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Behaviour of RC buildings with large lightly reinforced wallsalong the perimeter

Marisa Pecce 1, Francesca Ceroni ⇑,1, Fabio A. Bibbò 1, Alessandra De Angelis 1

Engineering Department, University of Sannio, Benevento, Italy

a r t i c l e i n f o

 Article history:

Received 21 September 2013

Revised 8 March 2014

Accepted 23 April 2014

Available online 22 May 2014

Keywords:

Large lightly reinforced walls

Seismic performances

Dynamic behaviour

Nonlinear analysis

Ductility

Over-strength

a b s t r a c t

Reinforced Concrete (RC) walls are defined as large lightly reinforced walls if they are not provided of 

high reinforcement percentage or if they are lack of reinforcement details usually required to improve

the ductility of the structure. This type of walls gained relevance in 1950s–1970s constructions because

of their good performances under seismic actions. Real earthquakes have, indeed, demonstrated that

buildings constructed with large lightly reinforced walls, characterised by adequate area respect to the

floor extension, could suffer lower damages in comparison with traditional RC framed buildings. More-

over, a widespread use of such a construction typology is outstanding thanks to the diffusion on the mar-

ket of new types of integrated formworks, including insulating materials such as polystyrene, that are

being used for casting concrete and are aimed to obtain a higher energetic efficiency and build structures

made of continuous lightly reinforced walls. Nevertheless, there is a lack of both experimental informa-

tion and specific design indications in technical codes on this type of construction.

This paper firstly reviews the European code requirements for large lightly reinforced walls. Then, some

experimental tests on RC walls in the existing literature are studied in detail also by means of a nonlinear

Finite Element (FE) model.

Finally, the performances of a whole RC building designed with both large lightly reinforced walls along

the perimeter and internal frames have been also exploited by linear dynamic and static nonlinear anal-

ysis. The analysis are mainly aimed to highlight the influence of in-plane stiffness of the floor on thedynamic behaviour of the structure and to assess the contribution of both ductility and over-strength

to the behaviour factor, i.e. to the seismic performance of such type of buildings, considering the lack

of information in the technical literature about these features.

 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Structural Reinforced Concrete (RC) walls are an efficient sys-

tem for buildings that must withstand significant seismic actions,

particularly because they allow limiting displacements in tall

buildings. In recent decades, buildings with large lightly reinforced

walls have been constructed in countries such as Kyrgyzstan,

Canada, Romania, Turkey, Colombia and Chile [1]. Recent analyses

of the performances of some of these buildings after the earth-

quake occurred in Chile in 1985 [2,3] have demonstrated a lower

damage level in comparison with RC framed buildings, if the walls’

area is adequate respect to the floor extension, as it will be dis-

cussed more in detail afterwards.

Buildings having both structural walls located along the perim-

eter and inner RC frames also fall in the category of RC buildings

made with large lightly reinforced walls; this particular distribu-

tion not only gives to the building high resistance and stiffness

to the lateral actions but also provides an increased flexibility

within the organisation of the internal spaces. This is possible

thanks to the presence of RC frames made of columns character-

ised by small sections that have to support only the vertical loads.

Many examples of such type of building were built during the

1950s through the 1970s; in particular, some of the most relevant

to be cited are: the Santa Monica Hospital in California that was

damaged by the Northridge earthquake of 1994, the St. Joseph’s

Healthcare Orange and the St. Jude Medical Center that have been

studied in detail especially for what concerned the behaviour of 

their outer walls [4–6].

Currently, the use of large lightly reinforced walls located along

the perimeter of the building is being rediscovered both to improve

the thermal insulation performance and reduce the construction

http://dx.doi.org/10.1016/j.engstruct.2014.04.038

0141-0296/ 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +39 0824305575; fax: +39 0824325246.

E-mail addresses: pecce@unisannio.it (M. Pecce),  ceroni@unisannio.it (F. Ceroni),

fabiobibbo@libero.it  (F.A. Bibbò), dea.alessandra@gmail.com (A. De Angelis).1 Tel.: +39 0824305575; fax: 39 0824325246.

Engineering Structures 73 (2014) 39–53

Contents lists available at   ScienceDirect

Engineering Structures

j o u r n a l h o m e p a g e :   w w w . e l s e v i e r . c o m / l o c a t e / e n g s t r u c t

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time. These goals are being realised in systems consisting of form-

works made of insulating materials or by ‘sandwiching’ the insula-

tion material between two layers of concrete [7,8]. The use of these

innovative and sustainable technologies improve the overall ther-

mal resistance of the building and allow the construction of the

walls. Furthermore, similar techniques are also utilised for realis-

ing RC floors in which the bricks are made of insulating materials

(such as expanded polystyrene (EPS)) that do not contribute to

the plane stiffness of the floor. In fact the maximum elastic modu-

lus of the usual bricks is bit lower than the one of concrete, i.e.

about 25,000 MPa, while the modulus along the orthogonal direc-

tion is about the half of the maximum one. Conversely, the EPS

bricks have a negligible elastic modulus with respect to concreteand, thus, the plane stiffness of the floor can be assumed as the

same of the solid concrete slab.

In this paper, firstly the characteristics of large lightly rein-

forced walls are surveyed to emphasise their differences from the

so-called ‘ductile walls’ in terms of mechanical behaviour and

requirements furnished by both Italian   [9]  and European codes

[10]   for seismic design. In particular, ductile walls require more

expensive reinforcement percentages and construction details.

The technical literature has been then examined in order to

highlight the behaviour of RC buildings made with large lightly

reinforced walls under seismic actions [3,11,12].

The nonlinear behaviour of two large lightly reinforced walls

experimentally tested has been also assessed by means of two

numerical Finite Element (FE) models developed by using theSAP2000  [13]  and DIANA 9.4  [14]  software. These analyses were

aimed to set constitutive relationships of materials, type of finite

elements and smeared cracking model to be introduced in the FE

model in order to achieve the best fitting with some experimental

results. In particular, two smeared cracking (fixed or rotating)

models have been considered and the parameter   b   defined as

‘‘shear retention factor’’ in the fixed cracked model has been varied

to examine its effect on the nonlinear behaviour of the wall.

Finally, a case study representing a RC building with lightly

reinforced walls along the perimeter has been addressed in a FE

model by adopting the same approach used in the numerical anal-

yses carried out on the single walls. Some features have been

investigated for this type of building that are still lack in the tech-

nical literature. Linear dynamic analysis have been developed inorder to define the influence of the in-plane stiffness of the floor,

that is usually assumed rigid without any verification, on the

dynamic behaviour of the whole structure. To this aim also a com-

parison with a traditional framed RC building has been carried out.

The influence of the floor stiffness is analysed both in terms of 

dynamic behaviour (vibration period and participating mass) and

shear force distribution among the walls and the columns. Such

an effect is examined also in order to evaluate the role of innova-

tive light floor systems, which cannot be considered as rigid in

their plane, in RC buildings made with large lightly walls.

Furthermore, nonlinear static analysis has been also attended in

order to evaluate for the case study the contribution of ductility

and over-strength to the behaviour factor,   q, i.e. to the seismic

performances.

2. Lightly reinforced walls

 2.1. Code indications for design

Large lightly reinforced walls are defined by Eurocode 8   [10]

based on various geometric requirements and on their dynamic

behaviour, as follows:

‘‘A wall system shall be classified as large lightly reinforced

walls system, if, in the horizontal direction of interest, it com-

prises at least two walls with a horizontal dimension of not less

than 4.0 m or 2/3hw, whichever is less, which collectively sup-

port at least 20% of the total gravity load from above in the seis-

mic design situation, and has a fundamental period   T 1, for

assumed fixity at the base against rotation, less than or equal

to 0.5 s. It is sufficient to have only one wall meeting the above

conditions in one of the two directions, provided that: (a) the

basic value of the behaviour factor,   q0, in that direction is

divided by a factor of 1.5 over the value given in  Table 5.1

and (b) that there are at least two walls meeting the above con-

ditions in the orthogonal direction’’.

In addition, a note in the same code clarifies that, for this type of 

wall, the seismic energy is transformed into potential energy

(through a temporary lifting of the structural mass) and that this

energy is dissipated through the rocking of the walls.

For these walls, the formation and rotation of plastic hinges donot occur due to their large dimensions and to the absence of a

Nomenclature

 Ac    effective area of concrete in tension A g  f 

0

c    compressive strength of the concrete section f 1   tensile stress f cm   compressive strength of the concrete f cd   design compressive strength of the concrete

 f  y   yielding strength of the steel f cr    tensile strength of the concreteF  y   yielding strength of the SDOF systemG   shear stiffness of the concretehw   total height of the wallH    height of the structureK    stiffness of the systemK C    stiffness of the columnsk stiffness of the SDOF systemLwi   length of the ith wallm mass of the SDOF systemPGA peak ground accelerationq   behaviour factorRl   ductility factor of the structureRs   over-strength factor of the structure

Rn   redundancy factor of the structureS    stiffness of the columnsS ref    reference stiffness of the columnsT 1   fundamental period of vibrationT  the period of vibration of the SDOF system

T C    the start period of the spectrum with constant velocityV    shear at the base of the buildingV  shear at the base of the SDOF systemV col   total shear of the columnsV wall   total shear of the wallsq1   wall area/floor area ratiob   reduction factor of shear stiffness Gc   shear strainC   participating factord   displacement at the top of the buildingd displacement at the top of the SDOF systeme1   tensile strains   shear stressqs   reinforcement percentage

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connectioneither at their base or with other large transverse walls;

therefore, they cannot be designed for dissipating energy by means

of plastic hinges at their base.

