Structural Fire Risk for Heritage Buildings by the Performance-Based Engineering Format

Full Terms & Conditions of access and use can be found at
https://www.tandfonline.com/action/journalInformation?journalCode=uarc20
International Journal of Architectural Heritage
Conservation, Analysis, and Restoration
ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/uarc20
Structural Fire Risk for Heritage Buildings by the
Performance-Based Engineering Format
F. Petrini, A. Aguinagalde & F. Bontempi
To cite this article: F. Petrini, A. Aguinagalde & F. Bontempi (2022): Structural Fire Risk for
Heritage Buildings by the Performance-Based Engineering Format, International Journal of
Architectural Heritage, DOI: 10.1080/15583058.2021.2022249
To link to this article: https://doi.org/10.1080/15583058.2021.2022249
Published online: 09 Feb 2022.
Submit your article to this journal
View related articles
View Crossmark data

Structural Fire Risk for Heritage Buildings by the Performance-Based Engineering
Format
F. Petrinia
, A. Aguinagaldeb
, and F. Bontempia
a
Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy; b
Fire Engineering Department
International Fire Consultants, London, UK
ABSTRACT
This paper discusses and presents an example of fire risk analysis for a case study of an existing
heritage building: the Duomo of Modena Cathedral, located in Italy. The main issues related to the
application of the fire risk analysis to heritage buildings are discussed in detail, and an ad-hoc
procedure is proposed to manage them for the case study. In order to assess the performances of
the building in probabilistic terms, the fire risk analysis is conducted by the event-tree method, the
fire dynamics are analyzed by numerical thermo-fluid dynamics models, while the structural
behavior is investigated by advanced nonlinear thermomechanical finite element models. Results
are expressed in terms of risk curves related to a fixed return period, which quantify the occurrence
probability of different damage levels induced by fire in the wooden roof of the case study building.
This kind of result is fully compatible with probabilistic performance-based engineering frameworks
commonly accepted for other hazards (i.e., earthquakes).
ARTICLE HISTORY
Received 12 May 2021
Accepted 20 December 2021
KEYWORDS
fire risk analysis;
performance-based design;
structures; thermoplastic
FEM; wooden roof
1. Introduction
In past years there have been well-known cases of fire that
have developed in sites of historical and artistic value, and
have irreparably damaged not only the structure but even
more seriously the content, destroying valuable evidence
of our history, e.g., the recent fire at Notre Dame
Cathedral (Ferreira 2019). Prescriptive approaches for
fire safety of this kind of structure have been demon
strated to be not adequate due to their peculiarities. For
example, it is unacceptable to alter value-historical build
ings to make them adequate for the prescriptive measures
indicated by fire safety codes by implementing modern
protection measures like sprinklers. In this context, it is
almost impossible to apply the general rules of the fire
safety codes to obtain code-compliant historical build
ings, similar to what happens in seismic engineering for
existing buildings (Tesfamariam and Goda 2015). The
most suitable way of dealing with these kinds of situations
to obtain “safe but non-compliant historic buildings”
(Torero 2019) is the implementation of an appropriate
ad-hoc Performance-Based Engineering (PBE) frame
work which allows for the investigation and application
of non-standard design solutions for the attainment of
pre-defined, satisfactory, performance levels. General
principles for PBE have been largely treated in fire safety
engineering during the last two decades in the framework
of Performance-Based Fire Engineering (PBFE) (Hurley
et al. 2015; SFPE 2000; Wang et al. 2013). The methods
developed for PBFE of modern buildings mainly focus on
life safety objectives (Chu et al. 2007, Pau et al. 2019), and
not on the structural behavior, while in the specific case of
fire safety in historical buildings, the performance is more
a matter of the integrity of the structure and its content
than the occupants’ safety (Torero 2019).
Traditionally, the PBFE is developed in deterministic
terms (Huang 2020) or by a scenario-based risk
approach (SFPE 2002). On the other hand, the true
implementation of PBE approaches should be pursued
in probabilistic terms (Augusti Ciampoli 2008), as is well
established for a number of different individual treats/
hazards that, aside from fire, can strike heritage struc
tures, including earthquakes (Franchin, Petrini, and
Mollaioli 2018; Maio et al. 2020), ambient-induced cor
rosion (Guo, Dong, and Gu 2020), and flooding/scour
ing (Pizarro and Tubaldi 2019; Tubaldi et al. 2017).
Probabilistic PBE approaches allow for the expression
of a performance of a building under a certain hazard
(characterized by a probabilistic intensity measure IM)
by an acceptable occurrence in a reference period of an
appropriate threshold value for a significant response
(or risk) parameter of the building. The final outcome
of a PBE analysis is the so-called risk curve, where each
damage or loss level (e.g., the above-mentioned thresh
olds, commonly expressed in monetary terms) is asso
ciated with the occurrence probability (expressed by the
CONTACT F. Petrini francesco.petrini@uniroma1.it Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy
INTERNATIONAL JOURNAL OF ARCHITECTURAL HERITAGE
https://doi.org/10.1080/15583058.2021.2022249
© 2022 Taylor & Francis

Complementary Cumulative Distribution Function —
CCDF) in the reference period for the analysis (see
Figure 1). This format has been largely accepted from
the scientific community, practitioners, stakeholders,
and insurance companies for performance evaluations
and risk assessment in the field of seismic engineering
(Günay and Mosalam 2013; O’Reilly and Calvi 2019).
If available probabilistic PBE approaches to fire
engineering problems are developed for new build
ings, then they do not consider the peculiarities of
heritage structures (Gernay et al. 2019; Lange,
Devaney, and Usmani 2014), or they focus on people
evacuation issues (NFPA 914, 2001, Guanquan,
Jinhui, and Qingsong 2012) and not on the structure.
In this context, the definition of a coherent and
exhaustive method for the probabilistic structural
fire risk quantification of heritage building in the
format of modern PBE (i.e., by a risk curve)
approach is an important and actual research goal.
Nevertheless, there are many currently unsolved
issues that prevented the application of well-established
probabilistic formats to the fire risk/performance analy
sis of heritage buildings.
(i) Cultural Heritage Buildings are complex structural
systems from the fire performance/risk analysis view
point (CFPA-E 2013; Bernardini 2017; Carattin and
Brannigan 2012). Their analysis may present critical
issues due to many interacting aspects (protection sys
tems, material strength, architectural characteristics,
urban and cultural/environmental implications).
(ii) Fire risk analysis is a complex matter due to the
peculiar aspects of the hazard (i.e., low-probability
event, human behavior-intensity dependent) and con
sistent research efforts are still due in order to express
the hazard occurrence in a way that is similar to the one
used for earthquakes (Jingji et al. 2020), or its coherent
implementation in PBE modern frameworks (Gernay,
Khorasani, and Maria Garlock 2016; Memari and
Mahmoud 2018).
iii) Heritage buildings are commonly built with fire-
sensitive (i.e., wood) or low-strength (i.e., historical
masonry) materials. Reliable, nonlinear numerical mod
els are then needed for the analysis of the structural
response under fire (Audebert et al. 2011; Hietaniemi
2007, Thi et al. 2017; Quin et al. 2021).
(iv) The expression of hazard-induced losses in the
common “monetary metrics” used in risk/performance
analyses for modern structures can be meaningless due
to the unquantifiable cultural value of both the building
envelope and content (Torero 2019).
This paper provides a contribution for partially sol
ving these issues and moving a step toward the quanti
fication of probabilistic structural fire risk of a heritage
building in the format of a modern PBE approach.
Specifically, the paper is developed to give the following
contributions with respect to issues (i)–(iv) listed
above:
(i) a list of the system vulnerability factors that are
specific of historical heritage buildings and that have an
impact on their structural risk/performances evaluation
under fire;
(ii) a procedure based on the traditional event-tree
approach for the probabilistic risk analysis (NFPA 2017;
SFPE 2002); and
(iii) a numerical model technique of wooden beams
under fire, with the goal of rendering it a practicable/
affordable way for the nonlinear analysis of heritage
structure by commercial Finite Element (FE) codes
implementing temperature-dependent material
characteristics.
The issue of the monetary assessment of the fire-
induced losses in heritage buildings and of their content
is NOT addressed in this paper, but a logical approach
for relative graduation of the losses in different discrete
levels that are directly connected with the quantifiable
structural damage is proposed.
In order to maintain an applicative orientation,
the proposed procedures and methods are applied
and discussed with reference to a case study of exist
ing heritage building: the Modena Cathedral, located
in Italy, which is cataloged as a United Nations
Educational, Scientific and Cultural Organization
(UNESCO) World Heritage Site since 1997 (https://
whc.unesco.org/en/list/827/).
The quantification of structural fire risk by the PBE
format reported in Figure 1 (contribution (ii) above) will
allow for the coherent comparison of PBFE results with
the PBE results obtained for other kinds of hazards,
something that is essential for the true development of
next-generation Performance-Based Multi Hazard
Engineering (PB-MH-E) approaches (Petrini et al.
2020).
Figure 1. Typical risk curve in the probabilistic PBE format.
2 F. PETRINI ET AL.

