EC3 Design of Steel Structures for Firelibrary.tee.gr/digital/m2247/m2247_l11c_eng.pdfDetails of Eurocode structural fire resistance calculations are given in the appropriate articles

NFATEC – L11c – Design of Steel Structures for fire (07/11/2003)

{LECTURE}

{LTITLE}

EC3 Design of Steel Structures for Fire

{/LTITLE}

{AUTHOR}

Roger

{/AUTHOR}

{EMAIL}

[email protected]

{/EMAIL}

{LASTEDIT}

Richard 07/11/03

{/LASTEDIT}

{OBJECTIVES}

On successful completion of this lecture you should:

• Understand that steel progressively loses strength and stiffness at elevated temperatures.

• Understand how passive fire protection works in increasing fire resistance of steel members.

• Understand that other strategies may be used in fire engineering design to provide the required fire resistance, including overdesign, selection of framing systems, and use of sprinklers.

• Understand the principles of the simple design calculations of resistance in fire conditions of beams and columns, and the concept of critical temperature.

• Understand the methods of calculating the thermal response of protected and unprotected members to increase of atmosphere temperature in a fire.

{/OBJECTIVES}

{OVERVIEW}

• Steel suffers a progressive reduction in both strength and stiffness as their temperature increases in fire conditions. EC3 provides material models of stress-strain curves for steel over an extensive range of temperatures.

• Fire resistance of structural elements is quoted as the time at which they reach a defined deflection criterion when tested in a furnace heated according to a standard ISO834 time-temperature curve.

• Traditional fire protection of steelwork is by covering it with insulating material during construction. However it may be possible under EC3 to use a combination of passive and active strategies to ensure fire resistance.

• EC3 calculation of fire resistance takes account of the loading level on the element. However the safety factors applied are lower than in those used in strength design.

• Fire resistance may be calculated in terms of time, as a load-bearing resistance at a certain time, or as a critical element temperature appropriate to the load level and required time of exposure.

• Critical temperature is calculated for all types of member of classes 1, 2 or 3 from a single equation in terms of the load level in fire. Class 4 sections are universally assumed to have a critical temperature of 350°C.

• EC3 provides simple calculations for the load resistance in fire of all types of elements. In cases where the strength is controlled by buckling an empirical correction factor of 1,2 is used to account for a number of effects.

• It is possible to calculate the temperature growth of protected or unprotected members in small time increments, in a way which can easily be implemented on a spreadsheet.

{/OVERVIEW}

{PREREQUISITES}

An appreciation of

• Simple element design for strength and serviceability according to EC3 and EC4.

• Framing systems currently used in steel-framed construction. • The basic concepts concerning fire behaviour, fire resistance and Eurocode

methods of simplified thermal analysis.

{/PREREQUISITES}

{SECTION}

{STITLE}

Basic structural fire resistance design of members

{/STITLE}

{SUMMARY}

Details of Eurocode structural fire resistance calculations are given in the appropriate articles on EC3 and EC4, together with an example design calculation using the simple calculation models, and so this section concentrates on the principles of these methods rather than their detail. {ECLINK}EC4 Part 1.2 {/ECLINK}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}

Notation

{/SUMTITLE}

Eurocode notation is very systematic, and a summary of notation used in fire engineering design is given here.

{PPT}eurocodes_general.pps{/PPT}

{DETAIL}

Eurocodes use a very systematic notation in which different symbols are used for general and particular versions of parameters. For example an effect of an action is denoted in general terms as E in establishing a principle; in particular members this might become the axial force N or the internal bending moment M. Subscripts denoting different attributes of a parameter may be grouped, using commas as separators, as in Efi.d.t which denotes the design value of the effect of an action in fire, at the required time of resistance. Commonly used notations in the fire engineering parts of Eurocodes 1, 3 and 4 are:

{EQN}e.gif{/EQN} Effect of actions

{EQN}g.gif{/EQN} Permanent action

{EQN}q.gif{/EQN} Variable action

{EQN}rfi.gif{/EQN} Load-bearing resistance

{EQN}tfi.gif{/EQN} Standard fire resistance time of a member

{EQN}tfirequ.gif{/EQN} Standard fire resistance time - nominal requirement

{EQN}theta.gif{/EQN} Temperature

{EQN}thetacr.gif{/EQN} Critical temperature of a member

{EQN}gamma.gif{/EQN} Partial safety factor

{EQN}psi.gif{/EQN} Load combination factor

{FIGURE}Table: Eurocode notation for fire engineering design{/FIGURE}

and the following subscript indices may be used alone or in combination:

{EQN}a.gif{/EQN} Accidental design situation

{EQN}cr.gif{/EQN} Critical value

{EQN}fi.gif{/EQN} Relevant to fire design

{EQN}d.gif{/EQN} Design value

{EQN}theta.gif{/EQN}Associated with certain temperature (may be replaced by value)

{EQN}k.gif{/EQN} Characteristic value

{EQN}t.gif{/EQN} At certain fire exposure time (may be replaced by value)

{EQN}rank.gif{/EQN} Ranking order for frequency of variable actions

{FIGURE}Table: Subscripts used in fire engineering design{/FIGURE}

{/DETAIL}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}

Loadings

{/SUMTITLE}

The loadings for which structures are designed at the Fire Limit State are lower than those used for ambient-temperature structural design, because it is recognised that there is a very low probability of a severe fire occurring at the same time as abnormally high structural loads.

{PPT}actions.pps{/PPT}

{DETAIL}

Eurocode 1 Part 1.2 presents rules for calculating design actions (loadings) in fire, which recognise the low probability of a major fire occurring simultaneously with high load intensities. The normal Eurocode classification of loads is as permanent and variable; in fire the characteristic permanent actions (dead loading) are used unfactored ({EQN}gammaga.gif{/EQN}=1,0) while the principal characteristic variable action (imposed loading) is factored down by a combination factor {EQN}psi11.gif{/EQN} whose value is between 0,5 and 0,9 depending on the

building usage. The reduction factor or load level for fire design can be defined either as

{EQN}etafit1.gif{/EQN} (loading in fire as a proportion of ambient-temperature design resistance),

which is relevant when global structural analysis is used, or {ECLINK}EC4 Part 1.2 {/ECLINK}

{EQN}etafit2.gif{/EQN} (loading in fire as a proportion of ambient-temperature factored design load),

which is the more conservative, and is used in simplified design of individual members, when only the principal variable action is used together with the permanent action. This may be expressed in terms of the characteristic loads and their factors as

{EQN}etafit_eqn.gif{/EQN} (1)

Typical values of the safety factors specified in Eurocode 1 are:

{EQN}gammaga.gif{/EQN} =1,0 Permanent loads - accidental design situations

{EQN}psi11.gif{/EQN} =0,5 Combination factor - variable loads - office buildings

{EQN}gammag.gif{/EQN} =1,35 Permanent loads - strength design

{EQN}gammaq1.gif{/EQN} =1,5 Variable loads - strength design

{FIGURE}Table: Generic Eurocode safety factors used for fire engineering design{/FIGURE}

{PPT}principles.pps{/PPT}

{/DETAIL}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}

Basic principles of fire resistant design

{/SUMTITLE}

Structural fire resistance of a member can be established in any one of three domains; time, load-bearing resistance or temperature. For members for which buckling is not the failure type the Critical Temperature method is the simplest design process. Compression members and beams which experience lateral-torsional buckling have to be designed for their reduced load-carrying resistance in fire.

