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TALAT Lectures 2503


                 Calculation Methods for Fire Design
                                  31 pages, 28 figures

                                      Basic Level

      prepared by Steinar Lundberg, Hydro Aluminium Structures, Karmoy




Objectives:

− to learn how to calculate the fire resistance of aluminium alloy structures with and
  without applied insulation



Prerequisites:

− general engineering background
− TALAT lectures 2501 and 2502


REVICED NOVEMBER 1997 in connection with the Leonardo da Vinci project:
TAS/WP 1 by Steinar Lundberg.




Date of Issue: 1998
 EAA - European Aluminium Association
2503 Calculation Methods for Fire Design



Contents

2503 Calculation Methods for Fire Design ...........................................................2
  2503.01 Tests and Calculation Methods ............................................................... 3
    2503.01.01 Introduction...........................................................................................3
     2503.01.02 Calculation Methods .............................................................................3
  2503.02 Fire Design according to ENV 1999 - 1 - 2................................................ 5
    2503.02.01 Resistance of aluminium structures at elevated temperatures ..............6
     2503.02.02 Tension members ..................................................................................6
     2503.02.03 Beams....................................................................................................7
     2503.02.04 Columns ................................................................................................9
     2503.02.05 Connections ........................................................................................10
     2503.02.06 Temperature analysis for unprotected aluminium structures ..............10
     2503.02.07 Temperature analysis for protected aluminium structures ..................14
     2503.02.08 Internal aluminium structures in a void which is protected by heat
                       screens. ..............................................................................................16
  2503.03 Simplified Calculation Methods ............................................................ 17
    2503.03.01 Uninsulated Aluminium Alloy Structures. .........................................18
     2503.03.02 Insulated Aluminium Structures .........................................................20
  2503.04 Insulation Techniques ............................................................................ 26
  2503.04 References/Literature ............................................................................. 29
  2503.06 List of Figures............................................................................................ 31




TALAT 2503                                                        2
2503.01        Tests and Calculation Methods


2503.01.01 Introduction
To document the fire resistance of an aluminium alloy structure, fire resistance tests can
always be used. Walls, floors, beams and columns can be tested in the fire test furnaces.
Load bearing structures can be tested with their actual load.
Temperatures will always be measured on the unexposed side of a tested partition. For
other building elements (beams, columns) usually temperatures are measured inside and
on the outside surface of the structure.
When testing an aluminium alloy structure, the temperature of the structural part is the
most interesting. The metal temperature measured can be used to determine the strength
available at that temperature. The structure can then be calculated with this reduced
strength. This constitutes an alternative way to practical fire testing under loads.
The good heat conduction ability of aluminium may be a problem when testing
aluminium alloy structures. Small test specimen may experience a significant amount of
heat transfer from the edges, and the temperature may be considerably higher than in
larger test sections. If the test laboratory has little experience with testing aluminium
structures, one should take care of minimizing the edge effects already when planning
the test.


2503.01.02 Calculation Methods


There are several computer programmes which can be used for temperature analysis of
structures exposed to fire. No particular programmes are available for calculations of
aluminium alloy structures.
When calculating aluminium alloy structures at high temperatures (150 - 250 °C) time
dependent creep effects will influence the behaviour of the material. One characteristic
feature of creep behaviour is that, at constant stress and temperature, strain develops as
shown by the creep curve in Figure 2503.01.01. Strain ε0 at t = 0 denotes the stress
dependent initial strain, elastic or elastic-plastic. The strain curve is generally
subdivided into three creep regimes: primary, secondary and tertiary. Creep rupture
occurs at the end of tertiary creep.
Tests have shown that the time dependent creep is neglectable for temperatures below
180 - 200 °C. ENV 1999-1-2 [15] disregard time dependent creep for temperatures
below 170 °C.
Creep properties of aluminium alloys are not taken into account by any computer
programme.
To design aluminium alloy structures exposed to fire, the first step will be to calculate
the metal temperature of the structure. Then we can determine the reduced strength of
the aluminium alloy. This value of reduced strength is used to check if the structure
meets the required fire resistance according to the national codes or standards.


TALAT 2503                                     3
ENV 1999-1-2 [15] is today the only standard which deal with fire design of aluminium
structures. The knowledge about the behaviour of aluminium structures at elevated
temperatures is, however, limited for both insulated and uninsulated structures. ENV
1999-1-2 has rules for simple calculation of the capacity of structures at elevated
temperatures. The rules for the temperature analysis are more complicated, and need the
properties of the insulation materials which match the rules. Today these properties are
only available for steel structures, but it is likely to believe that the same properties may
be used also for aluminium structures.
For calculating the temperature of structures exposed to fire computer programmes are
available. By introducing the thermal properties of aluminium alloys in these
programmes, they can be used to calculate the temperature of both insulated and
uninsulated aluminium alloy structures exposed to fire.



                                                        ε




                                                        ε0
                                                             Primary      Secondary       Tertiary
                                                              creep         creep          creep          t

                                                                                                     tR


                                                  alu
                                                                          Time Dependent Creep                2503.01.01
           Training in Aluminium Application Technologies




It is the transient two-dimensional heat transfer equation which has to be solved by the
finite element method [3].

                                                             ∂  ∂ T ∂  ∂ T ∂ e
                                                                k   +    k   +    +Q =0
                                                            ∂ x  ∂ x ∂ y  ∂ y ∂ t

         wherex, y                             =             coordinates (m)
                 T                             =             temperature (°K)
                 k                             =             thermal conductivity (W/m°K)
                 e                             =             specific volumetric enthalpy (J/m³)
                 t                             =             time (s)
                 Q                             =             internally generated heat (W/m³)




TALAT 2503                                                                            4
The specific volumetric enthalpy (J/m³) is defined as:

                T

            e = ∫ c ρ dT + ∑ li
                T0



         where T0    =    reference temperature, usually zero °K
               C     =    specific heat capacity (J/kg°K)
               ρ     =    density (kg/m³)
               li    =    latent heat at various temperature levels for instance due to
                          evaporation of water or chemical reactions (J/m³)


Heat flux to boundaries may be specified as:


                (         ) (             )
                                              γ
        q = ε ⋅ σ Tg4 − Ts4 + β Tg − Ts

         where ε     =    resultant emissivity
               σ     =    the Stefan-Boltzmann constant (W/m²K4)
               Tg    =    absolute surrounding gas temperature (e.g fire temperature) (K)
               Ts    =    absolute surface temperature (K)
               ß     =    convective heat transfer coefficient (W/m²K)
               γ     =    convective heat transfer power

The values for thermal conductivity and specific heat capacity, must be adapted
according to the higher temperatures at the different nodes.
The computer programmes are built up around the above mentioned equations. One-
dimensional calculation can be done by handcalculation but this seems rather time-
consuming.



2503.02 Fire Design according to ENV 1999 - 1 - 2

The European prestandard deals with design of aluminium structures for the accidental
situation of fire exposure. The prestandard must be used together with the general rules
of the prestandard, ENV 1999 - 1 - 1 |17|.

The contents of the prestandard is a general part with general information and basic
principles and rules, a part with material properties and a part with structural fire design
containing mechanical response and temperature analysis.

The part containing material properties fits in with the material properties in this course
(Section 2502.01).

The structural fire design part consists of simple calculation models for the resistance of
the different types of members in a member analysis and a temperature analysis part for

TALAT 2503                                        5
unprotected and protected aluminium structures together with aluminium structures in a
void protected by heat screens and external aluminium structures.



2503.02.01 Resistance of aluminium structures at elevated temperatures

In this section the symbols for design resistance becomes MRd, NRd, VRd depending on
whether the effect of actions concerned is bending moment, axial force or shear force
respectively.

In a fire design situation, the classification of cross-sections can be classified as for
normal temperature design according to 5.4 in ENV 1999-1-1 |17|, without any changes.



2503.02.02 Tension members

The design resistance Nfi,t,Rd of a tension member with a non uniform temperature
distribution over the cross section at time t may be determined from

            Nfi,t,Rd = ∑ Aik0,2,θ,i f0,2/γM,fi

where

         Ai is an elemental area of the net cross-section with a temperature θi , including
         a deduction when required to allow for the effect of HAZ softening. The
         deduction is based on the reduced thickness of kHAZ ⋅ t ;

         k0,2,θ,i is the reduction factor for the effective 0.2% proof stress at temperature
         θi. θi is the temperature in the elemental area Ai.

The design resistance Nfi,θ,Rd of a tension member with a uniform temperature θal should
be determined from

            Nfi,θ,Rd = k0,2,θ NRd (γM1/γM,fi)

where:

         k0,2,θ is the 0,2% proof stress ratio for the aluminium alloys strength at
         temperature θal;

         and NRd is the design resistance of the net section for normal temperature
         design according to ENV 1999-1-1.

It may be assumed that a tension member satisfies the requirements if at time t the
aluminium temperature θal at all cross-sections is not more than 170 °C.


TALAT 2503                                       6
2503.02.03 Beams

The design moment resistance Mfi,t,Rd of a cross-section in class 1 or 2 with a non
uniform temperature distribution at time t may be determined from:

            Mfi,t,Rd = ∑ Ai zi k0.2,θ,i f0.2/γM,fi

where:

         Ai is an elemental area of the net cross-section with a temperature θi , including
         a deduction when required to allow for the effect of HAZ softening. The
         deduction is based on the reduced thickness of kHAZ ⋅ t, according to ENV
         1999-1-1;

         zi is the distance from the plastic neutral axis to the centroid of the elemental
         area Ai ;

         k0,2,θ,i f0,2 is the strength of the elemental area Ai at temperature θal.

The plastic neutral axis of cross-section with a non uniform temperature distribution is
that axis perpendicular to the plane of bending which satisfies the following criterion:

            ∑ Ai k0,2,θ,i f0,2,i = 0

The design moment resistance Mfi,t,Rd of a cross-section in class 3 with a non-uniform
temperature distribution at time t may be determined from:

            Mfi,t,Rd = Mfi,θ,Rd

where

         Mfi,θ,Rd is the design moment resistance of the cross section for a uniform
         temperature θal equal to the maximum temperature θal,max reached at time t.

The design Mfi,t,Rd of a cross-section in class 4 with a non-uniform temperature
distribution at time t may be determined from:

            Mfi,t,Rd = k0,2,θmax MRd (γM1/γM,fi)

where:

         k0,2,θmax is the 0,2% proof stress ratio for the aluminium alloys strength at
         temperature θal equal to the maximum temperature θal,max of the cross section
         reached at time t;

         and MRd is the moment resistance of the cross-section for normal temperature
         design for class 4 according to ENV 1999-1-1.


TALAT 2503                                           7
The design Mfi,t,Rd of a cross-section in class 1, 2, 3 or 4 with a uniform temperature
distribution at time t may be determined from:

            Mfi,t,Rd = k0,2,θ MRd (γM1/γM,fi)

where:

         k0,2,θ is the 0,2% proof stress ratio for the aluminium alloys strength at
         temperature θal
         MRd is the moment resistance of the cross-section for normal temperature
         design.

For beams subjected to lateral-torsional buckling, the design buckling resistance
moment Mb,fi,t,Rd of a laterally unrestrained beam at time t may be determined using:

            Mb,fi,t,Rd = k0,2,θ,max Mb,Rd (γM1/γM,fi)

where:

         k0,2,θ,max is the 0,2% proof stress ratio of aluminium alloy at temperature θal
         equal to the maximum aluminium alloy temperature θal,max.
         Mb,Rd is the design buckling resistance moment for normal temperature design,
         according to ENV 1999-1-1.

