 model. Also see “3D Model Schematic”. Dimensions : Figure 1: Plan View of 3D Model Floor Plate

Figure 2: 3D Model Perspective View

Lp S3 wp

B

Lr S2

A

S1 Lp

wp

Table 1: 3D Model Dimensions

Plates

Length, Lp (in)

Width, Wp (in)

1 2 3 4 Average 2D SAP Model

17 7/16 17 7/16 17 7/16 17 7/16 17.44 --

11 3/4 11 3/4 11 3/4 11 11/16 11.73 11.75

Length, Lr (in) 35 3/4 35 7/8 35 3/4 35 3/4 35.78

Diameter, D r (in) 0.186 0.186 0.186 0.186 0.186

Thickness, Rod Spacing, Rod Spacing, Tp (in) A (in) B (in) 0.256 0.257 0.256 0.257 0.257 1/4

15 15 15 15 15.00 15

7 7 7 7

3/4 3/4 3/4 3/4 7.75 --

(a) Plate Dimensions

Rods 1 2 3 4 Average

Floor 1 2 3

Floor Spacing, S (in) 11 11 11

(c) Floor Spacing

(b) Rod Dimensions

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Mass: Table 2: 3D Model Masses

Plate 1 2 3 4 Average (a) Plate Masses

Mass (lb) 5.389 5.444 5.405 5.446 5.421

Rod 1 2 3 4 Sum Average

Mass (lb) 0.277 0.278 0.278 0.277 1.110 0.277

Accelerometers Mass (lb) 1 0.329 2 0.331 3 0.333 4 0.333 Average 0.331 (c) Accelerometer Masses

(b) Rod Masses

m1 = mPlate 2 + maccel 2 + 1/3 mrods = 5.964 lb = 0.015435 lb-s2 /in m2 = mPlate 3 + maccel 3 + 1/3 mrods = 6.108 lb = 0.015807 lb-s2 /in m3 = mPlate 4 + maccel 4 + 1/6 mrods = 6.144 lb = 0.015900 lb-s2 /in

Figure 3: Schematic

m3 Floor 3 Floor 2

m2 m1

Plate 4 Plate 3 Plate 2

Floor 1 Plate 1

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2.2 Stiffness Calculation for 3D Model SAP 2000 uses material properties (modulus of elasticity, E), section properties (moment of inertia, I), dimensions (length, L), and support conditions (i.e., fixed-fixed, pinned-pinned, fixed-pinned, etc.) to determine the stiffness of a model. In order to ensure that the SAP 2000 model has the same stiffness as the physical model, it is necessary to do a hand calculation of stiffness, the Stiffness Experiment, and compare the two results.

2.2.1 3D Model Stiffness Hand Calculation The 3D physical model has support conditions (for columns between each floor) that can be approximated by a fixed- fixed condition. Theory: For a fixed- fixed column: V 12 EI K= = 3 ∆ L

∆

L

From “3D Model Properties Experiment Results”: Dimensions of the 3D Model: L = 11 inches Diameter, d = 0.186 inches Calculations : Section Properties: E = 29,000,000 psi πd 4 I circlex = I circley = = 5.875 x10 −5 in4 64

y

x

d

Results: Solving for K, K rod

12( 29,000,000 psi )(5.875 x10 −5 in 4 ) = = 15.36lb / in / rod (11in ) 3

Since there are (4) rods per floor, K Floor = 4( K rod ) = (4rods )(15.36lb / in / rod ) Therefore, K Floor = 61.44lb / in

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2.2.2 Stiffness Experiment Results and Comparison to Hand Calculation After plotting the data and using linear regression analysis, the stiffness of the first floor (K 1 ) was calculated as 64.6 lb/in. The stiffness of the second floor (K 2 ) was 65.1 lb/in. The stiffness of the third floor (K 3 ) was 62.6 lb/in (see Figure 32 through Figure 35 for data). Based on the dimensions, support conditions, and material properties of the model, the theoretical stiffness (K calc) is 61.44 lb/in. The stiffness experiment results for each floor are within 6% of the theoretical stiffness (see Table 4 below). This consistency between the experimental results and the theoretical results shows that the stiffness for the SAP 2000 model should be reasonably close to the stiffness of the physical model.