{DETAIL}

Structural fire-resistant design of a member is concerned with establishing that it satisfies the requirements of national building regulations over the designated time period when subjected to the appropriate nominal fire curve. This can be expressed in three alternative ways: {ECLINK}EC1 Part 1.2{/ECLINK}

• The fire resistance time should exceed the requirement for the building usage and type when loaded to the design load level and subjected to a nominal fire temperature curve:

{EQN}tfid_ineq.gif{/EQN}

• The load-bearing resistance of the element should exceed the design loading when it has been heated for the required time in the nominal fire:

{EQN}rfidt_ineq.gif{/EQN}

These are Resistance Methods, and are available for all types of isolated structural members.

• The Critical Temperature Method The design temperature associated with the required exposure to the nominal fire should not exceed its failure ("Critical") temperature when loaded to the design loading level:

{EQN}thetacrd_ineq.gif{/EQN}

This is only available for members whose strength is not limited by buckling.

{/DETAIL}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}The critical temperature method{/SUMTITLE}

This is the simplest method of calculating the fire resistance of an isolated loaded member in fire conditions. The method can be used only for member types for which deformation criteria or stability considerations do not have to be taken into account when using normal Eurocode 3 design. This allows its use for tension members or restrained beams, but eliminates it for both columns and unrestrained beams.

{PPT}crit_temp.pps{/PPT}

{DETAIL}

The critical temperature of a member is the temperature at which it fails to meet the standard fire-test criteria under its given loading. It can be determined from the degree of utilisation {EQN}mu0.gif{/EQN} of the member in the fire design situation.

{IMAGE}critical_temp_fig.gif{/IMAGE}

{TIMAGE}Figure 1. Critical temperature, related to degree of utilisation.{/TIMAGE}

The critical temperature, plotted above, is defined by the empirical relationship

{EQN}critical_temp_eqn.gif{/EQN}(3)

This is used for all except the very slender Class 4 sections, for which a single critical temperature of 350°C is specified as a safe level.

The degree of utilisation {EQN}mu0.gif{/EQN} is basically the design loading in fire as a proportion of the design resistance, where the latter is calculated at ambient temperature (or at time {EQN}t_eq_0.gif{/EQN}) but using the material partial safety factors which apply in fire design rather than in normal strength design:

{EQN}mu0_eqn1.gif{/EQN}(4)

A simple conservative version is

{EQN}mu0_eqn2.gif{/EQN}(5)

in which the reduction factor {EQN}etafi.gif{/EQN} may already be conservative.

{/DETAIL}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}

Section classification

{/SUMTITLE}

{PPT}classification.pps{/PPT}

{DETAIL}

It is essential for both the ambient-temperature and fire design of all members which act wholly or partly in bending that they are classified in order to establish the appropriate design calculation methods to be used. This is basically a check on the slenderness of the parts of the cross-section which act in compression in order to

assess their vulnerability to local buckling. This applies just as much in fire as in normal design, since the strain levels in fire are liable to become very high, and since strengths are reduced in fire these elevated-temperature material properties should be used when performing a section classification. It is worth re-stating briefly the definitions of the four possible classes of member:

• Class 1. Stocky cross-sections which can be used reliably in plastic strength calculations.

• Class 2. Whilst the member resistance may be calculated on the basis of its plastic capacity, it is not capable of sufficient extra rotation without the occurrence of local buckling to allow other hinges to form as part of a fully developed mechanism. The frame should therefore be designed elastically.

• Class 3. The member resistance should be calculated elastically as its initial yield capacity.

• Class 4. Slender cross-sections whose resistance is governed by elastic local buckling below the yield strength of the material.

In fire design when the simple calculation model is used all cross-sections are classified as for ambient temperature design.

{/DETAIL}

{/SUMMARY}

{TEST}

{TTITLE}

Fire resistant design

{/TTITLE}

{QUESTION}

{QTITLE}

Main notation

{/QTITLE}

{QTEXT}

Below is a list of main notations used in structural fire engineering and their meanings. Match the general notations to their correct meanings.

{/QTEXT}

{QTYPE}

M

{/QTYPE}

{FEEDBACK}

Refer to the module on Eurocode 3 structural fire resistance of members for more information on the notation used.

{/FEEDBACK}

{ANSWER}

E

{MARK}

1

{/MARK}

{MATCH}

effect of actions

{/MATCH}

{/ANSWER}

{ANSWER}

G

{MARK}

1

{/MARK}

{MATCH}

permanent action

{/MATCH}

{/ANSWER}

{ANSWER}

Q

{MARK}

1

{/MARK}

{MATCH}

variable action

{/MATCH}

{/ANSWER}

{ANSWER}

R

{MARK}

1

{/MARK}

{MATCH}

load bearing resistance

{/MATCH}

{/ANSWER}

{ANSWER}

t

{MARK}

1

{/MARK}

{MATCH}

standard fire resistance of a member

{/MATCH}

{/ANSWER}

{/QUESTION}

{QUESTION}

{QTITLE}

Subscripts

{/QTITLE}

{QTEXT}

Below is a list of common subscripts used and their meanings. Match the particular notations to their correct meanings.

{/QTEXT}

{QTYPE}

M

{/QTYPE}

{FEEDBACK}

It is important to understand the notation used by the Eurocodes in order to understand the design calculations of resistance in fire conditions of beams and columns. For more information take a look at the Section on basic structural fire resistant design of members.

{/FEEDBACK}

{ANSWER}

A

{MARK}

1

{/MARK}

{MATCH}

accidental design situation

{/MATCH}

{/ANSWER}

{ANSWER}

cr

{MARK}

1

{/MARK}

{MATCH}

critical value

{/MATCH}

{/ANSWER}

{ANSWER}

fi

{MARK}

1

{/MARK}

{MATCH}

relevant to fire design

{/MATCH}

{/ANSWER}

{ANSWER}

d

{MARK}

1

{/MARK}

{MATCH}

design value

{/MATCH}

{/ANSWER}

{ANSWER}

k

{MARK}

1

{/MARK}

{MATCH}

characteristic value

{/MATCH}

{/ANSWER}

{/QUESTION}

{QUESTION}

{QTITLE}

Fire resistance domains

{/QTITLE}

{QTEXT}

Under the Eurocodes there are three alternative ways to establish whether the structural fire-resistance of a member satisfies the requirements of the national building regulations over the designated design period, when subjected to the appropriate nominal fire curve. These are listed below. Match the frequency with which these are used in fire-resistant design.

{/QTEXT}

{QTYPE}

M

{/QTYPE}

{FEEDBACK}

The critical temperature method is used where the limit to useful behaviour is caused by material strength rather than by buckling. It is used for beams without lateral

freedom and tension members. Resistance methods have to be used for columns and unrestaruined beams. Direct time-domain analysis is only used with advanced calculation methods.

{/FEEDBACK}

{ANSWER}

Most used

{MARK}

1

{/MARK}

{MATCH}

Critical temperature method

{/MATCH}

{/ANSWER}

{ANSWER}

Fairly often used

{MARK}

1

{/MARK}

{MATCH}

Resistance methods

{/MATCH}

{/ANSWER}

{ANSWER}

Special cases

{MARK}

1

{/MARK}

{MATCH}

Direct time-domain calculation

{/MATCH}

{/ANSWER}

{/QUESTION}

{QUESTION}

{QTITLE}Critical temperature method{/QTITLE}

{QTYPE}MC

{/QTYPE}

{QTEXT}

The design temperature of an element loaded to the design level should exceed the critical temperature. True or False?

Tick only one answer.

