Development of Design Equations for the Component Additive Method for Paroc eXtra

FIRE RESEARCH

Development of Design Equations for the

Component Additive Method for Paroc

eXtra

Katrin Nele Mäger, Alar Just

RISE Report 2017:68

Development of Design Equations for the

Component Additive Method for Paroc

eXtra

Abstract

Development of Design Equations for the Component Additive

Method for Paroc eXtra

This report details the development of effective thermal properties and design equations for Paroc eXtra which can be used for the improved component additive method for fire design of timber structures.

The results are validated with full scale fire tests where such reports are available. Key words: stone wool, fire design, timber structures, component additive method, separating function

RISE Research Institutes of Sweden AB RISE Report 2017:68

ISBN:978-91-88695-37-6 Stockholm 2017

Contents

Abstract ... 1 Contents ... 2 Preface ... 3 Summary ... 4 1 Introduction... 5

2 Improved component additive method ... 6

2.1 Insulation materials ... 7

3 Paroc eXtra ... 8

4 Model scale fire tests ... 9

4.1 Test description ... 9

4.2 Test results ... 12

4.2.1 Test of 45 mm insulation slab (T1) ... 13

4.2.2 Test with 290 mm insulation slab (T2) ... 15

5 Calibration of thermal properties ... 19

5.1 Simulation software ... 19

5.2 Calibration procedure ... 20

5.3 Effective thermal properties for Paroc eXtra ... 20

6 Design equations ... 23

7 Verification by full-scale tests (calculation examples) ...27

7.1 Example 1 ... 27

7.2 Example 2 ... 32

8 Conclusions ... 36

Preface

This report details the steps taken to include Paroc eXtra stone wool in the improved component additive method for calculation of fire separating function of timber structures. The improvement of design methods with new or better materials is always a joint effort between producers and researchers.

The results of this report would not have been possible without good collaboration with Paroc Group OY to whom the authors extend their gratitude.

Summary

This report details the development of effective thermal properties and design equations for Paroc eXtra which can be used for the improved component additive method for the design of fire separating timber structures.

The initial component additive method is described in Annex E of Eurocode 5 part 1-2 [1] and improved upon by Schleifer [2]. The work of Schleifer greatly expanded the usability and scope of the method by adding main material groups and defining a greater array of necessary equations.

The generally accepted procedure for the implementation of new materials to the component additive method [3] is applied in the following report on Paroc eXtra stone wool insulation. The design equations are provided as well.

The design and results of the necessary model-scale fire tests are detailed in this report. The data of these fire tests is the basis for the determination of the effective thermal properties. The development of effective thermal properties is described based on the work of Mäger [4]. A mathematical iteration method is used and the thermal properties are determined essentially by backwards calculation. These properties shall only be used as effective values as opposed to something inherent to the material.

Based on the effective thermal properties, the design equations are derived according to the procedure described by Schleifer [2]. These are validated with full scale fire tests where such reports are available.

1 Introduction

Different requirements may be set for structures in the fire situation, mainly load-bearing capacity and fire separating function. The latter is the ability of the structure to avoid the fire spread from one compartment (one or multiple rooms) to another by remaining intact (no cracks) and limiting the temperature rise on the fire unexposed side.

There are safe and accepted calculation methods for verification of the load-bearing and separating performance of timber (frame) structures which can consist of timber studs or beams, cladding boards and insulation in cavities formed by the studs and claddings. The improved component additive method, described further in the next chapter, is used for the analysis of the fire separating function of timber assemblies. The improved component additive method is based on summarising the contribution of each layer to the separating function of a structure considering different heat transfer paths. This method is applicable to timber assemblies consisting of an unlimited number of layers of gypsum plasterboards, wood panels, mineral wools and their combinations. A large amount of test data was studied by Schleifer [2] in order to develop the equations.

Design methods are being developed to be more versatile, transparent and open to new materials, combinations of materials and solutions. Currently there is strong initiative from producers of building materials to conduct expensive, resource and time intensive full-scale fire tests which give good results for the producers but are limited in application, meaning that the results are valid only for the tested configuration allowing for very minor changes in the layup. The aim for the future is the expansion of design methods which would decrease the need for fire testing. This report is part of this effort by including Paroc eXtra stone wool to the improved component additive method.

