evaluating assumptions for seismic assessment of existing buildings

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Soil Dynamics and Earthquake Engineering 27 (2007) 223233

Evaluating assumptions for seismic assessment of existing buildings

V.G. Bardakis, S.E. Dritsos

Department of Civil Engineering, University of Patras, Patras 26500, Greece

Received 15 December 2005; received in revised form 5 July 2006; accepted 6 July 2006

Abstract

This paper evaluates the American FEMA 356 and the Greek GRECO (EC 8 based) procedural assumptions for the assessment of the

seismic capacity of existing buildings via pushover analyses. Available experimental results from a four-storeyed building are used tocompare the two different sets of assumptions. If the comparison is performed in terms of initial stiffness or plastic deformation

capacities, the different partial assumptions of the procedures lead to large discrepancies, while the opposite occurs when the comparison

is performed in terms of structural performance levels at target displacements. According to FEMA 356 assumptions, effective yield

point rigidities are approximately four times greater than those of EC 8. Both procedures predicted that the structure would behave

elastically during low-level excitation and that the structural performance level at target displacement for a high-level excitation would be

between the Immediate Occupancy and Life Safety performance levels.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: RC buildings; Performance-based seismic assessment; Non-linear procedures; Pushover analysis; Effective rigidities; Plastic hinge rotations;

Chord rotations

1. Introduction

Pushover procedures, to evaluate the seismic capacity of

existing buildings, represent the current trend in structural

engineering and promise a more accurate prediction of a

structures behaviour. The American pre-standard FEMA

356 [1] and the recent draft version of Part 3 of the

European Code EC 8[2], which is founded on relevant fib

[3,4]and CEB[5]reports, adopt the above procedures but

have different partial assumptions.

The draft Greek Retrofitting Code, GRECO [6], acting

within the EC 8 framework, accepts the whole European

procedure but suggests the displacement coefficient meth-od, DCM, to determine the target displacement, while EC

8[2]proposes the N2 method[7].

The present paper aims to compare the influence of the

different assumptions of the American pre-standard and

the European Codes for the assessment of existing

buildings via pushover analyses. However, since both

FEMA 356 [1] and GRECO [6] adopt the DCM methodand since a comparison of differences due to the method

of determining the target displacement is outside the scope

of this paper, GRECO [6] has been chosen for a more

direct comparison between the American and the European

procedures.

Available experimental results from a four-storeyed

building, tested at the ELSA Laboratory [8,9], have been

used as reference data to compare the two different sets of

assumptions. Performance-based evaluations have been

made for two levels of seismic action. The first level was

considered as the serviceability earthquake (low-level

excitation) while the second level was considered as themaximum design earthquake (high-level excitation).

The results of these evaluations are used for a detailed

comparison and are divided into the following two parts.

The first part of the paper focuses on local character-

istics. Different approximations to determine the available

plastic hinge or chord rotation of RC elements at every

performance level and the effective rigidity at yielding have

been assessed.

The second part of the paper presents a comparison of

elastic periods of vibration, performance points or target

ARTICLE IN PRESS

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doi:10.1016/j.soildyn.2006.07.001

Corresponding author. Tel.: +30 2610997780; fax: +30 2610996575.

E-mail addresses: [email protected], [email protected]

(S.E. Dritsos).
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displacements, plastic mechanisms, drift distributions and

locations of plastic hinges. These global characteristics,

calculated according to the two procedures (FEMA 356[1]

and GRECO [6]), are also compared with the available

experimental values.

2. Building description

A full-scale four-storeyed bare frame building model,

constructed and tested in 1992 at the ELSA Laboratory

[8,9], has been used for the analytical work of the present

study. The building was designed as a high ductility framed

structure, according to the then current drafts of EC 8 [10]

and EC 2 [11]. The materials used for the building model

were normal concrete of grade C25/30 and B500 steel

reinforcement bars and welded meshes[8,9]. The buildings

behaviour factor, q, was assumed to equal 5 [8,9]. Fig. 1

presents the plan of the building model. Dimensions in plan

were 10m 10 m, measured from the column centrelines

[8,9]. The inter-storey height of the ground floor level was

3.5 m and the other inter-storey heights were 3.0 m [8,9].

Further details concerning the construction of the building

model, the mechanical characteristics of the materials and

the amount of reinforcement can be found in the ELSA

report[9].

3. Non-linear element modelling

Plastic hinges were used to model the material non-

linearity. Stress against strain relationships, according to

the EC 2 model [11], were used to model the confined and

the unconfined concrete. XTRACT software[12]was used

to analyse element sections and to calculate flexural load

resistances. Plastic hinge generalised load against deforma-

tion diagrams used for the modelling [1,2,6,13] were

considered to be elastic, perfectly plastic representations

(the yield stage moment, My, equals to the ultimate stage

moment). Twenty interaction diagrams of axial force, N,

against ultimate bending moment were produced so thateach different column plastic hinge could be represented.