The design shear resistance Vfi,t,Rd of a beam at time t may be determined from:

            Vfi,t,Rd = k0,2,θ VRd (γM1/γM,fi)

where:

         k0,2,θ is the 0,2% proof stress ratio for the aluminium alloys strength at
         temperature θal. θal is the max temperature of that part of the cross section
         which carry the shear force.
         VRd is the shear resistance of the net cross-section for normal temperature
         design, according to ENV 1999-1-1.

It may be assumed that a beam satisfy all the requirements if at time t the aluminium
alloy temperature θal at all cross-sections is not more than 170 °C.




TALAT 2503                                          8
2503.02.04 Columns

The design buckling resistance Nb,fi,t,Rd of a compression member at time t may be
determined from:

            Nb,fi,t,Rd = k0,2,θ,max Nb,Rd (γM1/1,2γM,fi)

where:

         Nb,Rd is the buckling resistance for normal temperature design according to
         ENV 1999 Part 1.1.

         k0.2,θmax is the 0,2% proof stress ratio of aluminium alloy at temperature θal
         equal to the maximum aluminium alloy temperature θal,max.

The constant 1,2 in this expression is a reduction factor of the design resistance due to
the temperature dependent creep of aluminium alloys.

For the determination of the slenderness ratio the provisions of ENV 1999-1-1 apply.

Column lengths in non-sway frames continuously or semi-continuously connected to
column lengths in other compartments, may be considered to be completely fixed in
direction at such connections, provided that the resistance to fire of the building
components which separate the fire compartments concerned is at least equal to the fire
resistance of the column.

The design buckling resistance Rfi,t,d of a member subjected to combined bending and
axial compression at time t may be determined from:

            Rfi,t,d = k0.2,θmax Rd

where:

         Rd represent a combination of axial compression and bending moments Nfi,Ed,
         My,fi,Ed, and Mz,fi,Ed such that for normal temperature design the provisions in
         ENV 1999-1-1 for all types of members are satisfied when:

               NSd = 1,2 Nfi,Ed
               My,Sd = My,fi,Ed
               Mz,Sd = Mz,fi,Ed

It may be assumed that a column satisfy these requirements if at time t the aluminium
temperature θal at all cross-sections is not more than 170 °C.




TALAT 2503                                           9
2503.02.05 Connections

The resistance of connections between members need not be checked provided that the
thermal resistance (dp /λp)c of the fire protection of the connection is not less than the
minimum value of the thermal resistance (dp /λp)m of the fire protection of any of the
aluminium alloy members joined by that connection.

where:

         dp is the thickness of the fire protection material

         λp is the effective thermal conductivity of the fire protection material.

For welded connections the reduced strength in the heat affected zones must be taken
into account.



2503.02.06 Temperature analysis for unprotected aluminium structures

For uninsulated aluminium structures with an equivalent uniform temperature
distribution in the cross-section, the increase of temperature ∆θ al ( t ) during a time
interval ∆t should be determined from:

                                   1      A &
               ∆θ al ( t ) =             ⋅ m ⋅ hnet ,d ⋅ ∆t
                               cal ⋅ ρ al V

where: cal         is the specific heat of aluminium alloys (J/kg ºC)
         ρal       is the unit mass of aluminium (kg/m³)
         Am V      is the section factor for unprotected aluminium alloy members (m-1)
         Am        is the exposed surface area of the member per unit length (m²/m)
         V         is the volume of the member per unit length (m³/m)
          &
         hnet ,d   is the design value of the net heat flux per unit area (W/m2)
         ∆t        is the time interval (seconds)

               &
Calculation of hnet ,d is described in ENV 1991 Part 2 - 2 |16|:

          &                  &                  &
          hnet ,d = γ n ,c ⋅ hnet ,c + γ n ,r ⋅ hnet ,r

         γ n ,c = γ n ,r = 1,0 for most cases.




TALAT 2503                                                    10
The previous equation will than be:

              &              (        )                         [
              hnet ,d = α c ⋅ θ g − θ m + Φ ⋅ ε res ⋅ 5,67 ⋅ 10 −8 ⋅ (θ r + 273) + (θ m + 273)
                                                                                4              4
                                                                                                   ]
where: α c       coefficient of heat transfer by convection (W/m2°K)
         θg      gas temperature of the environment of the member in fire exposure (°C)
         θm      surface temperature of member (°C)
         Φ       configuration factor
         ε res   resultant emissivity
         θr      radiation temperature of the environment of the member, may be
                 represented by the gas temperature, θ g , (°C)
         5,67 ⋅ 10-8 is Stefan Boltzmann constant in W/m2°K4.

The resultant emissivity, εres, is formulated as:

              ε res = ε f ⋅ ε m

where: ε f        emissivity related to the fire compartment, usually taken as 0,8
         εm       emissivity related to surface material; the following values may be used:
                  ε m = 0,3 (leading to ε res = 0,24) for clean uncovered surfaces and
                  ε m = 0,7       (leading to ε res = 0,56) for painted and covered surfaces,

In the performance of the calculation the following must be taken into consideration:

The value of ∆t should not be taken as more than 5 seconds.

The value of the shape factor Am V should not be taken as less than 10 m-1.

When calculating the exposed surface area of the member, Am , grooves with gap in the
surface less than 20 mm should not be included in the exposed surface area (see
Figure 2503.02.01).

Some design values of the section factor Am V for unprotected aluminium alloy
members are given in Figure 2503.02.02,. Figure 2503.02.03 and Figure 2503.02.04.




TALAT 2503                                            11
<20mm                           >2 m
                                                                                                0 m
                     Grooves with gap in the surface < 20 mm, area of groove not to be included in the area of
                     the exposed surface.
                     Grooves with gap in the surface > 20 mm, area of the groove to be included in the area of

                                              alu           Calculation of the exposed surface in case of grooves       2503.02.01
       Training in Aluminium Application Technologies




         Open section exposed to fire on all sides:                                      Tube exposed to fire on all sides:

                                Am                      perimeter
                                          =                                                           Am 1
                                  V             cross - section area                                    =
                                                                                                      V   t


                                                                                                              t




          Open section exposed to fire on three sides:                                 Hollow section (or welded box section of
                                                                                       uniform thickness) exposed to fire on all
                                  Am   surface exposed to fire                         sides:
                                     =
                                  V      cross - section area                          If t << b: Am/V = 1/t


                                                                                                                    t




                                                         Section factor Am/V for unprotected structural aluminium
                                              alu

       Training in Aluminium Application Technologies     alloy members when using the lumped mass method (I)
                                                                                                                        2503.02.02




TALAT 2503                                                                              12
I section flange exposed to fire on three sides:                             Box section exposed to fire on all sides:
       Am/V = (b + 2tf)/(b tf)
       If t<<b: Am/V = 1/tf

                                                                                    Am         2(b + h)                             h
                                                                                       =
                                                                                    V    cross - section area
                                                                                                                          b
                                                                    t
                                                            b




          Angle (or any open section of uniform                                       I section with box
          thick-ness) exposed to fire on all sides:                                  reinforcement, exposed
                                                                                     to fire on all sides:
                                                 Am/V = 2/ t
                                                                                                                                h



                                                                                    Am             2(b + h)
                                                                                         =
                                                                                                                      b
                                                                                     V       cross - section area
                        t

                                                        Section factor Am/V for unprotected structural aluminium
                                              alu

       Training in Aluminium Application Technologies   alloy members when using the lumped mass method (II)
                                                                                                                     2503.02.03



           Flat bar exposed to fire on all sides:                                    Flat bar exposed to fire on three sides:
           Am/V = 2(b + t)/(b t)                                                     Am/V = (b +2 t)/(b t)
           If t << b: Am/V = 2/ t                                                    If t << b: Am/V = 1/ t


                              t
                                                        b                                      t
                                                                                                              b




                                                        Section factor Am/V for unprotected structural aluminium
                                              alu

       Training in Aluminium Application Technologies   alloy members when using the lumped mass method (III)
                                                                                                                     2503.02.04




TALAT 2503                                                                           13
2503.02.07 Temperature analysis for protected aluminium structures

For insulated aluminium structures with an uniform temperature distribution in a cross-
section, the temperature increase ∆θ al ( t ) during a time interval ∆t , should be determined
from:

                                 λ p d p Ap  1 
                                                      (θ t − θ al )∆t − (e      − 1)∆θ ( t )
                                                                            φ 10
                 ∆θ al ( t ) =            ⋅  
                                 cal ⋅ ρal V 1 + φ 3 

but ∆θ al ( t ) ≥ 0

in which:

                       c pρ p         Ap
                 φ=              dp
                       calρal         V

where:     Ap V is the section factor for aluminium alloy members insulated by fire
                   protection material (m-1)
           Ap is the area of the inner surface of the fire protection material, per unit
                   length of the member (m²/m)
           V       is the volume of the member per unit length (m³/m)
           cal is the specific heat of aluminium alloys, (J/kg ºC)
           cp      is the specific heat of the fire protection material, (J/kg ºC)
           d p is the thickness of the fire protection material (m)
           ∆t is the time interval (seconds)
           θ ( t ) is the ambient gas temperature at time t (ºC)
           θ al ( t ) is the aluminium temperature at time t (ºC)
           ∆θ ( t ) is the increase of the ambient temperature during the time interval ∆t
                      (ºC)
           λp         is the thermal conductivity of the fire protection material, (W/m ºC)
           ρal        is the unit mass of aluminium alloys (kg/m³)
           ρp         is the unit mass of the fire protection material, (kg/m³)

In the performance of the calculation the following must be taken into consideration:

The value of ∆t should not be taken as more than 30 seconds.

Some design values of the section factor Ap V for insulated aluminium alloy members
are given in Figure 2503.02.05 and Figure 2503.02.06.

For moist fire protection materials the calculation of the aluminium alloy temperature
increase ∆θ al ( t ) may be modified to allow for a time delay in the rise of the aluminium
alloy temperature when it reaches 100 ºC. This delay time should be determined by a
method conforming with a prENV, ENV, prEN or EN.

TALAT 2503                                                    14
Sketch                                    Description                        Section factor Ap/V



                                                                         Contour encasement                    aluminium perimeter
                                                                         of uniform thickness.
                                                                                                         aluminium cross - section area




                                                                        Hollow encasement                             2 (b + h)
                                                                        of uniform thickness.
              h                                                                                           aluminium cross - section area




                                                        b


                                                        Section factor Ap/V for structural aluminium alloy members insulated
                                              alu

       Training in Aluminium Application Technologies
                                                         by fire protetion materials when using the lumped mass method (I)     2503.02.05



                                  Sketch                                    Description                        Section factor Ap/V


                                                                       Contour encasement of
                                                                       uniform thickness,                    aluminium perimeter - b
                                                                       exposed to fire on three
                                                                                                         aluminium cross - section area
                                                                       sides.
                                         b




                                                                       Hollow encasement of
                                                                       uniform thickness,                              2h + b
                 h
                                                                       exposed to fire on three
                                                                                                         aluminium cross - section area
                                                                       sides.
                                               b




                                                        Section factor Ap/V for structural aluminium alloy members insulated
                                              alu

       Training in Aluminium Application Technologies
                                                         by fire protetion materials when using the lumped mass method (II)    2503.02.06




TALAT 2503                                                                                  15
2503.02.08 Internal aluminium structures in a void which is protected by heat
screens.

The provisions given below apply to both of the following cases:

        ∗ aluminium members in a void which is bordered by a floor on top and by a
           horizontal heat screen below

        ∗ aluminium members in a void which is bordered by vertical heat screens
           onboth sides.

The properties and performance of the heat screens shall be determined using a test
procedure conforming with a prENV, ENV, prEN or EN.