Figure 4: Set-up for Stiffness Experiment - Schematics

Floor 3

K3

Floor 2

K2 Floor 1

K1 K1

K2

K3

Table 3: Stiffness Comparison

Stiffness, K (lb/in)

Floor 1 (1) Floor 1 (2) Floor 2 Floor 3

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Kexperiment

Kcalc

64.7 64.5 65.1 62.6

61.44 61.44 61.44 61.44

Percent difference 5.3% 5.0% 6.0% 1.9%

6


Figure 5: Floor 1 Stiffness Results (Using Dial Gage A)

Base clamped to shelf, pulling on floor #1, Dial Indicator (A) Tension (lb) 0 2.1 4.4 6 8 10.2 12.4 13.4

Deflection (1E-3 inch) 0 30 64 89 119 153 189 208

Regression analysis: y = 0.0647x + 0.1756 2 R = 0.9992

First Floor (1) 25 20 15 10 5 0

Slope = K (lb/in) =

0.0647

0

50

100

150

200

250

300

350

400

350

400

-3

Displacement (10 in)

64.7

Figure 6: Floor 1 Stiffness Results (Using Dial Gage B)

Base clamped to shelf, pulling on floor #1 (again), Dial Indicator (B) Tension (lb) 0 2.8 7.7 11.1 13.4 16.9 20 22.5

Deflection (1E-3 inch) 0 43 119 170 205 261 310 349


First Floor (2) 25 20 15 10 5 0

Slope =

0.0645

0

50

100

150

200

250

300

-3

K (lb/in) =


64.5

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Figure 7: Floor 2 Stiffness Results

Base clamped to shelf, floor #1 clamped to column, pulling on floor #2, Dial Indicator (B) Tension (lb) 0 2.9 5.4 7.5 9.4 11.5 13.3 15.8 19.6

Deflection (1E-3 inch) 0 44 80 112 142 174 203 242 300


Second Floor 25 20 15 10 5 0 0

Slope = K (lb/in) =

50

100

0.0651

150

200

250

300

350

-3


65.1

Figure 8: Floor 3 Stiffness Results

Base clamped to shelf, floor #1 & floor #2 clamped to column, pulling on floor #3, Dial Indicator (B) Tension (lb) 0 3.5 7.5 10.8 12.5 15.2 17.8 20.6 22.1

Deflection (1E-3 inch) 0 54 114 169 196 240 281 326 353


Third Floor 25 20 15 10 5 0 0

Slope = K (lb/in) =

50

100

0.0626

150

200

250

300

350

400

-3


62.6

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2.3 Damping Experiment Results Because the damping in the 3D model is small, δ = (1 /m) Ln (Vn / Vn+m ) was used to calculate the damping ratio. The Damping Experiment resulted in a calculated damping ratio that varied from 0.0073 to 0.0215 (see Table 5). The damping ratio calculated depended on what value was used for m and whether positive or negative displacements were used for Vn and Vn+m . The value calculated for damping ratio should be most accurate when a large value of m is used. There were five peak negative displacements and six peak positive displacements (see Table 6 and Figure 36). Using n=0, m=4, and negative peak displacements, the damping ratio was 0.0161. Using n=0, m=5, and positive peak displacements, the damping ratio was 0.0129. For the SAP 2000 analysis, a damping ratio of 0.015 was used. If time permitted, it would have been better to repeat the experiment several times to be sure that a damping ratio of 0.015 is an accurate number for the 3D model.

Table 4: Damping Values

n 0 1 2 3 4 5

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(negative) Vn (in) ξ, (n =0) -0.75 -0.7 -0.6 -0.5 -0.5

(positive) Vn (in) ξ, (n =0) 0.6 0.55 0.5 0.5 0.5 0.4

0.0161

9

0.0129


Table 5: Floor 3 Displ acement Values for Damping Experiment

Original Position:

3.9

Video Distance Displacement frame # (in) (in) 1 2.9 -1 2 3 -0.9 3 3.1 -0.8 4 3.35 -0.55 5 3.36 -0.54 6 3.95 0.05 7 4.2 0.3 8 4.4 0.5 9 4.5 0.6 10 4.45 0.55 11 4.25 0.35 12 3.95 0.05 13 3.65 -0.25 14 3.4 -0.5 15 3.25 -0.65 16 3.15 -0.75 17 3.25 -0.65 18 3.45 -0.45 19 3.75 -0.15 20 4.05 0.15 21 4.25 0.35 22 4.4 0.5 23 4.45 0.55 24 4.4 0.5 25 4.15 0.25 26 3.85 -0.05 27 3.6 -0.3 28 3.35 -0.55 29 3.2 -0.7 30 3.3 -0.6 31 3.5 -0.4 32 3.7 -0.2 33 4 0.1 34 4.2 0.3 35 4.4 0.5 36 4.3 0.4 37 4 0.1 38 3.7 -0.2 39 3.5 -0.4 40 3.4 -0.5

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in Video frame 41 42 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Peak