The EC8, and also the Italian code [9], provides the same behav-

ioural requirement (q0 = 3) associated with uncoupled wall sys-

tems having a medium ductility class (MDC). However, it should

be noted that the behaviour factor q0 must be corrected by a factor

kw  in order to have the real behaviour factor (

q =

kw 

 q0), as

follows:

kw ¼1:00  for frame and frame  equiv alent dual systems

0:5 6 ð1 þ a0Þ=3 6 1  for wall;   wall  equiv alent 

and torsionally flexible systems

8><>: ð1Þ

a0 ¼X

hwi

Xlwi

.  ð2Þ

where a0   is the more common value of the height-to-length ratio,

hwi/lwi, within the walls of the examined structural systems.

With regard to the hierarchy of resistance, both the Italian and

the European codes provide for the amplification of the shear in

order to ensure that flexural yielding occurs before shear failure.

Particularly, the shear force derived from the analysis should be

increased by the factor (q + 1)/2; furthermore, if  q > 2, the dynamic

component of the axial force acting on the wall may be taken into

account by varying of ±50% the axial force due to the gravity loads

present under the design seismic load condition; the sign has to be

individuated considering the most unfavourable situation.

As for the construction details, EC8 provides the following spe-

cific requirements for steel reinforcement:

– if the acting shear is lower than the shear strength of the section

without shear reinforcement, the minimum shear reinforce-

ment ratio in the web is not required; if this condition is not sat-

isfied, the shear reinforcement must be calculated by a variable

inclination truss model or a strut-and-tie model;– the anchorage length of the clamping bars connecting the hor-

izontal zones should be increased;

– the vertical bars, calculated for the flexural strength, should be

concentrated at the ends; moreover, in these boundary zones,

the longitudinal reinforcement has to be engaged by a hoop

or a cross-tie with a diameter not lower than 6 mm or than

1/3 of the vertical bar diameter,  dbL, and with a vertical spacing

not larger than 100 mm or 8dbL. In addition, the diameter of the

vertical bars should be not lower than 12 mm at the first floor

and not lower than 10 mm for the upper stories;

– the vertical reinforcement should not exceed the amount calcu-

lated for the flexural strength;

– continuous steel bars, both horizontal and vertical, should be

provided: (a) along all of the intersections between walls andat the web-flange connections of each wall, (b) at each floor

level, and (c) around the openings in the walls.

Conversely, the Italian code [9] does not provide any steel rein-

forcement requirements for this type of walls. Moreover, the code

seems to not distinguish the lightly reinforced walls from the duc-

tile ones, but it only suggests that the requirements provided for

seismic actions may not be applied. This means that the boundary

zones may not be strengthened with the same reinforcement

detailing usually adopted for RC columns in order to have an effec-

tive confinement of concrete along the critical height of the wall.

Such a critical length depends not only on the length and the

height of the wall, but also on the number of floors of the building.

However, the same behaviour factor of ductile walls with MDCshould be adopted.

 2.2. The seismic performance of buildings with walls

The use of RC walls to achieve strength and stiffness in build-

ings threatened by seismic actions has been adopted in many

cases, with various solutions in terms of dimension and distribu-

tion of the walls. The resisting systems with large lightly reinforced

walls, sometimes coupled with RC frames to support vertical loads,

have been applied in numerous countries such as Kyrgyzstan, Can-

ada, Romania, Turkey, Colombia, USA and Chile [1]. In some cases

after an earthquake, low damage levels were observed with respect

to framed buildings; for example, some buildings were analysed

after the seismic event of 1985 in Chile [3,2].

A typical case noted in Managua (Nicaragua) in 1972 has been

described by Fintel [15]. Two RC buildings were built in the early

1960s using different structural systems: one building had 15

floors made with frames, and the other had 18 floors with a mixed

structure made with frames and walls. The same seismic action

resulted in very different behaviours of the two buildings. The

framed building, judging by the significant damage occurred in

the non-structural elements (partitions, infill walls, etc.), was sub-

 jected to a violent shaking. Conversely, the building with mixed

structure did not show clear signs of the seismic action; indeed,

the walls, which constituted the core of the building since they

were centrally disposed with respect to its plan, limited the defor-

mability of the whole building and, consequently, protected the

non-structural elements, particularly those more sensitive to high

inter-story drift. The limited structural damages were repaired

without carrying out any evacuation.

As above mentioned the damage reconnaissance after the earth-

quake in Chile in 1985 (WHE reports from Chile, i.e. Moroni   [1])

evidenced a good performance of the buildings made with RC walls

under a strong earthquake (M s  = 7.8). In   [16]   the demand and

capacity of such type of buildings with refer to some Chilean real

cases are compared confirming the good performances observed

during the seismic event. The author evidences the existence of 

various parameters that play an important role in the seismic

response of buildings with RC walls according to their stiffnessand mass distribution in plan and elevation, but the fundamental

parameter results the wall density, defined in each direction as

the ratio of the area of the walls to the floor area. In particular,

the displacement demand, studied trough spectral analysis

referred to the site of Viña del Mar, is not much variable when

the wall density varies in the range 2–4%; in fact, a wall density

lower than 2% gives a significant increment of the displacement

demand, while a wall density greater than 4% does not allow a rel-

evant reduction. In particular, the displacement demand of the

Chilean buildings during the earthquake of 1985, expressed as

the drift of the whole construction, was of about 1% and moderate

damages were observed for such buildings. Furthermore, a large

number of the analysed buildings was not equipped with rein-

forcement details because they were designed according to theGerman rules of 1950 for non-seismic buildings. Only in some

cases the walls of the buildings were characterised by a longitudi-

nal reinforcement greater than in the case of non-seismic construc-

tions; this improved the flexural strength, but however the walls

lacked the transversal reinforcement necessary for improving the

concrete confinement.

The experimental studies on walls subjected to cyclic horizontal

forces up to failure, carried out also before the Chilean earthquake

and collected in [16], confirmed that the displacement capacity of 

the tested walls, measured as drift, is high also when there is no

confinement at the boundary of the walls.

More recently, other researchers   [17] have observed the good

performance of buildings with RC walls under seismic actions

and identified the ‘wall density’ as an efficient parameter for build-ings not exceeding fifteen floors. Furthermore, the studies show

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that for many of these buildings, the collapse condition is caused

by the shear failure of the walls; in fact, the authors observe that

in many cases the shear reinforcement is lacking and does not

allow for flexural failure occurs before shear failure under seismic

actions. Only a few codes  [10,18]   consider the amplification of 

shear through a specific factor in order to institute a strength

hierarchy.

Another parameter used to control the behaviour under seismic

actions of building with RC walls is the shear index, that, defined as

the ratio of the total weight of the building to the area of the walls

in each direction [19], represents the average compression stress in

the walls. A satisfactory behaviour of the buildings was observed

for values of this index less than 5 MPa. The importance of this

parameter and the beneficial effect of the confinement at the

boundaries of the walls were confirmed again after the Chilean

earthquake in 2010. In fact, the good performances of the wall

buildings during the earthquake in 1985 encouraged to not realise

the details for the confinement and increase the floors number, i.e.

the compressive stress in the walls, for the new structures built

after 1985 and before 2010, causing the bad performances of these

buildings, as widely discussed in Massone et al. [11], Wallace et al.

[12], and Telleen et al. [20]. In particular, the number of stories was

increased from about 15 to 25 without enlarging the wall density;

this led to enhance the level of the compression stresses to 10–30%

of the concrete strength [11].

During the Chilean earthquake in 2010, the most common phe-

nomenon was buckling of the longitudinal bars (especially those at

the ends of the walls) due to the large spacing of transversal rein-

forcements and the high value of stress in the concrete combined

with large compression–tension cycles. Another type of phenome-

non that may occur was the whole o partial buckling of the wall

out of the plane when the height/thickness ratio of the wall was

too high.

Before 1985, building American codes did not provide height-

to-thickness limitations for concrete wall panels, then a height-

to-thickness ratio limitation of 25 was imposed on bearing walls,

and 30 for non-bearing walls (14.5.3 of ACI-318 [21]); furthermorethe effect of restraints and compression stresses has to be consid-

ered in the design.

Obviously the damage spread in the buildings depends on the

configuration of the construction; the most frequently observed

problems are due to the elements coupling the walls, the variation

of the wall sections in elevation and the shape of the wall sections.

Numerical studies on the behaviour of buildings with large

lightly reinforced walls were conducted by Fischinger et al.   [22].

The authors performed a series of nonlinear analyses aimed to

evaluate the effect of the design requirements given by EC8 and

to assess the inelastic response of such buildings. In conducting

these analyses, the authors developed a simple model for buildings

made with walls, keeping constant the area of the walls and

varying the Peak Ground Acceleration (PGA,   a g ,max  = 0.1, 0.2,0.3 g), the structural factor (q = 1.5, 2, 3, 4, 5, 6), the number of 

floors (n = 5, 10, 15), and the wall area/floor area ratio (q1 = 1%,

1.5%, 2%, 3%).

