Residual strength of R.C. buildings after a fire: A case stud

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Concrete Repair, Rehabilitation and Retrofitting II Alexander et al (eds) 2009 Taylor & Francis Group, London, ISBN 978-0-415-46850-3

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Residual strength of R.C. buildings after a fire: A case study

I. Venanzi & A.L. MaterazziUniversity of Perugia, Perugia, Italy

M. ZappiaFire Department, Florence, Italy

ABSTRACT: In the present paper a procedure for the assessment of the residual strength of R.C. structuralmembers after a f ire is proposed. The procedure has been applied to the evaluation of the load bearing capac-ity of a storage and apartment building which experienced a real fire. The damage provoked by the fire was

evaluated through a survey and an experimental campaign carried out using non destructive techniques. Then,the analytical assessment of the residual strength using a simplified fire model based on the zone method was

performed. On the basis of the analysis results, a retrofitting programme was defined, with the aim at restoringcompletely the serviceability of the building.

how the fire started and developed. Probably a limitedamount of fuel was introduced in the gap between the

basement and the wall, through the grating that runsparallel to the perimeter of the basement. Then the fire,intentionally started, spread in the whole basement, ina condition of slow speed combustion (ventilation-controlled fire). The opening of windows and doors,necessary for the entrance of the fire brigade, pro-voked the sudden transition to a generalized fire (fuel

controlled fire). The lack of compartments within thebasement (Figure 2) allowed the diffusion of the fire

1 INTRODUCTION

The assessment of the residual load bearing capacityof reinforced concrete structures after their exposi-tion to fire is a complex task. It includes the estimate

of the actual strength of both concrete and steel andthe subsequent computation of the sections capacity.However in most cases the knowledge of materialsstrength, even after accurate and extensive testing, isnot sufficient for the purpose.

In fact in-situ testing cannot be extended over allthe sections depth, while every single spot of the sec-tions contributes to the overall bearing capacity witha strength that depends on the local maximum tem-

perature reached during the fire.The present paper is aimed at giving a contribution

to solve this problem, proposing an assessment meth-

odology based on a suitable analytical procedure.The proposed procedure was applied to a case-

study consisting in a seven-storey reinforced concretebuilding which was badly damaged by a severe fire.

2 DESCRIPTION OF THE FIRE

During the night between the 23rd and the 24th ofMarch 1991 a large fire developed in the basementand the ground floor of a building located in Rende,Cosenza, Italy, which was used for storage and sell-ing of clothing. The upper floors of the building were

occupied by houses (Figure 1). From the survey car-ried out after the fire, it was possible to reconstruct

Figure 1. Building involved in the fire.


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in the ground floor, through the opening of the steelstaircase, which was totally destroyed by the fire.Extremely high temperatures (higher then 1000C)were reached and maintained for several minutes, due

to the significant quantity of fuel in the compartmentson fire.

3 DESCRIPTION OF THE BUILDING

The structure damaged by the fire, built around thehalf of the seventies, is made of seven floors and the

basement. It has an L shape in plan, with a symme-try axis at an angle of 45 from the direction of theexternal walls.

The gross surface of the basement and the ground

floor is around 800 m2

, while the surface of the otherfloors is around 560 m2.

The building is made of reinforced concrete. Thenumber of columns is 57 at the f irst two levels and 50at the upper levels. The first floor is made of a rein-forced concrete 20 cm thick slab, while all the othersare cast in situ ribbed hollow block slabs.

4 DESCRIPTION OF THE DAMAGE

The high temperature reached in the structural ele-

ments in the compartments where the fire developedprovoked transversal cracks, separation and crum-bling away.

As a consequence of concrete spalling, in somecases the steel reinforcement was exposed directly tothe fire and so plastic strains, loss of bond and local-ized yielding occurred. The most damaged structuralelements were those at the basement. Minor damageswere observed at the ground floor.

