building periods

8/20/2019 Building Periods

http://slidepdf.com/reader/full/building-periods 1/4STRUCTURE magazine June 2008

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Building Periods: Moving Forward (and Backward) By William P. Jacobs, V, P.E.

The determination of the fundamental period of a building is an integral part ofthe lateral load calculation procedure in today’s building codes; however, navigatingyour way through the twists and turns of the various assumptions and limitsinvolved can become confusing rather quickly. Should the fundamental period becalculated differently for the determination of wind and seismic loading? Are theresults of a computer based eigenvalue analysis always adequate? What damping

values should be assumed? The purpose of this article is to try to answer these andseveral other questions regarding code-based period determination techniques tohelp remove the confusion and allow designers to “move forward.”

lating the seismic response coefficient,Cs, for base shear determination usingthe equivalent lateral force procedure.

A flow-chart for navigating these provi-sions is provided in Figure 1, and furtherdiscussion follows.The most straightforward method for

determining the building period involvesthe use of the empirical formulas for thecalculation of the approximate buildingperiod, Ta , presented in Chapter 12 of

ASCE 7-05. A subset of these formulasis displayed in the seismic section of Ta-ble 1 and plotted in Figure 2 (page 26).These equations are basedon data from several instru-mented buildings subjectedto ground motion duringseismic events such as theSan Fernando and Northridgeearthquakes. The data wasused to determine both lowerbound and upper boundapproximate period equationsusing regression analysis. Theformulas provided in ASCE7-05 represent the lowerbound equations and areintentionally formulated toprovide a conservative (short)estimation of the fundamen-tal building period. Shorterbuilding periods result inhigher and more conservativebase shears.

Properly Substantiated Analysis

If the engineer desires, thebuilding period used tocalculate equivalent lateralforces for both strength anddrift limits can be set equal tothe approximate period, Ta ,

without further calculation.Note that this practice may

result in significantly overly conservativresults, as ASCE 7-05 allows the use oa “properly substantiated analysis” tdetermine the fundamental buildinperiod in lieu of the approximatempirical equations – within certain

limits. A “properly substantiated analysiscan take many forms, such as the use oRayleigh’s method. Most commerciabuilding software programs will quickland easily perform an eigenvalue analysito determine the mode shapes anperiods of a building, and practicinengineers will most likely use thimethod. It is important to note that thperiods determined using an eigenvaluanalysis can be significantly longer thathose determined using the approximatequations. This discrepancy is primarildue to three factors. First, the analyticamodel on which the eigenvalue analysiis performed does not generally includthe stiffening effect of the non-structurainfill and cladding that is present in thactual building. Second, the analyticamodel does not generally include th

Determine Fundamental Period “T” For UseIn Equivalent Lateral Force Procedure Per

ASCE 7-05 Section 12.8.1.1

Determine Fundamental Period “T” For UseIn Equivalent Lateral Force Procedure Per

ASCE 7-05 Section 12.8.1.1

Calculate Approximate Period Ta

(Section 12.8.2.1)

T = Ta for StrengthAnd Drift Checks.

(Section 12.8.2)

T = Tactual T = Tactual

Will a ProperlySubstantiated Analysis

Be Performed to Calculate Tactual? (Section 12.8.2)2

Will a ProperlySubstantiated Analysis

Be Performed to Calculate Tactual? (Section 12.8.2)2

T = Tactual

(Section 12.8.6.2)

No

No

Drift

Y e s

Yes

S t r

e n g t h

Notes:1. Section numbers refer to ASCE 7-05.2. A “Properly Substantiated Analysis”can consist of an eigenvalue analysis, Rayleigh’s method, or any other valid analytical technique that considers the structural properties and deformational characteristics of the structure. Results of this analysis are noted as Tactual in this flow-chart.

Calculate Forces forStrength or for Drift?

Calculate Forces forStrength or for Drift?

T = Cu Ta

(Section 12.8.2)

T = Cu Ta

(Section 12.8.2)

Calculate Cu Factor(Table 12.8-1)

Is Tactual >Cu Ta?

Figure 1: Seismic Equivalent Lateral Force FundamentalPeriod Flow-Chart.