2. Materials and methods
2.1. System vulnerabilities for heritage building to
fire
This section focuses on circumstances/characteristics
that are recurrent in historical buildings, and that
make them particularly vulnerable to fire (i.e., the build
ing would be less vulnerable if the characteristics are not
present). These circumstances can include both intrinsic
characteristics of this building typology (e.g., presence of
wood), and aspects related to preventive measures (e.g.,
common absence of active protection measures). In a
systemic point of view (Skelton 2002; Sydenham 2004),
the presence of these characteristics can be intended as
“system vulnerabilities”, where the system is composed
by the structure and the protection/alarm measures.
Identification of the specific system vulnerabilities of
heritage buildings to fire is a crucial task to develop an
effective procedure for the PBFE.
From a literature review of the occurred cases of fires
in historical buildings, it clearly emerges that there are at
least seven common characteristics that make them vul
nerable to fire: (1) massive presence of wooden struc
tural and non-structural elements (or other elements
vulnerable to fire); (2) presence of valuable content; (3)
absence of active protection and of adequate compart
mentalization; (4) storage of flammable substances or
non-conformity of electrical installations; (5) planned
presence of a large amount of people (churches and
museums); (6) difficulties of being approached by fire
brigades and rescue vehicles; and (7) possible indirect
involvement due to the vulnerability of other units of the
building cluster which can subject the single heritage
building to fire spread or collapse spread.
The system vulnerabilities induced by these character
istics are detailed in Table 1. The consideration of these
characteristics is crucial for the procedure proposed in
the next section for structural fire risk assessment.
2.2. The Modena Cathedral
The Modena Cathedral (Figure 2) is located in northern
Italy and is a masterpiece of Romanesque architecture.
The Cathedral has a Latin cross plant with three naves, a
false transept, and the chancel (the area of the liturgical
altar) in an elevated position. It was completed in early
1300, its in-plan geometry is approximately 25 m wide,
in the transversal direction, and 66 m long, in the long
itudinal direction, for an area of roughly 1650 m2
, with a
maximum roof height of approximately 24 m.
The structural configuration consists of heavy
masonry walls and stone piers supporting the weight
of a thin masonry vaults. Both the central nave and
the side aisles have four spans. The maximum height
of the vaults of the central nave is around 20 m,
while that of the side aisles is approximately 13 m.
The roof of the Cathedral is made of wooden trusses
and beams and is separated from the main hall by a
wooden-concrete floor, as detailed in the next sec
tion. Next to the Cathedral, there is the Ghirlandina
Tower, a high tower of roughly 88 m high whose
construction proceeded in parallel with that of the
Cathedral up to the fourth level.
2.3. Specific fire system vulnerabilities of the
Modena Cathedral
The system vulnerabilities listed in the previous sec
tions are analyzed with respect to the Modena
Cathedral.
2.3.1. Massive presence of wooden structural and
non-structural elements (or other elements vulnerable
to fire)
The roof structure (both beams and trusses) is wood, while
the walls are made of massive masonry (see Figure 3).
2.3.2. Valuable content
A number of pieces of art are present in the Modena
Cathedral. (For an exhaustive list of valuable content
please see http://www.unesco.modena.it/en/plan-your-
visit/cathedral?set_language=en and https://it.wikipedia.
org/wiki/Duomo_di_Modena.) The most important
point is that all these contents can be damaged or get
lost due to fire. Also, many artistic elements are made in
wood, one of the most important masterpieces being the
Inlaid wooden “pontile” made in 1461–1465 (Figure 4),
having an inestimable monetary value.
2.3.3. Absence of active protection and of adequate
compartmentations
Although a fire suppression system is not present in
the Cathedral, there is a smoke detection system,
which is important for decreasing the fire fighters’
intervention time. As for a large part of cathedrals
around the world, two main (large) compartments
are individuated in the case study: the main hall for
religious functions is the first compartment (which
is relevant for evacuation studies), while the loft (the
service/ storage cubature under the roof, which is
relevant for fire development due to the presence of
the wooden roof) is the second one. It is important
to say that the two are divided by the floor of the
loft, which is made by a mixed wood-concrete struc
ture. This kind of dividing layer between the two
compartments is not fully fire-resistant; then it is
INTERNATIONAL JOURNAL OF ARCHITECTURAL HERITAGE 3

assumed to be a conventional fire strength of 30 min
when the fire develops in the loft. After that fire
exposition time, the floor is assumed to collapse
down in the main hall.
2.3.4. Storage of flammable substances or
non-conformity of electrical installations
The short electricity circuit is considered the most sui
table fire source in the Modena Cathedral, especially in
the loft where electrical cables and stations are present
(see Figure 5b).
2.3.5. Presence of a large amount of people
(churches and museums)
The presence of crowd is possible in the Modena
Cathedral during religious functions (see Figure 6a),
something that can be critical for the safety of people
in fire. Emergency exits are shown in Figure 6b.
2.3.6. Difficulties of being approached by fire
brigades and by rescue vehicles
This is a minor vulnerability of the case study. In fact,
the fire fighters’ station is quite near to the Modena
Cathedral (3 km), also it is located in a historical center
with narrow access reads (see Figure 7). The peculiarities
of the location of the case study, together with the above-
mentioned presence of a smoke detection system, allow
for the consideration of a time interval of 10 min as a
suitable average total intervention time (from the igni
tion to the arrival of fire fighters) in case of fire (see
details in Section 3.4).
2.3.7. Possible indirect involvement due to the
vulnerability of other units of the building cluster
which can make the single heritage building subject
to fire spread or collapse spread
The Cathedral Museum is stored in a building
located adjacent to the case study. The museum is
characterized by a significant combustible load due to
the presence of the library. Due to the presence of an
automatic fire detection and suppression system in
Table 1. Recurrent system vulnerabilities of heritage buildings for fire.
Characteristic Related system vulnerability
1 Massive presence of wooden structural and non-structural elements (or
other elements vulnerable to fire)
Roofs and slabs of heritage buildings are commonly made of wooden
structural elements, which may participate to the combustion process in
fire events.
2 Valuable content The value of the content and of the structure itself makes the risk for these
elements comparable with the risk for the safety of the occupants.
3 Absence of active protection and of adequate compartmentalization Due to their architecture, fire compartments in heritage buildings are large,
adequate compartmentation is not present. Active fire suppression
systems ae also rarely present, especially in churches and cathedrals.
4 Storage of flammable substances or non-conformity of electrical
installations
Electrical installations are often not certified from the fire safety point of
view and short electrical circuits are common fire ignition causes. In
addition, especially in churches and museums, some internal spaces of
the buildings (mainly those that are not accessible to external people) are
often used as storage of unused, disposed and flammable materials
(books, wood furniture, flammable chemical products, etc.).
5 Planned presence of a large amount of people (churches and museums) In some cases, heritage buildings are susceptible of crowding, such as in
churches and museum.
6 Difficulties of being approached by fire brigades and by rescue vehicles Heritage buildings are often located in the historical center of urban areas,
this implies significant difficulties (due to the narrow road or to the loss of
pressure in the hydraulic infrastructure) in being approached and served
by emergency vehicles in case of fire.
7 Possible indirect involvement due to vulnerability of other units of the
building cluster which can make the single Heritage Building subjected to
fire spread or collapse spread.
Heritage buildings are not isolated structures, but they are often part of
building aggregates in the historic center of the urban area. This make
them susceptible to events like fire spread from other adjacent units or of
being physically involved by partial or full collapses of these buildings.
Figure 2. External behind-lateral (a) and frontal (b) view of the
Modena Cathedral.
4 F. PETRINI ET AL.

