FloorVibrationsAnalysis_1107_s

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Walking Criterionor Floor Vibration Analysis.Floor Vibration Due to Human Activity

with the RAM Structural System

AISC/CISC Design Guide 11, by L. Allen Adams, S.E. and Thomas M. Murray, Ph.D., P.E.

Executive Overview

The RAM™ Structural System is now linked to FloorVibe, a sotware product developed by Tom Murray, Structural Engineers, Inc.,

Radord, Virginia. Using FloorVibe, a designer can analyze oor raming or Walking and Rhythmic Excitations and or suitability to

support Sensitive Equipment. The calculation procedures and criteria are rom the AISC/CISC Design Guide 11, Floor Vibrations

Due to Human Activity (DG11), which has become the de acto standard or oor vibration analysis in North American.

Art, in the orm o engineering judgment, is necessary to correctly apply the criterion or Walking Excitation in Chapter 4 o DG11.

Consequently, it is very difcult, i not impossible, to develop sotware that can consistently and reliably apply the criterion cor-

rectly without human input, except or the simplest o raming plans. The raming plan shown in Figure 1 is a real example o how

adjacent raming can aect oor response. The structural engineer reported that during design they checked typical Bays A, but

did not consider Bay B. Upon occupancy, complaints were immediately received rom ofce personnel in Bay B. The predicted

acceleration or Bays A, assuming paper ofces, is 0.5%g and or Bay B, 0.63%g. The ormer just satisfes the DG11 criterion and

the latter does not. Why? The Floor Length, as defned in DG11 or the Bays A is 81 t and or Bay B is 48.5 t. Simply looking at

individual beams and girders or individual bays is not sufcient; eects o adjacent raming must be considered.

The purpose o this White Paper is to explain and de-

monstrate with examples how to make good engineering

judgments when analyzing ofce and residential oors or

vibration, particularly with complex raming. It is assumed

that the reader is amiliar with Design Guide 11.

Figure 1: Example Framing



Contents:

Bay Classifcation 3Acceptance Criteria 3

Frequency 3

Modal Damping 4

Combined Mode Eective Weight 5

Bays in the RAM Structural System 7

Mezzanines in the RAM Structural System 9

Conclusion 9



Bay Classifcation

The RAM Structural System identifes bays as ‘Perect Bays’, ‘Imperect Bays’, or ‘Irregular Bays’. A Perect

Bay “perectly matches” DG11 bays, that is the bay is rectangular, all beams are identical, beam spacing is

uniorm, etc. Bays with some minor deviations may still be categorized as Perect Bays i those deviations are

“close enough” to Perect, that is, within some tolerances. An Imperect Bay is one or which the bay generallyexhibits characteristics o a Perect Bay but has one or more geometric eatures that deviate rom such. An

Irregular Bay is one that deviates signifcantly rom the bays described in DG11. Also, miscellaneous beams

that are not part o a bay are designated as ‘Irregular’.

Acceptance Criteria

In DG11, it is recommended that ofce residential and similar oor systems satisy:

(1)

where ap

/ g is the predicted peak acceleration o the oor due to walking as a raction o gravity, ao

/g is the

tolerance acceleration or the environment, Po

is a constant orce representing the excitation, n

is the unda-

mental requency o the oor system, ß is the modal damping in the oor system, and W is the combined mode

eective weight that is determined rom the weight o so-called beam and girder “panels”. Po

is 65 lb or ofce

oors, and ao

/g is 0.005g or 0.5%g or ofce environments. The terms n

and W require an estimate o the ac-

tual live loading, but the predicted peak acceleration is not particularly sensitive i the estimate is reasonable.

The Design Guide recommends 11 ps or paper ofces and 6-8 ps or electronic ofces, which have been

ound to be adequate. Damping, ß, must also be estimated. The Design Guide recommends between 0.02 and

0.05 (2% to 5% o critical damping), depending primarily on the presence o nonstructural components such as

partitions, or oors supporting quiet areas like ofces, churches, and residences.

Frequency.

The requency, n, is the undamental requency o the system, not that o an individual beam or girder. DG11

recommends the use o a orm o Dunkerley’s equation to estimate the requency o a rectangular bay,

(2)

where Δb

and Δg

are the beam and girder deections due to uniormly distributed actual expected loads, not

design loads, respectively. DG11 does not have provisions or non-rectangular bays as they are too complex

or manual calculations. Fortunately, most irregular bays rarely i ever exhibit vibration problems. For bays

with a low skew angle, say less than 10-15 degrees, using the average beam or girder span, as appropriate,

may be an acceptable approximation.