2 Improved component additive method

The initial component additive method is described in Annex E of Eurocode 5 part 1-2 [1] and improved upon by Schleifer [2]. The work of Schleifer greatly expanded the method’s usability and scope by adding main material groups and defining more necessary equations.

The total fire resistance of the assembly is the time between the start of the fire exposure and when the temperature on the unexposed side of the structure reaches a temperature rise of 140 K on average over the whole surface or 180 K in a single point. This temperature limitation prevents the ignition of nearby objects. Generally, the starting (ambient) temperature is 20°C, therefore the temperature criteria become 160°C and 200°C, respectively.

As the assembly can be multi-layered, an agreement on the naming of layers has been made. The symbols used for layer names are shown in Figure 1.

Timber frame member

Last layer with insulating function Layers with protective function Layer i=2

Layer i=1 Layer i=n-1

Layer n

Figure 1. Numbering and function of the layers in a timber frame structure

The insulation time tins is calculated according to ( 1 ).

𝑡_ins= ∑ 𝑡_prot,i

i=n−1 i=1

+ 𝑡_ins,n ( 1 )

Where 𝑡_ins is the total fire resistance of the assembly [min];

∑ 𝑡_prot,i

𝑖=𝑛−1 𝑖=1

is the sum of protection times of the layers in the direction of the heat flux [min];

𝑡ins,n is the insulation time of the last layer of the assembly on the

unexposed side [min].

The protection times of layers before the last layer can be calculated taking into account the basic values of the layers, the position coefficients and joint coefficients by equation ( 2 ).

𝑡_prot,i= (𝑡prot,0,i∙ 𝑘pos,exp,i∙ 𝑘pos,unexp,i+ ∆𝑡i) ∙ 𝑘i,j ( 2 )

Where 𝑡_prot,i is the protection time of the layer [min]; 𝑡prot,0,i is the basic protection time of the layer i [min];

𝑘_pos,exp,i is the position coefficient that takes into account the influence of layers preceding the layer considered;

of layers backing the layer considered;

∆𝑡i is the correction time for layers protected by Type F gypsum

plasterboards or gypsum fibreboards [min]; 𝑘_i,j is the joint coefficient.

Insulation time ( 3 ) of the last layer can be calculated taking into account the basic values of the layers, the position coefficients and joint coefficients.

𝑡ins,n= (𝑡ins,0,n∙ 𝑘pos,exp,n+ ∆𝑡n) ∙ 𝑘j,n ( 3 )

Where 𝑡_ins,n is the insulation time of the last layer of the assembly on the unexposed side [min];

𝑡ins,0,n is the basic insulation time of the last layer n on the unexposed

side [min];

𝑘pos,exp,n is the position coefficient that takes into account the influence

of layers preceding the layer considered;

∆𝑡_n is the correction time for layers protected by Type F gypsum plasterboards or gypsum fibreboards [min];

𝑘_j,n is the joint coefficient.

The coefficients and basic values are dependent on the material of the layer in question and the preceding and backing layers. These values are presented in European technical guideline Fire Safety in Timber Buildings (FSITB) [5] based on the work of Schleifer [2]. The procedure for implementing new materials to the improved component additive method has been published in English and is generally accepted across Europe [3].

2.1 Insulation materials

Currently only general values of the previously mentioned values (basic protection time tprot,0) and coefficients (position coefficients kpos,exp and kpos,unexp and joint coefficient kj)

for mineral wool insulations are detailed in the method. However, using these values for materials which have been designed for better performance means that the benefit of these materials is not taken into account.

Generally, the equations for insulation materials include the thickness and density of the material. Density can be a problematic detail for designers as it is not often specified by the producer. Therefore, assumptions must be made which lessen the accuracy of the calculations.

The improved component additive method assumes a material will have thermally degraded and will fall off when the temperature behind it reaches 270°C. Therefore, it should be proven that a new material has the ability to withstand such temperatures. Another important factor is whether the insulation is capable of staying in place by itself after the fall-off of previous (possibly cladding) layers.