the museum, the probability that a fire occurring in
one of the two buildings (Museum or Cathedral) can
spread to the other is considered irrelevant.
On the basis of identified system vulnerabilities for the
case study, the set of loss scenarios defined in the fault tree
are referred to the loss of the roof wooden elements in the
case of Figure 9 are associated with their collapse over the
loft, and then to the collapse of the loft floor on the inlaid
wooden “pontile”, which is located just in the bottom of
the loft area where the fire is located. The full list of the
considered loss scenario is: no damage, limited damages to
the roof, average damages to the roof wooden elements and
Figure 3. Structural elements in the case study of the Modena Cathedral. (a) Roof and walls schematic representation and (b) detail of
roof structural elements.
Figure 4. Inlaid wooden “pontile”. (a) Views and (b) location inside the main hall.
Figure 5. Electrical cables as main fire ignition sources (duo to a short circuit) in the loft.

Figure 6. Presence of large amount of people. (a) Presences during the Christmas midnight celebration and (b) emergency exits in the
main hall.
Figure 7. Difficulties of be approached by rescue vehicles. (a) Google® aerial view and (b) Google® street view of narrow connecting
roads.
6 F. PETRINI ET AL.

partial loss of it, considerable damages to the roof wooden
elements and loss of a considerable amount of it, complete
loss of the wooden roof, and significant damages to the
content below it (the inlaid wooden “pontile”).
The loss scenarios identified with the above charac
teristics will be treated as different values of the x-axis of
the graph in Figure 1.
2.4. Procedure and methods for structural fire risk
analysis
This section qualitatively summarizes the procedure
and methods for fire risk assessment in heritage
buildings that will be quantitatively applied to a
case study for the evaluation of the structural fire
risk in probabilistic terms and for obtaining the fire
Figure 8. Flowchart of the procedure for probabilistic risk assessment in the PBFE format.

risk curve of Figure 1 as a final outcome of the
procedure for probabilistic PBFE purposes. The risk
evaluation is based on the event tree approach
(NFPA 2017; SFPE 2002); then it implies the defini
tion of several fire scenarios and a series of plausible
events that define the tree for each scenario.
Furthermore, the event tree implies the assignment
of probabilities to each branch.
The procedure is resumed in the flowchart of Figure
8, and it is composed by six different analysis steps to be
developed in sequence.
Given a case study heritage building, step 1 consists of
evaluating which of the previously introduced system
vulnerabilities apply to the case study. The identification
of these system vulnerabilities is crucial for the definition
of the events to be considered in the tree analysis. An
example of events used in a tree analysis is shown in the
upper part of Figure 9, including: fire ignition, fire extin
guished by personnel; fire extinguished by sprinklers (if
present), intrusion of firefighters; and fire suppression.
Step 2 concerns the definition of appropriate fire
scenarios to be considered in the analysis. The defi
nition of such scenarios must take into consideration
the different compartments and the possible fire
ignition events that can occur in the case study.
The assignment of pertinent occurrences to the dif
ferent fire ignition event is a crucial point here, and a
detailed discussion on this point is provided in the
application section. A fire scenario is considered as
fully defined by four parameters: the fire location and
ignition cause, the fuel load, and the ventilation
parameter.
These parameters serve as input for step 3, which
implies the fire dynamic analysis by a numerical
thermo-fluid dynamic model, which is based on the
computational fluid dynamic (CFD) methods includ
ing thermal equilibrium equations for the air in the
compartment. The thermo-fluid dynamic governing
equations of fluids generally consist of a set of three-
dimensional, time-dependent, and nonlinear differen
tial equations known as Navier–Stokes equations (Salvi
2002). Since the closed form solution of Navier–Stokes
equations have not been provided in literature, the fire
dynamics id investigated by numerical methods. It is
necessary to model the fire compartment by dividing
the environment into cells (e.g., grid of parallelepi
peds): the differential equations must be discretized,
written and solved incrementally at each node of the
Figure 9. Example of event-tree diagram for fire risk analysis.
8 F. PETRINI ET AL.

grid. These models represent the most refined fire
simulation currently available but have the drawback
of being very expensive in terms of calculation time.
The detailed CFD analysis for fire dynamics is neces
sary for the obtainment of detailed air temperature
patterns around structural elements to be used as
input in the successive thermal and structural analy
sis (step 4). The fire dynamics numerical simulation
is needed especially in presence of wooden elements
(which can be involved in the fire) and in order to
explore the effect of different combinations of com
bustible load, ventilation, and compartmentation
geometry.
The successive step 4 (thermal and structural ana
lyses) is carried out by advanced, nonlinear, FE mod
els. As already anticipated, in this paper an affordable
method is proposed for the thermal and structural
analysis step: additional details on the proposed
method are given in the next section. The outcome
of step 4 is the detailed structural response under
fire. This will be efficiently identified by average
values for the collapse time (or capacity time) of
the structure under fire.
The knowledge of the capacity time for each fire
scenario allows the analyst to assign informed, heuristic,
probability values to the fault tree branches related to the
structural response, which, together with the considera
tions related with the probabilities of the other events of
the tree, permits the quantitative probabilities char
acterization of the event tree branches (step 5). At
the end of the first five steps of the procedure, for
each scenario an event-tree diagrams like the one
shown in Figure 9 is developed. The following well-
known points apply:
an occurrence probability must be assigned to
each couple of branches at each event (i.e., “Fire
ignition”, “Fire location”, etc. in Figure 9) concur
ring to the sequence which determines the fire
evolution. These couple of probabilities must be
intended as conditional to the previous event occur
rence and, inside the same event, the couple of
probability values must be mutually exclusive and
collectively exhaustive (sum of the probabilities of
the two branches must be 1);
the assignment of each of the occurrence prob
ability values is made by the fire analyst/designer,
and is based on the vulnerabilities of the building
(step 1), on the fire intensity parameters (step 2),
on the fire evolution computed by the numerical
(CFD) analyses (step 3), and on the structural
response evaluations (step 4) as described in next
sections for the case study and for each considered
scenario;
one of the most critical point of the risk analysis is about
the assignment (made by the risk analysts) of the triggering
event probability with reference to a specified “return per
iod” Tr (step 2). This probability (farthest black box on the
left in Figure 9) is assigned on the basis of the experience of
the risk analysts and, as of today, it is still quite arbitrary
due to the lack of sample statistics in the literature regard
ing fires affecting cultural heritage buildings; and the fire
intensity probability (which is conditional to the fire trig
gering event) has to be assigned. This probability can be
assigned on the basis of the building use and the material
stocked in the considered compartment.
As previously mentioned, the important point here is
how to define the fault tree for arriving to the quantifi
cation of the total structural fire risk for heritage build
ings by the PBE format shown in Figure 1. For this
purpose, it is necessary to assign, at the end of each
branch of the event tree, a damage or loss scenario,
which is related to the extension of the structural
damage suffered by the building and its content. The
set of loss scenarios in the fault tree should be identified
such as:
they are graduated from the less to the most
severe, depending on the successive activation of the
branches at each event of the tree;
they should be the same for all the considered fault
trees (all considered scenarios);
they should be connected to (or referred to) structural
limit states for the building, and be identifiable by the
verification of some response thresholds for the struc
tures (in the example figure, they are referred to limit
states of the wooden roof); and
if possible, they should be associated to the corre
sponding damage or loss of the valuable non-structural
content of the building.
2.5. Proposed affordable model for nonliner
thermal and structural analysis of wooden
structures under fire
In this section, a numerical model technique for the
evaluation of the structural behavior of wooden beams
under fire is presented, with the goal of rendering it a
practicable/affordable way for the nonlinear analysis of
heritage structure by the avail of commercial FE codes
implementing temperature-dependent material
characteristics.
The thermal (heat transfer) analysis is carried out by
using beam finite elements in order to investigate the
temperature transmission along the beams axis and not
along the cross-section. The FE numerical model of the
structural components must be capable of:

receiving the output coming from the CFD model
above, consisting in the time-air temperature curves in
different locations around the structural wooden ele
ments, and using them as input for a thermal analysis
to investigate heat diffusion and temperature along the
elements main axis. The thermal analysis should take
into account the wood thermal conductibility trend with
the temperature; and
the output of the above-mentioned thermal FE
analysis, consisting in the time-internal temperature
curves in structural elements, is used as input for
assigning material decay laws to the structural ele
ments. Then a nonlinear structural analysis with
material decaying (temperature–dependent) non
linear characteristics and large displacements is con
duced. Since dynamic inertial effects can be usually
neglected in fire structural response (excepting for
the final kinematic progressive collapse phase, if pre
sent), the analysis can be carried out by pseudo-static
solution techniques.
Before discussing the structural model proposed in
this work it is appropriate to briefly discuss the
behavior of the structural wood material when sub
jected to high temperatures.
Wood is a combustible organic material and in case
of fire it participates in the combustion by losing mass
from the surface exposed to the fire inward. The fire-
exposed layer of wooden surfaces carbonizes and con
tributes no more to the mechanical strength of the
structural wooden element. Under prolonged exposition
to fire, the carbonization gradually increases in depth,
then gradually involving successive inward layers.
Figure 10. Carbonization process for wood elements. (a) Schematization of surface carbonization; (b) schematization of beam cross-
section decreasing due to carbonization; and (c) experimental example of carbonization. Adapted from Ponticelli and Caciolai (2008).
Figure 11. Decay of wood mechanical proprieties with the temperature: (a) strength and (b) elastic modulus. Adapted from UNI EN
1995–1–2 (2005).
10 F. PETRINI ET AL.

Before the carbonization occurs in a specific layer, a
non-carbonized heated wood layer under the carbonized
one, experiments the decay of its mechanical proprieties
due to the exposition to high temperatures (“Altered
zone” in Figure 10). This effect is significant for the
structural tension and compression strength only in
the direction of the woodgrains/fibers. Decay coeffi
cients for fibers’ strengths as well as for the elastic
modulus with the temperature is shown in Figure 11,
the last one differentiating between tension and com
pression behaviors.
If not conducted with specialized numerical codes,
the numerical simulation of structural wooden elements
under fire is quite complicated to be carried out by
commercial finite element codes due to the presence of
the carbonization effect. Which is the reason why the
cross-section of the wooden structural elements must be
considered as layered. This can be accomplished by
using brick finite elements in a 3D analysis.
Nevertheless, when the considered structure is complex
in geometry or extended in size, and when there is the
need for carrying out a global structural analysis, the use
of brick FEs can be computationally prohibitive. Here an
affordable model made by beam finite elements is pro
posed for conducting the nonlinear structural analysis
phase by limiting the computational burdens. In the
proposed model, a wooden structural element is sche
matized by using different superimposed (i.e.,
connecting the same extremal and intermediate nodes)
beam elements, each one representing a different layer
considered for schematizing the carbonization.
Considering a beam under bending or axial loads,
and assuming that the discretization of the cross-
section for the simulation of the carbonization process
can be schematized by three different layers (see Figure
12): the first (external) and second (intermediate) layer
are constituted by hallow core cross-sections, while the
central (core) layer is constituted by a rectangular cross-
section. Each layer is assigned with the temperature-
dependent decay law characterizing the wood material
for the elastic modulus and the strength shown in Figure
11. In first instance, the thermal analysis along the cross-
section can be avoided (especially for normal thicknesses
wooden elements) and the heat propagation inside the
elements’ cross-section, implying the gradual involve
ment of internal layers can be taken into account by
differentiating the beginning time of the temperature-
dependent decay laws for the layers, by delaying the
beginning of the decay of the internal layer proprieties
with respect to the beginning of the external adjacent
one, e.g., the proprieties of the internal layers start
decaying when the adjacent external layer fully loses its
mechanical strength due to the carbonization.
Considered layers, reference can be made to the UNI
EN procedure for the determination of the carbonized
thickness shown in Figure 13. The procedure implies to
Figure 12. Discretization of the cross section by three layers.

set a correspondence (on the base of the time-
temperature curve obtained from the CFD analysis)
between the time (which is parameter used for the car
bonization thickness) and the temperature (fire intensity
measure used in the analysis).
3. Results
3.1. Fire hazard analysis (FHA) of the modena
cathedral
A detailed description of the FHA carried out for the
case study is provided in this section, implying the
pragmatic setting of different hazard parameters as
listed below. The considered cases are not exhaustive
for all fire scenarios that should be taken into
account in a complete FHA and are considered only
for illustrative purposes. It is worth noting that the
consideration of a very limited number of fire sce
narios in the FHA does not compromise the general
validity of the proposed approach. The relevant para
meters for the definition of fire hazard scenarios are:
the fire triggering event (location and cause), fuel
load, and compartment ventilation, set to the values
specified below for the FHA of the case study.
4. Fire triggering event
● Fire triggering location. Two fire locations are
considered inside the building: (1) loft in the
zone above the Inlaid wooden “pontile” in a 2
m^2 fire area; (2) main hall.
● Fire ignition causes. Two cases are considered for
the locations (1) and (2) above, respectively: (a)
electrical short circuit in the loft; (b) presence and
propagation of free flames in the main hall.
● Fire load q. Two different combustible loads q are
considered: (i) q = 500 MJ/m^2; (ii) q = 1000 MJ/
m^2.
● Ambient ventilation V. Two cases of ambient
ventilation conditions are taken into account: (i)
FULL ventilation (fuel-controlled fire — V = 1); (ii)
NO ventilation (combustible-controlled fire — V
= 0).
From the combinations of the above values of the
hazard parameters, a set of fire scenarios can be defined
to carry out (for each of them) the event tree analysis:
four cases can be considered coming from the combina
tion of fire loads and ventilation conditions:
(i) q = 500 MJ/m^2+ NO ventilation (V = 0);
(ii) q = 1000 MJ/m^2+ NO ventilation (V = 0);
(iii) q = 500 MJ/m^2+ FULL ventilation (V = 1); and
(iv) q = 1000 MJ/m^2+ FULL ventilation (V = 1).
The intensity parameters are used to define the Heat
Release Rate (HRR) curves (Buchanan and Abu 2017)
to use as input for the successive fire dynamics
simulations.
The two values assumed for the fuel load equal to 500
MJ/m^2 and 1000 MJ/m^2 are chosen in order to exam
ine extreme values in a significant range of fire severities.
The same is made for the ventilation values, taken as
two extreme possible cases. Regarding the adopted
values for the fuel loads, in Buchanan (2001), the fuel
load indicated for churches is equal to 200 MJ/m^2,
while in Duthin (2014) the fuel load indicated for
churches is equal to 400 MJ/m^2. These fuel loads
are considered reliable by the authors for the case of
fire in the main hall, while when fire is considered to
occur in the loft, with the additional assumption that
some combustible material is improperly stored there,
the above-mentioned values of 200 or 400 MJ/m^2 are
considered inadequate for this situation. The fuel value
to be considered for the fire in the loft strictly depends
on the kind of combustible material which is assumed
as stored in the loft. It, in theory, can range from
clothes or printing paper (500 MJ/m^2 from references
Figure 13. Determination of the carbonized thickness. Adapted from UNI EN 1995–1–2 (2005).