{/QTEXT}

{ANSWER}

True

{CHECKMARK}0{/CHECKMARK}

{CHECK}No{/CHECK}

{UNCHECKMARK}1{/UNCHECKMARK}

{UNCHECK}Correct{/UNCHECK}

{/ANSWER}

{ANSWER}

False


{CHECK}Yes{/CHECK}


{UNCHECK}No{/UNCHECK}

{/ANSWER}

{FEEDBACK}

The critical temperature of a member is the temperature at which it fails. The design temperature is the temperature which the member achieves in the required fire resistance period, so it must be less than this value.

{/FEEDBACK}

{/QUESTION}

{QUESTION}

{QTITLE}Class 1 members{/QTITLE}

{QTYPE}MC{/QTYPE}

{QTEXT}For a member with Class 1 cross-section in the fire limit state:{/QTEXT}

{ANSWER}

Member resistance can be calculated elastically


{CHECK}Member will work over the whole elastic range.{/CHECK}


{UNCHECK}Member will work over the whole elastic range.{/UNCHECK}

{/ANSWER}

{ANSWER}

Member resistance can be calculated plastically


{CHECK}Member can achieve its fully plastic moment.{/CHECK}


{UNCHECK}Member can achieve its fully plastic moment.{/UNCHECK}

{/ANSWER}

{ANSWER}

Frame can be designed elastically


{CHECK}Members all work over the whole elastic range.{/CHECK}


{UNCHECK}Members all work over the whole elastic range.{/UNCHECK}

{/ANSWER}

{ANSWER}

Frame can be designed plastically


{CHECK}Members can all achieve their full plastic moment and sustain it for a high hinge rotation.{/CHECK}


{UNCHECK}Members can all achieve their full plastic moment and sustain it for a high hinge rotation.{/UNCHECK}

{/ANSWER}

{FEEDBACK}Members Class 1 are stocky cross-sections so for the member resistance plastic strength calculations can be used. The sections have also sufficient rotation capacity, which allows plastic hinges formation and thats why for the frame design the plastic theory can be used. Both member resistance and frame design in the case of cross-sections with class 1, 2 and 3 can be calculated elastically.{/FEEDBACK}

{/QUESTION}

{QUESTION}


{QTYPE}MC{/QTYPE}


{ANSWER}






{/ANSWER}

{ANSWER}



{CHECK}Member can achieve its fully plastic moment.{/CHECK}


{UNCHECK}Member can achieve its fully plastic moment.{/UNCHECK}

{/ANSWER}

{ANSWER}






{/ANSWER}

{ANSWER}



{CHECK}Members can all achieve their full plastic moment but can not sustain it over the full hinge rotation.{/CHECK}


{UNCHECK}Members can all achieve their full plastic moment but can not sustain it over the full hinge rotation.{/UNCHECK}

{/ANSWER}

{FEEDBACK}The resistance of Class 2 members can be estimated plastically. The sections do not have sufficient rotation capacity to allow plastic design of frames because local buckling can occur before a fully developed mechanism can form,so for frame design only elastic theory can be used. Member resistance can also be calculated elastically.{/FEEDBACK}

{/QUESTION}

{QUESTION}


{QTYPE}MC{/QTYPE}


{ANSWER}






{/ANSWER}

{ANSWER}



{CHECK}Member can not achieve its fully plastic moment.{/CHECK}


{UNCHECK}Member can not achieve its fully plastic moment.{/UNCHECK}

{/ANSWER}

{ANSWER}






{/ANSWER}

{ANSWER}



{CHECK}Members can not achieve their full plastic moment.{/CHECK}


{UNCHECK}Members can not achieve their full plastic moment.{/UNCHECK}

{/ANSWER}

{FEEDBACK}The resistance of Class 3 members can only be estimated elastically. The sections can not develop a fully plastic moment because local buckling occurs after initial yield. For frame design only elastic theory can be used.{/FEEDBACK}

{/QUESTION}

{/TEST}

{/SECTION}

{SECTION}

{STITLE}Fire resistance of members{/STITLE}

{SUMMARY}

A reduced resistance based on fire limit state factors and the general principles of resistance calculation at ambient temperature can be performed for all types of members at elevated temperatures. The calculations given here are valid for members of Classes 1, 2 and 3; for Class 4 members a resistance calculation can be performed using the effective cross-section properties specified at 20°C in EC3 Parts 1-3 and 1-5, but using the 0,2% proof strength as the design strength.

The Critical Temperature method follows the flowchart below.

Fire Resistance: Steel Temperature:

Action in fire limit state

{EQN}efidt.gif{/EQN}

Building Regulations

{EQN}tfirequ.gif{/EQN}

Classify member

Resistance at ambient temperature according to

fire rules

{EQN}rfid20.gif{/EQN}

Find Section Factor and its box value

{EQN}section_factor.gif{/EQN} {EQN}section_factor_box.gif{/EQN}

Degree of utilisation

{EQN}mu0.gif{/EQN}

Iterate temperature/time until

{EQN}t_gt_tfirequ.gif{/EQN}

Critical temperature

{EQN}thetacrd.gif{/EQN}

Is

{EQN}thetacrd_gt_thetad.gif{/EQN} ????

{TIMAGE}Figure 2. Sequence of the critical temperature method.{/TIMAGE}

The Resistance method follows the flowchart below.

Fire Resistance: Steel Temperature:

Action in fire limit state

{EQN}efidt.gif{/EQN}

Building Regulations

{EQN}tfirequ.gif{/EQN}

Classify member

Resistance at ambient temperature according to fire

rules

{EQN}rfid20.gif{/EQN}

Find Section Factor and its box value

{EQN}section_factor.gif{/EQN} {EQN}section_factor_box.gif{/EQN}

Iterate temperature/time until

{EQN}t_gt_tfirequ.gif{/EQN}

to give design temperature {EQN}thetad.gif{/EQN}

Resistance at design

temperature

{EQN}rfidt.gif{/EQN}

Is {EQN}rfidt_gt_efidt.gif{/EQN}

????

{TIMAGE}Figure 3. Sequence of the reduced resistance calculation.{/TIMAGE}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}

Tension members

{/SUMTITLE}

Tension members can be designed for fire resistance using either the critical temperature or load resistance methods.

{DETAIL}

For a tension member under uniform cross-sectional temperature the design resistance in fire is calculated simply by using the reduction factor ky. on yield strength at elevated temperature, with an adjustment for the relative material safety factors in normal design and fire design:

{EQN}nfithetard_eqn.gif{/EQN} (6)

so that the degree of utilisation is simply

{EQN}mu0_n_eqn.gif{/EQN} (7)

{/DETAIL}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}

Restrained beams

{/SUMTITLE}

Simple beams restrained against lateral-torsional buckling (but allowed to expand or contract axially) can be designed for fire resistance using either the critical temperature or load resistance methods.

{DETAIL}

Moment resistance in fire for Class 1 or 2 sections with uniform cross-sectional temperature is again calculated from the normal plastic resistance moment for strength design, simply by using the reduction factor ky, on yield strength at elevated temperature, with an adjustment for the relative material safety factors in normal design and fire design:

{EQN}mfithetard_eqn.gif{/EQN} (8)

An example of the elevated-temperature reduction of moment resistance for an IPE600 section, heated uniformly, is shown in below. At a 0,6 degree of utilisation the critical temperature according to this method is found to be 558°C, as compared to the 554°C given by the general equation (3) for the Critical Temperature Method.

{IMAGE}beam_example_fig.gif{/IMAGE}

{TIMAGE}Figure 4. Example of the resistance decrease and the critical temperature for beam IPE 600{/TIMAGE}

For a Class 3 section the same expression applies, but with the elastic moment of resistance used for {EQN}mrd.gif{/EQN}.