The temperature development in the void in which the aluminium members are situated
shall be determined from a standard fire test or calculated using an approved method.

For internal aluminium structures protected by heat screens, the calculation of the
aluminium temperature increase ∆θ al should be based on the methods given in this
section, taking the ambient gas temperature θ t as equal to the gas temperature in the
void.

Values of the heat transfer coefficients α c and α r determined from tests conforming
with a prENV, ENV, prEN or EN may be used in the calculation of ∆θ al as an
alternative to the values given in Eurocode 1: Part 2.2.

External aluminium structures.

The temperature in external aluminium structures shall be determined taking into
account:

        ∗ the radiative heat flux from the fire compartment

        ∗ the radiative heat flux and the convection heat flux from flames emanating
           from openings

        ∗ the radiative and convective heat loss from the aluminium structure to the
           ambient atmosphere

        ∗ the sizes and locations of the structural members.

Heat screens may be provided on one, two or three sides of an external aluminium alloy
member in order to protect it from radiative heat transfer.




TALAT 2503                                    16
Heat screens should be either:

         ∗ directly attached to that side of the aluminium member which is intended to
            protect, or

         ∗ large enough to fully screen this side from the expected radiative heat flux.

Heat screens should have an integrity which corresponds to the fire resistance required
for the aluminium member.

When deciding the temperature in external aluminium structures protected by heat
screens, it should be assumed that there is no radiative heat transfer to those sides which
are protected by heat screens.

Calculations may be based on steady state conditions resulting from a stationary heat
balance using the methods given in ENV 1999 Part 1-2 Annex B.

Design using ENV 1999 Part 1-2 Annex B should be based on the model given in
Eurocode 1: Part 2.2 describing the compartment fire conditions and the flames
emanating from openings, on which the calculation of the radiative and convective heat
fluxes should be based.




2503.03        Simplified Calculation Methods

          •   Uninsulated aluminium alloy structures
          •   Insulated aluminium alloy structures


The temperature analysis according to the ENV 1999-1-2 may be difficult due to lack of
information about the insulation material and/or time consuming.
A simplified method is developed for calculating the metal temperature of aluminium
alloy structures exposed to a standard fire. This method is described in this section and
calculation examples are shown in TALAT Lecture 2504.
The graphs giving the metal temperature of the structure (Figure 2503.03.03 and Figure
2503.03.04, Figures 2503.03.09 till Figure 2503.03.14) are designed in such a way that
they always will give a metal temperature higher than the value obtained by an exact
computerized calculation. Using these simplified methods the results will always be
conservative.
The section factor has different notations in the litterature. In this course the two most
used notations are used:
F/V = Am/V = exposed surface area of member divided by the volume of the member,
both per unit length.
Fi/V = Ap/V = inner surface area of the insulation material divided by the volume of the
member, both per unit length.

TALAT 2503                                     17
2503.03.01 Uninsulated Aluminium Alloy Structures.

Uninsulated aluminium alloy structures exposed to the standard fire (ISO 834) may be
calculated according to this method.
F/V is to be determined according to the cross section of the member and the exposed
surfaces (Figure 2503.03.01 and Figure 2503.03.02). It describes the ratio of the
exposed surface area of the member and its volume per unit length.


                                                                                           F/V            F = exposed surface area
                                                                                                              of the member per
             Free-                                                                    2h + 4b - 2d            unit length (m2/m)
                                                            t




                                                                    d    h
             standing                                                                 section area
             columns:                                           b                                         V = volume of the exposed
                                                                                                              part of the member per
                                                                t        h              2h + 2b               unit length (m3/m)
                                                                                      section area
                                                                b
             Columns outside
             windows opening:                                                            2h + b
                                                                                      section area
                                                            Windows opening


                                                                                              1
              Beam inside
                                                                                              t
              floor:

                                                                                      2h + 3b -2d
                                                                                      section area
             Beam below
             floor:
                                                                                         2h + b
                                                                                      section area



                                                alu
                                                           Determination of F/ V for Columns and Beams                2503.03.01
         Training in Aluminium Application Technologies




                                                                                                              F/ V
                                        Truss below floor:
                                                                                    Separate calculation for each part of the truss:


                                                                                                            b2 + 2h2
                                                                                    Upper chord:
                                                                    h1




                                                                                                     upper chord section area

                                                          b2
                                                                                    Bracing:          4
                                                                                                      d
                                                                        d




                                                                                                             2b1 + 2h1
                                                                    h2




                                                                                    Bottom chord:
                                                                                                     bottom chord section area
                                                          b1

           F = exposed surface area of the member per unit length (m2/m)
           V = volume of the exposed part of the member per unit length (m3/m)



                                                alu
                                                          Determination of F/ V for Trusses                           2503.03.02
         Training in Aluminium Application Technologies




TALAT 2503                                                                          18
The surface of aluminium alloys has a very low emissivity. The major part of the heat
radiation energy is reflected from an aluminium surface. Painted metal or a surface
coated with other materials has, however, a much higher emissivity.
As a rule of thumb, the following resultant emissivities can be used:

       εr =                     0,2                                                           for external structures exposed by heat radiation through
                                                                                              openings in partitions and for structures not getting any soot
                                                                                              layer on the surface during the thermal exposure.

       εr =                     0,7                                                           for all other cases.

Knowing the resultant emissivity, the F/V and the exposure time for the standard fire,
the metal temperature can be found using Figure 2503.03.03 for εr = 0,2 and
Figure 2503.03.04 for εr = 0,7. When the metal temperature is known, the rules of ENV
1999-1-2 for the resistance can be used to determine the loadbearing capacity. These
rules are given in section 2503.02.(see also Figure 2503.03.05 for the procedure in the
case of uninsulated aluminium alloy structures).




                                         Metal Temperature - Time Curves for ε r = 0.2
                                                                                                               ( ε r= emissivity)
                                                                                        600
                                                  Metal temperature in degree Celsius




                                                                                        500
                                                                                                                        200        125
                                                                                        400
                                                                                                             300        150    100

                                                                                        300
                                                                                                                              75
                                                                                                                                     50
                                                                                                                                          37
                                                                                        200
                                                                                                                                          25
                                                                                        100

                                                                                         0
                                                                                              0          5         10         15        20     25   30
                                                                                                                        Time in minutes


                                                 alu
                                                                                                  Metal Temperature - Time Curves for εr = 0,2           2503.03.03
          Training in Aluminium Application Technologies




TALAT 2503                                                                                                                     19
Metal Temperature - Time Curves for ε r = 0.7
                                                                                                                    ( εr = emissivity)
                                                                                         600




                                                   Metal temperature in degree Celsius
                                                                                                            300              100
                                                                                         500
                                                                                                                  150
                                                                                                            200              75
                                                                                         400
                                                                                                             125
                                                                                                                             50
                                                                                         300
                                                                                                                             37
                                                                                                                                  25
                                                                                         200


                                                                                         100


                                                                                           0
                                                                                               0        5               10        15        20            25         30
                                                                                                                             Time in minutes



                                                  alu
                                                                                               Metal Temperature - Time Curves for εr = 0,7                           2503.03.04
           Training in Aluminium Application Technologies




               Required Fire
                                                                                                                                       Building Regulations, Codes, Standards
               Resistance

                                                                                                            F/V                        Structural Member:
                                                                                                                                       Determine surface area (F) and volume (V)
                                                                                                                                       of the member exposed to fire (m³/m)
            Metal temperature in member
                                                                                                            Resultant
            depending on emissivity of                                                                                                 Emissivity:
                                                                                                            emissivity εR
            0.2 (s. Fig. 2503.01.04) or of                                                                                             εR = 0.2 (for external structures with
            0.7 (s. Fig. 2503.01.05)                                                                                                   openings in partitions and for structures
                                                                                                                                       without any sootlayer during fire
                                                                                                                                       εR = 0.7 used for all other cases

             Reduced strength of                                                                                                       Strength:
             aluminium alloy                                                                                                           Fig. 2502.01.04 : modulus of elasticity
                                                                                                                                       Fig. 2502.01.05: yield strength


             Structural analysis with the reduced
             modulus of elasticity and strength.                                                                   not OK              The Member has to be fire insulated
             load factors and material factors as                                                                                      or protected in an approved way.
             for accidental load condition.


                           OK
                                                  alu
                                                                                                          Flow Chart for Design
           Training in Aluminium Application Technologies                                          of Uninsulated Aluminium Structures                                2503.03.05




2503.03.02 Insulated Aluminium Structures

Aluminium alloy structures insulated with rockwool, ceramic fibres, calcium silicate
boards, vermiculite boards or gypsum boards and exposed to a standard fire (ISO 834)
may be calculated according to this method.

Fi/V is to be determined according to the section of the member, the location of the
insulation and the exposed surfaces, see Figure 2503.03.06 and Figure 2503.03.07.


TALAT 2503                                                                                                                        20
d                                                Fi = area of inner surface of the
                                                                                             Fi/ V
                                                                                                                    exposed insulation material
                                                                                                                    per unit length of the




                                                                       t
                                                                                        2h + 4b - 2d                aluminium alloy member




                                                                           h
                                                                                        section area                (m2/m)
                                                                                                               V=   volume of the exposed part
                Freestanding                                  b                                                     of the insulated member
                columns:                                                                                            per unit length (m3/m)
                                                                                          2h + 2b
                                                                                        section area




                Column
                against fire                                                              2h + b
                rated wall:                                                            section area


                Column built
                                                                                              1
                inside fire
                                                                                              t
                rated wall:



                                                  alu
                                                                  Determination of F/ V for Insulated Columns                    2503.03.06
           Training in Aluminium Application Technologies




                                                                                                                      Fi = area of inner
                                                                                               Fi/ V
                                                                                                                           surface of the
                     Beam inside
                                                                                                                           exposed insulation
                     floor:                                                                       1                        material per unit
                                                                                                  t
                                                                                                                           length of the
                                                                                                                           aluminium alloy
                                                                                                                           member (m2/m)

                    Beam below                                                                                        V=   volume of the
                    floor:                                                                   2h + b                        exposed part
                                                                                           section area                    of the insulated
                                                                                                                           member per unit
                                                                                                                           length (m3/m)
                                                                                    Separate calculation for each
                                                                                    part of the truss:
                    Truss below                                                             Upper chord:
                    floor:                                                                   b2 + 2h2
                                                                           h2




                                                                                      upper chord sec. area
                                                                  b2
                                                                                           Bottom chord:
                                                                           d




                                                                                             2b1 + 2h1
                                                                           h1




                                                                                      bottom chord sec. area

                                                                                        Bracing:      4
                                                                  b1
                                                                                                      d


                                                  alu
                                                            Determination of F/ V for Insulated Beams and Trusses                2503.03.07
           Training in Aluminium Application Technologies




The type of insulation material and its thickness has to be chosen, the equivalent
insulation thickness to be calculated by

                                                                                t equ = C · t

where                 C = insulation correction factor
                      t = insulation thickness

The insulation correction factor to be taken from Figure 2503.03.08.



