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Performance of reinforced concrete frames using force and

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Engineering Structures 22(2000)

352–363

/locate/engstruct

displacement bad ismic asssment methods

A.M.Chandler a ,P.A.Mendis

b,*

Department of Civil Engineering,The University of Hong Kong,Pokfulam Road,Hong Kong

Department of Civil and Environmental Engineering,The University of Melbourne,Parkville,Victoria 3052,Australia

Received 23January 1998;received in revid form 6October 1998;accepted 6October 1998

Abstract

This paper reviews the traditional force-bad (FB)ismic design method and the newly propod displacement-bad (DB)ismic asssment approach.A ca study is prented for reinforced concrete (RC)moment-resisting frames designed and detailed according to European and Australian earthquake code provisions,having low,medium and high ductility capacity.The aim is to asss the performance characteristics of the frames,using the well known El Centro NS earthquake ground motion as the ismic input.Overall ductility demands have been computed for the force-bad analys conducted on the typical design frames.In the cond part of the paper,the performance of the ca study frames has been re-evaluated in the light of displacement-bad principles.A recently propod method for displacement-bad ismic asssment of existing RC frame structures has been implemented for this purpo,from which it has been concluded that the displacement-bad approach predicts very similar overall displacement demands for such frames.The results,whilst limited to the consideration of a small number of ismic frame structures and a single,typical strong earthquake ground motion,nevertheless give conﬁdence that the displacement-bad approach can rapidly and easily facilitate a ismic asssment of an existing RC structure,without the necessity to undertake detailed inelastic dynamic analys.©1999Elvier Science Ltd.All rights rerved.

Keywords:RC frames;Seismic asssment;Yielding;Ductility demands;Displacements

1.Introduction

Reinforced concrete (RC)moment resisting frames are a common lateral force resisting structural system in low to medium ri buildings in ismically active parts of Europe,Australia,Western U.S.A.and many other parts of the world.In Europe and Australia,with the introduction of the new uniﬁed ismic code EC8[1]and the new earthquake standard AS 1170.4[2],most of the medium to low ri buildings will be subjected to ismic design.

The major difference in the design approach for is-mic forces (as oppod to wind forces)as a lateral force is that the designer is allowed to utili the ductile capacity of the structure and design for reduced lateral forces.In this way,the elastic design strengths can be substantially reduced on the provision of adequate duc-

*Corresponding author.Tel:ϩ61-3-9344-6789;fax:ϩ61-3-9344-4616.

tility capacity of the structure,to sustain an appreciable amount of plastic deformation under a maximum cred-ible earthquake condition.Both EC8and AS1170.4specify three levels of lateral forces and corresponding ductility ratios for the design of RC moment resisting frames.The ductility demands experienced at critical locations in such frames when they form a plastic mech-anism under sustained inelastic loading (as generated by vere earthquakes),have traditionally been regarded as a key measure of potential ismic structural damage.Recently however there has been a shift of attention away from such traditional methods of ismic design,bad on the view that a strong correlation may be obrved between the global and local (storey)displace-ments or deformations of a structure,and the damage recorded in earthquakes [3–7].The development of the so-called displacement-bad (DB)design methods has been stimulated largely by the view that both damage and ultimate failure of an earthquake resistant structure are more fundamentally dependent on the exceedance of displacement or ductility capacity than the exceedance of

353 A.M.Chandler,P.A.Mendis/Engineering Structures22(2000)352–363

strength capacity.The latter is embodied in all existing ismic design codes which traditionally focus the designer’s attention on achieving required strength, rather than the required combination of elastic stiffness and inelastic energy-dissipating capacity,which is the focus of displacement-bad(D

B)approaches. Esntially,for standard types of building structures such as RC moment resisting frames,both the traditional force-bad(FB)design approach[8]and the newly pro-pod DB design methods have similar overall objec-tives which are to give an acceptable performance of the structure by limiting structural damage and preventing overall collap under the designated ultimate limit state earthquake,conventionally bad on the1in500year event.But becau the two methods tend to approach the problem from opposite ends of the design process, questions ari as to the comparability of the approaches and their relative effectiveness in achieving the aims. In the force-bad method,the structural displacements and element beam/column ductility demands are end products of the procedure which are not directly control-lable by the designer.In the displacement-bad method, by contrast,the displacements and ductility demands become fundamental design parameters and the pro-cedure aims to ensure that the design targets or capacities t for the parameters will not be exceeded under the design-level earthquake ground motion.

