1

Seismic Assessment of an Old Reinforced Concrete

Building in the City of Lisbon

Duarte Ferreira dos Santos

duartecsantos@tecnico.ulisboa.pt

Instituto Superior Técnico, Lisbon, Portugal, 2016

ABSTRACT: The design of new buildings for seismic resistance was not fully implemented until the 1980’s in many

countries, including Portugal. Therefore, most reinforced concrete (RC) buildings built in the 1960´s were designed with

less amount of reinforcing steel than the ones designed according to the most recent seismic codes. Thus, the adequate

seismic assessment of old RC structures is essential to determine the eventual need to retrofit and the targets of the

intervention. Recently, there has been an increasing interest in new methodologies based on the three-dimensional

computational modelling and nonlinear analysis of these structures. In order to evaluate the applicability of current

modelling techniques for the assessment of existing substandard RC buildings, a structure considered as representative of

the stock built in the 1960’s in Lisbon is modelled as a whole with SAP2000 (CSI, 2009). To validate the model, field

ambient vibration tests are performed. The EC8-3 (CEN, 2005a) methodology is then applied through the seismic

assessment of the structure with a nonlinear static analysis following the N2 method. The progressive collapse of the

different structural elements is also monitored. The methodology followed in this dissertation provides initial guidelines

to assess a RC building and select the retrofitting strategies that would be indicated to strengthen the structure. However,

the nonlinear static procedure which was used also presents some limitations, such as the influence of nonlinear

parameters for solution control, the inclusion of higher mode and torsional effects and the lack of consideration of some

structural effects (e.g. the nonlinear behaviour of masonry infill walls and the concrete-steel bond-slip mechanism).

Keywords: earthquake engineering, reinforced concrete building, seismic assessment, nonlinear static analysis,

structural modelling, SAP2000 software

1. INTRODUCTION

The relevance of design for seismic resistance in

reinforced concrete (RC) buildings has been demonstrated

by recent events. For example, in the 2015 Gorkha, Nepal

earthquake - which killed over 9,000 people – RC

moment-resisting frame buildings performed poorly.

The design of new buildings for seismic resistance was not

fully implemented until the 1980’s in many countries,

including Portugal. Provisions for seismic design and

detailing of members and structures resembling those

found in modern codes were not introduced until this

decade in most European countries. The first Portuguese

standard to explicitly consider seismic resistance was

introduced in 1958 while the importance of ductility in

structural design was only introduced in 1983 by the RSA

(Regulamento de Segurança e Acções para Estruturas de

Edifícios e Pontes) and the REBAP (Regulamento de

Estruturas de Betão Armado e Pré-Esforçado). The

resistance of buildings to lateral forces resulted in the past

only from wind considerations. Therefore, the Portuguese

building inventory, which is composed of a large number

of RC structures built between 1950 and 1980, was not

designed according to the current rules defined in the most

recent seismic codes.

Although actually the major earthquake threat to human

life comes from existing substandard buildings, the

emphasis of earthquake engineering research and practice

has been on new construction. Seismic resistance adds

very little to the construction cost of a new building,

whereas the seismic retrofitting cost of old existing

buildings is normally a large fraction of the building

refurbishment cost. In addition to the direct intervention in

structural members, seismic upgrading also includes

disruption of use, relocation of tenants and replacement of

non-structural members. Therefore, its cost may be

prohibitive for private owners or difficult for the local

economy to bear. However, in some regions characterized

by high rates of seismic activity, it is utterly essential to

mitigate the seismic risk posed by a substandard building

stock.

The determination of the need to retrofit or not a specific

building and the definition of the level of the retrofitting

intervention normally come out of a detailed seismic

assessment of the building. A technically sound seismic

assessment is a challenge, since there are different

possible approaches and types of analysis (linear or

nonlinear), and different software packages (each one with

its advantages and disadvantages). However, even when

the need to retrofit is obvious, a detailed seismic

2

assessment is worth carrying out: once a structural model

of the building as-is is set up and analysed, it can be used

at little extra cost as the basis for studying various

retrofitting options and for detailed retrofit design.

Besides, a detailed assessment in principle provides an

objective picture of the building’s seismic vulnerability

and resistance, independent of the perceptions of the

engineer responsible for the evaluation. Consequently,

there has been a recent shift from the use of empirical

rapid methods of analysis, used in the past to identify

whether seismic retrofitting was indeed necessary, to the

adoption of new methodologies based on three-

dimensional (3D) computational modelling and nonlinear

analysis of RC structures.

The main goal of this work was to model and analyse a

RC building considered representative of the building

stock designed and built between 1960 and 1970 in

Portugal, using the structural analysis software SAP2000

(CSI, 2009), in order to study the applicability and

accuracy of current nonlinear modelling techniques and

methodologies for the seismic assessment of existing

substandard RC structures. For this purpose, this work

aimed at: (i) identifying the main weaknesses and

deficiencies with impact on the seismic performance of

the RC structures designed and built during the

abovementioned period, and compare them with the

current capacity design detailing principles; (ii) analysing

the procedures adopted in the Part 3 of Eurocode 8, EC8-

3 (CEN, 2005a) for the seismic assessment and

retrofitting of existing RC structures; (iii) validating the

modelling options by comparing the fundamental modes

and frequencies of the model with the results obtained

from in-situ ambient vibration tests; (iv) analysing the

sensitivity of pushover analysis to different modelling

approaches and the calibration of the model; (v) assessing

the seismic performance of the structure with a nonlinear

static (pushover) analysis following the N2 method

proposed by the Part 1 of Eurocode 8, EC8-1, Annex B

(CEN, 2004a); and (vi) analysing and interpreting the

progressive collapse of structural members.

2. OVERVIEW OF THE CASE STUDY

The building concerned in this study is an eight-storey

(ground floor plus seven storeys above ground) RC

building located in Lisbon (Portugal) between Av. do

Brasil and Rua Aprígio Mafra that was designed and built

in the 1960’s. Its plan dimensions are 36.80m in the X-

direction and 10.85m in the Y-direction. Total building

height is 27m.

Figure 1 – Model building: (A) cross-section (Montepio-

Geral, 1960); and (B) perspective.

The building (Figure 1) features three main RC frames in

the X-direction carrying vertical gravity loads and beams

framing eccentrically to the columns in the Y-direction.

It also includes two stairs and lift cores and interior

masonry walls. One of the peculiarities of this project lies

in the distribution of the columns, all positioned in the

same direction (Figure 2). However, the two rigid RC

cores guarantee an acceptable rigidity in the transverse

direction.

Figure 2 – Structural design plan, adapted from

(Montepio-Geral, 1960).

The seismic response of the building was not directly

considered in the structural design. The design team

assumed that the response to earthquakes would be

similar to a wind load response (the lateral force method

of analysis), which was the common design procedure to

take into account the seismic action.

3. CONCEPTUAL ANALYSIS OF THE

EXISTING RC STRUCTURE

The studied building belongs to the category of RC

frame-wall buildings. The structure is composed of

columns, beams, slabs and walls. In a first conceptual

analysis, it can be noticed that: (1) the ground floor has

substantially fewer masonry walls than the upper storeys;

(2) in raised floors, the outer masonry walls are supported

by beams that are positioned in the end of the cantilevers;

(3) the columns have a reduced reinforcement area,

particularly in the upper storeys.

3.1. Conceptual design considerations

A number of general building characteristics have been

identified in the last decades as being responsible for

localized component deficiencies, including lack of

redundancy in the shear resisting system or a

discontinuous seismic load path. Typically, most RC

buildings built in the 1960´s contain an array of non-

ductile detailing of the reinforcing steel. Nowadays, Part

1 of Eurocode 8, EC8-1 (CEN, 2004a) adopts the

principle of “Capacity Design”, taking advantage of the

ductility and energy dissipation capacity of the structure.