TALAT 2503                                                                               21
Insulation Material                                                                                    Density kg/ m3            Ins. Corr. Factor

                               Rockwool Mats                                                                                         30 - 40                       0,45
                               Rockwool Mats                                                                                        100 - 120                      1,00
                               Rockwool Mats and Boards                                                                             150 - 170                      1,15
                               Rockwool Boards                                                                                      280 - 320                      1,50
                               Ceramic Fibres Mats                                                                                  120 - 150                      1,30
                               Ceramic Fibres Boards                                                                                240 - 300                      1,40
                               Calcium Silicate Boards                                                                              400 - 900               1/625 Fi / V +0,8
                               Vermiculite Boards                                                                                   400 - 900               1/625 Fi / V + 0,8
                               Gypsium Boards                                                                                       700 - 1000              1/160 Fi / V + 0,5




                                                 alu
                                                                                                                           Insulation Correction Factor                    2503.03.08
          Training in Aluminium Application Technologies




Knowing the equivalent insulation thickness, the Fi/V and the exposure time for the
standard fire, the metal temperature of the aluminium alloy structure can be found from:

       Figure 2503.03.09                                                                                   for 10 min. fire resistance
       Figure 2503.03.10                                                                                   for 15 min. fire resistance
       Figure 2503.03.11                                                                                   for 30 min. fire resistance
       Figure 2503.03.12                                                                                   for 60 min. fire resistance
       Figure 2503.03.13                                                                                   for 90 min. fire resistance

The metal temperature is used to find the modulus of elasticity and the 0,2% proof stress
ratio. These values are used for checking the loadbearing capacity according to the ENV
1999-1-2.



                                             Equivalent Insulation Thickness Versus Metal
                                               Temperature for 10 Min Fire Resistance
                                                                                                 600
                                                           Metal temperature in degree Celsius




                                                                                                 550
                                                                                                 500
                                                                                                 450
                                                                                                 400
                                                                                                 350
                                                                                                 300                   300
                                                                                                 250
                                                                                                 200        100
                                                                                                                           200
                                                                                                                           150
                                                                                                 150
                                                                                                            50               125
                                                                                                 100                   75
                                                                                                                 37
                                                                                                  50                  25

                                                                                                   0
                                                                                                       0         5          10      15   20      25   30      35    40
                                                                                                                      Equivalent insulation thickness in mm

                                                                                                       Equivalent Insulation Thickness Versus Metal
                                                       alu
                                                                                                                                                                             2503.03.09
               Training in Aluminium Application Technologies                                            Temperature for 10 min Fire Resistance




TALAT 2503                                                                                                                                22
Equivalent Insulation Thickness Versus Metal
                                                                    Temperature for 15 Min Fire Resistance
                                                                                                     600
                                                                                                     550




                                                         Metal temperature in degree Celsius
                                                                                                     500
                                                                                                     450
                                                                                                     400
                                                                                                     350
                                                                                                     300                                     300

                                                                                                     250                 125             200
                                                                                                     200                75                   150
                                                                                                                                  100
                                                                                                     150           37
                                                                                                                             50
                                                                                                     100
                                                                                                      50                           25

                                                                                                           0
                                                                                                               0   5          10         15         20        25    30   35   40   45    50
                                                                                                                                  Equivalent insulation thickness in mm

                                                                                                                        Equivalent Insulation Thickness Versus Metal
                                                                                                     alu

                                                                                                                          Temperature for 15 min Fire Resistance
                                                                                                                                                                                                 2503.03.10
              Training in Aluminium Application Technologies




                                         Equivalent Insulation Thickness Versus Metal
                                           Temperature for 30 Min Fire Resistance
                                                                                                 600
                                                                                                 550
                                       Metal temperature in degree Celsius




                                                                                                 500
                                                                                                 450
                                                                                                 400
                                                                                                                                                   300
                                                                                                 350
                                                                                                                                         200
                                                                                                 300
                                                                                                                                         150
                                                                                                 250
                                                                                                                             75          125
                                                                                                 200
                                                                                                                                             100
                                                                                                 150                              50

                                                                                                 100                     25             37
                                                                                                     50
                                                                                                           0
                                                                                                            0      10             20          30         40        50    60   70    80    90   100
                                                                                                                                             Equivalent insulation thickness in mm

                                                                                                                    Equivalent Insulation Thickness Versus Metal
                                                                                               alu
                                                                                                                      Temperature for 30 Min Fire Resistance                                   2503.03.11
         Training in Aluminium Application Technologies




TALAT 2503                                                                                                                                                    23
Equivalent Insulation Thickness Versus Metal
                                                       Temperature for 60 Min Fire Resistance
                                                                                             600
                                                                                             550

                                         Metal temperature in degree Celsius
                                                                                             500
                                                                                             450                                                 300
                                                                                                                                   150
                                                                                             400
                                                                                             350                          100                    200

                                                                                             300
                                                                                                                                              125
                                                                                             250                               75

                                                                                             200                37         50

                                                                                             150
                                                                                                                         25
                                                                                             100
                                                                                                  50
                                                                                                   0
                                                                                                    0   12,5   25        37,5        50          62,5           75   87,5   100 112,5 125
                                                                                                                         Equivalent insulation thickness in mm


                                                                                                          Equivalent Insulation Thickness Versus Metal
                                                                                            alu
                                                                                                            Temperature for 60 Min Fire Resistance                                     2503.03.12
            Training in Aluminium Application Technologies




                                    Equivalent Insulation Thickness Versus Metal
                                      Temperature for 90 Min Fire Resistance
                                                                                             600
                                                                                             550
                                                      Metal temperature in degree Celsius




                                                                                             500
                                                                                             450
                                                                                                                                                          300
                                                                                             400
                                                                                                                                                      200
                                                                                             350
                                                                                                                                          125
                                                                                             300                                                    150

                                                                                             250                                                100
                                                                                                                                         75
                                                                                             200
                                                                                                                                         50
                                                                                             150                              37
                                                                                                                    25
                                                                                             100
                                                                                                  50
                                                                                                  0
                                                                                                   25   37,5   50    62,5           75        87,5 100 112,5 125 137,5 150
                                                                                                                Equivalent insulation thickness in mm

                                                                                                          Equivalent Insulation Thickness Versus Metal
                                                                                            alu

                                                                                                            Temperature for 90 Min Fire Resistance                                     2503.03.13
            Training in Aluminium Application Technologies




When the thermal load is a hydrocarbon fire according to the time-temperature curve
described in Figure 2501.01.05, the same procedure can be used with the following
graphs:
       Figure 2503.03.14                                                                                 for             60 min. fire resistance (HC-fire)
       Figure 2503.03.15                                                                                 for        120 min. fire resistance (HC-fire)
(The values on the curves are the Fi /V - ratios)




TALAT 2503                                                                                                                                       24
Equivalent Insulation Thickness Versus Metal
                                                                                   Temperature for 60 Min HC Fire
                                                                                                                                600




                                                                                          Metal temperature in degree Celsius
                                                                                                                                500


                                                                                                                                400
                                                                                                                                                                              300
                                                                                                                                                                        200
                                                                                                                                300
                                                                                                                                                                125     150

                                                                                                                                                           75         100
                                                                                                                                200
                                                                                                                                                     37         50

                                                                                                                                100                        25



                                                                                                                                  0
                                                                                                                                   50                70                 90           110         130         150
                                                                                                                                                          Equivalent insulation thickness in mm

                                                                                                                                      Equivalent Insulation Thickness Versus Metal
                                                                                    alu

                                                                                                                                            Temperature for 60 Min HC Fire                                         2503.03.14
                  Training in Aluminium Application Technologies




                      Equivalent Insulation Thickness Versus
              Metal Temperature for 120 Min Fire Resistance, HC Fire
                                                                              600
                                       Metal temperature in degree Celsius




                                                                              500

                                                                                                                                                                 150
                                                                              400
                                                                                                                                                                125           200
                                                                                                                                                 75                                  300
                                                                                                                                                                100
                                                                              300
                                                                                                                                                50
                                                                                                                     25                    37
                                                                              200


                                                                              100


                                                                                   0
                                                                                    50                                                80                  110                  140         170         200
                                                                                                                                       Equivalent insulation thickness in mm

                                                                                                  Equivalent Insulation Thickness Versus
                                                                             alu

                                                                                          Metal Temperature for 120 Min Fire Resistance, HC Fire                                                               2503.03.15
        Training in Aluminium Application Technologies




See also Figure 2503.03.16 for the proceeding in the case of insulated aluminium alloy
structures.




TALAT 2503                                                                                                                                                                     25
Metal Temperature in Member                                              Required Fire           Building Regulations
           Graph 3 10min fire resistance                                            Resistance              Codes, Standards
           Graph 4 15min fire resistance
           Graph 5 30min fire resistance                                            Fi / V
           Graph 6 60min fire resistance
           Graph 7 90min fire resistance
           Graph 8 60min fire resistance, HC - fire                                  Structural Members
           Graph 9 120min fire resistance, HC - fire                                 F i = area of the inner surface of the insulation
                                                                                          material per unit length of the aluminium alloy
                                                                                          member (m² / m)
                                                                                     V = volume of the aluminium alloy member per unit
                                                                                          length (m³ / m)

                                                           Equivalent insulation
                                                                                    Insulation correction       Insulation Material
                                                           thickness (tequ)
                                                                                    factor (C)                  Insulation thickness (t)
                                                           tequ = C * t

           Reduced Strength of                                      Fig. 2502.01.04: modulus elasticity
           aluminium alloy                                          Fig. 2502.01.05: yield strength


            Structural Analysis with the reduced
            modulus of elasticity and strength.                                    not OK
            load factors and material factors
            as for accidental load condition                                       OK
                                                                      Flow Chart for Design of Insulated
                                                 alu

                                                                         Aluminium Alloy Structures                             2503.03.16
          Training in Aluminium Application Technologies




2503.04                     Insulation Techniques

The insulation techniques for wet insulation is different for each material. For dry
insulation, however, the insulation techniques are similar.

In any case, the insulation must always be installed on the exposed sides of the
aluminium alloy structures, and it must be fastened in such a way that it does not fall off
during exposure to fire.

For fixing dry insulation material to an aluminium alloy structure, bimetallic fixing pins
can be used. These pins, consisting of stainless steel with an aluminium alloy at the
fixing end can be pin-welded to the aluminium alloy structure. The insulation is to be
hanged up on the pins in such a way that the pins pierce the insulation material, and the
insulation is fixed by a lock washer at the end of the pins. At corners and other points
where it is difficult to fasten the insulation tight, steel netting, galvanized or stainless
steel, may be used (Figure 2503.04.01 and Figure 2503.04.02).




TALAT 2503                                                                                   26
∅3




                                                               A
                                                                                  Typical Bimetallic Fixing Pin




                                                               B


                                      Aluminium


                                                alu

         Training in Aluminium Application Technologies
                                                                   Typical Bimetallic Fixing Pin             2503.04.02


Many of the dry insulation materials shrink when they are exposed to fire. For this
reason the insulation must be laid out in two layers with overlap at the joints
(Figure 2503.04.03).




TALAT 2503                                                                         27
Examples for fixing insulation boards are given in Figure 2503.04.04 and Figure
2503.04.05.

                  Typical Fixing Method for Stiff Insulation Boards


                                                         metal anchor
                                                                             min
                                                           angle of steel    25 mm
                                                            min             screw
                                                            10 mm




                                                                              screw


                                                  insulation of beam                       insulation of column.




                                              alu
                                                        Typical Fixing Method for Stiff Insulation Boards      2503.04.04
       Training in Aluminium Application Technologies




TALAT 2503                                                                            28
6
                                                                             1
                                                                                                              5
                                                                             2
                                                                                                              7
                                                                             3

                                                                             4

                                                                             5

                                                                             6



                     Typical fixing method for gypsum boards for beams (left) and columns (right)

                                                               Steel Angles  : 1, 2, 3, 5, and 6
                                                               Gypsum plates : 4
                                                               5 mm air gap : 7

                                                           Typical Fixing Method for Gypsum Boards for
                                                 alu
                                                                 Beams (left) and Columns (right)        2503.04.05
          Training in Aluminium Application Technologies




2503.05                     References/Literature


[1]    Drysdale, Dougal: An Introduction to Fire Dynamics. John Wiley & Sons. 1987,
       ISBN 0-471-90613-1

[2]    NFPA/SFPE: Handbook of Fire Protection Engineering. NFPA/SFPE. 1988,
       ISBN 0-87765-353-4

[3]    Sterner, E. / Wickstrøm, U.: TASEF - User Manual. Statens Provningsanstalt.
       1990, ISBN 91-7848-210-0

[4]    Landrø, Harald: Verification of the fire resistance of construction elements and
       structures. SINTEF 1983.

