Journal of Constructional Steel Research 88 (2013) 34–42

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Journal of Constructional Steel Research

An approach for evaluating the residual strength of fire exposedbridge girders

Esam Aziz 1, Venkatesh Kodur ⁎Civil and Environmental Engineering, Michigan State University, United States

⁎ Corresponding author. Tel.: +1 517 353 9813; fax:E-mail addresses: azizesam@msu.edu (E. Aziz), kodu

1 Tel.: +1 517 802 1226; fax: +1 517 432 1827.

0143-974X/$ – see front matter © 2013 Elsevier Ltd. Alhttp://dx.doi.org/10.1016/j.jcsr.2013.04.007

a b s t r a c t

a r t i c l e i n f o

Article history:Received 3 October 2012Accepted 24 April 2013Available online 29 May 2013

Keywords:Bridge firesResidual strengthSteel girdersFinite element analysisFire resistance

This paper presents an approach for evaluating residual strength of fire exposed steel bridge girders. The ap-proach involves three stages of analysis that is to be carried out at ambient conditions, during exposure tofire, and after cooling of the fire exposed bridge girder. In the first stage, load carrying capacity of the girderis evaluated at room temperature. In the second stage of analysis, thermal and structural response of thebridge girder is traced under specified fire exposure and loading conditions. In the third stage (after thebridge girder has cooled down), residual capacity of the girder is evaluated by incrementing load on the gird-er till failure occurs. The proposed approach is applied to carry out a set of numerical studies on a typical steelgirder using finite element computer program ANSYS. Results from numerical studies indicate that the max-imum fire temperature (and associated temperature in steel) is the most critical factor that influences resid-ual strength of a fire exposed bridge girder. A girder exposed to typical “external” fire conditions, withmaximum fire temperatures reaching to 600–700 °C, retains about 70 to 80% of its strength on cooling. Onthe other hand, a steel bridge girder exposed to hydrocarbon fire, with a maximum temperature of about1100 °C, looses most of its strength during heating phase of the fire and experiences failure.

© 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In recent years there have been numerous fires in bridges andsome of these fires resulted in the collapse of steel girders [1,2].Thus, fire hazard in bridges can result in significant economic andpublic losses. Following the fires, traffic on fire damaged bridge(routes) is usually hard to detour and significantly affect the trafficquality in the region. In many cases, fires in bridges burn-out quicklyor are extinguished through fire fighting. Thus, structural members,in most cases, retain much of their capacity after exposure to a fireand the extent of strength recovery depends on the severity and du-ration of the fire, geometrical properties of the girder, and the degra-dation of strength properties for material used in construction [3].However, a quick assessment of residual capacity of fire exposedstructural members is necessary before routing the traffic on the brid-ges. Such an assessment also helps in developing strategies forretrofitting structural members in bridges.

A list of some of major fire incidents that occurred in steel bridgesduring 1995–2010 is tabulated in Table 1 [4]. Of the fire incidentsshown in Table 1, complete collapse of the bridge girders occurred inthree cases, namely 9-mile road overpass over I-75 expressway nearHazel Park, Michigan, MacArthur Maze I-80/880 interchange in Oakland,Californian, and I-95 Howard Avenue Overpass in Bridgeport, Connecticut.

+1 517 432 1827.r@egr.msu.edu (V. Kodur).

l rights reserved.

In the remaining cases, the bridges experienced some level of damage;however no collapse has occurred in the bridges. In these cases, an as-sessment of residual capacity of bridge girders is necessary for restora-tion of fire damaged bridges following fire incidents.

A review of literature indicates that there is lack of information onthe post-fire strength assessment of bridge girders. But, there are lim-ited studies on the residual strength of fire exposed building ele-ments. The residual strength studies on building elements did notconsider the effect of reversible material properties (thermal andmechanical) in evaluating residual strength of structural members[3,5,6]. Furthermore, this information on building elements mightnot be directly applicable to bridge girders due to different fire sce-narios, loading, boundary conditions, failure limit state, and sectionalproperties that are present in bridges. This paper presents the devel-opment of a numerical approach for evaluating residual strength offire exposed steel bridge girders.

