Brief Guide to Seismic Design Forces

8/12/2019 Brief Guide to Seismic Design Forces

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A Brief Guide to Seismic Design FactorsSEAOC Seismology Committee

Intent of SeismicDesign Factors

P

ast experience and observationof building behavior followingearthquakes has shown that a

structure can be economically designedfor a fraction of the estimated elasticseismic design forces, while maintainingthe basic life safety performance ob-

jective. This design philosophy impliesthat structural inelastic behavior (anddamage) is expected. This reductionin design seismic force is effectedthrough the use of a Seismic ResponseModification Factor, R . The intent ofthe R factor is to simplify the structuraldesign process such that only linearlyelastic static analysis (i.e., the equivalentlateral force procedure) is needed formost building design. While some deformation-controlledmembers, detailed to provide ductility,are expected to deform inelastically, force-controlled members that are designed toremain elastic would experience a sig-nificantly higher seismic force level thanthat predicted based on actual designseismic forces. To account for this effect,the code uses a seismic force amplificationfactor, Ωo, such that the realistic seismicforce in these force-controlled memberscan be conveniently calculated fromthe elastic design seismic forces. Ωo istermed the Structural OverstrengthFactor in ASCE 7-02/05. To controldrift or to check deformation capacityin some deformation-controlled mem-bers, a similar approach is also adopted.

A Deflection Amplification Factor isintroduced to predict expected maximumdeformations from that produced bythe design seismic forces. This factor istermed C d in ASCE 7-02/05.The typical response envelope relating

force to deformation is shown in Figure 1 and can be established from either test-ing or a pushover analysis (also knownas a “backbone curve”). The structurefirst responds elastically, which is thenfollowed by an inelastic response as thelateral forces are increased. A series ofplastic hinges form throughout the struc-ture, leading to a yielding mechanism atthe strength level V y .The design method follows a simplified

procedure. Based on the fundamental lin-

ear elastic period ofthe structure, a de-

signer first calculatesthe elastic designbase shear, V e (seepoint E in Figure 1).V e is then reduced bya factor, R , to estab-lish a design seismicforce level V s (pointS in Figure 1), be-yond which elasticanalysis is not valid: (UBC), the serviceability drift chec

was intended to minimize nonstructuradamage caused by more frequent minoor moderate earthquakes. A drift limof 0.005 of the story height is generallaccepted as effective for this purposeOriginally developed by ATC 3-06and later the NEHRP Seismic DesigProvisions , a second format checks inelastic story drift expected from the desigground motion at a value several timelarger than 0.005 of the story height. Thexpected inelastic drift, D u, is computeby amplifying the story drift, D s , by thdeflection amplification factor, C d (seFigure 1). The associated drift limit is ithe range of 0.015 to 0.025 of the storheight. In the 1985 UBC, the story driflimit for the design seismic forces, V wis 0.005K ; note that it is dependent othe system factor K . To understand thimplication of including K in the driflimit, consider the minimum requirestructural stiffness, which is representeby the initial slope of the response curvshown in Figure 2 . As both the desigbase shear and the drift limit contain thK factor, the minimum stiffness, whichis represented by the slope of segmenOW, required to minimize nonstructura

damage is independent of the ductilityrelated system factor K because thifactor is cancelled out in the designprocess. This practice of including the Kfactor in the drift limit (0.005) is justifiebecause the threshold for nonstructuradamage is the same, which is irrelevanto the structure’s ductility capacity. Thserviceability drift check is performed ithe elastic range because it is not expectethat structural damage would occur in minor or moderate earthquake.

Story D rif

E

Y

S

M

U

V e

V y

V s

Ds

Du

Dy

R1×

d R1×

oΩ×

d C ×

Ba se Sh e a r , V

Figure 1: Inelastic Force-Deformation Curve.

V s =V e R

To estimate internal forces that developin force-controlled members for capac-ity design, the corresponding forces atthe design seismic force level (V s ) arethen amplified by a system overstrengthfactor, Ωo. From an elastic analysis, thedrift at the V s level is determined via theamplification of displacement values bya deflection amplification factor, C d toestimate the maximum (inelastic) drift;this calculated drift is limited by build-ing code values.

Response Modification Factor The R factor can be traced back to

the K factor, which appeared in thefirst edition of the Blue Book (SEAOCRecommended Lateral Force Requirementsand Commentary ) in 1959. Althoughthe format of design base shear has beenchanged over the past four decades, thedesign base shear, after some adjustmentto account for the difference between

working stress design and strength de-sign, has not greatly varied. The purposeof any apparent change is to provide arational relationship between responsespectrum demand and the inelastic re-sponse reduction capabilities of a givenstructural system.

Deflection Amplification Factor

A deformation or story drift check in theforce-based design procedure has beenperformed in either of two formats inthe US: serviceability and ultimate limitstate check. Prior to the 1997 SEAOCBlue Book and Uniform Building Code



Story Dri f t , D

E

Y

1

M

V e

V y

V s

R1×

sΩ

B as e S hear, V

DΩ

M Ω2

3f i rst signi ficant

yield

S

O

Vs

0.005K o r 0.04/R w

R1

×

B as e S hear, V

WV

w

w R1

×

Story Dri f t Ratio

Figure 2: Story Drift Requirements. Figure 3: Components of System Overstrength.

