Modern Steel Construction / August 1998

By Thomas M. Murray,Ph.D., P.E.

Serviceability concerns area growing issue for manydesigners. Modern design

specifications, coupled with today’sstronger steel, allow for lighter sec-tions when strength is the governingfactor. However, in most offices—especially today’s electronicoffices—vibration requirementsare often more important.

Virtually paperless, theelectronic office is lighter andtherefore provides less inher-ent damping than conventionaloffices with large file cabinets,heavy desks and bookcases.Adding to the problem aremodern floor layouts, whichoften are very open, with fewfixed partitions, widely spaceddemountable partitions, or, insome cases, no partitions what-soever. Finally, atrium typeareas are more common andcurtain wall construction is less stiff,both of which can increase floor live-liness.

As a result, the structural engi-neer must pay much more attentionto floor serviceability and must care-fully critique the floor vibrationanalysis procedure that is beingused—whether the analysis is beingperformed by hand or with a com-puter program. Fortunately, the pro-cedures for designing comfortableoffices are available. This articleprovides information on evaluatingmodern floor systems supportingelectronic offices.

HISTORICAL PERSPECTIVE

Analysis procedures for floorvibration have two components: ahuman tolerance criterion and amethod to predict the response ofthe floor system. Analysis proce-dures are calibrated by measuringthe response of floor due to a stan-dard impact and then recording the

response of the building occupants.Adjustments are then made to effectgood results. Obviously, human per-ception is subjective and any proce-dure cannot ensure that no one willever complain about floor movement.The aim of the calibration procedureis to be sure that movement of thefloor due to human activity will notannoy the great majority of the floorusers.

Since the mid-1960s, four proce-dures have been commonly used inNorth American. The first was theModified Reiher-Meister scale pro-posed by Professor Kenneth H.Lenzen. This scale has regions of“perceptibility”—from “not” to“strongly” perceptible. The engineeris required to calculate the first nat-ural frequency and amplitude due toa heel-drop impact and then fromthe scale determine if the proposedfloor system is satisfactory or not.The procedure does not includedamping. However, because the pro-cedure was calibrated between about1966 and 1970 when floor construc-tion and occupancies were very dif-ferent than what is found today,between 4% and 8% critical logdecrement damping is inherentlyassumed.

In the early ’70s, both the MurrayCriterion and a Canadian StandardsAssociation procedure were pro-posed. Both of these procedures

include floor system damping. TheMurray Criterion states that a floorsystem is satisfactory if

D > 35 Ao fn + 2.5 where D is the required log decre-

ment damping in the floor system inpercent of critical damping, Ao is theamplitude in inches due to a heel-drop impact, and fn is the funda-mental natural frequency of the floorsystem. This procedure was calibrat-

ed with data gathered in thelate 1960s and early 1970s,again with steel framing andoffice occupancies very dif-ferent than are found today.Generally, if the requireddamping is less than 4-4.5%of critical log decrementdamping, the floor system fora conventional office will besatisfactory. However, thislevel must be adjusted downif the procedure is used foroffice buildings constructedtoday.

Because of the construc-tion and office configurations

used to calibrate them, these proce-dures are not recommended for eval-uating floor systems designed usingLRFD with A572 Gr 50 steel andsupporting electronic offices.

RECOMMENDED PROCEDURE

The 1997 AISC Design GuideFloor Vibrations Due to HumanActivity has a new procedure forevaluating floor designs. The proce-dure is based on avoiding resonancefrom walking. The criterion is satis-fied if ap/g = 65 exp (-0.35 fn )/bW

< ao /gwhere ap/g is the predicted accel-

eration ratio due to human activity,is the modal damping ratio for thefloor system, W is the equivalentfloor panel weight, and ao/g is theacceleration limit taken as 0.5%g foroffices. This procedure was calibrat-ed using measurements made inbuildings constructed in the 1980sbefore the advent of the electronic

FLOOR V i b rV i b r a t i o na t i o nAND THE

ELECTRONIC OFFICE

StrStructuructural engineersal engineersmmust carefullyust carefully

crcr itique the flooritique the floorvibrvibr tion analysistion analysisprocedure that isprocedure that is

being used.being used.

Modern Steel Construction / August 1998

office. However, the procedure isquite general and allows the evalua-tion of other than the standard bayin a sea of standard bays. Effects ofadjacent bays, including differentgeometry, as well as mezzanine con-struction, can be accounted for in thecalculations.

