Mass Timber Floor Vibration

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1 Mass Timber Floor Vibration Adam Gerber, M.A.Sc. Disclaimer: This presentation was developed by a third party and is not funded by WoodWorks or the Softwood Lumber Board.

2 The Wood Products Council is a Registered Provider with The American Institute of Architects Continuing Education Systems (AIA/CES), Provider #G516. Credit(s) earned on completion of this course will be reported to AIA CES for AIA members. Certificates of Completion for both AIA members and non-aia members are available upon request. This course is registered with AIA CES for continuing professional education. As such, it does not include content that may be deemed or construed to be an approval or endorsement by the AIA of any material of construction or any method or manner of handling, using, distributing, or dealing in any material or product. Questions related to specific materials, methods, and services will be addressed at the conclusion of this presentation.

3 Course Description While the look of a building gets most of the attention, effective detailing has just as much impact on client satisfaction over the long term. This workshop brings together three experts to discuss areas of multi-family and commercial wood design where effective detailing techniques can improve performance and mitigate occupant complaints. First, a WoodWorks expert will discuss best practices for accommodating wood shrinkage with a focus on effective detailing at wood framing to finish interfaces. An acoustics expert will then discuss acoustical design in light-frame wood structures, with a focus on assembly options, detailing techniques, material selection and proper installation. Finally, a structural engineer with expertise in wood design will examine floor vibration design parameters and strategies that result in effective mass timber floor systems.

4 Learning Objectives 1. Provide basic understanding of structural dynamic properties of floors and key influencing parameters. 2. Be able to identify vibration prone structural configurations and details 3. Become familiar with analysis techniques and acceptance criteria for vibration performance of floors 4. Awareness of mitigation techniques and analysis tips & tricks

5 Agenda 1. Introduction to Floor Vibrations 2. Dynamic Characteristics of Conventional Framed Systems 3. Mass Timber Floors With Examples 4. Design & Analysis Suggestions

6 4 Things to remember 1. You can t have your cake and eat it too, if mass is there, you have to consider it. 2. Stiffness and mass are represented by the frequency. 3. Inherent damping is free, supplemental damping is expensive! 4. Every person will experience and judge a floor s performance differently!

7 1. Floor Vibrations

9 1.1 Sources of Vibration Human activity (eg. walking, jumping, dancing, etc.) Vibrating machinery (air conditioners, fans, etc.) External forces (eg. traffic, wind buffeting)

10 1.2 Top Complaints Bouncy floors Dishes rattling on hard surfaces Floors that squeak Sensitive equipment doesn t operate correctly

11 1.3 The SDOF Dynamic Problem M a(t) + C v(t) + K d(t) = F(t)

12 1.3 The SDOF Dynamic Problem M a(t) + C v(t) + K d(t) = F(t) M - Mass à slugs [kg] C Viscous Damping Coefficient à lb*s/in [N*s/m] K Spring Stiffness à lb/in [N/m] F Forcing Function à lb [N]

13 1.3 The SDOF Dynamic Problem M a(t) + C v(t) + K d(t) = F(t)! " = % & à rad/s ' " = ( ) *+ = % & à Hz,(.) = (!t) à lb [N]

14 1.3 The SDOF Dynamic Problem M a(t) + C v(t) + K d(t) = F(t) d(t) v(t) a(t)

15 1.4 The MDOF Dynamic Problem [M] a(t) + [C] v(t) + [K] d(t) = [F](t) [M] - Mass Matrix à slugs [kg] [C] Damping Matrix à lb*s/in [N*s/m] [K] Stiffness Matrix à lb/in [N/m] [F] Loading Matrix à lb [N]

16 1.4 The MDOF Dynamic Problem [K] Stiffness Matrix à lb/in [N/m]

17 1.5 Modal Analysis For Floor Vibrations CCIP-016 (2006)

18 1.5 Modal Analysis For Floor Vibrations CCIP-016 (2006)

