vibrations of reinforced concrete floor...
TRANSCRIPT
1/14/2015
Vibration of Concrete Floor Systems 1
Vibrations of Reinforced Concrete Floor Systems
1
Copyright Materials
This presentation is protected by US and International Copyright laws. Reproduction, distribution, display and use
of the presentation without written permission of the speaker is prohibited.
© The Concrete Reinforcing Steel Institute
2
1/14/2015
Vibration of Concrete Floor Systems 2
About the Speaker
� Mike Mota» Member of ACI 318, 318B and 318R (2019)» Chair of ACI 314 “Simplified Design of Concrete
Structures”» Member of ASCE-7 (2016)» Board of Directors CIB/NYC-ACI Chapter» Fellow of ACI, ASCE and SEI
Vibration of RC Floor Systems
� First design guide solely dedicated to vibrations of RC floor systems
� Based on approximate methods
� Verified by FEA solutions
� Case study of actual voided slab structure
4
1/14/2015
Vibration of Concrete Floor Systems 3
Objectives
� Assist design professional when effects from vibration must be considered
� Provide simplified methods to determine key vibration characteristics of RC floor systems and compare against acceptance criteria
� Overview of Mitigation Strategies� Several detailed design examples
5
Outline
� CRSI Vibration Design Guide» Acceptance Criteria» Vibration Characteristics of Reinforced
Concrete Floor Systems54
» Examples• Voided Flat Plate Vibration Analysis
– Walking
– Rhythmic
– Sensitive
» Case Study6
1/14/2015
Vibration of Concrete Floor Systems 4
Acceptance Criteria
� Human Comfort» Walking excitation
• Dependent on peak acceleration experienced by structure
» Rhythmic excitation• Combination of peak acceleration and relationship
between natural and excitation frequencies
� Sensitive Equipment» Vibrational velocity
� Not mutually exclusive
7
Acceptance Criteria
� Human Comfort» Walking excitation
• Recommended acceleration limits �� �⁄• Ref (Allen and Murray, 1993)
8
1/14/2015
Vibration of Concrete Floor Systems 5
Acceptance Criteria
� Human Comfort» Walking excitation
• Peak acceleration less than or equal to recommended acceleration limit
9
��� � 65 �. ���
�� � ���
Acceptance Criteria
� Human Comfort» Rhythmic excitation
• k = 1.3 for dancing• k = 1.7 for concert or sporting event• k = 2.0 for aerobics or jumping
10
�� � � 1 � ��� �⁄
������
1/14/2015
Vibration of Concrete Floor Systems 6
Acceptance Criteria
� Human Comfort» Rhythmic excitation
11
Activity HarmonicForcing
Frequency �
Weight of Participants �� (psf)
Dynamic Coefficient
!Dancing 1 1.5 – 3.0 12.5 0.50Concert or sporting event
1 1.5 – 3.031.0
0.25
2 3.0 – 6.0 0.05
Aerobics or jumping
1 2.0 – 2.754.2
1.502 4.0 – 5.5 0.603 6.0 – 8.25 0.10
Acceptance Criteria
� Sensitive Equipment» Maximum velocity " � Limiting "
• Maximum velocity " � Δ$%& ��⁄• Limiting "
– Manufacturers’ criteria
– Generic criteria
12
1/14/2015
Vibration of Concrete Floor Systems 7
Acceptance Criteria
� Sensitive Equipment» Footfall impulse parameters
13
Walking Pace (steps/minute)
'((lb)
�) � */,)(Hz)
-.(lb Hz 2)
Fast (100) 315 5.0 25,000
Moderate (75) 280 2.5 5,500
Slow (50) 240 1.4 1,500
