1

Abstract

According to the existing technical codes and guidelines, various methods for the

seismic assessment of historical buildings exist. They range from simplified models

to equivalent frames, up to detailed finite element models. In the first part of this

paper the advantages and drawbacks of the various approaches are briefly discussed.

Some of them are simple but they rely on very strict assumptions and cannot be used

in all the situations. Others are able to give very detailed results but are

computationally intensive and time consuming. In this work, the attention is focused

on an intermediate approach, the nonlinear static analysis of equivalent frames

models. This method is able to give a measure of the response of the structure but at

the same time it is simple to implement. In particular, its application with the code

SAP2000 is presented. In the second part of the work, this approach is applied to a

façade of an historical building that was damaged by the 2009 L’Aquila earthquake

(central Italy). The considered building is the Camponeschi Palace, located in

L’Aquila city center. The damage mechanisms obtained are compared with the

observed damage and with those obtained from other approaches and reported in the

existing technical literature.

Keywords: masonry building, existent building, seismic assessment, non-linear

static analysis, Eurocode, Italian Code.

1 Introduction

The seismic assessment of historical masonry buildings is a complex task because

the global behaviour of this kind of structures depends on various factors, as the

behaviour of the single walls, the connections between them, the typology and

stiffness of the floor (flexible or rigid diaphragms), and the strong nonlinearities of

the material [1, 2, 3].

Paper 72

Seismic Assessment of an Historical Masonry

Building using Nonlinear Static Analysis

F. Bucchi, S. Arangio and F. Bontempi

Department of Structural and Geotechnical Engineering

Sapienza University of Rome, Rome, Italy

©Civil-Comp Press, 2013

Proceedings of the Fourteenth International Conference on

Civil, Structural and Environmental Engineering Computing,

B.H.V. Topping and P. Iványi, (Editors),

Civil-Comp Press, Stirlingshire, Scotland

2

Considering a single wall, for example, it is possible to distinguish two different

types of failure (Figure 1) that lead to two different collapse mechanisms: out-of-

plane and in-plane failures, which correspond to collapses that are called I and II

collapse mechanisms respectively. The first mechanism regards only parts of the

wall (Figure 1) and occurs when a wall is subjected to an out-of-plane action and

there is poor anchorage of the orthogonal walls or a poor connection between floor

and walls. The second mechanism regards entire panels and occurs when a load is

applied in the same plane of the masonry wall [4].

Usually, in the global analysis of the structures only in-plane mechanisms (II

mode) are considered. Actually, an exhaustive seismic verification would require to

take into account also the possible occurrence of out-of-plane mechanisms; however,

if the attention is focused on the overall seismic behavior of the structure, common

practice is to neglect this class of mechanisms because they usually involve parts of

the structure that does not affect significantly the global response [5, 6].

Figure 1: Out-of-plane and in-plane behaviour of a single wall (left) and collapse

mechanisms (right) (adapted from [5]).

In order to describe the seismic behaviour of masonry structures, it is possible to

identify two types of panels in each façade: the ‘piers’, which are the principal

vertical resistant elements for both dead and seismic loads; and the ‘spandrels’,

which are secondary horizontal elements, coupling piers in the case of seismic loads.

There are three classes of spandrels, which have different behaviors [7]: • “weak spandrels” that have not tension resistant elements, as steel chains or

similar; • “strut spandrels” that have at least one tensile resistant element that allows the

setup of a ‘strut and tie’ resistance mechanism; • “beam spandrels” that are reinforced with two elements, one above and one

below the panel.

The spandrel behaviour affects the response of the adjacent piers that can act as: • “cantilever”: in case of “weak” spandrels; • “partially coupled”: when the spandrel is of “strut” type; • “shear type”: in case of “beam” spandrels.

The different types of piers strongly influence the global seismic response of the

structure.

3

Another aspect that affects the response of masonry structure is its nonlinear

constitutive law because it is influenced by many factors that are difficult to

compute, as the type and dimension of bricks, lack or presence of mortar, physical

and chemical degeneration.

It is evident that there are a lot of source of uncertainty that have to be considered

for the seismic assessment of existing structures [8]. For this reason, according to

the available information, different methods can be implemented. In the following

they are briefly discussed, highlighting their advantages and drawbacks. Then, one

of them, the ‘equivalent frame model’, is presented in detail and an application is

carried out.