Peak

Peak

Peak

Peak

10

Distance Displacement (in) (in) 3.3 -0.6 3.4 -0.5 3.6 -0.3 3.7 -0.2 4.1 0.2 4.3 0.4 4.4 0.5 4.4 0.5 4.3 0.4 4.2 0.3 3.9 0 3.7 -0.2 3.5 -0.4 3.4 -0.5 3.4 -0.5 3.5 -0.4 3.7 -0.2 3.9 0 4.1 0.2 4.3 0.4 4.4 0.5 4.4 0.5 4.3 0.4 4.1 0.2 3.8 -0.1 3.6 -0.3 3.5 -0.4 3.4 -0.5 3.5 -0.4 3.6 -0.3 3.7 -0.2 3.9 0 4.2 0.3 4.3 0.4 4.3 0.4 4.2 0.3 4.1 0.2 4 0.1 3.8 -0.1

Peak

Peak

Peak

Peak

Peak

Peak


Figure 9: Peak Displacements as a Function of Time

Damping Experiment Peak Displacements 0.8

0.6

0.4

0.2

Distance (in)

0 0

20

40

60

80

100

-0.2

-0.4

-0.6

-0.8

-1

-1.2 Data Point (60 points per second)

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2.4 3D Model Schematic Figure 10: Schematic with 3D Model Characteristics

m3 K3

m3 11 in

K3

m2 K2

m2 11 in

K2

m1 K1

11 in

11 in m1

11 in

K1

15 in

11 in

7-3/4 in

K1 = K2 = K 3 = 61.4 lb/in Damping ratio, ξ = 0.015 m1 = 6.144 lb = 0.015435 lb-s2 /in m2 = 6.108 lb = 0.015807 lb-s2 /in m3 = 5.964 lb = 0.015900 lb-s2 /in

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3.0 El Centro Earthquake Scale Results For both the scaled and the original El Centro earthquake records, there was a period of time at the beginning of the earthquake data where the accelerations were essentially zero (see the circled parts of Figure 38 ). After neglecting the initial period of zero acceleration, the “Scaled” El Centro earthquake has a duration of 23.59 seconds. The “original” El Centro earthquake has a duration of 54.60 seconds. This results in a time factor of 2.31 (54.60 / 23.59 = 2.31). Since the model scale (S) equals the time factor squared (2.312 = 5.3), the model scale is approximately 1:5 (see Figures 39 and 40 for comparison graphs). Figure 39 shows the original data and the scaled data each on a graph with time plotted from 0 to 60 seconds. Figure 40 shows the original data plotted from 0 to 60 seconds and the scaled data plotted for 1/2.31 that time duration (from 0 to 25.97 seconds). The plots in the figure appear to be the same, and 1:2.31 is an appropriate time scale factor. Therefore, the model scale used for the El Centro earthquake was approximately 5. Figure 11: Graphs with Initial Period of Negligible Acceleration El Centro (Original Data) 0.4

Acceleration (g)

0.3 0.2 0.1 0.0 -0.1

0

10

20

30

40

50

60

40

50

60

-0.2 -0.3

Time (seconds)

El Centro (Scaled Data) 0.4

Acceleration (g)

0.3 0.2 0.1 0.0 -0.1

0

10

20

30

-0.2 -0.3

Time (seconds)

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Figure 12: El Centro Earthquake (Graphed With Same Time Scale)

El Centro Original Data 0.4

Acceleration (g)

0.3 0.2 0.1 0.0 0

10

20

30

40

50

60

50

60

-0.1 -0.2 -0.3 Time (seconds)

El Centro Scaled Data 0.4

Acceleration (g)

0.3 0.2 0.1 0.0 0

10

20

30

40

-0.1 -0.2 -0.3 Time (seconds)

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Figure 13: El Centro Earthquake (Scaled Data Graphed With Adjusted Time Scale)

El Centro Original Data 0.4

Acceleration (g)

0.3 0.2 0.1 0.0 0

10

20

30

40

50

60

-0.1 -0.2 -0.3 Time (seconds)

El Centro Scaled Data 0.4

Acceleration (g)

0.3 0.2 0.1 0.0 0

5

10

15

20

25

-0.1 -0.2 -0.3 Time (seconds)

Note: The pre-programmed earthquakes that came with the UCIST Shake Table are not scaled with the same scale factor. As noted in “El Centro Earthquake Scale Results,” the El Centro earthquake was scaled by a scale ratio of approximately 1:5. However, by doing the same analysis on the Kobe Earthquake, it was found that Kobe was scaled by a scale factor of approximately 1:10. Teacher’s Manual

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4.0 UCIST Shake Table Experiments The following two sections contain data collected from the UCIST Shake Table Experiments. Acceleration Data was collected using the accelerometers that came with the UCIST system. Displacement data was collected with a video camera.

