Basis of the analysis and design for fire-induced collapses in structures

Int. J. Lifecycle Performance Engineering, Vol. 1, No. 2, 2013 115

Copyright © 2013 Inderscience Enterprises Ltd.

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: [email protected] E-mail: [email protected] *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.

116 S. Arangio and F. Bontempi

1 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.

Basis of the analysis and design for fire-induced collapses in structures 117

2 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),


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)

HPLCHIGH PROBABILITY

LOW CONSEQUENCES

LPHCLOW PROBABILITY

HIGH CONSEQUENCES

COMPLEXITY:Nonlinear Behavior andStructural Organization

PROBLEMFRAMEWORK

Deterministic

Stochastic

QUALITATIVE /DETERMINISTIC

ANALYSIS

QUANTITATIVEPROBABILISTIC

ANALYSIS

PRAGMATICSCENARIOS ANALYSIS

HPLCHIGH PROBABILITY

LOW CONSEQUENCES

LPHCLOW PROBABILITY

HIGH CONSEQUENCES

COMPLEXITY:Nonlinear Behavior andStructural Organization

PROBLEMFRAMEWORK

Deterministic

Stochastic

QUALITATIVE /DETERMINISTIC

ANALYSIS

QUANTITATIVEPROBABILISTIC

ANALYSIS

PRAGMATICSCENARIOS ANALYSIS

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.


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)


Figure 3 General framework of the fire safety analysis (see online version for colours)

SS0aPRESCRIBED

DESIGNPARAMETERS

SS0bESTIMATED

DESIGN PARAMETERS

SS1initiation anddevelopment

of fire andfire efluent

SS2movement offire effluent

SS3structural response

and fire spreadbeyond enclosure

of origin

SS4detection,

activitation andsuppression

SS5life safety:

occupant behavior,location and

condition

SS6property

loss

SS7business

interruption

SS8contamination

ofenvironment

SS9destruction

ofheritage

(0)DESIGN

CONSTRAINTSAND

POSSIBILITIES

(1+2)ACTION

DEFINITIONAND

DEVELOPMENT

(3+4)SYSTEMPASSIVE

AND ACTIVERESPONSE

BU

S O

F IN

FOR

MA

TIO

N

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)


d 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.


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 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

2 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

STRUCTURAL TOPOLOGY

&GEOMETRY

threats

No

Yes

threats

STRUCTURALMATERIAL& PARTS

No

Yespassive structural

characteristics

threats

FIRE DETECTION& SUPPRESSION

No

Yes

active structural

characteristicsthreats

ORGANIZATION & FIREFIGHTERS

No

Yes

threats

MAINTENANCE& USE

No

Yes

threats

No

alivestructural

characteristics

Yes

STRUCTURAL SYSTEM

CHARACTERISTICS

STRUCTURALSYSTEM

WEAKNESSES


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:


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)

ESTIMATE PROBABILITIES(of occurrence)

DEFINE RISK SCENARIOS

RISK ASSESSMENT(compare risks against

criteria

SENSITIVITY ANALYSIS

RISK TREATMENTOption 1 – avoidanceOption 2 – reductionOption 3 – transfer

Option 4 - acceptance

MONITOR AND

REVIEW

RISK ANALYSIS

RISK ASSESSMENT

RISK MANAGEMENT

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.


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)

30%

50%

START

Option 1:RISK

AVOIDANCE

Option 2:RISK

REDUCTION

Option 3:RISK

TRANSFER

Option 4:RISK

ACCEPTANCE

100%

25%

20%

5%

50%

No

No

No

Yes

STOP

No

Yes

Yes

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


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 consequences

LPHC low probability high consequences

Release of energy Small Large Numbers of breakdown Small Large

Basic aspects

People involved Few Many Non-linearity Weak Strong Interactions Weak Strong

Main points

Uncertainty Weak Strong Decomposability High Low Analysis

criticalities Course predictability High 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)

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

Acceptable performance

Modify fire

protection features

Accept design

Establish performance requirements

No Yes

Source: Adapted from Buchanan (2002)


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.


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


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:

, ,m

a t net da a

A Vθ h tc ρ

Δ = ⋅ ⋅Δ⋅

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, ,net dh 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. ,net dh 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)


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)

Point A Point B

a)

(a)

Note: The position of the control floor points A and B is indicated.


Figure 12 (a) Fire scenarios as applied temperature-time curve for the 4th scenario (b) Deformations after 15 minutes (continued) (see online version for colours)

Point A Point B

b)

(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)

-0,05

0,00

0,05

0,10

0,15

0,20

0,250 5 10 15 20 25

-0,70

-0,60

-0,50

-0,40

-0,30

-0,20

-0,10

0,000 5 10 15 20 25

-0,60

-0,50

-0,40

-0,30

-0,20

-0,10

0,000 5 10 15 20 25

Vertical displacements - Point A Vertical displacements - Point B

Horizontal displacements - Point BHorizontal displacements - Point B


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.


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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Technology

Basis of the analysis and design for fire-induced collapses in structures