2. Methodology for evaluating residual strength

2.1. General approach

For evaluating residual strength, strength analysis on the bridgegirder has to be carried out in three stages, namely ambient condi-tions (stage 1), during exposure to fire (stage 2), and following thecooling of the fire exposed girder (stage 3). The strength analysiscan be carried out using finite element based computer programssuch as ANSYS or ABAQUES.

Table 1Some of the major fire accidents on steel bridges during the last 15 years [4].

Bridge/location Date offire incident

Cause of fire Bridge material Damage description

Metro-Northrailroad Bridgeover HarlemRiver, NY

Sep 20, 2010 Power transformer caused burning ofwood pilings under the bridge

Steel truss bridge Minor structural damage

Bridge over I-75near HazelPark, MI

July 15, 2009 A gasoline tanker struck an overpass on I-75. Composite deck (steel girders + reinforcedconcrete slab)

Complete collapse of the bridge tothe freeway below

Big Four Bridge,Louisville, KY

May 7, 2008 Electrical problem of the lighting system,took two and a half hours to control thefire

Steel truss bridge Minor structural damage resulting inlarge amount of debris on the bridge

Tappan ZeeBridge, overHudson River,NY

July 2, 2007 A car struck a tractor-trailer and caughton fire

Steel truss, cantilever type bridge Minor structural damage

I-80/880interchange inOakland, CA

April 29, 2007 A gasoline tanker crashed Composite deck (steel girders + reinforcedconcrete slab) supported by reinforced concretecolumns

Two spans of I-580 bridge collapsed

I-95 HowardAvenueOverpassin Bridgeport,CT

March 26,2003

A car struck a truck carrying 8000 gallonsof heating oil near the bridge

Composite deck (steelgirders + reinforced concrete slab)

Collapse of the southbound lanesand partial collapse of the northboundlanes

I­20/I­59/I­65interchange inBirmingham,AL

January 5,2002

A loaded gasoline tanker crashed steel girders Main span sagged about 3 meters(10 feet)

I-80W/I-580Eramp inEmeryville, CA

February 5,1995

A gasoline tanker crashed Composite deck (steel girders + reinforcedconcrete slab)

Deck, guardrail and some ancillaryfacilities were damaged

35E. Aziz, V. Kodur / Journal of Constructional Steel Research 88 (2013) 34–42

In the first stage of the analysis, prior to undertaking fire responseanalysis, load carrying capacity of the bridge girder is to be evaluatedthrough specified strength equations in design standards. Alterna-tively, detailed finite element analysis can be carried out by graduallyincrementing the load on the girder till failure is attained. For thisanalysis, room temperature strength and stiffness properties of struc-tural steel, concrete, and reinforcing steel are to be considered.

In the second stage of analysis, the bridge girder is to be analyzedby exposing the girder to a given fire scenario, load level, and re-straint conditions that are present during fire exposure. Both thermaland structural response of the girder is to be traced to evaluate thefire performance of the girder. In this stage, temperature dependentproperties of structural steel, concrete, and reinforcing steel, includ-ing the change in the material properties in the cooling phase, areto be considered. This stage of the analysis is carried out at varioustime increments till the failure of the girder occurs or till the total du-ration of fire exposure. Response parameters from the thermal andstructural analysis are to be utilized at the end of each time incrementto evaluate the state of the bridge girder under different failure limitstates.

Following the cooling down of the bridge girder, if there is no fail-ure in second stage, third stage of analysis is to be carried out. In thisstage of the analysis, the bridge girder is loaded incrementally and thestructural response of the girder is traced. For this analysis, residualproperties of material (concrete, steel, steel reinforcement) are tobe considered. The load increments continue till the girder attainsfailure. The three stages of the analysis for evaluating residualstrength of fire exposed bridge girders are illustrated in Fig. 1.