The Fundamentals

The fundamental building periodis simply the inverse of the buildingfrequency at the lowest harmonic –easy right? Basically, every system hasa set of frequencies in which it “wants”to vibrate when set in motion by somesort of disturbance (in building design,typically a seismic or wind event)based on the system’s mass and stiffnesscharacteristics. The shortest frequencyis known as the natural frequency. Theinverse of frequency is the period ofthe system, and more specifically, theinverse of the natural frequency is thefundamental period.In seismic design, the closer the fre-

quency of an earthquake is to the natu-ral frequency of a building, the moreenergy is introduced into the buildingstructure. Buildings with shorter fun-damental periods attract higher seismicforces as the code-based design spec-trum exhibits higher accelerations atshorter periods. For wind design, theopposite behavior is observed. Longerfundamental periods are indicative ofbuildings that are more susceptible todynamic amplification effects from sus-tained wind gusts and result in higherdesign forces. In order to investigate themagnitudes of these wind and seismiceffects, the fundamental period of thebuilding must first be determined.This article focuses on the provisions

of the American Society of CivilEngineers Minimum Design Loads forBuildings and Other Structures (ASCE7-05). The following sections coverthe specifics of ASCE 7-05 periodcalculations as they pertain to seismicand wind load determination.

Seismic Periods

Most designers are familiar with theuse of the fundamental period of thestructure, T, in conjunction with calcu-



stiffening effect of “gravity-only” columns,beams, and slabs. Third, as previously noted,the approximate equations are skewed toprovide shorter periods.For strength design, ASCE 7-05 limits

the maximum building period to theapproximate building period, Ta , multipliedby the factor Cu from Table 12.8-1. The capgenerally coincides with the upper bound ofbuilding periods as determined in the samestudy used to determine the lower boundapproximate equations. The cap is intendedto prevent possible errors resulting fromerroneous assumptions used in the “properlysubstantiated analysis” that could resultin unconservative building periods whencompared to those determined under actualseismic events. For the determination of

seismic drift, ASCE 7-05 removes the cap andallows the engineer to use the building periodresulting from analysis without restriction.

Code Quirks

Building period determination can have asubstantial impact on the seismic design ofa structure. For instance, did you know thata small dimensional change can result in 50percent less base shear? Look closely at thevalues for the approximate period parametersprovided in Table 1. If the lateral resisting

system consists of concentrically bracedframes, the approximate period equation

would be that of an “other” system and isequal to 0.02hn

0.75. If the brace work pointsare moved away from the joints, and the

system is now considered an “eccentrically”braced system, the approximate period equa-tion increases to 0.03hn

0.75. The change in ap-proximate fundamental period of 50 percent(0.03 vs. 0.02) could translate directly to acorresponding reduction in base shear. Ifthese systems were detailed as R=3 “SteelSystems Not Specifically Detailed for Seis-mic Resistance,” as is common on the eastcoast, this revision could be accomplished

with minimal additional detailing – and witha base shear reduction of 50 percent! Thisis an extreme example; however, it is worth

pointing out that seemingly minor assump-tions and changes in the fundamental build-ing period can have far reaching effects forseismic design.

Wind Periods

While the use of the fundamental buildingperiod for seismic design calculations is wellestablished, the parameters used for winddesign have traditionally not been as clear.For wind design, the building period is onlyrelevant for those buildings designated as“flexible” (having a fundamental building

period exceeding one second). When a buildis designated as flexible, the fundamenbuilding period is introduced into the geffect factor, Gf , in the form of the buildnatural frequency, which is simply the inveof the fundamental building period.So, what building period should be us

Prior to ASCE 7-05, little guidance provided and designers typically used eitthe approximate equations within the seism

section or the values provided by an automaeigenvalue analysis. Unfortunately, neitof these solutions is the best option, athe first can actually be unconservative.previously discussed, the approximate seismequations are intentionally skewed towashorter building periods. Thus for wdesign, where longer periods equate to higbase shears, their use can provide potentiunconservative results. Also, the resultsan eigenvalue analysis can yield buildperiods much longer than those observedactual tests, thus providing potentially ov

conservative results. So what is a designerdo? The good news is that the ASCE 7Commentary presents recommendations building natural frequencies to be used

wind design. These recommendations are written in the same form as the approximempirical equations provided in the seissection in Table 1 (page 25) and plottedFigure 2 for comparison. Many of threcommendations originated from the sastudy performed to determine approximequations for seismic design and represan upper bound of the measured build

periods. This upper bound equation resin conservative wind load estimates. Tratio of the “wind” periods to the “seismperiods is approximately 1.4 to 1.6, tmirroring the coefficient for the upper lion calculated period for seismic design.