In the case of beams supporting concrete slabs on the top flange the non-uniform temperature distributions may be accounted for analytically in calculating the design moment resistance, by dividing the cross-section into uniform-temperature elements, reducing the strength of each according to its temperature, and finding the resistance moment by summation across the section. Alternatively it may be dealt with conservatively by the use of two empirical adaptation factors {EQN}kappa1.gif{/EQN} and {EQN}kappa2.gif{/EQN} to define the moment resistance at time {EQN}t.gif{/EQN} as:

{EQN}mfitrd.gif{/EQN} (9)

where {EQN}kappa1.gif{/EQN} is the factor for non-uniform cross-sectional temperature and {EQN}kappa2.gif{/EQN} is the factor for temperature reduction towards the supports of a statically indeterminate beam. The actual values of {EQN}kappa1.gif{/EQN} and {EQN}kappa2.gif{/EQN} are specified in National Application Documents; in the UK {EQN}kappa1.gif{/EQN} is 0,7 with a slab supported on the top flange and {EQN}kappa2.gif{/EQN} is 0,85 for indeterminate beams, while the default value for each is unity.

Shear resistance is determined using the same general process as for bending and tension resistance, with the same adaptation factors as those above in cases with non-uniform temperature distribution. The general expression, covering uniform and non-uniform temperature cases, is:

{EQN}vfitrd.gif{/EQN} (10)

{/DETAIL}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}

Unrestrained beams: Lateral-torsional buckling

{/SUMTITLE}

In cases where the compression flange is not continuously restrained the design resistance moment against lateral-torsional buckling is calculated for Class 1 or 2 sections using the formula from Eurocode 3 Part 1-1, with minor amendment for the fire state.

Ambient-temperature calculation

{DETAIL}

The Eurocode 3 calculation for lateral-torsional buckling moment resistance is presented as a reduction to the section plastic moment capacity, as follows:

{EQN}mbrd_ambient.gif{/EQN}

The reduction factor {EQN}chilt.gif{/EQN} depends on a variety of factors, and is presented as

{EQN}chilt_eqn.gif{/EQN}

The term {EQN}philt.gif{/EQN} is defined as

{EQN}philt_eqn.gif{/EQN}

in which the non-dimensional slenderness {EQN}lamdalt.gif{/EQN} is given by

{EQN}lamdalt_eqn.gif{/EQN}

and the imperfection factor {EQN}alphalt.gif{/EQN} takes one of four different values 0,21; 0,34; 0,49 or 0,76 for different types of section and buckling axes.

The elastic critical moment {EQN}mcr.gif{/EQN} depends on the loading and support conditions of the particular case.

{/DETAIL}

{/SUMMARY}

{SUMMARY}

High-temperature calculation

Lateral-torsional buckling resistance of unrestrained beams is based on the ambient-temperature resistance equation given above.

{IMAGE}ltb_fig.gif{/IMAGE}

{DETAIL}

This equation includes the yield strength and elastic modulus, which are both amended using the high-temperature strength and modulus reduction factors.

{EQN}mbfitrd_eqn.gif{/EQN} (11)

where:

{EQN}chiltfi_equals.gif{/EQN} lateral-torsional buckling reduction factor in fire design situation

{EQN}kythetacom_equals.gif{/EQN} yield strength reduction factor at the maximum compression flange temperature at time {EQN}t.gif{/EQN}

The lateral-torsional buckling reduction factor is determined as in ambient-temperature design, except that the normalised slenderness used is adapted to the high-temperature steel properties:

{EQN}lamdabar_lt.gif{/EQN} (12)

where:

{EQN}kethetacom_equals.gif{/EQN} elastic modulus reduction factor at the maximum compression flange temperature at time {EQN}t.gif{/EQN}.

The imperfection factor for the fire situation is determined as

{EQN}alpha_equals.gif{/EQN} (13)

This uses a single value 0,65 for the ambient-temperature base case rather than the four different values which are used for ambient-temperature lateral-torsional buckling resistance.

{/DETAIL}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}

Resistance of compression members

{/SUMTITLE}

The design buckling resistance of compression members in fire follows the same principles as lateral-torsional buckling resistance, but has some unique aspects concerning the buckling length.

{DETAIL}

The buckling resistance of columns of Class 1, 2 or 3 is calculated as follows, allowing for a reduction in strength and an increase in normalised slenderness at high temperatures.

{EQN}

nfithetard_eqn.gif{/EQN} (14)

The flexural buckling reduction factor is the lower of its values about the yy and zz axes determined as in ambient-temperature design, except that the normalised slenderness used is adapted to the fire situation as follows:

The buckling length {EQN}lfi.gif{/EQN} is determined as shown below, provided that each storey of the building comprises a separate fire compartment, and that the fire resistance of the compartment boundaries is not less than that of the column.

{IMAGE}buckling_lengths.gif{/IMAGE}

{TIMAGE}Figure 5. Buckling lengths of columns in braced multi-storey buildings in fire{/TIMAGE}

Because the continuing columns are much stiffer than the column in the fire compartment it is assumed that they cause the end(s) of the heated column to be restrained in direction, so the effective length factor is taken as 0,5 for intermediate storeys and 0,7 for the top storey.

The normalised slenderness of the column for the maximum temperature is given by:

{EQN}lamdathetamax.gif{/EQN} (15)

The imperfection factor {EQN}alpha.gif{/EQN} is determined for the fire case as

{EQN}alpha_eqn.gif{/EQN}

{/DETAIL}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}

Members subject to combined bending and axial compression

{/SUMTITLE}

The calculation process for the high-temperature resistance of members of Classes 1, 2 or 3, subjected to combined uniaxial or biaxial bending and axial compression is very similar to that used in ambient-temperature design.

{DETAIL}

Two cases need to be considered:

• Flexural buckling combined with bending, but without lateral-torsional buckling,

• Flexural buckling combined with bending, allowing for the possibility of lateral-torsional buckling.

In the former case the member should satisfy the interaction equation:

{EQN}interaction_eqn1.gif{/EQN} (16)

The minimum flexural buckling reduction factor {EQN}chiminfi.gif{/EQN} is the lower of its values about the yy and zz axes. Note that the coefficients {EQN}kytheta.gif{/EQN} and {EQN}kztheta.gif{/EQN} are amplification factors which express the increase of internal bending moments due to compression force and flexural buckling (they should not be confused with the strength and modulus reduction factors), and are calculated in similar fashion to the ambient-temperature process specified in ENV 1993-1-1 with some small changes.

When taking into account also lateral-torsional buckling in bending, the member must satisfy the expression:

{EQN}interaction_eqn2.gif{/EQN} (17)

In this case flexural buckling is assumed to occur in the same direction as lateral-torsional buckling, so the flexural buckling reduction factor {EQN}chizfi.gif{/EQN} is used.

{EQN}klttheta.gif{/EQN} is the coefficient which must be equal to or less than 1,0 and is calculated as for ambient-temperature design. For beams with Class 1 or 2 cross-sections {EQN}wpl.gif{/EQN} is used, and for beams with Class 3 cross-sections {EQN}wel.gif{/EQN} is used. The equivalent uniform moment factors {EQN}betamy.gif{/EQN}, {EQN}betamz.gif{/EQN} and {EQN}betamlt.gif{/EQN} are estimated from figure 4.2 in the Eurocode.