This paper brieﬂy reviews the requirements of earth-quake standards,EC8and AS1170.4for design and detailing of RC frame structures under the traditional force-bad approach.A ca study is then prented for frames designed with low,medium and high ductility capacity,to asss the performance levels and the yield-ing mechanisms of the frames,using the well known El Centro N

S earthquake ground motion as the ismic input.The spectral characteristics of this earthquake are known to match cloly the design spectral shapes adopted in the European[1],Australian[2]and U.S.A.

[9]earthquake codes for earthquakes onﬁrm soil sites. From both static inelastic push-over analysis and dynamic time history analys,it has been concluded that the ismic frames with low and intermediate duc-tility both form column hinging collap mechanisms when subjected to the El Centro earthquake.The special moment resisting frame(SMRF)detailed for high duc-tility capacity generally has been found to develop plas-tic hinges in the beams rather than the columns,which is consistent with the ACI318[10]strong column-weak beam detailing philosophy ud in the design of this SMRF.Overall ductility demands have also been com-puted for the FB analys conducted on the typical design frames.

In the cond part of the paper,the performance of the designed frames has been re-evaluated in the light of displacement-bad principles.The method recently propod by rearchers such as Priestley[7]for dis-placement-bad asssment of RC frame structures has been implemented for this purpo,from which it has been concluded that the displacement-bad approach predicts very similar overall displacement demands for such frames.

2.Structural respon modiﬁcation

The respon modiﬁcation factor,R f,as implied by the ismic standards is the ratio of the total elastic strength demand under the design earthquake,C eu,and theﬁrst yield load level,C s(Fig.1).

R fϭ

C eu

C s

ϭC eu

C y

ϫC y

C s

(1)

As en from Eq.(1),the respon modiﬁcation factor depends on two parameters:

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(a)The available ductility,which is expresd by duc-tility reduction factor R␮,deﬁned as:

R␮ϭ

C eu

C y

(2)

Where,R␮ϭ␮for equal displacement R␮ϭ√2␮Ϫ1for equal energy and,

(b)The rerve strength that exists between the actual structural yield and theﬁrst member yield(assuming elastic-plastic idealisation),which is expresd by the over-strength factor,⍀,deﬁned as:

⍀ϭC y小明成人看看

C s

(3)

拒绝别人

Eq.(1)can be rewritten in terms of the over-strength factor and the ductility reduction factor as given by Eq.(4).

R fϭ

C eu

C y

ϫC y

C s

ϭR␮⍀(4)

It is evident that in redundant structures,the over-strength of the structural system can be equally as important as the ductility,in the lection of appropriate structural respon modiﬁcation factors.

In addition to the factors,extra over-strength is pro-vided to the structure indirectly by the strength reduction factor,␾,given in AS3600[11].In effect at the design stage,the strength reduction factors(

eg.␾ϭ0.8for bending)reduce the dependable elastic strength of the overall structure from C s to C e(Fig.1).

C eϭ

C s

1.25

(5)

354 A.M.Chandler,P.A.Mendis /Engineering Structures 22(2000)

352–363

Fig.1.Full range structural respon.

Both EC8and the Australian earthquake standard AS1170.4specify three levels of design elastic strengths,C s ,with appropriate ductility requirements for RC moment resisting frames.Table 1gives a summary of the Australian Standard requirements for ismic RC frames,where C is the ismic design ba shear coef-ﬁcient,S the soil parameter (ϭ1.0for rock sites and 1.2for stiff soil sites)and I ,the structure importance factor (ϭ1.25for structures with an important post-earthquake function).

