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Conference for PhD students in Civil Engineering

CE-PhD 2014, 10-13 December 2014,Cluj-Napoca, Romaniawww.cephd.ro

Behavior of steel columns in fire conditions

Milan Petrović*1, Todor Vacev2 Srđan Živković3

1,2,3 University of Niš, Faculty of Civil Engineering and Architecture, Aleksandra Medvedeva 14, 18000 Niš,

Serbia

Abstract

Upon outbreak of fire, gas temperature in fire compartment evolves in stochastic manner. Heat

energy is transferred from fluid – air by convection and radiation to surfaces with lower

temperature, i.e., to structural elements and boundary elements of the fire compartment, and furtherthrough the element by conduction. That way temeperature in elements increase. Thereby,

mechanical properties of steel are reduced and should be treated as such in analysis.

In this paper a comparative analysis of behavior of axially compressed steel elements (HE-A profile

and squared hollow profile) in fire conditions was performed. Comparison was conducted according

to the following criteria: development of temperature in elements and reduction of load bearing

capacity with temperature increase. Temperature development was obtained analitically, based on

the standard logarithmic curve, after EN 1993-1-2, as well as numerically, using the Finite Element

Method. In terms of load bearing capacity, calculation was performed using EN 1993-1-2. Results

indicate that no significant differences occur in behavior of these profiles in fire conditions, and

that, as well as in normal conditions, it is more convenient to use squared hollow profiles, as moreresistant to the loss of stability.

Keywords: Fire, Eurocode, Standard logarithmic curve, High temperature

1. Introduction

Over the last few decades design of objects resistant to fire actions is experiencing very intensive

development. New methods for analysis have been developed, based on realistic behavior of objects

in case of fire outbreak (performance-based design), which takes into account realistic conditionsduring the fire (properties of fire sectors, ventilation conditions, type of fuel), as well as actual

response of structures subjected to high temperature. Such approach overcame classic method,

where, according to fire resistance required by standards, element dimensions and potential

thckness of fireproof materials are chosen based on fire resistance of elements determined in

advance – prescriptive approach. Fire resistance of elements was determined by experimental

testing in standard testing furnace (standard ISO-834), with controlled temperature increment

according to standard logarithmic curve. Calculation is based on properties of steel at ambient

temperature, and required fire resistance of structure is achieved by encasement with certain layer

of fire insulation, unlike contemporary method which implies use of analytic methods for

determining fire resistance, considering variation of steel properties with temperature rise [1]. By

using contemporary method, required thickness of fireproof materials can be significantly

* Corresponding author: Tel./ Fax.:+381 63 73 71 654

E-mail address: [email protected]

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decreased, increasing that way the rationality and cost effectiveness of the structure. However, due

to the fact that large database exists with determined fire resistance of elements, conventional

method is, to a certain degree, retained in contemporary European technical regulations.

Upon outbreak of fire, gas temperature in fire compartment develops in stochastic manner. Heat

energy is transferred from fluid – air by convection and radiation to surfaces with lower

temperature, i.e. structural elements and boundary elements of fire compartment (floors, ceilings,

walls). Although heat transfer is treated by special field of science, results of that analysis is

important for engineers, because it provides ammount of heat which acts on the unit area of surface

– heat flux, which represents input data - loading of the structure. Based on such input data, it is

possible to evaluate temperature development in the element, which represents the basis for further

mechanical analysis. Hence, new approach treat fire action as a hazardeous action and it is

introduced in structural analysis. European standards [2] classify fire action as accidental,

considering probability and frequency of appearance of such actions during the service life of the

object. Analysis is based on limit state, and limit criteria that structure or its part need to meet are inthe strength domain, in the temperature domain, or in the time domain.

Taking everything afore mentioned into account, in this paper comparative analysis of behavior of

axially compressed steel elements was performed. Considered elements were HE-A profile and

squared hollow profile. Comparison was conducted by the following criteria: development of

temperature in elements and reduction of load bearing capacity with temperature increase.