Damping

Another consideration that goes hain-hand with the determination of buildperiods is the value of damping for structure. Damping is any effect that reduthe amplitude of vibrations. For buildin

damping results from many conditiranging from the presence of interior partit walls, to concrete cracking, to deliberately gineered damping devices. For seismic sign, five percent of critical dampingtypically assumed for systems withengineered damping devices. The dampvalues used for wind design are much lowebuildings subject to wind loads are generresponding within the elastic range as oppothe inelastic range for seismic loading, whadditional damping is provided from sev

Approximate Fundamental Period Equation:

T a = Ct hn x

(ASCE 7-05 Eqn. 12.8-7)

SEISMIC Approximate Fundamental Period Parameters

Structure Type Ct x Reference1

Steel Moment-Resisting Frames 0.028 0.8 Table 12.8-2

Concrete Moment-Resisting Frames 0.016 0.9 Table 12.8-2Eccentrically Braced Steel Frames 0.03 0.75 Table 12.8-2

All Other Structural Systems 0.02 0.75 Table 12.8-2

WIND Approximate Fundamental Period Parameters

Structure Type Ct x Reference1

Steel Moment-Resisting Frames 0.045 0.8Commentary Eqn.C6-14

Concrete Moment-Resisting Frames 0.023 0.9Commentary Eqn.C6-15

All Other Structural Systems (h<400 ft) 0.013 1Commentary Eqn.C6-18

All Other Structural Systems (h>400 ft) 0.0067 1Commentary Eqn.C6-19

Note 1: References are to ASCE 7-05

Table 1: Approximate Fundamental Period Parameters.



concrete cracking and/or plastic hinging. Again, the ASCE 7-05 Commentary pro-vides guidance, suggesting a damping valueof one percent be used for steel buildingsand two percent be used for concretebuildings. The Commentary is explicit thatthese wind damping values are typicallyassociated with determining wind loadsfor serviceability and simply states that“because the level of structural response inthe serviceability and survivability statesis different, the damping values associatedwith these states may differ.”

So, what values are design engineers sup-posed to use for ultimate level (1.6W) windloads? Several resources are available that

provide values of damping for service andultimate loads. The values provided varygreatly depending upon the resource andthe type of lateral force resisting system used– from a low of 0.5 percent to a high of 16percent or more. For simplicity, the authorsuggests using the recommended one per-cent and two percent values for steel andconcrete buildings, respectively, for bothservice and ultimate loads for two reasons.First, as buildings are subjected to ultimatelevel forces, severe cracking of concrete sec-tions and plastic hinging of steel sections

have the dual effect of both increasingdamping but also softening the building andincreasing the fundamental building period.

0 50 100 150 200 250 300 400350 450 500 6005500.950

1.000

1.050

1.100

1.150

1.200

1.300

1.400

1.500

1.250

1.350

1.450

G f l e x i b l e

/ ( G r

i g i d

= 0 . 8

5 )

Building Height (Feet)

Key:MRF = Moment Resisting FramesGflexible = Gust Factor for Flexible Buildings (ASCE 7-05 Section 6.5.8.2)Grigid = Gust Factor for Rigid Buildings (Taken as 0.85 as Allowed per ASCE 7-05 Section 6.5.8.1)

Steel MRF (Damping = 1%)(Recommended Damping)

Concrete MRF (Damping = 2%)(Recommended Damping)

Concrete MRF (Damping = 4%)(2x Recommended Damping)

Steel MRF (Damping = 2%)(2x Recommended Damping)

Figure 3: Effect of Building Flexibility on Gust Factor for 100-foot x 100-foot Building.

It has been postulated that the increase idamping and period generally compensateach other, and adequate results can be obtained by utilizing factored forces based oservice level periods and damping valuesSecond, as is shown in the following sectionthe level of damping has only a minor effecon the overall base shear for wind design foa large majority of low and mid-rise buildinstructures. Where serviceability criteria gov

ern, such as accelerations for tall buildingsa more in-depth study of damping criteria itypically warranted.

Low/Mid-Rise

Figure 3 illustrates the effect of the fundamental building period and damping valueon the gust factor for a representative 100-foox 100-foot building structure. The buildinfootprint has a considerable effect on thesvalues, and buildings with larger footprintare less prone to dynamic effects. In general, buildings less than 50 feet tall can b

considered rigid no matter the lateral forcresisting system used. For this representativcase, even at 150 feet tall, the overall effecof the building dynamic response on th

wind base shear (as predicted by the ratio othe flexible gust factor Gf to the rigid gusfactor G = 0.85) is less than 15 percent for steel moment resisting frame and less than percent for a concrete moment resistinframe with the recommended damping values. Stiffer structural systems, such as bracedframes and shearwall buildings, exhibieven less dynamic response. It can safely b

stated that for a large majority of buildinconstruction in the United States, whicconsists of low-rise and mid-rise construction, the effect of the building period o

wind base shears is minimal.