Consequently, EC8-1 introduces a series of guidelines

and rules in order to ensure a proper inelastic deformation

capacity of the structural elements without loss of

strength capacity. Some inadequate reinforcement

detailing conditions that were easily noticed in a

preliminary assessment of the studied building are:

(1) The spacing and number of column transverse

reinforcement ties is generally insufficient, originating

the premature failure of the section due to shear and

buckling of the compressed bars. Furthermore, the

distance between consecutive longitudinal bars

restrained by ties exceeds the EC8-1 limit (200 mm).

A B

Y

X

3

(2) The bottom beam longitudinal reinforcement near

column/beam joints is in general reduced, since its design

typically does not consider the effect of the seismic

actions that can lead to significant positive bending

moments in the support region, creating potential for bar

pullout under moment reversals.

(3) The transverse reinforcement in the beams is clearly

insufficient and the use of bent longitudinal beam bars

around the joints (instead of stirrups) originates an

undesirable behaviour of the system in case of stress

reversal, since the number of stirrups is not enough to

guarantee the formation of plastic hinges with the

necessary ductility (Appleton, 2013).

(4) The longitudinal column reinforcement bars were

designed to resist moments generated by code-specified

forces rather than the moments associated with the

capacities of the connecting beams. As opposed to

current ductile detailing design, based on the capacity

design principles, the columns are weaker than the

beams, leading to early column hinging and an

undesirable column side-sway mechanism.

(5) The size of the columns varies in each floor, since

only the vertical loads were considered in the design.

Consequently, there is a strong reduction in the stiffness

of the columns in the upper storeys, creating a relevant

vertical discontinuity.

(6) The column bars are spliced and anchored inside the

beam-column joint, which is a critical region for the

behaviour of the frame. Lap splices in columns generally

occur just above the floor level where the internal forces/

stress levels are the highest. In addition, the column lap

splices are generally very short and are not confined with

closely spaced column ties.

(7) In old RC buildings (pre-1970), it is common for

beams to frame eccentrically to the columns, as happens

in the design of the studied building. To increase the

seismic performance of the building, beams should be

supported on columns instead of indirectly supported on

other beams.

(8) According to EC8-1, in order to ensure a ductile

behaviour of the RC walls, the longitudinal

reinforcement required for flexural resistance should be

placed inside confined boundary elements whose length

𝑙𝑐 should not be taken as being smaller than 0.15𝑙𝑤 or

1.5𝑏𝑤. In the original detailing the longitudinal

reinforcement is distributed along the entire section.

3.2. Foundations detailing and design

The length of embedment used in the studied building for

the anchorage of the vertical reinforcement into the

foundations is not sufficient to develop the yield capacity

of the bars. The resulting slippage of the reinforcement

can lead to the same kind of performance as inadequate

lap splices. The footings were typically designed only for

gravity loads. The large concentration of stresses at the

end of the vertical elements resisting seismic loads can

exceed both the dead load and the compressive bearing

strength of the soils. Such conditions can give rise to

foundation rocking (ATC-40, 1996).

3.3. “Soft-storey” irregularity

The building in study belongs to a period of modern

architectural design that was strongly encouraged around

the world since the first half of the 20th century and is

characterized by the common application of “open

floors” or “pilotis”. The soft-storey irregularity refers to

the existence of a floor that presents a significantly lower

stiffness than the others. This irregularity is present, for

example, when the first storey of a framed structure is

free of walls (while non-structural walls are present in the

upper ones), when shear walls (located in the upper

storeys) do not follow down to the foundations or when

the height varies between storeys.

The soft first floor (ground floor) is the most common

feature of this kind of irregularity. It is usually present in

frame buildings when a large number of non-structural

components, such as masonry walls, are attached to the

columns of the upper storeys of a RC framed structure

while the first storey is left empty of walls or with a

reduced number of walls (Guevara-Perez, 2012). The

non-structural components, especially when they have a

significant rigidity, limit the ability of the columns to

deform, modifying the structural performance of the

building to horizontal forces.

Figure 3 - Examples of the "soft-storey" irregularity: (A)

Olive View Hospital, 1972 and (B) Imperial County

Service Building, 1985. Adapted from (Moehle, 1991).

If the soft-storey effect is not foreseen in the structural

design, irreversible damage will generally be present on

both the structural and non-structural components of that

floor. The lowest more flexible portion at the ground

floor may create a critical situation in the load path during

an earthquake: the stiffness discontinuity between the

first and the second storeys might cause significant

structural damage, or even the total collapse of the

building. This irregularity can be observed in the

residential buildings located in Av. do Brasil. The

structural elements are distributed throughout the

building, but the apartments are located on the upper

storeys with many masonry walls, while the lowest floor

is left partially free of partitions.

3.4. Weak column-strong beam mechanism

Current seismic codes recommend that in order to obtain

a ductile behaviour of the frames, the deformation

requirements in a nonlinear system should focus on

beams. In every joint, columns should have a greater

resistance than the beams. However, many existing

structures are not designed taking into account this

mechanism (Varum et al., 2005), including the studied

structure. In older RC frame buildings, where the beams

are often stronger than the columns, column hinging can

A B

4

lead to a storey mechanism, creating large p-delta effects

and inelastic rotations in the columns. Column hinging is

undesirable since this may lead to loss of the column's

gravity load carrying ability after only a very few cycles.

Furthermore, although isolated column hinging may be

tolerable in some circumstances (i.e. in dual systems),

hinging of most or all of the columns on a single level in

frame buildings will result in the loss of lateral stability.

3.5. Concrete-steel bond-slip mechanism

The seismic performance of RC structures depends

largely on the behaviour of the stress transfer mechanism

between concrete and reinforcement bars. The steel-

concrete bond is developed by friction and the wedging

action of small-dislodged sand particles between the bar

and the surrounding concrete, which ensures the transfer

of concrete stresses to the reinforcement surface

(Fernandes et al., 2007).

The analysis of RC structures generally assumes a perfect

bond between steel and concrete, implying full

compatibility between concrete and reinforcement

strains. This assumption is only valid in early loading

stages and small stress levels (e.g. Varum et al., 2005).

As the load increases, cracking and breaking of bond

occurs and relative slip between the concrete and the

reinforcement bars takes place in the structural elements

(bond-slip mechanism). Consequently, different strains

are observed in the steel bars and in the surrounding

concrete, affecting the stress distribution in both

materials. Bond-slip effects are particularly significant in

elements built with smooth plain reinforcing bars

(Fernandes et al., 2007), as was the case in the studied

building.

4. COMPUTATIONAL MODELLING OF THE

BUILDING

The 3D model of the studied building, presented in

Figure 4, was developed using SAP2000 (CSI, 2009),

which has different types of analysis available. The ones

used in this study were modal analysis (for the dynamic

characterization of the structure), linear static analysis

and nonlinear static (“pushover”) analysis.

Figure 4 – 3D model of the studied building in Av. do

Brasil, using SAP2000 (CSI, 2009).

4.1. Materials

The materials adopted for the RC structure (beams,

columns, slabs, shear walls and footings) - in accordance

with the original drawings - are the S235 steel with

smooth plain rebars and the B25 (C20/25) concrete.

4.1.1. Steel

S235 is a mild steel which properties were specified in

the old national standards (e.g. REBAP and RSA) in

terms of the main parameters: yield strength, ultimate

strength and strain at breaking. When compared to the

current properties of reinforcing steel (typically S400 or

S500), the difference lies mainly in the required ductility.

