Simplified Macro-Model for Infill Masonry Panels

This article was downloaded by: [b-on: Biblioteca do conhecimento online UA]On: 15 January 2013, At: 02:31Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Journal of Earthquake EngineeringPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/ueqe20

Simplified Macro-Model for Infill MasonryPanelsHugo Rodrigues a , Humberto Varum a & Aníbal Costa aa Civil Engineering Department, University of Aveiro, Aveiro,PortugalVersion of record first published: 01 Mar 2010.

To cite this article: Hugo Rodrigues , Humberto Varum & Aníbal Costa (2010): Simplified Macro-Modelfor Infill Masonry Panels, Journal of Earthquake Engineering, 14:3, 390-416

To link to this article: http://dx.doi.org/10.1080/13632460903086044

PLEASE SCROLL DOWN FOR ARTICLE

Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representationthat the contents will be complete or accurate or up to date. The accuracy of anyinstructions, formulae, and drug doses should be independently verified with primarysources. The publisher shall not be liable for any loss, actions, claims, proceedings,demand, or costs or damages whatsoever or howsoever caused arising directly orindirectly in connection with or arising out of the use of this material.

http://www.tandfonline.com/loi/ueqe20

http://dx.doi.org/10.1080/13632460903086044

http://www.tandfonline.com/page/terms-and-conditions

Journal of Earthquake Engineering, 14:390–416, 2010

Copyright � A.S. Elnashai & N.N. Ambraseys

ISSN: 1363-2469 print / 1559-808X online

DOI: 10.1080/13632460903086044

Simplified Macro-Model for Infill Masonry Panels

HUGO RODRIGUES, HUMBERTO VARUM,and ANIBAL COSTA

Civil Engineering Department, University of Aveiro, Aveiro, Portugal

In structural analyses, masonry infill walls are commonly considered to be non structural elements.However, the response of reinforced concrete buildings to earthquake loads can be substantiallyaffected by the influence of infill walls. In this article, an improved numerical model for thesimulation of the behavior of masonry infill walls subjected to earthquake loads is proposed andanalyzed. First, the proposed model is presented. This is an upgrading of the equivalent bi-diagonalcompression strut model, commonly used for the nonlinear behavior of infill masonry panelssubjected to cyclic loads. Second, the main results of the calibration analyses obtained with twoseries of experimental tests are presented and discussed: one on a single frame with one story andone bay tested at the LNEC Laboratory; and the second, on a full-scale four story and three-bayframe tested at the ELSA laboratory.

Keywords RC Buildings; Infill Masonry; Numerical Modeling; Non–Linear Analyses

1. Introduction

The vast majority of buildings, in earthquake prone areas in Europe, constructed

before the 1980s are seismic deficient in terms of our current understanding. In

fact, in some European countries until the 1960s no specific seismic design provi-

sions were included in building codes and, from that period on, only seismic

equivalent lateral loading were considered in building design. Provisions for the

design and detailing of members and structures resembling those of modern codes

only appeared in European national codes in the 1980s (e.g., Portuguese design code

- RSA [1983]; European design code - Eurocode 8 [CEN, 2003]). Consequently, most

of the existing buildings constitute a major source of risk of loss of human life and

property [Varum, 2003].

The presence of masonry infill walls in RC buildings is very common. However,

and even today, in the design of new buildings and in the assessment of existing ones,

infills are usually considered to be non structural elements and their influence on the

structural response is ignored [Stafford-Smith and Carter, 1969; Duarte and Campos-

Costa, 1988].

For the nonlinear analysis of large and complex structures under severe loadings, as

the induced by earthquakes, in many cases it is not suitable to adopt refined models. Thus,

many authors have in the last decades proposed and used simplified nonlinear models for

RC structures. For infilled frame structures, considering the complex behavior of the

masonry and its interaction with surrounding frame elements the need for simplified

models is even more evident.

Received 26 January 2009; accepted 25 May 2009.Address correspondence to Hugo Rodrigues, Civil Engineering Department, University of

Aveiro, Aveiro 3810-193, Portugal; E-mail: [email protected]

390

Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

However, as studied in previous works [Varum, 2003], in traditional bi-diagonal

masonry models, the behavior laws and hysteretic rules of each diagonal do not influence

the other. When structures are subjected to cyclic loadings, the damage of an infill panel

in one direction reduces the global stiffness and strength of the panel for any direction.

Therefore, it is proposed in this work a global infill panel model to account for the

interaction between the mechanical response of both struts.

The main objective of this work was to develop a numerical model to account for the

influence of infill masonry walls on the RC building’s response to cyclic loading, as

produced by earthquakes. The model was implemented in a computer program code,

VISUALANL [Rodrigues, 2005; Rodrigues et al., 2004].

2. The Influence of Infill Masonry Walls on Structural Seismic Response

It is inadequate to assume that masonry infill panels are always beneficial in terms of

structural response. The contributions of infills to the building’s seismic response can be

positive or negative, depending on a series of phenomena and parameters such as, for

example, relative stiffness and strength between the frames and the masonry walls

[Stafford-Smith, 1962; Mainstone, 1971; Oliveira, 1995].

In recent earthquakes, numerous buildings were severely damaged or even

collapsed as a result of the structural modifications to the basic structural system

induced by the non structural masonry partitions (Fig. 1). Even when relatively weak,

masonry infill can drastically modify the intended structural response, attracting

forces to parts of the structure that have not been designed to resist them [Paulay

and Priestley, 1992].

Masonry infill panels can increase substantially the global stiffness of the structure.

Consequently, its natural period will decrease and, depending on the seismic spectrum

values at the vicinity of the bare structure natural period, the seismic forces can increase

[Rodrigues et al., 2004; Liaw and Lee, 1977].

In some situations such as those, for example, in which masonry walls extend

to only part of the story-height (short-columns) leaving a relatively short portion of

the columns exposed, vulnerable behavior may also be induced. Frequently, a column

is shortened by elements which have not been taken into account in the global

building design (for example, window openings or staircase landing slabs; see

Fig. 2) [Varum, 2003].

FIGURE 1 Damage to masonry infill walls: a) RC frame building with almost fully

damaged masonry infills on the second story; b) diagonal tension failure of a masonry

wall.

Simplified Macro-Model for Infill Masonry Panels 391

Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

3. Infill Masonry Models and Standards Recommendations

To perform the safety assessment of existing RC infilled frame structures or to design

new ones, the highly nonlinear behavior of these structural systems during strong earth-

quakes should properly be taken into account [Dolsek and Fajfar, 2008].

There are many different techniques proposed in the literature for the simulation of

the infilled frames, which can be basically divided in two groups, namely the micro-

models and the simplified macro-models. The micro-models considers a high level of

discretization of the infill masonry panel, in which the panel is divided into numerous

elements to take into account the local effects in detail, the simplified models are

supported in simplifications with the objective of representing the global behavior of

the infill panel with a few structural elements [Crisafulli, 1997].

