Gone are the days of officeswith tall partitions, heavyfile cabinets, and large,filled bookshelves, and withthem has gone the inherent

redundancy of office buildings againstfloor vibration. Although sometimes mis-takenly associated with the choice ofstructural material for a floor system, theperceptibility of floor vibrations is actu-ally dependant on proper considerationof the available damping in a space. Apaper by Robert F. Mast “Vibration ofPrecast Prestressed Concrete Floors,” PCIJournal, November-December 2001, out-lines this problem in concrete systems,and AISC’s Design Guide 11 addressesfloor vibration concerns for steel systems.

Damping, as referred to in currentfloor vibration analysis criteria, is modaldamping (β) and is expressed as the ratioof actual damping to critical damping, oras the “percent of critical damping.”Damping is dependent upon the struc-tural and non-structural elements thatdissipate energy when a floor systemmoves, which includes office fit-out.

Historically, offices had tall partitions,heavy file cabinets, and large, filled book-shelves. Typical bays were 25ft. by 25ft.and floor slab thicknesses were between5½ in. and 7½ in. Office fit-out resulted inan actual loading of between 15 psf and25 psf and modal damping of 5% to 7%.

Today, typical damping ratios in officebuildings range from 0.02 to 0.05 (2% to5%). Electronic offices are becoming in-creasingly common, and new trends intenant fit-out are the most common causeof lively floors. Lightweight computersare replacing traditional file cabinets andbookshelves, and full-height partitionsare being abandoned, with preferencegiven to cubicle walls or open worksta-tions. New construction has typical baysof 25ft to 30ft wide by 40 ft or more inlength, with slab thicknesses of 4 in. to 5¼in. Office fit-out only contributes 6 psf-8

psf of the total loading, and modal damp-ing can be as low as 2% to 3%.

Why are modern floors so much moresensitive to damping than older ones?

Consider the plot in Figure 1, wherean acceleration-related amplitude is plot-ted on the vertical axis and the ratio ofnatural frequency to forcing frequency isplotted on the horizontal axis. When thefrequency ratio is one, the phenomenonof resonance occurs. If there is no damp-ing, the theoretical amplitude goes to in-finity. If there is a small amount ofdamping, say 2% to 3%, the amplitude isgreatly reduced as shown in the Figure,but still significant. If the damping is in-creased to 5% to 7%, the amplitude is re-duced very significantly. Floors designedin the 1960s and 1970s were in the 5% to7% range and resonance was not a prob-lem. (That is why the older criteria couldbe based on heel-drop impacts and not

walking resonance.) Modern floors are inthe 2% to 3% range, making damping animportant design variable. In addition,the amount of energy required to excite afloor decreases to zero as the dampingdecreases, so it takes considerably lessenergy to excite a floor if there is only 2%to 3% damping as opposed to 5% to 7%damping available.

How can we deal with these changes?The shift in fit-out of office spaces

makes the older vibration-design recom-mendations obsolete for today’s officebuildings. Because of this, we recom-mend that you do not use the ModifiedReiher-Meister or Murray Criterion pro-cedures under any circumstances. Thesecriteria were developed in the 1960s and1970s and were calibrated against floorsof that era. They are simply not applica-ble to newer floor systems and fit-outconditions.

April 2004 • Modern Steel Construction • 35

Office Fit-Out andFloor Vibrations

by Christopher M. Hewitt and Thomas M. Murray, P.E., Ph.D.

Figure 1. Acceleration-related amplitude vs. ratio of natural frequency to forcing frequency.

Taking a fresh look at the damping criteria you’ve been using to design offices can help you reduce oreliminate floor vibration issues from the very start—with minimal cost impact.

Modern floors should be analyzed forwalking-induced vibration using the rec-ommendations in the AISC’s DesignGuide 11: Floor Vibrations due to HumanActivity. All floors vibrate to some extent,but the vibration only becomes a problemwhen it is at an acceleration that peoplecan perceive or find annoying. In the de-sign guide procedure, the estimated ac-celeration of the system from walking iscompared to a tolerable acceleration. Ifthe estimated acceleration is less than thetolerable acceleration, as determinedfrom the following inequality, the floorsystem is considered to be satisfactory.

or 0.5% of gravity for officeswhere:ap/g= the predicted peak acceleration of

the floor due to walking as a frac-tion of gravity,

ao/g = the tolerance acceleration for theenvironment, 0.005g or 0.5%g foroffice environments,

Po = a constant force representing theexcitation, 65 lb for office floors,

fn = the natural frequency of the floorsystem,

β = the modal damping in the floorsystem, and

W = the effective weight, which movesbecause of the excitation.