The main properties assumed were as follows in Table 1.

Table 1 - Properties of S235 mild steel.

Modulus of Elasticity (GPa) 210.0

Poisson’s Ratio 0.30

Yield strength (MPa) 235.0

Minimum ultimate strength (MPa) 360.0

Hardening strain, 𝜀𝑠ℎ 0.015

Minimum strain at breaking, 𝜀𝑠𝑢 0.240

The model proposed by Park and Paulay (1975) was

adopted as the constitutive relation for steel in this work,

defined in Figure 5, since the S235 steel is characterized

by a high hardening rate in the plastic stage.

Figure 5 – Stress-strain diagram for S235 steel.

4.1.2. Concrete

The stress-strain relationship for confined concrete was

established in this work using the theory proposed by

Mander et al. (1988), which means that constant

confining pressure was assumed in the concrete core. The

main properties of the adopted C20/25 (old B25) concrete

are as follows in Table 2. Unconfined concrete was

applied in beams and shear walls.

Table 2 - Properties of C20/25 (old B25) concrete.

𝑬𝒄𝒎 (GPa) 30.0

𝑬𝒄 (GPa) 31.5

Poisson’s Ratio 0.20

𝒇𝒄𝒎 (MPa) 28.0

𝒇𝒄𝒕𝒎 (MPa) 2.2

𝜺𝒄𝟏 (%) 0.20

𝜺𝒄𝒖𝟏 (%) 0.35

Most seismic design codes do not precise the effective

stiffness to be used in seismic analysis for RC structures.

Therefore, uncracked section properties are usually

considered in computing structural stiffness. However,

using modal analysis with uncracked sections stiffness

for different elements makes it impossible to obtain

5

adequate seismic internal forces, even within elastic

range (Pique et al., 2008). Some design codes recognize

the influence of cracking. They consider stiffness of the

cracked section 𝐸𝐼𝑒 proportional to the stiffness of the

gross uncracked section 𝐸𝐼𝑔, specifying reduction factors

to be applied to the stiffness of the uncracked cross-

section. For this case study, the reduction factors

proposed by Paulay and Priestley (1992) were adopted

[0.40EIg for rectangular beams and 0.60EIg for columns]

which seem to be more realistic than the ones proposed

in EC8-1.

Given that different column elements have different

section dimensions and confinement detailing, a Mander

stress-strain relation was calculated for each different set

of properties. The properties of the stress-strain relations

for different structural elements are presented in Fig. 6.

Figure 6 – Stress-strain relations for different structural

elements with confined and unconfined C20/25 concrete.

4.2. Modelling of structural and non-structural

elements for linear analysis

The columns and beams of the case study building were

modelled as linear, horizontal and vertical, frame

elements. The cross-sections were modelled with

SAP2000 Section Designer (CSI, 2009). The central RC

core was modelled through linear vertical frame elements

that are connected with rigid horizontal frame elements

to the beams and slabs, at the floors level, considering a

material with a very high modulus of elasticity. These

rigid sections ensure the monolithic connection between

the vertical walls and the adjacent elements in each floor.

For the original model of the structure, given that the

building does not extend below grade, the foundations

were considered as flexible. To simulate this behaviour,

in this model the joints were restrained for translations in

all directions (X, Y and Z) and two springs were added

to allow limited rotations. The stiffness of the springs was

computed according to Castro (1970).

The building was designed with lightened slabs

completed with distribution reinforcement. These slabs

were modelled with thick shell elements of C20/25

concrete with 0.10m thickness (determined to ensure that

the mass per unit volume and the rigidity of the material

are similar to the properties of the original slab).

Considering that the slabs have a much higher

stiffness in-plane than out-plane and that there is not

significant stiffness discontinuity in the structural

wall system, in the original model these elements

were modelled as rigid diaphragms (rigid behaviour

in-plane), applying a diaphragm constraint.

To perform the seismic assessment of existing RC

infilled frame structures, the behaviour of these non-

structural systems should be properly taken into account

in the analyses, mainly if, for a certain seismic intensity

level, the structure behaves essentially in the linear range.

There are many techniques proposed in the literature for

the simulation of infilled frames, which can be divided in

two groups (Rodrigues et al., 2010): the micromodels and

the simplified macro-models. In micro-models, infill

panels are modelled in detail at the components level:

mortar, bricks and interface elements. With the micro-

models, a more accurate representation of infill panel

behaviour can be obtained. However, a huge calculation

effort is required and a large number of parameters has to

be calibrated. Macro-models allow for the representation

of the panel behaviour and its influence on a building’s

structural response in a simplified way. The most

commonly used macro-model is the bi-diagonal

equivalent-strut model (Rodrigues et al., 2010).

A solid infill panel can be modelled as a strut along its

compressed diagonal. A widely known strut model,

which was adopted in this work, is based on the beam-

on-elastic-foundation analogy for the estimation of the

strut width (Mainstone, 1971). For a better

characterization of this phenomenon, a double equivalent

connecting rod was adopted, in which the model

parameter shall correspond to half the calculated width of

the strut (𝑤𝑖𝑛𝑓/2). The equivalent connecting strut only

transmits forces directly to the node, which is a limitation

of this simplified model. Furthermore, it does not take

into account the panel failure mode, which significantly

affects the distribution of stresses in the frame.

After defining the type of model to be used, it is also

important to obtain the mechanical parameters of the

walls to be modelled. The exterior masonry walls in the

case study building are composed of two panels with

30x20x15cm + 30x20x7cm bricks, while the interior

ones are composed of a single panel with 30x20x15cm

bricks. The properties of bricks for masonry walls are

illustrated in Table 3.

Table 3 - Mechanical properties of bricks for masonry

walls according to NP 834 (1971).

To model the equivalent diagonal struts, each strut was

considered as a linear frame element. In order to ensure

that the struts are only subject to axial stresses

(tension/compression), the bending and torsional

moments were released in the end joints.

For the dynamic characterization of the building and its

seismic assessment, it is essential to define the mass of

the structure and the corresponding vertical loads.

Therefore, the definition of the dead and live loads that

were included in the model was carried out carefully

(Table 4). The dead load comprises the self-weight of the

RC structure while the super-imposed dead load includes

Brick Type Self-weight

(kN/m3)

Compressive

Strength (MPa) E (GPa)

30x20x15cm 10.0 – 13.0

2.5 - 4.9 2.775

30x20x7cm 3.7 – 7.0 4.013

6

other permanent loads, such as coatings (wood or

ceramic tiles) and partition masonry walls. The live loads

are variable loads which depend on the main use of the

building (in this case, residential). Given the lack of

information in the original drawings, the live loads were

defined according to EC1-1 (CEN, 2002).

Table 4 – Actions considered on the structure.

4.3. Nonlinear modelling strategy

There are several ways of distributing the plasticity of an

inelastic structural component through the member cross-

sections and along its length. It is commonly accepted

that two major modelling strategies are possible to

simulate nonlinearity: either a fibre-based model or

nonlinearity concentrated on plastic hinges located at

elements’ extremities (Deierlein et al., 2010).

4.3.1. Definition and modelling of plastic hinges

In SAP2000 v16.0.0 (CSI, 2009), nonlinear modelling of

structural elements is limited to concentrated plasticity,

through the implementation of plastic hinges. However,

the software provides several alternatives regarding the

hinges definition through hysteretic relationships:

automatically based on the FEMA 356 rules (FEMA-356,

2000) or on CALTRANS Flexural Hinges (Caltrans,

2009); or manually through hinges with decoupled

bending (P-M2 and P-M3) or P-M2-M3 (“PMM”)

interaction. The first step for the definition of the plastic

hinges consists in depicting the moment-curvature

relationships that will represent the corresponding

nonlinear behaviour of the end sections of the structural

element.