The columns had different properties because of differences

in geometry, concrete properties, longitudinal steel or

transverse steel. Each column plastic hinge had its own

axial load bending moment interaction diagram. For the

beams, forty-four pairs of flexural resistances (positive and

negative ultimate moment capacities) were calculated

because every different beam plastic hinge had its own

pair of flexural force resistances. Again, this was because of

differences in concrete properties, longitudinal steel or

transverse steel.

Average values for strength and maximum strain were

used to determine the flexural resistances (loads and

deformations), while characteristic values of the uniaxial

cylindrical concrete strength and the yield stress of the

longitudinal bars [9] were used to determine shear

resistances.

4. Local characteristics

4.1. Comparison of effective yield point rigidities and chord

rotations at yielding

The axial force at each plastic hinge was approximated

by an elastic analysis that took into account the quasi-

permanent gravity loads.

FEMA 356 [1] and ATC 40 [13] suggest modification

factors that decrease the elastic rigidity of the gross

concrete section. These modification factors usually equal

0.5 for columns and beams.

EC 8 [2] and GRECO [6] suggest the following

expression for the effective yield point rigidity:

EIeff My

3yyLs, (1)

where Ls denotes the shear span and yy is the chord

rotation at yielding evaluated from the following European(EC 8[2]and GRECO[6]) semi-empirical expression that is

based on the proposals of Panagiotakos and Fardis[14]:

yy 1=ryLsav z

3 0:0013511:5

h

Ls

y

d d1

db fy

6ffiffiffiffiffifc

p , 2where (1/r)yis the curvature at the yield stage, avis equal to

1 if shear cracking is expected, otherwise av is equal to 0,

zis the length of the internal level arm, h is the depth of the

cross-section, ey is the steel yield strain, d and d1 are the

respective depths to the tension and the compression

ARTICLE IN PRESS

5.0

0

5.0

0

6.00 4.00

Fig. 1. Plan of the bare frame building model [8,9].

V.G. Bardakis, S.E. Dritsos / Soil Dynamics and Earthquake Engineering 27 (2007) 223233224


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reinforcement, db is the average diameter of the tension

reinforcement, fy is the yield stress of the longitudinal bars

in MPa and fc is the uniaxial cylindrical concrete strength

in MPa.

It is obvious that the European expressions (Eqs. (1) and

(2)) are strongly related to internal axial forces and directly

involve one term for the slippage of longitudinal bars atjoints. The American modification factors do not strongly

take into account internal axial forces, nor do they directly

involve any slippage effect.

Another issue that affects results is the approximation

for the determination of the effective slab width. FEMA

356[1] suggests that the effective flange on each side of the

web of a beam is equal to the smaller of the provided flange

width, eight times the flange thickness, half the distance to

the next web or one-fifth of the span of the beam. GRECO

[6]suggests that the effective flange on each side of the web

is equal to the smaller of the provided flange width, half the

distance to the next web or one quarter of the span of the

beam. It is obvious that GRECO [6] gives slightly larger

values than FEMA 356 [1].

The calculated effective rigidities for columns from the

GRECO [6] procedure ranged from 6.7 103 to

23.8 103 kN m2 while values from the FEMA 356 [1]

procedure ranged from 30.5 103 to 57.4 103 kN m2. In

addition, the calculated effective rigidities for beams from

the GRECO [6] procedure ranged from 9.5 103 to

18.6 103 kN m2, while values from the FEMA 356 [1]

procedure ranged from 63.9 103 to 94.2 103 kN m2.

Fig. 2 presents a comparison of the calculated effective

rigidities of the columns (there are 36 values but some

points coincide because of symmetry) and of the calculatedeffective rigidities of the beams (there are 24 values but

again some points coincide because of symmetry), for the

direction of testing.

It can be seen from Fig. 2 that FEMA 356 [1]

assumptions lead to significantly higher values of EIeff.

For the columns, the average of the ratio of EIeffFEMA/

EIeffGRECO was equal to 3.55 with a standard deviation,s, of

0.72. For the beams, the average of the ratio of EI effFEMA/

EIeffGRECO was equal to 5.88 and s equalled 0.71.

The EC 8[2]and GRECO[6]assumptions correspond to

effective stiffness ratios (the ratio of the effective stiffness

to the elastic stiffness of the gross concrete section) for the

building model that range from 10% to 22% for the

columns and from 6% to 10% for the beams. As stated by

fib [4], values determined by expressions like Eq. (1) are

significantly lower than values implied by codes for thedesign of new buildings [1517].

The chord rotation at element yielding is not required by

the FEMA 356 [1] procedure and is only used in internal

computer program calculations based on the procedure. In

order to make comparisons for this evaluation, the FEMA

356 [1] effective chord rotation at element yielding was

defined by Eq. (1).

The calculatedyy values for columns from the GRECO

[6] procedure ranged from 0.01 to 0.013 rad while values

from the FEMA 356 [1] procedure ranged from 0.002 to

0.007 rad. In addition, the calculated yy values for beams

from the GRECO [6] procedure ranged from 0.011 to

0.016 rad while values from the FEMA 356 [1] procedure

ranged from 0.001 to 0.005 rad. Fig. 3 presents a

comparison of the calculated yy values for the columns

(there are 72 points because each of the 36 columns had 2

plastic hinges and 1 sign as the columns are symmetrical)

and for the beams (there are 96 points because each of the

24 beams had 2 plastic hinges and 2 signs as the beams are

not symmetrical), for the direction of testing.