3 Paroc eXtra

Paroc eXtra is a batt type stone wool insulation for general use applications (walls, attics, floors) in all kinds of buildings. It is non-combustible and does not settle, shrink or lose its insulation properties over time. [6] The characteristic density of Paroc eXtra is 26-40 kg/m3_.

The fixation of insulation is the second most important aspect guaranteeing the fire protection ability of the insulation (after the non-combustibility). Depending on the orientation of the structure and the thickness of the insulation batts used, the sufficient fixation of the insulation may be solved differently. If thick batts (more than 10omm) are used in wall cavities between timber studs, oversizing by 5 mm is sufficient (e. g. the width of the cavity is 555 mm, a 560 mm wide batt is installed slightly compressed). For floor applications, the insulation should be additionally fixed – overdimensioning is not enough to guarantee that the insulation stays in place after the fall-off of previous layers. Depending on the structure, the insulation may be held in place by a steel net underneath, timber battens cross-wise to the load-bearing timber members, screwed to the timber elements with long angled screws, glued to the substrate on the fire unexposed side, etc.

The fixation of the insulation should be designed considering the use scenario.

The fall-off of insulation is dependent on the fixation and the thermal degradation f the insulation material nad should be tested separately if necessary.

4 Model scale fire tests

To form the basis for the calibration of thermal properties two non-loaded model scale furnace tests were conducted in Paroc Group Oy Materials Research and Innovation laboratory on 12th _{and 14}th _{of September 2017. Tests were witnessed by Alar Just (RISE)}

and Katrin Nele Mäger (Tignum OÜ).

4.1 Test description

Two tests were conducted as listed in Table 1. In each specimen, four samples of the same product (Paroc eXtra) were tested, three of which (marked with B, C and D) were equipped with thermocouples. A detailed drawing of the test specimen is provided in Figure 2.

The tests were conducted in a furnace with a volume of ca 2 m3_{. It is fitted with 1 burner}

that uses oil as fuel. The temperature in the compartment for all tests followed the EN 1363-1 standard fire curve [7]. The temperature was controlled manually by changing the intensity of the burner.

The tests were both conducted with a horizontal structure. The specimens were built by Paroc Group Oy. The specimens were conditioned at room temperature (20°C and 65% RH) before the fire tests. In one of the tests the insulation thickness was 45 mm and in the other one 290 mm (composed of two batts, one 250 mm thick and another 45 mm thick, slightly compressed).

The test specimens were built similarly to the configuration proposed by Schleifer [2]. On the unexposed side a layer of plywood (thickness 20 mm, density 630 kg/m3_{) was}

used. Instead of timber members, very rigid stone wool served as a quasi-load-bearing element.

Test specimens were made without any protective cladding on the fire exposed side. The insulation material was fixed on the substrate using a clamping system normally designated for fastening the insulation in External Thermal Insulation Composite Sysem (ETICS) facades.

The test specimens were equipped with type K thermocouples placed at different characteristic locations behind the tested insulation material (Figure 3) and on the unexposed side of the specimen (Figure 4). Throughout the test the temperatures were recorded at regular intervals. Two loggers were used, one recorded the temperatures 10x/min, the other one 5x/min.

Table 1 Tests

Name Thickness of the _{tested insulation [mm]} Density of the tested insulation [kg/m

3

]

A B C D

T1 45 37,0 37,0 32,8 37,5

T2 290 (250+40) 30,0 30,5 29,9 30,6

See Figure 2 to Figure 5 for drawings and pictures showing the configuration of the test specimen.

Figure 3. Thermocouples placed on the interface of insulation and plywood

Figure 5. Specimen placed on top of furnace. Picture from the fire exposed side of the 45-mm insulation.

4.2 Test results

The specimen T1 was tested for 34 minutes in the standard fire. Furnace temperature during the fire test is presented in Figure 6. Furnace pressure was not recorded in any of the tests.

Figure 6. Furnace temperature in test T1

0 100 200 300 400 500 600 700 800 900 1000 0 5 10 15 20 25 30 35 T em p er atu re [° C] Time [min]

during the fire test is presented in Figure 7.