The major limitation of concentrated plasticity models is

the definition, a priori, of the plastic hinge length, which

is conditioned by the curvature distribution assumed

along the element. To estimate the equivalent plastic

hinge length (𝐿𝑝), many expressions based on

experimental results have been suggested. One of the

most commonly used expressions, recommended for

beams and columns, was proposed by Paulay and

Priestley (1992):

𝐿𝑝 = 0.08𝑙 + 0.022𝑓𝑠𝑦𝑑𝑏𝑙 (1)

Where 𝑙 is the length of the RC element, 𝑑𝑏𝑙 is the

diameter of the main longitudinal reinforcing bars, and

𝑓𝑠𝑦 is the yielding strength of the reinforcement (in MPa).

Some more recent proposals of plastic hinge lengths have

been employed, such as those included in Eurocode 8. In

Annex E of Part 2 of Eurocode 8, EC8-2 (CEN, 2005b)

the plastic hinge length is defined as:

𝐿𝑝 = 0.10𝑙 + 0.015𝑓𝑠𝑦𝑑𝑏𝑙 (2)

However, according to Varum (2003), the empirical

expressions do not properly evaluate the plastic hinge

length for existing RC structures with smooth plain

rebars (such as the one in this case study). This type of

reinforcement, with poor bond conditions, concentrates

the deformation at the elements’ extremities, resulting in

lower plastic hinge lengths.

Fernandes et al. (2010) carried out cyclic load tests on

two beam-column joints: one joint (A) with smooth plain

rebars and joint (B) with ribbed rebars. A plastic hinge

length corresponding to 25% of the section height was

observed in joint (A) while joint (B) showed a plastic

hinge length corresponding to 90% of the section height.

These tests showed the influence of the concrete-steel

bond-slip mechanism, described in section 3.5. Being this

case study about an old RC building with smooth plain

reinforcement bars, the plastic hinges for beams were

modelled with a plastic hinge length equivalent to 25%

of the section height. For columns, the plastic hinge

length was assumed as half the length estimated

according to Equation 1.

According to Filiatrault et al. (2013), ductile shear walls

are intended to form a single plastic hinge at their base.

Several authors have addressed the plastic hinge length

estimation in shear walls, not only in RC buildings but

also in bridge engineering (e.g. Hannewald et al., 2012).

The Canadian and American concrete codes also have

requirements for the detailing of shear walls. The

Canadian code, CSA A23.3-04 (CSA, 2010), provides a

definition of the plastic hinge length, 𝐿𝑝, which was

adopted in the original model of the structure (Eq. 3).

𝐿𝑝 = 0.5𝑙𝑤 + 0.1ℎ𝑤 (3)

Where 𝑙𝑤 is the length of the wall in plan and ℎ𝑤 is the

height of the wall above the plastic hinge location.

Given the complexity of the examined three-dimensional

model, the definition of plastic hinges was tested

comparing the three alternatives: manually using

interacting M3 and P-M2-M3 hinges and automatically

using CALTRANS (Caltrans, 2009) and FEMA-356

(FEMA-356, 2000) – with M3 hinges in beams and P-

M2-M3 in columns.

4.3.2. Generalised force-deformation curve and

acceptance criteria

Acceptance criteria are indicators of whether the

predicted performance is adequate. All structural and

non-structural components should be capable of resisting

internal forces and deformation within the applicable

acceptance criteria of the selected performance level in a

structure. In this work, the generalized force-deformation

curves used in common standards (e.g. FEMA-356, 2000

and ASCE 41-13, 2013) were adopted. In these curves

(Figure 7) , five points labelled A, B, C, D and E are used

to define the force-deformation behaviour of the hinge

and three points labelled IO, LS and CP are used to define

the acceptance criteria.

Linear response is depicted between point A (unloaded

component) and an effective yield point B. Point C has

an ordinate that represents the strength of the component,

Dead Load C20/25 (kN/m3) 25.00

Super Dead

Load

Masonry walls (kN/m2) 2.00

Floor coatings (kN/m2) 1.50

Exterior masonry infills (kN/m) 6.75

Live Load Residential activities (kN/m2) 2.00

7

and an abscissa value equal to the deformation at which

significant strength degradation begins (line CD).

Beyond point D, the component responds with

substantially reduced strength to point E.

Figure 7 – Generalized force-deformation relations for

depicting: (A) plastic hinge modelling; and (B)

acceptance criteria (FEMA-356, 2000).

The acceptance criteria IO (Immediate Occupancy), LS

(Life Safety) and CP (Collapse Prevention) values are

deformations (displacements, strains, or rotations) that

have been normalized by the same deformation scale

factors used to specify the load deformation curve, and are

typically located between points B and C on the curve

(Figure 7-B). They indicate the state of the hinges.

The plastic moment capacity for the definition of plasticity

curves was calculated by moment-curvature (Μ−φ)

analysis of each structural element. The Μ−φ curves were

determined automatically in SAP2000 Section Designer

(CSI, 2009) and verified manually, according to the

geometry and detailing of each section and based on

expected material properties. The yield point was defined

as the moment at which the strain in the longitudinal

reinforcement reaches the yield strain. The ultimate

moment occurs when one of the fibres reaches its ultimate

strain, which can be conditioned by the failure of

reinforcement or concrete.

5. SEISMIC ASSESSMENT OF THE EXISTING

RC STRUCTURE

Following the computational modelling of the existing

structure, this section describes the results obtained by

means of different types of analysis: experimental dynamic

characterisation (ambient vibration tests), modal dynamic

analysis and nonlinear static (“pushover”) analysis.

5.1. Experimental dynamic characterisation

The suitability of the 3D computational model is essential

for the adequate seismic assessment of the structure. To

validate the computational model, field ambient vibration

tests were performed and experimental and analytical

dynamic characteristics of the building were defined and

compared. Despite the information obtained in the original

drawings and the local visits, it was necessary to consider

several modelling hypotheses to simulate as close as

possible the current behaviour of the structure.

The dynamic characterization tests consist on the analysis

of data on the response of the structure to the dynamic

vibration of the environment. The microtremors are

vibrations in the order of several micrometers, caused by

natural phenomena and/or artificial sources. The response

is registered in terms of acceleration and it is possible to

identify the frequencies through the Fourier transform of

these signals, which correspond to the peaks of the

obtained Fourier spectrum (Oliveira et al., 2010). The

Fourier amplitude spectrum will show a pronounced peak,

centred at the fundamental frequency of the building. It is

also possible to identify the fundamental frequencies

overlaying the plots obtained for each direction in each

measurement location.

From the systematic analysis of the records illustrated in

Figure 8 it is possible to conclude that the fundamental

mode of translation along the X-direction occurs for a

frequency of approximately 0.95 Hz and the fundamental

mode of translation along the Y-direction occurs for a

frequency of approximately 1.00 Hz.

Figure 8 –Power spectral density functions, in different

locations, for: (A) X-direction; and (B) Y-direction.

5.2. Modal dynamic analysis

The numerical analysis for the computation of natural

frequencies and vibration modes was performed using

SAP2000 (CSI, 2009). In this analysis, two distinct

computational models were studied: considering the

presence of masonry infill walls or neglecting their

influence. All modes that provide together a total effective

modal mass along each direction of at least 90% of the total

mass of the structure were considered.

