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Control of floor vibration
Allen, D. E.; Pernica, G.
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NRC Publications Record / Notice d'Archives des publications de CNRC:
https://nrc-publications.canada.ca/eng/view/object/?id=7b6ad912-cd8f-4e22-b0de-e80842f6c5a5 https://publications-cnrc.canada.ca/fra/voir/objet/?id=7b6ad912-cd8f-4e22-b0de-e80842f6c5a5b y D.E. A lle n a nd G. Pe rnica
Excessive floor vibration has become a greater problem as new rhythmic
activities, such as aerobics, and long-span floor structures have become
more common. This Update describes the nature of floor vibration and
provides options for avoiding it through design, or in the case of existing
buildings, reducing or eliminating it through alterations.
C o n s t r u c t i o n T e c h n o l o g y U p d a t e N o . 2 2
Floor vibration is u p -an d -d ow n m otion cau sed by forces ap p lied d irectly to th e floor by p eop le or m ach in ery, or by vibration tran sm itted th rou gh bu ild in g colu m n s, from oth er floors or from th e grou n d .
Th e p roblem s associated w ith floor vibra-tion are n ot n ew. In 1828 Tred gold w rote “gird ers sh ou ld alw ays be m ad e as d eep as th ey can to avoid th e in con ven ien ce of n ot bein g able to m ove on th e floor w ith ou t sh akin g everyth in g in th e room .”1 A sim p le floor d eflection criterion (d eflection of less than span/360 under distributed live load) has been u sed to con trol ‘excessive sh akin g’ for m ore th an 100 years. Bu t tod ay, w h en lon ger sp an s, th in n er floor d ecks, less stru ctu ral d am p in g (an absen ce of m aterials an d com -p on en ts th at absorb vibration en ergy), or th e use of buildings for activities such as aerobics are resp on sible for vibration p roblem s, th is ap p roach d oes n ot w ork. How ever, n ew gu id elin es th at ad d ress an d d eal w ith th ese p roblem s — based on w h at p eop le p erceive an d fin d accep table in term s of floor vibra-tion — h ave recen tly been in trod u ced .
Vibra t ion Lim it s
Floor vibration gen erally m akes p eop le u n easy an d creates fear of stru ctu ral collap se, alth ou gh su ch fear is u su ally u n w arran ted becau se of th e sm all d isp lacem en ts an d stresses th at are actu ally p rod u ced . Never-th eless, p ercep tible vibration is u su ally con sid ered to be u n d esirable becau se it affects p eop le’s sen se of w ell bein g an d th eir ability to carry ou t tasks.
Vibration lim its, or accep table th resh old s, are best exp ressed in term s of acceleration , as a p ercen tage of th e acceleration d u e to gravity (g). Th e lim it d ep en d s p rim arily on th e con text, th at is, on w h at p eop le are d oin g w h en th ey exp erien ce th e vibration . For exam p le, p eop le sittin g or lyin g d ow n in offices or resid en ces fin d d istin ctly p ercep tible vibration (acceleration s of abou t 0.5% g) u n accep table, w h ereas th ose takin g part in an activity such as aerobics will accept much greater vibration (about 10% g). People d in in g besid e a d an ce floor or stan d in g in a sh op p in g m all w ill fin d vibration s th at fall betw een th ese tw o extrem es (abou t 2% g) accep table.
Gen erally, it is n ot th e p articip an ts in a p articu lar activity or even t w h o are m ost d istu rbed by floor vibration , bu t th ose w h o are located in ad jacen t sp aces, as th ey fin d it annoying or disruptive to their own activities.
If th e vibration is very large (m ore th an 20% g), an d occu rs frequ en tly (e.g., in a h ealth clu b), th en fatigu e failu re of th e floor can occu r. To p reven t collap se d u e to fatigu e or overload in g, th e Nation al Bu ild in g Cod e of Can ad a (NBC) requ ires a d yn am ic an alysis of a floor stru ctu re if it h as a n atu ral frequ en cy of less th an 6 Hz.2
Control of Floor Vibration
2
Princ ipa l Ca use
Th e m ain factor u n d erlyin g m ost vibration p roblem s is reson an ce, w h ich occu rs w h en a load is exerted on a floor at a p articu lar frequ en cy. For exam p le, a grou p of p eop le dancing applies a cyclic force (their footsteps) to th e floor at th e frequ en cy corresp on d in g to th e beat of th e m u sic (see Figu re 1). Th e cyclic force p rod u ces a m axim u m floor acceleration , w h ich d ep en d s on th e ratio of th e n atu ral frequ en cy of th e floor stru ctu re to th e cyclic frequ en cy of th e ap p lied force (see Figu re 2). Wh en th e n atu ral frequ en cy of th e floor coin cid es w ith , or is close to, th e forcin g frequ en cy, reson an ce occu rs an d th e con sequ en ces are m ost severe. Du rin g each cycle of load in g, m ore en ergy is fed in to th e system an d th e m agn itu d e of vibra-tion grow s, u n til a m axim u m is reach ed . Th is m axim u m is d ep en d en t on th e am ou n t of d am p in g in th e floor.