Figure 7. Furnace temperature in test T2

4.2.1 Test of 45 mm insulation slab (T1)

Thermocouple measurements during the test with 45 mm insulation slab are presented graphically in Figure 8 and Figure 9.

Figure 8. Thermocouple measurements.

0 200 400 600 800 1000 1200 0 20 40 60 80 100 120 140 T em p er atu re [° c] Time [min]

F1 F2 F3 Furnace avg EN 1363-1 curve

0 50 100 150 200 250 300 350 400 450 500 0 5 10 15 20 25 30 35 T em p er atu re ris e [° C] Time [min] B1 B2 B3 B4 B5 C1 C2 C3 C4 C5 D1 D2 D3 D4 D5 B6 C6 D6

Figure 9. Average thermocouple measurements.

The tested insulation material remained intact during the full duration of the test. No fall-off of material pieces or layers occurred. No sintering was observed.

Figure 10. Specimen after extinguishment.

0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 30 35 A v er ag e tem p er atu re ris e [° C] Time [min] Bavg Cavg Davg

4.2.2 Test with 290 mm insulation slab (T2)

Thermocouple measurements during the test with 290 mm insulation slab are presented graphically in Figure 11 and Figure 12.

Figure 11. Thermocouple measurements.

Figure 12. Average thermocouple measurements.

The tested material performed well as an insulation against the temperature rise behind it. No sintering nor fall-off of insulation material occurred.

0 50 100 150 200 250 300 0 20 40 60 80 100 120 140 T em p er atu re ris e [° C] Time [min] B1 B2 B3 B4 B5 C1 C2 C3 C4 C5 D1 D2 D3 D4 D5 B6 C6 D6 0 50 100 150 200 250 0 20 40 60 80 100 120 140 T em p er atu re ris e [° C] Time [min] Bavg Cavg Davg

Figure 13. Specimen directly after removal from the furnace

Figure 15. Specimen after the test. Locations of materials A...D shown.

Figure 16. Specimen after the test. No sintering occurred (some material was removed for inspection).

A

C

B

5 Calibration of thermal properties

5.1 Simulation software

The software used for thermal simulations was SAFIR v2014a1. It is a commercial software developed in the University of Liège [8]. The program can be used to model the behaviour of building structures subjected to fire and to perform a mechanical analysis afterwards. It uses the finite element method (FEM) [9].

SAFIR calculates the field of temperatures that develops during a specified length of time of exposure to a particular fire scenario. Fires can be represented in different manners (time-temperature curves, imposed heat flux or local models) [10]. The structures can be analysed in 2D and also 3D. A two-dimensional specimen with 1D heat transfer path has been used in this case.

The main concept for calculation in SAFIR is that heat is distributed in the structure by conduction since most construction elements are made of solid materials. This means that for some materials the calculation is an approximation. Such materials are, for example, fibrous insulation materials and wood. SAFIR does not take into account the migration of free water and its re-condensation nor heat transfer within the material via radiation between the fibres and air or by air convection. Such limitations mean that the thermal properties used in the conduction model have to be tuned.

On the surfaces heat is exchanged with the environment via convection and radiation. These phenomena are taken into account by specifying the appropriate coefficients. The coefficient of convection on the heated surface is αc,exp = 25 W/(m2∙K) and on the

unheated surface – αc,unexp = 4 W/(m2∙K) as suggested in Eurocode 1 [11]. The formulas

describing heat transfer at the surface and in internal cavities are presented in the technical documentation of SAFIR [10].

Calculation within solid materials is based on the Fourier equation representation in Cartesian coordinate system, see ( 4 )).

𝜕 𝜕𝑥(𝑘 𝜕𝑇 𝜕𝑥) + 𝜕 𝜕𝑦(𝑘 𝜕𝑇 𝜕𝑦) + 𝜕 𝜕𝑧(𝑘 𝜕𝑇 𝜕𝑧) + 𝑄 = 𝑐𝜌 𝜕𝑇 𝜕𝑡 ( 4 )

Where {𝑥, 𝑦, 𝑧} is the vector of Cartesian coordinates [m]; 𝑇 is the temperature [K];

𝑘 is the thermal conductivity [W/(m∙K)];

𝑄 is a term that accounts for internal generation of heat [W/m3]; 𝜌 is the density [kg/m3];

𝑐 is the specific heat [J/(kg∙K)]; 𝑡 is time [s].