It can be seen from Fig. 3 that FEMA 356 [1]

assumptions led to lower values. For the columns, the

average of the ratio ofyyeffFEMA/yy

GRECO equalled 0.3 with s

equal to 0.08 and for the beams, the average of the ratio of

yyeffFEMA

/yyGRECO

equalled 0.2 and s equalled 0.06.As demonstrated by Fig. 3, results for yyeff

FEMA are in

disagreement with the assumption of fib [4], which

considers that FEMA 356 [1] implies values for the yield

rotation that are approximately equal to 0.005 rad for RC

beams and columns.

4.2. Comparison of plastic rotations

In order to calculate plastic rotation capacities according

to either the American recommendations or the European

Codes, a pushover analysis must be performed to

determine internal forces (axial and shear) and moments.

More details about the pushover analyses (an iterative

procedure to calculate plastic rotation capacities) can be

found in Section 5 below.

The FEMA 356 [1] procedure provides values for the

plastic hinge rotation capacity of RC elements. These are

given as acceptable limiting values at every performance

level and are a function of the type of element (beam or

column), the reinforcement, the axial and the shear force

levels and the detailing of the RC elements. For this

evaluation, programmed spreadsheets were used to create

an interactive database [18] of plastic hinge capacities, as

determined according to Tables 67 and Tables 68 of

FEMA 356 [1]. Specifically, plastic hinge rotation capa-

ARTICLE IN PRESS

Columns Beams

EIFEMA(X103kNm

2)

55

45

255 20

90

75

60

8.5 18.5

eff

EIFEMA(X103kNm

2)

eff

EIGRECO (X103kNm2)eff

EIGRECO (X103kNm2)eff

Fig. 2. Comparison of EIeff values.

V.G. Bardakis, S.E. Dritsos / Soil Dynamics and Earthquake Engineering 27 (2007) 223233 225


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cities of beams depend on the shear or the flexure

controlled behaviour, the ratio (rr0)/rbal., the spacing

of the stirrups and the ratio V/(bwd(fc)1/2). Plastic hinge

rotation capacities of columns depend on the shear

controlled or the flexure controlled behaviour, the ratio

N/(bdfc), the spacing of stirrups and the ratioV/(bwd(fc)1/2).

In the above equations, Vis the shear force, ris the ratio of

tension reinforcement, r0 is the ratio of the compression

reinforcement, rbal is the ratio that produces balanced

strain conditions andb and bware, respectively, the widths

of the cross-section and the web.

Following on from semi-empirical expressions proposed

by Panagiotakos and Fardis[14], EC 8[2] and GRECO[6]

provide semi-empirical expressions for the ultimate plastic

chord rotation, yupl, and modification factors in order to

convert average values at the ultimate stage to acceptablelimiting values at every performance level.

For beam and columns with a rectangular cross-section,

EC 8 [2] and GRECO [6] suggest the following empirical

relationship:

yupl 0:01450:25n max0:01;o

0

max0:01;o

0:3fc

0:2 Ls

h

0:35

25ars

fywfc

1:275100rd , 3

wheren equalsN/(bhfc),o and o0, respectively, equalrfy/fc

and r0fy/fc,a is a confinement effectiveness factor,rsis the

ratio of transverse reinforcement parallel to the direction of

loading,fywis the transverse reinforcement steel yield stress

and rd is the ratio of diagonal reinforcement in each

diagonal direction.

For the acceptable limit values of Immediate Occupancy,

Life Safety and Collapse Prevention, GRECO [6] suggests

the following relationships:

yIOpllim 0; yLSpllim

0:5yupl=gRd; yCPpllim

yupl=gRd

andgRd 1:8, 4

where IO is Immediate Occupancy, LS is Life Safety and

CP is Collapse Prevention.

It should be noted that the gRd value is used to convert

mean values from Eq. (3) to mean minus one standard

deviation bounds and is used because of the unavoidable

uncertainty of the model.

For this evaluation, spreadsheets were used to create a

database[18]of plastic chord rotation capacities according

to the above expressions. It was decided to use plastic

chord rotation capacities instead of total chord rotation

capacities due to software limitations. The ETABS

computer program [19] provides a model with perfor-

mance-based point hinges at the ends that are rigid plastic.

This model is essential for an evaluation via an event to

event controlled pushover analysis with the ETABS

software[19].

Calculated available plastic chord rotations at the Life

Safety performance level from the GRECO [6] procedureranged from 0.002 to 0.042 rad, while values from the

FEMA 356[1] procedure ranged from 0.015 to 0.02 rad. In

addition, the calculated available plastic chord rotations at

the Collapse Prevention performance level from the

GRECO [6] procedure ranged from 0.003 to 0.083 rad,

while values from the FEMA 356 [1] procedure ranged

from 0.02 to 0.025 rad. Comparisons of available plastic

chord rotations at the local performance levels of the two

procedures that could be considered as similar (Life Safety

and Collapse Prevention) are presented in Figs. 4 and 5.