Micro-models can simulate the structural behavior with notable detail, requiring

different types of elements to represent, respectively, the bricks, mortar, interface

brick-mortar, interface masonry-frame, and the frame elements. However, they are

computational intensive and difficult to apply in the analysis of large structures.

Examples of application of micro-models can be found in [Asteris, 2003, 2008;

Combescure and Pegon, 2000]. This type of models can be very useful to study the

local behavior of masonry panels and to calibrate global simplified models. The analysis

of infilled frames with refined finite element models requires the use of at least three

types of elements to represent the masonry panel, the surrounding frame and the panel-

frame interfaces. In a more refined analysis, the masonry panels can be considered as a

two-phase material, in which the masonry units and the mortar joints are modeled

separately.

Relatively to the simplified models, the most commonly used technique to model

infill panels is based on a single or multiple compressive equivalent diagonal struts

strategy. The first model was proposed by Poliakov [Klingner and Bertero, 1976;

Polyakov, 1957], representing the infill panel by a diagonal bar under compression.

Other variants on the diagonal strut model, considering single or multiple compres-

sive equivalent diagonal struts, can also be found in the literature, for instance

Stafford-Smith [1962], Smyrou [2006], Puglisi et al. [2009a.b], Bertoldi et al.

[1994], Blandon-Uribe [2005], and Combescure and Pegon [2000]. A complete over-

view of the modeling techniques of infilled frame structures can be found in

Crisafulli et al. [2000].

FIGURE 2 Short column effect caused by: window openings, masonry walls, and stair-

case landing slabs.

392 H. Rodrigues, H. Varum, and A. Costa

Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

In global infill masonry models, the material/arrangement properties like anisotropy

of brick, dimension of brick, joint width, mechanical properties of bricks and mortar,

arrangement of bed joints, as well as the anisotropy of the masonry panel, are globally

expressed in the backbone curve and in the hysteretic rules associated to the model. To

fully describe the influence of these factors in the response of masonry infill walls, the

sophisticated numerical models are more appropriated.

Other weaknesses associated to the infill masonry panels are the out-of-plane failure

mechanisms, especially for high building floor accelerations [Magenes and Pampanin,

2004]. The common strut models cannot represent the out-of-plane response of an infill

masonry panel. The simplified infill masonry model proposed in this work for the

building’s analysis does not consider the out-of-plane behavior. Other authors have

already proposed simplified macro-models to account for the out-of-plane response of

infill masonry panels [Lam et al., 2003; Doherty et al., 2002]. In these approaches, it is

considered a combination of two simplified models, one for the in-plane behavior and

other for the out-of-plane behavior, which can be a good improvement to be implemented

in a future version of the proposed model for tridimensional analysis of buildings.

3.1. Codes Recommendations

Being aware of the importance of infill masonry elements in the behavior of RC buildings

in the last few years the new codes have included some provisions regarding the

consideration of the infills and their influence on the structural response. For example,

the European code, Eurocode 8 (EC8) [CEN, 2003], include provisions for the design of

infilled RC frames (in its Sec. 2.9). EC8 specifies that the period of a structure to be used

to evaluate the seismic base shear shall be the average of that for the bare frame and for

the elastic infilled frame. Frame member demands are then determined by modeling the

frame structure without the infills. The influence of irregular infill distributions, in plan

and in elevation, is addressed in EC8. The American guideline FEMA-273 [1997] and

FEMA 356 [2000] includes a procedure to assess the structural response of buildings,

considering the infills panels. According to this document, masonry infill panels shall be

represented by the equivalent diagonal struts. The struts may be placed concentrically

across the diagonals, or eccentrically to directly evaluate the infill effects on the columns.

The shear behavior of masonry infill panels is considered as a deformation controlled

action. FEMA-273 [1997] provided deformation acceptance criteria. The linear procedure

involves a comparison between the design elastic shear force in an infill panel with the

factored expected shear strength of the panel.

3.2. Limit States for Infill Masonry Panels

The definition of limit states for infill masonry panels can be directly related to the inter-

story drift demand. Based on the equivalent strut model, Magenes and Pampanin [2004]

proposed an empirical for the damage level at a masonry infill panel corresponding to a

certain Limit State, depending on the axial deformation. For example, an inter-story drift

value in the range of 0.4–1.0% can be associated to the infill panel’s failure.

The FEMA-306 [1999] and FEMA-307 [1999] documents provide also reference

values of inter-story drift ratios for RC buildings with infill masonry panels. The drift

limits proposed differ with the type of masonry, from 1.5% for brick masonry to 2.5%

for ungrouted concrete blocks masonry. In these documents are also indicated a drift

reference value of 0.25% for the initiation of diagonal cracking [FEMA-306, 1999;

FEMA-307, 1999; Bell and Davidson, 2001]. Other authors recommended inter-story


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

drifts to be considered for the serviceability check ranging from 0.2%–0.5%, depending

on the type of partitions. Values close to 0.2% are recommended for brick masonry

infills in contact to the surrounding frame [Valiasis and Stylianidis,1989], whereas

0.5% is more appropriate for plywood, plaster, gypsum, and similar light panels

[Freeman, 1977].

4. Proposed Model for Masonry Infill Panel

Infill masonry models can be classified as either micro or macro models [Oliveira,

1995]. In micro-models, infill panels are detail modeled at the components level:

mortar, bricks, and mortar/brick interface elements. With the micro-models, a more

accurate representation of infill panel behavior can be obtained. However, a huge

calculation is required and a large number of parameters have to be calibrated. Such

models can be useful for local analysis, but impractical for the global analysis of a

building [Krstevka and Ristic, 2004].

Macro-models allow for the representation of infill panel behavior and its influence

on a building’s structural response [Riddington and Stafford Smith, 1977]. The most

commonly used macro-model is the bi-diagonal equivalent-strut model. Many examples

of other macro-models can be found in the literature: (i) homogenized frames sections

[Liaw and Lee, 1977]; (ii) theory of plasticity [39]; (iii) behavior coefficients [Duarte and

Campos-Costa, 1988], among many others.

The macro-model proposed here is an improvement on the commonly used equiva-

lent bi-diagonal-strut model. The proposed model considers the interaction of masonry

panel behavior in both directions; damage to the panel in one direction affects its

behavior in the other direction. Therefore, the proposed model more accurately represents

global response and energy dissipation during structural response. The limitation of the

typical bi-diagonal model has already been highlighted and studied by Varum [2003]. It

should be referred that the proposed simplified macro-model does not account for the

short-column effects. For infilled frames where the short-column effect can be induced,

multiple strut model strategy should be adopted.

In the proposed infill panel model, each masonry panel is structurally defined by

considering four support strut-elements, with rigid behavior, and a central strut element,

where the nonlinear hysteretic behavior is concentrated (Fig. 3a). The forces developed in

the central element are purely of tensile or compressive nature.

