Abstract: This paper will present some simple ideas which form, in the authors’ experience, the basis for dealing with structural design and analysis in case of fire actions. To this aim, the following aspects are discussed: 1) the characteristics of high probability-low consequences (HPLC) versus low probability-high consequences (LPHC) events; 2) the systemic nature of fire accidents; 3) the concept of risk and the related activities, as risk analysis, risk assessment, and risk management; 4) the identification and development of fire scenarios. Specific attention is devoted to the interactions among the different aspects that need to be modelled, which are fire development, heat transfer, structural response and human behaviour. In the last part, some considerations are developed considering the case of a tall building subjected to fire and few critical results of the structural analysis are discussed. Reference to this paper should be made as follows: Arangio, S. and Bontempi, F. (2013) ‘Basis of the analysis and design for fire-induced collapses in structures’, Int. J. Lifecycle Performance Engineering, Vol. 1, No. 2, pp.115–134.

1. Int. J. Lifecycle Performance Engineering, Vol. 1, No. 2, 2013
Basis of the analysis and design for fire-induced
collapses in structures
Stefania Arangio and Franco Bontempi*
Sapienza University of Rome,
Via Eudossiana 18, 00184 – Rome, Italy
E-mail: stefania.arangio@uniroma1.it
E-mail: franco.bontempi@uniroma1.it
*Corresponding author
Abstract: This paper will present some simple ideas which form, in the
authors’ experience, the basis for dealing with structural design and analysis in
case of fire actions. To this aim, the following aspects are discussed: 1) the
characteristics of high probability-low consequences (HPLC) versus low
probability-high consequences (LPHC) events; 2) the systemic nature of fire
accidents; 3) the concept of risk and the related activities, as risk analysis, risk
assessment, and risk management; 4) the identification and development of fire
scenarios. Specific attention is devoted to the interactions among the different
aspects that need to be modelled, which are fire development, heat transfer,
structural response and human behaviour. In the last part, some considerations
are developed considering the case of a tall building subjected to fire and few
critical results of the structural analysis are discussed.
Keywords: fire structural design; design for critical events; extreme actions;
complexity; structural integrity; structural analysis.
Reference to this paper should be made as follows: Arangio, S. and
Bontempi, F. (2013) ‘Basis of the analysis and design for fire-induced collapses
in structures’, Int. J. Lifecycle Performance Engineering, Vol. 1, No. 2,
pp.115–134.
Biographical notes: Stefania Arangio is an Associate Researcher at Sapienza
University of Rome. She has been developing her research in Italy and in the
USA. Her work is focused on safety and reliability of complex structural
systems with specific attention to structural integrity monitoring and accidental
situations. In order to handle with complexity and uncertainty, the investigation
is oriented toward probabilistic methods and heuristic techniques.
Franco Bontempi is a Full Professor of Structural Analysis and Design at the
School of Engineering of Sapienza University of Rome since 2000, where he
teaches structural analysis and design, steel constructions, and fire structural
design. His research work is focused on various aspects of the analysis and
design of structures: safety and reliability, computational mechanics, non-linear
mechanics, stochastic mechanics, structural dynamics, identification,
optimisation and control.
This paper is a revised version of that presented at the Fourth International
Conference on Structural Engineering, Mechanics and Computation
(SEMC 2010), Cape Town, South Africa, 6–8 September 2010.
Copyright © 2013 Inderscience Enterprises Ltd.
115