2.2. Failure criteria

In undertaking residual strength analysis of a bridge girder, differ-ent failure criteria are to be considered at each stage of the analysisdepending on the response and the failure limit state of the girder.In the first stage of analysis, at ambient conditions, strength limitstate generally governs the failure and the capacity of the bridge

girder corresponds to the point at which failure (flexure or shear) oc-curs. In the second stage, under fire exposure, the girder experienceshigh temperatures and buckling of the web might dominate the fail-ure limit state due to higher slenderness of the web as compared tothe flanges. Also, significant deflections that develop under fire condi-tions can lead to high level of fire induced forces at the connectionswhen the girder is restrained from thermal expansion. These aspects(web buckling, mid-span deflection, and state of connections) are tobe considered at each time increment to evaluate failure. Therefore,strength and stability limit state criteria are to be considered to eval-uate the failure in the second stage of the analysis. In the third stage,strength (or deflection) limit state generally governs the failure andthis can be used to evaluate residual capacity of the fire exposedgirder.

2.3. Properties of constituent materials

The properties of constituent materials play a crucial role in deter-mining the capacity and response of a girder at different stages ofanalysis. The properties of steel and concrete degrade with tempera-ture and are also affected by the heating and cooling cycles of fire.Thus, relevant material properties are to be used at each stage ofthe analysis. In stage 1 of analysis, the room temperature strengthand stiffness properties of structural steel, concrete, and steel rein-forcement are to be used. During exposure to fire, (stage 2) the pro-gression of temperatures in the steel girder and concrete slabdepend on the fire intensity and thermal properties of constituentmaterials, namely thermal conductivity, specific heat and thermal ex-pansion. These thermal properties vary as a function of temperature.The mechanical properties of steel and concrete that govern the fireresponse of bridge girder are yield strength, modulus of elasticity(stress–strain response) and these are also a function of temperature.The thermal and mechanical properties of steel and concrete degradeduring heating phase of the fire; however these materials regain partof their strength and stiffness during cooling phase of the fire.

Start

Discretization of girder for thermal and structural analysis

Evaluate capacity at roomtemperature

Room temperaturemechanical properties

Evaluate response during fire exposure

High temperature thermal and

mechanical properties

Evaluate the residual strength after cooling

Stop

Residual strength (temperature dependent)

properties

No failure

Failure

Stage 1

Stage 2

Stage 3

Fig. 1. Flow chart illustrating various stages in undertaking residual strength analysis.

36 E. Aziz, V. Kodur / Journal of Constructional Steel Research 88 (2013) 34–42

In stage 3 of the analysis, after cooling down of the girder, theproperties of steel and concrete recover to some extent. The level ofrecovery in strength and stiffness properties of steel and concreteafter cooling of the girder and slab depends on the maximum temper-ature attained during fire exposure [5]. There is lack of information onresidual strength properties of steel and concrete after experiencinghigh temperature in fire.

3. Finite element model

3.1. General

The above methodology was applied for evaluating the residualstrength of fire exposed bridge girder. The analysis was carried outusing the finite element computer program ANSYS [7], which is capa-ble of handling coupled and uncoupled thermo-mechanical problems.For the analysis, a typical steel bridge girder comprising of differentstructural components, namely steel girder, reinforced concrete slab,and lateral supports, is selected. In stage 1 of the analysis, the strengthanalysis is carried out and the room temperature capacity was evalu-ated. The response of the girder during fire exposure (stage 2 analy-sis) is traced through two sets of discretization models, one forundertaking thermal analysis and the other for undertaking mechan-ical (strength) analysis. Results from thermal analysis are applied asthermal-body-loads on the structural model, uniformly along thegirder span. High temperature thermal and mechanical properties ofsteel and concrete, in both heating and cooling phases, are incorpo-rated in the analysis. The state of the girder, as well as capacity wasevaluated by applying relevant failure limit state as discussed in detailin Section 2.2. Following the cooling of the girder, residual capacity ofthe girder was evaluated by undertaking stage 3 of the analysis.

3.2. Discretization for thermal analysis

Stage 2 of the analysis requires heat transfer calculations to evaluatetemperature in the steel girder and concrete slab. For undertaking heattransfer analysis a composite girder, comprising of steel girder and con-crete slab, is discretized in to SOLID70 elements. This SOLID70 is a 3-D

element with three-dimensional thermal conduction capability andhas eight nodes with a single degree of freedom, namely temperature,at each node. This element is applicable to three-dimensional, steady-state or transient thermal analysis. The external surface areas ofSOLID70 elements that are exposed to fire from three sides were usedto simulate the surface effect of convection and radiation that occurfrom the ambient air to the steel girder.