Centralelement

Struts

a)

1

2

3

4

5

dc dy dcr du

Fu

c

Fy

K0

K1

K2

K3

K4

F

d

Fcr

b)

FIGURE 3 Macro-model for the simulation of an infill masonry panel and force-

displacement monotonic behaviour curve.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

The nonlinear behavior is characterized by a multi-linear envelope curve, defined

by nine parameters (Fig. 3b), representing: (i) cracking (cracking force, Fc; cracking

displacement, dc); (ii) yielding (yielding force, Fy; yielding displacement, dy);

(iii) maximum strength, corresponding to the beginning of crushing (Fcr; and correspond-

ing displacement, dcr); (iv) residual strength (Fu) and corresponding displacement (du);

the fifth branch of the behavior curve is defined by its stiffness (K4). A different behavior

curve can be defined for each loading direction, which allows for the consideration of non

symmetrical behavior. The hysteretic rules calibrated for masonry models are controlled

by three additional parameters, namely: a - stiffness degradation; b – ‘‘pinching’’ effect;

and, g - strength degradation [Rodrigues et al., 2005].

The infill walls openings affect its lateral stiffness and strength. Mallick and Gorg

[1971] and Asteris [2003] performed a series of tests on infilled frames with centered

openings, with and without reinforcement around these openings. They observed that the

openings can reduce the stiffness and strength of the infilled frames of about 60–70% and

45%, respectively, when compared to solid infill panels. Asteris [2003], based on

numerical studies, studied the influence of openings percentage in the decrease of the

lateral stiffness of infilled frames. Comparing with the infilled frame, the bare frame

lateral stiffness decreases 87% (100% openings). For openings exceeding 50% of the

panel area, the stiffness reduction factor remains practically constant [Asteris, 2003].

Simplified empirical expressions have been proposed to account in the macro-models for

the openings influence, in terms of lateral stiffness and strength reduction. Anil and Altin

[2007] performed experimental tests on 1/3 reduced scale one-bay one-story reinforced

concrete frames specimens with fully and partial infill walls under cyclic lateral loading.

They derived reduction factors that can be used for initial and ultimate stiffness.

However, they underlined that frame-infill connection mechanism have a considerable

effect on the global infill behavior and must be taken into account. To consider in the

numerical models the influence of infill openings in the behavior of a infill masonry panel

simplified strength and stiffness reduction factors are often adopted, based on refined

parametric analyses [Combescure, 1996] or on simplified empirical expressions [Sortis

et al., 1999; Zarnic and Gostic, 1998].

5. Hysteretic Rules of the Infill Masonry Model

The nonlinear behavior of the central element is characterized by the proposed penta-

linear monotonic curve and the corresponding hysteretic rules, inspired on the Costa

and Costa tri-linear model for RC elements [Costa, 1989; CEB, 1996], allowing the

determination of the response to cyclic loads as a function of the material’s behavior

(defined by the envelope curve and hysteretic parameters). The hysteretic rules are

briefly exemplified in Fig. 4.

Loading rules: The loading stiffness depends on the maximum displacement value

reached in the previous cycle (dmax) and on the corresponding force value, F(dmax).

The loading begins at the point corresponding to null-force (dr) and its stiffness is

defined by Eq. (1):

Kr ¼FðdmaxÞ

dmax � dr

: (1)


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

Unloading rules: Unloading happens when a load inversion occurs. The unloading

stiffness depends on the maximum displacement reached. Before the yielding-point

has been reached, the unloading stiffness (Kd) will be equal to the initial stiffness

(K0). If the maximum displacement reached is larger than the yielding displacement

(dy), but smaller than dcr (crushing displacement), the unloading stiffness (Kd) will

depend on the parameter a, and on the maximum displacement reached in that cycle,

defined by Eq. (2):

Kd ¼Fcr � � � Fy

K0 � dcr þ � � Fy

� K0: (2)

If the maximum displacement reached is larger than dcr, the unloading stiffness

(Kd) will depend only on the parameter a. The unloading stiffness is given by Eq. (3):

Kd ¼Fcr � � � Fy

dcr � K0 � � � dyKo

� K0: (3)

‘‘Pinching’’ effect: Simulates the masonry cracks closing in the unloading-reloading

branch. The pinching effect is represented by dividing the reloading path into two

branches with different stiffness (Fig. 5). In Eq. (4), K represents the stiffness

corresponding to the first branch of the reloading path. The pinching effect

is controlled through the pinching parameter b, and depends on the maximum

previously reached displacement (see Eq. (4)):

K ¼ FðdmaxÞdmax � dr

� dy

dmax

� ��: (4)

where dr is the displacement corresponding to null force in the previous cycle and dy is

the yielding displacement.

α.

α.

A

B

C

D

EF

G

H

I

J

K

L

M

N

O

P

Q

R0

F

D

FIGURE 4 Hysteretic rules for the implemented model.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

Stiffness degradation: The stiffness degradation is controlled by the parameter a (Eq. (2)).

Strength degradation: The strength degradation, for repeated cycles of certain dis-

placement amplitude, was implemented by taking into account the interaction

between the degradation in one direction with that in the other. The strength

degradation is given by Eqs. (5)–(8) (see also Fig. 6), where PD1 and PD2 are

the degradation factors in direction 1 and 2; di is the maximum displacement in

the cycle i; dy is the yielding displacement; df is a characteristic displacement

defined in function of the yielding displacement and of the parameter m; and, m,

c, n, and z are constant parameters that are calibrated with experimental results

or empirical formulae.

O

A

B

C

D

E

F

GH

I

JK

Q

L

M

N

P

R

S

T U

V

WX

Y

Z

Y'

S'

L'

V'

P'I'

F

d

FIGURE 5 ‘‘Pinching’’ effect.

O

A

B

C

D

E

F

G H

I

J K

Q

L

M

N

P

R

S

T U

V

W X

Y

Z

H'

N'

U'

K'

R'

F

FIGURE 6 Strength degradation.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

� ¼ c �XN

i¼1

di

df

(5)

df ¼ dy � � (6)

PD1 ¼en� � 1

en � 1� 1� PD2

�

� �(7)

PD2 ¼en� � 1

en � 1� 1� PD1

�

� �(8)

Internal cycles: When a load inversion takes place before the maximum force or the

maximum displacement is reached, the model is able to reproduce the so-called

internal cycles, with all the effects described above.

6. Calibration of the Proposed Infill Masonry Model

The proposed macro-model for the simulation of the influence of infilled masonry panels

on the behavior of the structure was verified using results obtained from two experimental

series. In the numerical models, the material parameters were defined accordingly to

results on test specimens for each material (concrete, steel, and masonry).

This article only presents the comparisons between the experimental and numerical

results in terms of overall structural response parameters, with the intention of illustrating

the validation of the proposed model.