2. 116
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S. Arangio and F. Bontempi
Introduction
One of the most challenging problems of the modern structural engineering regards the
conception and the subsequent analysis and design of constructions that were able to face
low probability-high consequences (LPHC) scenarios. These particular situations, that
can have catastrophic effects on the structures, are caused by a lot of different reasons
and include multifaceted aspects, so they are almost impossible to frame into any
well-recognised probabilistic format.
In these cases, in order to simulate the structural response and, then, to carry out the
decisional process concerning the design and the environmental control, one must
develop refined complex models, able to describe both non-linear and dynamic aspects.
Furthermore, it is common that the structural behaviour needs to be followed in a
post-critical range. In such a case the scenario changes along with the response of the
structure and one should be able to reconstruct the interaction between action and
structure step by step during the progress of the event.
A specific situation is represented by fire scenarios. In this case, one must follow:
a
the development of the fire (from the beginning to the spread inside the construction)
b
the thermal diffusion inside the construction
c
the structural response that depends both to the alterations of the material properties
with the temperature and to the large deformations that the structure can experience
during the fire; finally
d
the influence of the people’s behaviour during the accident.
Moreover, in case of fire actions, it is interesting to follow the path of the fire inside the
construction, analysing the alterations caused by the progression of failures inside the
structural system.
This paper will present straightforward ideas which, in the authors’ experience, form
the basis for dealing with structural analysis and design in case of fire actions. For this
purpose the following aspects are considered through the paper:
1
the distinguishing characteristics of high probability-low consequences (HPLC)
versus LPHC events
2
the systemic nature of fire accidents
3
the concept of risk and the connected activities, as risk analysis, risk assessment, and
risk management
4
the identification and development of the scenarios.
In the last part, a case study is considered. It is a 40 stories residential and office building
(160 m height – square base 30 m × 30 m), which has been designed on the basis of the
geometry and characteristics of a building recently built up in Latina, Italy. Some
considerations regarding the structural analysis of a tall building subjected to fire are
developed and some basic results are presented.

3. Basis of the analysis and design for fire-induced collapses in structures
2
117
HPLC-LPHC situations
During its design life a structure can experience different situations that can be classified
in two main groups:
•
HPLC events, intended as those that have a high probability to happen but that well
designed structures can usually withstand with low consequences. They are usually
characterised by small releases of energy, a small numbers of breakdowns and
involve only few people.
•
LPHC events, which can have significant consequences but are not likely to occur.
They are characterised by very large releases of energy, large numbers of
breakdowns and involve many people.
Table 1 collects the essential features of these situations: grossly speaking, natural events
(like storm, earthquakes…) belong to the first class, while accidental events fit in the
second class (Handling Exceptions, 2008); terroristic attacks, too, are intended to belong
to this latter class.
HPLC and LPHC events have generally very different characteristics both from the
design and analysis point of view (EN 1991-1-7, 2006).
From the design point of view, it has become clear that while a system might have
very good LPHC events performance, it can still be very vulnerable to failures induced
by HPLC events.
Looking at the existing codes and standards, it is possible to note that the procedures
for design situations regarding HPLC events are well established and the safety
assessment is usually founded on very reputable probabilistic-based formats (ISO 2394,
1998; JCSS, 2001). Of course, in the practice some aspects of the probabilistic
framework are usually softened, leading to the so-called semi-probabilistic approach, but
these approximations are usually not relevant. Associated with this standard of practice,
the check of a structure is usually conducted with a strong disaggregation of the structure,
considering an element by element procedure (EN 1990, 2002). For HPLC events this
way of thinking and the consequent operative steps seem reasonable and, effectively,
have conducted over the years to the realisation of large part of the constructions.
On the other hand, recently, very large and impressive structural failures have given
rise to doubts about the applicability of this approach not only in case of innovative
concepts but also in case of structures facing LPHC events (Starossek, 2009; Olmati
et al., 2011). In all these situations, it seems no more satisfactory to consider the structure
as a simple aggregation of elements: it is necessary to deal with the whole structure
considered as a system, with cooperative and emergent behaviours, or, at least, to analyse
coherent substructures, that are able to take into account aspects as the interactions
among elements, the robustness and redundancy, and the indirect loading actions (Brando
et al., 2010; Giuliani, 2009, 2012; Petrini et al., 2010).
To define the approach for solving the structural problem, in the case of possible
LPHC events, it is interesting to consider the plot in Figure 1 where the possible
frameworks for the solution (ranging from fully deterministic to stochastic) are
represented versus the complexity of the problem itself (Bontempi et al., 2008): problem
complexity increases passing from traditional designs to innovative concepts but also
increases passing from HPLC to LPHC events. This appears clear when one thinks that,
by definition, HPLC events are frequently observed (and then statistically describable),