The girder-slab assembly segment AB, that is shown in Fig. 2(a), wasmeshed with SOLID70 elements. The discretization adopted for thermalanalysis is shown in Fig. 2(b). Both (heat) convection and radiationloads were applied at the exposed surface areas of the solid element. Aconvection coefficient of αc = 50 W/(m2 °C) and αc = 35 W/(m2 °C)was used in the thermal analysis under hydrocarbon and external firerespectively and this is based on Eurocode 1 [8] recommendations.Depending on the exposure boundaries, different values of effective emis-sivity factor were used as per Eurocode 1 [8]. Effective emissivity factor of0.7 was used for the bottom and side surfaces of the bottom flange of thegirder. For the side surfaces of the web, an emissivity factor of 0.5 wasused,while an emissivity factor of 0.3was used for top flange and the bot-tom of the slab. This variation in emissivity factor is to reflect the fact thatthe web, top flange, and slab will experience slightly less radiation due tothe effect of larger depth of the girder. Stefan–Boltzmann radiation con-stant of 5.67 × 10−8 W/(m2 °C) was used in the thermal analysis.

The temperature (T) obtained at various points in the girder, viafinite element analysis, were averaged at every time step by takingthe arithmetic mean of the temperatures at several points for eachcomponent (flange, web, or slab portion) of the composite sectionas shown in Fig. 2(b).

3.3. Discretization for structural analysis

Evaluating residual capacity of the girder requires strength analy-sis in stages 1, 2, and 3. For undertaking structural analysis, the bridgegirder is discretized with two elements, namely SHELL181 elementfor bottom flange, web, top flange and bearing stiffeners, and aSOLID65 element for the concrete slab. SHELL181 element has fournodes with six degrees of freedom per node, three translations in x,y, and z directions and three rotations about x, y, and z-axes. This

(c)

3-D mesh Support and boundary condition

Lateral restraint

Support restraint

Lateral restraint

(b)

3-D mesh of segment (A-B)Cross section (A-A)

(a)B

B

A

A

Concrete slab StiffenerSteel girder Loading

Fig. 2. 3D discretization of bridge girder for thermal and structural analysis.

(a) Typical girder in a bridge(b) Discretization for thermal analysis(c) Discretization for structural analysis.

37E. Aziz, V. Kodur / Journal of Constructional Steel Research 88 (2013) 34–42

element can capture local buckling in flanges and web and also lateraltorsional buckling of the girder and therefore is well-suited for largerotation, large strain and nonlinear problems. SOLID65 has eight nodeswith three degrees of freedom;namely three translations in x, y, and z di-rections. This element can be used for three-dimensional modeling ofsolids with or without reinforcement and it is capable of accounting forcracking of concrete in tension, crushing of concrete in compression,creep and large strains. The output from the thermal analysis, namelytemperatures, can be applied as a thermal-body-load on the structuralmodel to evaluate the mechanical response of steel-concrete compositegirder. The 3-D structuralmodel and themeshing adopted in the analysisare shown in Fig. 2(c).

To account for composite action between concrete slab and topflange of the steel girder, node to node interaction was discretized

in the structural model. The same nodes are shared between thesolid elements of the concrete slab and the shell elements of the topflange of the steel girder. To discretize the boundary condition inthe structural finite element model, the support conditions of thebridge girder were applied on multi-line nodes at the lower face ofthe bottom flange as shown in Fig. 2(c). This boundary condition re-flects practical scenario, reduces stress concentration at boundarynodes, and improves convergence of (finite element) solution.

3.4. Material properties during heating, decay and after cooling

Thermal and mechanical properties of steel and concrete varyin different stages of the analysis. For stage 1 of analysis, at room

(b)

(a)

38 E. Aziz, V. Kodur / Journal of Constructional Steel Research 88 (2013) 34–42

temperature, typical stress-strain model of grade 50 steel (fy =345 MPa) is used for steel with strain hardening.

