LIST OF REFERENCES J. R. (1994) “Vibration Acceptability of Floors Under Impact Vibration.”...

54

LIST OF REFERENCES

American Plywood Association (1995). “Design Capacities of APA Performance RatedStructural-Use Panels.” Technical Note N375B.

Australian Standard. Domestic Metal Framing Code, AS3623 (1993). Standards Association ofAustralia, Homebush, NSW.

Band, B. S., Jr. (1996). “Vibration Characteristics of Joist and Joist-Girder Members.” MastersThesis, Department of Civil Engineering, Virginia Polytechnic Institute and State University,Blacksburg, Virginia.

Clough, R. W. (1993). Dynamics of Structures. McGraw-Hill, Inc., New York, New York.

Hibbitt, Karlson and Sorenson (1984) ABAQUS User’s Manual, Version 4.5. Hibbitt, Karlsonand Sorenson, Inc.

Johnson, J. R. (1994) “Vibration Acceptability of Floors Under Impact Vibration.” MastersThesis, Department of Civil Engineering, Virginia Polytechnic Institute and State University,Blacksburg, Virginia.

Kitterman, S. S. (1994) “Investigation of Several Aspects of the Vibration Characteristics ofSteel Member-Supported Floors.” Masters Thesis, Department ofCivil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.

Lenzen, K. H. and Dorsett, L. P. (1969) “Effect of the Variation of Structural Parameters on theVibrational Characteristics of Steel Joist-Concrete Slab Floor Systems and Suggested Designs.”Studies in Engineering Mechanics, No. 29, The University of Kansas Center for Research inEngineering Science, Lawrence, Kansas.

Murray, T. M. (1979) “Acceptability Criterion for Occupant-Induced Floor Vibrations.” Soundand Vibration, November, 1979.

Murray, T. M. (1991) “Building Floor Vibrations.” Engineering Journal, Third Quarter, 1991.

Murray, T. M., Allen, D. E., and Unger, E. E. (1997) “Design Guide - Floor Vibrations Due toHuman Activity.” Draft 10/10/96.

55

LIST OF REFERENCES Continued...

Ohlsson, S. V. (1988a) “Ten Years of Floor Vibration Research - A Review of Aspects and SomeResults.” National Research Council Canada, May 16-18, 1988.

Ohlsson, S. V. (1988b) “Springiness and Human-Induced Floor Vibrations - A Design Guide.”D12:1988, Swedish Council for Building Research, Stockholm, Sweden.

Ohmart, R. D. (1968) “An Approximate Method for the Response of Stiffened Plates toAperiodic Excitation.” Studies in Engineering Mechanics, Report No.30, The University ofKansas Center for Research in Engineering Science, Lawrence, Kansas.

Onysko, D. M. (1985) “Serviceability Criteria For Residential Floors Based on a Field Study ofConsumer Response.” Forintek Canada Corp. Report 03-50-10-008 toCanadian Forestry Service, Ottawa, Ontario, Canada.

Onysko, D. M. (1995) “Some Background on Factors Affecting Performance of Floors andSetting of Performance Criteria.” Task group Meeting, Forintek Canada Corp.

Runte, D. E. (1993) “Fundamental Frequencies of I-Joist, Solid-Sawn Wood Joist, and TrussFloors Based on Tee-Beam Modeling.” Masters Thesis, Department of Civil Engineering,Virginia Polytechnic Institute and State University, Blacksburg, Virginia.

Saksena, S. K. and Murray, T. M. (1972) “Investigation of a Floor Vibration Parameter.” Schoolof Civil Engineering, University of Oklahoma, Norman, Oklahoma.

Shamblin, C. L. (1989) “Floor System Response to Heel-Drop Impact.” Masters Thesis,Department of Civil Engineering, Virginia Polytechnic Institute and State University,Blacksburg, Virginia.

Shue, B. C. (1995) “Some Aspects of Vibration Serviceability in Wood Floor Systems.” MastersThesis, Department of Civil Engineering, Virginia Polytechnic Institute and State University,Blacksburg, Virginia.