[5]    ISO 834-1975 (E). Fire resistance tests - Elements of building construction.

[6]    ECCS-TC3: European Recommendations for the Fire Safety of Steel Structures.
       Elsevier 1983. ISBN 0-444-42120-3
[7]    GYPROC: Gyproc Håndbok. 1986. (In Swedish).

[8]    Holmen, J.P.: Heat Transfer. McGraw-Hill. Publ. Comp. 1990. ISBN 0-07-
       909388-4

[9]    Aluminium-Zentrale (Ed.): Aluminium Taschenbuch. Aluminium Verlag
       Düsseldorf, 1983. ISBN 3-87017-169-3 (In German)

[10]   Carborundum Resistant Materials: Fiberfrax Manual 1987.

[11]   Elkem Rockwool: Innføring i passive brannsikring. 1991. (In Norwegian).

TALAT 2503                                                                        29
[12]   NBR: NS 3478. Design rules for structural member for fire resistance. 1979. (In
       Norwegian).

[13]   Hydro Aluminium Structures a.s: Revisjon av NS 3471, Kap. 14.2 Brannteknisk
       dimensjonering. 1992. (In Norwegian).

[14]   Andersson, Leif & Jansson, Bengt: En undersøkning av gipsskivans termiske
       egenskaper - Teori och försök. Lund University 1986 (In Swedish).

[15]   CEN/TC 250/SC 9: ENV 1999-1-2. Design of aluminium structures. Part 1.2.
       Structural fire design. 1997.

[16]   CEN/TC 250/SC 1: ENV 1991-2-2. Basis of design and actions on structures.
       Part 2.2. Actions on structures exposed to fire. 1995

[17]   CEN/TC 250/SC 9: ENV 1999-1-1. Design of aluminium structures. Part 1.1.
       General rules. 1997




TALAT 2503                                  30
2503.06 List of Figures

Figure No.   Figure Title (Overhead)
2503.01.01   Time Dependent Creep
2503.02.01   Calculation of the exposed surface in case of grooves
2503.02.02   Section factor Am/V for unprotected structural aluminium alloy members when
             using the lamped mass method (I)
2503.02.03   Section factor Am/V for unprotected structural aluminium alloy members when
             using the lamped mass method (II)
2503.02.04   Section factor Am/V for unprotected structural aluminium alloy members when
             using the lamped mass method (III)
2503.02.05   Section factor Ap/V for structural aluminium alloy members insulated by fire
             protection when using the lamped mass method (I)
2503.02.06   Section factor Ap/V for structural aluminium alloy members insulated by fire
             protection when using the lamped mass method (II)
2503.03.01   Determination of F/V for Columns and Beams
2503.03.02   Determination of F/V for Trusses
2503.03.03   Metal Temperature-Time Curves for εr = 0,2
2503.03.04   Metal Temperature-Time Curves for εr = 0,7
2503.03.05   Flow Chart for Design of Uninsulated Aluminium Alloy Structures
2503.03.06   Determination of F/V for Insulated Columns
2503.03.07   Determination of F/V for Insulated Beams and Trusses
2503.03.08   Insulation Correction Factor
2503.03.09   Equivalent Insulation Thickness Versus Metal Temperature for 10 Min Fire
             Resistance
2503.03.10   Equivalent Insulation Thickness Versus Metal Temperature for 15 Min Fire
             Resistance
2503.03.11   Equivalent Insulation Thickness Versus Metal Temperature for 30 Min Fire
             Resistance
2503.03.12   Equivalent Insulation Thickness Versus Metal Temperature for 60 Min Fire
             Resistance
2503.03.13   Equivalent Insulation Thickness Versus Metal Temperature for 90 Min Fire
             Resistance
2503.03.14   Equivalent Insulation Thickness Versus Metal Temperature for 60 Min
             Resistance to HC Fire
2503.03.15   Equivalent Insulation Thickness Versus Metal Temperature for 120 Min Fire
             Resistance, HC Fire
2503.03.16   Flow Chart for Design of Insulated Aluminium Alloy Structures

2503.04.01   Fixing Insulation With Bimetallic Fixing Pins
2503.04.02   Typical Bimetallic Fixing Pin
2503.04.03   Avoid Air Gaps due to Shrinkage of Insulation
2503.04.04   Typical Fixing Method for Stiff Insulation Boards
2503.04.05   Typical Fixing Method forGypsum Boards for Beams (left) and Columns
             (right)



TALAT 2503                                 31

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TALAT Lecture 2503: Calculation Methods for Fire Design