In stage 2, during heating phase, the temperature dependent ther-mal and mechanical properties of steel and concrete are assumed tofollow as that of Eurocode 2 and 3 provisions [9,10]. The variation ofmechanical and thermal properties with respect to temperatures isdifferent in heating phase as compared to cooling phase and dependson the maximum temperature reached during heating phase. Duringthe cooling phase, the yield strength of steel is assumed to be reducedby 0.3 MPa/°C, when steel temperature exceeds 600 °C [5]. Also, thecompressive strength of concrete after cooling is assumed to be 10%less than the strength attained at the maximum temperature [11].This deterioration in strength properties are assumed to vary linearlybetween the maximum temperature attained and the room tempera-ture. However, all the thermal properties of steel and concrete includ-ing; thermal expansion, thermal conductivity, and specific heat areassumed to be fully reversible during the decay phase.

In stage 3, after cooling of the fire exposed girder, the residualyield strength of steel after cooling down to room temperature is as-sumed to have decreased by 0.3 MPa/°C, when maximum steel tem-peratures exceeded 600 °C [5]. The residual compressive strength ofconcrete after cooling down to room temperature is assumed to be10% less than the strength attained at the maximum temperature.This assumption is according to Eurocode 4 provisions [11].

L /30

Fig. 4. Comparison of predicted and measured response parameters in fire exposedbeam-slab assembly.

(a) Cross sectional temperatures(b) Mid-span deflection.

4. Model validation

There is lack of fire test data on the residual strength of bridgegirders under fire conditions. Therefore, the validation of the above de-veloped ANSYSmodel was carried out on a steel beam-concrete slab as-sembly (4.5 m span), typical to that in buildings, tested by British SteelCorporation under ISO 834 fire exposure [12]. The steel-concrete as-sembly, together with sectional dimensions are shown in Fig. 3. Thiscomposite assembly has steel yield strength of 255 MPa and a concretecompressive strength of 30 MPa. The steel beam in this case was notinsulated.

The validation is carried out for stages 1 and 2 of the analysis. Butno validation could be done in stage 3 as no test data is available forresidual strength of fire exposed bridge girder. The validation processduring fire exposure phase included comparison of both thermal andstructural response predictions from the analysis with that reported

P(a)

(b)

P P P1.125 m1.125 m 1.125 m

4.50 m

642.0 mm

Concrete Slab130.0 mm12.6 mm

257.0 mm

146.0 mm

7.57 mm

Fig. 3. Tested beam-slab assembly selected for validation.

(a) Beam layout(b) Transverse section.

in the fire test. The analysis was carried out with the same meshdiscretization and high temperature properties as discussed above.

As part of room temperature (stage 1) validation, predicted capac-ity of steel-concrete beam assembly from analysis is compared withthat reported by the authors. The authors computed the capacity ofthe steel-concrete beam assembly by applying relevant design equa-tions. Accordingly, the reported capacity of the beam-slab assemblyis 110 kN, while the current analysis predicted the capacity to be116 kN. Thus, the load carrying capacity predicted by finite elementmodel is within 5% variation of that reported by the authors. Theslightly higher capacity predicted from the analysis can be attributedto the nonlinear geometric and material nonlinearity considered inthe current analysis.

The validation process during fire exposure phase (stage 2) in-cluded comparison of both thermal and structural response predic-tions from the analysis with that reported in the fire test. Fig. 4(a)shows a comparison of predicted steel temperatures (by the finite el-ement model) with that measured in the fire test. It can be seen thatthe top flange of the beam experienced much lower temperatures ascompared to bottom flange. This is due to the “heat-sink” effect ofconcrete slab that dissipate the temperature in the top flange becauseof lower thermal conductivity and higher thermal capacity of con-crete as compared to steel. The web temperatures are slightly higher

Fig. 6. Time-temperature curves for different fire scenarios used in analysis.

39E. Aziz, V. Kodur / Journal of Constructional Steel Research 88 (2013) 34–42

than that in the bottom flange and this is due to the fact that thicknessof the web is much lower than that of the flanges. Overall, predictedtemperatures from the analysis compare well with measured datafrom the test. The slight differences can be attributed to variation ofthe heat transfer parameters, such as emissivity and convection coef-ficients, used in the analysis as compared to actual values encoun-tered in the test (furnace).