The authors observed that for levels of PGA equal to 0.1 g and

for high behaviour factors q, it is possible to introduce a reinforce-

ment ratio of 0.4%, in the boundary areas of the walls, for 5-story

buildings; furthermore, the buildings generally remain in the elas-

tic field. When the walls require more than the minimum rein-

forcement, the demand increases rapidly. The buildings subjected

to PGA greater than 0.1 g with a higher number of floors have

deformations in the plastic range, although with a limited inter-

story drift (<1%). Several walls have problems of local stress con-

centration and the authors argue that to solve this problem, it is

sufficient to increase the ratio of the wall area to the floor areato a value approaching 2%.

Many experimental results are now available for walls tested

under horizontal monotonic or cyclic loads. However, little infor-

mation is available on the global behaviour of buildings with walls

along the perimeters. Rezaifar et al.  [8] tested a full-scale building

constructed with RC ‘‘sandwich panels’’ consisting of one floor with

a 3.35 m square plan on a shaking table. The authors observed that

the development of cracking initially caused decreasing stiffness,

reducing the natural frequency of the vibration and, thus, increas-

ing the vibration period. Furthermore, the different distribution of 

cracks along two directions caused torsion modes that were con-

trasted by all four walls.

The authors also noted that the structural behaviour (with its

significant stiffness) was excellent for low or moderate earth-

quakes, while more construction details were required for strong

earthquakes characterised by high natural frequencies.

3. Numerical model of RC walls and comparisons with

experimental results

The authors have done some preliminary experimental–numerical

comparisons for RC walls available in the technical literature in

order to validate the reliability of the FE model implemented bytwo different software (SAP2000 and DIANA TNO). In particular,

the approach used in the FE model implemented in SAP2000 will

be used in the following also for carrying out the non-linear anal-

ysis of an entire building made with lightly reinforced walls under

seismic actions. Therefore, the walls selected fromthe technical lit-

erature for the comparisons with the FE model have low percent-

ages of reinforcement with negligible or without any details at

the ends, as in the case of the building. The efficiency of the consti-

tutive relationship assumed for the concrete in compression and in

tension is examined and the importance of the cracking model is

investigated by comparing different modelling approaches. The

effectiveness of the numerical model is appraised especially in

terms of maximum load, damage localisation, and post-elastic

deformability.

 3.1. The case study

Numerous results of experimental tests on RC walls [23–25] are

available in the technical literature, but, generally, they are

referred to specimens equipped of additional longitudinal and

transversal for confinement steel reinforcement at the ends of 

the cross section.

Conversely, there is little information about RC walls with a low

percentage of reinforcement uniformly distributed; among these,

the specimens tested by Orakcal et al.   [4]   and Gebreyohaness

et al. [26,27] were chosen for being simulated through a FE model.

In this section the primary characteristics and the experimental

results of the tested walls are examined, and the results arereported.

The specimens of Orakcal et al.   [4] were constructed in a 3:4

scale with refer to the walls of an actual building: the St. Jude Med-

ical Center in California [6]. The specimens have width of 152 mm,

length of 1370 mm, height of 1220 mm; the materials used in the

tests have properties similar to those used at the time of the build-

ing construction (approximately 30 MPa for the mean compressive

strength of concrete and 424 MPa for the yielding strength of the

steel bars). A single layer of reinforcement was used. The six tested

walls were divided into three different types, with two equal sam-

ples for each type. The three types differed in the value of the axial

force, which was 0%, 5% or 10% of the compressive strength of the

concrete section ( A g  f 0c ). The steel reinforcement was the same for

all samples and consisted of a longitudinal reinforcement with13 mm diameter bars spaced at 330 mm that were doubled at

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the ends of the elements; a transversal reinforcement with 13 mm

diameter bars spaced at 305 mm was also added (Fig. 1). The

resulting percentage of longitudinal reinforcement was 0.23%,

although the local percentage was slightly greater at the end of 

the element. No hooks were provided for the transversal

reinforcement.

The tests were conducted under displacement control by apply-

ing a constant axial load with two actuators that prevented the

rotation of the top of the model, and horizontal cyclic loads with

drift levels equal to 0.2%, 0.3%, 0.4%, 0.6%, 0.8%, 1.2%, 1.6%, 2.0%

and 2.4%. The experimental measures allowed for distinguishing

the shear from the flexural deformation, even if a negligible contri-

bution of the latter was observed; the primary cause of deforma-

tion was actually due to the sliding along the shear diagonal

cracks. The finale collapse was caused by the failure of the com-

pressed concrete in the central part of the inclined strut.

In [4] the influence of various parameters on the shear strength

of the walls was investigated through an analysis of several exper-

imental tests carried out by others researchers [28–30]. In particu-

lar, the investigated parameters were: the percentage of 

longitudinal steel reinforcement, the presence of one or two layers

of longitudinal reinforcement, the presence of 90   hooks at the

ends of the transversal steel reinforcement, the percentage of steel

reinforcement at the ends of the cross section and the level of nor-

mal stress. It was noted that the absence of hooks for the transver-

sal steel reinforcement at the end of the cross section did not affect

the shear strength, while the presence of axial stresses caused a

reduction in the lateral drift capacity of the wall.

In  [31]   new formulations for evaluating the residual vertical

resistant load in RC walls damaged by shear were analysed; these

formulations accounted for the resistant contributions to the verti-

cal normal load given by the sliding mechanisms developed along

the interfaces of the inclined shear cracks.

In   [26,27]   two wall specimens having length of 1300 mm,

height of 1750 mm, and width of 150 or 230 mm were experimen-

tally investigated. The concrete had a mean compressive strength

of approximately 20 MPa, and the steel bars had a yielding strengthof 515 MPa. A single layer of reinforcement was used. An axial

force representing 5% of the compressive strength of the concrete

section ( A g  f 0c ) was applied to each wall. The steel reinforcement

was the same for both specimens and consisted of longitudinal

and vertical bars with a diameter of 10 mm spaced at 305 mm.

The resulting percentage of longitudinal reinforcement was, thus,

0.20% for the first wall and 0.13% for the secondone. The tests were

conducted under displacement control, the constant axial load was

applied with pre-tensioned high strength bars, and the horizontal

cyclic loads reached drift levels of 3%. The authors observed that

the lacking of additional bars at the ends led to the critical failure;

in fact flexural cracks did not form but only a longitudinal crack at

the base opened allowed the rocking of the panel.

 3.2. The nonlinear numerical models

A nonlinear model of a RC wall was implemented through two

software programs: SAP2000 [13,32] and DIANA [14]. The general

approach is approximately the same for the two programs, though

DIANA allows assessing the cracking behaviour of bi-dimensional

elements under shear stresses by two types of smeared cracking

models.

The bi-dimensional element used for modelling the concrete in

both software is a four-node quadrilateral iso-parametric plane

stress element (in DIANA is named Q8MEM, in SAP2000 is individ-

uated as SHELL), i.e. it is a shell with a combination of membrane

and plate behaviour; this means that all forces and moments can

be supported and the thick-plate (Mindlin/Reissner) formulation

is used including the effect of transverse shear deformation.

Conversely, the approach to model the steel reinforcement is

different from that used for concrete, but is similar for the two soft-ware. A membrane element stiff only in its plane is used (in DIANA

is named CQ16M, in SAP2000 is individuated as Membrane); this

means that only the in-plane forces and the normal (drilling)

moment can be supported. Such a membrane element is embedded

in other structural elements (so-called mother elements) and, thus,

it has not any degrees of freedom of their own. The perfect bond is

assumed between steel and concrete and the tension stiffening

behaviour is introduced by the cracking model and the constitutive

relationship of the concrete in tension.

The membrane has to be set with an equivalent thickness in

order to simulate the same area of the bars and give the same stiff-

ness in a fixed direction; thus, two different membranes have to be

introduced for the longitudinal and transversal reinforcement,

since they can have different area.A multi-axial nonlinear behaviour was assumed for the con-

crete, and a mono-axial nonlinear behaviour was assumed for the

steel reinforcement. The constitutive relationship of the concrete

in tension takes the cracking phenomena into account through a

smeared cracking approach; the tension stiffening after cracking

is addressed through the softening branch according to the model

of Vecchio and Collins [33] reviewed by Bentz [34]. Therefore, the

first branch of the r–e  relationship in tension is linear up to the

strength, f t , and is followed by a nonlinear softening characterised

with the following relationship:

 f 1 ¼   f t 

1 þ  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3:6  M   e1

p    with  M  ¼   AC 

P dbp  ð3Þ

being  db  the diameter of the bars and  Ac  the effective area of con-

crete in tension; this last value is assumed as a circular area with

a diameter of 6db, as studied by a FE model in  [35]. Such a value

is not very different from the well-known value of 7.5db   suggested

in Model Code 78 [36].

The tensile strength, f t , is evaluated by means of the formulation

of Vecchio and Collins [33].

Also in compression a nonlinear behaviour with a softening

branch after the strength was assumed. In particular, the constitu-

tive relationship of the concrete in compression suggested by Mander

et al. [37] was adopted; such a model allows to consider also the

effect of confinement due to the stirrups, albeit in the analysis pre-

sented herein this effect was not introduced, but was utilised in

[32].   The constitutive relationships adopted in compression andtension for the concrete are graphed in Fig. 2.