4.1 Shake Table Experimental Results (Accelerations) Maximum acceleration data and the time it occurred are shown in Tables 7 and 8 respectively. These values are fairly consistent, but do vary slightly. The standard deviations and coefficients of variation are also shown. On the next few pages, three acceleration versus time plots are shown for each level of the three-dimensional model (Table, Floor 1, Floor 2, and Floor 3). The experiment was run five times to develop these plots. The plots for each level are shown together on one page for direct comparison. The three different plots of accelerations at the base level (“Table”) appear to be almost identical. The three plots of accelerations at “Floor 1” are fairly consistent. There is some noticeable variation in the plots between 10 and 15 seconds. The three plots for “Floor 2” are also fairly consistent; however some variation between plots occurs between 10 and 15 seconds as it did for “Floor 1.” The acceleration plots for “Floor 3” have the most inconsistencies. The plots of “Floor 3” for Test 1 and Test 2 are fairly consistent. However, these plots are a little different from the plot for Test 3. Again, most of the inconsistencies seem to occur between 10 and 15 seconds after the beginning of the scaled earthquake. This shows that the experiment is repeatable, but results vary slightly each time the earthquake simulation is run. This information should be kept in mind when comparing the shake table acceleration data to the SAP 2000 acceleration data.

Figure 14: Floor Locations

Floor 3 Floor 2 Floor 1 Base

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Table 6: El Centro Maximum Acceleration (g):

Test 1 Test 2 Test 3 Test 4 Test 5 Ave. Table 0.316 Floor 1 1.019 Floor 2 -Floor 3 2.039

0.341 1.037 -2.039

0.328 -1.375 2.167

-0.829 1.279 2.146

0.313 1.001 1.382 --

0.325 0.972 1.345 2.098

Stand. Coef. of Dev. Variation 0.011 0.083 0.047 0.059

0.0339 0.0856 0.0347 0.0283

Table 7: El Centro Time at Maximum Acceleration (sec):

Test 1 Test 2 Test 3 Test 4 Test 5 Ave. Table 2.784 Floor 1 3.965 Floor 2 -Floor 3 3.996

2.783 3.964 -3.995

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2.781 -4.219 3.998

-3.740 3.780 3.881

2.634 4.055 4.063 --

2.746 3.931 4.021 3.968

17

Stand. Coef. of Dev. Variation 0.064 0.116 0.181 0.050

0.0235 0.0296 0.0451 0.0126


Figure 15: Table Accelerations (at Model Base)

Acceleration (g)

El Centro Table Test 1 0.4 0.3 0.2 0.1 0 -0.1 0

5

10

15

20

25

30

20

25

30

20

25

30

-0.2 -0.3 Time (seconds)

El Centro Table Test 2

Acceleration (g)

0.4 0.3 0.2 0.1 0 -0.1 0

5

10

15


El Centro Table Test 3 0.4 Acceleration (g)

0.3 0.2 0.1 0 -0.1 0

5

10

15


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Figure 16: Floor 1 Accelerations

El Centro Floor 1 Test 1

Acceleration (g)

1.5 1 0.5 0 -0.5 0

5

10

15

20

25

30

20

25

30

20

25

30

-1 -1.5 Time (seconds)


Acceleration (g)

1.5 1 0.5 0 -0.5 0

5

10

15



Acceleration (g)

1.5 1 0.5 0 -0.5 0

5

10

15


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Acceleration (g)

El Centro Floor 2 Test 3 2 1.5 1 0.5 0 -0.5 0 -1 -1.5 -2

5

10

15

20

25

30

20

25

30

20

25

30

Time (seconds)


Acceleration (g)

1.5 1 0.5 0 -0.5 0

5

10

15

-1 -1.5 -2 Time (seconds)

Acceleration (g)


5

10

15

Time (seconds)

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El Centro Floor 3 Test 1 Acceleration (g)

3 2 1 0 -1 0

5

10

15

20

25

30

20

25

30

20

25

30

-2 -3 Time (seconds)


3 2 1 0 -1 0

5

10

15



Acceleration (g)

3 2 1 0 -1 0

5

10

15


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4.2 Displacement Experiment Results Based on the Displacement Experiment, the maximum displacement of Floor 3 relative to the base of the structure was 0.9 inches when shaken by the scaled El Centro earthquake. This value is accurate to +/- 0.05 inches. This maximum displacement occurred approximately 2.1 seconds after the earthquake began. The recorded data and graph are shown in Table 9 and Figure 46 respectively. Several trials were done with the same videotape. The trial shown in the following table and figure began at 2:12 (as displayed on the video). Table 8: Displacement Data