19 1.5 Modal Analysis For Floor Vibrations The MDOF dynamic problem becomes a series of SDOF dynamic problems! M a(t) + C v(t) + K d(t) = F(t) M - Modal Mass à slugs [kg] C Modal Damping à lb*s/in [N*s/m] K Generalized Stiffness à lb/in [N/m] F Forcing Function à lb [N] CCIP-016 (2006)

20 1.5 Modal Analysis For Floor Vibrations The MDOF dynamic problem becomes a series of SDOF dynamic problems! M 1 a(t) + C 1 v(t) + K 1 d(t) = F 1 (t) M 1 - Mode 1 Mass à slugs [kg] C 1 Mode 1 Damping à lb*s/in [N*s/m] K 1 Mode 1 Generalized Stiffness à lb/in [N/m] F 1 Forcing Function à lb [N] *REMEMBER -! " = % " &' = ( ) à Hz (ie. every mode has a natural frequency and one or more locations of maximum response associated with that mode) CCIP-016 (2006)

21 1.6 Humans as Forcing Functions M a(t) + C v(t) + K d(t) = F(t) T = 0.85s f w = 1/T = 1.2 Hz T = 0.6s f w = 1/T = 1.7 Hz T = 0.45s f w = 1/T = 2.2 Hz T = 0.35s f w = 1/T = 2.8 Hz CCIP-016 (2006)

22 1.7 Dynamic Response to Footfall T = 0.6s f w = 1/T = 1.67 Hz M a(t) + C v(t) + K d(t) = F(t) F(t) Damped Response at Resonance! " = % & '( = ) * à Hz CCIP-016 (2006)

23 1.7 Dynamic Response to Footfall M a(t) + C v(t) + K d(t) = F(t) Frequency Response Function (FRF) Damped Response at Resonance CCIP-016 (2006)

24 1.7 Dynamic Response to Footfall Frequency Response Function (FRF) 1 st Harmonic! "#$ & = " * + - *, à frequency ratio for first four harmonics of first mode. Does mode 1 have a natural frequency that matches a harmonic of the possible walking frequencies? Example:. $ = Harmonic Range of i*f w Matched f w r i 2 nd Harmonic 3 rd Harmonic 4 th Harmonic I = *1.5 = 1.5 Hz 4.0 I = *1.5 = 3.0 Hz 4.0 I = *2.0 = 6.0 Hz 3.0 I = *1.5 = 6.0 Hz 4.0 CCIP-016 (2006)

25 1.8 Human Perception SCI-P354 (2010)

26 1.8 Human Perception a(t) RMS AISC Design Guide 11 (2016)

27 1.8 Human Perception AISC Design Guide 11 (2016)

28 1.8 Human Perception AISC Design Guide 11 (2016)

29 1.8 Acceptance Criteria AISC Design Guide 11 (2016)

30 2. Dynamic Properties of Framing Systems

2.1 CIP Concrete Structures Mass 100 150 psf floor weight [heavy] Damping 1-5% of critical Stiffness E c_dynamic = 1.

unfavorable effect of lowering fundamental frequency ' ( $ ) Damping in similar range to other construction types.

31 2.1 CIP Concrete Structures Mass psf floor weight [heavy] Damping 1-5% of critical Stiffness E c_dynamic = 1.35*E c 2-way action General Observations: High dead load has favorable effect of reducing accelerations W $ % & but unfavorable effect of lowering fundamental frequency ' ( $ ) Damping in similar range to other construction types. Increased dynamic modulus of concrete has favorable effect of reducing accelerations ' ( * Not typically prone to complaints of disturbing floor vibrations

2.2 Steel & Composite Structures Mass 50 100 psf floor weight [moderate] Damping 0.5-5% of critical Stiffness E c_dynamic = 1.