Wilson, E. L. and Habibullah, A. (1992) “SAP90 - A Series of Computer Programs for the FiniteElement Analysis of Structures - Structural Analysis User’s Manual.” Computers and Structures,Inc., Berkeley, California.

56

APPENDIX AMULTI-JOIST FLOOR TEST SUMMARIES

57

A.1 Description of Materials

Joists 14K1 Steel Bar Joists supplied by Vulcraft Florence, SCWeight = 6.71 plf E = 29,000,000 psi

Sheathing 23/32 Tounge and Groove Oriented Strand BoardWeight = 2.255 psf E = 580,000 psi (axial)

Fasteners 2 in. No. 10 Self Tapping Screws Spaced 6 in. Around Perimeterand 12 in. Along Inside Joist Chords

Diagonal Bracing 1.25 x 1.25 x 0.107 Steel AngleWeight = 1.04 psf (average increase in weight of floor due

to the weight of the bracing)

All floors were built at the Charles E. Via, Jr. Structures and Materials Research Laboratoryusing standard building practices at that time.

A.2 Typical Floor Layout

58

Table A.1 Multi-Joist Floor System Parameters

Span Joist

Floor Length Spacing Bracing

Designation (ft) (in.) Configuration

16-360H 34.00 16 Horizontal (H)

16-360XH 34.00 16 Cross & Horizontal (XH)

16-360X 34.00 16 Cross (X)

16-480H 31.25 16 Horizontal (H)


16-480X 31.25 16 Cross (X)

16-720H 27.29 16 Horizontal (H)


16-720X 27.29 16 Cross (X)

24-360H 30.00 24 Horizontal (H)


24-360X 30.00 24 Cross (X)

24-480H 27.67 24 Horizontal (H)


24-480X 27.67 24 Cross (X)

24-720H 24.50 24 Horizontal (H)


24-720X 24.50 24 Cross (X)

Designation: xx-yyaa

Bracing Type

Span - to - Live Load Deflection Ratio

Joist Depth

59

Table A.2 Measured Data for Multi-Joist Floor Systems

FloorName

FrequencyMeasured at

Midspan

(Hz)

FrequencyMeasured atQuarter Point

(Hz)

MeasuredDeflection*

(in.)

SubjectiveAcceptability

Rating

16-360H 7.81 8.06 0.034 Unacceptable

16-360XH 7.81 8.00 0.026 Unacceptable

16-360X 7.81 8.06 0.030 Unacceptable

16-480H 8.94 9.25 0.028 Unacceptable

16-480XH 9.00 9.75 0.024 Unacceptable

16-480X 8.94 9.81 0.027 Unacceptable

16-720H 10.69 11.13 0.023 Unacceptable

16-720XH 10.75 11.94 0.020 Unacceptable

16-720X 10.75 11.13 0.023 Unacceptable

24-360H 8.94 9.31 0.037 Unacceptable

24-360XH 8.94 9.81 0.030 Unacceptable

24-360X 8.84 9.19 0.032 Unacceptable

24-480H 9.94 10.38 0.030 Unacceptable

24-480XH 9.75 10.03 0.026 Unacceptable

24-480X 9.81 10.13 0.028 Unacceptable

24-720H 11.60 12.00 0.023 Unacceptable

24-720XH 11.56 12.06 0.018 Unacceptable

24-720X 11.50 12.06 0.020 Unacceptable* Due to a 225 lb midspan concentrated load

60

A.3 Force, Acceleration, Power Spectrum, and Deflection Graphs for Each Floor System

16-360H

Heel Drop 1 Force vs Time Plot HDS @ 1/2,1/2, Accelerometer @ 1/2,1/2

Heel Drop Acceleration vs Time Plot HDS @ 1/2,1/2, Accelerometer @ 1/2,1/2

Heel Drop Acceleration vs Time Plot HDS @ 1/2,1/2, Accelerometer @ 1/2,1/2

-200

-100

0

100

200

300

400

500

600

700

800

0 4 8 12 16TIME (S)