  • 1. TALAT Lectures 2503 Calculation Methods for Fire Design 31 pages, 28 figures Basic Level prepared by Steinar Lundberg, Hydro Aluminium Structures, Karmoy Objectives: − to learn how to calculate the fire resistance of aluminium alloy structures with and without applied insulation Prerequisites: − general engineering background − TALAT lectures 2501 and 2502 REVICED NOVEMBER 1997 in connection with the Leonardo da Vinci project: TAS/WP 1 by Steinar Lundberg. Date of Issue: 1998  EAA - European Aluminium Association
  • 2. 2503 Calculation Methods for Fire Design Contents 2503 Calculation Methods for Fire Design ...........................................................2 2503.01 Tests and Calculation Methods ............................................................... 3 2503.01.01 Introduction...........................................................................................3 2503.01.02 Calculation Methods .............................................................................3 2503.02 Fire Design according to ENV 1999 - 1 - 2................................................ 5 2503.02.01 Resistance of aluminium structures at elevated temperatures ..............6 2503.02.02 Tension members ..................................................................................6 2503.02.03 Beams....................................................................................................7 2503.02.04 Columns ................................................................................................9 2503.02.05 Connections ........................................................................................10 2503.02.06 Temperature analysis for unprotected aluminium structures ..............10 2503.02.07 Temperature analysis for protected aluminium structures ..................14 2503.02.08 Internal aluminium structures in a void which is protected by heat screens. ..............................................................................................16 2503.03 Simplified Calculation Methods ............................................................ 17 2503.03.01 Uninsulated Aluminium Alloy Structures. .........................................18 2503.03.02 Insulated Aluminium Structures .........................................................20 2503.04 Insulation Techniques ............................................................................ 26 2503.04 References/Literature ............................................................................. 29 2503.06 List of Figures............................................................................................ 31 TALAT 2503 2
  • 3. 2503.01 Tests and Calculation Methods 2503.01.01 Introduction To document the fire resistance of an aluminium alloy structure, fire resistance tests can always be used. Walls, floors, beams and columns can be tested in the fire test furnaces. Load bearing structures can be tested with their actual load. Temperatures will always be measured on the unexposed side of a tested partition. For other building elements (beams, columns) usually temperatures are measured inside and on the outside surface of the structure. When testing an aluminium alloy structure, the temperature of the structural part is the most interesting. The metal temperature measured can be used to determine the strength available at that temperature. The structure can then be calculated with this reduced strength. This constitutes an alternative way to practical fire testing under loads. The good heat conduction ability of aluminium may be a problem when testing aluminium alloy structures. Small test specimen may experience a significant amount of heat transfer from the edges, and the temperature may be considerably higher than in larger test sections. If the test laboratory has little experience with testing aluminium structures, one should take care of minimizing the edge effects already when planning the test. 2503.01.02 Calculation Methods There are several computer programmes which can be used for temperature analysis of structures exposed to fire. No particular programmes are available for calculations of aluminium alloy structures. When calculating aluminium alloy structures at high temperatures (150 - 250 °C) time dependent creep effects will influence the behaviour of the material. One characteristic feature of creep behaviour is that, at constant stress and temperature, strain develops as shown by the creep curve in Figure 2503.01.01. Strain ε0 at t = 0 denotes the stress dependent initial strain, elastic or elastic-plastic. The strain curve is generally subdivided into three creep regimes: primary, secondary and tertiary. Creep rupture occurs at the end of tertiary creep. Tests have shown that the time dependent creep is neglectable for temperatures below 180 - 200 °C. ENV 1999-1-2 [15] disregard time dependent creep for temperatures below 170 °C. Creep properties of aluminium alloys are not taken into account by any computer programme. To design aluminium alloy structures exposed to fire, the first step will be to calculate the metal temperature of the structure. Then we can determine the reduced strength of the aluminium alloy. This value of reduced strength is used to check if the structure meets the required fire resistance according to the national codes or standards. TALAT 2503 3
  • 4. ENV 1999-1-2 [15] is today the only standard which deal with fire design of aluminium structures. The knowledge about the behaviour of aluminium structures at elevated temperatures is, however, limited for both insulated and uninsulated structures. ENV 1999-1-2 has rules for simple calculation of the capacity of structures at elevated temperatures. The rules for the temperature analysis are more complicated, and need the properties of the insulation materials which match the rules. Today these properties are only available for steel structures, but it is likely to believe that the same properties may be used also for aluminium structures. For calculating the temperature of structures exposed to fire computer programmes are available. By introducing the thermal properties of aluminium alloys in these programmes, they can be used to calculate the temperature of both insulated and uninsulated aluminium alloy structures exposed to fire. ε ε0 Primary Secondary Tertiary creep creep creep t tR alu Time Dependent Creep 2503.01.01 Training in Aluminium Application Technologies It is the transient two-dimensional heat transfer equation which has to be solved by the finite element method [3]. ∂  ∂ T ∂  ∂ T ∂ e k + k + +Q =0 ∂ x  ∂ x ∂ y  ∂ y ∂ t wherex, y = coordinates (m) T = temperature (°K) k = thermal conductivity (W/m°K) e = specific volumetric enthalpy (J/m³) t = time (s) Q = internally generated heat (W/m³) TALAT 2503 4
  • 5. The specific volumetric enthalpy (J/m³) is defined as: T e = ∫ c ρ dT + ∑ li T0 where T0 = reference temperature, usually zero °K C = specific heat capacity (J/kg°K) ρ = density (kg/m³) li = latent heat at various temperature levels for instance due to evaporation of water or chemical reactions (J/m³) Heat flux to boundaries may be specified as: ( ) ( ) γ q = ε ⋅ σ Tg4 − Ts4 + β Tg − Ts where ε = resultant emissivity σ = the Stefan-Boltzmann constant (W/m²K4) Tg = absolute surrounding gas temperature (e.g fire temperature) (K) Ts = absolute surface temperature (K) ß = convective heat transfer coefficient (W/m²K) γ = convective heat transfer power The values for thermal conductivity and specific heat capacity, must be adapted according to the higher temperatures at the different nodes. The computer programmes are built up around the above mentioned equations. One- dimensional calculation can be done by handcalculation but this seems rather time- consuming. 2503.02 Fire Design according to ENV 1999 - 1 - 2 The European prestandard deals with design of aluminium structures for the accidental situation of fire exposure. The prestandard must be used together with the general rules of the prestandard, ENV 1999 - 1 - 1 |17|. The contents of the prestandard is a general part with general information and basic principles and rules, a part with material properties and a part with structural fire design containing mechanical response and temperature analysis. The part containing material properties fits in with the material properties in this course (Section 2502.01). The structural fire design part consists of simple calculation models for the resistance of the different types of members in a member analysis and a temperature analysis part for TALAT 2503 5
  • 6. unprotected and protected aluminium structures together with aluminium structures in a void protected by heat screens and external aluminium structures. 2503.02.01 Resistance of aluminium structures at elevated temperatures In this section the symbols for design resistance becomes MRd, NRd, VRd depending on whether the effect of actions concerned is bending moment, axial force or shear force respectively. In a fire design situation, the classification of cross-sections can be classified as for normal temperature design according to 5.4 in ENV 1999-1-1 |17|, without any changes. 2503.02.02 Tension members The design resistance Nfi,t,Rd of a tension member with a non uniform temperature distribution over the cross section at time t may be determined from Nfi,t,Rd = ∑ Aik0,2,θ,i f0,2/γM,fi where Ai is an elemental area of the net cross-section with a temperature θi , including a deduction when required to allow for the effect of HAZ softening. The deduction is based on the reduced thickness of kHAZ ⋅ t ; k0,2,θ,i is the reduction factor for the effective 0.2% proof stress at temperature θi. θi is the temperature in the elemental area Ai. The design resistance Nfi,θ,Rd of a tension member with a uniform temperature θal should be determined from Nfi,θ,Rd = k0,2,θ NRd (γM1/γM,fi) where: k0,2,θ is the 0,2% proof stress ratio for the aluminium alloys strength at temperature θal; and NRd is the design resistance of the net section for normal temperature design according to ENV 1999-1-1. It may be assumed that a tension member satisfies the requirements if at time t the aluminium temperature θal at all cross-sections is not more than 170 °C. TALAT 2503 6
  • 7. 2503.02.03 Beams The design moment resistance Mfi,t,Rd of a cross-section in class 1 or 2 with a non uniform temperature distribution at time t may be determined from: Mfi,t,Rd = ∑ Ai zi k0.2,θ,i f0.2/γM,fi where: Ai is an elemental area of the net cross-section with a temperature θi , including a deduction when required to allow for the effect of HAZ softening. The deduction is based on the reduced thickness of kHAZ ⋅ t, according to ENV 1999-1-1; zi is the distance from the plastic neutral axis to the centroid of the elemental area Ai ; k0,2,θ,i f0,2 is the strength of the elemental area Ai at temperature θal. The plastic neutral axis of cross-section with a non uniform temperature distribution is that axis perpendicular to the plane of bending which satisfies the following criterion: ∑ Ai k0,2,θ,i f0,2,i = 0 The design moment resistance Mfi,t,Rd of a cross-section in class 3 with a non-uniform temperature distribution at time t may be determined from: Mfi,t,Rd = Mfi,θ,Rd where Mfi,θ,Rd is the design moment resistance of the cross section for a uniform temperature θal equal to the maximum temperature θal,max reached at time t. The design Mfi,t,Rd of a cross-section in class 4 with a non-uniform temperature distribution at time t may be determined from: Mfi,t,Rd = k0,2,θmax MRd (γM1/γM,fi) where: k0,2,θmax is the 0,2% proof stress ratio for the aluminium alloys strength at temperature θal equal to the maximum temperature θal,max of the cross section reached at time t; and MRd is the moment resistance of the cross-section for normal temperature design for class 4 according to ENV 1999-1-1. TALAT 2503 7
  • 8. The design Mfi,t,Rd of a cross-section in class 1, 2, 3 or 4 with a uniform temperature distribution at time t may be determined from: Mfi,t,Rd = k0,2,θ MRd (γM1/γM,fi) where: k0,2,θ is the 0,2% proof stress ratio for the aluminium alloys strength at temperature θal MRd is the moment resistance of the cross-section for normal temperature design. For beams subjected to lateral-torsional buckling, the design buckling resistance moment Mb,fi,t,Rd of a laterally unrestrained beam at time t may be determined using: Mb,fi,t,Rd = k0,2,θ,max Mb,Rd (γM1/γM,fi) where: k0,2,θ,max is the 0,2% proof stress ratio of aluminium alloy at temperature θal equal to the maximum aluminium alloy temperature θal,max. Mb,Rd is the design buckling resistance moment for normal temperature design, according to ENV 1999-1-1. The design shear resistance Vfi,t,Rd of a beam at time t may be determined from: Vfi,t,Rd = k0,2,θ VRd (γM1/γM,fi) where: k0,2,θ is the 0,2% proof stress ratio for the aluminium alloys strength at temperature θal. θal is the max temperature of that part of the cross section which carry the shear force. VRd is the shear resistance of the net cross-section for normal temperature design, according to ENV 1999-1-1. It may be assumed that a beam satisfy all the requirements if at time t the aluminium alloy temperature θal at all cross-sections is not more than 170 °C. TALAT 2503 8
  • 9. 2503.02.04 Columns The design buckling resistance Nb,fi,t,Rd of a compression member at time t may be determined from: Nb,fi,t,Rd = k0,2,θ,max Nb,Rd (γM1/1,2γM,fi) where: Nb,Rd is the buckling resistance for normal temperature design according to ENV 1999 Part 1.1. k0.2,θmax is the 0,2% proof stress ratio of aluminium alloy at temperature θal equal to the maximum aluminium alloy temperature θal,max. The constant 1,2 in this expression is a reduction factor of the design resistance due to the temperature dependent creep of aluminium alloys. For the determination of the slenderness ratio the provisions of ENV 1999-1-1 apply. Column lengths in non-sway frames continuously or semi-continuously connected to column lengths in other compartments, may be considered to be completely fixed in direction at such connections, provided that the resistance to fire of the building components which separate the fire compartments concerned is at least equal to the fire resistance of the column. The design buckling resistance Rfi,t,d of a member subjected to combined bending and axial compression at time t may be determined from: Rfi,t,d = k0.2,θmax Rd where: Rd represent a combination of axial compression and bending moments Nfi,Ed, My,fi,Ed, and Mz,fi,Ed such that for normal temperature design the provisions in ENV 1999-1-1 for all types of members are satisfied when: NSd = 1,2 Nfi,Ed My,Sd = My,fi,Ed Mz,Sd = Mz,fi,Ed It may be assumed that a column satisfy these requirements if at time t the aluminium temperature θal at all cross-sections is not more than 170 °C. TALAT 2503 9