Formula ( 4 ) can be simplified further to express one-dimensional conduction without internal heat generation. This is presented in equation ( 5 ).

𝑘

𝜕2_𝑥= 𝑐𝜌_𝜕𝑡 ⇒ _𝜕𝑡 =_𝑐𝜌∙_𝜕2_𝑥

From equation ( 5 ) it can be seen that thermal conductivity is divided by the product of specific heat and density. This means that theoretically only one of these values needs to be calibrated to fit test data if there is sufficient certainty in the values of the other. Generally, it is simpler to determine the mass loss and therefore the decrease in density. In the following, thermal conductivity and specific heat have been calibrated and density values acquired from FSITB [5].

5.2 Calibration procedure

The effective thermal properties are needed to develop the design equations. The calibration was conducted by simulating known configurations (tested configurations) with SAFIR and comparing the simulation and test results.

For the purpose of determining the effective properties, a MATLAB code was used. The working principle is rather simple – it changes some values of the thermal properties in the input file of the simulation software and compares the results with fire test data in the same point. This process is repeated until an acceptable correlation with test results is obtained. During the process the graphs are shifted iteratively closer.

Temperature measurements from Figure 9 and Figure 12 were used as the basis for calibration.

5.3 Effective thermal properties for Paroc

eXtra

In the following the graphs of effective thermal properties obtained from calibration to fit the unprotected tests are presented.

Figure 18 presents a comparison of the effective thermal conductivity curve of Paroc eXtra and the generic curve presented in FSITB [5].

Figure 18. Effective thermal conductivity curve used for simulations

0 0,5 1 1,5 2 2,5 0 200 400 600 800 1000 1200 T h er m al co n d u ctiv ity [ W /( m ·K) ] Temperature [°C] Paroc eXtra Generic (FSITB)

simulated material. In comparison with the generic values from FSITB, Paroc eXtra has a slightly lower effective thermal conductivity.

Figure 19 shows the comparison of the specific heat curves obtained from calibration of Paroc eXtra and generic values from FSITB [5].

Figure 19. Effective specific heat curve used for simulations

Higher specific heat values in combination with lower thermal conductivity result in slower heat transfer and, therefore, slower temperature rise on the unexposed surface of the investigated material.

Figure 20 shows the generic density change curve from FSITB [5].

Figure 20. Effective density

Density was not calibrated as it has a comparatively smaller effect on the overall results of simulations and can be determined by testing relatively accurately.

These curves presented in Figure 18-Figure 20 yielded the best agreement between the simulations and experimental results in the simulated configurations. It must be

0 1 2 3 4 5 6 7 0 200 400 600 800 1000 1200 Sp ec if ic h ea t [k J/( k g ·K) ] Temperature [°C] Paroc eXtra Generic (FSITB) 0,88 0,9 0,92 0,94 0,96 0,98 1 0 200 400 600 800 1000 1200 Den sity [ ρ/ ρ20 ] Temperature [°C]

changes in the material. Therefore, even if there is no particular chemical reaction happening in the material at that temperature, there might be cracks forming, which increase the effective thermal conductivity.

6 Design equations

The procedure for developing the design equations is based on the work of Schleifer [2] and it is applied to Paroc eXtra.

As shown in chapter 2 there are multiple components to be specified for a material to be added to the improved component additive method. For insulation materials, these are basic protection time and position coefficients. All these values are based on specific simulations conducted with the effective thermal properties obtained in previous chapters. In all simulation configurations different thicknesses were used for the investigated material (45, 95, 145, 195 and 290 mm). This is necessary to provide correlations based on material thickness.

The basic protection time is the time until the temperature rise behind the layer in question is 250 K on average and 270 K in a single point. This work focuses on the average temperature rise to 270°C (initial temperature of 20°C with the temperature rise of 250°C added).