The comparison of mid-span deflections predicted by ANSYS modeland those measured in the test is shown in Fig. 4(b). It can be seen thatthe mid-span deflection gradually increases with time at the earlystages of fire (up to 13 min). These initial deflections are mainly dueto high temperature gradients that develop across the top and bottomflanges of the steel section and the slight reduction in elastic modulusof steel resulting from increased temperatures in the girder. After13 min, the rate of deflection increases slightly due to spread of plastic-ity that result from faster strength and stiffness degradation of steel as aresult of high temperatures. At about 21 min, bottom flange and webtemperatures exceed 600 °C and this leads to rapid rise inmid-span de-flection due to the formation of plastic hinge at themid-span section. Fi-nally, the failure occurs at 23 min when the mid-span deflectionexceeds the deflection limit (L/30).

Overall, predictions from the ANSYS match well with the reportedtest data. The slight differences in deflection predictions can be attrib-uted to minor variations in idealization adopted in the analysis, suchas stress-strain relationship of steel and concrete. It can be seen thatANSYSmodel can predict the time to failure with a good acceptability.For instance, the predicted failure time was almost at the same time(23 min) for both ANSYS model and the test considering deflectionlimit state as the governing failure criterion.

5. Case study

The applicability of the above developed finite element model toevaluate the residual capacity of the fire exposed steel-concrete com-posite bridge girder is illustrated through a case study.

5.1. Selection of bridge girder

A simply supported bridge girder, that is part of a steel bridge, wasselected for residual strength analysis [13]. The steel bridge comprisesof five hot rolled steel girders of W33x141 supporting a reinforcedconcrete slab of 200 mm thickness. The steel girder is assumed tobe in full composite action with slab and to be laterally supportedby transverse diaphragms at the mid span, as well as at both ends,to prevent lateral movement as shown in Fig. 5. The bridge girder is12.2 m in span length and has two expansion joints at its ends witha width of 36 mm. The girders are assumed to be fabricated fromGrade 50 steel (yield strength of 350 MPa), while the concrete usedin slab is of compressive strength of 30 MPa.

5.2. Fire and loading scenarios

In the analysis, three fire scenarios namely, hydrocarbon fire, mod-erate design fire, and external design fire were considered to studythe effect of fire severity on the residual capacity of the bridge girder.

Concrete slab of 0.20m thickness Steel girder (W

2.59 m

Loading

Fig. 5. Transverse section of a brid

In Case 1, the bridge girder was exposed to hydrocarbon fire, while inCase 2, a designfire exposurewas consideredwith the peakfire temper-ature reaching to 800 °C, followed by a 60 min steady state burning,and then entering the decay (cooling) phase. In Case 3 an external de-sign fire with a maximum temperature of 680 °C and a 45 min steadystate burn-out prior to decay phase was used. The time-temperaturecurves representing Cases 1, 2, and 3 are shown in Fig. 6.

The structural analysis on the bridge girder was carried outunder static applied loading comprising of dead load plus 30% liveload. The self-weight of the girder section (2.0 kN/m) and that con-tributed from the tributary area of the concrete slab and wearingsurface of the deck (22.5 kN/m) were considered in the dead loadaccording to AASHTO provisions [14]. For the live load, a uniformlydistributed load of 9.3 kN/m, representing 0.3 times the live loadwas applied.

6. Results and discussion

Result of stage 1 of the analysis, at room temperature is presentedin Fig. 7 in the form of load-mid-span deflection response. It can beseen that the mid-span deflection increases linearly with load incre-ments till yielding of steel and then the response becomes nonlineardue to the onset of material and geometric nonlinearity that havebeen incorporated in the analysis. In the nonlinear range of response,the mid-span deflection increases at a faster pace with small incre-ments in loading and this is mainly due to spread of plasticity in thegirder. This increase in the load carrying capacity can be attributedto strain hardening of steel. Finally, the girder attains failure when itcan no longer sustain any further increase in load.

In stage 2 of the analysis both thermal and structural responses arecritical in evaluating the fire performance of the girder. Results fromANSYS thermal analysis are plotted in Fig. 8 to illustrate the tempera-ture distribution in the steel-concrete composite girder as a functionof time for three cases of fire exposure under Cases 1, 2, and 3. It canbe seen in Fig. 8 that the top flange temperature in all three cases is

33x141) Diaphragm (lateral support)

Stiffener(16mm thickness)

2.59 m 1.3 m

ge girder near the supports.