The proposed model for infill masonry panels was implemented in the nonlinear

structural frame program PORANL. In these software, RC structural elements (beams and

columns) are modeled by a macro-element defined by the association of three bar finite

elements, two with nonlinear behavior at its extremities (plastic hinges), and a central

element with linear behavior. The nonlinear monotonic behavior curve of an element is

characterized through a tri-linear moment-curvature relationship, and is able to represent

the response evolution of the global RC section to cyclic demands and contemplates

mechanical behavior effects as stiffness and strength degradation, pinching, slipping and

internal cycles [Varum, 1996].

6.1. Concrete Model

To simulate the structural behavior of the building each RC structural element is modeled

by a macro-element defined by the association of three bar finite elements, two with

nonlinear behavior at its extremities (plastic hinges), and a central element with linear

behavior, as schematically represented in Fig. 7.

The nonlinear behavior of the plastic hinge elements is controlled through a modified

hysteretic procedure, based on the Takeda model, as illustrated in Fig. 8. This model

developed by Costa-and-Costa [CEB, 1996; Cotsa and Costa, 1987] represents the

response moment-curvature evolution of the RC section to cyclic actions and


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

contemplates mechanical behavior effects as stiffness and strength degradation, pinching,

slipping, internal cycles, etc.

The nonlinear monotonic behavior curve of a cross-section is characterized through a

tri-linear moment-curvature relationship, corresponding, respectively, to: the initial non-

cracked concrete, concrete cracking, and steel reinforcement yielding. The monotonic

curve is obtained using a fiber model procedure from: the geometric characteristics of the

cross-sections, reinforcement and its location, and material properties.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18 19

2021

22

D+yD−

y D−c

D+c

F

23

D

12A

13A

FIGURE 8 Global hysteretic model for RC elements [Costa and Costa, 1987].

y'

l pesq

x'

dirpl

l

2Δ

1Δ

3Δ

5Δ4Δ

6Δ

FIGURE 7 Macro-element used for the behavior simulation of reinforced concrete

elements.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

6.2. One-Bay One-Story Infilled Frame

The proposed macro-model for infill masonry was first calibrated with the results of a

cyclic test performed by Pires [1990]. The infilled reinforced concrete model is a single-

story single-bay, scaled 2:3. The geometrical characteristics of the frame, the cross

sections dimensions and the reinforcement detailing of the columns and beam are

presented in Fig. 9. Vertical forces were applied to the top of the columns, to simulate

the dead load, and imposed cyclic horizontal displacements were applied (see Fig. 10).

The properties of the models (RC frame and masonry infill) were calibrated with test

results from material specimens. The reinforcement steel used in the construction of the

frame had an average Young modulus of 190 GPa and a yielding strength of 434 MPa.

–100

–80–60

–40

–20

020

40

6080

100

Dis

plac

emen

t (m

m)

FIGURE 10 Imposed cyclic horizontal displacement.

0.150.42 4.20 0.420.15

0.1650.20

1.625

0.35

[m]

a)

0.15

0.20ø4//0.05

3ø8

3ø8

ø4//0.05

0.15

0.15

8ø8

b)

c)

FIGURE 9 Single-story single-bay infilled masonry RC frame: a) Frame geometry,

b) Cross-section dimensions and detailing of RC elements; c) Testing layout [Bertoldi

et al., 1994].


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

From the compressive strength tests on reference specimens it was obtained a compres-

sive strength of 25.3 MPa and a Young modulus of 30 GPa. From diagonal compressive

tests on masonry wallets it was obtained a tensile strength of 270 kPa, and a shear

modulus of 480 MPa. More detailed information about the experimental campaign on

masonry wallets and it components can be found in Pires [1990].

The results obtained with the numerical model are in good agreement with

the experimental response, in terms of shear-drift (Fig. 11) and energy dissipation

(Fig. 12), demonstrating the ability of the proposed macro-model to simulate the global

hysteretic response of infilled frames. The differences observed in the shear-drift

response are acceptable considering that the model proposed is simplified, modeling

globally the entire infill masonry panel and its interaction with the surrounding RC

frame elements.

–140

–100

–60

–20

20

60

100

140

–11.00 –5.50 0.00 5.50 11.00

Bas

e Sh

ear

(kN

)

Drift (cm)

Experimental

Numerical

FIGURE 11 Base-shear versus inter-story drift.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 5000 10000 15000 20000 25000

Ene

rgy

(MN

.m)

Step

Experimental

Numerical

FIGURE 12 Total energy dissipation.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

In terms of energy dissipation, it was verified that the numerical results leads to a

slight overestimation of the energy dissipation. At the end of the test the difference in

terms of total energy dissipated was inferior to 10%. The evolutions of the energy

dissipated (numerical and experimental) follow a similar path, however it should be

mentioned that larger differences were noticed in the intermediate steps.

6.3. Three-Bay Four-Story Infilled Frame

The research network ICONS (financed by the European Commission) has addressed

the issue of seismic assessment and the retrofitting of existing structures, covering the

related deficiencies and viable retrofitting solutions. In particular, the assessment of

reinforced concrete buildings, with and without infill panels, and several strengthening

solutions and techniques, were investigated through numerical and experimental work.

The experimental research work includes several studies carried out at the ELSA

reaction-wall laboratory, at the JRC. In order to evaluate the efficiency of different

retrofitting solutions and to investigate bare and infilled frame test conditions, two

representative identical full-scale four-story, three-bay reinforced concrete frames (one

as a bare frame and one as a frame with brick infilled walls), were designed, constructed,

and placed parallel to each other and were tested in sequence using pseudo-dynamic

testing procedures (see Fig. 13).

The frames were subjected separately to pseudo-dynamic tests to assess the earth-

quake performance of both the bare concrete frame and the frame structure with infill

masonry walls.

The concrete frame under analysis was essentially designed for gravity loads. The

reinforcement details were specified in order to be representative of buildings constructed

up to the late 1970’s in European Mediterranean countries such as Portugal, Italy, Greece,

Turkey, etc.

The general layout and dimensions of the structure under investigation are given in

Fig. 14. This was a four-story frame with three bays, two with a 5.00 m span and one

external one with a 2.50 m span. Inter-story height was 2.70 m for all four stories, and a

concrete slab 2.00 m wide on each side and 0.15 m thick was cast together with the

beams. Equal beams (geometry and reinforcement details) were considered for all floors.

FIGURE 13 Four-stories, three-bays full-scale plane frame structures.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

All beams in the direction of loading were 0.25 m wide and 0.50 m deep. The stocky

column had section dimensions of 0.25 m · 0.60 m at the 1st and 2nd story and at the 3rd

and 4th story are 0.25 m · 0.50 m. The other columns had equal geometric characteristics

at all stories. The vertical loads are shown in Fig. 15.