4. 118
S. Arangio and F. Bontempi
whereas LPHC events are only rarely experienced and, above all, more variable in nature.
From the structural point of view furthermore, complexity is increased by non-linear
behaviour and depends on the organisation of the structural elements (Perrow, 1984).
Figure 1 HPLC vs. LPHC situations and corresponding problem solving strategies
(see online version for colours)
HPLC
PROBLEM
FRAMEWORK
Deterministic
LPHC
HIGH PROBABILITY
LOW CONSEQUENCES
LOW PROBABILITY
HIGH CONSEQUENCES
QUALITATIVE /
DETERMINIS
TIC
ANALYS
IS
PRAGMATIC
S
CENARIOS
ANALYS
IS
COMPLEXITY:
Nonlinear Behavior and
S
tructural Organization
S
tochastic
QUANTITATIVE
PROBABILIS
TIC
ANALYS
IS
As shown in Figure 1, one can adopt two different frameworks to solve the problem:
•
a deterministic approach
•
a stochastic approach.
In the first case all the aspects of the problem are fixed in a definite way, while in the
second case the intrinsic probabilistic nature of some aspects can be taken into account.
Considering the problem solving strategies and the complexity, in the plot of Figure 1
three different regions can be identified:
•
the first one is a region that includes problems with low complexity, i.e., evolutive
and traditional designs or HPLC events, where even direct qualitative analysis finds
place; usually, here, proper deterministic analysis are conducted
•
in the second region the complexity of the problem has grown and some aspects of
the problem can be usefully considered adding stochastics in the formulation; in this
way uncertainties of different kinds can be taken into account
•
finally, the complexity reaches a certain critical size (mainly due to the non-linear
behaviour and the organisation of the structural system) and the probabilistic
approach is not appropriate anymore; the only way to deal with the problem is
turning back to some ad-hoc deterministic approach; it means that, with an act of
force, the problem is solved by using the so-called heuristic way of thinking.

5. Basis of the analysis and design for fire-induced collapses in structures
119
This last point of view can be, at first glance, a little bit surprising. In effect, it means
from one side that one can resort to a very old way of operating, based on the true and
deep engineering sense, but, on the other side, it opens the door to innovative and
advanced approaches-based, for example, on artificial intelligence (Sgambi, 2005). This
discipline tries to extend the human capability of reasoning and can then be usefully
applied to complex structural systems problems. Even soft-computing techniques, like
fuzzy logic, can be useful in the problem definition (Arangio et al., 2011).
3
Systemic character of fire accidents in structures
A specific example of LPHC events are the fire accidents. The progression of a fire in a
construction is a really complex phenomenon with unexpected developments. Figure 2
shows a useful model for the comprehension of an accident as a fire, starting from the
hazard chance to the final possibility of catastrophe (Reason, 1990). According to this
model, the generic construction is considered as composed by a series of firewalls (in the
Computer Science meaning) that blocks the progression of the hazard to a crisis. These
firewalls are of different nature: at the beginning, they are connected with the conception
of the structure, and so they are of logical type; then some others are related to the
specific action; others depend on intrinsic, passive, properties of the structure (ability to
sustain temperature damages, …), while some others are associated with active safety
measures (sprinklers, …). Realistically, each of these firewalls has imperfections and
deficiencies: in the graphical representation of Figure 2, these are represented by holes in
the firewalls. The model predicts that, also if a single shortage is not critical, an
alignment of these weaknesses, can lead to a crisis.
Figure 2 Model of development of fire accidents (see online version for colours)
Source: Adapted from Reason (1990)