32 2.2 Steel & Composite Structures Mass psf floor weight [moderate] Damping 0.5-5% of critical Stiffness E c_dynamic = 1.35*E c Depends on framing sizes and layout General Observations: Dead load has favorable effect of reducing accelerations W $ but unfavorable effect of lowering fundamental % & frequency ' ( $ ). The governing requirements (more or less weight) depends on ' (. Ranges from very lightly damped (high probability of resonance) to moderately damped Increased dynamic modulus of concrete has favorable effect of reducing accelerations ' ( +, =, +, à à flexibility in the system (eg. girders vs. walls) ALWAYS reduces your fundamental frequency! 2 Vibration problems in light weight composite structures are generally well understood and designed for.

2.3 Light Wood Frame Mass 10 40 psf floor weight [lightweight] Damping 2-12% of critical Stiffness Depends on framing sizes and layout General Observations: Dead load has favorable effect of reducing

33 2.3 Light Wood Frame Mass psf floor weight [lightweight] Damping 2-12% of critical Stiffness Depends on framing sizes and layout General Observations: Dead load has favorable effect of reducing accelerations W $ but unfavorable effect of lowering fundamental % & frequency ' ( $ ). Typically the dead load is insufficient to reduce accelerations adequately on a low frequency floor. Ranges from lightly damped to heavily damped (depends on fit out, joist bridging, partitions, M&E, ceiling etc.) + = à,, -, /, -, 1 à flexibility in the system (eg. beams vs. walls) ALWAYS reduces your fundamental frequency! 1 Vibration problems in light wood frame structures are generally poorly understood but adequate designs are still often achieved due to industry sponsored research and software tools, as well as inherent redundancy and relatively large damping values.

34 2.4 Mass Timber & Hybrid Systems Typical Mass Timber Materials: Cross Laminated Timber Nail/Dowel Laminated Timber Glue-laminated Timber Mass Plywood Panels Mass LSL panels

35 2.4 Mass Timber & Hybrid Systems Mass psf floor weight [lightweight ish] Damping 1-6% of critical Stiffness Depends on framing sizes and layout General Observations: Dead load has favorable effect of reducing accelerations W $ but unfavorable effect of lowering fundamental frequency % & ' ( $ ). At low end, dead load is insufficient, however at high end of range, may be sufficient to reduce accelerations on a low frequency floor. Ranges from lightly damped to moderately damped (depends on fit out, M&E, support conditions, partitions, etc.) + = à,, -, /, -, 1 à flexibility in the system (eg. beams vs. walls) ALWAYS reduces your fundamental frequency! 1 There is general awareness of vibration problems in mass timber structures, but little direct guidance. CLT Design Guide, FPInnovations/CSA-086 formulae inadequate to address range of design scenarios and are potentially misleading regarding their scope of application.

36 3. Mass Timber Vibration Design

37 3.1 MT Panels on MT Walls Typical Design Process Span: 20 D: 40 psf (self-weight + topping) SDL: 20 psf (partition load) L: 40 psf 1.2D + 1.6L = 136 psf Deflection Limits: "" = $% " ()* = 1/2" _567 = 89" : ;)( << = 2.88?10 ) AB DE F /GH % = I J5 "% + $% L 240 = 1" _567 = 5OL( 384 % = 576?10 S AB DE F /GH

38 3.1 MT Panels on MT Walls If we make 2-span continuous: = single = : 455 ; < = 336 x CD < /BF _HIJ = 239 x CD < /BF

39 3.1 MT Panels on MT Walls Typical Design Process Span: 20 D: 40 psf (self-weight + topping) SDL: 20 psf (partition load) L: 40 psf 1.2D + 1.6L = 136 psf Deflection Limits: "" = $% " ()* = 1/2" _567 = 89" : ;)( << = 2.88?10 ) AB DE F /GH % = I J5 "% + $% L 240 = 1" _567 = 5OL( 384 % = 576?10 S AB DE F /GH TUV = 356 x 10 S ABG DE F /GH