In the European ismic code EC8,with regard to the required hysteretic dissipation capacity three ductility class DC“L”(low ductility),DC“M”(medium ductility)and DC“H”(high ductility)are distinguished for concrete structures:

DC“L”.Ductility Class “L”corresponds to structures designed and dimensioned according to EC2[12],supplemented by rules enhancing available ductility.DC“M”.Ductility Class “M”corresponds to struc-tures designed,dimensioned and detailed according to speciﬁc earthquake resistant provisions,enabling the structure to enter well within the inelastic range

Table 1

AS 1170.4requirements for reinforced concrete frames Type

Seismicity

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C s

R f Detailing

Ordinary Moment Resisting All areas h Ͻ50m for a .S >C s ϭCSI/425%of C eu 4AS 3600(low ductile)

Frames (OMRF)

0.10Intermediate Moment Resisting All areas C s ϭCSI/617%of C eu 6AS 3600,Appendix A (limited Frames (IMRF)

理论和实践的关系ductility)

Special Moment Resisting All areas冷风里

C s ϭCSI/812.5%of C eu

ACI 318–95Ch.21(fully ductile)

Frames (SMRF)

a ϭdesign ground acceleration (g).

under repeated reverd loading,without suffering brittle failures.

DC“H”.Ductility Class “H”corresponds to struc-tures for which the design,dimensioning and detailing provisions are such as to ensure,in respon to the ismic excitation,the development of chon stable mechanisms associated with large dissipation of hysteretic energy.

In order to provide the appropriate amount of ductility in the three ductility class,speciﬁc provisions for all structural elements must be satisﬁed in each class [13].In correspondence with the different available ductility in the three ductility class,different values of the behaviour factor,q ,are ud for each class.The behav-iour factor is the equivalent of the ductility reduction factor R ␮in Eq.(4).

In low ismicity zones such as in northern Europe,concrete buildings may be designed under the ismic load combination following only the rules of EC2[12]and neglecting the speciﬁc provisions given in EC8[1]provided a speciﬁc asssment of the behaviour factor q is made bad on the principles of EC8.

355 A.M.Chandler,P.A.Mendis/Engineering Structures22(2000)352–363

The behaviour factor q,introduced fundamentally to account for energy dissipation capacity is derived for each design direction as follows:

qϭq0k D k R k WՆ1.5(6) where,q0ϭbasic value of the behaviour factor,depen-dent on the structural type,k Dϭfactor reﬂecting the ductility class,k Rϭfactor reﬂecting the structural regu-larity in elevation,and k Wϭfactor reﬂecting the prevail-ing failure mode in structural systems with walls.

For regular RC moment-resisting frames,the factors k R and k W are both equal to unity and the basic value of the behaviour factor,q0is5.0.The factor k D reﬂecting the ductility class is taken as follows:

k Dϭ1.00for DC“H”,(7) 0.75for DC“M”and0.50for DC“L”

and hence for the equivalent three categories of regular RC frame structures given in Table1,the EC8values for q are as follows:

OMRF qϭ2.5

IMRF qϭ3.75(8) SMRF qϭ5.0

Hence,comparing the EC8q-values with the Aus-tralian code R f values in Table1,together with Eq.(4), it may be deduced that RC frame systems with over-strength factor,⍀ϭ1.6will have identical lateral design strengths(ba shear)when designed according to either EC8or AS1170.4,assuming equal soil and importance factors.In single degree of freedom systems,the respon modiﬁcation factor and the displacement duc-tility ratio are the same since the over-strength factor,⍀,equals unity[14].However the parameters are dif-ﬁcult to quantify in redundant structures.Conquently the current practice ud for predicting the non linear respon of complex redundant structures subjected to dynamic loading is bad on the simple scaling of the elastic respon of an equivalent single degree of free-dom system by the structural respon modiﬁcation fac-tor.This respon modiﬁcation factor,R f,is independent of ground motion and structural dynamic characteristics. Further discussion of the points and estimates of the over-strength factor,⍀,for the RC frame systems exam-ined in the ca studies of this paper are given el-where[15].