System Overstrength Factor

To assist in the evaluation of the systemoverstrength factor, the 2001 NEHRPRecommended Provisions in its Commentarysuggest that the factor be subdivided intothree categories such that Ω o = Ω D Ω M Ω S (see Figure 3). Ω D represents the ratio in

lateral strength between Points 2 and 1 inthe figure, where Point 1 is the prescribedminimum design seismic force level, andPoint 2 represents the point of “nominal”first significant yield (e.g., the formationof a plastic hinge in a moment frame)based on nominal material strengths.This portion of the overstrength variesconsiderably from one system to another,yet it is the one that can be quantified easilyby elastic structural analysis tools. First, it issystem dependent. For systems like bracedframes and shear wall structures, ΩD can

be very low and close to unity; for othersystems like steel special moment-resistingframes whose design is usually dictated bydrift limitations, it is common that the ΩD value varies between 2 and 3. Second,ΩD ishighly dependent on the seismic zone.Ω M represents material overstrength. This

portion of the system overstrength, i.e., theratio in lateral strength between Points 2and 3 in the figure reflects the differencebetween the nominal and actual materialstrengths. Reinforced masonry, concrete,and steel provisions have historically useda factor of 1.25 to account for the ratio ofmean to specified strengths. A survey of

wide-flange shapes indicated that the ratiosof mean to specified yield strengths were1.37 and 1.15 for A36 and A572 Gr. 50steels, respectively.ΩS represents the systemoverstrength beyond the first significantyield point (Point 2 in the figure). It isdependent on the level of redundancycontained in the structure as well as theextent to which the designer has optimized



the various elements that participate in lateralforce resistance. See the NEHRP Provisionsfor further discussion on these components.


A comparison of deflection amplificationfactors in relation to response modificationfactors of several seismic provisions is sum-marized in Table 1.

Note that the C d /R ratio as specified in ASCE7-05, ranges from 0.5 to 1.0. The theoreticalrelationship of this ratio can be stated as:

for better performance of the building after

a major seismic event. This incentive ispromulgated through the use of R factorsin Building Frame Systems that are slightlyhigher than those for Bearing Systems.

Additionally, values of R assigned to DualSystems recognize the inherent redundancyof these designs.One might consider the variation of system

design factors across the continuum of struc-tural systems. Two systems, one with a highductility capacity and low overstrength andthe other with a low ductility capacity andhigh overstrength, can have the same value

of R . Nevertheless, numerous studies haveshown that the largest source of uncertaintyin predicting seismic response is contributedfrom the earthquake ground motion input.

For a single-degree-of-freedom system,Newmark and Hall in their 1982 EERImonograph, Earthquake Spectra and Design,suggested that that the C d /R ratio should beequal to 1.0 in the equal displacement range,and larger than 1.0 in the shorter periodrange. Table 1 shows that, except for the USseismic provisions, codes of other countriesfollow this rule.

Remaining ChallengesCurrently, the Applied Technology Coun-

cil is attempting to quantify certain aspectsof seismic design factors. Considering thecomplexity of a building structure withcomponents such as gravity load-carryingsystems and “nonstructural” components thatare not accounted for, and the limitations ofthe tools for analyzing idealized models, it is

expected that in the foreseeable future engi-neering judgment and lessons learned fromobserved building performance in earth-quakes will continue to play a vital role foradjusting the values of these system parameters.Current seismic design codes still do not

address the issue of permanent drift, whichcan be large, especially for near-fault groundmotions. While no provisions for permanentdrift currently exist, building codes havedeveloped an indirect consideration of thisissue through the provision of an incentive

T he Structural Engineers Association of California (SEAOC) is professionalassociation of four member organizations representing the structural engineeringcommunity in California. Their stated mission is “to advance the structural

engineering profession; to provide the public with structures of dependable performancethrough the application of state of the art structural engineering principles; to assist thepublic in obtaining professional structural engineering services; to promote natural hazard

mitigation; to provide structural engineers with the most current information and tools toimprove their practice; and to maintain the honor and dignity of the profession.”The SEAOC Blue Book, the new edition of SEAOC’s signature publication, provides

articles collected by the SEAOC Seismology Committee. New articles are added on anongoing basis. For specifics on the Blue Book, or for additional information on SeismologyPosition Statements and other Seismology related articles, visit www.SEAOC.org.Neither SEAOC, nor its members organizations, committees, authors, editors, or indi-

viduals who have contributed to this publication make any warranty, express or implied,or assume any legal liability or responsibility for the use, application of, and/or reference toopinions, findings, conclusions, or recommendations included in this publication.

SeismicProvisions

ResponseModification

Factor

Deflection

Amplification

Factor


Response Modification Factor

UBC 1994 1997

R w

R (3/8) R w

0.7R 0.3750.7

ASCE 7-05 R C d 0.5 – 1.0

Eurocode 8 q a q 1.0c

Mexico Q a Q 1.0c

New Zealand b

1.0c

NBC of Canada 1995 2005

R/U R d R o

R R d R o

U (=0.7)1.0

a period-dependent in the short period range; reduces to 1.0 at T = 0 sec.bperiod-dependent in the 0.45 (or 0.6) – 0.7 sec range; does not reduce to 1.0 at T = 0 sec.cgreater than 1.0 in the short period range.

Table 1: Comparison of Response Modification and Deflection Amplification Factors

Therefore, increased ductility capacity at

tained through detailing for enhanced ductility is preferred over the use of higher systemstrength with little improved ductile detailingOn this basis, although two systems may havthe same value of R , it may be appropriate tassign a higher reduction factor to a system

with greater ductility.The R -factor design approach was develope

as a compromise to achieve an economicadesign by accepting inelastic action in thstructure, yet allowing the structural engineea greatly simplified elastic analysis methofor use in routine design. It is critical to th

progression of the profession to retain thvision in our future efforts to improve thaccuracy of seismic design factors.

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R

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R dΩo

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Brief Guide to Seismic Design Forces