2 Masonry buildings modelling

Different models for the assessment of masonry structures exist in the literature:

they are both one-dimensional (frame or macro-element) and two-dimensional

(finite elements).

A simple approach includes models that schematize the structure as an equivalent

frame. The first frame model was proposed by Tomazevic (1978) and it is the well-

known POR method [9], where the masonry walls are schematized by a set of piers

connected by a rigid spandrel. This model considers the piers working in parallel

with a shear-type behaviour. This scheme is reliable only for structures with few

floors and rigid spandrels because, if used in different conditions, it could

overestimate the resistance.

Another model, proposed by Calderoni et al. [5, 7], schematizes the wall as a set

of panels. The resistant part for each panel, is schematized as a strut, where the

inclination and stiffness are calculated in such a way to reproduce the global

behaviour of the panel. The panel collapses when it reaches a limit equilibrium

configuration or the maximum compression strength of the strut.

A more detailed approach, that is also considered in the building codes, is the

Simplified Analysis Method (SAM), developed since 1996 by Magenes and Calvi

[5], and then modified by Magenes and Della Fontana [10]. The SAM, differently

from the POR, considers that spandrel as deformable; furthermore it can move

horizontally (as in POR) and can rotate (not allowed in POR). In the SAM, the wall

is schematized with an equivalent frame (Figure 2, [11]) composed by: column

elements representing the piers; beam elements representing the spandrels; rigid

offsets describing the joint panel. The joint is considered infinitely rigid because

generally (but not always) this area is not cracked.

Figure 2: Equivalent frame of the Simplified Analysis Method (SAM).

4

Both the pier and the spandrel have an elastic-plastic behaviour with a

deformation limit; in particular, the element is considered elastic until it reaches the

threshold of a failure criterion (rocking, diagonal shear and sliding shear for pier;

rocking and shear for spandrel); once the threshold is exceeded, a plastic hinge is

activated.

Another method to schematize a masonry wall is the one-dimensional model at

macro-elements. Various authors proposed these kinds of models, as for example

D’Asdia and Viskovic [12], Gambarotta and Lagomarsino [13, 14], Caliò et al.[15].

In this approach the wall is described by a set of macroscopic no tensile elements,

which represent the piers, spandrels and joints. The advantage of the macro-elements

approach is represented by a reduction of the degrees of freedom that reduces the

computational effort.

D’Asdia and Viskovic [1995] suggested an approach based on linear finite

elements with variable adaptive geometry (known with the Italian acronym PEFV).

In this method the pier and the spandrel are subdivided into triangular elements that

can change dimensions according to the existing stress state.

Figure 3: Discretization of a masonry wall with PEFV [12].

Gambarotta et al. [13, 14] proposed a macro-element that works in plane. This

macro-element (with width b and thickness s) consists of three parts. In Figure 4, the

top and bottom elements 1 and 3 have an infinitesimal height Δ and are infinitely

rigid to shear action; the central element 2 has a finite height h and it is rigid to

axial force and bending.

The DOFs of a single end joints (i, j in Figure 4) and interface joint (1, 2 in

Figure 4) are three: two horizontal translations u, w and one rotation φ, so the entire

macro-element has 12 DOFs. By applying some simplifying assumptions, the

compatibility conditions can be defined and the DOFs became 8 for each macro-

element: six components at the end joints i, j (ui, wi, φi, uj, wj, φj) and two

components that describe the entire macro-element (δ, φ). This model is

implemented in the code 3Muri and more details are given in the manual of the

software [16].

Another type of macro-element was proposed by Caliò at al. [15]. It is

represented by an articulated quadrilateral frame with four rigid edges connected by

four hinges and two diagonal nonlinear springs (Figure 4). Each side of the panel

can interact with other elements, or external supports, by means of nonlinear

interface orthogonal and longitudinal springs. The internal and external springs are

5

able to reproduce the in-plane failures. Each macro-element has three DOFs that

describe the displacements in the plane and a further DOF describing the shear

deformation.