Fo

rce

(lb

s)

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (

IN/S

^2)

0

100

200

300

400

500

600

0 10 20 30 40FREQUENCY Hz

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (

IN/S

^2)

0

50

100

150

200

250

300

350

400

450

500


61

Walking Parallel to Floor Joists HDS @ 1/2,1/2, Accelerometer @ 1/2,1/2

Walking Perpendicular to Floor Joists HDS @ 1/2,1/2, Accelerometer @ 1/2,1/2

-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (

IN/S

^2)

0

20

40

60

80

100

120

140


-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (

IN/S

^2)

0

20

40

60

80

100

120

140


Floor Deflection Due to Concentrated Load at MidspanTest Floor 16-360H

-0.04-0.035-0.03

-0.025-0.02

-0.015-0.01

-0.0050

0.005

1 3 5 7 9 11 13

Joist Number

Def

lect

ion

(in.

)

62

16-360XH


Heel Drop 1 Acceleration vs Time Plot HDS @ 1/2,1/2, Accelerometer @ 1/2,1/2


-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400

0 10 20 30FREQUENCY Hz

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


63




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16

TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


64



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-80

-60

-40

-20

0

20

40

60

80

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


Floor Deflection Due to Concentrated Load at MidspanTest Floor 16-360XH

-0.04-0.035-0.03

-0.025-0.02

-0.015-0.01

-0.0050

0.005

1 3 5 7 9 11 13

Joist Number

Def

lect

ion

(in.

)

65

16-360X




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


66




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


67



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-80

-60

-40

-20

0

20

40

60

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


Floor Deflection Due to Concentrated Load at MidspanTest Floor 16-360X

-0.04-0.035-0.03

-0.025-0.02

-0.015-0.01

-0.0050

0.005

1 3 5 7 9 11 13

Joist Number

Def

lect

ion

(in.

)

68

16-480H




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


69




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16

TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


70



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-100

-80

-60

-40

-20

0

20

40

60

80

100

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.04-0.035-0.03

-0.025-0.02

-0.015-0.01

-0.0050

0.005

1 3 5 7 9 11 13

Joist Number

Def

lect

ion

(in.

)

71

16-480XH




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


72




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16

TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


73



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-80

-60

-40

-20

0

20

40

60

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.04-0.035-0.03

-0.025-0.02

-0.015-0.01

-0.0050

0.005

1 3 5 7 9 11 13

Joist Number

Def

lect

ion

(in.

)

74

16-480X




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


75




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16

TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


76



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-80

-60

-40

-20

0

20

40

60

80

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.04-0.035-0.03

-0.025-0.02

-0.015-0.01

-0.0050

0.005

1 3 5 7 9 11 13

Joist Number

Def

lect

ion

(in.

)

77

16-720H




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


78




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16

TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


79



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-80

-60

-40

-20

0

20

40

60

80

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.04-0.035-0.03

-0.025-0.02

-0.015-0.01

-0.0050

0.005

1 3 5 7 9 11 13

Joist Number

Def

lect

ion

(in.

)

80

16-720XH




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


81




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16

TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


82



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-50

-40

-30

-20

-10

0

10

20

30

40

50

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.04-0.035-0.03

-0.025-0.02

-0.015-0.01

-0.0050

0.005

1 3 5 7 9 11 13

Joist Number

Def

lect

ion

(in.

)

83

16-720X




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


84




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


85



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-60

-40

-20

0

20

40

60

80

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.04-0.035-0.03

-0.025-0.02

-0.015-0.01

-0.0050

0.005

1 3 5 7 9 11 13

Joist Number

Def

lect

ion

(in.

)

86

24-360H




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


87




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


88



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-80

-60

-40

-20

0

20

40

60

80

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.05

-0.04

-0.03

-0.02

-0.01

0

1 2 3 4 5 6 7 8 9

Joist Number

Def

lect

ion

(in.