330   3        0        5

        1        5        2

        1        2        2        0

        1        5        2

1370

64 330

Ø13/305mm

Ø13/330mm

Fig. 1.  Steel reinforcement in the wall WP-T5-N10-S2  [4] (measures in mm).

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Further information must be offered concerning the cracking

behaviour. SAP2000 adopts a smeared cracking approach in which

a  s–c   curve is generated by considering rotating smooth cracks,

while DIANA allows for the use of both ‘‘rotating smeared cracking ’’

and ‘‘ fixed smeared cracking ’’. The two methods can be syntheticallydefined as follows:

(1) In the ‘rotating smeared cracking ’ approach, the concrete has

an elastic behaviour up to the point of cracking, i.e., up to

attaining its tensile strength,   f t . After this point, the cracks

assume an inclination angle perpendicular to the direction

of the principal tensile stresses and vary with them.

(2) In the ‘ fixed smeared cracking ’ approach, the concrete has an

elastic behaviour until the point of cracking, but the nonlin-

ear behaviour is governed by the shear stiffness  G   reduced

by the factor   b, which is smaller than 1. In this approach,

the cracks have a constant inclination angle that is perpen-

dicular to the direction of the principal tensile stresses when

cracking begins.

The actual behaviour of reinforced concrete during the cracking

development is influenced by both the interface shear stresses

along the cracks and the dowel effect; both phenomena control

the deviation between the principal directions of stress and strain.

Such a deviation increases the damage and the energy dissipation

in the element. This means that, when the fixed smeared cracking

approach is adopted, the influence of the interface behaviour is fic-

titiously introduced in the model by a reduced shear stiffness of 

the elements.

The value of the factor  b  was assessed using the experimental

results of the diagonal tests on RC panels described below.

 3.3. Calibration of the parameter  b

The authors conducted two diagonal tests on RC panels to cali-

brate the shear deformability in the DIANA model after cracking in

the fixed smeared cracking approach. In fact, nevertheless the

value of the retention factor, b, has been suggested in the literature

for quite some time as 0.20–0.25 [38,39], the authors decided to

assess again this parameter by carrying out suitable experimental

tests on RC panels with a low percentage of reinforcement. Such

a reinforcement percentage is similar to the value currently used

for lightly reinforced walls and the experimental tests were aimed

to check the influence of the reinforcement percentage on the

shear stresses along the cracks interfaces.

The two tested specimens were equal; they had dimensions of 

900 mm 900 mmwith a thickness of 150 mm. The reinforcementwas realised by ordinary steel bars with a diameter of 10 mm

spaced of 200 mm in both directions. The average strength in com-

pression of concrete, obtained by three tests on cubes with side of 

150 mm, was 36 MPa. The average yielding and ultimate strength

of the steel bars, obtained by three tensile tests, was 467 MPa

and 551 MPa, respectively.

The load was applied by a servo-hydraulic universal machine

(maximum load 3000 kN) with a speed of 0.015 mm/min and mea-

sured by a load cell. Two inductive displacement transducers

(LVDT) were placed on each side of the panel with a 400 mm gauge

along the two diagonals corresponding to the direction in compres-

sion (vertical direction V ) and in tension (horizontal direction  H ).

The testing set-up is shown in Fig. 3a and a picture of the panel

after the test is shown in  Fig. 3b.

The load–displacement curves (F –d) measured by the four

LVDTs are reported in Fig. 4a for both the specimens.

The relationship between the shear stress and the shear defor-

mation (s–c) is graphed in Fig. 4b. In particular, the shear stress is

calculated as

s ¼ 0:707  F 

 An

ð4Þ

where s  is the shear stress; F  the applied load; and An  is the net area

of the specimen, calculated as follows:

 An ¼   w þ h

2

 t    ð5Þ

where w,  h  and  t  are the width, height and thickness of the speci-

men, respectively.

The shear strain is calculated as:

c ¼ DV  þDH 

 g   ð6Þ

where c  is the shear strain; DV  the vertical shortening; DH  the hor-

izontal elongation; and  g  is the gauge length of DV  and DH .

The experimental results are quite the same for the two speci-

mens. Fig. 4b shows that the behaviour is linear up to a stress value

of a 3.5 MPa, and then becomes nonlinear up to approximately

6.1 MPa.

The model of the panel has been implemented in DIANA accord-

ing to the features previously introduced by considering both the

‘rotating smeared cracking ’ and the ‘ fixed smeared cracking ’

approaches; in the latter case,   b  was varied in the range 0.005–

0.1. Such range was chosen to refine the assessment of  b, because

the numerical results evidenced that for   b   greater than 0.1 the

strength of the panel was excessively overestimated, while values

lower than 0.01 corresponded to a smooth crack. Finally, in  Fig. 5the results in terms of  sc   curves obtained for three values of  b

(0.005, 0.01, and 0.1) in the case of fixed smeared cracking model

were graphed. In the same figure also the results obtained from

the rotating smeared cracking model are reported. The constraint

conditions were simulated by introducing also the bi-dimensional

model of the steel shoes used in the test.

The comparison in Fig. 5 highlights a good fitting of the models

with the experimental curves, but also confirms the role of the

parameter   b, which allows a better agreement after the shear

cracking in the fixed smeared cracking approach. Similar numerical

curves have been obtained in the case of rotating smeared

approach or for the fixed one when   b   is 0.1. If   b   increases, the

strength and deformation at the end of the elastic field also

increases. The fitting with the experimental curve, especially interms of strength, is more efficient for  b  = 0.01 and b  = 0.005.

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

-0.004 -0.002 0 0.002 0.004 0.006

[MPa]

[/]

Fig. 2.  Constitutive laws in tension and compression for concrete.

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 3.4. Numerical–experimental comparison of the shear tests

The FE models implemented in SAP2000 and DIANA were also

applied to the wall WP-T5-N10-S2 tested by Orakcal et al.   [4]

and to the wall WPS1 tested by Gebreyohaness et al.   [26,27].

For the two models, the thickness of the three layers (one made

of concrete and two of steel reinforcement, one for each direction)

is defined as follows:

– the concrete layer has a thickness equal to the total thickness of the section without subtracting the steel thickness;

– the thickness of the layer simulating the longitudinal reinforce-

ment was calculated by dividing the reinforcement area by the

reinforced length of the panel, with value of 0.35 mm and

0.30 mm for the two tests, respectively. For the panel tested

by Orakcal et al. [4] at the ends of the cross section the thickness

is 2.47 mm due to the increment of the reinforcement steel, and

is evaluated according to the same procedure for a length of 

229 mm;

– the thickness of the layer made of transversal reinforcement is

0.44 mm and 0.25 mm for the two tests, respectively.

The mechanical properties indicated by the authors were

assumed in the model: the average compressive strength of theconcrete was f cm = 31.4 MPa, and the yielding strength of the steel

was f  y = 424 MPa for the panel from Orakcal et al. [4]. Analogously,

 f cm   was 19.4 MPa and   f  y   was 500 MPa for the panel from

Gebreyohaness et al.   [26,27]. For the steel reinforcement, an elas-

tic–plastic law up to failure with an ultimate strain of   eu = 12%

was assumed, lacking more detailed information. However, sensi-

tivity analyses evidenced that the numerical results are little

affected by a moderate hardening of the steel bars.

The comparison between the numerical and experimental

results for the wall tested by Orakcal et al. [4] is shown in Fig. 6a

in terms of the force–displacement relationship. The numerical

curves refer to the both FE models developed in SAP2000 and

DIANA; in particular, for the DIANA model both the rotating and

fixed smeared cracking approaches have been used and variousvalues for the factor  b   (0.005, 0.01, 0.1) have been considered in

     4     0     0    m    m

400mm

F

Fixed fundation

Steel block

Steel block

lvdt2

lvdt1

(a)   (b)

Fig. 3.   (a) Setup of diagonal tension test on a RC wall and (b) the specimen after the test.

Fig. 4.  Results of the diagonal tests on RC walls: (a) experimental curves  F –d  and (b) experimental curves  s–c.

β=0.1

0

1.5

3

4.5

6

7.5

0 0.00035 0.0007 0.00105 0.0014

γ  [/]

τ [MPa]   rotating

β=0.005β=0.01

experimental

Fig. 5.  Theoretical and experimental comparison of the diagonal test.

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the latter one. The curves in  Fig. 6a show that the all numerical

models of DIANA are stiffer than the experimental behaviour in

the linear field, while the model of SAP2000 is more in agreement

in that field since it shows a better simulation of the cracking

before steel yielding. The difference between the initial stiffness

of the numerical curves given by the DIANA and SAP2000 models

is due to the different modelling strategy of the shear behaviour,

which governs the behaviour of the panel. The SAP2000 approach

assumes, indeed, a shear–strain relation that after cracking is more

deformable than the one assumed by DIANA.

In the post-elastic field, the best agreement with the experimen-

tal results was achieved by the ‘ fixed smeared cracking ’ approach with

b = 0.005, as already demonstrated by the previous calibration of  b;

when the b  value increases significantly (i.e., b = 0.1), the numerical

results wander from the experimental result.