{/DETAIL}

{TEST}

{TTITLE}Member fire resistance{/TTITLE}

{QUESTION}

{QTITLE}Critical temperature calculation{/QTITLE}

{QTYPE}MC{/QTYPE}

{QTEXT}

When calculating critical temperature of a member we need to know:

{/QTEXT}

{ANSWER}

Boundary conditions of a member


{CHECK}Boundary conditions affect the internal forces.{/CHECK}


{UNCHECK}Boundary conditions affect the internal forces.{/UNCHECK}

{/ANSWER}

{ANSWER}

Cross-section properties


{CHECK}Cross-section properties control the section capacity.{/CHECK}


{UNCHECK}Cross-section properties control the section capacity.{/UNCHECK}

{/ANSWER}

{ANSWER}

Steel grade


{CHECK}Steel grade affects strength of the member.{/CHECK}


{UNCHECK}Steel grade affects strength of the member.{/UNCHECK}

{/ANSWER}

{ANSWER}

Specified fire-resistance time of a member


{CHECK}Fire resistance rating affects the design temperature.{/CHECK}


{UNCHECK}Fire resistance rating affects the design temperature.{/UNCHECK}

{/ANSWER}

{ANSWER}

Heating curve


{CHECK}Usually ISO834, but different heating curves change the design temperature.{/CHECK}


{UNCHECK}Usually ISO834, but different heating curves change the design temperature.{/UNCHECK}

{/ANSWER}

{ANSWER}

Thermal gradient across the member


{CHECK}Temperature gradient is not calculated explicitly, but {EQN}kappa1.gif{/EQN} factoris used to account for concrete slab effect.{/CHECK}


{UNCHECK}Temperature gradient is not calculated explicitly, but {EQN}kappa1.gif{/EQN} factoris used to account for concrete slab effect.{/UNCHECK}

{/ANSWER}

{ANSWER}

Thermal gradient along the member


{CHECK}Not needed explicitly, but {EQN}kappa2.gif{/EQN} factoris used to account for cooler ends of continuous beams.{/CHECK}


{UNCHECK}Not needed explicitly, but {EQN}kappa2.gif{/EQN} factoris used to account for cooler ends of continuous beams.{/UNCHECK}

{/ANSWER}

{ANSWER}

Loading for ambient-temperature ultimate limit state design


{CHECK}Partial safety factors on loading are different for the fire limit state.{/CHECK}


{UNCHECK}Partial safety factors on loading are different for the fire limit state.{/UNCHECK}

{/ANSWER}

{ANSWER}

Loading for the fire limit state


{CHECK}The degree of utilisation is the fire limit state loading as a proportion of the load resistance at ambient temperature.{/CHECK}


{UNCHECK}The degree of utilisation is the fire limit state loading as a proportion of the load resistance at ambient temperature.{/UNCHECK}

{/ANSWER}

{FEEDBACK}The critical temperature is a function of the degree of utilisation, which is a ratio of the design effect of actions in fire (loading in fire situation and boundary conditions of a member must be known) and the design fire resistance for time {EQN}t_eq_0.gif{/EQN}. To calculate the design fire resistance we need to know cross section properties and steel grade. The value of the critical temperature is then compared with the temperature of the member at the required fire resistance time. For this the heating curve must be known. {/FEEDBACK}

{/QUESTION}

{QUESTION}

{QTITLE}Degree of utilisation{/QTITLE}

{QTYPE}MC{/QTYPE}

{QTEXT}

The degree of utilisation is the ratio of the design effect of actions for the fire design situation and the design effect of actions at ambient temperature.

{/QTEXT}

{ANSWER}

True


{CHECK}It is not fair to assume that the ultimate limit state loading is identical to the resistance of the member.{/CHECK}


{UNCHECK}It is not fair to assume that the ultimate limit state loading is identical to the resistance of the member.{/UNCHECK}

{/ANSWER}

{ANSWER}

False


{CHECK}It is not fair to assume that the ultimate limit state loading is identical to the resistance of the member.{/CHECK}


{UNCHECK}It is not fair to assume that the ultimate limit state loading is identical to the resistance of the member.{/UNCHECK}

{/ANSWER}

{FEEDBACK}

The degree of utilisation {EQN}mu0.gif{/EQN} is the ratio of the design effect of actions for the fire design situation and the design resistance calculated at ambient temperature (or at time {EQN}t_eq_0.gif{/EQN}) but using the material partial safety factors which apply in fire design.

{/FEEDBACK}

{/QUESTION}

{QUESTION}

{QTITLE}Moment resistance in fire (i){/QTITLE}

{QTYPE}MC{/QTYPE}

{QTEXT}The moment resistance in fire {EQN}mfithetard.gif{/EQN} for section classes 1, 2 and 3 is calculated from the plastic moment resistance for ambient temperature design using reduction factor {EQN}kytheta.gif{/EQN}.{/QTEXT}

{ANSWER}

True


{CHECK}Plastic resistance only applies to stocky sections.{/CHECK}


{UNCHECK}Plastic resistance only applies to stocky sections.{/UNCHECK}

{/ANSWER}

{ANSWER}

False


{CHECK}Plastic resistance only applies to stocky sections.{/CHECK}


{UNCHECK}Plastic resistance only applies to stocky sections.{/UNCHECK}

{/ANSWER}

{FEEDBACK}

This is true only for classes 1and 2, for class 3 it is necessary to use elastic moment resistance.

{/FEEDBACK}

{/QUESTION}

{QUESTION}

{QTITLE}Moment resistance in fire (ii){/QTITLE}

{QTYPE}MC{/QTYPE}

{QTEXT}The moment resistance in fire {EQN}mfithetard.gif{/EQN} can be calculated according to equation {EQN}mfithetard_eqn.gif{/EQN} only in the case of uniform cross-section temperature.{/QTEXT}

{ANSWER}

True


{CHECK}The highest section temperature could be used conservatively.{/CHECK}


{UNCHECK}The highest section temperature could be used conservatively.{/UNCHECK}

{/ANSWER}

{ANSWER}

False


{CHECK}The highest section temperature could be used conservatively.{/CHECK}


{UNCHECK}The highest section temperature could be used conservatively.{/UNCHECK}

{/ANSWER}

{FEEDBACK}

The moment resistance in fire {EQN}mfithetard.gif{/EQN} can be calculated according to this equation also in the case of a non-uniform temperature distribution, with the member temperature conservatively taken as the highest temperature.

{/FEEDBACK}

{/QUESTION}

{QUESTION}

{QTITLE}"Kappa" factors{/QTITLE}

{QTYPE}MC{/QTYPE}

{QTEXT}When taking into account a non-uniform temperature distribution across a section by the use of the empirical adaptation factor {EQN}kappa1.gif{/EQN} mark the one correct statement about the moment resistance calculated in this way.

{/QTEXT}

{ANSWER}

70% of {EQN}mfithetard.gif{/EQN}


{CHECK}{/CHECK}


{UNCHECK}{/UNCHECK}

{/ANSWER}

{ANSWER}

Identical to {EQN}mfithetard.gif{/EQN}


{CHECK}{/CHECK}

{UNCHECKMARK}{/UNCHECKMARK}

{UNCHECK}{/UNCHECK}

{/ANSWER}

{ANSWER}

143% of {EQN}mfithetard.gif{/EQN}


{CHECK}Correct{/CHECK}



{/ANSWER}

{FEEDBACK}Basic equation is {EQN}mfitrd_eqn.gif{/EQN}. If {EQN}kappa1eq07.gif{/EQN} and {EQN}kappa2eq10.gif{/EQN} then {EQN}mfitrdeq14.gif{/EQN}.{/FEEDBACK}

{/QUESTION}

{QUESTION}

{QTITLE}Lateral-torsional buckling resistance{/QTITLE}

{QTYPE}MC{/QTYPE}

{QTEXT}

In the case of lateral-torsional buckling, when calculating the moment resistance in fire {EQN}mbfitrd.gif{/EQN} it is necessary to estimate both reduction factors {EQN}kythetacom.gif{/EQN} and {EQN}kethetacom.gif{/EQN}. True or False?