Fig. 7. Load-deflection response of the bridge girder at ambient conditions (Stage 1).

(a)

(b)

(c)

Fig. 8. Temperatures progression in a bridge girder subjected to different fire scenarios(Stage 2).

(a) Hydrocarbon fire (Case 1)(b) Moderate design fire (Case 2)(c) External design fire (Case 3).

40 E. Aziz, V. Kodur / Journal of Constructional Steel Research 88 (2013) 34–42

much lower as compared to the bottom flange. This is mainly due to theheat sink effect of concrete slab that dissipates heat from top flange ofsteel girder to concrete slab. Also, temperatures in the web are slightlyhigher as compared to that in bottom flange and this is because theweb is much more slender (lower thickness) than flanges and thisgenerates rapid rise in web temperatures. But after the steady stateperiod and entering the decay phase, web temperatures decreaseat a faster rate than that in bottom flange temperature due tolower thickness and higher surface area of the web as compared tothe flange. In the cooling phase, the top flange looses heat at a slowerrate as compared to theweb and bottom flange. This is because of thepresence of concrete slab that gains and dissipates heat slowly due tolower thermal conductivity and higher specific heat of concrete.Therefore, it takes longer time for concrete slab and top flange tocool down.

The large difference in temperatures between theweb andmid-depthof the slab leads to significant thermal gradients across the girder-slabcross section. These thermal gradients are primarily influenced by thefire scenario (fire severity). For example, at 15 min the thermal gradientis 950 °C in Case 1, as compared to 580 °C in Case 2 and 480 °C in Case 3.In general, higher thermal gradients produce higher thermal strains atthe bottom of the steel girder (and in web), as compared to that in con-crete slab. Thus, a significant curvature (thermal bowing) is developedin the girder, resulting in high thermal stresses even in a statically deter-minate girder (unrestrained girder). The developed curvature at the ini-tial stages of fire exposure is independent of applied loading becausethis curvature results mostly from the thermal gradient effect. Therefore,the curvature, resulting from the thermal gradients, alone contributes tothe deflection at the early stage of fire exposure.

The structural response of the bridge girder in stage 2 of the analysis,during fire exposure is illustrated in Fig. 9, whereinmid-span deflectionis plotted as a function of fire exposure time. The load-deflection re-sponse is plotted for three fire exposure scenarios (Case 1, Case 2, andCase 3) that are considered in the analysis. The general trend of deflec-tion progression can be grouped in to different stages. At the early stageof thefire exposure, themid-span deflection increases due to significantthermal gradients that develop along the cross section of the girder.During the intermediate stage of fire exposure, mid-span defection in-creases linearly up to occurrence of first yielding, which depends onthe temperature progression in the girder cross section. Therefore, thetime at which yielding occurs varies with type of fire exposure. Aftertemperature in steel exceeds 400 °C, during the heating phase of fireexposure, girder deflection increases with time at a faster rate due tospread of plasticity and deterioration in strength and stiffness proper-ties of steel and concrete. During the steady state burning (when firetemperatures remain constant), the progression of mid-span deflectionslows down significantly due to steady state temperature in the girder(steel) section. However, in Case 1 themid-span deflection in the girder

continue to increase till failure since the plasticity spreads to much ofthe girder section, which resulted fromhigh fire temperatures. Towardsfinal stages of fire exposure (in the cooling phase), the mid-span

Fig. 9. Effect of fire severity on the flexural response of bridge girder during fire expo-sure (Stage 2). Fig. 10. Effect of fire severity on the residual capacity of fire exposed bridge girder

(Stage 3).

41E. Aziz, V. Kodur / Journal of Constructional Steel Research 88 (2013) 34–42

deflections in Cases 2 and 3 decrease since the girder temperature re-duced significantly. This is due to recovery of strength and stiffnessproperties of steel and concrete due to cooling phase of fire.