By the contrast, the ‘rotating smeared cracking ’ approach fur-

nishes results similar to the ‘ fixed smeared cracking ’ with   b = 0.1

in the first branch, but then diverges and tends to the results

obtained by adopting lower values of  b  (0.01 and 0.005).Finally, the model developed in SAP2000 appears to be less effi-

cient into predicting the steel yielding load since the numerical

value is much greater than the experimental one; by contrast,

the model is able to simulate the post-peak softening behaviour

that the DIANA models do not show.

The distribution of the principal tensile stress at the maximum

load is reported in Fig. 6b; the maximum values are attained at the

central zone of the panel (at the ends more reinforcement is pres-

ent) due to shear; this result is in good agreement with the failure

mode observed during the experimental test characterised by

‘‘diagonal cracking ,   followed by widening of cracks and sliding along 

the diagonal cracks’’.

The comparison between the numerical and experimental

results for the wall tested by Gebreyohaness et al. [26,27] is shownin   Fig. 7   in terms of the force–displacement relationship. The

numerical curves refer to the same DIANA and SAP2000 models

considered in the previous comparisons. The curves in Fig. 7a show

that all the numerical models are stiffer than the experimental

behaviour in the linear field; for such a panel both software give

the same trend since the flexural behaviour, not the shear one, gov-

erns the failure. Anyway, the difference between the numerical and

the experimental results could be due to a deformability of the base

restraint device, since the stiffness of the numerical models corre-

sponds exactly to the theoretical elastic one of an un-cracked wall.

Probably, the introduction of the base deformability could improve

the agreement between the experimental and numerical curves.

Moreover, all the numerical curves overestimate the steel yield-

ing load by approximately 20%, but in the post-elastic field, thebest agreement with the experimental results was achieved by

the model of SAP2000. About the DIANA model, both the ‘ fixed’

and the ‘rotating ’ smeared cracking approach furnished results

similar to the SAP2000 up to the yielding load, while they overes-

timated the experimental behaviour in the post-elastic branch.

It is worth to note that the experimental behaviour shows a low

ductility since the capacity loss is higher than the 15% when a

small plastic deformation has been exploited.

In Fig. 7b the stress distribution in the vertical steel is depicted

pointing out the steel strength (300 MPa was assumed in the

model) is reached and concentrated at the base, in good agreement

with the experimental failure mode that showed a crack extended

along the entire length (the experimental test is a cyclic test) with

the rupture of the steel bars .

The experimental behaviour highlighted the mechanism of 

rocking after the rupture of steel at the base was able to retaining

strength but with poor energy dissipation.

In conclusion, the numerical results given by the FE model

developed in SAP2000 give a reliable fitting with the experimental

behaviour for both the simulated panels in terms of global behav-iour (strength and ductility), post-elastic trend of the load–

displacement relationship and failure mode.

4. Numerical analysis of buildings

4.1. The case study

In the following, a RC building equipped with large lightly rein-

forced walls placed along the perimeter and with internal frames is

analysed. The building has a rectangular plant with dimensions of 

20 m 30 m and has 3 floors each with height of 3 m. The struc-

ture consists of a perimeter RC wall having thickness of 150 mm

and of RC columns having square section with dimensions

300 mm 300 mmat all levels and spaced of 5 m in both direction x  and y. The perimeter walls have openings that form panels with

dimensions of 1.0 m and 2.0 m in both directions. The structure

was designed considering the elastic spectral PGA of 0.35 g acting

at the base (such a value refers to a high seismic hazard site in

Italy), following the indications provided by EC8 [10] for buildings

with walls, since the columns bear a negligible role under seismic

actions. Due to the use of large lightly reinforced walls, a medium

ductility class and a design behaviour factor   q = 1.50 were

assumed; the shape factor of the walls (kw) was calculated with

reference to the dimensions of the perimeter walls without open-

ings. However, the longitudinal reinforcement of the walls was

determined without ductility details; the steel bars are uniformly

distributed and have a diameter of 10 mm.

Another RC building made entirely of RC frames was designedwith the same dimensions in plan of the first one and to experience

Fig. 6.   Panel tested by Orakcal et al. [4]: (a) theoretical and experimental comparison of the load–displacement curves and (b) principal tensile stress distribution in concrete

at the maximum load from SAP2000 in MPa.

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the same seismic actions. Also for the frame building the design

was carried out assuming a medium ductility class with a behav-

iour factor q  = 3.12. The dimensions of beam and column sections

resulted clearly larger than those designed for the building with

walls; for all of the beams and columns, the constructive details

provided by the building codes for design in seismic areas were

considered.   Table 1   reports the relevant information concerning

the dimensions and reinforcement percentages of the columns

(with refer to the total steel reinforcement) and beams (with refer

to the only steel reinforcement in tension).

For both buildings, the class of concrete is C25/30 ( f ck = 25MPa)

and the reinforcing steel is B450C ( f  yk  = 450 MPa, ultimate strain

eu = 7.5%). In Fig. 8 the schemes of the two buildings implemented

in the software SAP2000 [13] are shown.

4.2. Linear dynamic behaviour 

The dynamic behaviour of the two RC buildings was analysed in

terms of:

– vibration modes;

– periods;

– participant masses.

Different cases of in-plane stiffness of the floor were considered

for the RC wall building; in particular, the floor was modelled by an

equivalent shell, so that by changing the thickness of such a shell

different values of the in-plane stiffness can be achieved and sev-

eral cases, varying from the case of deformable floor to the rigid

one, have been simulated.

Two types of light elements for a RC floor have been considered:

(1) bricks with an equivalent thickness of 200 mm and with an

elastic modulus a bit lower than concrete and (2) panels made of 

expanded polystyrene (EPS) having an equivalent thickness

40 mm as the solid concrete slab.

The behaviour of the RC frame and walls buildings are com-

pared for the case of a rigid floor made of reinforced concrete

and EPS; Table 2  shows the numerical results in terms of funda-

mental periods of vibration and participant masses obtained by

the FE model developed in the software SAP2000 [13].

The participant masses associated to the first mode exceed 85%

only for the wall building along both directions, while nine modes

are necessary to reach the same result for the framed building.

Therefore, the wall building appears to be slightly more regular.

Since both buildings are regular structures, the first period of 

vibration can be also assessed by using the approximate formula-

tions suggested by Eurocode 8 [10]:

Frame building:

T 1 ¼ C 1  H 3=4 ð7Þ

Walls building:

T 1 ¼ C t   H 3=4 C t  ¼  0:075= ffiffiffiffiffi Ac 

p 

 Ac  ¼ R ½ Ai  ð0:2 þ ðlwi=H ÞÞ2 ð8Þ

where  C 1  for RC structures is equal to 0.075,  Ac   the total effective

area of shear walls on the first floor of the building, Ai  the effective

area of the ith shear wall on the first floor of the building, H the total

height of the building measured from the foundation or from the

rigid basement, and lwi  is the length of the ith wall shear on the first

floor in the direction parallel to the applied forces, with the limita-

tion that lwi/H  must be less than 0.9. Note that in the calculation of 

the areas, the openings have been excluded and  lwi  was calculated

for the entire wall with the openings.

Fig. 7.   Panel tested by Gebreyohaness et al. [26]: (a) theoretical and experimental comparison of the load–displacement curves and (b) stress distribution in the vertical steel

membrane at the ultimate condition from SAP2000 in MPa.

 Table 1

Dimensions and reinforcement percentage of the elements.

Wall building Framed building

Columns L    L  (mm mm)   qs  (%) Columns L    L  (mm mm)   qs  (%)

I floor 300 300 1.40 300 400 2.24

II floor 300 300 1.40 300 350 2.24

III floor 300 300 1.40 300 300 2.01

Beams  B   H  (mm mm)   qs  (%) Beams B   H  (mm mm)   qs  (%)

I floor in x   300 250 1.26 400 250 0.75

I floor in y   500 250 0.75 500 250–400 250 0.94–0.75

II floor in x   300 250 0.69–1.26 350 250 1.07

II floor in y   400 250 0.52–0.94 400 250–350 250 0.75–1.07

III floor in  x   300 200 1.57 350 200 1.35

III floor in  y   500 200 0.94 450 200–350 200 1.05–1.35

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The fundamental period result in:

– Frame building:  T 1 = 0.39 s.

– Walls building: T 1x = 0.127 s in the x   direction and T 1y = 0.152 s

in the y   direction.

In comparison with the results of the numerical dynamic anal-

ysis, the period given by the simple code formulation is lower forthe frame building (about 40% lower) and higher for the wall build-

ing (approximately 100% higher); in the latter case, it is interesting

to note that the vibration period assumes a very low value, usually

not considered for RC buildings.

In addition, the RC wall building was also modelled as a canti-

lever (with flexural and shear deformability) with hollow sections

neglecting both the presence of the columns and of the openings

due to doors and windows distributed along the perimeter; the

masses were applied as concentrated at the level of each floor.

The dynamic analysis of this cantilever furnished a period of 

T 1 x  = 0.058 s and   T 1 y  = 0.071 s for the   x   and  y   directions, respec-

tively. It can be observed that the periods of the building provided

by the detailed FE model (T 1 x = 0.064 s and T 1 y = 0.079 s) are prac-

tically coincident with those of the cantilever in both directions.About the discrepancy between the periods given by the FE

model and the simplified Eq.  (7), it is worth to note that the code

formulations refer to buildings having RC frames or walls as seis-

mic resisting elements and disposed everywhere in the building

plan. In the case of walls, the factor C t  is reduced respect to the fac-

tor C 1  used for frame structures since the effect of the shear stiff-

ness of the walls is introduced through the area of the wall

section extended along the direction of the seismic action; the

effect of this stiffness reduces when the slender ratio (H /lw) of 

the walls increases.