Figure 4: Kinematics (a) and statics (b) of the macro-element proposed by [16]

(left); Simulation of the main in-plane failure mechanisms of a macro-element with

springs proposed by [15]: (a) rocking, (b) diagonal shear, (c) sliding shear (right)

A more detailed modelling can be obtained by using finite elements codes

because:

- the interaction between the different parts of the structure can be properly taken

into account, obtaining information about the redistribution of loads;

- the nonlinear behaviour of the structure can be considered;

- the development of cracking in the walls can be reproduced in an accurate way.

There are several drawbacks, however. The main limitation is that they are very

computationally and time consuming [17, 18]. Moreover, to perform a finite element

analysis, a detailed model of the existing building is needed; thus the structural

element characteristics shall be (exactly, as much as possible) known. This requires

a full set of plans that lay out each member size, locations and connections.

Constructing a model with this amount of detail will be extremely time consuming.

For old buildings, plans with enough details are often not available, and many

assumption need to be made in the model, thus reducing the confidence level of the

results.

Summarizing, the main limitation of the simpler models is that they rely on strict

assumptions and cannot be used if the basic assumptions are verified. On the other

hand, more detailed methods require a large computational effort. The choice of the

modelling strategy should be in accordance with the available information and

related to the importance of the structure [19].

In this work, after a brief description of the approaches accepted by the European

technical codes, an intermediate model has been chosen, the equivalent frame

approach known with the acronym SAM. This method is able to give a measure of

the response of the structure but at the same time it remains enough simple. In the

following, its implementation for the seismic assessment of the wall of an historical

masonry building in L’Aquila (Italy) is presented.

6

3 European and Italian codes for the assessment of

masonry structures

According to European code for the seismic design of building, Eurocode 8 ([20], §

4.3.3), a seismic analysis of a masonry building can be carried out with different

methods: • “lateral force method”, that is a linear static analysis; • “modal response spectrum analysis”, that is a linear dynamic analysis; • “pushover”, that is non-linear static analysis; • “non-linear time-history analysis” or non-linear dynamic analysis.

An important difference among the different methods is the way the seismic

action is modelled; for example in the first method it is schematized with equivalent

horizontal static forces while in the last one it is applied in form of accelerograms.

These methods can be applied both for the design of new buildings and for the

assessment of the existing ones. In this paper the attention is focused on this latter

category. As support at the analysis of existing building, the Eurocodes have

introduced two important concepts: the knowledge levels (KL) and the confident

factors (CF) ([20]§ 3.3). Three different levels of knowledge are defined: • KL1: limited knowledge; • KL2: normal knowledge; • KL3: full knowledge.

The level is assigned according to the available information on geometry, details,

materials, and boundary conditions [21].

On the other hand, the confident factors are additional partial factors that are

considered in the analysis for taking into account the uncertainties due to the actual

conditions of the structure. Of course, if the level of knowledge is high, the

uncertainties will be less and the confidence factor will be small, or even unitary. In

the practice, the KL influences two aspects: the type of seismic analysis that have to

be used (for example for KL1 it is possible to carry out only linear analysis) and the

values to be adopted for the confidence factors (CF). The Eurocode 8 recommends

the following values: CFKL1=1.35, CFKL2=1.20 and CFKL3=1.00. They are applied

together with the coefficient for the material γM to reduce the masonry strength.

The concepts of level of knowledge and confident factors have been introduced in

other technical code, as for example the Italian National Technical Code for

Constructions, shortly named NTC08 [22], and the relative Guidelines [CNTC08,

2009], which have been written in accordance with the Eurocodes. In this paper the

analyses are carried out by using the Italian code.

4 Non-linear static analysis with commercial codes

In this work, the seismic analyses are carried out using the equivalent frame

approach known with the acronym SAM and implemented with the software

SAP2000® (see for example, Pasticier et al. [23]).

7

The various panels of the masonry façade have been modelled by defining the

dimensions and position of the piers, spandrels and rigid joints. The linear part of the

constitutive law of the masonry has been modelled with a stress–strain linear curve

where the Young modulus is half of the real one (E/2) in order to consider the

material in cracked conditions.