The terms fn and W require an esti-mate of the actual live loading, but thepredicted peak acceleration is not partic-ularly sensitive if the estimate is reason-able. The design guide recommendedactual live loadings (11 psf for paper of-fices and 6 psf to 8 psf for electronic of-

fices) are generally adequate, but any ex-pected lower-than-typical loadingsshould be taken into account in theanalysis of the floor system.

The modal damping term, β, mustalso be estimated. Design Guide 11 rec-ommends a value between 0.02 and 0.05(2% to 5% of critical damping) for floorssupporting quiet areas like offices,churches, and residences. The predictedpeak acceleration is very sensitive to thedamping value.

For example, if an estimate of 3%damping for a paper office correlates to apredicted acceleration of 0.4% of gravity,the system is acceptable. However, if theactual damping is only 2% as for an elec-tronic office, the predicted accelerationrises to 0.6% of gravity, and the floor sys-tem is unacceptable. Obviously, the per-ceptible acceleration is dependant on thedamping, which is highly dependent onthe tenant fit-out of the space. In thiscase, complaints will not be received ifthe fit-out is a paper office, but com-plaints are expected if the space is fit-outas an electronic office.

How do I estimate damping for the design?And, what do I tell the owner?

First, determine the intended office fit-out. If the fit-out is known and not ex-pected to change over the life of thebuilding, the damping ratio can be esti-mated at about 0.03 (3%) for paper officeswithout permanent partitions or 0.02 to0.025 (2-2.5%) for electronic or paperlessoffices. If permanent, drywall partitionsare in all of the bays, the damping ratio isabout 0.05. To aid you in making this as-sessment, several typical office fit-outs

with recommended live-loading anddamping estimates are shown in Figure 2.

If the office fit-out is not known, dis-cuss the consequences of damping esti-mates with the owner. Changes in fit-outtranslate to changes in the damping ratiofor the floor system. If a lower than ex-pected damping ratio is used, the floorcould vibrate at an intolerable accelera-tion. The owner may want the space tobe designed conservatively for vibration,using damping ratios consistent withthose of an electronic office. Conser-vatism in the design will add someweight to the structural system, but willmake the space more adaptable to futurefit-out changes.

In a retrofit situation, the Design Guide11-recommended tolerable accelerationcan be used to back-calculate the re-quired damping for a proposed framingscheme, and to determine acceptable of-fice fit-out schemes for the space. If thefit-out options that provide a sufficientlevel of damping are not acceptable to theowner, the structural system can be retro-fit to provide the necessary damping forthe desired fit-out design. This situationshould be avoided where possible.

SummaryAs floor vibration concerns become

more common in all types of framing, thestructural system is often blamed for thisannoying phenomenon, but office fit-outplays a very important role in the vibra-tion characteristics of the floor system.The designer must carefully consider theeffects of modern office layouts on thisserviceability condition considering thestructural performance of office spaces. �

36 • Modern Steel Construction • April 2004

−= <

βexp( 0.35 )

= 0.005 p o n o

a P f ag W g

Longer spans, stronger steel, and open office layouts have all dramaticallychanged steel design in the office market over the last 15 years. How do all ofthese factors impact the floor system? Below is a typical (by today’s standards)30'-0" by 40'-0" bay, designed for a traditional office fit-out of full height parti-tions: LL = 50 psf; partitions = 20 psf; DL = self + 10 psf mechanical; damping =5%. The design results in a steel weight of 6.9 psf for the gravity framing.

Using the this design as a base line,what happens if:

1. the traditional office becomes anopen office with cubes (dampingreduces to 3%), while maintainingthe original beam depths? Result:in-fill beams and girders remainconstant, and there is no increasein weight.