When the model of a cantilever is used for simulating the wall

buildings, the increment of the flexural and shear stiffness of the

entire hollow section respect to the walls, considered separately

in each one direction, is taken in account, providing a period closerto the effective one.

In conclusion, the period of a RC building with walls extended

only along the perimeter could be reliably estimated by modelling

a simple cantilever having a hollow section, without openings and

having the same mass of the building at each floor, if the hypoth-

esis of rigid floor is true and the stiffness of the frames is negligible

respect to the one of the cantilever.

The effect of the floor stiffness in the RC wall building is exam-

ined in Table 3 by considering more cases: (1) infinitely deform-

able floor whit the masses applied where they are supported by

the beams and slabs, (2) deformable floor with variable stiffness,

obtained as variation of the shell thickness; in this case, the masses

and stiffness are evaluated for a RC slab with bricks and (3) rigid

floor. The values of the period decrease as the floor stiffness

increases; however, the stiffness of the floor 24 cm thick is insuffi-

cient to reach a regular behaviour in the  X  direction because the

percentage of participant masses of the first mode is only 30%.

Moreover, the different behaviour exploited in the   X   and   Y 

direction confirms the well-known concept that the floor stiffness

is not an absolute concept, but it might be estimated by comparingwith the lateral stiffness of the building   [40,41]. For the case at

hand, in the X  direction the slab stiffness (considered as a flat beam

in its plane) is too low (the slab is, indeed, long) with respect to the

lateral stiffness of the two shorter walls (those placed along

the short side of the building). This means that the hypothesis of 

the rigid floor for this type of building could provide a significant

error into assess the dynamic behaviour of the structure.

Such an analysis of the effect of the in-plane stiffness of the slab

has been carried out because of the widespread technology of real-

ising RC floors lightened by EPS panels in substitution of the tradi-

tional bricks. In this technology the role of the bricks for the

definition of the in-plane stiffness is, thus, completely neglected.

In order to define more accurately the role of the in-plane floor

stiffness for RC wall buildings, the ratio of the horizontal displace-ment at the end point of the slab to that at the centre (d1/d2) along

the direction  Y  (the floor is the longer flat beam in the plane) is

examined; it is clear that this ratio is equal to 1 when the floor is

rigid.

In Fig. 9, the variation of such a ratio is graphed at each floor

versus the variation of the slab thickness (i.e., the stiffness of the

floor), but without varying the weight of the floor. It can be

observed that the ratio d1/d2, for the same slab thickness, increases

with the position of the floor along the height of the building. As

the level of the floor is higher, the translational stiffness of the wall

reduces and, thus, the relative in-plane stiffness of the slab

increases, making its constraint effect more efficient. Furthermore,

for a thickness of 4 cm (i.e., a RC floor with EPS panels) the ratio

d1/d2 is approximately 0.4–0.5, which is very far from representinga rigid behaviour.

Fig. 8.  3D Models of (a) the wall building and (b) the framed building.

 Table 2

Dynamic parameters for the wall and the framed buildings with rigid floor in RC with

EPS.

Framed building Wall building

Fundamental period dir. X  (s) 0.624 0.064

Participant masses dir. X  (%) 81 89

Fundamental period dir. Y  (s) 0.597 0.079

Participant masses dir. Y  (%) 80 86

Total mass (kg) 1,326,100 1,394,875

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Finally, the effect of the floor stiffness is examined also in terms

of the shear distribution between the walls and the columns.

Fig. 10 shows the ratio between the total shear acting on the col-

umns, V col, and on the walls,  V wall, by varying the thickness of the

floor; the thickness zero represents the limit condition of infinite

deformability of the floor. It can be observed that only in the ideal

case of infinite deformability of the floor, the columns participate

in the bearing capacity of the building under seismic actions. Avery small thickness of the floor (1 cm) is, indeed, sufficient to

make the shear acting on the columns negligible (less than 5%)

with respect to that of the walls. This result is due to the very dif-

ferent translational stiffness of the two types of vertical resisting

elements (walls and frames).

Therefore, a very deformable floor canbehave very stiffly for the

frames and distribute the shear between the frames and the walls

as a rigid floor. Furthermore, only two symmetrical walls are avail-

able in each direction so that the shear distribution between them

does not depend on the stiffness of the floor. For this type of build-

ing, the hypothesis of a rigid floor creates reliable results in terms

of stresses in the structural elements, albeit the thickness of the

floor that induces a different dynamic behaviour.

To confirm the validity of this result, a parametric analysis was

developed to analyse the effect of the stiffness of the columns (i.e.

of the frames). In Fig. 11, the ratio of the total shear of all the col-

umns to the total shear of the walls is reported versus the stiffness

of the columns along the direction  Y  amplified by various factors

(5, 16, 50).

It is worth noting that the rate of shear acting on the columns

increases as their stiffness is enhanced; in particular, the rate of 

shear in the columns at the 1st floor varies from 0.9% for columns

with section 300 mm 300 mm to 11% for columns with section

800 mm 800 mm, that is the 0.6% of the entire shear. However,

the maximum percentage of shear spread over the columns occursat the 3rd floor (4–18%) since the translational stiffness of the

walls, as already discussed, reduces along the height due to the

cantilever behaviour.

4.3. Nonlinear static analysis

For the wall building designed in the previous section, a non-

linear static analysis was performed using the same modelling

approach implemented in the SAP2000 software for simulating

the behaviour of the panels experimentally tested and described

in Section  3. The RC walls were modelled by a multi-layer sec-

tion made of three perfectly bonded layers representing the

concrete and the longitudinal and transversal steel reinforce-

ments. The same nonlinear model previously introduced is imple-mented assuming for both concrete and steel the design values

of the strength (i.e.   f cd = 250.85/1.5 = 14.1 MPa and   f  yd = 450/

1.15 = 391 MPa) as effective strength in the constitutive relation-

ship. Therefore, the results neglect the safety factors due to the

semi-probabilistic approach into the definition of the material

strength, taking in account only the design redundancy of the

dimension and steel reinforcement.

The model takes also into account the nonlinear behaviour of 

columns and beams by lumped plasticity and by defining the

plastic hinges according to the plastic rotational capacity

suggested by EC8 [10].

 Table 3

Vibration period and participant masses for the RC wall building in the case of RC floor with bricks.

Deformable floor Slab thickness Rigid floor

12 cm 16 cm 20 cm 24 cm

Period of vibration dir.  X  (s) 0.653 0.068 0.067 0.067 0.103 0.070

Participating mass dir. X  (%) 55 38 38 34 30 89

Period of vibration dir.  Y  (s) 0.754 0.106 0.103 0.101 0.100 0.087

Participating mass dir. Y  (%) 60 76 83 85 87 87

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1°

2°

3°

δ1/δ2

thickness [mm]

rigid floor

0 2 4 6 8 10 12

Fig. 9.  The variation in the  d1/d2   ratio along the direction  y  for the wall building

with RC floor with bricksversus the thickness of the slab, considering the three floor

levels.

 / 

0.0

0.3

0.6

0.9

1.2

1.5

1.8

XY

Vcol Vwall

thickness[mm]

0 2 4 6 8 10 12

Fig. 10.  Variation of the ratio  V col/V wall  for the RC wall building with the RC floorwith bricks versus the thickness of the slab.

0

0.1

0.2

0.3

0.4

3rd FLOOR

2nd FLOOR

1st FLOOR

1 5 16 50

Fig. 11.  Variation of the ratio  V col/V wall  ratio versus the stiffness of the columnsalong the direction  Y .

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Two distributions of seismic forces along the height were con-

sidered for each direction, as indicated in EC8 [10]. The first distri-

bution (No. 1) corresponds to a distribution of accelerations

proportional to the fundamental modal shape and is applicable

only if the modal shape in the considered direction has a partici-

pant mass at least of 75%. Conversely, the second distribution

(No. 2) is uniform and corresponds to an uniform distribution of 

accelerations along the height of the building.

The results of nonlinear analyses are usually represented by

load–displacement curves (capacity curves), where the load is

the total shear at the base of the building (V ) and the displacement

(d) is measured at the top of the building.

In Fig. 12, the four capacity curves (V –d) obtained for the two

principal directions and the two force distributions are shown.

All curves were stopped when   V  = 0.85V max   along the softening

branch, and the corresponding displacement was assumed as the

maximum one  [10]. It is worth to note that when the capacity

curves reach their ultimate point, the RC columns were still in

the elastic field.

These curves are representative of a system with more degrees

of freedom (MDOF) and must be transformed in order to be used

for safety verifications. In particular, both values of shear and dis-

placement have to be divided by the participation factor C [10] to

have the capacity curve (V –d) of the equivalent single degree of 

freedom system (SDOF). The participation factor of the first and

second mode has been used respectively for the  Y  and X  direction.

The values of the participation factor of the first 3 modes for both

directions are listed in Table 4.