When calculating Δb

and Δg, ull composite action should always be assumed unless the oor deck is not in

direct contact with the top ange or chord o the supporting member. Vertical amplitudes o 0.004-0.010 in.

cause annoying oor vibrations. Such small deections result in very small shear orces at the ange or chord

and oor deck interace and thereore the member will vibrate as i a ully composite cross-section. I the

Walking Criterion or Floor Vibration Analysis. p. 3



oor deck is not in continuous contact with the supporting member, or example a girder supporting joists, ull

composite action is not achieved. DG11 and FloorVibe have procedures or determining the eective moment

o inertia or such members.

When analyzing oors supported by trusses, shear deormation o the web must be considered. I joists or

joist girders are the supporting members, both web shear deormations and eccentricity at the chord panelpoints must be considered. Again, DG11 and FloorVibe have procedures or both.

Modal Damping.

Lightly damped, modern oors are sensitive to vibration because o possible resonance with a multiple o the

walking pace. Resonance can occur when one, two, or three times the walking pace is at or near the unda-

mental requency o the oor system and the damping is low. (Multiples o the walking pace are reerred to

as “harmonics” in DG11). Consequently, the predicted peak acceleration, ap/g, is very sensitive to the

damping value.

Ofces can be classifed depending on the ft out, as (1) with dry wall partitions, (2) a paper ofce, or (3) an

electronic ofce. The corresponding recommended damping values are 5%, 3%, or 2-2.5% i there is typi-cal ductwork and suspended ceiling below the oor. I ductwork or a suspended ceiling is not present, the

damping values should be reduced by 0.5-1%. Care is needed when assessing damping provided by dry wall

partitions. I the partitions are only above the girder(s), their contribution to damping is not signifcant; i the

dry wall partitions are in the bay and perpendicular to the beam span, their contribution is very signifcant and

the 5% damping estimate is reasonable. A paper ofce is an ofce with demountable partitions, desks, fle

cabinets, etc., as in a typical engineering ofce. An electronic ofce is one with very light and widely spaced

urniture, no fle cabinets, etc., as in a call center.

Figure 2 is a photograph o a paper ofce. There are ductwork and a hung ceiling below; thereore a damp-

ing value o 3% is justifed. Figure 3 shows an electronic ofce, again with ductwork and hung ceiling below.

Thereore the damping is estimated to be between 2 and 2.5%.

I the predicted acceleration is say 0.4% o gravity based on an estimate o 3% damping assuming a paper

ofce, the actual acceleration may be as high as 0.6% o gravity i the actual damping is only 2% as or an elec-

tronic ofce. The 0.4% value predicts an acceptable oor; the 0.6% value represents an unacceptable oor.

Complaints will not be received i the ft-out is a paper ofce, but complaints are expected i it is an electronic

ofce. So, what should the design engineer do? First determine the intended ofce ft-out. I known, estimate


Figure 2: Photograph o a Paper Oce Figure 3: Photograph o an Electronic Oce (courtesy o Steelcase



the damping ratio. I the intended ft-out is other than electronic ofces, warn the architect and owner that

a uture change in ft-out may result in occupant complaints. I ofce ft-out is not known, discuss with the

owner consequences o damping estimates. Using tolerance criterion recommended in the Design Guide,

the required damping can be back calculated or a proposed raming scheme and an acceptable ofce ft-out

determined. Once a decision has been made, a change in ofce ft out that reduces damping should be con-

sidered the same as a change in ft out that results in an increased live loading, e.g. retroft may be required.

The bottom line is that assumed ft out can aect initial cost as well as possible retroft costs over the lie o

the building.

Combined Mode Eective Weight.

The combined mode eective weight, W, in Equation (1) is obtained rom

(3)

where Wb and Wg are the beam and girder panel weights rom

(4)

(5)

where Cjand C

gare coefcients, L

jand L

gare the beam (joist) and girder spans, and B

jand B

gare the eective

panel widths that are determined rom anisotropic plate theory.

