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R Software Verification

PROGRAM NAME: SAP2000

REVISION NO.: 0

EXAMPLE 1-024 - 1

EXAMPLE 1-024

FRAME RESPONSE SPECTRUM ANALYSIS OF A THREE-DIMENSIONAL MOMENT FRAME

PROBLEM DESCRIPTION

In this example a two-story, two-bay in each direction, three-dimensional, fixed

base frame structure is analyzed using a response spectrum analysis. The modal

frequencies and X direction displacement at the story level centers of mass arecompared with independent results from another computer program presented inPeterson 1981.

The structure is doubly symmetric in plan, except that the center of mass at each

story level is eccentric and is given by the coordinates X = 38 feet and Y = 27

feet, as shown in the figure. Additional joints labeled 28 and 29 are added at the

center of mass location at each story level. All of the story mass is applied atthese joints.

The masses are applied in the X and Y directions only. No rotational mass inertia

is used for consistency with Peterson 1981. Thus the problem has four natural

modes. All four modes are used in the response spectrum analysis.

Two rigid diaphragm constraints are defined, one for each of the story levels. All

of the joints at Level 2 are constrained together, including the joint at the centerof mass. Similarly, all of the joints at the Roof level are constrained together. For

each of the story levels, the X and Y displacements and the Z rotations for all

joints are dependent on each other.

An eigenvector solution is used to obtain the modal frequencies. Four different

response spectrum analyses are performed, with each using a different type ofmodal combination. The combination types used are CQC (complete quadratic

combination), SRSS (square root sum of the squares), ABS (absolute) and NRC

10 Percent. The results are compared with results using CQC, SRSS, ABS andNRC 10 Percent modal combinations in the independent reference.

The applied response spectrum is a constant 0.4g for all modes. This spectrum is

applied in the X direction of the structure only. Modal damping is assumed to be

4% for all modes.

Important Note: Only bending and axial deformations are considered in this

example. Shear deformations are ignored by setting the shear area to zero foreach frame object in the structure.

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EXAMPLE 1-024 - 2

GEOMETRY AND PROPERTIES

1

1

10

19

2

11

20

3

12

21

4

13

22

5

14

23

6

15

24

7

16

25

8

17

26

9

18

27

28

29

ZY

X

10

2

11

3

124

13

5

14

6

157

16

8

17

9

18

19

25

37 26

38

27

39 28

40

29

41 30

42

20

31 32

21 22

33 34

23 24

35 36

35'

13'

1

1

19

- Joint number

- Column number

- Beam number

1

1

19

- Joint number

- Column number

- Beam number

13'

35'

25'

25'

Column Properties

E = 350,000 k/ft2

A = 4 ft2

I33 = 1.25 ft4

I22 = 1.25 ft4

Beam Properties

E = 500,000 k/ft2

A = 5 ft2

I33 = 2.61 ft4

I22 = 1.67 ft4

Center of Mass and Mass Information

Level 2 CM (Joint 28) at (38, 27, 13)Level 1 CM (Joint 29) at (38, 27, 26)

Typical story mass located at

joints 28 and 29 = 6.2112 k-sec2/ft

Column Local Axes

3

2

1

X-Direction Beam Local Axes Y-Direction Beam Local Axes

1

2

32 1

3

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REVISION NO.: 0

EXAMPLE 1-024 - 3

TECHNICAL FEATURES OF SAP2000 TESTED

Three-dimensional frame analysis Modal analysis using eigenvectors Rigid diaphragm constraint

Joint mass assignments

Response spectrum analysis

RESULTS COMPARISON

The SAP2000 results are compared with independent results presented inPeterson 1981.

Output Parameter SAP2000 IndependentPercent

Difference

Mode 1 period, sec 0.2271 0.2271 0%

Mode 2 period, sec 0.2156 0.2156 0%

Mode 3 period, sec 0.0733 0.0733 0%

Mode 4 period, sec 0.0720 0.0720 0%

X Displacement (jt 29) ft

CQC modal combination0.02014 0.02014 0%


SRSS modal combination0.02012 0.02012 0%

X Displacement (jt 29) ftABS modal combination

0.02050 0.02050 0%


10% modal combination0.02016 0.02016 0%

COMPUTER FILE: Example 1-024

CONCLUSION

The SAP2000 results show an exact comparison with the independent results.

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