Tick only one answer

{/QTEXT}

{ANSWER}

True


{CHECK}Correct{/CHECK}



{/ANSWER}

{ANSWER}

False


{CHECK}{/CHECK}


{UNCHECK}{/UNCHECK}

{/ANSWER}

{FEEDBACK}

The reduction factors {EQN}kytheta.gif{/EQN} and {EQN}ketheta.gif{/EQN} are needed for estimation of the normalised slenderness in the fire limit state.

{/FEEDBACK}

{/QUESTION}

{QUESTION}

{QTITLE}Buckling of columns{/QTITLE}

{QTYPE}M{/QTYPE}

{QTEXT}

Consider a column in a multi-storey braced frame building. Each storey is a fire compartment, and the separating slabs have the same fire resistance requirement as the elements of structure. Match the following buckling lengths to the appropriate cases for the fire limit state.

{/QTEXT}

{ANSWER}

Intermediate storey continuous column

{MARK}1{/MARK}

{MATCH}Half of the system length{/MATCH}

{/ANSWER}

{ANSWER}

Top storey continuous column

{MARK}1{/MARK}

{MATCH}70% of the system length{/MATCH}

{/ANSWER}

{ANSWER}

Non-continuous column

{MARK}1{/MARK}

{MATCH}Same as the system length{/MATCH}

{/ANSWER}

{FEEDBACK}

When estimating the critical length the rules for normal temperature design are used. In the case of braced frame and when each storey of the building comprises a separate fire compartment and the fire resistance of the compartment boundaries is not less than that of the column, the buckling lengths of continuous columns can be determined on the assumption that the heated column is restrained in direction.

{/FEEDBACK}

{/QUESTION}

{/TEST}

{/SUMMARY}

{/SECTION}

{SECTION}

{STITLE}

Thermal analysis

{/STITLE}

{SUMMARY}

{SUMTITLE}

Incremental linearised equations

{/SUMTITLE}

The same calculation rules are given in both EC3 Part 1.2 and EC4 Part 1.2 for calculating the temperatures of unprotected and protected steel beams. The temperatures of the lower and upper flanges may differ considerably, so it is very important that they should be calculated properly in order to obtain an accurate estimate of the bending moment resistance of the composite section.

The heat transfer to the member is predominantly by two mechanisms; radiation and convection. Since the rate of heating by both mechanisms is dependent at any time on the temperatures of both the fire atmosphere and the member, the member temperature is related to time via a fairly complex differential equation. This is dealt with in Eurocode 3 by linearising the temperature increments over small time steps, which is impractical for hand calculation but is ideal for setting up in spreadsheet software. {ECLINK}EC3 Part 1.2{/ECLINK}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}

Fire resistance time of an unprotected steel member

{/SUMTITLE}

{IMAGE}steel_heating.gif{/IMAGE}

{TIMAGE}Figure 6. Heating of unprotected steel.{/TIMAGE}

{DETAIL}

For an unprotected steel section the temperature increase {EQN}deltatheta1.gif{/EQN} in a small time interval {EQN}deltat.gif{/EQN} (up to 5 seconds) is given by the net amount of heat which the section acquires during this time:

{EQN}unprotected_heating_equation.gif{/EQN} (2)

in which

{EQN}ca_equals.gif{/EQN} Specific heat of steel

{EQN}rhoa_equals.gif{/EQN} Density of steel

{EQN}section_factor_unprot_equals.gif{/EQN} "Section factor" composed of

{EQN}am_equals.gif{/EQN} Exposed surface area of member per unit length

{EQN}v_equals.gif{/EQN} Volume of member per unit length

{EQN}hnetd_equals.gif{/EQN} Design value of heat flux per unit area

{EQN}ksh_equals.gif{/EQN} Correction factor for the shading effect of flanges, defined as

{EQN}ksh_equation09.gif{/EQN}

For I-section under normal fire conditions

{EQN}ksh_equation10.gif{/EQN}

For all other cases, but 1,0 for all convex shapes

The net heat flux has radiative and convective components, of which the radiative component is:

{EQN}hnet.gif{/EQN} (3)

in which, apart from the Stefan-Boltzmann constant of 5,67x10-8,

{EQN}phi_equals.gif{/EQN}Configuration factor (can be set to 1,0 in the absence of data)

{EQN}eres_equals.gif{/EQN}

Resultant emissivity = emissivity of fire compartment x emissivity of member surface (0,8x0,625=0,5 if no specific data)

{EQN}thetar_thetam_equals.gif{/EQN}Environment and member surface temperatures

and the convective heat flux is:

{EQN}hnetc.gif{/EQN}

(4)

in which

{EQN}alphac_equals.gif{/EQN}

Convective heat transfer coefficient (subject to National Annex values, but 25W/m2°K for hydrocarbon fire)

{EQN}thetag_thetam_equals.gif{/EQN}Environment (gas) and member surface temperatures

When forming the net heat flux from these, each may be factored in order to account for differences in national practice in fire testing, but usually they are simply added together.

The Section Factor {EQN}secfactor_unprot.gif{/EQN} uses the exposed perimeter in calculating an appropriate value of {EQN}am.gif{/EQN} and this means the actual surface which is exposed to radiation and convection. In determination of the Section Factor for the case of a composite slab with profiled steel sheets the three-sided exposure case can be considered, provided that at least 90% of the upper flange is covered by the steel sheet. If this is not the case then void-fillers made from appropriate insulating material must be used.

The correction factor {EQN}ksh.gif{/EQN} attempts to reduce the temperature gain for sections whose flanges cause a "shadow effect" on the inner perimeter areas in order to reproduce test results better. This effectively substitutes the circumscribing rectangular box area in the section factor {EQN}secfactor_box.gif{/EQN}for the true perimeter area (as shown below), as well as an empirical factor of 0,9 which particularly applies to I- or H-sections. For any other section this extra correction is not applied, and in the case of convex cross-sections (the most usual being circular) the value of {EQN}ksh.gif{/EQN} is set to 1,0. In any case, neglecting to use {EQN}ksh.gif{/EQN} results in a conservative (higher) estimate of the section temperature in design.

{IMAGE}section_factors_unprotected.gif{/IMAGE}

{TIMAGE}Figure 7. Examples of section factor calculation for unprotected sections.{/TIMAGE}

{/DETAIL}

{/SUMMARY}

{SUMMARY}

{SUMTITLE}

Fire resistance time of a passively protected steel member

{/SUMTITLE}

For protected sections the EC3 temperature calculation process assumes that the heated surface is at the fire temperature, so that the heating of the steel is governed simply by the conduction rate through the insulating layer and the section factor of the steel.

{DETAIL}

For members with passive protection the basic mechanisms of heat transfer are identical to those for unprotected steelwork, but the surface covering of material of very low conductivity induces a considerable reduction in the heating rate of the steel section. Also, the insulating layer itself has the capacity to store a certain, if small, amount of heat. It is acceptable to assume that the exposed insulation surface is at the fire atmosphere temperature (since the conduction away from the surface is low and very little of the incident heat is used in raising the temperature of the surface layer of insulation material).