The nonlinearity of the material is taken into account through the use of plastic

hinges, in accordance with the Italian Code (NTC08, §7.8.1.5.4). Three types of

plastic hinges are used: shear hinges (V type), bending hinges (M type) and rocking

hinges (PM type). For example, with reference to a one-span frame (Figure 5, left): • for the piers are used V and PM hinges. The V hinges are placed in the middle of

the deformable part of the piers, the PM hinges at the end of it; • for the spandrels are used V hinges in the middle of the spandrel, and M hinges at

the end of it.

In the right part of Figure 6 the behavior that has been assigned to the various

hinges, according to the Italian code NTC08, is shown: the V hinges take into

account the relationship between the ultimate displacement of the panel δu and the

limit shear Vu, and the M hinges between the moment Mu and ultimate rotation φu;

on the other hand, the PM hinges consider the interaction between the normal

stress P and the ultimate moment Mu.

Figure 5: Location and type of plastic hinges (left); behavior of the different plastic

hinges according to the Italian Building Code NTC08 (right).

5 Case study: Camponeschi Palace (L’Aquila, Italy)

The SAM approach has been applied for the seismic assessment of a wall of an

historical building, Camponeschi Palace, located in the centre of the city of L’Aquila

(Italy) (Figure 6) [24, 25]. The building was severely damaged by a strong

earthquake on April 2009.

It has an L shape (Figure 6) and it is organized on three levels: ground floor, first

floor, and second floor. The geometry of the Palace is not very complex, but it was

built in different steps that go from 1626 to 1933, so it exhibits a complex

stratification (Figure 7). The various phases of construction have influenced the

structural organization that is extremely varied: there are different horizontal

structural systems as vaults, reinforced concrete floors, wooden trusses, as well as

different kind of walls (small and large bricks, different types of mortar, etc). In this

8

work is analysed in detail the wall situated along Camponeschi street (Figure 7). It is

59 m long and 6 m high with fairly regular openings on the three levels. Part of the

wall is below the street level.

Figure 6: Render of Camponeschi Palace (L’Aquila, Italy). Aerial view (left); view

from Camponeschi street (right) [24, 25].

Figure 7: Construction phases of Camponeschi Palace (from [24]).

The first two floors of the considered brace along Camponeschi street have barrel

vaults on the hallway and cross vaults on the corner between the two brace of the L

(Figure 8). The roof of the last floor is supported by wood trusses. Considering the

observed floors, in the model of the wall it is assumed for the spandrels a “weak”

behaviour. On the base of the available information, for the analysis it has been

assigned an intermediate knowledge level (normal), KL2 of the Eurocode. The

corresponding confident factor CF is equal to 1.2. The main properties of the

material are summarized in Table 1. For pushover analysis, the partial coefficient of

the material γM is equal to one.

The wall is loaded by: dead weight of the masonry (see Table 1), dead weight

(structural and non-structural) and the variable loads given by the different type of

floors (Table 2).

9

Figure 8: Ground floor of the brace along Camponeschi street (from [24]).

Properties of the masonry

Volume weight w 18 kN/m3

Longitudinal elastic modulus E (cracked conditions) 601 N/mm2

Tangential elastic modulus G (cracked conditions) 150 N/mm2

Compression strength fm 270 N/cm2

Design compression strength fd 225 N/cm2

Shear strength 0τ (o fvm0) in absence of normal stress 6 N/cm2

Design shear strength 0dτ (o fvd0) in absence of normal stress 5 N/cm2

Diagonal shear strength ftd 9 N/cm2

Sliding shear strength fvd in absence of normal stress Function of the

normal stress nσ

Characteristic compression strength of the elements in the parallel direction on the

acting force bkf 202.5 N/cm2

Table 1: Mechanical properties of the considered masonry.

Gravity loads -Roof Gravity loads - Barrel and cross vaults

Type of load Value Type of load Value

Variable 0.50 kN/m2 Variable 3.00 kN/m2

Dead weight of wood beams 0.41 kN/m2 Floor tiles 0.40 kN/m2

Wooden system of the floor 2.80 kN/m2 Concrete slab (5 cm) 1.25 kN/m2

Tiles 0.60 kN/m2 Cement mortar screed 0.40 kN/m2

Ceiling 0.30 kN/m2 Abutment 18.00 kN/m3

Table 2: Gravity loads.