Temperature development was obtained analitically, based on the standard logarithmic curve [3], as

well as numerically, using the Finite Element Method, and ANSYS software, which provides

opportunity of solving thermal problems, among others. In terms of load bearing capacity,

calculation was performed using [3]. It is assumed that elements are located inside the fire

compartment, being that way exposed to fire on all four sides.

2. Steel properties at high temperatures

Analysis of behavior of structural elements in fire conditions comprises of two categories: thermal

and mechanical analysis. With the intention of as realistic analyzing of problem as possible, it is

hence neccessary to know the thermal as well as the mechanical properties of steel at high

temperatures. Steel is classified as non-combustible and non-burning material, but its properties are

significantly reduced at high temperatures. They were obtained based on the experimental testing

[4], and they are included in European standards for steel [3].

2.1 Thermal properties of steel at high temperatures

Thermal properties that are significant for the conducted analysis comprise of: specific heat,

thermal conduction and emissivity.

Specific heat represents amount of heat Q necessary to change the temperature of the body unit

mass m for ΔT=1°C . Expression for obtaining specific heat states:

Qc

m ΔT

=

⋅

⋅

J

kg K

(1)

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Figure 1 represents temperature dependent specific heat, obtained from expressions given in [3]. In

temperature range of 700-800 °C a sharp increase of the necessary heat occurs, due to crystal phase

change of the steel. Recommendations that can be found in literature [5] state that for simple

calculation models approximate value of 600 J/kgK can be used, since it provides accurate

solutions.

Figure 1. Variation of specific heat of steel Figure 2. Variation of thermal conductivity

with temperature. of steel with temperature.

Thermal conductivity represents amount of heat Q transferred during the time t through distance L

in direction perpendicular to cross-section area S with temperature difference of Δt :

= ⋅

⋅

Q Lλt S Δt

⋅ ° W

m K (2)

Steel is characterized by high thermal conductivity, but with temperature increasing thermal

conductivity coefficient decreases, which is presented by curve on Figure 2. For simple calculation

models it is recommended to use coefficicient of thermal conductivity as a constant value of

45W/mK.

In case of elements heated only from one side (when elements are located on fire compartment

boundary) temperature of steel on the opposite, unexposed side will, due to the high thermal

conductivity of steel, in short period of time reach the same temperature as on the fire exposed side.

For that reason, small thermal gradient across the cross-section can be neglected, and uniform

temperature across the cross section assumption can be made. As a consequence, no bending occurs

in elements due to the different temperatures on opposite edges, but only longitudinal deflections

occurs (elongation).

Emissivity is the ability of the material to emit thermal energy through radiation, and it is defined

as the ratio of the radiation emitted by the surface of the material to the radiation emitted by an ideal

black body at the same temperature. Value of the emissivity is in range of 0 to 1. According to

recommendations given in [3], emissivity of steel is taken as 0.7, while emissivity of fire is 1.

2.2 Mechanical properties of steel at high temperatures

Structural analysis requires knowing of the stress-strain diagram for steel at various temperatures


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(Figure 3), as well as variation of the yield limit and the modulus of elasticity with temperature

(Figure 4). From the curve k y,θ in Figure 4, it is obvious that steel at the temperature of 600 °C

loses approximately 50 % of its load-bearing capacity, and the temperature of 1200 °C was taken as

the limit at which steel completely loses its load bearing capability.

Figure 3. Stress-strain diagram of steel Figure 4. Reduction factors for mechanical

at high temperatures. properties of steel

Density of steel is taken as the constant value of 7850 kg/m3 during the fire exposure, too.

3. Development of temperature in steel elements

Fire compartment is a room or a set of rooms limited with elements (walls, celing, floor and doors)

which have fire resistance required by standards, i.e., it is assumed that in required period of time

fire will be kept within the fire compartment.

Development of gas temperature inside the fire compartment can be obtained using nominal time–

temperature curves (standard logarithmic curve) or using natural fire models [2]. Although standard

logarithmic curve does not correspond to real fire curve, it is retained in European standards for its

simplicity and because of the large database with fire resistance of elements obtained using that

same curve. It resulted from the necessity for controlled conditions in testing furnace, which will be

used repeatedly for every element tested. Although such curves do not simulate real fire conditions,

they are convenient for wide practical usage. More realistic view of fire is obtained using natural

fire models. European standards for fire classify fire models as simplified and advanced models.