Acceptance Criteria
� Sensitive Equipment» Generic criteria
14
Equipment or UseVibrational
Velocity (/12./3456
• Computer systems• Operating rooms• Surgery facilities• Bench microscopes at up to 100x
magnification
8,000
1/14/2015
Vibration of Concrete Floor Systems 8
Acceptance Criteria
� Sensitive Equipment» Generic criteria
15
Equipment or UseVibrational
Velocity (/12./3456
• Bench microscopes at up to 400x magnification
• Optical and other precision balances• Coordinate measuring machines• Metrology laboratories• Optical comparators• Microelectronics manufacturing
equipment – Class A (inspection, probe test and other manufacturing support equipment
2,000
Acceptance Criteria
� Sensitive Equipment» Generic criteria
16
Equipment or UseVibrational
Velocity (/12./3456
• Micro surgery• Eye surgery• Neuro surgery• Bench microscopes greater than 400x
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
1/14/2015
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
1/14/2015
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
1/14/2015
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
1/14/2015
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
1/14/2015
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
1/14/2015
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
1/14/2015
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
– Estimated by 9: 9C⁄– Square panels: Average9: � 0.79d � 0.15e9:; � 9:N6– Rectangular panels:
9:|�g�:h � Fi|@j,lmFi|nj,o m Fi|@j,omFi|nj,lN
– Contribution of shrinkage restraint to cracking
�E � 4.5X �8=
29
Vibration Characteristics
� Natural Frequency» Flat plate system / Voided slab system
• Constant �N– Accounts for effect of rigidity at the joint between the
slab and column
– �N � q1.9foru; � 24in.2.1foru; x 24in.
30
1/14/2015
Vibration of Concrete Floor Systems 16
Examples
� Flat plate - Voided slab system » Walking» Rhythmic Excitation (Dancing)» Sensitive
31
ConcreteCompressive strength �8= � 4,000psiDensity �8 � 150pcf
Reinforcing steel
Yield strength �| � 60,000psi
LoadsSuperimposed dead load = 20 psfLive load (design) = 100 psfLive load (vibration) = 12.5 psf
Examples
� 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"
1/14/2015
Vibration of Concrete Floor Systems 17
Design Data
� Section Properties
33Ref: Cobiax Engineering Manual
Examples
� Flat plate - Voided slab system » Concrete properties
• 78 � �8;.�33 �8= � 150 ;.� } 33 4,000 �3,834,254psi
• Dynamic78 � 1.278 � 4,601,104psi �662,559,007psf
• Reduced 78 due to voids � 0.90 } 4,601,104 �4,140,994psi � 596,303,078psf
34
1/14/2015
Vibration of Concrete Floor Systems 18
Examples
� Flat plate - Voided slab system » Concrete properties
• Modulusofrupture�E � 4.5X �8= � 4.5 }1.0 4,000 � 284.6psi (accounts for shrinkage restraint)(1)
• Modularratio� � 7� 1.278⁄ �29,000,000 4,140,994 � 7.0⁄
• Poisson’s ratio � � 0.2 (conservatively takes into account dynamic effects)
35(1) ACI Structural Journal 105(4):498-506 (2008)
Examples
� Flat plate - Voided slab system » Effective and gross moments of inertia
• 9:|�g�:h � 0.79m +0.15(I e1 + I e2)(1)