Displacement Experiment 2:12

Max = Min = Abs. Max =

Table starts moving at 2:15 Video Time (sec) 2:15 2:16 2:16 2:16 2:16 2:16 2:17 2:17 2:17 2:17 2:17 2:17 2:17 2:17 2:17 2:18 2:18 2:18 2:18 2:18 2:18 2:18 2:18 2:19 2:19 2:19 2:19

0.8 -0.9 0.9

in in in

Frames Frame Relative Time (sec) Top Bottom after prev. (cumulative) displacement --4 4 0 28 8 5 8 7 8 6 7 8 7 7 6 7 7 7 8 8 6 7 7 7 7 6 7 7 7

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28 36 41 49 56 64 70 77 85 92 99 105 112 119 126 134 142 148 155 162 169 176 182 189 196 203

0.47 0.60 0.68 0.82 0.93 1.07 1.17 1.28 1.42 1.53 1.65 1.75 1.87 1.98 2.10 2.23 2.37 2.47 2.58 2.70 2.82 2.93 3.03 3.15 3.27 3.38

3.1 3.3 3.15 4 2.9 4.6 3.55 4.5 3.1 4.3 2.9 3.7 2.9 4.5 3.3 5.2 3.25 4.3 3.1 4.4 3.3 4.5 3.35 4.6 3.5 4.8

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3.25 3.3 3.4 3.6 3.45 4.1 4.2 4 3.65 3.75 3.4 3.4 3.5 3.9 4.2 4.4 4 3.75 3.8 3.9 3.9 4 4 4.1 4.2 4.4

-0.15 0 -0.25 0.4 -0.55 0.5 -0.65 0.5 -0.55 0.55 -0.5 0.3 -0.6 0.6 -0.9 0.8 -0.75 0.55 -0.7 0.5 -0.6 0.5 -0.65 0.5 -0.7 0.4


Figure 19: Relative Displacement vs. Time

Floor 3 Displacements 1

0.8

0.6

Relative Displacement (inches)

0.4

0.2

0 0.0

1.0

2.0

3.0

4.0

-0.2

-0.4

-0.6

-0.8

-1 Time, t (seconds)

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5.0 SAP 2000 Results A 2D model of the 3D physical model was created in SAP 2000. The section properties, dimensions, masses, and damping ratio from “3D Model Specifications” were entered into SAP 2000. Because there are two rods on each side of the physical model, a general section was used in the 2D SAP 2000 model. The cross-sectional area entered for the general section was equal to twice the cross-sectional area of one rod. The moment of inertia entered for the general section was equal to twice the moment of inertia of one rod. The general section was named “ROD2.” See Figures 47 and 48 for SAP 2000 Schematics with labeling. The connections between columns and floor are assumed to be rigid. Masses for each floor were entered at the joints with the mass for each floor split evenly between the two joints on each floor (see Figure 49).

Figure 20: SAP 2000 Model

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Figure 21: SAP Model Section Labels

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Figure 22: SAP 2000 Model Masses (lb - s 2 / in)

The input data was printed and reviewed. That data is shown in Table 12 at the end of this section. After all appropriate data was entered into the SAP 2000 model, the model was analyzed. The resulting maximum accelerations at each floor and maximum displacements at the top floor are shown in Table 10 and Table 11, respectively. Time History Functions with acceleration versus time and displacement versus time are displayed on the following few pages (Figures 50 through 53).

Table 9: SAP 2000 Maximum Acceleration

Floor 1 2 3

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Table 10: SAP 2000 Maximum Displacement of Top Floor

Max Acceleration (g) 0.717 0.943 1.173

Floor 3

25

Max Displacement (inches) 0.992




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Figure 26: Floor 3 Displacements

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To check the reasonableness of the SAP 2000 model, the first three mode shapes were displayed (see figure below). The mode shapes came out as expected. Figure 27: Mode Shapes and Natural Periods

(a) Mode 1 (Period = 0.3049 sec)

(b) Mode 2 (Period = 0.1079 sec)

(c) Mode 3 (Period = 0.0742 sec)

The stiffness of the SAP 2000 model was also checked. This was done by adding a 1-kip load to joint 2 (Floor 1). Since the theoretical stiffness, K = 61.44 lb/in (see “3D Model Stiffness Hand Calculation”) and ∆ = (load) / (stiffness), the displacement of Floor 2 in the SAP 2000 model should be:  in  ∆ = 1000lb  = 16.28in  61.44lb  From the SAP 2000 output (see Table 13 at the end of this section), the displacement was 16.52 inches. These values are within 1.5%. The measured stiffness of Floor 1 was K=64.7 lb/in (see “Stiffness Experiment Results . . .”). Using this value, the displacement of Floor 2 should be:  in  ∆ = 1000lb  = 15.5in  64.6lb 

The SAP 2000 displacement of Floor 2 (∆ = 16.52 inches) is within 6.6% of that predicted by the measured stiffness of the physical model. Figures 55 and 56 show the unit load on the model and the deflected shape of the model due to that load.