6. 120
S. Arangio and F. Bontempi
Figure 3 General framework of the fire safety analysis (see online version for colours)
(0)
DESIGN
CONSTRAINTS
AND
POSSIBILITIES
SS0a
PRESCRIBED
DESIGN
PARAMETERS
(1+2)
ACTION
DEFINITION
AND
DEVELOPMENT
(3+4)
SYSTEM
PASSIVE
AND ACTIVE
RESPONSE
SS5
life safety:
occupant behavior,
location and
condition
SS1
initiation and
development
of fire and
fire efluent
SS6
property
loss
SS2
movement of
fire effluent
BUS OF INFORMATION
SS0b
ESTIMATED
DESIGN
PARAMETERS
SS7
business
interruption
SS3
structural response
and fire spread
beyond enclosure
of origin
SS8
contamination
of
environment
SS4
detection,
activitation and
suppression
SS9
destruction
of
heritage
RESULTS
Source: Adapted from ISO 13387
An operative framework for the qualitative and quantitative analysis of fire safety, which
is in accordance with Reason’s model (Figure 2), is shown in Figure 3, adapted from
ISO/TR 13387. The various interacting items are represented with different colours:
SS0 – design constraints and possibilities (blue)
SS1/SS2 – action definition and development (red)
SS3/SS4 – passive system and active response (yellow)
SS5/… SS9 – safety and performance (purple).
Specifically:
a
design is connected with parameters that can be considered fixed (SS0a) and others
that are modifiable (SS0b)
b
action is modelled both at the beginning (SS1) and during its development (SS2)
c
system response originates both from passive characteristics (SS3) and active
measures (SS4)

7. Basis of the analysis and design for fire-induced collapses in structures
d
121
safety is related fundamentally with human life (SS5); after that, performance can be
progressively associated with loss of property (SS6), interruption of business (SS7),
contamination of the environment (SS8), and destruction of heritage (SS9).
In the central part of the chart of Figure 3 there is a yellow rectangle that symbolises the
crossing point of information arising from the various parts. From this sort of bus of
information (in the Computer Science language), the various results are collected and the
decisions are taken in a performance-based design framework (Petrini, 2010; Gentili
et al., 2010a). Of course, iterative corrections are not only possible but often necessary;
various lines of feedback connect the items that can be modified.
A further step is presented in the fire safety tree shown in Figure 4 as adapted from
NFPA 550 (2002): here, the road to achieve safety if subdivided in nine steps, each one
with a specific role.
Figure 4 Fire safety tree (see online version for colours)
Source: Adapted from NFPA (2002)
For each scope there are different strategies; for example, looking at Figure 4:
•
Line 4 – exposed persons and property can be managed by moving them from the
building or by defending them in place; in order to move people (line 5), the fire
must be detected, people must be notified and there must be a suitable safe path for
movement.
•
Line 6 – there are three options for managing a fire: the first one is to control the fuel
source by limiting the amount of fuel or the geometry; the second option is to
suppress the fire; the third one is to control the fire by construction conception.

8. 122
S. Arangio and F. Bontempi
To control the fire is necessary both to check the movement of the fire and provide the
structural stability (line 8). In fact:
•
Line 9 – the two strategies for controlling fire movement are:
1
2
fire venting, which can be obtained by an active system of mechanically
operated vents, or by a passive system that relies on the melting of plastic
skylights; in either case, the increased ventilation may increase the local severity
of the fire, but the fire will spread within the building and the overall thermal
impact on the structure will be reduced
containment of a fire to prevent spread, which is the principal tool of passive fire
protection; preventing fire growing to a large size is one of the most important
components of a fire safety strategy; radiant spread of the fire to neighbouring
buildings must also be prevented, by limiting the size of openings in the exterior
walls.
Smoke can also be controlled by venting or containment; pressurisations and smoke
barriers can also be used.
Figure 5 Detailed model for fire safety engineering: structural system characteristics and
weaknesses (see online version for colours)
STRUCTURAL
CONCEPTION
threats
Yes
No
STRUCTURAL
TOPOLOGY
&
GEOMETRY
passive
structural
characteristics
threats
Yes
No
STRUCTURAL
MATERIAL
& PARTS
threats
Yes
No
STRUCTURAL
SYSTEM
CHARACTERISTICS
FIRE DETECTION
& SUPPRESSION
active
structural
characteristics
threats
Yes
No
ORGANIZATION &
FIREFIGHTERS
threats
Yes
No
alive
structural
characteristics
MAINTENANCE
& USE
threats
No
Yes
STRUCTURAL
SYSTEM
WEAKNESSES