Du rin g an y rh yth m ic activity, p eop le ap p ly rep eated forces to th e floor, ran gin g from 2 to 3 Hz. (Th is frequ en cy is kn ow n as th e step frequ en cy). For d an cin g, reson an ce occu rs if th e n atu ral frequ en cy of th e floor is betw een 2 an d 3 Hz.
If th e rep eated force h as an im p act com p o-nent, as is the case for aerobics in which every-one ju m p s at th e sam e tim e (see Figu re 1), th en reson an ce can occu r n ot on ly at th e step frequ en cy, bu t also at m u ltip les, or h ar-m on ics, of th is frequ en cy. For exaar-m p le, an aerobics class ju m p in g to a beat of 2.5 Hz (th e step frequ en cy) w ill p rod u ce h arm on ic vibration s at m u ltip les of 2.5 Hz — i.e., at 2.5 Hz (first h arm on ic), 5 Hz (secon d h ar-m on ic), an d 7.5 Hz (th ird h arar-m on ic). Sin ce th e n atu ral frequ en cies of m ost floors are greater th an 3 Hz (th ey often fall betw een 4 Hz an d 8 Hz), p roblem s are m ost likely to occur as a result of the second and third har-monics. However, the lower the harmonic the larger th e vibration p rod u ced by reson an ce. Rhythmic Activities
Vibration p roblem s d u e to rh yth m ic activities occu r in stad iu m s, au d itoriu m s, bu ild in gs w ith d an ce an d h ealth clu bs, an d con ven tion cen tres, w h ich are u sed for a w id e variety of activities.
Becau se of th e large forces gen erated by rh yth m ic activities, reson an ce vibration is gen erally too large to be accep table. To con trol floor vibration d u e to a rh yth m ic activity, th e floor stru ctu re m u st be d esign ed to h ave a n atu ral frequ en cy greater th an th e forcin g frequ en cy of th e h igh est sign ifican t h arm on ic, as sh ow n in Figu re 2. Min im u m accep table n atu ral frequ en cies are p rovid ed in Table 1 for several com bin ation s of activ-ities an d floor con stru ction s.
For d esign p u rp oses, th e n atu ral floor frequ en cy (fn in Hz) can be estim ated u sin g a sim p le form u la,
w h ere ∆ is th e total d eflection of th e floor stru ctu re d u e to th e w eigh t su p p orted by all its m em bers (joists, gird ers an d colu m n s). For exam p le, if th e floor d eflects 9 m m , th e n atu ral frequ en cy is 6 Hz. To get a n atu ral frequ en cy of 9 Hz, th e floor m u st d eflect on ly 4 m m , w h ich is p ractically im p ossible for floors su p p orted on very lon g m em bers to ach ieve. (See Referen ces 2–4 for m eth od s of calcu latin g n atu ral frequ en cy an d floor acceleration .)
Th e p rim ary factors affectin g th e d esign of floor stru ctu res for rh yth m ic activities are: Span. Th e lon ger th e floor sp an th e low er th e n atu ral frequ en cy. Con ven tion cen tres, in p articu lar, h ave very lon g floor sp an s (ap p roxim ately 30 m ). It is gen erally n ot p ractical to d esign su ch floor stru ctu res to ach ieve th e m in im u m n atu ral frequ en cy
Rh yth m ic Activity Steel/ Con crete Floor Ligh t-Fram e Floor Dan cin g an d Din in g 5 10
Aerobics 9 13
Table 1.Minimum Floor Frequencies (Hz) for Typical Activities and Floor Constructions
Figure 2.Floor acceleration due to a cyclic force for a range of natural frequencies
fn (Hz) = 18
sh ow n in Table 1 for rh yth m ic activities th at h ave im p act (e.g., aerobics). In th is situ ation , th e ch oice is to relocate eith er th e rh yth m ic activity (to a stiffer floor) or th e sen sitive occu p an ts.
Storey height. Th e taller th e colu m n s su p p ortin g th e floor on w h ich th e rh yth m ic activity takes p lace th e low er th e n atu ral frequ en cy of th e floor. An exam p le of th is occu rred w h en aerobics on th e top storey of a 26-storey bu ild in g cau sed secon d h arm on ic reson an ce d u e to th e axial flexibility of th e columns. This resonance produced annoying vibration s of ap p roxim ately 1% g in th e offices below. Becau se th e aerobics activity cou ld n ot be relocated in th e bu ild in g, it h ad to be term in ated .