The simulation configuration for obtaining the basic protection time is presented in Figure 21. hi 19 ,0 _WFB INV T=270°C

Basic protection time tprot

Figure 21. FE simulations for Basic protection time (INV – investigated material, WFB - wood fibreboard)

The results obtained from simulations with different thicknesses of the investigated material are plotted against material thickness in Figure 22.

Figure 22. Comparison of FE simulation results and values from proposed formula

0 20 40 60 80 100 120 140 160 40 90 140 190 240 290 B asic p ro tectio n tim e tprot ,0,i [ m in ] Thickness h_i [mm] eXtra (FE simulations) eXtra (equation)

Generic stone wool (FSITB)

EN 1995-1-2 Annex E

presented depending on the thickness of the material hi. Similarly, basic protection

time tprot,0,i of Paroc eXtra, obtained according to FE simulations of the configuration

presented in Figure 21 is:

𝑡prot,0,i= 0,45 ∙ ℎi− 1,35 [min] ( 6 )

For the development of position coefficients, a more elaborate system of FE simulations and configurations was needed.

The position coefficient kpos,exp takes into account the effect the preceding layer (in the

direction of heat flow) has on the layer in question. For insulation materials the preceding layer could be either a cladding or some (other) type of insulation. This is simplified to some extent in the simulations which are narrowed down to two configurations presented in Figure 23.

hi

19

,0 _WFB

INV T=270°C

Position coefficient k

pos,exp,i

10

..

.50 MTB/SW

T=270°C

Figure 23. FE simulations for position coefficient kpos,exp,i (INV – investigated material, WFB –

wood fibreboard, MTB – massive timber board, SW – stone wool)

The position coefficient kpos,exp,i was developed from the configuration in Figure 23.

Initially, the setup shown was simulated until the temperature between the preceding layer (massive timber panel or stone wool) and the investigated material reached 270°C and the time was recorded as t1. After that, the preceding layer was removed and the

simulation continued. When the temperature behind the investigated material reached 270°C the simulation was stopped, and the time recorded as t2.

𝑘_pos,exp,i= 𝑡prot,i

𝑡prot,0,i ( 7 )

Where 𝑡𝑝𝑟𝑜𝑡,𝑖 is the protection time of the layer i, calculated as 𝑡2− 𝑡1 [min];

𝑡_{𝑝𝑟𝑜𝑡,0,𝑖} is the basic protection time of layer i [min].

The setup from Figure 23 was simulated with all the different thicknesses of the preceding layer for all the investigated thicknesses of Paroc eXtra (denoted on the drawing as INV). After these simulations graphs were compiled of the position coefficients versus the protection times of preceding layers which are shown in Figure 24 and Figure 25.

Figure 24. Simulation results with different thicknesses of the investigated material plotted kpos,exp,i vs. tprot,i-1 with stone wool as the preceding layer

Figure 25. Simulation results with different thicknesses of the investigated material plotted kpos,exp,i vs. tprot,i-1 with timber as the preceding layer

The effect of material thickness on the position coefficient is evident. Based on the equations published in FSITB [5], the position coefficients were expressed using the basic protection time and thickness of the investigated layer. The resulting equations for the position coefficient kpos,exp,i are expressed as ( 8 ).

𝑘pos,exp,i= { 1 − 0,55 ∙ 𝑡_prot,0,i−0,9 _{∙ ∑ 𝑡} prot,p 𝑖−1 𝑝=1 , 𝑖𝑓 ∑ 𝑡prot,p 𝑖−1 𝑝=1 <𝑡prot,0,i 4 (0,3 − 0,001 ∙ 𝑡prot,0,i) ∙ ln ( 𝑡prot,0,i ∑𝑖−1𝑝=1𝑡prot,p ) + 0,31 ∙ ℎi0,1 , 𝑖𝑓 ∑ 𝑡prot,p 𝑖−1 𝑝=1 ≥𝑡prot,0,i 4 ( 8 )

In the next step, the position coefficient kpos,unexp,i was developed. This coefficient takes

into account the effect the backing layer has on the layer under investigation. In FSITB [5] the values provided for different materials backed by timber or gypsum are given as 1.0. Based on this, a simulation of the setup presented in Figure 26 is needed.