2. the traditional office becomes apaperless office, such as a tele-phone call center (damping re-duces to 2%), while maintaining

the original beam depths? Result: in-fill beams and girders increase toW18x65 and W24x94, respectively. The gravity steel weight increases to8.9 psf—29% more than the traditional office.

3. the slab thickness increases to 2” metal deck with 4” concrete for a total slabdepth of 6”, while maintaining the original beam depths? The in-fill beamsand girders increase to W18x65 and W24x62, respectively. The total weightincreases to 8.0 psf, which is a 17% increase in gravity steel weight

4. the depth of the infill beams increases to W21, while maintaining the origi-nal girder and slab depths? Result: The in-fill beams and girders increase toW21x55 and W24x84, respectively. The total weight increases to 7.6 psf,which is a 10% increase in gravity steel weight.

The percentages above reflect only the increase in weight of the the gravity fram-ing (which commonly ranges from 50% to 65% of the total frame weight, de-pending on building height.) Keep in mind that total frame weight usually onlymakes up 25% of the total steel frame budget, and that the usual steel framebudget only makes up 10% of the total project cost! With these facts, assuringyour client that a vibration-less floor is inexpensive will be easy.

—Todd Alwood, Advisor, AISC’s Steel Solutions Center

Stop Shaking!

Traditional, full-height partitioned offce. Full-height partitionsrunning parallel to the beam span with suspended ceiling and duct-work attached below the slab.

Estimated actual dead load: 4 psfEstimated actual floor live load: 11 psfEstimated actual partition load: 4 psf

Effective Damping: β = 5%

Full-height partitions running perpendicular to the beam span willprovide sufficient damping to eliminate floor-vibration problems,and the damping ratio need not be considered.

Traditional, full-height partitioned office. Full-height partitionsrunning parallel to the beam span with no suspended ceiling or duct-work attached below the slab.

Estimated actual dead load: 4 psfEstimated actual floor live load: 11 psfEstimated actual partition load: 4 psf

Effective Damping: β = 5%

Full-height partitions running perpendicular to the beam span willprovide sufficient damping to eliminate floor-vibration problems,and the damping ratio need not be considered.

Electronic Office. Nearly no paperwork. Limited numbers of filecabinets. No full-height partitions, with suspended ceilings andductwork attached below the slab.Estimated actual dead load: 4 psfEstimated actual floor live load: 8 psfEstimated actual partition load: 0 psf

Effective Damping: β = 2 - 2.5%

Electronic Office. Nearly no paperwork. Limited numbers of filecabinets. No full-height partitions, no suspended ceilings or duct-work attached below the slab.Estimated actual dead load: 1 - 2 psfEstimated actual floor live load: 8 psfEstimated actual partition load: 0 psf

Effective Damping: β = 2%

April 2004 • Modern Steel Construction • 37

Figure 2: Office Fit-Outs and Recommended Damping Ratios

All office photos courtesy Steelcase.

Open office plan. Cubicles and no full height partitions, withsuspended ceiling and ductwork attached below the slab.

Estimated actual dead load: 4 psfEstimated actual floor live load: 8 psfEstimated actual partition load: 0 psf

Effective Damping: β = 2.5 - 3%

Open office plan. Cubicles and no full height partitions, withno suspended ceiling or ductwork below the slab.

Estimated actual dead load: 2 psfEstimated actual floor live load: 8 psfEstimated actual partition load: 0 psf

Effective Damping: β = 2 - 2.5%

Office Library. Full-height bookcases in heavily loaded room.Suspended ceiling and ductwork attached below the slab.

Estimated actual dead load: 4 psfEstimated actual floor live load: 11 - 15 psfEstimated actual partition load: 0 psf

Effective Damping: β = 3 - 4%

Office Library. Full-height bookcases in heavily loadedroom. No suspended ceiling or ductwork attached below the slab.

Estimated actual dead load: 4 psfEstimated actual floor live load: 11 - 15 psfEstimated actual partition load: 0 psf

Effective Damping: β = 3%

38 • Modern Steel Construction • April 2004

Figure 2: Office Fit-Outs and Recommended Damping Ratios

All office photos courtesy Steelcase.