Selectin g th e location for a rh yth m ic activity (i.e., storey, floor area, etc.) is th ere-fore th e m ost im p ortan t con sid eration in th e d esign of floors. Prop erly p osition in g sen sitive occu p an cies relative to rh yth m ic activities is also im p ortan t. See th e “Measu res to Rem ed y Vibration Problem s” section of th is Up d ate for gu id an ce. Walking Vibration
Walkin g vibration , w h ich is largely d ep en -d en t on th e typ e of floor con stru ction , is also an im p ortan t con sid eration in th e d esign of floor stru ctu res of m ost bu ild in gs. S te e l/Concre te Floor Construction
A steel floor w ith a con crete d eck u su ally h as a n atu ral frequ en cy of betw een 3 Hz an d 10 Hz. A p erson w alkin g across a floor ap p lies a force at a step frequ en cy of ap p rox-im ately 2 Hz, w h ich can resu lt in reson an ce bu ild -u p w h en th e n atu ral floor frequ en cy is arou n d 2, 4, 6 or 8 Hz. As for p reviou sly m en tion ed activities, th e h igh er th e h arm on ic th e low er th e m agn itu d e of reson an ce.
A d esign criterion h as recen tly been d ev-elop ed3in w h ich th e acceleration d u e to h ar-m on ic reson an ce is calcu lated an d coar-m p ared w ith a vibration lim it, e.g., 0.5% g, for office an d resid en tial occu p an cies. If th e lim it is exceed ed , d esign alteration s can in clu d e: Increased damping. Dam p in g of th e floor system (in creasin g th e rate of rem oval of vibration al en ergy) red u ces reson an ce vibra-tion (see Figu re 2) an d th u s an n oyan ce. It d ep en d s p rim arily on th e p resen ce of n on -stru ctu ral com p on en ts su ch as p artition s, ceilings, mechanical services and furnishings. Fu ll-h eigh t p artition s are m ost effective in ad d in g d am p in g to th e floor system .3
Increased stiffness. Th is raises th e n atu ral frequ en cy of th e floor, sh iftin g reson an ce to a h igh er h arm on ic, w h ich red u ces th e m ag-n itu d e of resoag-n aag-n ce vibratioag-n aag-n d h eag-n ce an n oyan ce. Stiffen in g m eth od s in clu d e in creasin g floor m em ber d ep th s an d en su r-in g th at th ere is com p osite action betw een th e beam s an d th e con crete slab.3
In th e case of solid con crete floors, w h ich h ave h igh m ass an d stiffn ess, w alkin g vibration is rarely a p roblem . Som e p recast con crete floor system s m ay, h ow ever, requ ire evalu ation .4
Light-Fra m e Construction
Ligh t-fram e floors of w ood or cold -form ed steel joists w ith a w ood d eck typ ically h ave floor frequ en cies of betw een 10 Hz an d 30 Hz. Som eon e w alkin g across a floor can be a sou rce of an n oyan ce to a p erson sittin g in a room becau se of th e jolts cau sed by su d -d en ch an ges in floor elevation p ro-d u ce-d by each footstep .
Design con sid eration s for ligh t-fram e con stru ction in clu d e:
Stiffening. Th e actu al stiffn ess of a ligh t-fram e floor d ep en d s n ot on ly on th e stiffn ess of th e joists bu t also on th e tran sverse stiffn ess of th e floor system (from floor d eck, cross brid gin g, blockin g, etc.) an d on th e com p osite action of th e joists an d d eck. In creasin g floor stiffn ess red u ces th e jolts d u e to w alkin g.
Deflection criterion. Wh en w alkin g vibra-tion is likely to be an issu e, e.g., in a h ou se or m u lti-fam ily d w ellin g, ligh t-fram e floors sh ou ld be d esign ed to m eet th e d eflection criterion for a 1 kN con cen trated force (as sh ow n in Figu re 3). Th is d ecrease in allow able d eflection w ith in crease in sp an is d u e to a n u m ber of factors d escribed in Referen ce 4.
Th e m ost p ractical ap p roach for d esign in g ligh t-fram e floors to m in im ize th e effects of w alkin g is to d evelop sp an tables based on calculations that satisfy the Figure 3 criterion, e.g., th ose con tain ed in Part 9 of th e NBC. To evalu ate floor system s n ot covered by th e NBC sp an tables, see Referen ce 4.