above) to more hazardous material like paints (1000
MJ/m^2 from the references above). The combinations
of the assumed values for the fuel load and the ventila
tion allowed the authors to analyze the structural
response under different fires (high temperature and
fast fires to lower temperature-slow fires and inter
mediate situations).
For sake of clarity, the four fire intensities (i) to
(iv) are represented in Figure 14 in terms HRR
curves, clearly showing how the file load plays a
role in defining the peak value of the HRR, while
the ventilation conditions play a role in the fire
duration.
Due to the facts that the fire load q in the loft is
uncertain, and that the ventilation conditions in the
loft can vary during the life cycle of the structure
because it mainly depends on the doors that regu
late the air exchange between the loft and the main
hall, all the (i) to (iv) cases should be considered in
the loft, while in the main hall the NO ventilation
condition is not applicable due to the large value of
the ratio between the size of the compartment (the
whole main hall) and the size of the volume occupied
by the combustible material (wooden benches and
cloth curtains), which implies high ventilation condi
tions are always realized, then in the main hall the
fire intensities can be limited to (iii) and (iv).
In the view of the above considerations, a total of
six fire scenarios are identified for definition of the
event tree analysis: the four scenarios related to the
verification of the above fire intensity conditions (i)
to (iv) in the loft (i.e., 1 + a fire triggering events
above), and the two scenarios related to the verifica
tion of the fire intensity conditions (iii) and (iv) in
the main hall (i.e., 2 + b fire triggering events above).
As explained in previous sections, for each sce
nario the event-tree diagrams like the one shown in
Figure 9 (referring the scenario coming up from the
1 + a fire triggering events and the fire intensity (i)
above) is developed. The triggering event probability
is here fixed with reference to a specified “return
period” Tr equal to 50 years. As already said, the
assignment of this probability value is arbitrary, espe
cially in case of heritage buildings. For the consid
ered case study, the occurrences assigned to the
different triggering events are shown in Table 2.
4.1. Fire dynamic modeling in the Modena
Cathedral for fire risk analysis purposes
The fire simulation software solving CFD equations used
in the present study is the Fire Dynamic Simulator (FDS)
provided by the NIST (McGrattan et al. 2009). CFD
model both of the whole Modena Cathedral and of the
loft compartment has been created and analyzed in FDS,
the wooden elements of the roof (beams and trusses) are
modeled as combustible material. FDS models are shown
in Figure 15 (whole building) and 16 (loft compartment
only). The fire FDS simulations allowed, for each
Figure 14. Fire Intensity. HRR curves for different combinations of q (combustible load) and V (ventilation factor).
Table 2. Arbitrary occurrences assigned (for Tr = 50 yrs) to the
triggering events.
Triggering event
(reference is made to the list of parameters
provided in the main text above)
Assumed occurrence
is 50 years
1)+a)
short electrical circuit in the loft compartment
30%
2 + b)
free flames in the main hall
1%

considered fire scenario to: (1) assign informed probabil
ities P1 and P2 at some branches of the event-tree dia
gram of Figures 9 and 20 on the basis of the evolution
time and severity/diffusion of the fire in the compartment;
and (2) extract the temperature time histories at the loca
tions of the external surfaces of the structural elements to
be used as input for the successive structural analysis.
FDS outputs (temperature contour plots, air tempera
ture time histories, smoke visualizations) are not shown
here for sake of brevity. What is important to highlight
here is that accurate sensitivity and convergence analyses
have to be carried out before accepting the results pro
vided by the working model as reliable for fire dynamics.
4.2. Thermal and structural analyses carried out for
the modena cathedral
Results coming from the CFD, thermal and structural
analyses, when conducted in series for the risk evalua
tions related to the fire scenarios involved in the event
tree analysis of Figure 9 (case 1 + a: fire in the loft
compartment), are shown in Figures 16, 17 and 18 for
the cases: q = 1000 MJ/m^2+ NO ventilation (V = 0); q
= 500 MJ/m^2+ FULL ventilation (V = 1); and q = 1000
MJ/m^2+ FULL ventilation (V = 1), respectively. The FE
model for thermal and structural nonlinear analysis is
built by the commercial code STRAUS 7® (www.hsh.
info) and is shown in the bottom-left panel of the fig
ures, focusing on the portion of wooden roof interested
by the fire.
The output of the Fire Dynamics CFD analyses in the
loft (time–air temperature curves around different loca
tions in structural elements) are used to conduct first a
heat transfer analysis on beams finite elements (tem
perature is diffused along the beam axis), and then a
subsequent structural analysis to investigate the struc
tural response of the wooden roof in Modena Cathedral.
For demonstrative purposes, results of the heat transfer
analysis in terms of time-temperature curves for the
node 61 (which is located at mid-span at the wooden
beam just above the fire location) are shown in the
Figure 15. FDS model of the whole building (developed in Pyrosim®https://www.thunderheadeng.com/pyrosim/).
Figure 16. FDS model of the loft compartment (blue layers are for output reading purposes only).

upper-left panels of the figures. Proceeding in clockwise
direction, the time history of the vertical displacements
of the nodes at midspan of transversal wooden trusses
are shown in the upper-right panels of the figures, while
the time history of the vertical displacement of the
bottom wooden truss (node 15 in the figure) is shown
in the bottom-right panel.
Results shown in Figures 16, 17, and 18 are crucial to
formulate an informed judgment about the structural
performances and to quantify the necessary time for
the structural damage or collapse under fire (called
“capacity time” in what follow) to occur, and to con
nect them to the fire intensity in the considered sce
nario. The capacity time under a certain fire scenario is
directly related with the chance, for fire fighters, to
enter in the building and suppress the fire before struc
tural response degenerates in a collapse, or with the
chance of suppressing the fire by automatic systems
(e.g., sprinklers).
The damage or collapse of the structural elements can
be identified by a set maximum acceptable vertical dis
placement thresholds under fire. Specifically, by assum
ing (both for the transversal wooden beams and the
bottom beam of the truss) that a significant damage to
the elements occurs at a vertical displacement equal to 1/
50 of the length of the element, and that the collapse
occurs for a vertical displacement equal to 1/20 of the
length of the element, the capacity time of the structural
elements can be quantified from Figures 16, 17, and18 as
shown in Tables 3, 4, and 5, respectively. It is evident
from the figures and the tables that the fully ventilated
fire cases are critical for structural performances
Figure 19
This is something driving the attribution of condi
tional probability values to the arms corresponding to
the semi-last step in the event-tree diagram of Figure 9
(event “3. Intrusion of the fire fighters”). This step of the
procedure will be discussed in detail in the next section.
As a preliminary consideration it can be said that if large
peak vertical displacements are reached in very short
time by the roof beams during the fire (low values of
the capacity time), it can be pertinently assumed that the
probability of suppressing fire before collapse is very
low. In the considered cases, it can be quantified that
the capacity time for the “significantly damaged” condi
tion ranges between 400 and 700 sec at different fire
intensities, while the capacity time for the “collapse”
(occurring only in fully ventilated fires) ranges between
480 and 700 sec. The already-defined loss severities (see
Section 2.4) are associated to each outcome of the ther
mal and structural analysis as shown in the last line of
Tables 3, 4, and 5.
Figure 17. Summary of the thermal/structural response. Location: loft compartment; Ignition: short electric circuit; q = 1000 MJ/m2
; NO
ventilation.