4.1 Floors

The RC slab (20 cm thick) located between the base-ment and the ground floor, directly subjected to the

fire, underwent a significant increment of tempera-ture that provoked the expansion of the slab.

Such expansion caused the failure of the slab itselfand the failure of most of the basement columns sub-

jected to important shear forces. Also on the secondfloor the cracks are diffused (Figure 3).

4.2 Beams

Some of the beams of the basement appeared exces-sively deformed and without reinforcements cover(Figure 4), while the beams at the first and secondfloors did not undergo significant damage.

4.3 Columns

Transversal, longitudinal and oblique cracks occurred

in all the columns. Also a significant spalling occurredwith the consequent yielding of the web reinforce-ment. In some columns, cracks are particularly evi-dent and in one column (Figure 5) it was observed thefailure of the reinforcement in compression.

Another type of damage was attributable to thequick cooling of the structural elements provoked by

EXTERNAL WALL GRATING

RETAINING

WALL

Figure 2. 3D view of the basement of the building.

Figure 3. Damage of the second floor.

Figure 4. Damage of a beam at the basement.


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the water jets. In fact the most damaged columns arenear the entrances, used by the fire brigade.

5 ANALYSIS OF THE RESIDUAL STRENGTHAFTER FIRE

In order to program the repair of the structure, it wasnecessary to assess the residual strength of the mem-

bers after the fire. The procedure proposed for thispurpose is reported in the following sections.

5.1 The proposed analysis procedure

The load bearing capacity of the structural membersafter the fire is assessed by evaluating the interactiondiagrams between the ultimate compressive force

Nult

and the bending moment Mult

of the relevantcross-sections.

The MultN

ultdiagrams are computed considering

the residual strength of materials after their coolingdown after the fire. The residual strength of steel isassumed not to be affected by the fire.

On the contrary the residual compressive strength ofconcrete depends on the maximum temperature reachedat each point within the cross-section during the fire.

As the maximum local temperature is hardlyavailable, it is estimated through the analysis of the

thermal field, induced by a proper time history of theair temperature, representing the actual fire.

5.2 Fire modeling

The variation of the air temperature with time duringa real fire can be obtained studying the evolution ofthe chemical-physical phenomena that occur duringthe combustion of the material contained in the com-

partment. The evaluation of the tT curve is based onthe resolution of the equations of energy and mass

balance that analytically describe the heat and masstransfer between different regions of the compart-ment. Due to the complexity of the problem, it is ingeneral not possible to obtain closed form solutions.It is necessary to resort to numerical analysis proce-dures, based on discretization techniques.

The available methods are classified into threecategories. The parametrical models use analyti-cal curves dependant on the characteristics of thecompartment and the contained material. The fieldmodels divide the space of the compartment in manytwo- or three-dimensional cells and solve the prob-lem using computational fluid dynamics techniquesrequiring a significant computational effort.

Intermediate difficulty methods of analysis arethe so-called zone models, which operate divid-ing the compartment in a reduced number of zones,having similar characteristics, that interact betweeneach other through mass and energy exchange. The

zone models operate solving, for each region in whichthe compartment is divided, a system of differentialequations that express the conservation of mass andenergy, assuming valid the ideal gas law and definingthe density and the internal energy. Usually, only twozones are considered, an upper and a lower one withrespect to the surface of separation between the hotand cold gas. The solution of the differential equa-tions governing the problem can be carried out bysuitable computer codes.

5.3 Analysis of the thermal field

The thermal field of the cross-section during the fireis evaluated by solving the Fourier equation througha finite element approach. For this purpose the cross-section of each member exposed to fire is discretizedin rectangular or triangular finite elements. The tem-

perature may be reasonably assumed constant in eachelement, hypothesizing no variation over the lengthof the member. The solution of the thermal analysisrequires the definition of the boundary condition andthe temperatures of the surfaces directly exposed tofire, obtained by the fire modeling (see section 5.2).