Specifically, 144 points (36 columns have 2 plastic hinges

and 2 directions of loading) for columns and 96 points (24

beams have 2 plastic hinges and 2 directions of loading) for

beams are presented in Figs. 4 and 5. At the Immediate

Occupancy performance level, FEMA 356 [1] considers

small plastic deformations in the order of 0.01 rad for

beams and 0.005 rad for columns, while GRECO [6]

considers no plastic deformations.

FromFig. 4, it can be seen that, on average, the GRECO

[6]expression for yLSpllimgives lower values than FEMA 356

[1] while, from Fig. 5, on average, the GRECO [6]

expression for yCPpllimgives higher values than FEMA 356

[1]. Even for the case of the Collapse Prevention level, it

can be seen that a small percentage of FEMA 356[1]values

are greater than GRECO [6] values. The above compar-

ARTICLE IN PRESS

Columns

FE

MA

ye

ff

FEMA

ye

ff

0.007

0.004

0.0010.009 0.013 0.017

0.005

0.003

0.0010.010 0.014 0.018

Beams

GRECO

y

GRECOy

Fig. 3. Comparison ofyy values



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isons appear to agree with the statements of fib [4].

According to fib[4], if the values given by FEMA 356 [1],

at the Collapse Prevention level, are meant to be mean, m,

minus one standard deviation bounds, then in some cases,

for well-detailed elements, they provide larger values than

the fib- [4]based expressions. Values given by FEMA 356

[1] could be considered as more conservative than the

values given by the GRECO [6] expression, if they are

meant to be average values (not ms values) at the

ultimate stage. In this case, the GRECO[6]values shown in

Fig. 5should be multiplied by gRd equal to 1.8.

In addition, it is obvious that FEMA 356 [1] values are

generally constant for both columns and beams. In

contrast, the GRECO [6] values appear to be more case

dependent. FEMA 356 [1] tables give the same value for

columns with an axial force ratio (N/(bdfc)) lower than 0.1.

For beams, FEMA 356 [1] tables give slightly different

values because the ratio (rr0)/rbal is controlled by the

section flexural failure mode (failure of steel reinforcement

bars, failure of concrete, etc.). Furthermore, FEMA 356[1]

tables do not strongly relate the plastic rotation capacity to

the amount of transverse steel. The conforming property

that FEMA 356 [1] proposes is a very gross check that

depends on the spacing of the hoops (lower or greater than

d/3) and on the element shear strength provided by these

hoops (lower or greater than three quarters of the design

shear). As can be seen from Eqs. (3) and (4), the European

Codes strongly relate the plastic rotation capacity to the

ratio of the internal axial force to the gross section

compression capacity, as well as the product of the ratio

of the transverse steel parallel to the direction of loading

and the confinement effectiveness factor and the ratio of

yield stress of the transverse steel to the uniaxial cylindrical

concrete strength. In addition, the shear ratio check,

V/(bwd(fc)1/2), proposed by FEMA 356 [1] is not as

sensitive as the shear span ratio factor, (Ls/h)0.35, that is

inherent in Eq. (3) from the European Codes.

5. Pushover analysis

The evaluation of the structural system was performed

via three-dimensional pushover analyses. ETABS software

[19] was used only as a non-linear solver and a graphical

postprocessor because the remainder of the data had been

calculated with either programmed spreadsheets and/or

databases or XTRACT software [12]. Plastic hinges were

used to model the material non-linearity and the ETABS

[19]performance-based event to event strategy was used

for the solution. Geometric non-linearity effects only were

taken partially into account. Specifically, programmed

ARTICLE IN PRESS

Columns Beams0.021

0.019

0.017

0.0150.00 0.02 0.04 0.060.030.020.01

0.014

0.015

0.016

LSFEMA

p

llim

LSFEMA

p

l lim

pllim

LS GERCO pllim

LS GERCO

Fig. 4. Comparison ofyLSpllimvalues.

Columns Beams

CPFEMA

CPFEMA

pllim

pllim

pl l

im

pl l

im

CP GRECO

CP GRECO

0.027

0.025

0.023

0.0210.00 0.05 0.100.04 0.060.020.00

0.019

0.020

0.021

Fig. 5. Comparison ofyCPpllimvalues.



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databases were created for ultimate moment capacities,

chord rotations at element yielding, effective rigidities,

available plastic rotations (at the three performance levels),

shear capacities and element forces from the analysis. All

these databases were interactive [18]. For example, the

database of plastic rotation capacities received the element

forces from the corresponding database in order tocalculate ypl values. For the calculation of ypl capacities,

an iterative procedure must be used to find the final

internal element forces. The software could not manage

such an iterative procedure and this was done externally.

At least three analyses were carried out for each evaluation

and for each direction of loading. An elastic analysis was

performed to first yield, then a non-linear analysis was

carried out using the yplcapacities that had been calculated

according to the elastic element forces and, finally, a non-

linear analysis was performed using the ypl capacities that

had been calculated according to the previous non-linear

analysis.