  • 10. 2503.02.05 Connections The resistance of connections between members need not be checked provided that the thermal resistance (dp /λp)c of the fire protection of the connection is not less than the minimum value of the thermal resistance (dp /λp)m of the fire protection of any of the aluminium alloy members joined by that connection. where: dp is the thickness of the fire protection material λp is the effective thermal conductivity of the fire protection material. For welded connections the reduced strength in the heat affected zones must be taken into account. 2503.02.06 Temperature analysis for unprotected aluminium structures For uninsulated aluminium structures with an equivalent uniform temperature distribution in the cross-section, the increase of temperature ∆θ al ( t ) during a time interval ∆t should be determined from: 1 A & ∆θ al ( t ) = ⋅ m ⋅ hnet ,d ⋅ ∆t cal ⋅ ρ al V where: cal is the specific heat of aluminium alloys (J/kg ºC) ρal is the unit mass of aluminium (kg/m³) Am V is the section factor for unprotected aluminium alloy members (m-1) Am is the exposed surface area of the member per unit length (m²/m) V is the volume of the member per unit length (m³/m) & hnet ,d is the design value of the net heat flux per unit area (W/m2) ∆t is the time interval (seconds) & Calculation of hnet ,d is described in ENV 1991 Part 2 - 2 |16|: & & & hnet ,d = γ n ,c ⋅ hnet ,c + γ n ,r ⋅ hnet ,r γ n ,c = γ n ,r = 1,0 for most cases. TALAT 2503 10
  • 11. The previous equation will than be: & ( ) [ hnet ,d = α c ⋅ θ g − θ m + Φ ⋅ ε res ⋅ 5,67 ⋅ 10 −8 ⋅ (θ r + 273) + (θ m + 273) 4 4 ] where: α c coefficient of heat transfer by convection (W/m2°K) θg gas temperature of the environment of the member in fire exposure (°C) θm surface temperature of member (°C) Φ configuration factor ε res resultant emissivity θr radiation temperature of the environment of the member, may be represented by the gas temperature, θ g , (°C) 5,67 ⋅ 10-8 is Stefan Boltzmann constant in W/m2°K4. The resultant emissivity, εres, is formulated as: ε res = ε f ⋅ ε m where: ε f emissivity related to the fire compartment, usually taken as 0,8 εm emissivity related to surface material; the following values may be used: ε m = 0,3 (leading to ε res = 0,24) for clean uncovered surfaces and ε m = 0,7 (leading to ε res = 0,56) for painted and covered surfaces, In the performance of the calculation the following must be taken into consideration: The value of ∆t should not be taken as more than 5 seconds. The value of the shape factor Am V should not be taken as less than 10 m-1. When calculating the exposed surface area of the member, Am , grooves with gap in the surface less than 20 mm should not be included in the exposed surface area (see Figure 2503.02.01). Some design values of the section factor Am V for unprotected aluminium alloy members are given in Figure 2503.02.02,. Figure 2503.02.03 and Figure 2503.02.04. TALAT 2503 11
  • 12. <20mm >2 m 0 m Grooves with gap in the surface < 20 mm, area of groove not to be included in the area of the exposed surface. Grooves with gap in the surface > 20 mm, area of the groove to be included in the area of alu Calculation of the exposed surface in case of grooves 2503.02.01 Training in Aluminium Application Technologies Open section exposed to fire on all sides: Tube exposed to fire on all sides: Am perimeter = Am 1 V cross - section area = V t t Open section exposed to fire on three sides: Hollow section (or welded box section of uniform thickness) exposed to fire on all Am surface exposed to fire sides: = V cross - section area If t << b: Am/V = 1/t t Section factor Am/V for unprotected structural aluminium alu Training in Aluminium Application Technologies alloy members when using the lumped mass method (I) 2503.02.02 TALAT 2503 12
  • 13. I section flange exposed to fire on three sides: Box section exposed to fire on all sides: Am/V = (b + 2tf)/(b tf) If t<<b: Am/V = 1/tf Am 2(b + h) h = V cross - section area b t b Angle (or any open section of uniform I section with box thick-ness) exposed to fire on all sides: reinforcement, exposed to fire on all sides: Am/V = 2/ t h Am 2(b + h) = b V cross - section area t Section factor Am/V for unprotected structural aluminium alu Training in Aluminium Application Technologies alloy members when using the lumped mass method (II) 2503.02.03 Flat bar exposed to fire on all sides: Flat bar exposed to fire on three sides: Am/V = 2(b + t)/(b t) Am/V = (b +2 t)/(b t) If t << b: Am/V = 2/ t If t << b: Am/V = 1/ t t b t b Section factor Am/V for unprotected structural aluminium alu Training in Aluminium Application Technologies alloy members when using the lumped mass method (III) 2503.02.04 TALAT 2503 13
  • 14. 2503.02.07 Temperature analysis for protected aluminium structures For insulated aluminium structures with an uniform temperature distribution in a cross- section, the temperature increase ∆θ al ( t ) during a time interval ∆t , should be determined from: λ p d p Ap  1  (θ t − θ al )∆t − (e − 1)∆θ ( t ) φ 10 ∆θ al ( t ) = ⋅  cal ⋅ ρal V 1 + φ 3  but ∆θ al ( t ) ≥ 0 in which: c pρ p Ap φ= dp calρal V where: Ap V is the section factor for aluminium alloy members insulated by fire protection material (m-1) Ap is the area of the inner surface of the fire protection material, per unit length of the member (m²/m) V is the volume of the member per unit length (m³/m) cal is the specific heat of aluminium alloys, (J/kg ºC) cp is the specific heat of the fire protection material, (J/kg ºC) d p is the thickness of the fire protection material (m) ∆t is the time interval (seconds) θ ( t ) is the ambient gas temperature at time t (ºC) θ al ( t ) is the aluminium temperature at time t (ºC) ∆θ ( t ) is the increase of the ambient temperature during the time interval ∆t (ºC) λp is the thermal conductivity of the fire protection material, (W/m ºC) ρal is the unit mass of aluminium alloys (kg/m³) ρp is the unit mass of the fire protection material, (kg/m³) In the performance of the calculation the following must be taken into consideration: The value of ∆t should not be taken as more than 30 seconds. Some design values of the section factor Ap V for insulated aluminium alloy members are given in Figure 2503.02.05 and Figure 2503.02.06. For moist fire protection materials the calculation of the aluminium alloy temperature increase ∆θ al ( t ) may be modified to allow for a time delay in the rise of the aluminium alloy temperature when it reaches 100 ºC. This delay time should be determined by a method conforming with a prENV, ENV, prEN or EN. TALAT 2503 14
  • 15. Sketch Description Section factor Ap/V Contour encasement aluminium perimeter of uniform thickness. aluminium cross - section area Hollow encasement 2 (b + h) of uniform thickness. h aluminium cross - section area b Section factor Ap/V for structural aluminium alloy members insulated alu Training in Aluminium Application Technologies by fire protetion materials when using the lumped mass method (I) 2503.02.05 Sketch Description Section factor Ap/V Contour encasement of uniform thickness, aluminium perimeter - b exposed to fire on three aluminium cross - section area sides. b Hollow encasement of uniform thickness, 2h + b h exposed to fire on three aluminium cross - section area sides. b Section factor Ap/V for structural aluminium alloy members insulated alu Training in Aluminium Application Technologies by fire protetion materials when using the lumped mass method (II) 2503.02.06 TALAT 2503 15
  • 16. 2503.02.08 Internal aluminium structures in a void which is protected by heat screens. The provisions given below apply to both of the following cases: ∗ aluminium members in a void which is bordered by a floor on top and by a horizontal heat screen below ∗ aluminium members in a void which is bordered by vertical heat screens onboth sides. The properties and performance of the heat screens shall be determined using a test procedure conforming with a prENV, ENV, prEN or EN. The temperature development in the void in which the aluminium members are situated shall be determined from a standard fire test or calculated using an approved method. For internal aluminium structures protected by heat screens, the calculation of the aluminium temperature increase ∆θ al should be based on the methods given in this section, taking the ambient gas temperature θ t as equal to the gas temperature in the void. Values of the heat transfer coefficients α c and α r determined from tests conforming with a prENV, ENV, prEN or EN may be used in the calculation of ∆θ al as an alternative to the values given in Eurocode 1: Part 2.2. External aluminium structures. The temperature in external aluminium structures shall be determined taking into account: ∗ the radiative heat flux from the fire compartment ∗ the radiative heat flux and the convection heat flux from flames emanating from openings ∗ the radiative and convective heat loss from the aluminium structure to the ambient atmosphere ∗ the sizes and locations of the structural members. Heat screens may be provided on one, two or three sides of an external aluminium alloy member in order to protect it from radiative heat transfer. TALAT 2503 16
  • 17. Heat screens should be either: ∗ directly attached to that side of the aluminium member which is intended to protect, or ∗ large enough to fully screen this side from the expected radiative heat flux. Heat screens should have an integrity which corresponds to the fire resistance required for the aluminium member. When deciding the temperature in external aluminium structures protected by heat screens, it should be assumed that there is no radiative heat transfer to those sides which are protected by heat screens. Calculations may be based on steady state conditions resulting from a stationary heat balance using the methods given in ENV 1999 Part 1-2 Annex B. Design using ENV 1999 Part 1-2 Annex B should be based on the model given in Eurocode 1: Part 2.2 describing the compartment fire conditions and the flames emanating from openings, on which the calculation of the radiative and convective heat fluxes should be based. 2503.03 Simplified Calculation Methods • Uninsulated aluminium alloy structures • Insulated aluminium alloy structures The temperature analysis according to the ENV 1999-1-2 may be difficult due to lack of information about the insulation material and/or time consuming. A simplified method is developed for calculating the metal temperature of aluminium alloy structures exposed to a standard fire. This method is described in this section and calculation examples are shown in TALAT Lecture 2504. The graphs giving the metal temperature of the structure (Figure 2503.03.03 and Figure 2503.03.04, Figures 2503.03.09 till Figure 2503.03.14) are designed in such a way that they always will give a metal temperature higher than the value obtained by an exact computerized calculation. Using these simplified methods the results will always be conservative. The section factor has different notations in the litterature. In this course the two most used notations are used: F/V = Am/V = exposed surface area of member divided by the volume of the member, both per unit length. Fi/V = Ap/V = inner surface area of the insulation material divided by the volume of the member, both per unit length. TALAT 2503 17
  • 18. 2503.03.01 Uninsulated Aluminium Alloy Structures. Uninsulated aluminium alloy structures exposed to the standard fire (ISO 834) may be calculated according to this method. F/V is to be determined according to the cross section of the member and the exposed surfaces (Figure 2503.03.01 and Figure 2503.03.02). It describes the ratio of the exposed surface area of the member and its volume per unit length. F/V F = exposed surface area of the member per Free- 2h + 4b - 2d unit length (m2/m) t d h standing section area columns: b V = volume of the exposed part of the member per t h 2h + 2b unit length (m3/m) section area b Columns outside windows opening: 2h + b section area Windows opening 1 Beam inside t floor: 2h + 3b -2d section area Beam below floor: 2h + b section area alu Determination of F/ V for Columns and Beams 2503.03.01 Training in Aluminium Application Technologies F/ V Truss below floor: Separate calculation for each part of the truss: b2 + 2h2 Upper chord: h1 upper chord section area b2 Bracing: 4 d d 2b1 + 2h1 h2 Bottom chord: bottom chord section area b1 F = exposed surface area of the member per unit length (m2/m) V = volume of the exposed part of the member per unit length (m3/m) alu Determination of F/ V for Trusses 2503.03.02 Training in Aluminium Application Technologies TALAT 2503 18
  • 19. The surface of aluminium alloys has a very low emissivity. The major part of the heat radiation energy is reflected from an aluminium surface. Painted metal or a surface coated with other materials has, however, a much higher emissivity. As a rule of thumb, the following resultant emissivities can be used: εr = 0,2 for external structures exposed by heat radiation through openings in partitions and for structures not getting any soot layer on the surface during the thermal exposure. εr = 0,7 for all other cases. Knowing the resultant emissivity, the F/V and the exposure time for the standard fire, the metal temperature can be found using Figure 2503.03.03 for εr = 0,2 and Figure 2503.03.04 for εr = 0,7. When the metal temperature is known, the rules of ENV 1999-1-2 for the resistance can be used to determine the loadbearing capacity. These rules are given in section 2503.02.(see also Figure 2503.03.05 for the procedure in the case of uninsulated aluminium alloy structures). Metal Temperature - Time Curves for ε r = 0.2 ( ε r= emissivity) 600 Metal temperature in degree Celsius 500 200 125 400 300 150 100 300 75 50 37 200 25 100 0 0 5 10 15 20 25 30 Time in minutes alu Metal Temperature - Time Curves for εr = 0,2 2503.03.03 Training in Aluminium Application Technologies TALAT 2503 19