The heat exchanged at the section surface is com-puted considering both convection and radiation

Figure 5. Damage of a column at the basement.


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at the interface between air and concrete using theboundary condition:

q A T T V f s f f s s= ( ) + 4 4 (1)

in which Tf, T

s,

f,

srepresent the air and concrete

temperatures and the corresponding absolute values,Ais the convection factor, is the Stefan-Boltzmannconstant, V is the shape factor, is the absorptioncoefficient of the surface exposed to fire.

After having solved the thermal problem in corre-spondence of several fire exposition times, the maxi-mum temperature reached by each concrete elementduring the fire is evaluated. It must be pointed outthat the maximum temperatures reached in the cross-sections elements generally dont occur at the same

time.

5.4 Interaction diagrams

For this purpose the cross-section is discretized infinite elements, usually adopting the same discretiza-tion used for the thermal problem.

The MultN

ultdiagrams are obtained assigning over

the considered cross-sections the full set of the straindiagrams corresponding to all possible failure con-ditions and computing the corresponding ultimateinternal forces. To evaluate M

ult,i

and Nult,i

it is neces-sary to integrate the residual strength of the concretefibers corresponding to the assigned strain distribu-tions. The relation of the residual strength and themaximum concrete temperature is taken from the

bibliography.As the residual compressive strength of concrete

depends on the maximum temperature reached ateach point within the cross-section during the fire,the temperature computed during the analysis of thethermal field is used.

For every strain value, the corresponding stress isevaluated by means of the constitutive law of con-

crete having the appropriate temperature-dependentstrength. The parabola-rectangle diagram is used forthe concrete stress-strain law. The outline of the pro-cedure is presented in Figure 6.

5.5 Assessment of safety

The safety of the considered structural membersis ensured if the points representative of the designloads (M

d, N

d) are internal to the edge of the interac-

tion diagram.Naturally the loads are factored applying the

standard load factors used for the design in coldcondition.

6 NUMERICAL ANALYSIS

6.1 Fire modeling

To simulate the variation of temperature with time inthe compartments exposed to fire, the zone model has

been adopted. In particular, it was used the CFAST

software, contained in the package HAZARD I dis-tributed by the NIST, that uses a two zones model. Thecompartment was preliminarily divided into seven sub-compartments. Compartment no. 1 to 5 are located inthe basement (Figure 8) and compartments no. 6 and 7are located at the ground floor. The fire load, esti-mated on the basis of the material present in thecompartments, is 2063 MJ/m2 for the basement and1345 MJ/m2for the ground floor. The fire loads usedfor the sub-compartments are reported in Table 1.

After having identified the sub-compartment wherethe fire developed (no. 2), it was hypothesized a wayof propagation towards the other sub-compartments,dependent on the time and the ignition temperatureof the materials. The propagation is from no. 2 to

Figure 6. Schematic representation of the procedure forthe assessment of the residual load bearing capacity.


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no. 3, 4, 5, 6 and 7 (Figure 8). In Figure 7 is shown thetime-temperature curve obtained by the simulation for

the compartment no. 2, compared to the conventionalISO 834 curve, considered as a useful reference. Thesimulated real fire curves display a growing branch fol-lowed by a descending one. The temperature of 700Cis reached after 500s from the beginning of the fire.Then the temperature continues growing more slowlyup to 1070C after 125 minutes and finally decreaseto the ambient temperature.

6.2 Residual strength analysis of the relevantstructural members

In order to assess the residual strength of the struc-tural members after the fire and define a program forthe repairing of the building, both in-situ tests andnumerical analyses were carried out.

The experimental campaign included non destruc-tive testing (rebound index measurements) on all thedamaged structural members. The numerical assess-ment of the residual strength after fire was performedon the structural members using the procedure pro-

posed in the section 5.In Figure 8 is represented the position in plan of

the analyzed structural elements. They are the col-umn 43 and beam 3442 at the basement, that weredirectly exposed to fire. Both the analyzed membersare located in the compartment no. 2. The column 43

was heated on four sides and the beam 3442 washeated on the bottom surface and on part of the lateralsurfaces (due to the presence of the slab).