15.1 15.1

15.1 15.1

15.1 15.1

12.7 12.7

15.1

15.1

15.1

12.7

56.4

56.4

56.4

44.3 76.1

88.2

88.2

72.3

72.3

60.2

72.3

88.2

40.5

40.5

40.5

28.4

FIGURE 15 Distribution of vertical static loads [kN; m].

2.70

2.70

2.70

2.70

5.00 5.00 2.50

(1.2x1.0)

(1.2x1.0)

(1.2x1.0)

(1.2x1.0)

(2.0x1.0)

(2.0x1.0)

(2.0x1.0)

(2.0x1.75)

[ m ]

1 2 3 4

FIGURE 14 Frame geometrical characteristics and infill openings dimensions.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

The brick masonry panels (0.20 m thick) were constructed according to the following

specifications: (a) the left-hand bay infill contained a window (1.20 m · 1.00 m) at each

level; (b) the central bay contained a doorway (2.00 m · 1.75 m) at ground level and

window openings (2.00 m · 1.00 m) at each of the upper three levels of the building; and,

(c) the right-hand (2.50 m span) bay contained solid infill, i.e., without openings.

The masonry blocks used in the construction of the infills are ceramic, horizontally

perforated, and have the following dimensions: 0.12 m thick, 0.245 m base-length, and

0.245 m height. The infill walls were constructed with the block units bedded on the

0.120 m · 0.245 m face and the hollows in the horizontal direction (0.120 m thick). The

mortar used in the joints and plaster was manually prepared as the current construction

practice until the late 1970’s. The mortar joints are approximately 1.5 cm thick for both

vertical and horizontal joints, so-called perpend and bed joints, respectively. A 1.5 cm

thick plaster was applied on both sides of the walls [Varum, 2003].

Tests on mortar specimens and block units were carried out in order to characterize

the masonry infill wall components. Wallets representative of the masonry infill walls

were also constructed and tested in compression (perpendicular and parallel to the bed

joints and in the diagonal direction). In the next, a summary of the test results on

specimens of block units, mortar, and infill wallets are presented. A more detailed

description of the infill properties can be found elsewhere [Varum, 2003; Pinto et al.,

2001]. Table 1 summarizes the results obtained for the tests on brick units, mortar and

masonry panels (parallel and perpendicular to the bed joints and diagonal compression

tests, for the nominal areas). Using the empirical expressions proposed by Zarnic and

Gostic [1998], to estimate the infill masonry global properties and the average mechan-

ical properties obtained from the tests on infill masonry wallets, were obtained the

behavior curves for each infill masonry panel used in the modeling of the infilled

frame structure.

The building studied in the present numerical analysis is represented by a plane

frame model (with three degrees of freedom per node, i.e., two translations and one

rotation) with four stories and three bays. The geometrical characteristics of the cross

sections and the reinforcement detailing of the columns and beams are summarized in

Tables 2 and 3, respectively. The reinforcement steel used in the construction of the

frames had an average Young modulus of 204.5 GPa and a mean yielding strength of

343.6 MPa [Pinto et al., 1999]. Compressive strength tests on concrete reference speci-

mens were performed for each casting phase. The average values obtained from these

tests are given in Table 4.

From diagonal compressive tests on masonry wallets it was obtained a tensile

strength of 575 kPa, and a shear modulus of 1.17 GPa. More detailed information

about the experimental campaign on masonry wallets and it components can be found

in Varum [2003].

Considering that two full scale test series were performed, one the bare and another

on the infilled frame, and both RC structures have the same dimensions, materials, and

detailing, the calibration of the infilled frame was made as explained in next. Firstly, a

model for the bare structure was developed and calibrated with the pseudo-dynamic test

results of the bare frame. To model the infilled structure, the mechanical parameters

adopted for the RC frame elements were the ones that resulted from the numerical model

calibration of the bare frame done in the first phase and discussed in Rodrigues [2005].

6.3.1. Bare Frame Structure. The nonlinear response of the RC bare frame was

computed for each earthquake input motion applied in the pseudo-dynamic tests

[Varum, 2003]. A first earthquake of 15 s duration corresponding to a 475 years return


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

period (yrp), and subsequently, the first 7.5 s of an earthquake signal corresponding to a

975-yrp earthquake were applied to the structure (see Fig. 16). In the dynamic analysis

performed, it was considered an equivalent Rayleight damping of 1%, associated to the

first two natural modes.

The results obtained with the numerical model for the bare frame are compared with

the experimental pseudo-dynamic test results. The displacements time histories (experi-

mental pseudo-dynamic results and numerical calculations) are shown in Fig. 17.

Comparing the numerical results obtained with the nonlinear structural model for the

bare frame with the experimental results, it can be observed a good matching between the

experimental results and the numerical, despite the former tend to underestimate dis-

placement demands in the last cycle, corresponding to the imminent structure collapse.

6.3.2. Infilled Frame Structures. A first analysis of results in terms of natural frequen-

cies and modal shapes intends to constitute the first validation of the numerical models.

The natural frequencies were computed with the initial stiffness of the frame elements

TABLE 1 Summary table of materials (brick units and plaster) and masonry specimens

test results [Varum, 2003]

Element tested Test Symbol Units Value

Brick units Compressive strength

(parallel to the bed joints)

�nnc MPa 15.36

Compressive strength

(perpendicular to the bed

joints)

�?c MPa 2.80

Mortar (joints and

plaster)

Tensile strength �t MPa 0.59

Compressive strength �c MPa 1.33

Masonry wallets Vertical

and horizontal

compressive tests

(without plaster)1


(parallel to the bed joints)

�nnc MPa 1.11



joints)

�?c MPa 1.10

Young modulus (parallel to

the bed joints)

Enn GPa 0.991

Young modulus


joints)

E? GPa 1.873

Masonry wallets

Diagonal compressive

tests (without plaster)1

Tensile strength �t MPa 0.233

Shear modulus G GPa 0.657

Masonry wallets Tensile strength �t MPa 0.575

Diagonal compressive

tests (with plaster in

both sides)1

Shear modulus G GPa 1.171

1 – tests performed at laboratory of University of Pavia.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

(with the gross-sections and with the elastic stiffness of the concrete and steel) and with

the initial stiffness for the infill masonry panels (K0). Table 5 compares the first natural

frequencies measured in the structure under test with those estimated through the models.

In general terms, a good agreement was obtained.

TABLE 3 Beams cross-sections (m · m) and reinforcement detailing

TABLE 2 Columns cross-sections (m · m) and reinforcement detailing


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

By the numerical models implemented, the nonlinear response of the RC infilled

frame was computed for each earthquake input motion applied in the pseudo-dynamic

tests. Earthquakes of 15 s duration and increasing return periods, corresponding to 475,

975, and 2,000 yrp, were applied to the infilled frame. During the pseudo-dynamic tests,

collapse was observed at 5.0 s of the 2,000-yrp earthquake input motion. Therefore, to

reproduce the testing sequence, the numerical analysis was performed for the earthquake

accelerogram shown in Fig. 18. The input motion is composed of three consecutive

accelerograms. The first two are 15 s in duration and correspond to the 475 and

975 yrp accelerograms, and the third corresponds to the initial 5 s of the 2,000 yrp

input motion. The three accelerograms are separated by 5 s of zero ground acceleration.