  • 20. Metal Temperature - Time Curves for ε r = 0.7 ( εr = emissivity) 600 Metal temperature in degree Celsius 300 100 500 150 200 75 400 125 50 300 37 25 200 100 0 0 5 10 15 20 25 30 Time in minutes alu Metal Temperature - Time Curves for εr = 0,7 2503.03.04 Training in Aluminium Application Technologies Required Fire Building Regulations, Codes, Standards Resistance F/V Structural Member: Determine surface area (F) and volume (V) of the member exposed to fire (m³/m) Metal temperature in member Resultant depending on emissivity of Emissivity: emissivity εR 0.2 (s. Fig. 2503.01.04) or of εR = 0.2 (for external structures with 0.7 (s. Fig. 2503.01.05) openings in partitions and for structures without any sootlayer during fire εR = 0.7 used for all other cases Reduced strength of Strength: aluminium alloy Fig. 2502.01.04 : modulus of elasticity Fig. 2502.01.05: yield strength Structural analysis with the reduced modulus of elasticity and strength. not OK The Member has to be fire insulated load factors and material factors as or protected in an approved way. for accidental load condition. OK alu Flow Chart for Design Training in Aluminium Application Technologies of Uninsulated Aluminium Structures 2503.03.05 2503.03.02 Insulated Aluminium Structures Aluminium alloy structures insulated with rockwool, ceramic fibres, calcium silicate boards, vermiculite boards or gypsum boards and exposed to a standard fire (ISO 834) may be calculated according to this method. Fi/V is to be determined according to the section of the member, the location of the insulation and the exposed surfaces, see Figure 2503.03.06 and Figure 2503.03.07. TALAT 2503 20
  • 21. d Fi = area of inner surface of the Fi/ V exposed insulation material per unit length of the t 2h + 4b - 2d aluminium alloy member h section area (m2/m) V= volume of the exposed part Freestanding b of the insulated member columns: per unit length (m3/m) 2h + 2b section area Column against fire 2h + b rated wall: section area Column built 1 inside fire t rated wall: alu Determination of F/ V for Insulated Columns 2503.03.06 Training in Aluminium Application Technologies Fi = area of inner Fi/ V surface of the Beam inside exposed insulation floor: 1 material per unit t length of the aluminium alloy member (m2/m) Beam below V= volume of the floor: 2h + b exposed part section area of the insulated member per unit length (m3/m) Separate calculation for each part of the truss: Truss below Upper chord: floor: b2 + 2h2 h2 upper chord sec. area b2 Bottom chord: d 2b1 + 2h1 h1 bottom chord sec. area Bracing: 4 b1 d alu Determination of F/ V for Insulated Beams and Trusses 2503.03.07 Training in Aluminium Application Technologies The type of insulation material and its thickness has to be chosen, the equivalent insulation thickness to be calculated by t equ = C · t where C = insulation correction factor t = insulation thickness The insulation correction factor to be taken from Figure 2503.03.08. TALAT 2503 21
  • 22. Insulation Material Density kg/ m3 Ins. Corr. Factor Rockwool Mats 30 - 40 0,45 Rockwool Mats 100 - 120 1,00 Rockwool Mats and Boards 150 - 170 1,15 Rockwool Boards 280 - 320 1,50 Ceramic Fibres Mats 120 - 150 1,30 Ceramic Fibres Boards 240 - 300 1,40 Calcium Silicate Boards 400 - 900 1/625 Fi / V +0,8 Vermiculite Boards 400 - 900 1/625 Fi / V + 0,8 Gypsium Boards 700 - 1000 1/160 Fi / V + 0,5 alu Insulation Correction Factor 2503.03.08 Training in Aluminium Application Technologies Knowing the equivalent insulation thickness, the Fi/V and the exposure time for the standard fire, the metal temperature of the aluminium alloy structure can be found from: Figure 2503.03.09 for 10 min. fire resistance Figure 2503.03.10 for 15 min. fire resistance Figure 2503.03.11 for 30 min. fire resistance Figure 2503.03.12 for 60 min. fire resistance Figure 2503.03.13 for 90 min. fire resistance The metal temperature is used to find the modulus of elasticity and the 0,2% proof stress ratio. These values are used for checking the loadbearing capacity according to the ENV 1999-1-2. Equivalent Insulation Thickness Versus Metal Temperature for 10 Min Fire Resistance 600 Metal temperature in degree Celsius 550 500 450 400 350 300 300 250 200 100 200 150 150 50 125 100 75 37 50 25 0 0 5 10 15 20 25 30 35 40 Equivalent insulation thickness in mm Equivalent Insulation Thickness Versus Metal alu 2503.03.09 Training in Aluminium Application Technologies Temperature for 10 min Fire Resistance TALAT 2503 22
  • 23. Equivalent Insulation Thickness Versus Metal Temperature for 15 Min Fire Resistance 600 550 Metal temperature in degree Celsius 500 450 400 350 300 300 250 125 200 200 75 150 100 150 37 50 100 50 25 0 0 5 10 15 20 25 30 35 40 45 50 Equivalent insulation thickness in mm Equivalent Insulation Thickness Versus Metal alu Temperature for 15 min Fire Resistance 2503.03.10 Training in Aluminium Application Technologies Equivalent Insulation Thickness Versus Metal Temperature for 30 Min Fire Resistance 600 550 Metal temperature in degree Celsius 500 450 400 300 350 200 300 150 250 75 125 200 100 150 50 100 25 37 50 0 0 10 20 30 40 50 60 70 80 90 100 Equivalent insulation thickness in mm Equivalent Insulation Thickness Versus Metal alu Temperature for 30 Min Fire Resistance 2503.03.11 Training in Aluminium Application Technologies TALAT 2503 23
  • 24. Equivalent Insulation Thickness Versus Metal Temperature for 60 Min Fire Resistance 600 550 Metal temperature in degree Celsius 500 450 300 150 400 350 100 200 300 125 250 75 200 37 50 150 25 100 50 0 0 12,5 25 37,5 50 62,5 75 87,5 100 112,5 125 Equivalent insulation thickness in mm Equivalent Insulation Thickness Versus Metal alu Temperature for 60 Min Fire Resistance 2503.03.12 Training in Aluminium Application Technologies Equivalent Insulation Thickness Versus Metal Temperature for 90 Min Fire Resistance 600 550 Metal temperature in degree Celsius 500 450 300 400 200 350 125 300 150 250 100 75 200 50 150 37 25 100 50 0 25 37,5 50 62,5 75 87,5 100 112,5 125 137,5 150 Equivalent insulation thickness in mm Equivalent Insulation Thickness Versus Metal alu Temperature for 90 Min Fire Resistance 2503.03.13 Training in Aluminium Application Technologies When the thermal load is a hydrocarbon fire according to the time-temperature curve described in Figure 2501.01.05, the same procedure can be used with the following graphs: Figure 2503.03.14 for 60 min. fire resistance (HC-fire) Figure 2503.03.15 for 120 min. fire resistance (HC-fire) (The values on the curves are the Fi /V - ratios) TALAT 2503 24
  • 25. Equivalent Insulation Thickness Versus Metal Temperature for 60 Min HC Fire 600 Metal temperature in degree Celsius 500 400 300 200 300 125 150 75 100 200 37 50 100 25 0 50 70 90 110 130 150 Equivalent insulation thickness in mm Equivalent Insulation Thickness Versus Metal alu Temperature for 60 Min HC Fire 2503.03.14 Training in Aluminium Application Technologies Equivalent Insulation Thickness Versus Metal Temperature for 120 Min Fire Resistance, HC Fire 600 Metal temperature in degree Celsius 500 150 400 125 200 75 300 100 300 50 25 37 200 100 0 50 80 110 140 170 200 Equivalent insulation thickness in mm Equivalent Insulation Thickness Versus alu Metal Temperature for 120 Min Fire Resistance, HC Fire 2503.03.15 Training in Aluminium Application Technologies See also Figure 2503.03.16 for the proceeding in the case of insulated aluminium alloy structures. TALAT 2503 25
  • 26. Metal Temperature in Member Required Fire Building Regulations Graph 3 10min fire resistance Resistance Codes, Standards Graph 4 15min fire resistance Graph 5 30min fire resistance Fi / V Graph 6 60min fire resistance Graph 7 90min fire resistance Graph 8 60min fire resistance, HC - fire Structural Members Graph 9 120min fire resistance, HC - fire F i = area of the inner surface of the insulation material per unit length of the aluminium alloy member (m² / m) V = volume of the aluminium alloy member per unit length (m³ / m) Equivalent insulation Insulation correction Insulation Material thickness (tequ) factor (C) Insulation thickness (t) tequ = C * t Reduced Strength of Fig. 2502.01.04: modulus elasticity aluminium alloy Fig. 2502.01.05: yield strength Structural Analysis with the reduced modulus of elasticity and strength. not OK load factors and material factors as for accidental load condition OK Flow Chart for Design of Insulated alu Aluminium Alloy Structures 2503.03.16 Training in Aluminium Application Technologies 2503.04 Insulation Techniques The insulation techniques for wet insulation is different for each material. For dry insulation, however, the insulation techniques are similar. In any case, the insulation must always be installed on the exposed sides of the aluminium alloy structures, and it must be fastened in such a way that it does not fall off during exposure to fire. For fixing dry insulation material to an aluminium alloy structure, bimetallic fixing pins can be used. These pins, consisting of stainless steel with an aluminium alloy at the fixing end can be pin-welded to the aluminium alloy structure. The insulation is to be hanged up on the pins in such a way that the pins pierce the insulation material, and the insulation is fixed by a lock washer at the end of the pins. At corners and other points where it is difficult to fasten the insulation tight, steel netting, galvanized or stainless steel, may be used (Figure 2503.04.01 and Figure 2503.04.02). TALAT 2503 26
  • 27. ∅3 A Typical Bimetallic Fixing Pin B Aluminium alu Training in Aluminium Application Technologies Typical Bimetallic Fixing Pin 2503.04.02 Many of the dry insulation materials shrink when they are exposed to fire. For this reason the insulation must be laid out in two layers with overlap at the joints (Figure 2503.04.03). TALAT 2503 27
  • 28. Examples for fixing insulation boards are given in Figure 2503.04.04 and Figure 2503.04.05. Typical Fixing Method for Stiff Insulation Boards metal anchor min angle of steel 25 mm min screw 10 mm screw insulation of beam insulation of column. alu Typical Fixing Method for Stiff Insulation Boards 2503.04.04 Training in Aluminium Application Technologies TALAT 2503 28
  • 29. 6 1 5 2 7 3 4 5 6 Typical fixing method for gypsum boards for beams (left) and columns (right) Steel Angles : 1, 2, 3, 5, and 6 Gypsum plates : 4 5 mm air gap : 7 Typical Fixing Method for Gypsum Boards for alu Beams (left) and Columns (right) 2503.04.05 Training in Aluminium Application Technologies 2503.05 References/Literature [1] Drysdale, Dougal: An Introduction to Fire Dynamics. John Wiley & Sons. 1987, ISBN 0-471-90613-1 [2] NFPA/SFPE: Handbook of Fire Protection Engineering. NFPA/SFPE. 1988, ISBN 0-87765-353-4 [3] Sterner, E. / Wickstrøm, U.: TASEF - User Manual. Statens Provningsanstalt. 1990, ISBN 91-7848-210-0 [4] Landrø, Harald: Verification of the fire resistance of construction elements and structures. SINTEF 1983. [5] ISO 834-1975 (E). Fire resistance tests - Elements of building construction. [6] ECCS-TC3: European Recommendations for the Fire Safety of Steel Structures. Elsevier 1983. ISBN 0-444-42120-3 [7] GYPROC: Gyproc Håndbok. 1986. (In Swedish). [8] Holmen, J.P.: Heat Transfer. McGraw-Hill. Publ. Comp. 1990. ISBN 0-07- 909388-4 [9] Aluminium-Zentrale (Ed.): Aluminium Taschenbuch. Aluminium Verlag Düsseldorf, 1983. ISBN 3-87017-169-3 (In German) [10] Carborundum Resistant Materials: Fiberfrax Manual 1987. [11] Elkem Rockwool: Innføring i passive brannsikring. 1991. (In Norwegian). TALAT 2503 29
  • 30. [12] NBR: NS 3478. Design rules for structural member for fire resistance. 1979. (In Norwegian). [13] Hydro Aluminium Structures a.s: Revisjon av NS 3471, Kap. 14.2 Brannteknisk dimensjonering. 1992. (In Norwegian). [14] Andersson, Leif & Jansson, Bengt: En undersøkning av gipsskivans termiske egenskaper - Teori och försök. Lund University 1986 (In Swedish). [15] CEN/TC 250/SC 9: ENV 1999-1-2. Design of aluminium structures. Part 1.2. Structural fire design. 1997. [16] CEN/TC 250/SC 1: ENV 1991-2-2. Basis of design and actions on structures. Part 2.2. Actions on structures exposed to fire. 1995 [17] CEN/TC 250/SC 9: ENV 1999-1-1. Design of aluminium structures. Part 1.1. General rules. 1997 TALAT 2503 30
  • 31. 2503.06 List of Figures Figure No. Figure Title (Overhead) 2503.01.01 Time Dependent Creep 2503.02.01 Calculation of the exposed surface in case of grooves 2503.02.02 Section factor Am/V for unprotected structural aluminium alloy members when using the lamped mass method (I) 2503.02.03 Section factor Am/V for unprotected structural aluminium alloy members when using the lamped mass method (II) 2503.02.04 Section factor Am/V for unprotected structural aluminium alloy members when using the lamped mass method (III) 2503.02.05 Section factor Ap/V for structural aluminium alloy members insulated by fire protection when using the lamped mass method (I) 2503.02.06 Section factor Ap/V for structural aluminium alloy members insulated by fire protection when using the lamped mass method (II) 2503.03.01 Determination of F/V for Columns and Beams 2503.03.02 Determination of F/V for Trusses 2503.03.03 Metal Temperature-Time Curves for εr = 0,2 2503.03.04 Metal Temperature-Time Curves for εr = 0,7 2503.03.05 Flow Chart for Design of Uninsulated Aluminium Alloy Structures 2503.03.06 Determination of F/V for Insulated Columns 2503.03.07 Determination of F/V for Insulated Beams and Trusses 2503.03.08 Insulation Correction Factor 2503.03.09 Equivalent Insulation Thickness Versus Metal Temperature for 10 Min Fire Resistance 2503.03.10 Equivalent Insulation Thickness Versus Metal Temperature for 15 Min Fire Resistance 2503.03.11 Equivalent Insulation Thickness Versus Metal Temperature for 30 Min Fire Resistance 2503.03.12 Equivalent Insulation Thickness Versus Metal Temperature for 60 Min Fire Resistance 2503.03.13 Equivalent Insulation Thickness Versus Metal Temperature for 90 Min Fire Resistance 2503.03.14 Equivalent Insulation Thickness Versus Metal Temperature for 60 Min Resistance to HC Fire 2503.03.15 Equivalent Insulation Thickness Versus Metal Temperature for 120 Min Fire Resistance, HC Fire 2503.03.16 Flow Chart for Design of Insulated Aluminium Alloy Structures 2503.04.01 Fixing Insulation With Bimetallic Fixing Pins 2503.04.02 Typical Bimetallic Fixing Pin 2503.04.03 Avoid Air Gaps due to Shrinkage of Insulation 2503.04.04 Typical Fixing Method for Stiff Insulation Boards 2503.04.05 Typical Fixing Method forGypsum Boards for Beams (left) and Columns (right) TALAT 2503 31