40 3.1 MT Panels on MT Walls Typical Design Process Span: 20 D: 40 psf (self-weight + topping) SDL: 20 psf (partition load) L: 40 psf 1.2D + 1.6L = 136 psf Strength Requirements:! " = $ % &' ( = "0/"0 2 " = " 8 = "/"0

41 3.1 MT Panels on MT Walls! " # $%% = 4675,-..0/.0

42 3.1 MT Panels on MT Walls Typical Design Process Span: 20 D: 40 psf (self-weight + topping) SDL: 20 psf (partition load) L: 40 psf 1.2D + 1.6L = 136 psf Strength Requirements (NDS 2015):! " = 6800 ()" "+/"+ -. / = -. / λ = BC/BC D " = 1700 ()"/"+ - G H. JI 2 = -G H. 011 JI = 3 5 = 3 6 =1.0 λ = 0.8

43 3.1 MT Panels on MT Walls Typical Design Process Span: 20 D: 40 psf (self-weight + topping) SDL: 20 psf (partition load) L: 40 psf 1.2D + 1.6L = 136 psf Verify Vibration Performance:???

44 3.1 MT Panels on MT Walls Typical Design Process Span: 20 D: 40 psf (self-weight + topping) SDL: 20 psf (partition load) L: 40 psf 1.2D + 1.6L = 136 psf Verify Vibration Performance: 1. Consult Manufacturer s Literature

46 3.1 MT Panels on MT Walls Verify Vibration Performance: 1. Consult Manufacturer s Literature

48 Hz 0.01 in ft

49 Limitations of the Simplified Method: 1. Bare floors with finishing, partitions and furniture, but without heavy topping. 2. Vibrations are induced by normal walking 3. Well supported floors** 4. Well-jointed CLT panels 5. Inclusion of the self-weight of CLT panels only (ie. without live load) Vibration Controlled Span for our Design Scenario:! 18.7 () (US CLT Handbook)! 17.5 () (CSA permits 20% increase for continuous span à +,-./)! 16.8 () (Manufacturer s literature implies > 20ft for double span)

50 3.2 Post & Beam Configurations Typical Design Process Span: 20 x 30 grid D: 40 psf (self-weight + topping) SDL: 20 psf (partition load) L: 40 psf 1.2D + 1.6L = 136 psf Deflection Limits For Beams: "" = $% " ()* = 3/4" = 56" 7 8)( 99 = CD E % = F G2 "% + $% I 240 = 1.5" = 5LI( 384 % = CD E Try 8.5 x f-1.8E Glulam

51 3.2 Post & Beam Configurations Typical Design Process Span: 20 x 30 grid D: 40 psf (self-weight + topping) SDL: 20 psf (partition load) L: 40 psf 1.2D + 1.6L = 136 psf Strength Requirements (NDS 2015):! " = $ % &' ( = / "1 = 2612 psi = & %9 5 : 5 ; λ = BCCD EFG H " = $ % & I = 40.8 kip = 229 psi = JK λ = CMN EFG 5 6 = 5 7 = 5 & = 5 %9 = 5 : = 5 ; = 5 JK = =0.83 λ = 0.8

52 3.2 Post & Beam Configurations Verify Vibration Performance: Remember Limitations of the Simplified Method: 1. Bare floors with finishing, partitions and furniture, but without heavy topping. 2. Vibrations are induced by normal walking 3. Well supported floors 4. Well-jointed CLT panels 5. Inclusion of the self-weight of CLT panels only (ie. without live load)

53 3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical) AISC Design Guide 11 (2016)! " - what is the system natural frequency!!