For simplified models uniform temperature distribution in the compartment through time isassumed, as well as for nominal curves, but additionally the following parameters are considered:

ventilation conditions, specific fire load and thermal properties of materials used for boundary

elements of fire compartment. Furthermore, cooling phase is taken into account. These fire

conditions are described using parametric curves. On the other side, advanced models (one zone,

two zone, Computational Fluid Dynamic - CFD models), evaluate temperature development in fire

compartment fully in time and space dependent manner. CFD models require application of

software developed for that purpose. One such software is Fire Dynamics Simulator [6]. Analysis

conducted in the paper is limited only to standard logarithmic curve, based on which development

of temperature in elements with time is evaluated.

Based on everything mentioned in this chapter, temperature development in steel elements (HEA profile and squared hollow profile) were obtained, due to the high temperatures exposure. Curves

are obtained using two approaches: analytic, based on expressions given in [3], and numeric, using


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the Finite Element Method (FEM), and ANSYS software. For the analysis, profiles with nearly the

same cross-section area were chosen: HEA 240, with cross-section area of A=76.80 cm2, and

squared hollow profile with cross-section area of A=74.71cm2. Analogue to supporting boundary

conditions in static analysis, in thermal analysis boundary conditions represent initial value of

temperature of the gas in the fire compartment and on the surfaces of the elements when the fire

starts. In this case both values are taken as T 0=Tm0=20 °C. Standard logarithmic curve is defined by

expression (3):

( )log= + ⋅ +g 10θ 20 345 8t 1 (3)

3.1 Analytic evaluation of temperature development in steel elements according to EN1993-1-2

Expression for determining temperature increment in unprotected steel element in time interval Δt[3] states:

ma,t sh net,d

a a

A / V Δθ k h Δt

c ρ= ⋅ ⋅ ⋅

⋅ (4)

Section factor Am /V represents ratio between the surface area of the member per unit length Am and

the volume of the member per unit length V . For considered elements section factors are:

- for HE-A profile: Am/V=178,24- for squared hollow profile: Am/V=107,08.

These values indicate that, with nearly the same volume per unit length, HE-A profiles have slightlyhigher value of the surface area per unit length directly exposed to fire. However, shadow effect

takes into account surfaces of the elements that are not directly exposed to fire, but are slightly

sheltered, which is the case with jagged profiles, such are I or HE-A profiles, while for squared

hollow profiles that effect doesn’t exist. Value of the correction factor for the shadow effect for I

and similar profiles is obtained from expression (5), while for squared hollow profiles value of the

factor is 1.

[ ]

[ ]m b

sh

m

A / Vk 0.9

A / V= ⋅ (5)

[Am/V] b - box value of the section factor [1/m].

k sh=0,62 - for HE-A profile

k sh=1 - for squared hollow profile

Figure 5 – Section factor for a) HE-A profile and b) squared hollow profile


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By multiplying section factors for both elements with shaddow effect factor k sh, approximately the

same values are obtained (k sh,HE-A=110,50 ≈ k sh,[]=107.08). Considering the fact that remaining parameters in expression (4) are the same in both cases, it can be concluded that temperature

increment for both profiles during the time interval Δt will be nearly the same. Heat flux hnet,d comprises of the components of heat flux due to convection hnet,c and due to

radiation hnet,r , and represents amount of heat energy that acts on the unit area of the material

surface.

Time interval Δt is, based on the recommendation given in [3], taken as 5 s. Based on expression(4), using tabular processing of data in Microsoft Excel, temperature was evaluated for the first 60

min upon outbreak of fire. Further, obtained results will be presented in the form of time–

temperature curves.