4.3. Fire risk assessment for the Modena Cathedral
In this section, the procedure for the fire risk evalua
tion and expression by the PBE format shown in
Figure 1 is explained.
Depending on the specific vulnerabilities identified in
the building in Section 2.3, taking into consideration the
fire hazard scenarios defined in Section 3.1, and thanks
to the numerical analyses carried out for the case study
concerning the thermal and structural response as
described in Section 3.3, pertinent assignments of the
conditional probabilities to each couple of arms at each
event (concurring to the sequence which determines the
fire evolution like the one shown in Figure 9) can be
accomplished by expert judgment of the risk scenario.
As already said (see Section 3.1), four fire intensity
scenarios are defined for the fire-triggering condition
implying an electrical short circuit in the loft. First of all,
appropriate probabilities (which are conditional to the
occurring of fire in the loft due to an electrical short circuit)
are assigned to the different fire intensities, as shown in
Figure 20.
;
FULL ventilation (V = 1).
Table 3. Evaluated capacity times. Short electrical circuit in the loft compartment with q = 1000 MJ/m^2+ NO
ventilation (V = 0).
Case
q = 1000 MJ/m^2+ NO
ventilation (V = 0)
Significantly
damaged
(1/50*L)
Collapsed
(1/20*L)
Structural element Transversal beam (L = 4.0
m)
(vert displ =0.08 m)
600 sec (only
one truss)
(vert displ =0.2 m)
No
Bottom beam of the truss
(L = 9,6 m)
(vert displ =0.2 m)
No
(vert displ =0.5 m)
No
Loss severity Limited damages to
the roof
Average damages to the roof wooden elements
and partial loss of it

Table 4. Evaluated capacity times. Short electrical circuit in the loft compartment with q = 500 MJ/m^2+ FULL
ventilation (V = 1).
Case
q = 500 MJ/m^2
+ FULL ventilation
(V = 0)
Significantly damaged
(1/50*L)
Collapsed
(1/20*L)
Structural element Transversal beam
(L = 4.0 m)
400 sec
(vert displ =0.2 m)
No
Bottom beam of
the truss (L = 9,6
m)
(vert displ =0.2 m)
410 sec
(vert displ =0.5 m)
480 sec
Loss severity Average damages to the roof
wooden elements and partial
loss of it
Considerable damages to the roof wooden
elements and loss of a considerable amount
of it
;
FULL ventilation (V = 1).
Table 5. Evaluated capacity times. Short electrical circuit in the loft compartment with q = 1000 MJ/m^2+ FULL ventilation (V = 1).
Case
q = 1000 MJ/m^2+ FULL
ventilation (V = 1)
Significantly damaged
(1/50*L)
Collapsed
(1/20*L)
Structural element Transversal beam
(L = 4.0 m)
700 sec
(vert displ =0.2 m)
700 sec
Bottom beam of the
truss (L = 9,6 m)
(vert displ =0.2 m)
700 sec
(vert displ =0.5 m)
700 sec
Loss severity Considerable damages to the roof wooden elements
and loss of a considerable amount of it
Considerable damages to the roof wooden elements
and loss of a considerable amount of it

On the basis of the results obtained by the CFD,
thermal, and structural analyses, for each scenario,
appropriate conditional probabilities are assigned to
different paths of the event-tree diagram for fire risk
analysis. As already said, the structural capacity time
can be used to attribute pertinent values of the condi
tional probability characterizing the event named “3.
Intrusion of fire fighters” in Figure 9. For example, the
value P2 = 20% attributed to the “YES” realization of the
event for the case q = 1000 MJ/m^2; and FULL ventila
tion (V = 1) considered herein, is based on the following
considerations (Kerber 2012; Särdqvist and Holmstedt
2000):
3–4 min (=120–180 sec) is the time lapse that can be
considered from the fire ignition to the starting of the fire
fighters from the station. This time lapse includes the
following phases: (i) smoke detection (by the automatic
detection system which is present in the case-study); (ii)
fire alarm communication to the fire fighters; and (iii)
preparation of the fire fighters squad and intervention
starting;
4–6 min (=240–360 sec) is the time evaluated as
necessary for the fire fighters to travel from the nearest
fire fighters station to the structure in emergency
(alarm on) conditions. This time is evaluated by appro
priately decreasing the time evaluated as necessary for a
car to start from the nearest fire fighters station to the
structure (see Figure 7), that is equal to 10 min
(=600 sec);
1–2 min (=60–120 sec) is the time elapsing from
arrival to the intrusion and the intervention of the fire
fighters; and
2–6 min (=120–360 sec) is the necessary time for fire
suppression in the case of a 2 m^2 fire area as assumed
in the case study.
On the basis of the above considerations, the total
necessary time for the fire detection, the fire fighters’
intervention and intrusion, and the fire suppression in
the case study is evaluated as varying between 600 to
1080 sec (10 to 18 min). By considering an uniform
probability density function for the distribution of this
total time, it emerges that it is less than the evaluated
capacity time (700 sec as reported in Table 5 for the
considered case) in 20% of cases (evaluated as [700–
600]/[1080–600]), which is exactly equal to the prob
ability P2 assigned to the tree corresponding to the fire
fighters intrusion and fire suppression in Figure 9, and
corresponding to the pertinent loss severity, as shown in
Table 5. Regarding the last point, it has to be said that if
the fire fighters cannot enter in the building (e.g.,
because the a certain loss severity already occurred at
their arrival), the fire fighters are considered to operate
externally to the building, with a consequent increasing
of loss severity.
Regarding the other events and the probabilities
assigned to the branches in Figure 9, they can be
explained as follows (starting from the left toward the
right side of the figure):
the occurrence of the 30% for having an electrical
short circuit in the loft is referred to a reference period
of 50 years and is assigned on the basis of the occur
rences of fire in historic buildings found in literature (see
e.g., Li et al. 2020);
given the above-mentioned occurrence, the condi
tional probability for the fire intensity equal to 1% is
assigned on the basis of the use of the loft as chaotic
storage for dismissed flammable goods or paper. The
conditional probability assigned to the different consid
ered intensities (also shown in Figure 20) are mainly
based on the plausibility of the fire load, while ventila
tion is simply set to the maximum or minimum plausi
ble values due to the large uncertainty affecting this
parameter;
the conditional probability P0 assigned to the fire
ignition is still based on the literature survey and is
taken as inversely proportional to the fire load (the
more is the fire load q, the less is the P0);
the probability P1 for the fire (if ignited) to be
suppressed by the personnel is fixed on the basis of
the fact that the building is not presided 24 hr per
day (something limiting the P1 to some maximum
values) and on the facts that, from one side the fire
alarm is supposed to be very efficient due to the
presence of a smoke detection system (something
increasing P1 with respect to the case where the
smoke detection is not present), and from the other
side is supposed that the chance of suppressing the
fire by personnel is (as logical) inversely proportional
to the fire load (the more is the fire load q, the less is
the P1);
Figure 20. Conditional probabilities assigned to the fire intensity
parameters in the loft compartment.

P2 has been already discussed above; and
the quantification of P3 regards the possibility of the
fire to be suppressed by the fire fighters acting from the
outside of the building due to the fact that they was
prevented to enter in the building due to the unsafety
of the action. In Figure 9 the P3 is set equal to 10%
(lower than other fire intensity cases) because it is
assumed that, if fire fighters reach the building and
cannot enter inside it due to such a unsafe conditions,
the fire is extensively diffused along the roof.
On the basis of the above considerations, for explana
tion and comparison purposes, the probabilities attribu
ted to the branches of the event tree diagram for different
fire intensities are shown in Figure 20 and Table 6.
Obviously, such a probability values are arbitrary and
assigned by an expert judgment on the basis of all the above
considerations and analyses applied to the case study. This
is the critical point of the fire risk analysis and large
research efforts are required in defining clear and reliable
criteria for the assignment of these probabilities. Figure 21
Figure 21. Comparison of the probabilities attributed to the branches of the event tree diagram for different fire intensities. Short
electrical circuit in the loft compartment.
Table 6. Comparison of the probabilities attributed to the branches of the event tree diagram for different fire
intensities. Short electrical circuit in the loft compartment.
P0
(Fire
ignition)
P1
(Fire extinguished by
personnel)
P2
(Intrusion of fire
fighters)
P3
(Fire
Suppression)
q = 500 MJ/m^2+ NO ventilation 40% 80% 90% 90%
q = 1000 MJ/m^2+ NO ventilation 50% 30% 30% 90%
q = 500 MJ/m^2+ FULL ventilation 50% 30% 20% 30%
q = 1000 MJ/m^2+ FULL
ventilation
50% 5% 20% 10%