54 3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical)! " - what is the system natural frequency!! AISC Design Guide 11 (2016)

55 1.7 Dynamic Response to Footfall T = 0.6s f w = 1/T = 1.67 Hz M a(t) + C v(t) + K d(t) = F(t) F(t) Damped Response at Resonance! " = % & '( = ) * à Hz CCIP-016 (2006)

56 3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical)! " - what is the system natural frequency!! Dead Loads: CLT conc. topping 34.2 psf Mechanical and Ceiling Installations 4 psf Superimposed Live Loads (Electronic Office) 6 psf AISC Design Guide 11 (2016)

57 3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical)! " - what is the system natural frequency!! Effective Panel Weight, W (4.1.2 DG 11) # = %&' B = effective panel width (ft) L = member span (ft) w = supported weight per unit area (psf) AISC Design Guide 11 (2016)

58 3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical)! " - what is the system natural frequency!! # $%& = ) $%& *+,--_/0 *+,--_ $%& 2 3!899: ;<=>h ) $%& = 2.0 (>CD<EF8 GH8IJJ DF:F88I8 >9!:II I=KI) 4 $%& = 20!> JDFH 8IHK>h # $%& = 2.0 M1 NON P Q 20!> = ST. UVW 60!> AISC Design Guide 11 (2016)

59 3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical)! " - what is the system natural frequency!! # $%& = ( * $%& + $%& =,-,,// 123 ( = 44 psf * $%& =,8. :3; + $%& =,/ 3; AISC Design Guide 11 (2016)

60 3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical)! " - what is the system natural frequency!! )* +,,_. # $% = ( $% )* $% 2 /0% / $% 2 3!899: 8;<=>h ( $% = ** / $% = 30!> FGH< 8;<=>h # $% = 1.8 IJIK3.L M.N3K3. L O P 30!> = RS TU 53.33!> AISC Design Guide 11 (2016)

61 3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical)! " - what is the system natural frequency!! # $% = ' ) $% * $% = +,,./0 234 ' = (44 + 3) psf (add self-weight of beam) ) $% =./4J * $% =.0 4J AISC Design Guide 11 (2016)

3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical)! " - what is the system natural frequency!

62 3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical)! " - what is the system natural frequency!! # = Δ '() Δ +( # Δ '() + Δ '() + # +( Δ '() + Δ +( +( Δ '() = Δ +( = # = , ,340 = 78, 998 :;< AISC Design Guide 11 (2016)

63 3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical)! " - what is the system natural frequency!! β = $. $&' (&. '%) AISC Design Guide 11 (2016)

64 3.2 Post & Beam Configurations We need to know: W what is the Modal Mass (aka Participating Mass) β what is the damping (in percent of critical)! " - what is the system natural frequency!!! #$% = 0.18, -./0 = ! 7$ = 0.18, - 8/ = ! :;:<=> = 0.18? Δ #$% + Δ 7$ = B. C3 56 AISC Design Guide 11 (2016)

65 3.2 Post & Beam Configurations Compare with Acceptance Criteria:! " # = & '()* +' ! ' # 9 : ; = ;B9CDEF) H : = 65 lbf A MNMO(P = 3.74 TU β = (2.5% XBDEDX9Y) Z = Y\A 9 * ; = ]. ]^_` AISC Design Guide 11 (2016)

66 Hz 0.01 in ft

67 3.3 System Comparison Verify Vibration Performance: Remember Limitations of the Simplified Method: 1. Bare floors with finishing, partitions and furniture, but without heavy topping. 2. Vibrations are induced by normal walking 3. Well supported floors 4. Well-jointed CLT panels 5. Inclusion of the self-weight of CLT panels only (ie. without live load, also neglects topping weight)

68 3.3 System Comparison Compare MT panels on MT walls with DG 11 Acceptance Criteria:! " # = & '()* +' ! ' #! ' # = (0.5% =>?@ABCDE) G H = 65 lbf > MNO = 8. 32ST β = (2.5% V@CDCVAW) X = X MNO = 8465 WZ> ([\] ^_W> `_C?hD =bwe) A *? = c. cde AISC Design Guide 11 (2016)