The effect of fire scenario on the performance of the bridge girdercan be gauged by comparing mid-span deflections from Cases 1, 2,and 3 as shown in Fig. 9. In Cases 2 and 3, the bridge girder survivedburn-out conditions under moderate design fire and external designfire scenarios; however in Case 1, the girder failed at 20 min into hy-drocarbon fire exposure. This can be attributed to the fact that thefires in Cases 2 and 3 are less severe as compared to hydrocarbonfire in Case 1. For instance, the maximum fire temperature attainedin hydrocarbon fire is about 1100 °C, (Case 1) as compared to680 °C in the case of external design fire (Case 3) and 800 °C in thecase of moderate design fire (Case 2). Also, the heating rate at earlystages of fire is much higher in a hydrocarbon fire, than under exter-nal or moderate design fires, and this produces higher thermal gradi-ents in the section. As an illustration, the fire temperatures at 12 mininto fire is 1053 °C in Case 1, as compared to 800 °C and 680 °C inCase 2 and 3 respectively. This differential in peak fire temperatureand variation in heating rate between these three fires lead to slowerdeterioration in strength and stiffness properties in steel and concreteunder Cases 2 and 3, as compared to Case 1. As a result, the bridgegirder sustained the applied loading for the entire fire durationunder external and moderate fire exposure scenarios (Case 2 andCase 3) and survived in the fire.

A summary of the analysis results, including the post-fire residualcapacity of the bridge girder under different fire scenarios arepresented in Table 2. The residual capacity (strength) of bridge girderexposed to maximum fire temperature of 800 °C (in Case 2) is about70% of the room temperature capacity, as compared to 84% under firescenario with 600 °C peak (fire) temperature (Case 3). The lower re-sidual capacity in Case 2, is due to higher temperatures reached in thesteel section in Case 2, as compared to that in Case 3. Therefore, steel(girder) in Case 2 lost about 20% of its room temperature (yield)strength and stiffness permanently, which occurred mainly due tosteel temperatures exceeding 600 °C. As a result, the steel girder inCase 2 regained less stiffness and strength after cooling down toroom temperature as compared to that of girder in Case 3. This

Table 2Results from residual strength analysis of fire exposed bridge girder.

Case Fire scenario Max. fire temperature Max. steel temperature Ro

Case 1 Hydrocarbon fire 1100 °C 1000 °C 42Case 2 Moderate fire 800 °C 795 °C 42Case 3 External fire 680 °C 670 °C 42

resulted in permanent residual strains (deformations), which can beseen in Fig. 10, and this reflects the level of plasticity reached in thegirder during fire exposure. The residual deformation is higher inCase 2, as compared to Case 1, since the steel temperature in Case 2reached 800 °C as compared to 680 °C in Case 3. Furthermore, theconcrete slab in Case 2 also lost some of its strength due to spreadof temperature in the bottom layer of the slab, which reached about500 °C as compared to about 300 °C in Case 3.

7. Conclusions

A nonlinear finite element analysis was applied to evaluate resid-ual capacity of fire exposed steel bridge girders. Based on the resultsof analysis the following conclusions can be drawn:

1. Three stages of analysis is required for evaluating the residualstrength of fire exposed steel bridge girders, namely at ambientconditions, during fire exposure, and following cooling of fire ex-posed girder.

2. ANSYS can successfully be applied to evaluate the response of fireexposed bridge girders. The thermal response can be simulatedusing SOLID70 elements, while structural response can be simulat-ed using SHELL181 and SOLID65 elements.

3. The type of fire exposure and fire severity has significant influenceon resulting residual capacity of fire exposed steel bridge girders.

4. A bridge girder when exposed to external design fire with maxi-mum fire temperature of 680 °C has a residual capacity of about84% as compared to 70% when exposed to moderate design firewith a maximum fire temperature reaching 800 °C.

5. A steel bridge girder experiences failure under fire conditionswhen the maximum fire temperature is around 1100 °C, as in thecase of typical hydrocarbon fires.

Acknowledgments

This material is based upon work supported by the National Sci-ence Foundation (NSF) under Grant No. CMMI-1068621 and the au-thors wish to acknowledge NSF's support. Any opinions, findings,

om temperature capacity (kN) Residual capacity (kN) % of original capacity

70 Failure under fire –

70 2974 70%70 3579 84%

42 E. Aziz, V. Kodur / Journal of Constructional Steel Research 88 (2013) 34–42

conclusions, or recommendations expressed in this paper are those ofthe authors and do not necessarily reflect the views of the NSF.

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