M e a sure s t o Re m e dy Vibra t ion Proble m s
Th ere are a w id e variety of action s th at can be taken to correct floor vibration p roblem s in existin g bu ild in gs. Th ese action s can be categorized as follow s:
Damping. For steel/ con crete con stru ction , w alkin g vibration s can be im p roved by in creasin g th e am ou n t of d am p in g of th e floor system . Th e less d am p in g th ere is in th e existin g floor, th e m ore effective th e ad d ed d am p in g. Th e ad d ition of n on stru c-tu ral com p on en ts th at in teract w ith th e floor structure, such as drywall in the ceiling space, p rovid es som e d am p in g if th ere is little to begin w ith . Th ere are also oth er d am p in g d evices, su ch as d am p er p osts or tu n ed m ass d am p ers, th at can be effective in red u cin g floor vibration .3
Isolation. An effective m eth od for red u cin g floor vibration d u e to m ach in ery is to isolate th e m ach in e from th e floor by p lacin g it on soft sp rin gs.3,4
Sum m a ry
Most floor vibration p roblem s are cau sed by reson an ce an d , for ligh t-fram e con stru ction , sudden deflections due to footsteps. Vibration can usually be controlled by stiffening the floor stru ctu re, alth ou gh som etim es th e p roblem s can be ad d ressed by ad d in g d am p in g or by isolatin g equ ip m en t. Prop er p lacem en t of an activity (e.g., aerobics) or m ach in ery in th e bu ild in g is th e m ost im p ortan t con sid eration .
Re fe re nc e s
1. Tred gold , T., 1824, Elem en tary Prin cip les of Carp en try, 2n dEd ., Pu blish er u n kn ow n . 2. User’s Gu id e — NBC 1995 Stru ctu ral
Com m en taries (Part 4). Com m en tary A: Serviceability Criteria for Deflection s an d Vibration s.
3. AISC/ CISC Steel Design Gu id e Series No. 11: Floor Vibration s Du e to Hu m an Activity. Am erican In stitu te of Steel Con stru ction , Ch icago, Ill., 1997. 4. ATC Gu id e on Floor Vibration . Ap p lied
Tech n ology Cou n cil. Red w ood City, CA, 1999.
Dr. D.E. A lle n is a gu est research officer in th e Bu ild in g En velop e an d S tru ctu re Program at th e N ation al Research Cou n cil’s In stitu te for Research in Con stru ction .
Dr. G. Pe rnica is a research officer with IRC’s Bu ild in g En velop e an d S tru ctu re Program . Reduction of effects. It m ay su ffice to d o n oth in g abou t th e floor vibra-tion itself, bu t rath er to m ake alteration s th at red u ce th e an n oyan ce associated w ith th e vibration . Th ese in clu d e th e elim in ation of n oise (e.g., rattlin g) d u e to floor vibration , an d rem ovin g or rearran gin g articles th at vibrate n oticeably. Relocation of activities. Eith er th e sou rce of vibration (e.g., aerobics or m ach in ery) or th e sen sitive occu p an cy m ay be relocated . For exam p le, a p lan n ed aerobics exercise area m igh t be relocated from th e top floor of a bu ild in g to th e grou n d or first floor. Com p lain ts of w alkin g vibration can som e-tim es be resolved by relocatin g p eop le, or equ ip m en t, to areas w h ere vibration is less likely to occu r, e.g., p lacin g th em n ear a colu m n .
Stiffening. In creasin g th e stiffn ess of th e floor can red u ce vibration d u e to w alkin g or oth er rh yth m ic activities. In trod u cin g n ew colu m n s betw een existin g colu m n s from th e affected floor d ow n to th e fou n d ation s is very effective in th e case of flexible floor stru ctu res, bu t is often u n accep table to th e ow n er. If th ere is su fficien t ceilin g sp ace, w eld in g n ew com p on en ts to th e bottom flan ges of steel beam s or joists (as sh ow n in Figu re 4) is an effective tech n iqu e.3 Ligh t-fram e floors can be stiffen ed by ad d in g tran sverse stiffen in g, su ch as d eckin g or blockin g.4 How ever, it is im p ortan t to d eterm in e w h eth er th e vibration is cau sed by flexible su p p orts (p oor seatin g, flexible beam s, etc.) before p roceed in g w ith stiffen -in g th e joists.4
“Construction Te chnology Up d a te s” is a se rie s of te chnica l a rticle s conta ining p ra ctica l inform a tion d istille d from re ce nt construction re se a rch.
For more information, contact Institute for Research in Construction, National Research Council of Canada, Ottaw a K1A 0R6
Telephone: (613) 993-2607; Facsimile: (613) 952-7673; Internet: http://irc.nrc-cnrc.gc.ca
© 1998
Nation al Research Cou n cil of Can ad a Decem ber 1998
ISSN 1206-1220
Figure 3.Design criterion for light-frame floors
Unacceptable Acceptable 2.5 2.0 1.5 1.0 0.5 0 0 1 2 3 4 5 6 7 8 9 10 Span, m
Floor deflection due to 1 kN f
orce
, mm
0.6 + 2.5e-0.6(L-2)