Therefore, the dynamic movement at the end of each 15 s accelerogram is damped till the

beginning of the subsequent accelerogram, reproducing real testing conditions. The

numerical analysis was performed for the 45 s duration earthquake input motion shown

in Fig. 18. In the dynamic analysis performed, it was considered an equivalent Rayleigh

damping of 1%, associated to the first two natural modes.

The results obtained with the numerical model are compared with the experimental

pseudo-dynamic test results. The time histories (experimental pseudo-dynamic results and

numerical calculations) in terms of story displacements are shown in Fig. 19. Figure 20

shows both the computed and the experimentally measured plots of story-shear force

versus inter-story drift, at story levels (shear-drift hysteresis diagrams). Figure 21 shows

the evolution of the dissipated energy, at story level, for the infilled frame under analysis.

Figure 22 shows the observed damage at the end of the pseudo-dynamic tests and

the numerical results in terms of plastic hinges location and damage state estimation in

these regions.

TABLE 4 Concrete properties

Columns Beams

Material properties

1st

story

2nd

story

3rd

story

4th

story

1st

story

2nd

story

3rd

story

4th

story

Ecm [GPa] 22.8 22.8 19.9 21.1 24.4 24.4 24.4 24.4

fcm [MPa] 16.6 13.78 16.50 13.58 13.24 18.10 21.63 16.98

–3

–2

–1

0

1

2

3

0 5 10 15 20 25

Acc

eler

atio

n (m

/s2 )

Time (s)

FIGURE 16 Earthquake input motion for the bare frame structure.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

Comparing the nonlinear dynamic numerical results for the infilled frame with the

experimental results, the following main conclusions can be drawn.

� The numerical model was able to reproduce the modifications in structural response

induced by the infill panels. The natural frequencies of the infilled structure were

considerably increased, when compared to the original bare frame. As already observed,

the numerical model also reproduces the frequencies of the structural system well.

� The numerical analyses confirm that the infill panels can protect the reinforced

concrete frame for low intensity seismic input, but for larger input motion, the

fragile behavior of the masonry induces an explosive rupture.

4th

Stor

y

–100

–50

0

50

100

150

0 5 10 15 20 25

Dis

plac

emen

t (m

m)

–100

–50

0

50

100

150

Dis

plac

emen

t (m

m)

Time (s)

Time (s)

Time (s)

Time (s)

Experimental

Numerical

Experimental

Numerical

Experimental

Numerical

Experimental

Numerical

3rd

Stor

y

0 5 10 15 20 25

2nd

Stor

y

–50–40–30–20–10

01020304050

0 5 10 15 20 25

Dis

plac

emen

t (m

m)

1st S

tory

–15

–10

–5

0

5

10

15

20

0 5 10 15 20 25

Dis

plac

emen

t (m

m)

FIGURE 17 Story displacement evolutions.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

� The numerical model was able to predict the failure of the infill walls well. In fact,

the soft-story mechanism at ground level is well identified with the numerical

models.

� Comparing the numerical with the experimental results, significant differences

were found at the 2nd-story global shear-drift curve. However, on one hand the

level of deformations at this story is significantly smaller then the corresponding to

the first story and, on the other hand, the global response of the overall structure is

leaded by the first story response, where the soft-story mechanism was verified.

The proposed numerical model was able to represents the global behavior of the

infilled RC structure.

� The global numerical model of the structure was able to reproduce the experi-

mental results, not only in terms of story shear and inter-story drift time-histories

and envelopes, shear-drift curves, but also in terms of energy dissipation.

� The numerical results confirm that the adopted models (RC elements with flexural

nonlinearity concentrated at their extremities and the macro-model for the infill

panels) are suitable for the simulation of the nonlinear seismic response of

masonry infilled RC frames.

7. Conclusions and Final Considerations

Masonry infill walls have a complex behavior due to the properties of their materials and

to the interaction with the surrounding frame. The global response of infilled RC frames

is largely dependent of the masonry infills properties and dimensions. However, its

TABLE 5 Natural frequencies and vibration modes of infilled frame

–3

–2

–1

0

1

2

3

0 5 10 15 20 25 30 35 40

Acc

eler

atio

n (m

/s2 )

Time (Sec)

FIGURE 18 Earthquake input motion.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

consideration is not current in the design practice. The response prediction of masonry

infilled frame structures can be achieved by computational modeling. The response of

such structures to horizontal loads is highly complex and depends on many factors, from

material properties to the quality of the workmanship. The development of simplified

nonlinear numerical models, together with increased computational power, permit the

inclusion of infill masonry models in the structural assessment of existing structures and

in the design of new buildings.

This article describes a proposed simplified macro-model for the representation

of the hysteretic behavior of infill masonry panels, and its implementation on a

computer program. The masonry model proposed consists in a variation of the typical

strut model, considering now the interaction of masonry panel behavior in both

directions, i.e., damage in the panel in one direction affects its behavior in the

other direction. The masonry panel hysteretic procedure consider different rules for

loading, reloading, and unloading and considers also stiffness and strength degrada-

tion, and pinching effect.

4th St

ory

3rd St

ory

2nd St

ory

1st St

ory

–0.04

–0.03

–0.02

–0.01

0.00

0.01

0.02

0 10 20 30 40

Time (s)

Time (s)

Time (s)

Time (s)

Dis

plac

emen

t (m

)

Experimental

Numerical

Experimental

Numerical

Experimental

Numerical

Experimental

Numerical

–0.03

–0.04

–0.02

–0.01

0.00

0.01

0.02

0.03

0 10 20 30 40

Dis

plac

emen

t (m

)

–0.04

–0.03

–0.02

–0.01

0.01

0.02

–0.04

–0.03

–0.02

–0.01

0.01

0.02

0 10 20 30 40

Dis

plac

emen

t (m

)D

ispl

acem

ent (

m)

0 5 10 15 20 25 30 35 40

FIGURE 19 Story displacement evolutions.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

4th S

tory

3rd S

tory

2nd S

tory

1st S

tory

–750

–550

–350

–150

50

250

450

650

–0.30 –0.20 –0.10 0.00 0.10 0.20 0.30

Drift (%)

–0.30 –0.20 –0.10 0.00 0.10 0.20 0.30

Drift (%)

–0.30 –0.20 –0.10 0.00 0.10 0.20 0.30

Drift (%)

–1.5 –1 –0.5 0 0.5 1 1.5

Drift (%)

Shea

r (k

N)

Shea

r (k

N)

Shea

r (k

N)