It is important that the level of ductility assumed in the design can be delivered by the structural system.The overall displacement ductility␮is deﬁned as⌬max/⌬yield where⌬max and⌬yield are the maximum and yield dis-placements at the top of the structure.This overall dis-placement ductility is generally considerably less than the local ductility demand of individual members deﬁned

by the rotational ductility,␪max/␪yield or the curvature ductility,␾max/␾yield(␪yield and␾yield are rotation and cur-vature at the yield level and␪max and␾max are the maximum rotation and curvature).The detailing require-ments and the drift limitations speciﬁed in Australia (AS3600[11]and AS1170.4[2])and in Europe(EC8

Part1.3[1])attempt to ensure that the local ductility demands of members can be achieved so that the overall

displacement ductility is not compromid.

A discussion of design and detailing requirements for the three class of RC frames studied herein,has been

given by DeSilva et al.[16].Overall,very similar requirements pertain to the design of ismic RC frames in Europe,as detailed in CEB[13].

In the ca of special moment resisting frames (SMRF),the recommended earthquake resistant design approach is to ensure that a rational yielding mechanism

develops when the structure is subjected to vere inelas-tic deformations.The concept of a strong c

olumn-weak beam is recommended by codes such as ACI318[10]

in regions of high ismicity.Generally,the curvature ductility demands are greater if the columns commence yielding prior to the beams,particularly if plastic hinges

form in the columns of one storey creating a‘soft’sto-rey.The above design and detailing requirements have been speciﬁed in ACI318–95to encourage plastic

hinges to develop in beams.However it should be noted that the requirements do not guarantee the prevention

of plastic hinges forming in columns.

3.Ca study1:force-bad(FB)ismic asssment

A ca study has been carried out to asss the per-

formance levels of different types of moment resisting frames recommended in AS1170.4and EC8.A typical 6storey building shown in Fig.2was chon for the ca

study and designed for three different ductility levels(R f ϭ4,6and8)in accordance with the recommendations of AS3600and AS1170.4.As noted above,the three

ductility levels correspond very cloly to tho desig-nated in EC8as DC“L”,“M”and“H”,respectively, e Eqs.(7)and(8).An additional frame structure was designed for gravity and wind loads,ignoring ismic loads.This structure is labeled as an existing structure as most of the existing structures in Australia are designed for gravity and wind forces only.A brief description of the design procedure,member reinforce-ment details,respon and yielding mechanisms are prented in this paper.A complete description is given by DeSilva[17].

356 A.M.Chandler,P.A.Mendis /Engineering Structures 22(2000)

352–363

Fig.2.Structure conﬁguration and member properties.

3.1.Design procedure

The preliminary estimation of member properties was bad on the equivalent static method speciﬁed in AS 1170.4[2].Main design parameters are summarid in Table 2.The ismicity is taken typical of that for a low to moderately active ismic region,with a design peak

Table 2

Design parameters,bad on the Australian earthquake code AS 1170.4

Lateral load resisting system 100%Moment resisting frames Dead Load due to lf weight 5.5kPa Dead Load due to ﬁxtures 1.3kPa Live Load (Floors)3kPa Live Load (Roof)1kPa

Load combinations

1.25DL ϩ1.5LL (All Spans)1.25DL ϩ1.5LL and 1.0DL (Alt.Spans)0.8DL ϩ1.5LL 1.1DL ϩ0.4LL

1.25DL ϩ0.4LL ϩW u 0.8DL ϩW u

1.0DL ϩ0.4LL ϩF eq

0.8(1.0DL ϩ0.4LL)ϩF eq

a ϭ0.11,S ϭ 1.0,R f ϭ4

Seismicity,Importance factor,Site

(OMRF),R f ϭ6(IMRF),R f ϭ8

factor and Respon modiﬁcation

(SMRF)I ϭ1.25(Structure with

factors

a post disaster function)

ground acceleration (500year return period)of a ϭ0.11g ,as further discusd below.3.2.Estimation of ismic forces

The fundamental or the natural period of a structure is required to estimate the ismic loads.The accurate estimation of the natural period depends on the mass and stiffness distribution of the struct

ure which in turn can-not be determined without the knowledge of the design loads.Conquently AS 1170.4provides an empirical formula for the calculation of the fundamental natural period bad on the height of the structure.T ϭ

h 46

(9)

Where h is the height of the building in metres.For the frame structure considered in this study,Eq.(9)gives a period estimated at 0.5conds.