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Figure 28: Unit Load - Stiffness Check (Load in Kips)

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Figure 29: Unit Load Deflected Shape


Table 11: SAP 2000 Input (For 1-kip Load and For El Centro Time History)

SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12 S T A T I C

L O A D

CASE TYPE

SELF WT FACTOR

LOAD1

DEAD

0.0000

H I S T O R Y

C A S E S

HISTORY CASE

HISTORY TYPE

NUMBER OF TIME STEPS

TIME STEP INCREMENT

EC1

LINEAR

25400

0.00100

SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12 J O I N T

Kip-ft Units

PAGE 2

D A T A

JOINT

GLOBAL-X

GLOBAL-Y

GLOBAL-Z

1 2 3 4 5 6 7 8

-0.62500 -0.62500 -0.62500 -0.62500 0.62500 0.62500 0.62500 0.62500

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.91667 1.83333 2.75000 0.00000 0.91667 1.83333 2.75000


PAGE 1

C A S E S

STATIC CASE

T I M E

Kip-ft Units

M A S S

RESTRAINTS 1 0 0 0 1 0 0 0

1 0 0 0 1 0 0 0

1 0 0 0 1 0 0 0

Kip-ft Units

1 0 0 0 1 0 0 0

1 0 0 0 1 0 0 0

ANGLE-A

ANGLE-B

ANGLE-C

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

1 0 0 0 1 0 0 0

PAGE 3

D A T A

JOINT

M-U1

M-U2

M-U3

M-R1

M-R2

M-R3

2 3 4 6 7 8

9.261E-05 9.484E-05 9.540E-05 9.261E-05 9.484E-05 9.540E-05

0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000

SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12 F R A M E FRAME 1 2 3 4 5 6 7 8 9