• 9:|�g�:h � 143,751in.�• 9C|�g�:h � 266,936in.�• Crack coefficient
– �; � ;� ,��;N��,� � � 0.54
36(1) Fanella, D.A. 2011, Reinforced Concrete Structures – Analysis and Design, The McGraw-Hill Companies, NY
1/14/2015
Vibration of Concrete Floor Systems 19
Examples
� Flat plate - Voided slab system » Properties of voided slab
• Volumeofonesphericalvoid ��O
������������N
� �O };,�N�
;�.;N�N
� 0.854ft
• Concretedisplacement �volumeofonesphericalvoid }numberofvoidspersqft � 0.854 } 0.58 �0.50ft /ftN
37
Examples
� Flat plate - Voided slab system » Properties of voided slab
• Volumeofconcrete � ;�.�;N D 0.50 � 1.13ft /ftN
• Slabweight � 1.13 } 150 � 169.5psf• Deadloadreduction � ;�.�
;N } 150 D 169.5 �74.3psf
38
1/14/2015
Vibration of Concrete Floor Systems 20
Examples
� Flat plate - Voided slab system » Properties of voided slab
• Assuming an average void area in the slab of 70%:
– Averagedeadloadofslabwithvoids � ;�.�;N } 150 D
0.7 } 74.3 � 191.7psf• Total average weight of a panel �
� 191.7 } 40N � 306,720lbs
39
Examples
� Flat plate - Voided slab system » Properties of voided slab
• Mass � ��,�N�m N�m;N.� }��H N.N � 11,140lbsecN/ft
• W � ¡�¢¢£��� �
;;,;����H � 6.96slugs/ftN
40
1/14/2015
Vibration of Concrete Floor Systems 21
Examples
� Flat plate - Voided slab system » Natural frequency (1st Harmonic)
• �; � KHLQHNOℓQH
KQR@ST;NU ;VH
;/N(1)
• �; � N.;e�.;N6NO��H
�.��e���, � ,���6eQ¤.¥QH 6T;Ne�.��6 ;�.NH
;/N� 6.2Hz
– �N � 2.1 since the column is greater than 24 in.
– X;N � 7.12 from Table 4.1 for ℓ;/ℓN � 1.0
41(1) Blevins, R.D. 2001 “Formulas for Natural Frequency and Mode Shapes”Krieger Publishing Company, Malabar, FL
Examples
� SAFE Analysis of voided-slab (3-span)» ¨~0.17ªue�; � 5.9Hz ~ 5% error)
42
1/14/2015
Vibration of Concrete Floor Systems 22
Examples
� Voided slab system » Natural frequency (2nd Harmonic)
• �N � KHLHHNOℓQH
KQR@ST;NU ;VH
;/N
• �N � ;�.��.;N ∗ 6.2 � 13.8Hz
– �N � 2.1 since the column is greater than 24 in.
– XNN � 15.8 from Table 4.1 for ℓ;/ℓN � 1.0
43
Examples
� Voided slab system – Walking Excitation» Check acceptance criterion
•g¬C � ��: ®.T¥¯�
°± � g²C
– For office occupancy, � � 0.03 for offices that have some nonstructural components but no full-height partitions
•g¬C � ��: ®.T¥}³.H
�.� } ��,�N� ~0.001• �� � 0.10%� µ 0.50%� for office occupancies
44
1/14/2015
Vibration of Concrete Floor Systems 23
Examples
� Check walking acceptance criteria » Ok for office/residential application
45
Examples
� Voided slab system – Rhythmic Excitation» Check acceptance criterion
• Since �� x �� E:¶=·, implies that unacceptable vibrations are not expected due to rhythmic excitations
46
1/14/2015
Vibration of Concrete Floor Systems 24
Examples
� Voided slab system – Rhythmic Excitation» Highest harmonic causing resonance
• �� E:¶=· x � 1 � Kg² C⁄
¸M¹¬¹º
– �� �⁄ � 0.02– �� � weightofparticipants � 12.5psf– �» � 191.7 � 12.5 � 204.2psf– k=1.3fordancing
– k =2.0aerobicsorjumping
47
Acceptance Criteria
� Voided slab system – Rhythmic Excitation» Rhythmic excitation
48
Activity HarmonicForcing
Frequency �e¾¿6
Weight of Participants �� (psf)