In EC8[1],for buildings with heights up to 80m,the value of the fundamental period T may be approximated from the following formula.T ϭC t h 3

(10)

Where C t ϭ0.075for moment resisting concrete

357

A.M.Chandler,P.A.Mendis/Engineering Structures22(2000)352–363

frames as studied here.This empirical method gives a

period Tϭ0.8c,considerably larger than that esti-

mated from Eq.(9).

Signiﬁcant changes to the calculated design earth-

quake loads can result from inaccuracies in the esti-

mation of the natural period of the structure.However

the lateral load estimation,design,and detailing of the

frames are bad on the equivalent static method of AS

1170.4,with the intention of reprenting general design

practice,not only in Australia but also in other regions

of low to moderate ismicity.

The equivalent static ba shear was estimated using

the AS1170.4code formula for three ductility levels:

VϭC s G g(11)

Where C s is given in Table1and G g is the gravity

force,and deﬁned in AS1170.4as

G gϭGϩ␺c Q(12)

where,G is the dead load,Q is the live load,and␺c is

the factor for strength and stability limit state(␺cϭ0.4).

Lateral ismic load at each storey level was calcu-

lated using the inver triangular distribution rec-

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ommended in AS1170.4.A static analysis was perfor-

med for all the load combinations given in Table2.

Comparison of overturning moments due to wind and

earthquake forces are given in Fig.3.The members were

designed according to AS3600and detailed to the AS

1170.4requirements described in the previous ction.

Designed cross ctions and reinforcement details are

prented in Table3.

A push-over analysis was ud in this study[15]to

conﬁrm the over-strengths of the frames.The over-

strengths(⍀)calculated by Eq.(3)for OMRF,IMRF

and SMRF were1.3,1.4and1.8respectively.The

values conﬁrm that RC frame systems will approxi-

mately have identical lateral design strengths(ba

shear)when designed according to either EC8

Fig.3.Overturning moments due to lateral forces.AS1170.4,assuming equal soil and importance factors (e Section2).

3.3.Ground motions

The El Centro earthquake(PGAϭ0.33g)was lec-ted to reprent a major inter-plate earthquake(Fig.4). The time history analys were performed using the non-linear dynamic structural analysis program DRAIN2D [18].The beams were modelled by the Modiﬁed Takeda Model provided in the program.The column behaviour was modelled by the axial force-moment interaction relationship of the column cross-ction.A ground motion was also developed for the time history analys in the form of a synthetic accelerogram generated using the earthquake simulation program SIMQKE[19].This synthetic ground motion was generated with the AS1170.4design spectrum as the target spectrum.The details of this latter analysis are given elwhere[15].

3.4.Results from force-bad method

The following respon parameters are prented here to illustrate the dynamic behavioural charact

eristics of the structures designed for different ductility levels.The maximum storey displacements of frames with different ductility levels are compared in Fig.5.The roof dis-placement time history results of three moment resisting frames under theﬁrst10conds of the El Centro exci-tation are compared in Fig.6.The roof displacements of the three frame types do not differ substantially and are in all three cas less than0.6%of the building height (0.006hϭ13cm).It has been suggested by rearchers such as De Stefano et al.[20]that the ont of vere structural damage occurs approximately at an overall (roof)displacement of0.01h.Hence the damage levels in the considered frames are expected to be moderate, when subjected to the El Centro earthquake ground motion.

The yielding mechanisms of three moment resisting frames under El Centro earthquake are shown in Fig.7. The yielding mechanism of the“existing”frame (designed only for wind forces)is also compared in Fig.

7.All the structures other than the special moment resisting frame,which was designed using the capacity design concept,exhibited a column side sway mech-anism,as expected.Finally a comparison of the critical displacement ductility ratios are given in Table4under the El Centro earthquake.The yield displacement,⌬y,in Table4is the displacement at the top of the structure, when theﬁrst plastic hinge is formed.The displacement ductility demand of the special moment resisting fra

me was about three times more than that of the ordinary moment resisting frame.The additional ductility demands have resulted from the50%reduction(Table 1)in design elastic lateral force of the special moment

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