Basing on the curve   V –d of the SDOF system, an equivalent

bilinear curve is then drawn. Such a bilinear curve is characterised

by an elastic–plastic behaviour as suggested in the Annex B of 

Eurocode 8   [10]. In  Fig. 13  the curve   V –d of the SDOF system

and the corresponding equivalent bilinear curve is presented for

the direction X  under the distribution of force No. 1. In particular,

as indicated in Anne B, the linear branch was fixed imposing the

passage at the point 0.6V u, while the plastic range is characterised

by the same ultimate displacement,  du, of the curve  V –d of the

SDOF system. It is clear that the linear branch, characterised by a

stiffness lower than the one of the effective SDOF equivalent sys-

tem (see Fig. 13), points out that the nonlinear behaviour occurred

before 60% of the maximum shear,  V u, effectively attained by the

SDOF system.

A summary of the main properties of the SDOF systems corre-

sponding to the capacity curves obtained for each direction for

both force distributions (No. 1 and No. 2) is reported in  Table 5.

In the same table also the values of the displacement demand,

dmax, are listed; such values have been calculated referring to the

expected PGA. For both force distributions an expected peak

ground acceleration of 0.35 g was considered, that is the same

value used for design the building.

The results of nonlinear analyses are usually represented by

load–displacement curves (capacity curves), where the load is

the total shear at the base of the building (V ) and the displacement

(d) is measured at the top of the building.

The results show that each bilinear curve furnishes a displace-

ment capacity of the structure higher than the demand

(duP dmax), with seismic safety factors ranging between 1.4

and 2.0.

The behaviour factor q  is due to various contributions [42]:

q ¼ Rl  Rs  Rn ¼ V eV  y

 V  yV 1

 V 1V d

¼ V eV d

ð9Þ

where   V e   is the base shear required by the seismic action if the

structure remains in the elastic field, V  y the base shear at the forma-

tion of the mechanism, V 1 the base shear when the first plasticiza-

tion occurs, and  V d   is the design resistance obtained by the design

spectrum (i.e., the elastic spectrum reduced by the design behaviour

factor).Therefore, the term Rl  represents the ductility of the structure

and for the examined building assumes values ranging between

1.3 and 1.4, the term   Rs   represents the over-strength of the

0

4000

8000

12000

16000

20000

distribution 1

distribution 2

V [kN]

δ [mm]

(a)

0

4000

8000

12000

16000

distribution 1

distribution 2

V [kN]

δ [mm]

(b)

0 3 6 9 12 15

0 3 6 9 12 15

Fig. 12.   Capacity curves for the wall building for two force distributions: (a)  X direction and (b) Y  direction.

 Table 4

Participation factor of the RC wall building for the first three modes.

Participation factor Mode 1 Mode 2 Mode 3

 X Y X Y X Y 

C   0.02 1.25 1.28 0.16 0.82 0.51

0

4000

8000

12000

0 2 4 6 8 10

equivalent bilinearsystemSDOF system

V [kN]

δ [mm]

Fig. 13.   Curve  V 

–d

for the SDOF system representing the RC wall building in  X direction for force distribution No. 1.

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structure due to the energy dissipation by plasticization of materi-

als and assumes values ranging between 1.3 and 1.4, and the term

Rn  represents the over-strength (redundancy) of the structure due

to the design approach and assumes values ranging between 1.1and 1.6. These low values of Rn are due to the design procedure that

was aimed to use for all the walls the minimum reinforcement

required in the most stressed wall (in any case not less than the

minimum percentage of 0.2% required by both the European  [10]

and Italian   [9]  code). The effect of partial safety factors of the

materials has been neglected since the design strength has been

used for the constitutive relationship introduced in the nonlinear

model.

Considering the only contribution of  Rl   and Rs, that represent

the effective resource of the structure, not depending on the design

redundancy, the behaviour factor results about 1.8 (i.e., 1.31.4),

that is greater than the value 1.5 assumed in the design procedure.

Thus, the provision of Eurocode 8 [10] is safe since the structure

shows an adequate capacity for energy dissipation, both in termsof ductility and resistance. Taking into account also the contribu-

tion of redundancy,  Rn, the global behaviour factor q varies in the

range 2–3. The performance exploited for the building examined

in this study can be considered significant of usual conditions of 

walls designed with a low redundancy, i.e., with the minimum

reinforcement ratio and a low level of the mean compressive

strength due to the vertical loads (0.04 fcd) This low level of the

axial load reduces the ductility of the walls facilitating the mecha-

nism of sliding at the wall foundation interface, that gives a limited

energy dissipation trough the rocking as already observed in tests

of Gebreyohaness et al. [26].

In the following, the behaviour of the columns is also analysed

in order to observe whether they still remained in the elastic field,

when the ultimate load was reached in the capacity curve of the

whole building. Considering that the analysed building is charac-

terised by T  < T C , the line 1 in Fig. 14 represents the elastic behav-

iour of the entire building that reaches the elastic strength  V e, line

2 represents the elastic–plastic behaviour of the building assuming

the design strength  V d  as elastic limit, and line 3 represents the

elastic–plastic behaviour of the building considering the strength

at yielding V  y  as elastic limit.

The ultimate elastic displacement of the building can be calcu-

lated as:

deU  ¼

 V eK 

 ¼ V d  ðq þ 1ÞK 

  ð10Þ

where K   is the stiffness of the system and q is defined as:

q ¼ V 

e  V d

V d ð11Þ

Applying the principle of equal energy for the linear (line 1) and

elastic plastic system (line 2) of   Fig. 14, the following relation is

obtained:

ðdeU   ddÞ ðV e  V dÞ

2  ¼ ðdU   ddÞ  V d

) ðdeU   ddÞ  V d  ð1 þ q  1Þ

2

¼ ðdU   ddÞ  V d  )   dU 

¼ ðdeU   ddÞ

2   q þ dd   ð12Þ

where  dd

  represents the displacement of the system at the design

strength.

Replacing Eq. (10) of the ultimate elastic displacement, dU e , inEq.

(12),  the ultimate displacement,  dU , can be expressed as:

dU  ¼ V d  ðq þ 1Þ  q

2K   þ dd

q

2 þ 1

  ð13Þ

In Fig. 14, the line 4 represents the elastic behaviour of the col-

umns. Therefore, the force that permits the columns to remain in

an elastic range is defined as:

V ec  ¼ K C   dU  ¼ K C 

K    V d

2 ðq þ 1Þ  q þ K C   dd

q

2 þ 1

  ð14Þ

being  K c  the stiffness of the columns.

If  V e

C  < V d, the columns are in the elastic range, otherwise theyrevert to a plastic range.

 Table 5

Main properties of the SDOF systems.

SDOF system Force distribution No. 1 Force distribution No. 2

 X  direction   Y  direction   X  direction   Y  direction

k (kN/m) 4482 2769 5360 3483

F  y (kN) 13,091 8887 14,250 9931

m (kg) 859,465 829,343 859,465 829,343

T C   (s) 0.543 0.543 0.543 0.543

T  (s) 0.087 0.109 0.080 0.097

dmax   (mm) 0.877 1.504 0.708 1.137

Rl   (/) 1.4 1.4 1.3 1.4

Rs  (/) 1.3 1.3 1.4 1.4

Rn  (/) 1.6 1.1 1.6 1.1

q (/) 3.1 2.0 3.0 2.1

l  (/) 3.8 3.0 2.9 3.0

dmax   (mm) 4.3 5.5 3.4 4.7

du  (mm) 11.1 9.6 7.7 8.7

du/d

max   2.0 1.9 1.7 1.4

V

δ

Ve

δu

Vy

Vd

VdC

δde

δu

Vce

Vd·q*

Vd·(q*+1)= Ve

1

4

2

3

Fig. 14.   F –d  graph in the case of  T  < T C .

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In the following, the formulations previously illustrated are

applied to the building analysed for the case of force distributions

proportional to the masses in the X  direction (No. 2).

deU  ¼

 V eK 

 ¼ V d  ðq þ 1ÞK 

  ¼  41; 265

5360  ¼  7:7 mm

q ¼ V e

  V d

V d ¼ 41; 265

3347

3347   ¼ 11

:3

dU  ¼ V d  ðq þ 1Þ  q

2K   þ dd

q

2 þ 1

¼  3347 ð11:3 þ 1Þ 11:3

2 5360  þ 0:353

  11:3

2  þ 1

¼  45:7 mm

V eC  ¼ K C   dU  ¼  50 45:7 ¼ 2285 kN

For the case at hand, it is determined that:

V eC  ¼  2285 kN <  3347 kN ¼ V d

and, thus, it is confirmed that the columns are in an elastic range

when the walls collapse.

5. Conclusions

Large lightly reinforced walls are still not commonly used in

many seismic countries, but innovative technologies currently ori-

ented towards thermal insulation are utilising them along the

perimeter of structures giving impulse to their application.