5.1. Load patterns

According to the technical report [9], the mode shapes

had not significantly changed after the high-level excitation

test. Because of this and because of the fact that the

fundamental mode had a participating mass ratio of

approximately 85%, a modal pattern proportional to the

shape of the fundamental mode was applied in the

direction under consideration (for two signs of loading).

5.2. Determination of the structural performance level

For this paper, it was considered that local performance

levels determined the structural performance level in a

conservative way. That is, the structural performance level

was equal to the worst local performance level of all the

primary elements.

5.3. Seismic demand

Performance-based design procedures propose checking

the structural system for seismic demands from multiple

Seismic Hazard Levels. Similarly, pseudo-dynamic, PsD,

tests were performed for two values of peak ground

acceleration, PGA [8,9].

According to the technical report [9], an artificial

accelerogram was used as a basis for PsD tests. This

accelerogram fitted the response spectrum given by EC 8

[8,9] for soil profile B with 5% damping [9]. The nominal

PGA was considered to equal 0.3 g[8,9].

A low-level PsD test was performed with the reference

signal scaled by 0.4, while a high-level PsD test was

performed with the reference signal multiplied by 1.5[8,9].

The low-level excitation test, with a nominal PGA equal to

0.12 g, was assumed to correspond to the serviceability

limit state[8,9]. The high-level excitation test, with nominal

PGA equal to 0.45 g, was considered to be representative of

the maximum seismic action for which the frame had been

designed [8,9]. The corresponding pseudo-acceleration

spectra of these signals were calculated in order to

determine the demand spectra (for target displacement

calculation).

5.4. Performance point (target displacement) determination

The development of a capacity curve for a structure can

be extremely useful to the engineer. However, for evalua-

tion or for retrofit purposes, the probable maximum

displacement (performance point or target displacement,

dt) for the specified ground motion must be estimated [13].

An estimate of the displacement due to a given seismic

ground motion may be made by using the equal displace-

ment approximation. This approximation is based on the

assumption that the inelastic spectral displacement is the

same as the elastic spectral displacement. Because of the

possible inaccuracy of this approximation, a significant

amount of effort has been expended in the last few years to

develop simplified methods to estimate this displacement

[1,7,13,15,20]. Both FEMA 356[1]and GRECO[6]suggest

the DCM, which is based on a statistical analysis of the

results of time history analyses of single degree of freedom

systems.

The application of the DCM for this exercise was applied

via programmed spreadsheets and/or databases. An

iterative process must be performed in order to calculate

displacements from the DCM, as many variables (for

example, the structural performance level) are unknown. In

addition, bilinear idealisations of base shear against roof

displacement diagrams have to be performed. The equalenergy rule was applied in order to idealise the capacity

curve to the target displacement point. In order to calculate

the areas enclosed by the curve, above and below the

bilinear approximations, the linear part of the curve was

modelled by a linear function while the non-linear part of

the curve was modelled by a polynomial function.

6. Global characteristics

6.1. Effective (secant at yield) stiffness

It was expected that the different assumptions for

effective rigidities (Section 4.1 above) would produce

noticeable differences in the structural stiffness. Table 1

presents the mode periods from the elastic analyses

according to the FEMA 356 [1] and GRECO [6]

procedures.Table 1 also presents the periods measured at

ELSA Laboratory[8,9]from dynamic snap-back tests. As

stated in the technical report [9], different theoretical

models were analysed with different assumptions for the

collaborating slab width (ranging from 0 to the full width),

the initial stiffness (uncracked cross-section, cracked cross-

section) and the inclusion of slippage effect. The range of

calculated values[8,9]from these analyses is also presented

inTable 1.

ARTICLE IN PRESS



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From Table 1, it is obvious that GRECO [6] proposalslead to a large underestimation of the structural effective

stiffness. If the demand, in terms of section moments, is a

small portion of section moment capacity at yielding, then

GRECO[6] does not provide a good estimation of element

rigidity because GRECO [6] applies to element yielding.

The FEMA 356 [1] procedure leads to a slight under-

estimation. The proposals of FEMA 356 [1], regarding

effective rigidities, are similar to the assumptions of codes

for the design of new structures and so the conclusions of

this comparison may have a wider application.

6.2. Comparison of capacity curves

Fig. 6 shows a comparison of the calculated capacity

curves (in terms of base shear against roof displacement)

and the test measurements[8,9]for the low-level excitation

test.

FromFig. 6, it is clear that both the FEMA 356[1] and

GRECO[6] procedures are partially in agreement with the

test results[8,9]. Both procedures predicted that the model

structure would not develop plastic deformations but were

unable to predict the value of the experimentally obtained

base shear, Vb, that equalled 594 kN. The FEMA 356 [1]

procedure led to a base shear at target displacement, Vbt,

of 925 kN while the GRECO[6] procedure predicted a Vbt

equal to 321 kN. The FEMA 356 [1] procedure predicted

the initial stiffness of the model structure, while GRECO

[6] appears unable to predict the initial stiffness. The

maximum experimentally obtained displacement of 39 mm

was accurately predicted by both procedures. FEMA 356

[1] led to dt equal to 39.6 mm while GRECO [6] led to dt

equal to 44.0 mm.Fig. 6demonstrates that the FEMA 356[1] modelling assumptions are close to the pre-yield

characteristics of structural systems.