Dynamic Coefficient
!Dancing 1 1.5 – 3.0 12.5 0.50Concert or sporting event
1 1.5 – 3.031.0
0.25
2 3.0 – 6.0 0.05
Aerobics or jumping
1 2.0 – 2.754.2
1.502 4.0 – 5.5 0.603 6.0 – 8.25 0.10
1/14/2015
Vibration of Concrete Floor Systems 25
Acceptance Criteria
� Voided slab system – Rhythmic Excitation» Criteria for dancing (1st harmonic)
» Criteria for aerobics (1st harmonic)
» Criteria for aerobics (2nd harmonic)
49
�; � 3 1 � ;. �.�N
�.�e;N.�6N��.N = 5.2 < 6.2 Hz (ok)
�; � 2.75 1 � N.��.�N
;.�e�.N6;��.� = 5.6 < 6.2 Hz (ok)
�N � 5.5 1 � N.��.�N
�.�e�.N6;��.� = 8.3 < 13.8 Hz (ok)
Examples
� Voided slab system – Design for Sensitive Equipment» Check acceptance criterion
• " � À¬ÁÂ�� � Limiting" � 1,000Äin./sec
• Δ� � Å�ÆuÇÈÉ�É��ÆÉÉʪ˪ÇÌÍÎÇÉÎ�ÈÇÆÉ�Í• %& � ÏÐd��N (basedon185lb personatvariouswalkingpaces)
50
Walking Pace
(steps/minute)'((lb)
�) � */,)
(Hz)
-.(lb
Hz2)
Fast (100) 315 5.0 25,000
Moderate (75) 280 2.5 5,500
Slow (50) 240 1.4 1,500
1/14/2015
Vibration of Concrete Floor Systems 26
Examples
� Voided slab system – Design for Sensitive Equipment» Check acceptance criterion
• Maximum deflection of floor system subjected to a unit concentrated load
• Rectangular plate of uniform thickness with simply supported edges with point load at geometric center
– Δ� ��ℓH
H ;VH
KQR@SiTOT
∑;
dTtanh�d D ¸n
Ò�¢ÓH ¸nÔdÕ;, ,�⋯
– �d � dON
ℓQℓH , ℓ; � ℓN
51
Examples
� Voided slab system – Design for Sensitive Equipment» Check acceptance criterion
• Series in this equation converges quickly– �d � ÌÏ/2– Series is equal to 0.72
• Δ� � �} ��};N H ;�.NH�.��}�,;��,���};�.�T}OT } 0.72 � 1.86 } 10�in./lb
52
1/14/2015
Vibration of Concrete Floor Systems 27
Examples
� Voided slab system – Design for Sensitive Equipment» Check acceptance criterion
• Slow walking pace
– " �;.��};�³};,���
�.N� 449Äin./sec
• Moderate walking pace
– " �;.��};�³}�,���
�.N� 1,649Äin./sec
• Fast walking pace
– " �;.��};�³}N�,���
�.N� 7,494Äin./sec
53
Case Study
� University of Wisconsin» Experimental measurement of vibration
properties of flat plate voided slab while building was under construction
54
1/14/2015
Vibration of Concrete Floor Systems 28
Case study
� Edge floor panel
55
Case study
� Impulsive loading and response
56
0.0278 g
-0.0205 g
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Acc
ele
rati
on
(g
)
Time (sec)
Impact
Lift Off
Signal NoiseVertical Offset
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0 0.5 1 1.5 2 2.5 3
Acce
lera
tion
(g)
Time (sec)
1/14/2015
Vibration of Concrete Floor Systems 29
Case study
57
� FFT of response
Case study
� Dominant modes from experiment» f1 ~ 12 Hz» f2 ~ 22 Hz» f3 ~ 35 Hz
� Conclusions» Experimental frequencies are higher than
approximate analysis:• Shorter (stiffer) spans • Small damping since building was under construction
58
1/14/2015
Vibration of Concrete Floor Systems 30
References
� CRSI Design Guide for Vibrations of Reinforced Concrete Floor Systems
� ATC Design Guide 1 “Minimizing Floor Vibration”
� Blevins “Formulas for Natural Frequency and Mode Shape”
� AISC DG 11 ‘Floor Vibrations Due to Human Activity”
60
Questions?