The analyses developed in this paper gives the following addi-

tional information about the structural performances of this

typology:

– the nonlinear FE models of lightly reinforced walls based on

smeared fixed cracking appears to be more effective than the

approach based on smeared rotating cracking, if the parameter

governing the shear deformability after cracking is well cali-brated. Within this context, the model implemented in

SAP2000 appears to be efficient in terms of global behaviour;

– the dynamic linear analysis of the building with walls only

along the perimeter, assumed as case study, indicated that the

vibration period is overestimated by the simple code formula-

tion; it can be approximated well by the model of a cantilever

with the transversal section represented only by the perimeter

walls;

– the role of the in-plane stiffness of the floor is important in

terms of the vibration period and participant masses. Innovative

floors with light elements in EPS cannot provide the effect of a

rigid slab for a wall building, however, the special configuration

with walls only along the perimeter allow for the transfer of the

entire seismic action to the walls (i.e., the effect on the columnsis negligible), albeit a very deformable floor is realised because

the column stiffness is much lower than the wall stiffness;

– the nonlinear behaviour evidenced that, considering ductility

and energy dissipation, the behaviour factor results about 1.8,

that is greater than the value 1.5 assumed in the design proce-

dure; adding the redundancy, values of 2–3 can be reached;

– a simple procedure can be applied to predicting the load that

induces the frame plasticization; generally the high rigidity of 

the walls does not allow for the plasticization of the frame ele-

ments (beams and columns) that can be designed by neglecting

the details required for the ductile elements.

In conclusion, RC buildings with large lightly reinforced walls

on the perimeter seem to be a structural type characterised by acertain global ductility, though the constructive details at the end

of the cross section are lacking. Thus, the structural solution exam-

ined is interesting and promising, but more accurate modelling

with deeper and wider numerical analyses are necessary to gener-

alise the results.

References

[1]  Moroni MO. Concrete shear wall construction. Santiago, Chile: University of Chile; 2002.

[2] Pentangelo V, Magliulo G, Cosenza E. Analysis of buildings with large lightly

reinforcedwalls. In: The 14thEuropean conference on earthquake engineering,

Ohrid, Macedonia; 2010.

[3]  Wood S, Greer W. Collapse of eight-story RC building during 1985 Chile

earthquake. J Struct Eng 1991;117(2):600–19.

[4] Orakcal K, Massone L, Wallace J. Shear strength of lightly reinforced wall piers

and spandrels. ACI Struct J 2009;106(4):455–65.

[5] Wallace JW, Massone LM, Orakcal K. St. Joseph’s Healthcare Orange, California.

SPC-2 upgrade: E/W wing component test program—final report. Report no.

UCLA SEERL 2006/1. Los Angeles, CA: University of California Los Angeles;

2006. 66 pp.

[6] Wallace JW, Orakcal K, Massone LM, Kang THK. St. Jude Medical Center,

Fullerton, California. Horizontal wall segment component test program—final

report. Report no. UCLA, SEERL 2007/1. Los Angeles, CA: University of 

California Los Angeles; 2007.

[7] Palermo M, Gil-Martın LM, Trombetti T, Hernandez-Montes E. In-plane shear

behaviour of thin low reinforced concrete panels for earthquake re-

construction. Mater Struct 2012;46:841–56.[8]  Rezaifar O, Kabir MZ, Taribakhsh M, Tehranian A. Dynamic behaviour of 3D-

panel single-storey system using shaking table testing. Eng Struct

2008;30:318–37.

[9] Min. LL.PP, DM 14 gennaio 2008. Code design for construction (NTC2008).

Gazzetta Ufficiale della Repubblica Italiana, n. 29 [in Italian].

[10] Eurocode 8, 2004. Design of structures for earthquake resistance – Part 1:

general rules, seismic actions and rules for buildings; 2004.

[11]  Massone LM, Bonelli P, Lagos R, Lüder C, Moehle J, Wallace JW. Seismic design

and construction practices for reinforced concrete structural wall buildings.

Earthq Spectra 2012;28(S1):S245–56.

[12]  Wallace JW, Massone LM, Bonelli P, Dragovich J, Lagos R, Lüder C, Moehle J.

Damage and implications for seismic design of RC structural wall buildings.

Earthq Spectra 2012;28(S1):S281–99.

[13] SAP 2000. Version 14, CSI – Computers and Structures Inc.; 2000.

[14] TNO DIANA BV. DIANA. Release 9.4.

[15] FintelMPE.Performance of buildings with shear walls in earthquakeof the last

thirty years. Boca Raton, FL: Consulting Engineer; 1995.

[16]   Wood SL. Performance of reinforced concrete buildings during 1985 Chile

earthquake: implication for the design of structural walls. Earthq Spectra

1991;7(4):607–38.

[17] Fischinger M, Rejec K, Isakovic  T. Modeling inelastic shear response of RC

walls. In: Proceedings of the 15th world conference on earthquake

engineering, 15WCEE, Lisboa, 24–28 September; 2012.

[18] New Zealand Standard – Concrete structures standard. Part 1 – the design of 

concrete structures.

[19] Riddel R. Performance of R/C buildings in the 1985 Chile earthquake. In:

Earthquake engineering, tenth world conference. Rotterdam: Balkema;

1992.

[20] Telleen K, Maffei J, Heintz J, Dragovich J. Practical lessons for concrete wall

design, based on studies of the 2010 Chile earthquake. In: Proceedings of the

15th world conference on earthquake engineering, 15WCEE, Lisboa, 24–28

September; 2012.

[21] ACI Committee. Building code requirements for structural concrete and

commentary. Farmington Hills, MI: ACI.

[22] Fischinger M, Isakovic  T, Kante P. Seismic vulnerability evaluation of lightly

reinforced walls. In: 13th World conference on earthquake engineering,

Vancouver, B.C., Canada, August 1–6; 2004 [paper no. 468].[23] Vallenas, Bertero, Popov. Hystereticbehaviour of reinforced concrete structural

walls. Report no. UCB/EERC-79/20. Berkeley: Earthquake Engineering Research

Center, University of California; 1979.

[24]  Salonikios TN, Kappos AJ, Tegos IA, Penelis GG. Cyclic load behaviour of low-

slenderness reinforced concrete walls: design basis and test results. ACI Struct

 J 1999;96(4):649–61.

[25]  Salonikios TN, Kappos AJ, Tegos IA, Penelis GG. Cyclic load behaviour of low-

slenderness reinforced concrete walls: failure modes, strength and

deformation analysis, and design implications. ACI Struct J 1999;97(1):

132–42.

[26] Gebreyohaness A, Clifton C, Butterworth J. Experimental investigation on the

in-plane behaviour of non-ductile RC walls. In: Australian earthquake

engineering society 2011 conference, Barossa Valley, South Australia, 18–20

November; 2011.

[27] Gebreyohaness A, Clifton C, Butterworth J. Behaviour of inadequately detailed

reinforced concrete walls. In: Proceedings of the ninth Pacific conference on

earthquake engineering building an earthquake-resilient society, Auckland,

New Zealand, 14–16 April; 2011.

[28]  Hidalgo PA, Ledezma CA, Jordan RM. Seismic behaviour of squat reinforcedconcrete shear walls. Earthq Spectra 2002;18:287–308.

52   M. Pecce et al. / Engineering Structures 73 (2014) 39–53

7/23/2019 seismic reinforcement 3

http://slidepdf.com/reader/full/seismic-reinforcement-3 15/15

[29]   Barda F, Hanson JM, Corley WJ. Shear strength of low-rise walls with

boundary elements, reinforced concrete structures in seismic zones, SP-

53. Farmington Hills, MI, USA: American Concrete Institute; 1977. p. 149–

202.

[30]   Cardenas AE, Russell HG, Corley WJ. Strength of low-rise structural

walls, reinforced concrete structures subject to wind and earthquake

forces, SP-63. Farmington Hills, MI, USA: American Concrete Institute; 1980.

p. 221–42.

[31]   Wallace JW, Elwood KJ, Massone LM. Investigation of the axial load capacity

for lightly reinforced wall piers. J Struct Eng 2008;134:1548–57 .

[32] Pecce M, Bibbò FA, Ceroni F. Seismic behaviour of R/C buildings with largelightly-reinforced walls. In: Proceedings of 15th WCEE, Lisbon, Portugal,

September 24–28; 2012.

[33]  Vecchio FJ, Collins MP. The modified compression-field theory for reinforced

concrete element subjected to shear. ACI J 1986:219–31.

[34]  Bentz EC. Explaining the riddle of tension stiffening models for shear panel

experiments. J Struct Eng 2005;131(9):1422–5.

[35]   Manfredi G, Pecce M. Behaviour of bond between concrete and steel in large

post-yielding field. Mater Struct 1996;29(192):506–13.

[36] CEB-FIP. Model code for concrete structures. Comité Euro-International du

Béton (CEB), 3rd ed. Lausanne; 1978.

[37]  Mander JB, Priestley MJN, Park R. Theoretical stress–strain model for confined

concrete. J Struct Eng 1988;114(8):1804–26.

[38]  Crisfield M, Wills J. Analysis of R/C panels using different concrete models. J

Eng Mech 1989;115(3):578–97.

[39] Barzegar F, Schnobich WC. Non linear finite element analysis of reinforced

concrete under short term monotonic loading. Civil Engineering Studies SRS

no. 530. Illinois: University of Illinois at Urbana; 1986.[40]  Saffarini HS, Qudaimat MM. In-plane floor deformations in RC structures. J

Struct Eng 1992;118(11):3089–102.

[41]   Ju SH, Lin MC. Comparison of building analyses assuming rigid or flexible

floors. J Struct Eng 1999;125(1):25–31.

[42] ATC. Structural response modification factors. ATC-19 report. Redwood City,

CA: Applied Technology Council; 1995.

M. Pecce et al. / Engineering Structures 73 (2014) 39–53   53