9. Basis of the analysis and design for fire-induced collapses in structures
123
After the discussion about the main aspects that should be taken into account for the
assessment of fire safety, it is possible to reconsider the ideal model of Reason (Figure 2)
that can be detailed as shown in Figure 5. This plot represents a reference model for the
activities of fire safety engineering: on the left there are the system characteristics while
on the right there are the weaknesses of the system represented as holes in the firewalls.
4
Risk
The concept of hazard introduced in Figure 2 can be expanded introducing the concept of
risk and the related processes (Haines, 1998). Risk is a very general and very basic notion
in all the human activities and, of course, for every engineering enterprise. Here, risk is
considered simply as the following product:
RISK = (EXTENT OF NEGATIVE CONSEQUENCES)
× (PROBABILITY OF OCCURRENCES)
Figure 6 summarises from an engineering point of view all the activities connected to
risk. Fundamentally, one has different actions related to risk, nested one inside the other,
which can be arranged from the more specific one to the broader one in the following
order:
•
RISK ANALYSIS
•
RISK ASSESSMENT
•
RISK MANAGEMENT.
The last one, RISK MANAGEMENT:
•
defines the CONTEXT of the engineering enterprise, covering the social, individual,
political, organisational, and technological features;
•
develops the RISK ASSESSMENT
•
decides the RISK TREATMENT, meaning what to do in terms of risk; there are four
possibilities:
option 1
avoidance
option 2
reduction
option 3
transfer
option 4
acceptance.
Measures connected with the option (4) are called structural; measures connected with
options (2) and (3) are generally non-structural, while measures connected with (1) are
essentially decisional or political ones.
RISK ASSESSMENT is the part specifically devoted to the judgement of the risk in
comparison with specified criteria or in relation with historical cases; by the way, in the
case of fire safety, just case histories are a strong source of knowledge. The phase of risk
assessment puts the qualitative and the quantitative basis for the decisions to be taken to
treat risk.
The engine of the whole process is anyway RISK ANALYIS where:

10. 124
S. Arangio and F. Bontempi
a
one defines the system and its boundary; the system is usually decomposed in
smaller subsystems or parts that are easily to be described
b
for the system identified in this way, one develops the hazard scenarios analysis that
recognises which negative events can happen
c
the qualitative aspects of the previous point are quantitatively fixed by estimating:
•
the consequences (magnitudes)
•
the probabilities of occurrences.
Sensitivity analyses are carried out to evaluate the relevant characteristics of the various
scenarios.
Figure 6 Risk and relevant processes (see online version for colours)
DEFINE CONTEXT
(social, individual, political,
organizational, technological)
DEFINE SYSTEM
(the system is usually decomposed
into a number of smaller
subsystems and/or components)
HAZARD SCENARIO ANALYSIS
(What can go wrong?
How can it happen?
What controls exist?)
ESTIMATE
CONSEQUENCES
(magnitude)
RISK
ANALYSIS
ESTIMATE
PROBABILITIES
(of occurrence)
DEFINE RISK
SCENARIOS
RISK
ASSESSMENT
RISK
MANAGEMENT
SENSITIVITY
ANALYSIS
RISK ASSESSMENT
(compare risks against
criteria
MONITOR
AND
REVIEW
RISK TREATMENT
Option 1 – avoidance
Option 2 – reduction
Option 3 – transfer
Option 4 - acceptance
The intrinsic nature of LPHC events, as discussed in Section 2, usually leads to
deterministic problem solving approaches and the possibility of developing accurate risk
analyses is strongly undermined because they necessitate the computation of the
probability of occurrence. Practically, as explained before, this part must be reverted to a
heuristic assessment. Even if the probabilistic part of the analyses mentioned in Figure 6
is not easily applicable in the case of fire risk, it is widely accepted that the general
framework proposed in the plot is a useful tool for describing the activities connected to
fire risk because it is able to clearly point out all the key aspects of the problem.