)

89

24-360XH




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


90




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


91



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-80

-60

-40

-20

0

20

40

60

80

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.05

-0.04

-0.03

-0.02

-0.01

0

1 2 3 4 5 6 7 8 9

Joist Number

Def

lect

ion

(in.

)

92

24-360X




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


93




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


94



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-60

-40

-20

0

20

40

60

80

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.05

-0.04

-0.03

-0.02

-0.01

0

1 2 3 4 5 6 7 8 9

Joist Number

Def

lect

ion

(in.

)

95

24-480H




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-400

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


-400

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


96




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


97



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-50

-40

-30

-20

-10

0

10

20

30

40

50

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.05

-0.04

-0.03

-0.02

-0.01

0

1 2 3 4 5 6 7 8 9

Joist Number

Def

lect

ion

(in.

)

98

24-480XH




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


99




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


100



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-60

-40

-20

0

20

40

60

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.05

-0.04

-0.03

-0.02

-0.01

0

1 2 3 4 5 6 7 8 9

Joist Number

Def

lect

ion

(in.

)

101

24-480X




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


102




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


103



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-60

-40

-20

0

20

40

60

80

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.05

-0.04

-0.03

-0.02

-0.01

0

1 2 3 4 5 6 7 8 9

Joist Number

Def

lect

ion

(in.

)

104

24-720H




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


105




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


106



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-100

-80

-60

-40

-20

0

20

40

60

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.05

-0.04

-0.03

-0.02

-0.01

0

1 2 3 4 5 6 7 8 9

Joist Number

Def

lect

ion

(in.

)

107

24-720XH




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


108




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


109



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-100

-80

-60

-40

-20

0

20

40

60

80

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.05

-0.04

-0.03

-0.02

-0.01

0

1 2 3 4 5 6 7 8 9

Joist Number

Def

lect

ion

(in.

)

110

24-720X




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

350

400


111




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300

0 10 20 30

FREQUENCY Hz

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


112



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300


-80

-60

-40

-20

0

20

40

60

80

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

50

100

150

200

250

300



-0.05

-0.04

-0.03

-0.02

-0.01

0

1 2 3 4 5 6 7 8 9

Joist Number

Def

lect

ion

(in.

)

113

APPENDIX B

TWO-JOIST FLOOR TEST SUMMARIES

114

B1 Description of Materials

Joists 14K1 Steel Bar Joists supplied by Vulcraft Florence, SCWeight = 6.71 plf E = 29,000,000 psi

Sheathing 23/32 Tounge and Groove Oriented Strand BoardWeight = 2.255 psf E = 580,000 psi (axial)

Fasteners 2 in. No. 10 Self Tapping Screws at 12 in. Spacing Along JoistChords

Diagonal Bracing 1.25 x 1.25 x 0.107 Steel AngleWeight = 1.04 psf (average increase in weight of floor due

to the weight of the bracing)

Both floors were built at the Charles E. Via, Jr. Structures and Materials Research Laboratoryusing standard building practices at that time.

B2 Midspan Concentrated Load Tests

2J16-720 Span Length = 27.29 (ft)Without Sheating With Sheating

Moment of Inertia From Deflection Test is 59.05 in^4 Moment of Inertia From Deflection Test is 60.91 in^4

2J24-720 Span Length = 24.50 (ft)Without Sheating With Sheating

Moment of Inertia From Deflection Test is 57.60 in^4 Moment of Inertia From Deflection Test is 58.16 in^4

Load vs Deflection

0

50

100

150

200

250

300

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Vertical Deflection (in.)

Loa

d (l

bs)

S. Joist N. Joist Predicted

Load vs Deflection

0

50

100

150

200

250

300

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14


Loa

d (l

bs)


Load vs Deflection

0

50

100

150

200

250

300

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14


Loa

d (l

bs)


Load vs Deflection

0

50

100

150

200

250

300

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14


Loa

d (l

bs)


115

Table B1 Properties of Two-Joist Floor Systems

Floor System: 2J16-720

Average Measured Properties of Joists

Top Angles Bottom Angles

Depth Length WebDia.