Fig. 7 shows the comparison of the resistances for the

high-level excitation test.Fig. 7also shows the envelope

curve of the experimental values. It is informative to

compare this idealised curve with the calculated curves to

their respective performance points.

As can be seen fromFig. 7, the FEMA 356[1] modelling

assumptions led to an overestimation of the elastic stiffness

of the structure and, because of this, the developed

experimental displacement of 210 mm was underestimated

(dtFEMA 164 mm). The predicted base shear at the target

displacement (VbtFEMA 1242 kN) could be considered to

be close to the experimental value [8,9]of 1442 kN and the

structural performance level was between the Immediate

Occupancy and the Life Safety levels.

Fig. 7also shows that the GRECO [6]procedure led to

an underestimation of the initial stiffness of the structure

and some events of the resistance history are neglected.

However, the target displacement (dtGRECO 181 mm) was

in better agreement with the experimental value [8,9]than

the FEMA 356 [1] prediction. The small difference in the

predicted base shear between the GRECO [6] procedure

(VbtGRECO 1149 kN) and the FEMA 356 [1] procedure

could be considered as negligible. The predicted structuralperformance level was between the Immediate Occupancy

and the Life Safety levels, as was the case with the FEMA

356[1]procedure.

Obviously, the very large difference in effective stiffness

observed from the two procedures does not substantially

ARTICLE IN PRESS

FEMA

GRECO

Targetdisplacement

Experimentalcurve [9] Roof Displacement (m)

Base

Shear

(kN)

1000

600

200

-0.100 -0.050 -0000 0.050 0.100-200

-600

-1000

Fig. 6. Comparison of capacity curves for the low-level excitation test.

FEMA

GRECO

Experimental curve [8,9]

Roof Displacement (m)

BaseShear(kN)

1500

1000

500

-0.6 -0.4 -0.2 0.2 0.4 0.600

-600

-2000

-1500

-1000

Envelope curve

IO level

LSlevel

CPlevel

Target displacement

(after Targ,Disp.)

Fig. 7. Comparison of capacity curves for the high-level excitation test.

Table 1

Comparison of periods

Period (s) Procedure ELSA theoretical and experimental

values [8,9]

FEMA GRECO Theoretical

analyses

Dynamic snap-

back tests

1st mode 0.62 1.10 0.45 0.53 0.53

2nd mode 0.20 0.36 0.17

3rd mode 0.11 0.20 0.10

4th mode 0.08 0.14 0.06



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influence the target displacement. It is worth noting that, in

principle, for periods corresponding to the descending

branch of the design acceleration spectrum, the target

displacement is linearly dependent on the square root of

the stiffness. In general, for most existing buildings, it can

be expected that GRECO [6] provisions will produce

periods that correspond to the descending branch of thedesign spectrum. Moreover, the frequency content of the

pseudo-acceleration spectrum corresponding to the test

accelerogram gave much lower values than the targeted

design spectrum (EC 8[15]) for the GRECO[6] model and

slightly higher values than the targeted design spectrum for

the FEMA [1] model, making target displacements even

closer despite the large difference in the stiffnesses from the

two procedures. It must be noted that the closeness of the

target displacements is a result peculiar to the specific tests.

In order to investigate the generality of the above findings,

additional calculations were performed using the EC 8 [15]

design spectrum instead of the test pseudo-acceleration

sspectrum. The following target displacements were ob-

tained:dtFEMA 38 mm anddt

GRECO 67 mm for the low-

level excitation test and dtFEMA 159 mm and dt

GRECO

273 mm for the high-level excitation test. In addition, if

the design spectrum of EC 8[15]was used, the GRECO[6]

procedure would lead to a more gradual manifestation of

plastic hinges. In other words, by following the GRECO [6]

procedure, more plastic hinges would be created and

greater rotations would occur. Therefore, if the design

spectrum of EC 8[15]was used, the plastic mechanism and

the performance level of the plastic hinges from GRECO

[6]would be closer to the FEMA [1]predictions. It has to

be pointed out that the degree of validity of calculatedresults involving only one time-history of base accelera-

tions is identical to the degree of validity of the test

program.

6.3. Comparison in terms of storey resistances

Fig. 8 presents a comparison of storey drift displacement

profiles at target displacement, dtstorey, for the two procedures

and the experimental maximum storey drift displacements for

the low-level excitation test. The FEMA 356 [1] procedure

predicted drift displacements that had an average of 10%

absolute difference from the experimental values. It could be

considered that the absolute difference (d (Danal.Dexper.)/

Dexper.) was uniformly distributed with storey level

(dstorey1 9%,dstorey2 +9%,dstorey3 7% anddstorey4

13%). The GRECO[6] procedure did not so accurately

predict drift displacements. The average absolute difference

from experimental values was 22% and the difference was

significant non-uniformly distributed (dstorey1 20%,

dstorey2 +20%, dstorey3 +21% and dstorey4 +25%).