The Design Guide recommendsthat the modal damping ratio, b, betaken as “0.05 for offices with fullheight partitions between floors,0.03 for floors with non-structuralcomponents and furnishings, butwith only small demountable parti-tions, typical of many modular officeareas, and 0.02 for floors with fewnon-structural components (ceilings,ducts, partitions, etc.) as can occurin open work areas and churches”.These damping values will seemvery low to engineers experiencedwith heel-drop based procedures.The reason is that modal damping isassociated only with energy loss;whereas log decrement damping,which is used with heel-drop crite-ria, is associated with both energyloss and transmission of vibrationalenergy to other structural compo-nents. Modal damping is approxi-mately two thirds to one half of logdecrement damping. For the elec-tronic office, the modal dampingratio should be taken as 0.02 –0.025.

The criterion requires a close esti-mate of the natural frequency of thefloor system under everyday load-ings. The Guide recommends that

the fundamental natural frequencyof the floor system be calculatedusing where b and g are the beam(or joist) and girder deflections dueto the weight supported. The deadand live loads used to calculate thesedeflections will significantly affectthe estimated natural frequency.Strength design dead and live loadsshould not be used for vibrationanalysis. A floor system will notexhibit annoying vibrations whenfully loaded; problems occur whenthe system is lightly loaded. (Forexample, a number of problem floorshave been reported in schools, notduring the day when the childrenwere there, but after school whenonly one or two people were in theclassroom.) The Guide recommendsthe dead load should be estimated as4 psf plus the weight of the floordeck and supporting members,unless a heavy ceiling and/or unusu-al ductwork is present. For live load,the Guide recommends 11 psf foroffices and 6 psf for residences.These values are found in anAppendix of ASCE-7-95 “MinimumDesign Loads for Buildings andOther Structures” and were deter-mined by the National Bureau ofStandards during calibration ofLRFD. This calibration was doneduring the late 1970s when electron-ic offices were only just beginning tobe envisioned. The live load for anelectronic office may be less than 7psf, depending on the number ofdemountable partitions and deskspacing.

EXAMPLES

The following examples are usedto illustrate the concepts discussedabove.

Example 1. The partial framingplan shown in Figure 1 is a mezza-nine area of a proposed building.The proposed floor deck is 2 in. ofnormal weight concrete on 2 in. steeldeck (total depth is 4 in.). The com-posite design provisions of the AISCLRFD Specification and A572 Gr. 50steel were used. The floor will sup-port an office with closely spaceddemountable partitions. All of thebuilding occupants use computers;paper record storage is minimal; andthe estimated actual live load is 7psf.

The floor framing was analyzedusing the software FLOORVIB2 andthe Modified Reiher-Meister Scale,the Murray Criterion, and the proce-dure in the 1997 AISC DesignGuide. The former two proceduresdo not have provisions to account forthe additional flexibility because ofthe mezzanine construction; thus,results from this analysis will tendto be unconservative. A dead load of4 psf plus the weight of the floordeck and supporting members and alive load of 7 psf were used in theanalysis.

The floor framing plots in the“Slightly Perceptible” range of theModified Reiher-Meister Scale,which means that the floor framingsatisfies that criterion. However, theimplied damping in this criterion is4%-8%, which does not exist in thefloor system and, therefore, the eval-uation is in error.

Using the Murray Criterion, therequired damping is 4%. Thisrequirement is usually satisfied forconventional offices. But, for thisfloor system, the loading is verylight and the damping probably doesnot exceed 3% and it is a mezzanine.

UsefulUsefulRefReferenceserences

“Minimum Design Loads for“Minimum Design Loads forB u i l d i n g s a n d O t h e rB u i l d i n g s a n d O t h e rStructures”, ASCE StandardStructures”, ASCE Standard7-93, American Soceity of Civil7-93, American Soceity of CivilE n g i n e e r s , N e w Y o r k , N Y ,E n g i n e e r s , N e w Y o r k , N Y ,1993.1993.