Top Leg BottomLeg

Thickness Top Leg BottomLeg

Thickness

(in.) (ft) (in.) (in.) (in.) (in.) (in.) (in.) (in.)

14 24.50 0.503 1.506 1.507 0.145 1.508 1.506 0.128

Note: Measured properties taken from an average of 8 readings

Calculated Properties of Joist

d Yx Igross L/d Eq. 3.1 Calc. Ieff Meas. Ieff

(in.) (in.) (in.)4 - % Ichords (in.)4 (in.)4

13.15 6.61 67.84 21.00 87.33 59.24 59.05

Floor System: 2J24-720

Average Measured Properties of Joists

Top Angles Bottom Angles

Depth Length WebDia.

Top Leg BottomLeg

Thickness Top Leg BottomLeg

Thickness

(in.) (ft) (in.) (in.) (in.) (in.) (in.) (in.) (in.)

14 27.33 0.502 1.506 1.507 0.140 1.508 1.507 0.123

Note: Measured properties taken from an average of 8 readings

Calculated Properties of Joist

d Yx Igross L/d Eq. 3.1 Calc. Ieff Meas. Ieff

(in.) (in.) (in.)4 - % Ichords (in.)4 (in.)4

13.15 6.61 65.48 23.39 89.08 58.32 57.60

116

B3. Force, Acceleration, Power Spectrum, and Deflection Graphs for Two-Joist Tests2J16-720Heel Drop 1 Force vs Time Plot HDS @ 1/2,1/2, Accelerometer @ 1/2,1/2



-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

10

20

30

40

50

60

70

80

90

100


-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

10

20

30

40

50

60

70

80

90

100


117



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

10

20

30

40

50

60

70

80

90

100


-150

-100

-50

0

50

100

150

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

10

20

30

40

50

60

70

80

90

100


118

2J24-720




-200

-100

0

100

200

300

400

500

600

700

800

900

1,000

0 4 8 12 16TIME (S)

For

ce (l

bs)

-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

10

20

30

40

50

60

70

80

90

100


-300

-200

-100

0

100

200

300

400

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

10

20

30

40

50

60

70

80

90

100


119



-4

-3

-2

-1

0

1

2

3

4

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

10

20

30

40

50

60

70

80

90

100


-150

-100

-50

0

50

100

150

0 4 8 12 16TIME (S)

AC

CE

LE

RA

TIO

N (I

N/S

^2)

0

10

20

30

40

50

60

70

80

90

100


120

APPENDIX CSAMPLE CALCULATIONS

121

C1 Acceptability Criteria

Floor system 24-360H is used for all sample calculations. The floor system properties are listedbelow.

L = 30.00 ft (9.14 m) Ej = 29,000,000 psi (200 x 109 Pa)s = 24 in. (0.610 m) Ef = 580,000 psi (4 x 109 Pa)B = 16.00 ft (4.88 m) tf = 0.7188 in. (18.26 mm)It

* = 58.16 in.4 (2.462 x 10 -5 m4)*f1 = 8.94 Hz *∆meas. = 0.037 in. (0.940 mm)

*Measured results

Equation 1.24 was used to calculate the fundamental frequency of each floor system and thevalues are listed in Table 3.9.

fgEIwL

t= 157 4. = 157386 4 29 000 000 5916

1257 30 00 12

2 4

4 3.( . / )*( , , )*( . )

( . / )*( . ) *( / )in s psi in

lb ft ft in ft = 9.64 (Hz)

Swedish Criterion

Frequency > 8 Hz ?

f1 = 8.94 Hz > 8 Hz ∴ Yes

1) ∆meas. < 1.5 mm ?