Fig. 9presents a comparison of storey drift displacement

profiles at target displacement from the two procedures

and the experimental maximum storey drift displacements

for the high-level excitation test. The FEMA 356 [1]

procedure predicted storey displacements that had an

average of 33% absolute difference from the experimental

values. The difference was not uniformly distributed and its

absolute value increased with the height of the storey level

(dstorey1 16%, dstorey2 25%, dstorey3 37% and

dstorey4 53%). The GRECO [6] procedure predicted

storey displacements that had an average of 21% absolute

difference from the experimental value and the difference

was more uniformly distributed (dstorey1 30%, dstorey2

19%, dstorey3 16% and dstorey4 18%) than

the difference from the FEMA 356 [1] procedure. The

absolute difference decreased as the storey level increased.

For the left and the right loading directions,Figs. 10 and

11 present the deformed shapes and the patterns of the

inelastic mechanism at the target displacement for the high-

level excitation test, for the two procedures, according to

the results of the ETABS software [19]. These figures also

show the ETABS[19]coded state of the plastic hinges. The

ARTICLE IN PRESS

experimental

values [9]

FEMA

procedure

GRECO

procedure

4

3

2

1

00.00 0.01 0.02

Storey Drift Displacement (m)

Storey

Fig. 8. Comparison of storey drift displacement profiles, low-level

excitation test.

experimental

values [8,9]

FEMA

procedure

GRECO

procedure

4

3

2

1

0

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Storey Drift Displacement (m)

Storey

Fig. 9. Comparison of storey drift displacement profiles, high-level

excitation test.



9/11

IO coded state indicates that the plastic hinge performance

level was greater than, or equal to, the Immediate

Occupancy performance level and was lower than the Life

Safety performance level. The B coded state indicates that a

plastic hinge developed (the section had yielded) and its

performance level was lower than the Immediate Occu-

pancy performance level. For the GRECO [6] procedure,

there is no B coded state because the yield displacement is

equal to the limit displacement of the Immediate Occu-

pancy performance level. The damage according to the

FEMA 356[1]procedure (12 beam plastic hinges at the B

coded state, 24 beam plastic hinges at the IO coded state, 9

column plastic hinges at the B coded state and 9 column

plastic hinges at the IO coded state) is greater in global

ARTICLE IN PRESS

FEMA

B B B B

B B

BIO IO IO IO

IO IO IO IO

IOIO IO

FEMA

B B B B

B

B

IO IO IO IO

IO IO IO IO

IOIO IO

IO

IO IO

IOIO

IO

IO IO IO

IOIO IO

Experimental [8,9]

Experimental [8,9]GRECO GRECO

IO

Fig. 10. Comparison of the deformed shapes of the internal frame[8,9]and predictions.

FEMA

B B B B

B

B

IO IO IO IO

IO IO IO IO

IOIO IO

FEMA

B B B B

B

B

IO IO IO

IO IO IO IO

IOIO IO

IO

IO IO IO

IO IOIO

IO

IO IO IO

IOIO IO

Experimental [8,9]

Experimental [8,9]GRECO GRECO

Fig. 11. Comparison of the deformed shapes of the external frames[8,9]and predictions.



10/11

terms than the damage according to the GRECO [6]

procedure (30 beam plastic hinges at the IO coded state).

In order to broadly check theoretical predictions, the

middle frames of Figs. 10 and 11 show the experimental

results at the plastic hinge level, where the sizes of the

rhombuses represent (in scale) the size of the maximum

measured total rotation [8,9] for the high-level excitationtest. Because of the fact that the present comparison (at the

plastic hinge level) is performance based, a brief description

of the overall building behaviour during the high-level

excitation test, from the technical report [9], is reproduced

here: During the test, cracks opened (and closed) in the

critical regions of the beams of the first three storeys and of

most of the columns. Only cracks at the beam-to-column

interfaces remained permanently open. Neither spalling of

the cover, nor local instabilities of reinforcement was

observed. Beside the cracks at the beam-to-column inter-

face, which are apparent in the first three storeys and

represent an evidence of local yielding of the rebars, the

specimen remained apparently undamaged. In addition,

the report [9] stated that: The pattern of the maximum

rotations appears to be the one of a weak beam-strong

column mechanism, limited to the first three storeys.

Apparently no plastic hinges took place in the beams of

the external frame at the intersection with the central

column of the second storey. Finally, the report [9] also

stated that: The amount of slippage of the longitudinal

bars in the joint, leading to an increase of both the fixed-

end rotations and the pinching effect.

From Figs. 10 and 11 and from the above brief

description, it is obvious that both procedures predicted

the plastic mechanism and its absence in the fourth storey.Neither the FEMA 356[1] procedure nor the GRECO [6]

procedure predicted the behaviour of the beams of the

external frame at the intersection with the central column

of the second storey. The observed damage, as described in

the technical report [9] and briefly described above, in

terms of local performance levels, could be assumed to be

between the two predictions.