Shea

r (k

N)

ExperimentalNumerical




–800

–600

–400

–200

0

200

400

600

800

–1000

–800

–600

–400

–200

0

200

400

600

800

1000

–1000

–800

–600

–400

–200

0

200

400

600

800

1000

FIGURE 20 Story-shear versus inter-story drift.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

4th S

tory

3rd S

tory

2nd S

tory

1st S

tory

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25 30 35 40

Time (s)

0 5 10 15 20 25 30 35 40

Time (s)

0 5 10 15 20 25 30 35 40

Time (s)

0 5 10 15 20 25 30 35 40

Time (s)

Dis

sipa

ted

ener

gy (

kN.m

)D

issi

pate

d en

ergy

(kN

.m)

Dis

sipa

ted

ener

gy (

kN.m

)D

issi

pate

d en

ergy

(kN

.m)





0

2

4

6

8

10

0

5

10

15

20

25

30

35

40

0

20

40

60

80

100

FIGURE 21 Story energy dissipation evolution.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

The proposed infill masonry model was calibrated with the results of two tests on infilled

RC structures, namely of a cyclic test on a single-story single-bay, scaled 2:3, and on a full-

scale frame four-stories, three-bays frame. The structural response was calculated by impos-

ing, although the vertical load, the displacements history on the single-story, single-bay frame

structure, and for the full-scale frame four-stories structure it was applied the acceleration time

histories considered in the corresponding pseudo-dynamic tests. The numerical results were

compared to the experimental, for both test series, and generally it was observed that the

model proposed was able to represent the response of the structures in terms of displacements

evolution, global shear-drift at each story, and cumulative dissipated energy.

The proposed macro-model can be a useful tool in the development and calibration

of simplified rules for the analysis of infilled frame structures under horizontal loadings,

accounting for important mechanical features as hysteretic behavior, strength and stiff-

ness degradation, pinching, damage evolution, and function of the deformation demands.

A more exhaustive testing campaign on masonry infilled structures, considering the

effects of apertures dimensions and location, infill dimensions, relative stiffness frame/

infill, etc., would help to calibrate the model here proposed for a more wide range of

conditions. This could lead to empirical expressions valid for a broad range of situations,

which could be considered in future seismic structural assessment standards.

Acknowledgments

The experimental data used in this article were obtained from two test series. The first

were developed at the LNEC Laboratory, in Lisbon, and the second at the Joint Research

Centre’s ELSA Laboratory, financed by the European Commission, under the Training

and Mobility of Researchers program, the TMR- Large-Scale Facilities and the ICONS

TMR-Network.

FIGURE 22 Damage state a) experimental results [Varum, 2003]; b) numerical results.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

References

Anil, O. and Altin, S. [2007] ‘‘An experimental study on reinforced concrete partially infilled

frames,’’ Engineering Structures 29: 449–60.

Asteris, P. G. [2008] ‘‘Finite element micro-modeling of infilled frames,’’ Electronic Journal of

Structural Engineering 8:1–11.

Asteris, P. G. [2003] ‘‘Lateral stiffness of brick masonry infilled plane frames,’’ Journal of

Structural Engineering, ASCE 129(8):1071–1079.

Bell, D. K. and Davidson, B. J. [2001] ‘‘Evaluation of earthquake risk buildings with masonry infill

panels,’’ 2001 Technical Conference, Future Directions: A Vision for Earthquake Engineering

in New Zealand, New Zealand Society for Earthquake Engineering Taupo, New Zealand.

Bertoldi, S. H., Decanini, L. D., Santini, S., and Via, G. [1994] ‘‘Analytical models in infilled frames,’’

Proc. of the 10th European Conference in Earthquake Engineering, Vienna 1533–1538.

Blandon-Uribe, C. A. [2005] ‘‘Implementation of an infill masonry model for seismic assessment

of existing buildings,’’ Individual Study, European School for Advanced Studies in Reduction of

Seismic Risk (ROSE School), Pavia, Italy.

CEB [1996] ‘‘RC frames under earthquake loading,’’ Comite Euro-International du Beton,

Bulletin 231:1–303.

CEN [2003] ‘‘Eurocode 8: Design of structures for earthquake resistance - Part 1–3: Strengthening

and repair of buildings - European prEN 1998-1-3,’’ European Committee for Standardization,

Brussels, Belgium.

Combescure, D. [1996] ‘‘Modelisation du comportement sous chargement sismique des structures

de batiment comportant des murs de remplissage en maconnerie,’’ PhD thesis (in French Ecole

Centrale de Paris, France.).

Combescure, D. and Pegon, P. [2000] ‘‘Application of the local to global approach to the study of

infilled frame structures under seismic loading,’’ Proc. of the 12th World Conference on

Earthquake Engineering, Auckland, New Zealand.

Costa, A. G. [1989] ‘‘Analise sısmica de estruturas irregulares,’’ Ph.D. Thesis, Civil Engineering

Department, University of Porto (in Portuguese).

Costa, A. C. and Costa, A. G. [1987] ‘‘Hysteretic model of force displacement relationships for

seismic analysis of structures,’’ National Laboratory for Civil Engineering, Lisbon.

Crisafulli, F. J. [1997] ‘‘Seismic behavior of reinforced concrete structures with masonry infills,’’

Ph.D. thesis, University of Canterbury, New Zealand.

Crisafulli, F. J., Carr, A. J., and Park, R. [2000] ‘‘Analytical modelling of infilled frames structures -

A general review,’’ Bulletin of the New Zealand Society for Earthquake Engineering 33: 30–47.

Doherty, K., Griffith, M. C., Lam, N., and Wilson, J. [2002] ‘‘Displacement-based seismic analysis

for out-of-plane bending of unreinforced masonry walls,’’ Earthquake Engineering and

Structural Dynamics 31: 833–850.

Dolsek, M. and Fajfar, P. [2008] ‘‘The effect of masonry infills on the seismic response of a four-storey

reinforced concrete frame: a deterministic assessment,’’ Engineering Structures 30: 1991–2001.

Duarte, R. T. and Campos-Costa, A. [1988] ‘‘Earthquake behaviour of reinforced concrete frames

structures infilled with masonry panels,’’ Technical Report, LNEC, Lisbon.

FEMA-273 [1997] NEHRP Guidelines for the Seismic Rehabilitation of Buildings, Federal

Emergency Management Agency, Washington, D.C.

FEMA-306 [1999] Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings –

Basic Procedures Manual, Federal Emergency Management Agency, Washington, D.C.

FEMA-307 [1999] Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings –

Technical Resources, Federal Emergency Management Agency, Washington, D.C.

FEMA-356 [2000] Prestandard and Commentary for the Seismic Rehabilitation of Buildings,

Federal Emergency Management Agency, Washington, D.C.

Freeman, S. A. [1977] ‘‘Racking tests of high rise building partitions,’’ Journal of Structural

Division ASCE 103(ST8).