0,8 0,82 0,84 0,86 0,88 0,9 0,92 0,94 0,96 0,98 0 1 2 3 4 5 P o sitio n co ef ficien t kpos ,exp,i

Protection time of preceding layer t_prot,i-1 [min]

45 95 145 195 290 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 10 20 30 40 50 60 70 80 P o sitio n co ef ficien t kpos ,exp,i

Protection time of preceding layer t_prot,i-1 [min]

45 95 145 195 290

hi INV T=270°C

60 SW

Figure 26. FE simulation for position coefficient kpos,unexp,i (INV – investigated material, SW – stone

wool)

The position coefficient kpos,unexp,i for a layer of Paroc eXtra backed by insulation is

calculated according to the equation ( 9 ) as presented in FSITB [5]:

7 Verification by full-scale tests

(calculation examples)

In this chapter the equations developed in chapter 6 are used to calculate the fire resistance of structures and the result compared with data from two full-scale standard fire tests. For other materials the formulas used are from the European technical guideline Fire Safety in Timber Buildings [5]. If materials used in tests do not have equations in the guideline, calculated results may be substituted with test data.

Two calculation options for both full-scale test configurations are presented:  “Calculation I” using only the analytical equations

 “Calculation II” using the protection times of protective claddings taken from the temperature measurements in the test reports.

The component additive method detailed in the current EN 1995-1-2 Annex E has very limited applications and none of the examples could be calculated using this method which is only able to consider symmetrical structures with the voids filled with one layer of insulation. In Example 1, the void is filled with two layers of insulation and the assumption cannot be made to calculate these two layers as a single thick layer.

7.1 Example 1

The first full-scale test conducted according to EN 1363-1 [7] and EN 1364-1 [12] used for verification was of one partition wall element measuring 3x3 m which included light weight steel studs, boards and Paroc eXtra (named UNS 37 in the report [13]).

The load-bearing elements were 2xC steel studs 66x0,25 mm. The cavities between the studs were completely filled with two layers of 66 mm insulation batts with the measured density of 31,2 kg/m3_{. The partition was symmetrical, on both sides were two}

layers of 12,5 mm type A gypsum plasterboards.

The length of the test was 104 minutes. The maximum temperature rise criterion of 180°C at any point above the initial average temperature was reached at 99 minutes after the start of the test. The ignition of the cotton pad occurred at 104 minutes. Layer 1 – Gypsum plasterboard type A (12,5 mm)

tprot,0,1 = 30∙( h₁ 15) 1,2 =24,1 min k_pos,exp,1=1 k_pos,unexp,1=1 k_j,1=1

tprot,0,2 = 30 ∙( h₂ 15) 1,2 = 24,1 min kpos,exp,2 = 0,5 ∙√ tprot,0,2 ∑ t_prot,i-1 = 0,5 ∙√ 24,1 24,1 = 0,5 k_pos,unexp,2 = 0,5 ∙ h_i0,15=0,5 ∙ 12,50,15 _{= 0,730} kj,2 = 1

t_prot,2 = (t_prot,0,2 ∙ k_pos,exp,2 ∙ k_pos,unexp,2 + ∆t₂) ∙ k_j,2 = (24,1 ∙ 0,5 ∙ 0,730 + 0) ∙ 1 = 8,8 min

Based on the test report, the sum of protection times of the first two layers (for Calculation II) is:

∑ t_prot,2* _{= 52 min}

Layer 3 – Paroc eXtra (66 mm)

tprot,0,3 = 0,45 ∙ h3 - 1,35 = 0,45 ∙ 66 - 1,35 = 28,4 min kpos,exp,3 = (0,3 - 0,001∙ tprot,0,3) ∙ ln ( t_prot,0,3 ∑2p=1tprot,p ) + 0,31∙ h₃0,1 = = (0,3 - 0,001∙28,4) ∙ ln ( 28,4 24,1+8,8) + 0,31∙ 66 0,1_{= 0,431}