{IMAGE}section_factors_protected.gif{/IMAGE}

{TIMAGE}Figure 8. Examples of section factor calculation for protected sections.{/TIMAGE}

The calculation of steel temperature rise {EQN}deltatheta1.gif{/EQN} in a small time interval {EQN}deltat.gif{/EQN} (up to 30 s) is now concerned with balancing the heat conduction from the exposed surface with the heat stored in the insulation layer and the steel section:

{EQN}protected_heating_equation.gif{/EQN} but {EQN}protected_heating_condition.gif{/EQN} (5)

in which the relative heat storage in the protection material is given by the term

{EQN}phi_equation.gif{/EQN} (6)

in which

{EQN}section_factor_prot_equals.gif{/EQN}

Section factor for protected steel member, where {EQN}ap.gif{/EQN} is generally the inner perimeter of the fire protection material (see figure)

{EQN}ca_cp_equals.gif{/EQN} Specific heats of steel and protection material

{EQN}dp_equals.gif{/EQN} Thickness of fire protection material

{EQN}thetaat_thetagt_equals.gif{/EQN} Temperatures of steel and furnace gas at time {EQN}t.gif{/EQN}

{EQN}deltathetagt_equals.gif{/EQN} Increase of gas temperature

during the time step {EQN}deltat.gif{/EQN}

{EQN}lamdap_equals.gif{/EQN} Thermal conductivity of the fire protection material

{EQN}rhoa_rhop_equals.gif{/EQN} Densities of steel and fire protection material

Fire protection materials often contain a certain percentage of moisture which evaporates at about 100°C, with considerable absorption of latent heat. This causes a dwell in the heating curve for a protected steel member at about this temperature while the water content is expelled from the protection layer. The incremental time-temperature relationship above does not model this effect, but this is at least a conservative approach. A method of calculating the dwell time is given, if required, in the European pre-standard for fire testing.

{/DETAIL}

{/SUMMARY}

{TEST}

{TTITLE}

Thermal analysis

{/TTITLE}

{QUESTION}

{QTITLE}Section factor{/QTITLE}

{QTYPE}

MC

{/QTYPE}

{QTEXT}The section factor {EQN}secfactor_unprot.gif{/EQN} is higher for heavy, massive sections and lower for slim, light ones.{/QTEXT}

{ANSWER}

True


{CHECK}The section factor is heated perimeter divided by cross-section area.{/CHECK}


{UNCHECK}The section factor is heated perimeter divided by cross-section area.{/UNCHECK}

{/ANSWER}

{ANSWER}

False


{CHECK}The section factor is heated perimeter divided by cross-section area.{/CHECK}


{UNCHECK}The section factor is heated perimeter divided by cross-section area.{/UNCHECK}

{/ANSWER}

{FEEDBACK}

The section factor {EQN}secfactor_unprot.gif{/EQN} is the ratio of exposed surface area of a member per unit length to its volume per unit length - in most cases this is more easily considered as heated perimeter divided by cross-section area. In the case of slender sections the heated surface is greater and the volume is less, so the section factor is higher and temperature rises more quickly than in the case of massive members.

{/FEEDBACK}

{/QUESTION}

{QUESTION}

{QTITLE}

Unprotected sections

{/QTITLE}

{QTEXT}

The equation

{EQN}unprotected_heating_equation.gif{/EQN}

allows us to calculate a value for the length of time required for an unprotected member to reach its critical temperature.

Which one of the following statements correctly describes the meaning of this equation:

{/QTEXT}

{QTYPE}

MC

{/QTYPE}

{ANSWER}

{EQN}deltatheta1.gif{/EQN} is the difference between normal room temperature and the member’s critical temperature, and {EQN}deltat.gif{/EQN} is the total length of time taken for the member to reach its critical temperature.

{CHECKMARK}

0

{/CHECKMARK}

{CHECK}

This is a linearised equation for a temperature increment which is only valid for a short time step; in this case up to 5 seconds.

{/CHECK}

{UNCHECKMARK}

1

{/UNCHECKMARK}

{UNCHECK}

This is a linearised equation for a temperature increment which is only valid for a short time step; in this case up to 5 seconds.

{/UNCHECK}

{/ANSWER}

{ANSWER}

{EQN}deltatheta1.gif{/EQN} is the difference in the member’s temperature over a fixed time step {EQN}deltat.gif{/EQN}. The total time taken for the member to reach its critical temperature is the sum of the individual time steps {EQN}deltat.gif{/EQN} over which the sum of the temperature increments {EQN}deltatheta1.gif{/EQN} gives the difference between room temperature and the member’s critical temperature. The solution in this case would have to be reached by iteration. Steel temperature values are altered at each step.

{CHECKMARK}

1

{/CHECKMARK}

{CHECK}

This is the correct statement. The equation is only valid for a short time step; in this case up to 5 seconds.

{/CHECK}

{UNCHECKMARK}

0

{/UNCHECKMARK}

{UNCHECK}

This is the correct statement. The equation is only valid for a short time step; in this case up to 5 seconds.

{/UNCHECK}

{/ANSWER}

{ANSWER}

{EQN}deltatheta1.gif{/EQN}is the difference between normal room temperature and the member’s critical temperature, {EQN}deltat.gif{/EQN} is the length of time taken for the member to reach its critical temperature. The correct value of {EQN}deltat.gif{/EQN} which would produce the required {EQN}deltatheta1.gif{/EQN} value is reached by estimating two initial values, one which produces a temperature difference greater than that desired, one which gives a temperature difference smaller than that desired. It is then necessary to iterate in order to reduce the range of possible values for {EQN}deltat.gif{/EQN} until the correct value is reached.

{CHECKMARK}

0

{/CHECKMARK}

{CHECK}

This is an incorrect statement.

{/CHECK}

{UNCHECKMARK}

1

{/UNCHECKMARK}

{UNCHECK}

This is an incorrect statement.

{/UNCHECK}

{/ANSWER}

{/QUESTION}

{QUESTION}

{QTITLE}

Protected sections

{/QTITLE}

{QTEXT}

If insulating board is used as the most convenient means of protection for a steel member, select the appropriate equation to calculate the thickness of board required. The equation contains the following terms:

{EQN}dp.gif{/EQN} Thickness of gypsum boarding

{EQN}lamdap.gif{/EQN} Thermal conductivity of gypsum boarding

{EQN}thetagt.gif{/EQN} Gas temperature

{EQN}secfactor.gif{/EQN} Section factor: Internal surface area of board/volume of member

{EQN}phi.gif{/EQN} Relative heat storage in the protection material

{/QTEXT}

{QTYPE}

MC

{/QTYPE}

{ANSWER}

{EQN}protected_heating_equation.gif{/EQN}

{CHECKMARK}

1

{/CHECKMARK}

{CHECK}

Correct

{/CHECK}

{UNCHECKMARK}

0

{/UNCHECKMARK}

{UNCHECK}

This is the correct equation

{/UNCHECK}

{/ANSWER}

{ANSWER}

{EQN}protected_heating_equation_x1.gif{/EQN}

{CHECKMARK}

0

{/CHECKMARK}

{UNCHECKMARK}

1

{/UNCHECKMARK}

{CHECK}

This heating depends on conduction, so must use temperature difference.

{/CHECK}

{UNCHECK}

This heating depends on conduction, so must use temperature difference.

{/UNCHECK}

{/ANSWER}

{ANSWER}


{CHECKMARK}

0

{/CHECKMARK}

{UNCHECKMARK}

1

{/UNCHECKMARK}

{CHECK}

Heating of steel must be a function of heating of fire.