∆meas. = 0.940 mm < 1.5 mm ∴ Yes

2) Impulse Velocity Response, h’max

( )

hN

mBL'

. .max =

++

4 0 4 0 6200

40 (m/s/Ns)

Find N40 from charts in “Springiness and Human-Induced Floor Vibrations - A DesignGuide” (Ohlsson 1988a)

N40 cannot be found by this method since L/B and Dy/Dx ratios do not plot on given charts.Therefore h’max cannot be calculated.

3) Continuous Loading Test, W’RMS

wmBL

NfRMS' .=

+100 121 2

2

13ζ

[(m/s)RMS]

Find N1.2 from charts in “Springiness and Human-Induced Floor Vibrations - A Design Guide”(Ohlsson 1988a)

N1.2 cannot be found by this method since L/B and Dy/Dx ratios do not plot on given charts.Therefore W’RMS cannot be calculated.

122

Australian Criterion

1) Frequency > 8 Hz ?

f1 = 8.94 Hz > 8 Hz ∴ Yes

2) ∆meas. < 1.5 mm ?

∆meas. = 0.940 mm < 1.5 mm∴ Yes

3) Log10(Vmax) < 1.2 + 2σ ?

( )V

NmBLmax

. .=

++

4 0 4 0 6200

40 (m/s/Ns)

N40 = BL

r fr

+ −

−

2 11

r = Ky/Kx

Kx = E I

sj j =

( ) *( . ).

200 10 0 000024620 610

9 4x Pa mm

= 8,072,000 N-m

Ky =E tf f

3

12 =

( )*( . )4 10 0 0182612

9 3x Pa m= 2029 N-m

r = KK

y

x

=2029

8 072 000N m

N m−

−, , = 0.000251

f = 40/f1 = 40

894.= 4.47

N40 = BL

r fr

+ −

−

2 11 =

488914

0 000251 4 47 10 000251

12.

.. .

.+ −

−

= 8.84

( )V

NmBLmax

. .=

++

4 0 4 0 6200

40 = ( )4 0 4 0 6 884

3451 488 914 200. . * .

. * . * .+

+ = 0.0131 (m/s/Ns)

Log10(Vmax) = Log10(0.0131) = 1.88

Calculate 1.2 + 2σ

σ = f1*ζ† = 8.94*0.009 = 0.0805 ∴ 1.2 + 2σ = 1.36

Log10(Vmax) = 1.88 > 1.2 + 2σ = 1.36 ∴ Floor System is Unacceptable

† ζζ is the modal damping ratio. The Australian Code assumes the value 0.9 % and should beused unless other values are proved to be more appropriate.

123

Canadian Criterion

Midspan Deflection

y8 .0L1.3≤ (mm)

∆required = 8 .0L1.3 =

8 .09 .141.3 = 0.4507 mm (0.018 in.)

y = ∆meas. = 0.914 mm (0.037 in.) > 0.4507 mm ∴ Floor System is Unacceptable

Murray’s Criterion

1) Is f1 < 10 Hz ?

f1 = 8.94. < 10 Hz ∴ Yes

2) D > 35 Ao f + 2.5

Determine Ao

( )A DLFL

EIott

=

*

max60048

3

= ( )11041600 30 00 12

48 29 500 000 5816

3

. **( . * )

*( , , )*( . )

= 0.375 in.

*(DLF)max is found by Figure 1.9From Kitterman Equation, Neff = 3.98 (See Appendix C2)

AANo

ot

eff

= = 0375398..

= 0.0942 in.

Solve for minimum DampingD > 35 Ao f + 2.5 = 35*(0.0942)*(8.94) + 2.5 = 31.98Minimum Damping Required = 31.98 % of CriticalThis level of damping is impractical for these floor systems. Therefore this criteriondoes not apply.

Johnson’s Criterion

f1 > 15 Hz ?

f1 = 8.94 Hz < 15 Hz ∴ Floor System is Unacceptable

124

C2 Prediction of Deflection

Floor system 24-360H is used for all sample calculations. The floor system properties are listedbelow.