The coefcients Cjand C

ghave the ollowing defnitions in DG11:

Cj

= 2.0 or joists or beams in most areas

= 1.0 or joists or beams parallel to an interior edge

Cg = 1.6 or girders supporting joist connected to the girder ange(e.g. joist seats)

= 1.8 or girders supporting beams connected to the girder web

FloorVibe deaults to Cj= 2.0 as “in most areas” means in bays where there is an adjacent bay, a wall, or rela-

tively sti external cladding support along the edge beam(s). For a balcony, mezzanine, or when the exterior

cladding connection is very exible, the “Mezzanines” option in FloorVibe should be invoked by the user.

Walking Criterion or Floor Vibration Analysis. p.



FloorVibe deaults to Cg

= 1.6 i joists are specifed and to 1.8 or any other type o member. I the bottom

chords o joists are extended and connected beore the concrete is poured, Cg

= 1.8 may be justifed. The

higher value o Cg

is obtained by checking “Joist Extended Bottom Chords”.

The eective beam and girder panel widths, Bj and Bg are limited to 2/3 o the oor width or 2/3 o the oor

length, respectively. Determining the oor width and oor length requires judgment on the part o the designer

Floor Width represents the portion o the oor perpendicular to the beam span that is associated with the

undamental requency (mode) o the beams. When oor raming is excited, there is an associated mode

shape. Figure 4 shows a typical undamental mode shape or a series o beams supported by a wall, that is, a

rigid support. A fnite element analysis o this system would show movement o every beam, regardless o the

width o the raming. Because o energy dissipation, such movement will not occur in a real structure. The

provisions or determining Bj take into account this act with

(6)

For a series o perect bays, the Floor Width is the sum o the supporting girder spans perpendicular to the

beam span. Non-perect raming will reduce the Floor Width and engineering judgment is required.

Similarly, there is a mode shape associated with girder movement as shown in Figure 5 and or the same rea-

sons as or beams the Floor Length is limited by

(7)


Figure 4: Mode Shape Associated with Beams rom a Finite Element Analysis



For a series o Perect Bays, the Floor Length is the sum o the beam spans perpendicular to the girder spans

o the bay being analyzed. Again, non-perect raming will reduce the Floor Length and engineering judgment

is required.

Bays in the RAM Structural System

The oor raming shown in Figure 6 is used to illustrate how Floor Width and Floor Length are determined or

complex raming. The bays with the beams shown in Blue are RAM Structural System Perect Bays. Yellow

indicates Imperect Bays and Gray, Irregular Bays. The numbers in each Perect Bay are the values reported

to FloorVibe by the RAM Structural System or Floor Width (upper number) and Floor Length (lower number)

or that bay. The FloorVibe user must veriy the suitability o these dimensions, and modiy them i necessary,

beore completing an analysis.

The Floor Widths shown are distances perpendicular to the beam span o the bay based on the adjacent

Perect Bays. For example, the Floor Width o the three bays between grids C-F and 3-4 is 90 t. The width o

Bays B/C and F/G are not included in the oor Width dimensions because they are either Imperect or Irregular

Bays. The same rule applies or the other Perect Bays in the center portion o the raming, that is, Imperect

and Irregular bay widths are not included in the Floor Width dimensions.

The Floor Lengths shown are distances perpendicular to the girder span o the bay, again, based on adjacent

perect bays having beam spans o at least 50% o the beam span o the bay under consideration and subse-

quent adjacent bays having beam spans o at least 50% o that o the previous bay.

For example the Floor Length o the bays between grids C-E and 2-5 is 120 t. Bays between grids 1-2 and 5-6are not included in the reported Floor Lengths because o their short beam spans. The Floor Length or the

bays between grids C-E and 1-2 and 5-6 is 135 t because the spans in the successive adjacent perect bays

are at least 50% o these bays. It is noted that the Floor Lengths o the other Perect Bays between grids B-G

are restricted in length by adjacent Imperect or Irregular Bays.


Figure 5: Mode Shape Associated with Girders rom a Finite Element



Bays between grids A and B are imperect bays because the interior girder is supported by a second girder at

the intersection o grids B and 3.5. I the girder along grid 3.5 is very sti or vibration purposes, or instance, i

it supports a wall, these bays can be analyzed using FloorVibe. I this is done, the Floor Width and Floor Length

or the two bays are 30 t and 120 t, respectively. Note that i there was a column at B-3.5, the Floor Width and

Floor Length dimensions would likewise be 30 t and 120 t, respectively.