10

Two non-linear static analyses have been carried out on the wall, considering two

different distributions of the forces: the first one proportional to the seismic masses,

the second one to the equivalent static forces. These distributions, according to the

CNTC08, are used regardless of the participant mass of the principal modal shape.

It has been hypothesized for the spandrel a “weak” behaviour and, according to

the Italian Code, the equations in Table 3, have been used to calculate the ultimate

values of moment and shear. For a complete description of the quantities, the reader

should refer to the Italian Code [22].

Pushover analysis for existing masonry building with “weak” spandrels

Panel

type

Collapse moment uM

and ultimate rotation uϕ

Collapse shear uV

and ultimate displacement uδ

pier ⎟⎟⎠⎞⎜⎜⎝

⎛⋅−⎟⎟⎠

⎞⎜⎜⎝⎛ ⋅⋅=

d

uf

tlM

85.01

2

00

2 σσ

Minimum between:

vdt ftlV ⋅⋅= ' and

td

tdt

fb

ftlV 01

σ+⋅⋅=

%6.0=uϕ hu ⋅= %4.0δ

spandrel uM negligible uV negligible

%6.0=uϕ hu ⋅= %4.0δ

Table 3: Values of Mu and Vu in case of existing buildings with “weak” spandrels.

5.1 Pushover analysis

The pushover analysis was carried out by means of the code SAP2000®. In Figure 9

the drawings of the considered façade, its equivalent frame model and the extruded

model are shown. The control node 31 is also indicated.

The vertical loads have been applied as concentrated forces at the upper end of

the piers and have been evaluated taking into account the different types of floors

described below. The V, M and PM hinges have been defined according to the

Italian code. For convergence issues, a little hardening has been assigned to the φu –

Mu curve. The horizontal force distribution, proportional to the equivalent static

forces, has been calculated using the software “Spectrums – NTC ver 1.03”.

Two different response curves are compared in Figure 10. The black one is obtained

considering the distribution of forces proportional to the seismic masses, while the

grey one considering the distribution proportional to the equivalent static forces. In

the first case the maximum shear at the base is about 2500 kN, in the second one is

around 2000 kN [11].

In Figure 11(a) the final distribution of the plastic hinges is shown: first the

hinges in the “weak” spandrels are activated then the hinges of the piers. It is

interesting to compare these damage mechanisms with those obtained with other

approaches and reported in the existing technical literature. In Figure 12(b) for

example the results obtained with the software 3Muri® [24, 25] are shown. It is

11

possible to notice that the damage pattern is in substantial accordance. Moreover, the

damage on the spandrels is observable on the actual structure (Figure 13).

node #31

Figure 9:Considered façade of the Camponeschi Palace: drawing (a), equivalent

frame model (b), extruded model in SAP2000® (c).

0

500

1000

1500

2000

2500

3000

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

Sh

ear

[kN

]

Displacement - control node #31 [m]

Distribution of forces proportional to

seismic masses

Distribution of forces proportional to

equivalent static forces

Figure 10: Pushover curves obtained with different distributions of the forces.

12

(b)

(a)

Figure 11: Comparison of the damage mechanisms obtained by using SAP2000®

and 3muri® (image from [25]).

Figure 12: Observed damage due to L’Aquila earthquake on April 2009 (picture shot

in July 2010)

6 Conclusions and future works

In the first part of this work, various methods for the seismic assessment of existing

masonry buildings have been briefly discussed. Then, in the second part a case study

has been carried out by applying one of this methods. The chosen buildings is

Camponeschi Palace in the city of L’Aquila (Italy). It has a L shape and it is

organized on three levels. Its geometry is not very complex, but it was built in

different steps so it exhibits a complex behaviour due to the stratification. A façade

of the building has been studied in detail by applying the SAM approach to evaluate

its shear at the base. The obtained results are in substantial accordance with results

13

reported in the technical literature on the same structures and with the observed

damage. In order to improve the results further studies could be carried out, by

considering different types of constraints, able to accurately represent the interaction

with the adjacent building and the part of the façade that is under the level of the

street, and by developing different models, as more detailed finite element models.

Acknowledgements

The team www.francobontempi.org from Sapienza University of Rome is gratefully

acknowledged. This work was partially supported by StroNGER s.r.l. from the fund

“FILAS - POR FESR LAZIO 2007/2013 - Support for the research spin off”.

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