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1/14/2015
Vibration of Concrete Floor Systems 1
Vibrations of Reinforced Concrete Floor Systems
1
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magnification• Optical equipment at isolation tables• Microelectronics manufacturing
equipment – Class B (Aligners, steppers, and other critical equipment for photolithography with lines widths of 3 microns or more)
1,000
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Vibration of Concrete Floor Systems 9
Acceptance Criteria
� Sensitive Equipment» Generic criteria
17
Equipment or UseVibrational
Velocity (/12./3456
• Electron microscopes at up to 30,000x magnification
• Microtomes• Magnetic resonance imagers• Microelectronics manufacturing
equipment – Class C (Aligners, steppers, and other critical equipment for photolithography with lines widths of 1 micron)
500
Acceptance Criteria
� Sensitive Equipment» Generic criteria
18
Equipment or UseVibrational
Velocity (/12./3456
• Electron microscopes at greater than 30,000x magnification
• Mass spectrometers• Cell implant equipment• Microelectronics manufacturing
equipment – Class D (Aligners, steppers, and other critical equipment for photolithography with lines widths of ½ micron, including electron-beam systems)
250
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Vibration of Concrete Floor Systems 10
Acceptance Criteria
� Sensitive Equipment» Generic criteria
19
Equipment or UseVibrational
Velocity (/12./3456
• Microelectronics manufacturing equipment – Class E (Aligners, steppers, and other critical equipment for photolithography with lines widths of ¼ micron, including electron-beam systems)
• Unisolated laser and optical research systems
130
Vibration Characteristics
� Floor Stiffness» Direct effect on natural frequency of the
floor system» 789:
20
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Vibration of Concrete Floor Systems 11
Vibration Characteristics
� Floor Stiffness» Modulus of elasticity
• 78 � �8 ;.�33 �8=» Dynamic modulus of elasticity
• 1.278
21
Vibration Characteristics
� Floor Stiffness» Effective moment of inertia
• ACI Eq. (9-8)
– 9: � ?@A?B
9C � 1 D ?@A?B
98E � 9C• Bischoff and Scanlon
– 9: � F@A; G@A
GBH ;I@AIJ
� 9C
22
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Vibration of Concrete Floor Systems 12
Vibration Characteristics
� Effective Floor Weight, �» Dead load of floor system» Superimposed dead load» Actual live load
23
Vibration Characteristics
� Natural Frequency» Flat plate system
24
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Vibration of Concrete Floor Systems 13
Vibration Characteristics
� Natural Frequency» Voided slab system
25
Vibration Characteristics
� Natural Frequency» Flat plate system / Voided slab system
• Assumptions– Thin, rectangular, isotropic plate
– Primary vertical deflection due to flexure
26
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Vibration of Concrete Floor Systems 14
Vibration Characteristics
� Natural Frequency» Flat plate system / Voided slab system
• �� � KHLMHNOℓQH
KQR@ST;NU ;VH
;/N
– ℓ; = longer of two center-to-center spans
– W = mass per unit area
– Based on Kirchoff Plate Theory
27
Vibration Characteristics
� Natural Frequency» Flat plate system / Voided slab system
• Rectangular plate, corner supports
• Dimensionless parameter X�N• Y*- long span
• Ref (Blevins – 2000)
28
Y*/YZ [*Z [ZZ
1.0 7.12 15.8
1.5 8.92 21.5
2.0 9.29 27.5
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Vibration of Concrete Floor Systems 15
Vibration Characteristics
� Natural Frequency» Flat plate system / Voided slab system
• Constant �;– Accounts for level of cracking in the concrete slab
� Flat plate - Voided slab system » System properties
32
Spans Typical bay: 40′−0"} 40′−0"
Member sizesVoided slab
Slab thickness ~� � 19.5"Void diameter � 14.125"Clear space between voids � 1.625"Number of void formers per sq ft = 0.58Stiffness reduction factor = 0.90
Columns 36" } 36"
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Vibration of Concrete Floor Systems 17
Design Data
� Section Properties
33Ref: Cobiax Engineering Manual
Examples
� Flat plate - Voided slab system » Concrete properties