Analysing the results presented in Table 5, one can easily

notice that the frequency obtained in the computational

model, considering the presence of infills, is very close to

the frequency obtained in the ambient vibration tests

(approximately 1 Hz). The first mode of vibration is the

mode associated with the lowest frequency (0.799 Hz,

model with infills), representing the fundamental mode.

For the studied building, it can be noted that this mode is

associated with torsion about the central axis of the

structure. This is related to the fact that the RC cores are

eccentric. Furthermore, the length of the structure in plan

is approximately 3.5 times larger than its width, which

favours existence of torsional modes. The second mode of

vibration is the first translational mode along the Y-

direction, with a frequency of 0.942 Hz and an effective

modal mass representing approximately 70% of the total

mass of the structure applied in this translation. The third

mode of vibration is the first translational mode along the

X-direction, with an effective modal mass representing

approximately 75% of the total mass of the structure.

A B

A

B

8

Table 5 – Modal identification analysis of the case study

building in Av. do Brasil.

Frequency (Hz) Modal mass ratios

Mode Without

Infills

With

Infills In-situ UX UY

1 0.704 0.799 ----------- 0.25% 0.00%

2 0.795 0.942 1.00 0.00% 70.39%

3 0.860 0.967 0.95 74.79% 0.00%

4 2.794 3.002 ----------- 13.18% 0.00%

5 3.084 3.289 ----------- 2.55% 0.00%

6 3.557 3.731 ----------- 0.00% 19.45%

5.3. Nonlinear static (“pushover”) analysis

Pushover analysis is the extension of the “lateral force”

procedure of static analysis into the nonlinear regime. This

analysis is carried out under constant gravity loads and

monotonically increasing lateral (horizontal) loading

applied on the masses of the structural model

(displacement control analysis). This loading simulates

inertia forces due to a horizontal component of the seismic

action (Fardis, 2009). While the lateral forces increase in

the course of the analysis, it is possible to follow the

development of plastic hinges across the structural

elements and the formation of plastic mechanisms.

Buildings not conforming to the regularity criteria defined

in section 4.2.3.2 (Regularity in Plan) and in section

4.3.3.1(8) of EC8-1 (CEN, 2004a) shall be analysed using

a spatial model (3D model) and two independent analyses

with lateral loads applied in each direction. According to

EC8-1, pushover analyses should be applied to buildings

using both of the following lateral load patterns: (1) a

“uniform” pattern corresponding to uniform unidirectional

lateral accelerations; (2) a “modal” pattern simulating the

inertia forces of the translational mode in the horizontal

direction in which the analysis is carried out. Nowadays,

more sophisticated versions of the pushover analysis do not

use a fixed pattern of applied lateral loads, “adapting” it to

the evolution of nonlinearity (e.g. Fardis, 2009 and Bhatt,

2012). However, the increase in accuracy contrasts with a

decrease in the simplicity of the procedure. In this work,

the N2 procedure (Fajfar, 2000), was used, as suggested in

Annex B of EC8-1 (CEN, 2004a).

Unless the structure is symmetric about an axis

perpendicular to the considered seismic action component,

the lateral forces should be applied in both the positive and

negative directions (Figure 9). The most unfavourable

result of the analyses with the two patterns should then be

used. For this analysis the presence of masonry infills was

neglected, due to the high magnitude of the earthquake and

the reduced strength of these elements.

Figure 9 – Identification of the RC frames and directions/

signs of the lateral acceleration patterns.

5.3.1. Sensitivity analysis on the influence of

modelling alternatives

Before assessing the seismic performance of the RC

structure, an attempt has been made in order to study the

sensitivity of the pushover analysis to different modelling

options assumed in the 3D model. Nonlinear static analyses

were carried out using SAP2000 to investigate the

behaviour of the alternative models described below.

A. Impact of the foundations modelling

In the first model, the foundations were considered as

flexible. However, after analysing the original drawings,

there is no evidence that the foundations were designed to

withstand bending moments and restrain any type of

rotation, since an isolation material might have been

applied at the interface between the supports and the

columns (which will work as a hinge). Consequently, a

new model was created assuming pinned foundations for

the columns: the joints were only restrained for translations

in all directions. In the case of RC shear walls, the rotations

were also restrained in the direction of the highest moment

of inertia (i.e. it was assumed that the foundations only

provide flexural resistance in this direction, to avoid the

concentration of high bending moments and the subsequent

premature failure of the section). The new model originates

a decrease in stiffness as the ultimate capacity is

approached, when compared to the original model.

B. Impact of the hinge modelling for shear walls

As mentioned above, ductile shear walls are intended to

form a single plastic hinge at their base. Therefore, in the

original model only one hinge was defined for each wall.

However, after the analysis of the structural design, it was

possible to notice the strong reduction of reinforcement

area between the base floor and the first floor, and between

the first and the second floors, which must be taken into

account. Consequently, new PMM hinges were introduced

in the sections characterized by a variation of the

reinforcement area, which creates a relevant vertical

discontinuity that might cause significant structural

damage and originate the failure of the element. The new

hinges introduced in RC shear walls originate a decrease in

both the ultimate displacement and the stiffness, as the

ultimate capacity is approached, when compared to the

original model.

C. Impact of the diaphragm constraint for slabs

As described above, in the original model the slabs were

modelled as rigid diaphragms, assuming that they have a

much higher stiffness in-plane than out-plane and that

there is not a significant stiffness discontinuity in the

structural wall system. However, since the studied building

was designed with lightened slabs of masonry blocks,

oriented in the Y-direction, it is not clear that the storeys

would have a rigid diaphragm behaviour. In fact, an

anisotropic flexible behaviour might be expected, given

that all the infill masonry blocks and concrete beams are

oriented in the same direction. Therefore, a new model was

studied assuming a stiffness modifier of 0.75 in the X-

direction (to simulate the anisotropic effect of the masonry

blocks) and no diaphragm constraint.

9

The model without diaphragm constraint originates, for the

Y- direction and the modal load pattern, a decrease in

stiffness. For the X direction, the new model originates a

very similar result when compared to the original model.

D. Impact of the moment-curvature relationships

assumed for the PMM hinges definition

As mentioned above, for the definition of plasticity curves,

the yield point was originally defined as the moment at

which the strain in the longitudinal reinforcement reaches

the yield strain. The ultimate moment occurs when one of

the fibres reaches its ultimate strain, which can be

conditioned by the failure of reinforcement or concrete.

However, in some sections the moment-curvature

relationship is conditioned by the high normalized axial

load applied in the column. When comparing the M-φ

relationship of the same section when subject to a high

normalized axial load or without axial load, one can notice

a strong reduction of the ultimate curvature (Figure 10-A).

Figure 10 – M-φ relationships for a column: (A)

influence of axial load; and (B) PMM hinge modelling.

The M-φ data for the interacting PMM hinges was obtained

as described in Figure 10-B (solid line). As soon as a

degradation of capacity is noticeable after yielding, it was

firstly assumed that the ultimate point (C) coincides with

the yielding point. However, after performing a pushover

analysis, it was possible to notice that the local collapse of

secondary columns (which was originating the end of the

analyses) was caused by the lack of rotation capacity of the

plastic hinges to contain the imposed displacement and

balance the gravity load. In order to avoid the premature

local collapse of the structure, a new hinge modelling

approach was studied. Instead of considering a brittle

failure, the M-φ relationships were idealised and the

collapse was considered to take place only when one of the

fibres reaches its ultimate strain, even if the moment

capacity decreases substantially. With the new approach

for the definition of PMM hinges the structure reaches a

significantly higher ultimate displacement, which is caused

by the higher rotation capacity of the structural members.