High-Rise

Figure 3 also illustrates that the effect odynamic building response and dampinvalues on wind forces can be significant fotaller buildings. The topic of dynamic winresponse is an involved one, and there ia wealth of information in the literatur

regarding it. The ASCE 7-05 Commentarand References serve as an excellent startinpoint for those looking to broaden theiknowledge in this area.It should first be recognized that the us

of the code-based gust effect factor is aapproximation based on several simplifyinassumptions. One of these assumptions ithat the building has a linear mode shape ana uniform mass distribution over the height othe building. The ASCE 7-05 Commentarprovides an alternate procedure which ca

00 50 100 150 200 250 300 400 500 600350 450 550

1

2

3

4

5

6

7

8

0.5

1.5

2.5

3.5

4.5

5.5

6.5

7.5

F u n d a m e n t a l P e r i o d ( S e c o n d s )

Building Height (Feet)

Key:MRF = Moment Resisting FramesEBSF = Eccentrically Braced Steel FramesSee Table 1 for Formulas Used

Steel-MRF (Wind)

Steel-MRF (Seismic)

Concrete-MRF (Seismic)

EBSF (Seismic)

Other (Seismic)

Concrete-MRF ( Wind)

Other (Wind)

Figure 2: Approximate Fundamental Period vs. Building Height.



be used to capture more accurately thedistribution of mass and stiffness throughoutthe building height based on redistributingthe peak-base moment throughout thebuilding, similar to the equivalent lateralforce procedure for seismic design. Also,the code-based provisions assume that onlyalong-wind response (wind blowing againstthe face of the building) and not across-windor torsional response will control the buildingdesign. Again, the Commentary provides useful

insight into this issue including a web-site(http://aerodata.ce.nd.edu/interface/interface.html) that can be used to aid in thedetermination of the effects of across-windand torsional response in the preliminarystages of design. Finally, the prescribedforces in ASCE 7-05 are for “regular-shaped”buildings only. A wind-tunnel analysis shouldbe performed for all unusually shapedstructures. It has also been the experience ofthe author’s firm that a wind tunnel analysis isbeneficial for buildings exceeding thirty storiesin height in terms of accelerations, cladding

pressures, and base overturning moments.

Conclusion

In summary, the computation of the funda-mental building period is an essential element

Will Jacobs, P.E., is a s tructural engineerat SDL Structural Engineers in Atlanta,Georgia. Will is also an active memberof AISC’s Committee on CompositeConstruction and ASCE’s Methods ofDesign Committee and may be reachedvia email at [email protected] .

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for calculating lateral load effects due to bothseismic and wind forces. Code prescribedempirical equations for calculating approxi-mate building periods are easy to implementand are now provided for both seismic and,in a slightly different form, wind design. Byunderstanding the background behind theseequations and the assumptions inherent in theCode, the designer can confidently “move for-

ward” with their implementation.▪

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- ,

References

Amanat, K.M., & Hoque, E. (2006). A rationale for determining the natural period of building frames having infill. Engineering Structures, 28 (4), 495-502.

American Society of Civil Engineers (ASCE). (2005). Minimum Design Loads for Buildings Other Structures . ASCE/SEI 7-05. Reston, VA: Author.

Goel, R.K., & Chopra, A.K. (1997). Period formulas for moment-resisting frame buildingStruct. Engrg., 123(11), 1454-1461.

Goel, R.K., & Chopra, A.K. (1998). Period formulas for concrete shear wall buildingsStruct. Engrg., 124 (4), 426-433.

Robertson, L., & Naka, T. (1980). Tall Building Criteria and Loading (Monograph: CounciTall Buildings & Urban Habitat). Reston, VA: American Society of Civil Engineers.

Sataka, N., Suda, K., Arakawa, T., Sasaki, A., & Tamura, Y. (2003). Damping evaluatusing full-scale data of buildings in Japan. J. Struct. Engrg., 129 (4), 470-477.

Smith, B.S., & Coull, A. (1991). Tall Building Structures. Hoboken, NJ: Wiley-Interscience.

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