11. Basis of the analysis and design for fire-induced collapses in structures
125
While all the previous activities can be recognised as analysis activities, the last
aspect, that is risk treatment, is considered as a design activity. Starting from a known
risk, one decides what measures to adopt for its reduction. As shown in Figure 7, the flow
of risk is subdivided into different channels, which are the various options for risk
treatment, with different percentage of reduction.
Figure 7 Risk treatment: avoidance, reduction, transfer and acceptance (see online version
for colours)
START
100%
Option 1:
RISK
AVOIDANCE
50%
50%
No
Yes
Option 2:
RISK
REDUCTION
20%
30%
No
Yes
Option 3:
RISK
TRANSFER
5%
25%
No
Yes
Option 4:
RISK
ACCEPTANCE
No
STOP
5
Scenarios identification and development
What has been said about the intractability from the probabilistic point of view of LPHC
events is valid also for the definition of the fire scenarios.
In this sense, it is interesting to consider in a more detailed way the characteristic
features of HPLC versus LPHC events, as exposed in Table 1 where basic aspects, main

12. 126
S. Arangio and F. Bontempi
points and analysis criticalities are summarised. The basic aspects (release of energy,
numbers of breakdowns, and people involved) have been already discussed in Section 2.
The main points regard the complexity of the problem: the LPHC events are more
complex, being characterised by non-linearity, strong interactions, and uncertainty. The
critical aspects of the analysis for the LPHC events are the low decomposability and the
scarce predictability of the scenarios that, in case of fire, are difficult to predict both in
the initial development and in the subsequent evolution.
Table 1
HPLC versus LPHC events
HPLC high probability low LPHC low probability high
consequences
consequences
Release of energy
Numbers of breakdown
People involved
Main points Non-linearity
Interactions
Uncertainty
Analysis
Decomposability
criticalities Course predictability
Small
Small
Few
Weak
Weak
Weak
High
High
Basic
aspects
Large
Large
Many
Strong
Strong
Strong
Low
Low
From the operative point of view, Figure 8 shows an iterative path to generate plausible
scenarios in the frame of the performance-based fire engineering, starting from the initial
definition of the requirements to the acceptance of the performance after the fire analysis.
In this process, the role of the heuristics cannot be underestimated because it represents
the founding point of the fire safety and performance checks.
Figure 8 Scenarios generation (see online version for colours)
Establish
performance
requirements
Determine geometry,
construction and use of the
building
Establish maximum likely
fuel loads
Estimate maximum likely
number of occupants and
their locations
Assume certain fire
protection features
Carry out fire engineering
analysis
Modify
fire
protection
features
No
Acceptable
performance
Source: Adapted from Buchanan (2002)
Yes
Accept
design

13. Basis of the analysis and design for fire-induced collapses in structures
127
After the identification of the scenario, the simulation of its progression can be carried
out with the help of Figure 9 (Bontempi and Petrini, 2010). Here, the different kinds of
models involved in the simulation are shown. In order to follow coherently the
progression of a fire accident and its consequences, it is necessary to consider the
couplings among (Gentili et al., 2010b):
1
the fire model
2
the heat transfer model
3
the structural model
4
the human behaviour model.
Figure 9 Interaction among fire-, heat transfer-, structural- and human behaviour-models
(see online version for colours)
Source: Adapted from Buchanan (2002)
6
Excerpt from the analysis of a tall building
In this section, a case study is discussed. It regards the analysis of a tall building under
fire actions. The fire safety design of high-rise structures is challenging for a number of
reasons (Craighead, 2003; Gentili et al., 2011), including not only the enhanced
difficulties in evacuating the building, but also the description of the development of fire
(i.e., the characteristic of the action) and the analysis of the response of the building (i.e.,
the characteristics of the structural system) (Petrini and Ciampoli, 2011). According to
the already discussed plot in Figure 1, these constructions belong to the third region of
the chart and have a high level of complexity.