5.3.2. Comparison between plastic hinge

modelling approaches

Comparing the conclusions published by Belejo et al.

(2012) with the results obtained in this work, it is possible

to conclude that the definition of plastic hinges with

hysteretic relationships automatically based on FEMA-356

does not lead to good results for RC 3D structures in

SAP2000. It was possible to notice that in the Y- analysis

the capacity curve stops in a clearly early stage.

The results obtained using the CALTRANS method are

almost coincident with the results obtained using the

original model with PMM hinges. Therefore, one can

conclude that the CALTRANS automatic idealization of

the moment-curvature relationship is similar to the one

assumed for the original model. This approach limits the

rotation capacity of the plastic hinges, assuming that the

structural members would not be capable of containing the

imposed displacement and balance the gravity load. For old

RC structures, the capacity degradation of many sections

after yielding is common. Since this capacity degradation

is very rare in structures designed according to modern

seismic codes, many automatic tools are not prepared to

deal with substandard structural members. Thus, when

using the CALTRANS automatic hinge modelling, the

engineer must be aware of the idealized M-φ relationship

assumed by the model and analyse thoroughly the results,

as the pushover analysis might stop prematurely. It is also

important to mention that, as suggested by Belejo et al.

(2012), none of the tested SAP2000 modelling approaches

was able to reproduce the softening effect of the curve in

the post-peak range, since the analysis stops at the

maximum base shear force.

As described above, in the original model the plastic hinge

length for the RC shear walls was determined according to

the Canadian code (CSA, 2010). However, one can easily

notice that the Canadian formulation is merely dependent

on the member geometry. Annex A of EC8-3 (CEN,

2005a) recommends a plastic hinge length in which the

member geometry, shear span and material properties are

included:

𝐿𝑝 = 𝐿𝑠

30+ 0.2𝑙𝑤 + 0.11

𝑑𝑙𝑓𝑦

√𝑓𝑐

(4)

Where 𝐿𝑠 is the shear span, 𝑙𝑤 is the wall length and 𝑑𝑙 is

the reinforcing bars diameter.

The plastic hinge length estimated according to EC8-3 is

lower that the results obtained according to the Canadian

formulation. In fact, one can easily notice that the EC8-3

formulation is sensitive to the yield strength and

reinforcing bars diameter, which, for the studied building,

are clearly lower than the current practice in modern

seismic design. Therefore, the capacity curves obtained

with the Canadian code approach represent a higher base

shear and ultimate displacement than the curves defined by

the EC8-3 approach. Considering the concrete-steel bond-

slip mechanism caused by the use of smooth plain

reinforcing bars, the low yield strength of reinforcing steel

and the lack of confinement, a conservative option may be

assumed. Therefore, for the application of the N2 method

only the EC8-3 modelling approach was considered.

5.3.3. N2 method for the final model

STEP 1: Definition of the seismic action

According to section 4.4.1. of EC8-3 (CEN, 2005a), the

seismic action to be used for the assessment of existing RC

structures shall be the one corresponding to the elastic (i.e.

unreduced by the behaviour factor q) response spectrum.

In the N2 method, the response spectrum is defined in the

Acceleration-Displacement Format (ADRS), for an elastic

single-degree-of-freedom (SDOF).

A B

10

STEP 2: Pushover analysis – capacity curve

Based on the interpretation of the sensitivity analysis

performed in section 5.3.1. and considering the EC8-3

(CEN, 2005a) formulation for the plastic hinge length, a

final model of the building was created. The capacity

curves obtained by conventional pushover analysis for P-

M2-M3 manual hinges for the original and final models are

presented in Figure 11.

As expected, the curves obtained with a uniform load

pattern represent higher base shear for the same roof

displacements than the curves defined by means of a modal

load pattern. Therefore, adopting a conservative option, the

application of N2 method relates only to the curves

obtained under the action of a modal load pattern.

Figure 11 – Capacity curves for interaction PMM

hinges, for uniform and modal loads.

Analysing the capacity curves of both models, one can

notice that the structure reaches a higher ultimate

displacement for the final model. This difference is caused

by the higher rotation capacity of the structural members,

as a consequence of the new approach for the idealized M-

φ relationship. When analysing the results for the final

model, one can also notice a stiffness reduction and a

shorter elastic stage when compared to the original model,

which are caused by the new M-φ relationships and the new

modelling options (foundations, hinges in shear walls, no

diaphragm constraint and EC8-3 hinge length).

It is possible to observe that the structure presents more

strength along the X-direction due to the orientation of the

main RC frames. Analysing the capacity curves presented

in Figure 11, it turns out that the structure has a similar

initial stiffness in both directions. This conclusion is

consistent with the analytical and experimental natural

frequencies obtained from the modal identification

analysis presented in section 5.2., which were very similar

for both translational modes. The maximum base shear and

the ultimate displacement are presented in Table 6.

Table 6 – Ultimate capacity of the structure for the modal

load pattern.

STEP 3: Equivalent SDOF system

In the N2 method, the structure is modelled as a single-

degree-of-freedom (SDOF) system. The transformation

from the MDOF system to the SDOF system is controlled

by the modal participation factor 𝛤 (Equation 5).

𝛤 = ∑ 𝑚𝑖Φ𝑖𝑖

∑ 𝑚𝑖Φ𝑖2

𝑖

= 𝑚∗

∑ 𝑚𝑖Φ𝑖2

𝑖

(5)

𝛤𝑋 = 1960.1

1415.5= 1.39 𝛤𝑌 =

1774.0

1245.1= 1.42

After obtaining the modal participation factors, the

capacity curves of a SDOF system were computed

following Equations 6.

𝑑∗ = 𝑑𝑛

𝛤=

∆𝑛 𝑅𝑜𝑜𝑓

𝛤 𝐹∗ =

𝑉𝐵

𝛤 (6)

The yield displacement of the SDOF system, dy*, and its

period T* may be computed from Equations 7.

𝑑𝑦∗ = 2 (𝑑𝑚

∗ − 𝐸𝑚

∗

𝐹𝑦∗ ) 𝑇∗ = 2𝜋√

𝑚∗𝑑𝑦∗

𝐹𝑦∗ (7)

Table 7 – Definition of the SDOF capacity curves.

STEP 4: Seismic performance of the structure

For a structure with period T* and unlimited elastic

behaviour the target displacement is given by:

𝑑𝑒𝑡∗ = 𝑆𝑒(𝑇∗) [

𝑇∗

2𝜋]

2

(8)

Where 𝑆𝑒(𝑇∗) is the elastic acceleration response spectrum

at the period T*. For the determination of the target

displacement dt* for structures in the short-period range and

for structures in the medium and long-period ranges

different expressions should be used. According to the

results presented in Table 8, 𝑇∗ ≥ 𝑇𝐶 for both directions

(X and Y), which means that 𝑑𝑡∗ = 𝑑𝑒𝑡

∗ . The last step of the

N2 procedure consists in the transformation of the SDOF

system in a MDOF system, using the transformation factor

previously determined.

Direction 𝑽𝑴𝒂𝒙 (kN) 𝜟𝑹𝒐𝒐𝒇𝑴𝒂𝒙. (m)

X+ and X- 5583 0.173

Y+ 3570 0.115

Y- 2494 0.098

Y+ Analysis Y- Analysis X+ / X- Analysis

Fy* (kN) 2505.8 1750.7 4028.8

dm* (m) 0.081 0.069 0.125

Em* (kJ) 131.62 77.26 308.79

dy* (m) 0.056 0.049 0.097

T* (s) 1.25 1.40 1.36

11

Table 8 – Definition of the target displacement of the

SDOF and MDOF systems.