L = 30.00 ft (9.14 m) Ej = 29,000,000 psi (200 x 109 Pa)s = 24 in. (0.610 m) Ef = 580,000 psi (4 x 109 Pa)B = 16.00 ft (4.88 m) tf = 0.7188 in. (18.26 mm)It

* = 58.16 in.4 (2.462 x 10 -5 m4)*f1 = 8.94 Hz *∆meas. = 0.037 in. (0.940 mm)

*Measured results

Load Reduction Factor (Australian Code)

∆ =k PL

E Id

j j

3

48 (m)

k Logkkd

c

b

= −

+

0883 034 04410. . .

kE t L

scf f

=3

312 =

( )*( . ) *( . )*( . )

4 10 0 01826 91412 0 610

9 3

3

x Pa mm mm

= 81,722 (N/m)

kE I

Lbj j

= 3 = ( )*( . )

.200 10 0 0000254

914

9 4

3

x Pa mm

= 6653 (N/m)

k Logd = −

+

0883 034

81 7226653

0 4410. .,

. = 0.507

∆ =k PL

E Id

j j

3

48

( . )*( )*( . )*( , , )*( . )

0507 1 91448 200 000 000 0 0000254

3

4

kN mPa m

= 0.0016 m (0.0625 in.)

∆calc. = 0.0625 in. > ∆meas. = 0.037 in. ∴ Method is very conservative

SJI Equation to Predict Neff

Neff = +

∑1 2

2cos

πxxo

for x ≤ xo

xo = 1.06*ε∗L

125

ε = DD

x

y

0 25.

Dx = E tf f

3

12 =

( , )*( . )580 000 0 718812

3psi in = 17,950 lb-in.

Dy = E I

sj j =

( , , )*( . )29 000 000 581624

4psi inin

= 70,276,000 lb-in.

ε = 17 950

70 276 000

0 25,, ,

.

= 0.1264

xo = 1.06*ε∗L = 1.06*0.1264*30.00ft*12in./ft = 48.23 in.

Neff = +

∑1 2

2cos

πxxo

= Neff = + +

∑1 2

242 48 23

482 48 23

cos*

* .cos

** .

π π= 2.43

Kitterman Equation to Predict Neff

NdS

xLI

LSeff

e

t= + + −

−0 4898 3419 8 99 10 0 00059394 2

. . . .

N xeff = + + −

−0 4898 34190 7188

24899 10

30 125816

0 00059330 12

249

4 2

. ..

.( * )

..

* = 3.98

Limitations:

0.18 ≤ DS

e < 0.208 0.018 ≤ 07188

24.

= 0.03 < 0.208 ∴ OK

4.5x106 ≤ LIt

4

≤ 257x106 4.5x106 ≤ ( . * )

.30 00 12

5816

4

= 289x106 ≥ 257x106 ∴ No Good

2 < LS

< 30 2 < 30 00 12

24. *

= 15 < 30 ∴ OK

If Limitations are Ignored, Then Neff = 3.98 By Kitterman’s MethodNote: Limitations on Kitterman’s Method were Ignored

126

VITA

Alaric Lee Anderson

Alaric L. Anderson was born in Hattiesburg, MS on April 12, 1973. He was raised in Sumrall,MS and graduated from Columbia Academy in 1991. He attended the University of SouthernMississippi for two years and then Mississippi State University for two years where he received aBachelor of Science Degree in Civil Engineering in 1995. In August 1995 he entered graduateschool in the Structures Division of Civil Engineering at Virginia Polytechnic Institute and StateUniversity. In May 1997, he will receive his Masters of Science Degree in Civil Engineering atVirginia Tech. He will begin work as a design engineer for Ferrell Engineering in Birmingham,AL in April 1997.

LIST OF REFERENCES J. R. (1994) “Vibration Acceptability of Floors Under Impact Vibration.”...

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Transcript of LIST OF REFERENCES J. R. (1994) “Vibration Acceptability of Floors Under Impact Vibration.”...