{/CHECK}

{UNCHECK}

Heating of steel must be a function of heating of fire.

{/UNCHECK}

{/ANSWER}

{ANSWER}


{CHECKMARK}

0

{/CHECKMARK}

{UNCHECKMARK}

1

{/UNCHECKMARK}

{CHECK}

Wrong factor on heat retained in board.

{/CHECK}

{UNCHECK}

Wrong factor on heat retained in board.

{/UNCHECK}

{/ANSWER}

{ANSWER}


{CHECKMARK}

0

{/CHECKMARK}

{UNCHECKMARK}

1

{/UNCHECKMARK}

{CHECK}

Heating of steel is not based on heat capacity of protection material

{/CHECK}

{UNCHECK}

Heating of steel is not based on heat capacity of protection material

{/UNCHECK}

{/ANSWER}

{/QUESTION}

{QUESTION}

{QTITLE}

Heat stored in protection material

{/QTITLE}

{QTEXT}

Select the equation from the following list which correctly represents the relative heat storage {EQN}phi.gif{/EQN} in the protection material insulating a steel member. The equations contain the terms:

{EQN}rhop.gif{/EQN} Density of gypsum boarding

{EQN}cp.gif{/EQN} Specific heat of gypsum boarding

{/QTEXT}

{QTYPE}

MC

{/QTYPE}

{ANSWER}

{EQN}phi_equation_x1.gif{/EQN}

{CHECKMARK}

0

{/CHECKMARK}

{CHECK}

This equation uses the section factor for an unprotected section.

{/CHECK}

{UNCHECKMARK}

1

{/UNCHECKMARK}

{UNCHECK}

This equation uses the section factor for an unprotected section.

{/UNCHECK}

{/ANSWER}

{ANSWER}

{EQN}phi_equation.gif{/EQN}

{CHECKMARK}

1

{/CHECKMARK}

{CHECK}

Correct

{/CHECK}

{UNCHECKMARK}

0

{/UNCHECKMARK}

{UNCHECK}

This is the correct equation

{/UNCHECK}

{/ANSWER}

{ANSWER}


{CHECKMARK}

0

{/CHECKMARK}

{CHECK}

The protection thickness has been applied to the heat capacity of steel.

{/CHECK}

{UNCHECKMARK}

1

{/UNCHECKMARK}

{UNCHECK}

The protection thickness has been applied to the heat capacity of steel.

{/UNCHECK}

{/ANSWER}

{ANSWER}


{CHECKMARK}

0

{/CHECKMARK}

{CHECK}

This equation takes no account of the protection thickness.

{/CHECK}

{UNCHECKMARK}

1

{/UNCHECKMARK}

{UNCHECK}

This equation takes no account of the protection thickness.

{/UNCHECK}

{/ANSWER}

{ANSWER}


{CHECKMARK}

0

{/CHECKMARK}

{CHECK}

This equation takes no account of the protection thickness and is reversed.

{/CHECK}

{UNCHECKMARK}

1

{/UNCHECKMARK}

{UNCHECK}

This equation takes no account of the protection thickness and is reversed.

{/UNCHECK}

{/ANSWER}

{FEEDBACK}

The equation for heat retained in the protection increases with its heat capacity and thickness, but this is not the best way of taking heat away from the steel because materials with high heat capacity tend to have high conductivity.

{/FEEDBACK}

{/QUESTION}

{/TEST}

{/SECTION}

{SECTION}

{STITLE}

Use of advanced calculation models

{/STITLE}

{SUMMARY}

Both Eurocodes 3 and 4 permit the use of advanced calculation models based upon fundamental physical behaviour, in order to give a realistic analysis of the behaviour in fire of the structure. They may be used to represent the behaviour of individual members, the whole structure or sub-assemblies.

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{TIMAGE}Figure 9. Analysis of 3-dimensional building subframes.{/TIMAGE}

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Principles for use of advanced calculation models

• All computational methods are to some extent approximate, are based on different assumptions, and are not all capable of predicting all possible types of behaviour. It is therefore stipulated that the validity of any such model used in design analysis must be agreed by the client, the designer and the competent building control authority.

• Any potential failure modes which are not covered in the models must be checked by other means, such as the simplified methods covered earlier.

• Computational models may cover the thermal response of the structure to any defined fire, either nominal or parametric, and should not only be based on the established physical principles of heat transfer but should also on known variation of thermal material properties with temperature. The more advanced models may consider non-uniform thermal exposure, temperature gradients within structural components and heat transfer to adjacent structure. Since the influence of moisture content in protection materials is inevitably an additional safety feature it is permissible to neglect this in analysis.

• EC1 parametric fire curves calculated from the fire load and compartment properties may be used with such models

• When modelling the mechanical response of structures, the analysis must be based on acknowledged principles of structural mechanics, given the change of material properties with temperature, including strain reversal if this is disadvantageous. Thermally induced strains and their effects due to temperature increase and temperature differentials must be included.

• Geometric non-linearity is essential when modelling in a domain of very high structural deflections, as is material non-linearity when stress-strain curves are highly curvilinear. It is, however, acknowledged that within the time-scale of accidental fires transient thermal creep does not need to be explicitly included provided that the elevated-temperature stress-strain curves given in the Code

are used. These curves are based on transient materials testing in which short-term creep is allowed to occur.

• Where relevant initial geometric imperfections must be included. This is particularly the case for isolated vertical columns, for which a sinusoidal shape with a maximum out-of-straightness of h/1000 should be used.

• Although structural stability up to the modelled ultimate limit state is the main criterion in such analysis, the deformation of the structure must be limited to ensure that integrity failures do not occur, or that any members cease to be supported adequately.

Validation of advanced calculation models

Advanced calculation models should be verified against relevant test results and other calculation methods, and checked for compliance with normal engineering principles by the use of sensitivity studies.

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Concluding summary

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{SUMMARY}

• Fire resistance of structural elements is quoted as the time at which they reach a defined deflection criterion when tested in a furnace heated according to a standard ISO834 time-temperature curve.

• Traditional fire protection of steelwork is usually achieved by covering it with an insulating material during construction. However it may be possible under EC3 to use a combination of strategies to ensure fire resistance.

• EC3 calculation of fire resistance takes account of the loading level on the element. However the safety factors applied are lower than in those used in strength design.

• Fire resistance may be calculated in terms of time, as a load-bearing resistance at a certain time, or as a critical element temperature appropriate to the load level and required time of exposure.

• EC3 provides simple calculations for the load resistance in fire of common types of elements. In case of columns the buckling fire resistance can be estimated according to code rules only for the case of braced frames.

• Critical temperature is calculated for all types of member of classes 1, 2 or 3 for which instability is not the limiting behaviour, from a single equation in

terms of the load level in fire. Class 4 sections are universally assumed to have a critical temperature of 350°C.

• It is possible to calculate the temperature growth of protected or unprotected members in small time increments, in a way which can easily be implemented on a spreadsheet.

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{REFERENCES}

(essential & background reading)

o prEN 1991-1-1: Eurocode 1: Actions on Structures. Part 1-1: Basis of Design.

o prEN 1991-1-2: Eurocode 1: Actions on Structures. Part 1-2: Actions on Structures Exposed to Fire.

o prEN 1993-1-1: Eurocode 3: Design of Steel Structures. Part 1-1: General Rules and Rules for Buildings.

o prEN 1993-1-2: Eurocode 3: Design of Steel Structures. Part 1-2: General Rules: Structural Fire Design.

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