When the assignment of the above-mentioned
probabilities is made, the structural fire risk asso
ciated to a return period Tr can be evaluated by
two steps:
first, the conditional probabilities corresponding to the
loss severities are evaluated for each fire intensity by the
series event combination rule applied to the P0 to P3
probabilities and their complements to 1. For example, as
shown in Figure 23, the value 7.2% assigned to the loss
severity “Average damages to the roof wooden elements
and partial loss of it” in the case of lower fire intensity in the
loft (q = 500 MJ/m^2+ NO ventilation) is evaluated as: P0*
(1-P1)*P2 = 0.4*(1–0.8)*0.9 = 0.072. All the conditional
probabilities found for the loss severities in the case of the
lower fire intensity is shown in Figure 22; and second, the
total risk associated to a certain loss severity is evaluated by
the combination of the conditional probabilities associated
to that loss severity at different fire intensities multiplied by
the occurrence assigned to the fire intensity and the occur
rence assigned to the triggering event with reference to a
return period Tr, as shown in Figure 23 for the loss severity
“Limited damages to the roof”.
The resulting total risks assigned to the loss severities
refers to a return period of 50 years and are the y-axis
values of the risk curve shown in Figure 24, representing
the complementary cumulative distribution function
(CCDF) probability in the return period Tr = 50 years:
5. Discussion
The procedure presented is quite complex and com
posed by different analysis steps implying a number of
solution methods (see Figure 8). Strong assumptions are
made regarding fuel loads, fire occurrences, firefighters
intervention times, and structural materials behavior.
Also, if the general validity of the proposed procedure
is not compromised by the assumptions, it is recognized
that significant additional research efforts are needed to
improve the reliability of quantitative results given by
the different steps and to decrease the current amount of
arbitrary/heuristic assignments made by the expert ana
lyst, which is currently the main weakness of the results
obtained by the proposed procedure. The main weak
ness/needed research efforts are detailed as follows:
Figure 22. Fire in the loft compartment. Conditional probabilities assigned to different paths of the event-tree diagram and probability
of each defined loss severity. q = 500 MJ/m2
; NO ventilation.

Figure 23. Fire in the loft compartment. Total fire risk evaluation for the loss scenario 1.
Figure 24. Obtained fire risk curve for the loft compartment with reference to Tr = 50 years.

● the definition of a reference period for risk eva
luation is conventional and, among other cri
teria, it should be calibrated on the structural
typology. In this sense the chosen Tr = 50 years
is probably the minimum value that can be
chosen for heritage buildings, and a collabora
tive discussion should be opened between expert
to indicate what is the most appropriate value to
consider for Tr;
● at of today, there are not adequate statistics (or
probability distributions) for fire events, espe
cially for heritage buildings. This is one of the
gaps that should be covered by further research
efforts and collaborative data sharing between
buildings administrators;
● the data assumed for the evaluation of the interven
tion time of the firefighters are highly arbitrary. All
the necessary actions for the establishment of the
performances of firefighting in historical buildings
(and in the built environment in general) depending
on some specific parameters (e.g., geographical region
where the building is located, the building typology,
the building dotation by a smoke detection system, or
distance and street congestion between the firefight
ing station and building, etc.) should be put in place to
decrease the arbitrarity of this point. This can be done
by recording and disseminating regional statistical
data regarding the performances of the firefighting,
and by categorizing the data in dependence of the
above-mentioned parameters; and
● as a final remark, it is suggested that additional
research efforts should be focused on the definition
of reliable and clear criteria for the assignment of the
conditional probability values to the different
branches of the event tree analysis, that is at the base
of the structural fire risk analysis and that, as of today,
is higly dependent to the arbitrary judgment of the
analyst.
6. Conclusions
A detailed methodology for structural fire risk analy
sis in heritabe Buildings has been conceived and
applied to a case study (the Modena Cathedral).
Peculiarities of both events like fire, and of the heri
tage buildings (related to specific system vulnerabil
ities to fire), are taken into account for the pertinent
definition of relevant fire scenarios and for the cor
rect estimation of the conditional probabilities asso
ciated to the different events to be considered in the
fire risk analysis. The fire hazard analysis is con
ducted by the event-tree method while the structural
behavior is investigated by advanced nonlinear
thermmechanical finite element models in order to
assess the performances of the building. As a final
result, the procedure produces a fire risk curve (loss
severity VS occurrences) with a reference to a pre-
defined return period Tr which, for fire hazard, has
been set to 50 years at least.
Following points can be highlighted as contributions
of the paper to the research in the field:
guidelines for the identification of the system vulner
abilities of heritage building to fire are provided to the
reader as a tool for the correct application of the event-
tree method;
an affordable model for the nonliner numerical struc
tural analysis of wooden structures under fire is pro
posed by the avail of n FE code able to consider the
degradation of the structural mechanical characteris
tics; and
the final outcome of the structural fire risk analysis is
presented by the performance-based risk curves which is
compatible to the modern performance-based engineer
ing format extensively implemented with reference to
other hazards like earthquake and wind.
Acknowledgments
Prof. Mario De Stefano of University of Florence, Prof.
Tommaso Trombetti and Dr. Michele Palermo from
University of Bologna are acknowledged for providing data
about the case study. Many thanks to Ing. Michele Fronterrè
for providing the license of the Pyrosim pre- post-processor
code (http://www.cantene.it/products/pyrosim/) used for the
models solved by FDS and to Ing. Piergiorgio Perin - HSH srl
Padova for providing the Staus7 software license used for all
the structural analysis (http://www.hsh.info/).
Disclosure statement
No potential conflict of interest was reported by the author(s).
Funding
This work was supported by the Italian Ministry of University
and Research (MIUR), PRIN 2015 funding framework,
research project MiCHe Mitigating the Impacts of natural
hazards on Cultural Heritage sites, structures, and artifacts
(ID No 2015WELAX9).
References
Audebert, M., D. Dhima, M. Taazount, and A. Bouchaïr. 2011.
Numerical investigations on the thermo-mechanical behavior
of steel-to-timber joints exposed to fire. Engineering Structures
33 (12):3257–68. doi:10.1016/j.engstruct.2011.08.021.