Klingner, R. Y. and Bertero, V. [1976] ‘‘Infilled frames in earthquake-resistant construction,’’

Report No. EERC 76-32, University of California, Berkeley.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

Krstevka, L. and Ristic, D. [2004] ‘‘Seismic response of RC infilled frames – micro-model for

non-linear numerical simulation,’’ Proc. of the 13th World Conference on Earthquake

Engineering, Vancouver, Canada, Paper No. 1119.

Lam, N. T. K., Griffith, M., Wilson, J., and Doherty, K. [2003] ‘‘Time-history analysis of URM

walls in out-of-plane flexure,’’ Engineering Structures 25:743–754.

Liaw, T. C. and Kwan, K. H. [1983] ‘‘Plastic theory of infilled frames with finite interface shear

strength,’’ Proc. of the Institution of Civil Engineers, Part 2, 75:707–723.

Liaw, T. C. and Lee, S. W. [1977] ‘‘Analysis of the behaviour of multi-storey infilled frames

subject to lateral loading,’’ Proc. of the Institution of Civil Engineers Part 2, 63:641–657.

Magenes, G. and Pampanin, S. [2004] ‘‘Seismic response of gravity-load design frames with

masonry infills,’’ 13th World Conference on Earthquake Engineering, Vancouver, B.C.,

Canada.

Mainstone, R. J. [1971] ‘‘On the stiffnesses and strengths of infilled frames,’’ Proc. of the

Institution of Civil Engineers, Supplement (IV), Paper 73605:57–90.

Mallick, D. V. and Garg, R. P. [1971] ‘‘Effect of openings on the lateral stiffness of infilled

frames,’’ Proc. of the Institution of Civil Engineers, Structural Buildings, 49:193–209.

Oliveira, D. [1995] ‘‘Comportamento de porticos de betao armado preenchidos com paredes de

alvenaria,’’ MSc Thesis, FEUP, Portugal.

Paulay, T. and Priestley, M. [1992] Seismic Design of Reinforced Concrete and Masonry Buildings,

John Wiley & Sons, Inc., New York.

Pinto, A. V., Verzeletti, G., Molina, F. J., Varum, H., Carvalho, E. C., and Coelho, E. [2001]

‘‘Pseudo-dynamic tests on non-seismic resisting RC frames (infilled frame and infill strength-

ened frame tests),’’ EU Special Publication, ELSA, JRC-Ispra, EC, Italy.

Pinto, A. V., Verzeletti, G., Molina, F. J., Varum, H., Coelho, E., and Pinho, R. [1999] ‘‘Pseudo-

dynamic tests on non-seismic resisting RC frames (bare and selective retrofit frames),’’ EUR

Report 20244 EN, ELSA, JRC-Ispra, EC, Italy.

Pires, F. [1990] ‘‘Influencia das Paredes de Alvenaria no comportamento de Estruturas Reticuladas

de Betao Armado sujeitas a Accoes Horizontais,’’ LNEC, Lisboa (in Portuguese).

Polyakov, S. V. [1957] Masonry in Framed Buildings. An Investigation into the Strength and

Stiffness of Masonry Infilling, Moscow.

Puglisi, M., Uzcategui, M., and Florez-Lopez, J. [2009a] ‘‘Modeling of masonry of infilled frames,

Part I: The plastic concentrator,’’ Engineering Structures 31:113–118.

Puglisi, M., Uzcategui, M., and Florez-Lopez, J. [2009b] ‘‘Modeling of masonry of infilled frames,

Part II: Cracking and damage,’’ Engineering Structures 31:119–124.

Riddington, J. R. and Stafford Smith, B. [1977] ‘‘Analysis of infilled frames subject to racking with

design recommendations,’’ The Structural Engineer 55(6):263–268.

Rodrigues, H. [2005] ‘‘Development and calibration of numerical models for building

seismic analysis,’’ MSc Thesis, Civil Engineering Department, University of Porto (in

Portuguese).

Rodrigues, H., Varum, H., and Costa, A. G. [2005] ‘‘Modelo numerico nao-linear para paineis de

alvenaria de enchimento em porticos de betao armado,actas do Congreso Metodos Numericos en

Ingenierıa,’’ E.T.S. de Ingenieros de Caminos de la Universidad de Granada, Spain.

Rodrigues, H., Varum, H., Costa, A. G., and Romao, X. [2004] ‘‘Interface Grafico para

Analise Nao-Linear de Porticos Planos Sujeitos a Cargas Dinamicas e/ou Estaticas,’’

Congresso de Metodos Computacionais em Engenharia - CMCE 2004, LNEC, Lisboa (in

Portuguese).

RSA [1983] ‘‘Regulamento de seguranca e accoes para estruturas de edifıcios e pontes - Decreto-

Lei N.� 235/83,’’ Imprensa Nacional, Casa da Moeda, Lisbon, Portugal (in Portuguese).

Smyrou, E. [2006] ‘‘Implementation and verification of Masonry panel model for nonlinear

dynamic analysis of Infilled RC frames,’’ MSc Thesis, European School for Advanced Studies

in Reduction of Seismic Risk (ROSE School), Pavia, Italy.

Sortis, A., Pasquale, G., and Nasini, U. [1999] ‘‘Criteri di calcolo per la progettazione degli

interventi - Terremoto in Umbria e Marche del 1997,’’ Servizio Sismico Nazionale, Editrice

Sallustiana, Roma (in Italian).


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

Stafford-Smith, B. [1962] ‘‘Lateral stiffness of infilled frames,’’ Proc. of the American Society of

Civil Engineers, ASCE 88:183–199.

Stafford-Smith, B. and Carter, C. [1969] ‘‘A method of analysis for infilled frames,’’ Proc. of the

Institution of Civil Engineers, 44:31–48.

Valiasis, T. N. and Stylianidis, K. C. [1989] ‘‘Masonry infilled R/C frames under horizontal

loading — experimental results,’’ European Earthquake Engineering 3(3): 10–20.Varum, H.

[1996] ‘‘Modelo numerico para a analise de porticos planos de betao armado,’’ MSc Thesis,

Civil Engineering Department, University of Porto (in Portuguese).

Varum, H. [2003] ‘‘Seismic assessment, strengthening and repair of existing buildings,’’ PhD

Thesis, Department of Civil Engineering, University of Aveiro, Portugal.

Zarnic, R. and Gostic, S. [1998] ‘‘Non-linear modelling of masonry infilled frames,’’ Proc. of the

11th European Conference on Earthquake Engineering, Paris.


Dow

nloa

ded

by [

b-on

: Bib

liote

ca d

o co

nhec

imen

to o

nlin

e U

A]

at 0

2:31

15

Janu

ary

2013

Simplified Macro-Model for Infill Masonry Panels

Documents

Transcript of Simplified Macro-Model for Infill Masonry Panels