Analysing the results presented in Table 8 for the reduced

spectrum, the ultimate displacement du* in the Y- direction

is lower than the target displacement dtarget* determined for

the seismic action, which means that the building does not

verify the no-collapse requirement and needs to be

retrofitted. For the analyses in the X and Y+ directions, the

ultimate displacement du* is higher than the target

displacement dtarget*. Furthermore, one can also notice that

if the original elastic spectrum was considered, the ultimate

displacement du* would be lower than the target

displacement dtarget* for both the Y- and Y+ analyses.

5.3.4. Progressive collapse of the RC structure

Progressive collapse occurs when a structure has its

loading path or boundary conditions changed such that

other structural elements within the structure are loaded

beyond their capacity and fail. The spread of local failure,

from element to element, results eventually in the collapse

of the entire structure or a large part of it. The prediction of

possible progressive collapse under specific conditions

may provide very important information that could be used

to assess the performance of the structure and investigate

possible retrofitting strategies to be applied in the most

critical structural members. The structural elements

reaching their ultimate capacity are identified in Figure 12.

Figure 12 – Hinges reaching ultimate capacity.

After analysing the progressive development of plastic

hinges, it was possible to identify the structural members

requiring an upgrade of their capacities. It was also

possible to conclude that the main causes for the collapse

of this structure are the variation of the size and

reinforcement area of the columns between storeys

(originating a strong reduction in the stiffness and flexural

resistance and creating a relevant vertical discontinuity)

and the lack of longitudinal reinforcement and confinement

ties in RC shear walls.

Furthermore, it was also possible to notice that the columns

reaching their ultimate capacity are mainly located in the

external frames. As a matter of fact, the external columns

are characterized by a small reinforcement area when

compared to the columns belonging to the internal frame.

As mentioned above, in the 1960’s the structural elements

were designed only to support gravity loads, which means

that internal columns (typically with larger influence areas

for gravity loads) used to have higher reinforcement ratios

than external columns (with smaller influence areas).

Santos et al. (2015) re-designed the RC structure of the

case study building following the EC8-1 guidelines. In this

building, the external RC frames assume an essential role,

together with the internal frames and the shear walls, in the

lateral force resisting system. Consequently, these

elements must be classified as primary elements and

designed for earthquake resistance according to ductility

requirements. When designing the building according to

EC8-1, the external frames have significantly higher

reinforcement ratios.

6. CONCLUSIONS

An eight-storey RC building, located in Lisbon and built in

the 1960’s, was studied in this research. With a preliminary

assessment of the structure some inadequate reinforcement

detailing conditions were noticed. Moreover, some system

and layout mechanisms and deficiencies were identified,

such as the “soft-storey” irregularity, the “weak column-

strong beam” mechanism and the concrete-steel “bond-

slip” mechanism. These deficiencies can lead to the failure

of individual members.

The 3D model of the studied building was developed using

SAP2000 (CSI, 2009). Despite the information obtained in

the original drawings and the local visits, it was necessary

to consider several modelling hypotheses to simulate as

close as possible the current behaviour of the structure. To

validate the model, field ambient vibration tests were

performed and the experimental and analytical dynamic

characteristics of the building were compared. However, it

Y+ Analysis Y- Analysis X Analysis

T* (s) 1.25 1.40 1.36

det* (m) 0.071 0.080 0.078

dt* (m) 0.071 0.080 0.078

ORIGINAL SPECTRUM

SDOF du* (m) 0.081 0.069 0.125

dtarget* (m) 0.092 0.103 0.100

MDOF du* (m) 0.115 0.098 0.173

dtarget* (m) 0.131 0.147 0.139

REDUCED SPECTRUM

SDOF du* (m) 0.081 0.069 0.125

dtarget* (m) 0.071 0.080 0.078

MDOF du* (m) 0.115 0.098 0.173

dtarget* (m) 0.101 0.114 0.108

LEGEND

Does not verify the condition dtarget* < du*

Verifies the condition dtarget* < du*

Frame 1 Frame 2

Y- Analysis X Analysis Y+ Analysis

Frame 3 Walls 1 Walls 2

12

should be noted that the identification of frequencies with

in-situ vibration tests was difficult, mainly due to the low

recorded ambient vibration around the building.

The influence of the masonry infill walls on the modal

identification analysis was easily noticed when comparing

the frequencies considering the presence of infills with the

result when their effect was neglected. It is also important

to mention that the frequencies obtained in the SAP2000

computational model after calibration of the input

parameters were very close to the results of the ambient

vibration tests mentioned above.

Comparing the conclusions published by Belejo et al.

(2012) with the results obtained in this research, it is

possible to conclude that the definition of plastic hinges

automatically based on FEMA-356 does not lead to good

results for RC 3D structures in SAP2000.

For old RC structures, the capacity degradation of many

sections after yielding is common, due to the high

normalized axial loads, reduced cross-sections and low

reinforcement ratios. It was possible to conclude that the

CALTRANS automatic hinge modelling limits the rotation

capacity of the plastic hinges, assuming that the structural

members would not be capable of containing the imposed

displacement and balance the gravity load. This

assumption originates the premature failure of some

elements and the end of the analysis due to numerical

instability. In order to avoid the premature local collapse of

the structure, instead of considering a brittle failure of the

sections, the M-φ relationships for the PMM hinges were

idealised and the collapse was considered to take place

only when one of the fibres reaches its ultimate strain, even

if the moment capacity decreases substantially. With this

approach for the manual definition of plastic hinges, the

structure reached a higher ultimate displacement, which is

caused by the higher rotation capacity of the elements.

Once a reasonably accurate model was obtained, new

pushover analyses were run. These analyses showed that

the ultimate displacement in the Y- direction is lower than

the target displacement determined for the reduced

spectrum, which means that the building does not verify

the no-collapse requirement and needs to be retrofitted. If

the original elastic spectrum were considered, the ultimate

displacement would be lower than the target displacement

for both the Y- and Y+ analyses.

After analysing the progressive development of plastic

hinges, it was possible to identify the structural members

requiring an upgrade of their capacities. It is clear that the

main causes for the collapse of this structure are the

variation of the size and reinforcement area of the columns

between storeys, the lack of longitudinal reinforcement and

confinement ties in shear walls and the lack of longitudinal

reinforcement in columns located in the external frames.

Nonlinear static procedures (NSP) were developed with the

aim of overcoming the insufficiency and limitations of

linear methods, whilst at the same time maintaining a

relatively simple application. The methodology followed

in this research provides initial guidelines to assess a RC

building and select the retrofitting strategies and

techniques that would be indicated to strengthen the lateral

force resisting system of the building. However, it must be

emphasized that the N2 method also presents some

limitations. For instance, this procedure does not take into

account higher mode effects and the inclusion of three-

dimensional and torsional effects is very difficult.

The software package used in this work, SAP2000 (CSI,

2009), also presents some limitations. Firstly, and as

suggested by Belejo et al. (2012), none of the tested

SAP2000 modelling approaches was able to reproduce the

softening effect of the curve in the post-peak range, since

the analysis stops at the maximum base shear force.

Secondly, when running pushover analyses in SAP2000,

one must be aware of the influence of nonlinear parameters

for solution control on the capacity curves. Before drawing

conclusions from the results, it is recommended to test

different solution control parameters in order to assess the

sensitivity of the model to these analysis options. In the

future, different software packages, such as PERFORM-

3D (CSI, 2009a) and SeismoStruct (Seismosoft, 2011),

should be tested in order to validate the results obtained

with SAP2000 (CSI, 2009).

REFERENCES

Appleton J. (2013). Estruturas de Betão – Volumes 1 e 2.