Augusti, G., and M. Ciampoli. 2008. Performance-Based
Design in risk assessment and reduction. Probabilistic
Engineering Mechanics 23 (4):496–508. doi:10.1016/j.
probengmech.2008.01.007.
Bernardini, G. 2017. Fire safety of historical buildings.
Traditional versus innovative “behavioural design” solutions
by using wayfinding systems. Switzerland: Springer
International Publishing.
Buchanan, A. H., ed. 2001. Fire engineering design guide. New
Zeland: Centre for Advanced Engineering, University of
Canterbury.
Buchanan, A. H., and A. K. Abu. 2017. Structural design for fire
safety. Chichester, Uk: John Wiley & Sons.
Carattin, E., and V. Brannigan 2012. Controlled evacuation in
historical and cultural structures: Requirements, limitations
and the potential for evacuation models, Proceedings of the
5th International Symposium on Human Behavior in Fire,
Interscience Communications Ltd., London, UK, pp. 447–59.
CFPA-E (confederation of fire protection associations in
Europe), 2013. Guideline No 30: Managing fire safety in
historical buildings. [Online]. https://cfpa-e.eu/wp-content
/uploads/files/guidelines/CFPA_E_Guideline_No_30_
2013_F.pdf .
Duthin, D. 2014. Structural design for fire: A survey of building
codes and standards. Gaithersburg, MD, Maryland: NIST
Technical Note 1842. doi:10.6028/NIST.TN.1842.
Ferreira, T. M. 2019. Notre dame cathedral: Another case
in a growing list of heritage landmarks destroyed by fire.
Fire 2 (2):20. doi:10.3390/fire2020020.
Franchin, P., F. Petrini, and F. Mollaioli. 2018. Improved
risk-targeted performance-based seismic design of rein
forced concrete frame structures. Earthquake
Engineering & Structural Dynamics 47 (1):49–67.
doi:10.1002/eqe.2936.
Gernay, T., N. E. Khorasani, and M. Maria Garlock. 2016.
Fire fragility curves for steel buildings in a community
context: A methodology. Engineering Structures
113:259–76. doi:10.1016/j.engstruct.2016.01.043.
Gernay, T., R. V. Coile, N. E. Khorasani, and D. Hopkin.
2019. Efficient uncertainty quantification method applied
to structural fire engineering computations. Engineering
Structures 183:1–17. doi:10.1016/j.engstruct.2019.01.002.
Guanquan, C., W. Jinhui, and W. Qingsong. 2012. Time-
dependent fire risk assessment for occupant evacuation
in public assembly buildings. Structural Safety 38:22–31.
doi:10.1016/j.strusafe.2012.02.001.
Günay, S., and K. M. Mosalam. 2013. PEER performance-based
earthquake engineering methodology, revisited. Journal of
Earthquake Engineering 17 (6):829–58. doi:10.1080/
13632469.2013.787377.
Guo, H., Y. Dong, and X. Gu. 2020. Durability assessment
of reinforced concrete structures considering global
warming: A performance-based engineering and experi
mental approach. Construction and Building Materials
233:117251. doi:10.1016/j.conbuildmat.2019.117251.
Hietaniemi, J. 2007. Probabilistic simulation of fire endur
ance of a wooden beam. Structural Safety 29 (4):322–36.
doi:10.1016/j.strusafe.2006.07.016.
Huang, Y.-H. 2020. The use of parallel computing to
accelerate fire simulations for cultural heritage
buildings. Sustainability 12 (23):10005. doi:10.3390/
su122310005.
Hurley, M. J., and E. R. Rosenbaum. 2015. Performance-
Based Fire Safety Design. Boca Raton, FL: CRC Press.
Jingji, L., L. Hongwen, B. Zhou, X. Wang, and H. Zhang. 2020.
Investigation and statistical analysis of fire loads of 83
historic buildings in Beijing. International Journal of
Architectural Heritage 14 (3):471–82. doi:10.1080/
15583058.2018.1550535.
Kerber, S. 2012. Analysis of changing residential fire dynamics
and its implications on firefighter operational timeframes.
Fire Technology 48 (4):865–91. doi:10.1007/s10694-011-
0249-2.
Lange, D., S. Devaney, and A. Usmani. 2014. An application of
the PEER performance-based earthquake engineering fra
mework to structures in fire. Engineering Structures
66:100–15. doi:10.1016/j.engstruct.2014.01.052.
Li, J., H. Li, B. Zhou, X. Wang, and H. Zhang. 2020.
Investigation and statistical analysis of fire loads of 83
historic buildings in Beijing. International Journal of
Architectural Heritage 14: 3 (3):471–82. doi:10.1080/
15583058.2018.1550535.
Maio, R., T. M. Ferreira, J. M. C. Estêvão, B. Pantò, I. Caliòe,
and R. Vicente. 2020. Seismic performance-based assess
ment of urban cultural heritage assets through different
macroelement approaches. Journal of Building Engineering
29:101083.
McGrattan, K., B. Klein, S. Hostikka, and J. Floyd. 2009. Fire
research division building and fire laboratory in cooperation
with building and transport: Fire dynamics simulator (version
5) – user guide. Washington: NIST: NIST Special Publication
1019 – 5.
Memari, M., and H. Mahmoud. 2018. Framework for a
performance-based analysis of fires following earthquakes.
Engineering Structures 171:794–805. doi:10.1016/j.
engstruct.2018.05.099.
NFPA 914. 2001. National fire protection association, Code
for fire protection of historic structures. Quincy, MA:
National Fire Protection Association.
NFPA. 2017. National Fire Protection Association, NFPA 550:
Guide to the Fire Safety Concepts Tree. [Online] https://
www.nfpa.org/codes-and-standards/all-codes-and-
standards/list-of-codes-and-standards/detail?code=550 .
O’Reilly, G. J., and G. M. Calvi. 2019. Conceptual seismic
design in performance-basedearthquake engineering.
Engineering & Structural Dynamics 48 (4):389–411.
doi:10.1002/eqe.3141.
Pau, D., C. Duncan, and C. Fleischmann. 2019.
Performance-based fire engineering design of a heritage
building: McDougall house case study. Safety 5 (3):45.
doi:10.3390/safety5030045.
Petrini, F., K. Gkoumas, C. Rossi, and F. Bontempi. 2020.
Multi-Hazard assessment of bridges in case of hazard
chain: State of Play and Application to Vehicle-Pier
Collision Followed by Fire. Frontiers in Built
Environment - Bridge Engineering 6. doi:10.3389/
fbuil.2020.580854.
Pizarro, A., and E. Tubaldi. 2019. Quantification of modelling
uncertainties in bridge scour risk assessment under multi
ple flood events. Geosciences 9 (10):445. doi:10.3390/
geosciences9100445.
Ponticelli, L., M. Caciolai, and C. De Angelis. 2008.
Resistenza al fuoco delle costruzioni. Milan, Italy: UTET.
italian.

Quin, R., A. Zhou, C. L. Chow, and D. Lau. 2021. Structural
performance and charring of loaded wood under fire.
Engineering Structures 228:111491. doi:10.1016/j.
engstruct.2020.111491.
Salvi, R. 2002. The Navier-Stokes Equations. Theory and
Numerical Methods. London, UK: CRC Press.
Särdqvist, S., and G. Holmstedt. 2000. Correlation between fire
fighting operation and fire area: Analysis of statistics. Fire
Technology 36 (2):109–29. doi:10.1023/A:1015450308130.
SFPE. 2000. The SFPE engineering guide to performance-
based fire protection analysis and design of buildings.
Quincy, MA: Society of Fire Protection Engineers and
SFPE. 2002. SFPE Handbook of Fire Protection Engineering.
Quincy, MA: Society of Fire Protection Engineers and
Skelton, R. E. 2002. Structural system: A marriage of
structural engineering and system science. Journal of
Structural Control 9 (2):113–33. doi:10.1002/stc.8.
Sydenham, P. H. 2004. Systems approach to engineering design.
Boston, US: Artech house.
Tesfamariam, S., and K. Goda. 2015. Seismic performance evalua
tionframework considering maximumand residual inter-story
drift ratios: Application to non-code conforming reinforced
concrete buildings in Victoria, BC, Canada. Frontiers of Built
Environment 1:18. doi:10.3389/fbuil.2015.00018.
Thi, V. D., M. Khelifa, M. Oudjene, M. El Ganaoui, and Y.
Rogaume. 2017. Finite element analysis of heat transfer
through timber elements exposed to fire. Engineering
Structures 143:11–21. DOI:10.1016/j.engstruct.2017.04.014.
Torero, J. L. 2019. Fire safety of historical buildings: Principles
and methodological approach. International Journal of
Architectural Heritage 13 (7):926–40. doi:10.1080/
15583058.2019.1612484.
Tubaldi, E., L. Macorini, B. A. Izzuddin, C. Manes, and F. Laio.
2017. A framework for probabilistic assessment of
clear-water scour around bridge piers. Structural Safety
69:11–22. doi:10.1016/j.strusafe.2017.07.001.
UNI EN 1995–1–2. 2005. Eurocode 5 – Design of wooden
structures – Part 1–2: General Rules – Structural design
against fire (CEN: Bruxelles).
Wang, Y., I. Burgess, F. Wald, and M. Gillie. 2013.
Performance-Based Fire Engineering of Structures.
Boca Raton, FL: CRC Press.

Structural Fire Risk for Heritage Buildings by the Performance-Based Engineering Format

Recomendados

Recomendados

Más contenido relacionado

Similar a Structural Fire Risk for Heritage Buildings by the Performance-Based Engineering Format

Similar a Structural Fire Risk for Heritage Buildings by the Performance-Based Engineering Format (20)

Más de Franco Bontempi

Más de Franco Bontempi (20)

Último

Último (20)

Structural Fire Risk for Heritage Buildings by the Performance-Based Engineering Format