Time-temperature curves for the gas in fire compartment and in the steel elements are presented

simultaneously on Figure 6-a. Time-temperature curves for the HE-A profiles, taking the shadow

effect into account and neglecting it, are presented on Figure 6-b. Comparison of results for specific

heat taken as a variable and as a constant value according to recommendations given in [5], is presented on Figure 6-c.

a) b) c)

Figure 6 – a) Temperature development in elements; b) influence of the shadow effect;

c) Influence of specific heat

3.2 Numerical evaluation of temperature development in steel elements

Numerical calculation of steel temperature evolution was conducted using FEM and ANSYS

software, which is convenient for analyzing of thermal problems. For modeling, ‘shell’ finite

element was used, suitable for simulating conduction through element thickness, as well as in-plane

thermal conduction. Material properties are entered as temperature dependent, as it was explained in

Section 2.

a) b)


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Figure 7 – Element temperatures after 60 min exposure: a) HE-A profile ; b) [] profile

a) b)

Figure 8 – Time-temperature curves for elements: a) HE-A profile; b) [] profile

Element temperatures after 60 min of exposure to fire are presented on Figure 7. Temperature

development through time is presented on Figure 8.

4. Structural analysis of behavior of columns

Thermal analysis, which provides time-temperature curve for steel elements, combined with

structural analysis, which provides critical temperature of steel, as a result provide fire resistance of

an element [1]. In this section, one of the criteria mentioned in the first section will be analyzed –

criteria of the strength limit state. Eurocode 3 provides methods for determining design resistance ofelements in fire conditions, depending on the stress state in the elements themselves. For elements

subjected to compression, for cross-section classes 1, 2, and 3, design buckling resistance in fire

conditions is determined by:

, , , , ,/b fi t Rd y θ y M fiN χ A k f γ= ⋅ ⋅ ⋅ (6)

For considered elements, dependence of the load bearing capacity from temperature was obtained

using expression (6), Figure 9. Based on this curve, load bearing capacity after the time period

representing the fire resistance required by standards is determined, and it is compared with the

design value for actions in fire conditions.


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Figure 9 – Reduction of load bearing capacity of an element with temperature increment

5. Review of the results and conclusions

Based on the analysis conducted in the paper, a few conclusions and recommendations for practicalapplication can be obtained. From the curve in Figure 7, it can be concluded that, by taking the

shadow effect into account for jagged profiles, lower increment of temperature is obtained, which

influences on the rationality of the structure, while by neglecting it, more conservative solutions are

obtained. From the curve in Figure 8 it is obvious that no significant differences occur if specific

heat is taken as the constant value and as a variable, except in the region of 700-800 °C, when

structural phase change occurs. However, for practical application this deviation does not have

influence on final results, so the authors have the opininon that such approximation is justified.

Time-temperature curves for both profiles are matching (Figure 6-a), which is verified by numerical

results (Figure 8). Furthermore, from Figure 9 it can be seen that curves are approximately parallel,

i.e., percentual loss of the load bearing capacity is the same in both cases, which is directly

dependent only on mechanical properties reduction, and not on the profile type.

It can be concluded that in terms of thermal and structural analysis, choice between the two

considered profiles does not have influence on rationality of the structure. Hence, as well as in

normal conditions, squared hollow profiles can be characterized as more convenient for compressed

members, due to the higher resistance to the loss of stability.

This paper is limited only to nominal time-temperature curves for gas in fire compartment, which

are more convenient for practical usage. More realistic overview of fire conditions can be obtained

by using of natural fire models. Thus, temperature development in elements could be more

precisely determined, which can be subject for further investigation in this field.

6. References

[1] Buđevac D, Marković Z, Bogavac D, Tošić D. Steel structures, Faculty of civil engineering, Universityof Belgrade, 1999.

[2] EN 1991-1-2:2002. General actions – Actions on structures exposed to fire

[3] EN 1993-1-2:2005. General rules – Structural fire design

[4] Schleich J.B.: Maximum stress level of structural steel in function of the temperature – strain hardeningincluded – through numerical simulations of uniformly heated steel beams during transient state bendingtests, Working documents, Luxembourg, 1988-1989.

[5] Purkiss J.A, Fire safety engineering, Design of structures, 2nd ed.Oxford: Elsevier 2007.

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