14. 128
S. Arangio and F. Bontempi
The considered building is shown in the left part of Figure 10. It has 40 stories (160 m
height – square base 30 m × 30 m) and it is devoted to offices and residential use. It has
been designed on the basis of a building recently built up in Latina, Italy. The global
finite element model is shown in the right part of Figure 10.
It has a steel framed structural system. A vertical bracing system provides stiffness
against horizontal actions, while no horizontal bracings are present in the floor planes: the
stiffness at the floor planes is achieved by means of bidirectional concrete floor slabs,
which maintain the biaxial symmetry of the floors and are lightened by spherical hollows.
The slab characteristics allow for long spans and slender beams, which can be contained
within the height of the slabs.
Figure 10
Designed tall building (on the left) and its global structural model (on the right)
(see online version for colours)
For the fire safety design some relevant fire scenarios are pragmatically identified
(Crosti, 2009): for this study it has been assumed that the vertical compartmentalisation
of the building remains intact and the fire originates and spreads in one floor only. In
principle, different fire scenarios along the building height should be considered, since
floors have different elements and loads and the vertical propagation of the failure can be
different. In the following the results related to four fire scenarios on the 5th floor (shown
in Figure 11) of the building are presented.
To this aim, a three-dimensional finite element model of a substructure, representing
the considered floor of the building, has been investigated. The temperature-time curve
considered for the fire is the basic ISO 834, while the heating curves of the beams

15. Basis of the analysis and design for fire-induced collapses in structures
129
involved in each fire scenario have been calculated under the assumption of uniform
temperature in the element, according to the Eurocodes formula for unprotected steel:
Δθa ,t =
Am V
⋅ hnet , d ⋅ Δt
ca ⋅ ρa
where the ratio Am/V is the section factor for unprotected steel members, with Am the
exposed surface area of the member per unit length and V the volume of the member per
unit length, ca is the specific heat of steel expressed inJ/kgK, hnet , d is the design value of
the net heat flux per unit area [W/m2], ∆t is the time interval [s], and ρa is the unit mass of
steel. hnet , d has been calculated considering a convective coefficient α = 25 W/(m2K) and
a total emissivity ε = 0.5 (no shadow effect have been considered). These assumptions
have been made to establish the baseline behaviour of the structure under fire.
Figure 11 Fire scenarios considered and floor plan FEM model extracted from the global
structural model (see online version for colours)

16. 130
S. Arangio and F. Bontempi
It has been observed that a particular dangerous situation for high-rise buildings under
fire is represented by an indirect involvement of the columns, which are either pushed
outside by the horizontal thermal expansion of the beams, or pulled inwards by the
vertical runaway of the beams (Izzudin et al., 2007). This mechanism is particularly
relevant for frames where the stiffness of the beam is comparable with the flexural
stiffness of the columns, whereas for systems with stronger column and slender beams
the involvement of the column can be due to the stress redistribution and loss of lateral
restrain consequent to the buckling of the horizontal members. In both cases, the collapse
would not remain localised and would propagate downwards through failures of columns
at other floors. This is an example of how the organisation of the structural system can
strongly influence the mechanical behaviour.
In order to see a possible influence of the fire effects on the columns and to model
with a sufficient accuracy the translational and rotational capability of the beam end
nodes, columns are included in the model of the single floor to the extent of half-length
of the columns pertinent to the 4th floor (below the floor level) and half length of the
columns pertinent to the 5th (above the floor level). The columns are continuous and
restrained by hinges at the bottom end, and by vertical sliding support at the top. They are
considered to be unloaded in this preliminary investigation. In case a significant
overloading of the column is evidenced in the analysis, a refined model which include
more floors and a more realistic loading conditions should be considered.
The analyses take into account thermo-plastic material and geometric non-linearities.
Dead and live loads are applied on the beams as line forces and considered in a first static
analysis step, together with self-weight, while in a second load step the temperatures of
the calculated steel heating curves of the beams are applied to the beam nodes. An
implicit dynamic solver has been used in order to overcome convergence problems due to
local mechanisms and to follow the propagation of failures.
The main purpose of these analyses is to evaluate the sensitivity of the structural
response of the beams to the fire scenario and the possible involvement of the columns.
Figure 12
(a) Fire scenarios as applied temperature-time curve for the 4th scenario
(b) Deformations after 15 minutes (see online version for colours)
a)
Point B
Point A
(a)
Note: The position of the control floor points A and B is indicated.

