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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 dependent on proper considerationof the available damping in a space. Apaper by Robert F. Mast Vibration ofPrecast Prestressed Concrete Floors, PCI

Journal, November-December 2001, out-lines this problem in concrete systems,and AISCs Design Guide 11 addressesfloor vibration concerns for steel systems.

Damping, as referred to in currentfloor vibration analysis criteria, is modal

damping () 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 book-shelves. Typical bays were 25 by 25 andfloor slab thicknesses were between 5-and 7- . Office fit-out resulted in an ac-tual loading of between 15 psf and 25 psfand modal damping of 5% to 7%.

Today, typical damping ratios in officebuildings range from 0.02 to 0.05 (2% to5%). Electronic offices are becomingcommon, and new trends in tenant fit-out are a common cause of lively floors.Lightweight computers replace tradi-tional file cabinets and bookshelves, andcubicle walls and open workstations arepreferred to full-height partitions. Newconstruction has typical bays of 25 to 30wide by 40 or more in length, with slabthicknesses of 4 to 5-. Office fit-outonly contributes 6 psf-8 psf of the total

loading, and modal damping can be aslow as 2% to 3%.

Why are modern floors so much more

sensitive 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 the

frequency 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 could

be 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 todays office

buildings. 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.

Modern floors should be analyzed forwalking-induced vibration using the rec-ommendations in the AISCs Design

April 2004 Modern Steel Construction

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 youve been using to design offices

can help you to eliminate floor vibration issues from the very start.

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Guide 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. If

the 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 offices

where: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,

= 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 anyexpected lower-than-typical loadings

should be taken into account in theanalysis of the floor system.

The modal damping term, , mustalso be estimated. Design Guide 11 recom-mends a value between 0.02 and 0.05 (2%to 5% of critical damping) for floors sup-porting quiet areas like offices, churches,and residences. The predicted peak accel-

eration is very sensitive to the dampingvalue.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 dependent on thedamping, which is highly dependent onthe tenant fit-out of the space. In thiscase, complaints will not be received if

the 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 the

building, 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 paperless

offices. 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-outswith 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 might want the space to

be 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 sufficient

level 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.

Looking Forward

As floor vibration concerns becomemore 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. 5

Modern Steel Construction April 2004

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