E L E M E N T

JNT-1

JNT-2

SECTION

1 2 3 5 6 7 2 3 4

2 3 4 6 7 8 6 7 8

ROD2 ROD2 ROD2 ROD2 ROD2 ROD2 FLOOR FLOOR FLOOR

Teacher’s Manual

Kip-ft Units

PAGE 4

ANGLE RELEASES SEGMENTS

R1

R2

FACTOR

LENGTH

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

0.917 0.917 0.917 0.917 0.917 0.917 1.250 1.250 1.250

D A T A

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

000000 000000 000000 000000 000000 000000 000000 000000 000000

30

2 2 2 2 2 2 4 4 4


SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12 M A T E R I A L

P R O P E R T Y

MAT LABEL

MODULUS OF ELASTICITY

POISSON'S RATIO

STEEL CONC OTHER ALUMINUM

4176000.0 518400.000 518400.000 1440000.00

0.300 0.200 0.200 0.330

D E S I G N

MAT LABEL

DESIGN CODE

STEEL FY

STEEL CONC OTHER ALUMINUM

S C N S

5184.000

THERMAL WEIGHT PER COEFF UNIT VOL 6.500E-06 5.500E-06 5.500E-06 1.300E-05

S E C T I O N

SECTION LABEL

MAT SECTION LABEL TYPE

FSEC1 STEEL ROD STEEL FLOOR ALUMINUM ROD2 STEEL ROD3 STEEL

REBAR FY

CONCRETE FCS

REBAR FYS

576.000

8640.000

576.000

5760.000

1.250 1.887E-04 2.040E-02 3.774E-04 3.835E-04

DEPTH

TORSIONAL INERTIA 0.189 0.000 2.912E-06 4.823E-05 4.823E-05

SECTION LABEL FSEC1 ROD FLOOR ROD2 ROD3

S E C T I O N

0.234 0.000 0.000 0.000 0.000

0.313 0.000 7.083E-05 5.787E-04 5.787E-04

Teacher’s Manual

0.174 0.000 3.329E-03 5.787E-04 5.787E-04

7.234E-02 0.000 1.630E-03 4.823E-05 4.823E-05 Kip-ft Units

0.000 0.000 0.000 0.000 0.000

FLANGE WIDTH BOTTOM 0.000 0.000 0.000 0.000 0.000

FLANGE THICK BOTTOM 0.000 0.000 0.000 0.000 0.000

PAGE 8

A2

SHEAR AREAS A3

1.042 1.698E-04 1.700E-02 6.944E-03 6.944E-03

1.042 1.698E-04 1.700E-02 6.944E-03 6.944E-03

PAGE 9

D A T A

PLASTIC MODULII Z33 Z22 0.469 0.000 1.062E-04 5.787E-04 5.787E-04

WEB THICK

D A T A

MOMENTS OF INERTIA I33 I22

P R O P E R T Y

SECTION MODULII S33 S22

FLANGE THICK TOP 0.000 0.000 0.000 0.000 0.000

Kip-ft Units

P R O P E R T Y

PAGE 7

D A T A

FLANGE WIDTH TOP 0.833 1.550E-02 0.979 0.833 0.833

SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12 F R A M E

Kip-ft Units

P R O P E R T Y

1.500 1.550E-02 2.083E-02 1.500 1.500

S E C T I O N

FSEC1 ROD FLOOR ROD2 ROD3

PAGE 6

CONCRETE FC

SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12

AREA

Kip-ft Units

1.519E-02 4.658E-03 4.658E-03 5.201E-03

5760.000

F R A M E

SECTION LABEL

0.489 0.150 0.150 0.170

MASS PER UNIT VOL

D A T A

SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12

F R A M E

PAGE 5

D A T A

SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12 M A T E R I A L

Kip-ft Units

0.260 0.000 4.994E-03 5.787E-04 5.787E-04

31

RADII OF GYRATION R33 R22 0.433 3.875E-03 6.014E-03 8.333E-02 8.333E-02

0.241 3.875E-03 0.283 8.333E-02 8.333E-02


SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12 F R A M E

S E C T I O N

P R O P E R T Y

SECTION LABEL

TOTAL WEIGHT

TOTAL MASS

FSEC1 ROD FLOOR ROD2 ROD3

0.000 0.000 1.300E-02 1.015E-03 0.000

0.000 0.000 3.978E-04 3.152E-05 0.000

SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12 S H E L L

Kip-ft Units

S E C T I O N

PAGE 10

D A T A

Kip-ft Units

P R O P E R T Y

PAGE 11

D A T A

SECTION LABEL

MAT LABEL

SHELL TYPE

MEMBRANE THICK

BENDING THICK

MATERIAL ANGLE

SSEC1

CONC

4

8.333E-02

8.333E-02

0.000

SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12 S H E L L

S E C T I O N

P R O P E R T Y

SECTION LABEL

TOTAL WEIGHT

TOTAL MASS

SSEC1

0.000

0.000


F O R C E S

Kip-ft Units

Load Case

PAGE 12

D A T A

Kip-ft Units

PAGE 13

LOAD1

JOINT

GLOBAL-X

GLOBAL-Y

GLOBAL-Z

GLOBAL-XX

GLOBAL-YY

GLOBAL-ZZ

2

1.000

0.000

0.000

0.000

0.000

0.000

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32


Table 12: SAP 2000 Output (For 1-kip Load – “Load 1”)

SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12 J O I N T JOINT

Kip-ft Units

PAGE 1

D I S P L A C E M E N T S LOAD

U1

U2

U3

R1

R2

R3

1

LOAD1

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

2

LOAD1

1.3769

0.0000

2.122E-04

0.0000

0.0449

0.0000

3

LOAD1

1.3977

0.0000

2.133E-04

0.0000

5.636E-04

0.0000

4

LOAD1

1.3981

0.0000

2.133E-04

0.0000

3.424E-04

0.0000

5

LOAD1

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

6

LOAD1

1.3768

0.0000

-2.122E-04

0.0000

0.0449

0.0000

7

LOAD1

1.3977

0.0000

-2.133E-04

0.0000

5.655E-04

0.0000

8

LOAD1

1.3981

0.0000

-2.133E-04

0.0000

3.423E-04

0.0000

SAP2000 v7.40 File: 2D SAP OF 3D MODEL 12 J O I N T JOINT

Kip-ft Units

PAGE 2

R E A C T I O N S LOAD

F1

F2

F3

M1

M2

M3

1

LOAD1

-0.5000

0.0000

-0.3648

0.0000

-0.2303

0.0000

5

LOAD1

-0.5000

0.0000

0.3648

0.0000

-0.2303

0.0000

Teacher’s Manual

33


6.0 Comparison of SAP 2000 and UCIST Shake Table Results The Shake Table Results and the SAP 2000 results were not as close as was expected. Table 14 and Table 15 show the comparison between maximum accelerations for each floor and maximum displacements of Floor 3, respectively. The maximum displacement for the SAP 2000 model was only 10% higher than the shake table maximum displacement. This is reasonably close. However, the maximum accelerations at each floor in the SAP 2000 model are 26% to 44% lower than the shake table maximum accelerations. These values are further apart than they should be. Since the SAP 2000 model predicts higher displacements and lower accelerations, this would suggest that the SAP 2000 model was using a lower value for story stiffness. As was shown in “SAP 2000 Results,” the SAP 2000 model is less stiff than the physical model; however, this stiffness is within 6.6% of the physical model’s measured stiffness. Another possible explanation of the discrepancy between the SAP 2000 results and the Shake Table results lies in the input function for SAP 2000. The El Centro scaled data was used as the input function in SAP 2000. This is the same function that was used as input data for the UCIST Shake Table. However, it should be noted that the accelerometer mounted at the base of the model (on the moving part of the shake table) recorded lower peak accelerations (Accel T) than were supposed to be input by the scaled El Centro earthquake. This discrepancy is shown in Figure 57 and Table 16. If the Accel T data more accurately represents the motions input into the physical model, then one would expect the displacements recorded from the physical model to be less than those recorded from the SAP 2000 model. However, this is not consistent with the fact that the physical model actually experienced higher accelerations than the SAP 2000 model while lower accelerations were input into the physical model (as indicated by the Accel T data). Table 13: Maximum Acceleration Comparison

Floor 1 2 3

SAP 2000 (g) 0.717 0.943 1.173

UCIST (g) 0.972 1.345 2.098

UCIST/SAP % ratio Difference 1.36 -26% 1.43 -30% 1.79 -44%

Table 14: Maximum Displacement Comparison

Floor 3

SAP 2000 (in) 0.992

Teacher’s Manual

UCIST (in) 0.9

UCIST/SAP % ratio Difference 0.9 10.2%

34


Figure 30: Scaled El Centro vs. Table (Accel R) Data

El Centro (Scaled Data) 0.4

Acceleration (g)

0.3 0.2 0.1 0.0 0

5

10

15

20

25

30

20

25

30

-0.1 -0.2 -0.3 Time (seconds)

El Centro (Table - Test 1) 0.4

Acceleration (g)

0.3 0.2 0.1 0 0

5

10

15

-0.1 -0.2 -0.3 Time (seconds)

Table 15: El Centro Scaled vs. Accel T - Maximum Accelerations

El Centro Scaled El Centro Accel T

Teacher’s Manual

Max Acceleration (g) 0.3481 0.3164

35


The following figures show graphs of acceleration data as a function of time. These graphs are shown in previous sections of this manual, but appear here for direct comparison between SAP 2000 results and UCIST Shake Table results. When comparing the graphs from SAP 2000 to the graphs from the UCIST Shake Table, it can be seen that the graphs have similar general shapes; however some discrepancies are apparent. Figure 31: Floor 1 Results Comparison


Acceleration (g)

1.5 1 0.5 0 -0.5 0

5

10

15

20

25

30


(a) UCIST Shake Table Results

(b) SAP 2000 Results

Teacher’s Manual

36


Figure 32: Floor 2 Results Comparison

Acceleration (g)


5

10

15

20

25

30

Time (seconds) (a) UCIST Shake Table Results


Teacher’s Manual

37


Figure 33: Floor 3 Results Comparison


3 2 1 0 -1 0

5

10

15

20

25

30


(a) UCIST Shake Table Results


Teacher’s Manual

38


7.0 Other Uses 1. Create a 3D model in SAP 2000. 2. An eccentric mass could be mounted on the physical model to demonstrate torsion. Data could be recorded in two perpendicular directions if two accelerometers were mounted on each floor. Orienting one accelerometer in one direction and a second accelerometer in a direction 90o from the first accelerometer would allow for data collection in the “x” and “y” directions. 3. Build a smaller 3D model and clamp both models (3D model discussed in this manual and the smaller one) to the UCIST Shake Table. Experiments could be done with the two buildings to demonstrate pounding. 4. Cross bracing could be installed. 5. A cylinder could be mounted to the shake table. It could be filled with sand and water for liquefaction experiments and demonstrations. 6. The UCIST Shake Table and models could be used with outreach programs at elementary, junior high, and high schools.

Teacher’s Manual

39


BIBLIOGRAPHY

Dyke, Shirley. “Instructional Shake Tables: A Cooperative Effort in Earthquake Engineering Education.” University Consortium on Instructional Shake Tables. 29 May 2001 . Sabnis, Gajanan M., et al. Structural Modeling and Experiment Techniques. Englewood Cliffs: Prentice-Hall, Inc., 1983.

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