17. Basis of the analysis and design for fire-induced collapses in structures
Figure 12
131
(a) Fire scenarios as applied temperature-time curve for the 4th scenario
(b) Deformations after 15 minutes (continued) (see online version for colours)
b)
Point B
Point A
(b)
Note: The position of the control floor points A and B is indicated.
Figure 12 shows:
a
the application of the 4th scenario as temperature-time curves on the beam elements
b
the results in terms of deformation; in particular, the position of the control points A
and B is indicated.
Figure 13 Vertical and horizontal displacements versus time for the floor control points A and B
during the 4th scenario (see online version for colours)
Vertical displacements - Point A
0
5
10
15
20
Vertical displacements - Point B
0
25
5
10
15
20
25
0,00
0,00
-0,10
-0,10
-0,20
-0,20
-0,30
-0,30
-0,40
-0,40
-0,50
-0,50
-0,60
-0,60
-0,70
Horizontal displacements - Point B
Horizontal displacements - Point B
0
0,25
0,20
0,15
0,10
0,05
0,00
-0,05
5
10
15
20
25

18. 132
S. Arangio and F. Bontempi
The displacements versus time of the control points A and B are plotted in Figure 13.
Point A belongs to a secondary beam and reaches relatively large displacements
essentially in the vertical direction Y after 10 minutes, while point B, which belongs to a
principal beam shows also an out of vertical plane deformation, with large displacements
in X direction after 15 minutes. In this configuration then, the principal beam buckles in
the horizontal plane, while the secondary beams deform essentially in the vertical plane.
Columns seem not to be sensible to the thermal dilatation of beams.
This case study has shown that for the considered events, the selected substructure
can adequately represent the consequences of the analysed scenario because the
deformation affects mainly the beams and the columns are not directly involved. In case
the columns were significantly influenced by the deformation, the interaction with the
other planes could not be neglected.
7
Conclusions
This paper has presented some simple ideas which form, in the authors’ experience, the
basis for dealing with the fire action in structural design and analysis. To this aim, the
following aspects have been discussed:
1
the characteristics of HPLC versus LPHC events
2
the systemic nature of fire accidents
3
the concept of risk and the related activities, as risk analysis, risk assessment and risk
management
4
the identification and development of the scenarios.
As shown, one of the most challenging problems of the modern structural engineering
regards the conception and the subsequent analysis and design of constructions able to
face LPHC events. These situations arise for a lot of different reasons and include
multifaceted aspects, being possibly followed by catastrophic consequences and being
almost impossible to frame into any well-recognised probabilistic format.
To simulate the structural response and, then, to carry out the decisional process for
the design and control, one must eventually develop a refined complex modelling, able to
describe both non-linear and dynamic aspects. Furthermore, it is common the case that
the structural behaviour needs to be followed in a post-critical range.
A specific situation is represented by fire scenarios. In this case, one must follow:
a
the development of the fire (from the beginning to the spread inside the construction)
b
the thermal diffusion inside the construction
c
the structural response that depends to the alterations of the material properties with
the temperature and to the large displacements and deformations.
Finally,
d
the influence of the people’s behaviour during the accident must.
In these situations, it is particularly interesting to follow the path of the fire inside the
construction and the related progression of failures inside the structural system.

19. Basis of the analysis and design for fire-induced collapses in structures
133
The systemic nature of fire accidents and the overall strategy to face this kind of
events have been summarised by different schemes. Moreover, the activities related to
fire risk have been discussed and it has been shown that the intrinsic nature of LPHC
events strongly undermines the possibility to develop accurately the part of the risk
analysis that should compute the probability of occurrence. As explained, this part should
be handled by means of heuristic methods. Nevertheless, it is accepted that the discussed
framework, even if the possibility of a sound quantitative evaluation of the probabilistic
format appears often illusory, is effective for presenting in an ordinate way all the aspects
of the problem.
Finally, some of the discussed concepts have been are applied in a case study
regarding the fire safety analysis of a substructure of a tall building.
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