7. Conclusions

The present paper has evaluated the American and

European procedural assumptions for the assessment of

the seismic capacity of existing buildings via pushover

analyses. The FEMA 356- [1] and the Eurocode-based

GRECO [6] procedures have been followed in order to

assess a four-storeyed bare framed building and a

comparison has been made with available experimental

results [9]. The GRECO [6] procedure acts within the

European Code framework and broadly adopts EC 8 [2].

The conclusions of the present study are as follows:

(1) According to FEMA 356 [1] assumptions, effective

yield point rigidities are approximately three times

greater than those of the GRECO [6] procedure for

columns and are roughly five times greater for beams.

This is because effective chord rotations at element

yielding, according to the FEMA 356[1]procedure, are

in the order of one-third the effective chord rotations of

the GRECO [6] procedure for columns and one-fifth

the effective chord rotations for beams. Because of

these differences, there is a large divergence between the

two procedures when approximating the initial stiffnessof the model structure.

(2) The FEMA 356 [1] assumptions are close to the pre-

yield characteristics of structural systems and may be

rationalised for low-level earthquakes. The FEMA 356

[1] predictions of storey drift displacements for such

earthquakes appear to be more consistent with experi-

mental measurements. If the demand, in terms of

section moments, is a low percentage of the capacity,

then the GRECO [6] assumptions underestimated the

initial stiffness of the model structure because they refer

to yielding. However, the range of calculated base shear

values, when compared to the experimental measure-

ments [8,9] was greater for the low-level test than for

the high-level test. For the low-level test, the results

were not controlled by the strength of the structural

elements, which appear to be more predictable than the

rigidities of the structural elements[8,9].

(3) The FEMA 356 [1] available plastic rotations at the

Life Safety performance level are on average greater

than those of GRECO [6], while the opposite happens

for the Collapse Prevention performance level. The

GRECO assumptions appear to be more sensitive to

local characteristics (axial load level, shear force level,

amount of confinement, etc.), while the FEMA 356 [1]

tables give case-independent, steady values. As statedby fib[4], values at the ultimate stage given by FEMA

356 [1] for the case of well-detailed (conforming)

elements could be considered to be more conservative

than values given by the fib-based GRECO [6]

expression, if they are meant to be average values

(not mean minus one standard deviation bounds).

Because of the fact that these values refer to

performance limits (values at the ultimate stage equal

values at the Collapse Prevention level for primary

elements), it could be hypothesised that they are mean

minus one standard deviation bounds.

(4) At high-level excitation, the structural system had a low

rigidity due to slippage of the longitudinal bars at the

joints [8,9]. This phenomenon is directly taken into

account in plastic hinge models only by the GRECO[6]

procedure.

(5) For high-level earthquakes, the FEMA 356 [1] proce-

dure appears to overestimate rigidities and under-

estimate demand deformations. However, the

assumptions for deformation capacities lead the ap-

proach to essentially estimate the structural perfor-

mance level. Undoubtedly, the GRECO [6] procedure

followed a more direct route. Some events of the

resistance history on the capacity curve were neglected

but GRECO [6] essentially predicted the demand

ARTICLE IN PRESS



11/11

displacement of the system (performance point). It is

obvious that it also predicted the structural perfor-

mance level. In addition, the GRECO [6]prediction of

storey drift displacements was closer to the experi-

mental results.

(6) For the building under investigation, the GRECO [6]

procedure predicted higher deformations than theFEMA [1] procedure for high and low levels of

excitation. This was also found to be valid when the

EC 8[15]design spectrum was used.

(7) Essentially, both procedures predicted the elasto-plastic

collapse mechanism [8,9] and its storey-to-storey

distribution [9]. Both procedures also predicted the

creation of a plastic hinge in a region that behaved

elastically during the high-level test [9]. In addition, if

the design spectrum of EC 8 [15]was used rather than

the test accelerogram, the GRECO[6]procedure would

predict more plastic hinges and greater rotations.

Therefore, the plastic mechanism and the local

performance levels would be closer to the FEMA [1]

model.

(8) It is clear that, for the building under investigation, the

GRECO [6] procedure gave more reasonable predic-

tions for displacements at high levels of excitation,

while the FEMA [1] procedure gave better predictions

for displacements at low levels of excitation. This

conclusion appears to be valid in the more general case

when the EC 8 [15] design spectrum is used instead of

the test pseudo-acceleration spectrum.

Results of this comparison are only based on theevaluation of one model structure, which may not

represent all RC frame structures. However, although it

appears that the above conclusions could be generalised for

the case of framed RC structures with well-detailed critical

regions (potential plastic hinge regions) and low levels of

axial section forces, further research is required that

investigates other buildings using accelerograms with

different frequency contents.

Acknowledgements

The authors would like to express their gratitude to

ELSA (European Laboratory for Structural Assessment)

for providing the technical report [9] entitled Tests on a

Four-Storey Full-Scale RC Frame Designed According to

Eurocodes 8 and 2 and to Imbsen & Associates, Inc. for

providing a free license for the XTRACT software [12]

within the scope of[18]. In addition, the authors would like

to thank Dr. V. J. Moseley for his invaluable help during

the preparation of this paper.

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evaluating assumptions for seismic assessment of existing buildings

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