Murray, Thomas M., DavidMurray, Thomas M., DavidE. Allen and Eric E. Ungar,E. Allen and Eric E. Ungar,“ F l o o r V i b r a t i o n s D u e t o“ F l o o r V i b r a t i o n s D u e t oHuman Activity”, Steel DesignHuman Activity”, Steel DesignGuide Ser ies 11 , Amer i canGuide Ser ies 11 , Amer i canI n s t i t u t e o f S t e e lI n s t i t u t e o f S t e e lCons t ruc t i on , Ch i cago , IL ,Cons t ruc t i on , Ch i cago , IL ,19971997

F L O O R V I B 2 , U s e r ' sF L O O R V I B 2 , U s e r ' sManual, Structural Engineers,Manual, Structural Engineers,Inc., Radford, VA, 1997Inc., Radford, VA, 1997

Figure 1: Mezzanine are with 2” of normal weight concrete on a 2” metal deckfor a total floor depth of 4”

The AISC Design Guide proce-dure predicts a peak acceleration of1.05%of gravity for 2.5% modaldamping. The beam, girder, andcombined mode frequencies are 4.1Hz, 5.4 Hz and 3.2 Hz, respectively.The tolerance acceleration criterionfor offices is 0.50% of gravity.Obviously, the system does not satis-fy the criterion and occupant com-plaints would be expected.

The Design Guide recommendsthat “where the edge member is ajoist or beam, a practical solution isto stiffen the edge by adding anotherjoist or beam, or by choosing an edgebeam with moment of inertia 50 per-cent greater than for the interiorbeams”. When either option is used,the bay is analyzed as an interiorbay. Increasing the edge beam to aW16x45 and reanalyzing as an inte-rior bay, the predicted accelerationis 0.75% gravity, which is still notacceptable.

Since the natural frequency ofthe beams is lower than the girder,the beams should be stiffened beforestiffening the girders. If the floorbeams are increased to W21x57 with

a W21x83 edge beam, the predictedpeak acceleration is 0.48% gravity.This solution requires a significantincrease in steel weight; however,part of the cost is offset becausecomposite construction would not berequired for strength.

An alternate solution is toincrease the floor deck depth to 5 in.by adding 1 in. of concrete. WithW18x40 beams, a W21x50 edgebeam, and W21x101 girders, the pre-dicted acceleration is 0.50% gravity,an acceptable solution.

Example 2. The partial framingplan in Figure 2 is for a proposedoffice building which will house elec-tronic offices. There will be virtuallyno paper at the computer worksta-tions and the workstations will bewidely spaced. No fixed partitionsand few demountable partitions areanticipated. The proposed floor is 3in. of normal weight concrete on0.6C deck. The proposed framingplan is shown in Figure 2; the fram-ing meets ASD stress criteria andthe live load deflection is less thanspan/360.

The floor framing was analyzedusing the software FLOORVIB2 andthe Modified Reiher-Meister Scale,the Murray Criterion, and the proce-dure in the 1997 AISC DesignGuide. A dead load of 4 psf plus theweight of the floor deck and support-ing members and 7psf live load wasused for the analysis. The area andmoment of inertia of the joist girderwere taken as 17.3 in2 and 3585in.4, respectively.

The amplitude and frequency plotin the lower half of the “DistinctlyPerceptible” region of ModifiedReiher-Meister scale. Therefore, thefloor is considered acceptable by thisprocedure. As in Example 1, theinherent damping in the procedureis assumed to be 4-8% of critical logdecrement damping which would notbe realized for the conditions given

The required damping from theMurray Criterion is 4.5%. Dampingof this magnitude would not be real-ized and redesign is necessary.

Using a modal damping value of2.5%, the predicted peak accelera-tion from the AISC Design Guideprocedure is 0.90% gravity whichexceeds the criterion limit of 0.50%gravity and redesign is necessary.The joist, joist girder, combinedmode frequencies are 5.7 Hz, 6.1 Hz,and 4.2 Hz, respectively.

Increasing the concrete depth to 5in., the deck height to 1.0 in., thejoists to 30K7, and the joist girderproperties to an area of 21.4 in.2 andmoment of inertia to 4440 in.4,results in a predicted acceleration of0.52% gravity. This accelerationvalue is marginally acceptable forthe proposed office building.

Figure 2: Building housing electronic offices with no fixed partitions and only afew demoutable partitions; workstations are widely spaced.

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SUMMARY. In summary, electronic offices

are lighter and have less dampingthan traditional offices in the past.Floor vibration provisions developedand calibrated in the 1960s and1970s are generally not valid foroffice floors constructed in the1990s. Instead, it is recommendedthat engineers follow the design pro-cedure in the 1997 AISC DesignGuide 11 for new office buildingsthat will house electronic offices.

Thomas M. Murray, Ph.D., P.E.,is the Montague-Betts Professor ofStructural Steel Design in theDepartment of Civil andEnvironmental Engineering atVirginia Tech in Blacksburg, VA. Healso is the co-author of AISC DesignGuide #11: Floor Vibration Due toHuman Activity.