In Table 2 are summarized the dimensions and thereinforcement of each analyzed member.

6.2.1 Thermal analysisIn order to simplify the computations, the tempera-ture was assumed constant along each structural ele-ment, hypothesizing no variation over the length ofthe member. It was than possible to study a 2D prob-lem instead of a 3D problem. The cross-section of themember exposed to fire was discretized in rectangu-lar or trapezoidal finite elements. The variation ofthe thermal field in the cross-section during the fire,was evaluated solving the Fourier equation through afinite element approach. With this aim, it was neces-

sary to define the variation with the temperature ofthe thermal properties of the materials, as the thermalconductivity, the specific heat and the density of theconcrete. For the specific case study the thermal prop-erties of the concrete were taken from EN 1992-1-2.Since the ratio between the reinforcements and theconcrete surfaces was very small, the presence of thereinforcements was neglected and the cross-sectionwas considered homogeneous.

The air temperature time-history of figure 7 wasused for the analysis.

As regards the boundary conditions the convectionfactor Ais assumed equal to 0.25 W/(m2K) and theabsorption coefficient of the surface exposed to firewas assumed equal to 0.9. In Figures 9 and 10 are

Table 1. Surfaces and fire loads of the sub-compartments.

Sub-compartment (no.) Surface (m2) Fire load (MJ/m2)

1 139.12 20632 139.12 20633 252.81 20634 139.12 20635 139.12 20636 266.12 13457 90.63 1345

0

200

400

600

800

1000

1200

0 30 60 90 120 150 180 210 240 270

time (min)

temperature(C)

Real fire - compartment no.2 Standard ISO 834 fire

Figure 7. Simulated temperature in the sub-compartmentno. 2.

Figure 8. Location of the analyzed members in the base-ment and compartments numbering.

Table 2. Dimensions and reinforcements of the elements.

Reinforcements

Element Dimensions Lower Upper

Column 43 55 40 218 + 114 218 +114Beam 3442 40 60 212 + 28 212


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represented the thermal fields of the two analyzedstructural members after 30 minutes of exposition tothe real fire.

6.2.2 Mechanical analysisTo evaluate the interaction diagrams MN of theanalyzed cross-sections it was necessary to knowthe variation of the residual compressive strength ofconcrete as a function of the maximum temperature

reached during the exposition to fire by each ele-ment in which the members cross-section is divided.In the present study the graph suggested by the ACI216.1-97 for unstressed carbonate aggregate concreteseemed to best fit the in situ testing and thus wasadopted. The effect of rapid cooling of some columnswas neglected. In Figure 12 is shown the reductionin percentage of the maximum compressive strengthwith respect to the initial value, as a function of thetemperature.

For the constitutive laws of concrete and reinforc-ing steel, the stress-strain relationships proposed bythe EN 1992-1-1 were adopted. It is assumed that themaximum strength of steel does not depend on thetemperature reached during the fire, i.e. the residual

Figure 9. Column no. 43: thermal field after 30 of fireexposition.

Figure 10. Beam no. 3442: thermal field after 30 of fire

exposition.

Figure 11. Residual compressive strength of carbonateaggregate concrete as a function of the maximum heatingtemperature (from ACI 216.1-97).

-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

-250 -200 -150 -100 -50 0 50 100 150 200 250

M (KNm)

N (KN)

(Md,Nd)

(Mult,Nult)

Figure 12. Diagram MN for column 43 after the exposi-tion to the real fire.

-500

0

500

1000

1500

2000

2500

3000

3500

4000

-300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300

M (KNm)

N (KN)

Figure 13. Diagram MN for beam 3442 after the exposi-tion to the real fire.


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Residual strength of R.C. buildings after a fire: A case stud

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