69 3.3 System Comparison Compare MT panels on MT walls with DG 11 Acceptance Criteria:! " # = & '()* +' ! ' #! ' # = (0.5% =>?@ABCDE) G H = 65 lbf > MNO = PP. QR ST β = (2.5% W@CDCWAX) Y = Y MNO = 8465 X\> (]^_ `ax> bac?hd =dxe) A *? = e. eer AISC Design Guide 11 (2016)

70 3.3 System Comparison Compare MT panels on MT walls with DG 11 Acceptance Criteria:! " # = & '()* +' ! ' #! ' # = (0.5% =>?@ABCDE) G H = 65 lbf > MNO = 8.32 ST β = V. VWX (8.5% Y@CDCYAZ) [ = [ MNO = 8465 Z]> (^_` abz> cbc?hd =eze) A *? = V. VVX AISC Design Guide 11 (2016)

$@ABCDE) G H = 65 lbf > MNO = 8.32 ST β = 0.025 (2.5% V@CDCVAW) X = X MNO = YZ, \Z] ^_` (abc + D=eeCf? & hib) A *? = ]. ]]j 0.$

71 3.3 System Comparison Compare MT panels on MT walls with DG 11 Acceptance Criteria:! " # = & '()* +' ! ' #! ' # = (0.5% =>?@ABCDE) G H = 65 lbf > MNO = 8.32 ST β = (2.5% V@CDCVAW) X = X MNO = YZ, \Z] ^_` (abc + D=eeCf? & hib) A *? = ]. ]]j AISC Design Guide 11 (2016)

72 4. Design & Analysis Suggestions

73 4.1 MT Vibration Analysis Flow Chart

74 4.1 MT Vibration Analysis Flow Chart

75 4.1 MT Vibration Analysis Flow Chart

76 4.1 MT Vibration Analysis Flow Chart

77 4.2 Insights from FEM General: Unique structural dynamic model is required with special consideration of the following: boundary conditions (take advantage of continuity and supports that can be considered rigid under small amplitude vibrations) loads applied to floor (is an appropriate mass being used to determine fundamental frequency and resulting accelerations?) extent of modeled area (is an appropriate mass being represented for the area under consideration?) Appropriate material properties (weights, dynamic modulus, etc.) Time History and FRF Analysis is very location specific, so be sure that you are capturing a representative design scenario. Response Spectrum Methods are powerful and generally conservative but remain sensitive to user inputs and appropriate modeling (eg. Damping)

78 4.3 Mitigation Techniques Mass: Can you activate more mass? Can you add mass without making system more susceptible to vibrations? Stiffness: Adjust panel and beam spans! # $ à most efficient Increase timber element depth! % & à next most efficient Account for fixity from reliable sources of support (eg. façade connections) Damping: Only efficient at significant levels of damping

79 4.3 Mitigation Techniques What if you could add stiffness AND mass?...

80 4.3 Mitigation Techniques Timber Concrete Composites

81 4.3 Mitigation Techniques Continuous Bonded Systems

82 Further Resources

83 US CLT Handbook AISC Design Guide 2nd Edition (2016) CCIP-016 (2006) SCI-P354 (2009) HIVOSS (2007) CSA-086 (2014) EN 1995 design of timber structures (Eurocode 5) à See also supplier specific documents and white papers

84 Questions? This concludes The American Institute of Architects Continuing Education Systems Course Adam Gerber ASPECT Structural Engineers This presentation was developed by a third party and is not funded by WoodWorks or the softwood lumber check-off.

85 TCC Economics

25/01/2013. Agenda. Advanced Approaches to Modeling and Assessment of Floors for Control of Human Activity. Ultra-Low Vibration Environments

25/01/2013. Agenda. Advanced Approaches to Modeling and Assessment of Floors for Control of Human Activity. Ultra-Low Vibration Environments // Advanced Approaches to Modeling and Assessment of Floors for Control of Human Activity Brad Pridham, Ph.D., P.Eng. February, Finite Element Modeling Application Example Air Quality Wind & Climate Sound,