Bay B-C/3-4 is an Imperect Bay because o the opening. I there are walls around the opening and they are

sufciently sti to restrain vibration, the bay could be analyzed using FloorVibe with the girder span and Floor

Width taken as 15 t, and the Floor Length as 40 t. However, it is unlikely that walking will cause signifcant

accelerations in this area and analysis may not be required, because it is a single bay surrounded by totally

dissimilar bays.

Bay KK-MM/44-50 is an Imperect Bay because o the slight skew o the beam along column line KK between

grids 44 and50. Engineering judgment allows this bay to be analyzed by FloorVibe with a Floor Width o 30 t

and a Floor Length o 94 t.

Bay JJ-KK/33-44 is obviously an Imperect Bay and is not a vibration concern because o the irregular raming

along grid JJ. Bay KK-MM/25-33 is an Imperect Bay because o the adjacent raming in Bay JJ-KK/22-33.

Since the girder along grid 25 is supported by a beam along grid KK, the bay cannot be analyzed by FloorVibe.

The remaining triangular and multi-sided bays are designated as Irregular Bays by the RAM Structural System.

They are not o concern as, to our knowledge, there has never been a reported oor vibration problem or such

bays.


Figure 6. Example Framing Plan



Mezzanines in the RAM Structural System

Design Guide 11 procedures require consideration o “interior oor edges, as in mezzanine areas or atria”

because o the reduced eective mass due to the ree edge or edges. Unless the beam or joist along a ree

edge is stiened, the coefcient Cj in Equation (4) is taken as 1.0. For bays with a girder along a ree edge,

the girder panel width is taken as 2/3 times the supported beam or joist span. For bays with beam or joist andgirder ree edges, both requirements are invoked by FloorVibe. According to DG11, i the ree edge beam or

joist has a moment o inertia 50% greater than the interior beams or joists, Cj in Equation (4) can be taken as

2.0. In general, walls built over edge members at mezzanine areas or atria provide sufcient stiness such tha

interior oor edge considerations are not needed. However, neither the RAM Structural System nor FloorVibe

has provisions to detect a stiened edge beam or joist.

It is also stated in DG11 that “experience so ar has shown that exterior oor edges o buildings do not require

special consideration as do interior oor edges. Reasons or this include stiening due to exterior cladding

and walkways generally not being adjacent to exterior walls. I these conditions do not exist, the exterior oor

edges should be given special consideration.” This statement was written in 1995 beore the prolieration o

electronic ofces, which generally do not have well defned walkways. The reader is cautioned that, when the

exterior cladding is not frmly attached in the vertical direction to the spandrel raming members, to considerusing the ree edge option(s) in FloorVibe.

The RAM Structural System assumes: (1) Exterior edge members (spandrel members) are not exterior oor

edges, so the mezzanine option in FloorVibe is not tagged, and conservatively, that (2) all interior oor edges

are mezzanines, so the mezzanine option in FloorVibe is tagged. For example, Bays C-D/3-4 and E-F/3-4 are

tagged as a Mezzanine with a “Beam Parallel to Open Side”, that is, this option is invoked in FloorVibe when it

is launched rom the RAM Structural System. The FloorVibe user must veriy that this is a correct assumption

and, i necessary, activate or deactivate the Mezzanine designation beore an analysis is done.

Conclusion

Even or complicated raming confgurations, the RAM Structural System can be very helpul in interpreting the geometric conditions o oor raming that, when appropriately confrmed by the engineer, can be used in

FloorVibe to assess the vibration sensitivity o oor raming.

L. Allen Adams is Chie Design Engineer, Structural Products at Bentley Systems, Inc.

He can be reached at [email protected].

Thomas M. Murray is the Montague-Betts Proessor o Structural Steel Design at Virginia Tech and President

o Structural Engineers, Inc. He can be reached at [email protected].


©2007 Bentley Systems, Incorporated. Bentley, the Bentley “B” logo, and RAM are either registered or unregistered trademarks or service marks o Bentley Systems, Incorporated or one o its

direct or indirect wholly-owned subsidiaries. Other brands and product names are trademarks o their respective owners. DAA037620-1/0001 11/07

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