Edições Orion, Portugal.

ASCE 41-13 (2013). ASCE/SEI Standard 41-13 - Seismic

Rehabilitation of Existing Buildings. American Society of

Civil Engineers, Reston, VA, USA.

ATC-40 (1996). Seismic Evaluation and Retrofit of

Concrete Buildings. Applied Technology Council, 1, 334,

California, USA.

Belejo A., Bento R., Bhatt C. (2012). Comparison of

different computer programs to predict the seismic

performance of the SPEAR building by means of Pushover

Analysis. In Proceedings of the 15th World Conference on

Earthquake Engineering – WCEE 2012.

Bhatt C. (2012). Seismic Assessment of Existing Buildings

Using Nonlinear Static Procedures (NSPs) – A New 3D

Pushover Procedure. European PhD, Instituto Superior

Técnico – Universidade de Lisboa, Portugal.

Caltrans (2009). Caltrans Seismic Design Criteria –

Version 1.5. Department of Engineering Services,

California Department of Transportation, California, USA.

Castro G. (1970). Deformabilidade das fundações e sua

consideração no cálculo das estruturas. Memória 353,

Laboratório Nacional de Engenharia Civil, Lisboa.

CEN (2002). European Standard EN1991-1-1:2002

Eurocode 1: Actions on structures – Part 1-1: General

actions – Densities, self-weight, imposed loads for

buildings. Comité Européen de Normalisation, Brussels.

CEN (2004a). European Standard EN1998-1:2004

Eurocode 8: Design of structures for earthquake resistance,

Part 1: General rules, seismic actions and rules for

buildings. Comité Européen de Normalisation, Brussels.

CEN (2005a) European Standard EN1998-3:2005

Eurocode 8: Design of structures for earthquake resistance,

Part 3: Assessment and retrofitting of buildings. Comité

Européen de Normalisation, Brussels.

13

CEN (2005b) European Standard EN1998-2:2005

Eurocode 8: Design of structures for earthquake resistance,

Part 2: Bridges. Comité Européen de Normalisation,

Brussels.

CSA (2010). CAN/CSA-A23.3-04 - Design of Concrete

Structures. CSA, Canada.

CSI (2009). SAP2000, Version 16. Software for Structural

Analysis and Design. Computers and Structures Inc. (CSI).

Berkeley, California, USA.

CSI (2009a). PERFORM-3D. Computers and Structures

Inc. (CSI). Berkeley, California, USA.

Deierlein G. G., Reinhorn A. M., Willford M. R. (2010).

Nonlinear Structural Analysis for Seismic Design – A

Guide for Practicing Engineers. NEHRP Seismic Design

Technical Brief No. 4. National Institute of Standards and

Technology, Gaithersburg, MD, USA.

Fajfar P. (2000). A Nonlinear Analysis Method for

Performance Based Seismic Design. Earthquake Spectra,

16(3), 573-592.

Fardis M. N. (2009). Seismic Design, Assessment and

Retrofitting of Concrete Buildings: based on EN- Eurocode

8. Springer, Dordrecht.

FEMA-356 (2000). FEMA 356 - Prestandard and

Commentary for the Seismic Rehabilitation of Buildings.

Federal Emergency Management Agency, USA.

Fernandes C., Varum H., Costa A. (2007). Concrete-steel

bond characterization of RC structural elements built with

smooth plain reinforcement bars. 2nd Symposium

“Connections between Steel and Concrete”, 1-10.

Fernandes C., Melo J., Varum H., Costa A. (2010).

Comportamento cíclico de nós viga-pilar com armadura

lisa. VI Congreso Internacional sobre Patología y

Recuperación de Estructuras, Córdoba (Argentina).

Filiatrault A., Tremblay R., Christopoulos C., Folz B.,

Pettinga D. (2013). Elements of Earthquake Engineering

and Structural Dynamics. Cursus, Presses Internationales

Polytechnique. 3rd Edition. Montreal, Québec, Canada.

Guevara-Perez L. T. (2012). “Soft Story” and “Weak

Story” in Earthquake Resistant Design: A

Multidisciplinary Approach. In Proceedings of the 15th

World Conference on Earthquake Engineering – WCEE

2012, 518-519.

Hannewald P., Beyer K. (2012). Plastic hinge models for

the seismic assessment of reinforced concrete wall-type

piers with detailing deficiencies. In Proceedings of the 15th

World Conference on Earthquake Engineering – WCEE

2012, 518-519.

Mainstone R.J. (1971). On the stiffnesses and strengths of

infilled frames. Proceedings of Institution of Civil

Engineers v 7360s.

Mander J. B., Priestley M. J. N., Park R. (1988).

Theoretical stress-strain model for confined concrete.

Journal of Structural Engineering 114(8): 1804–1826.

McKenna F., Fenves G. L., Scott M. H. and Jeremic B.

(2000). Open System for Earthquake Engineering

Simulation (OpenSees). Pacific Earthquake Engineering

Research Center, University of California, Berkeley, CA.

Moehle J. P., Mahin S. A. (1991). Observations on the

Behaviour of Reinforced Concrete Buildings during

Earthquakes. American Concrete Institute, SP-127,

Earthquake-Resistant Concrete Structures – Inelastic

Response and Design, USA.

Montepio-Geral (1960). Peças Desenhadas do Projeto de

Edifício sito na Avenida do Brasil, Lote 6, Blocos A e B.

Lisboa, Portugal.

NP 834 (1971). Tijolos de barro vermelho para alvenaria.

Formatos. IPQ, Lisbon, Portugal.

Oliveira C. S., Navarro M. (2010). Fundamental periods of

vibration of RC buildings in Portugal from in-situ

experimental and numerical techniques. Bulletin of

Earthquake Engineering, 8(3), 609-642.

Park R., Paulay T. (1975). Reinforced concrete structures.

J. Wiley, New York, USA.

Paulay T., Priestley M. J. N. (1992). Seismic Design of

Reinforced Concrete and Masonry Buildings. Wiley

Interscience.

Pique J. R., Burgos M. (2008). Effective Rigidity of

Reinforced Concrete Elements in Seismic Analysis and

Design. In Proceedings of the 14th World Conference on

Earthquake Engineering, WCEE 2008.

REBAP (1983). Regulamento de Estruturas de Betão

Armado e Pré-Esforçado. Decreto-Lei nº349-C/83, de 30

de Julho. Lisboa, Portugal.

Rodrigues H., Varum H., Costa A. (2010). Simplified

Macro-Model for Infill Masonry Panels. Journal of

Earthquake Engineering, 14(3), 390-416.

RSA (1983). Regulamento de Segurança e Acções para

Estruturas de Edifícios e Pontes. Decreto-Lei nº235/83, de

31 de Maio. Lisboa, Portugal.

Santos D., Costa M., Amorim M., Marques, G. (2015).

Projeto Base de um Edifício de Betão Armado na Avenida

do Brasil, Lisboa. Project for the course “Estruturas de

Edifícios”, Instituto Superior Técnico - Universidade de

Lisboa, Portugal.

Seismosoft (2011). SeismoStruct - A computer program for

static and dynamic nonlinear analysis of framed

structures. Available from http://www.seismosoft.com.

Varum H. (2003). Seismic Assessment, Strengthening and

Repair of Existing Buildings. Thesis to obtain the PhD in

Civil Engineering, Universidade de Aveiro, Portugal.

Varum H., Costa A. G., Pinto A. (2005). Reforço Sísmico

do Património Edificado em Betão Armado. Atas do

2ºSeminário – A Intervenção No Património. Práticas de

Conservação e Reabilitação, 1-22.