Position coefficient for Calculation II: kpos,exp,3* = (0,3 - 0,001∙ tprot,0,3) ∙ ln ( tprot,0,3 ∑2 t_prot,p* p=1 ) + 0,31∙ h30,1 = = (0,3 - 0,001∙28,4) ∙ ln(28,4 52 ) + 0,31∙ 66 0,1_{= 0,307} k_pos,unexp,3 = 0,18 ∙ h₃(0,001 ∙ ρ3+0,08) _{= 0,18 ∙ 66}(0,001∙31,2+0,08)_{= 0,287} k_j,3 = 1

t_prot,3 = (t_prot,0,3 ∙ k_pos,exp,3 ∙ k_pos,unexp,3 + ∆t₃) ∙ k_j,3 = (28,4 ∙ 0,4308 ∙ 0,287 + 0) ∙ 1 = 3,5 min

Layer 4 – Paroc eXtra (66 mm) tprot,0,4 = 0,45 ∙ h4 - 1,35 = 0,45 ∙ 66 - 1,35 = 28,4 min kpos,exp,4 = (0,3 - 0,001∙ tprot,0,4) ∙ ln ( tprot,0,4 ∑3p=1tprot,p ) + 0,31∙ h₄0,1 = = (0,3 - 0,001∙28,4) ∙ ln ( 28,4 24,1+8,8+3,5) + 0,31∙ 66 0,1_{= 0,403}

Position coefficient for Calculation II:

k_pos,exp,4* = (0,3 - 0,001∙ t_prot,0,4) ∙ ln ( tprot,0,4 ∑3 t_prot,p* p=1 ) + 0,31∙ h₄0,1 = = (0,3 - 0,001∙28,4) ∙ ln ( 28,4 52+2,5) + 0,31∙ 66 0,1_{= 0,294} k_pos,unexp,4 = 1 kj,4 = 1

t_prot,4 = (t_prot,0,4 ∙ k_pos,exp,4 ∙ k_pos,unexp,4 + ∆t₄) ∙ k_j,4 = (28,4 ∙ 0,4033 ∙ 1 + 0) ∙ 1 = 11,4 min

Protection time for Calculation II: t_prot,4* _{= (t}

prot,0,4 ∙ kpos,exp,4* ∙ kpos,unexp,4 + ∆t4) ∙ kj,4 = (28,4 ∙ 0,294 ∙ 1 + 0) ∙ 1 = 8,3 min

Layer 5 – Gypsum plasterboard type A (12,5 mm) t_prot,0,5 = 30 ∙(h5 15) 1,2 = 24,1 min k_pos,exp,5 = 0,5 ∙√_∑tprot,0,5 t_prot,p 4 p=1 = 0,5 ∙√ 24,1 24,1+8,8+3,5+11,4 = 0,355

Position coefficient for Calculation II:

kpos,exp,5* = 0,5 ∙√

t_prot,0,5

∑4 t* = 0,5 ∙√

24,1

k_pos,unexp,5 = 1 k_j,5 = 1

tprot,5 = (tprot,0,5 ∙ kpos,exp,5 ∙ kpos,unexp,5 + ∆t5) ∙ kj,5 = (24,1∙ 0,355 ∙ 1 + 0) ∙ 1 = 8,6 min

Protection time for Calculation II: t_prot,5* _{= (t}

prot,0,5 ∙ kpos,exp,5* ∙ kpos,unexp,5 + ∆t5) ∙ kj,5 = (24,1∙ 0,310 ∙ 1 + 0) ∙ 1 = 7,5 min

Layer 6 – Gypsum plasterboard type A (12,5 mm) t_ins,0,6 = 24 ∙ (h6 15) 1,4 = 24 ∙ (12,5 15 ) 1,4 = 18,6 min k_{pos,exp,6 = 0,5 ∙√} tins,0,6 ∑5p=1tprot,p = 0,5 ∙√ 18,6 24,1+8,8+3,5+11,4+8,6= 0,287

Position coefficient for Calculation II:

kpos,exp,6* = 0,5 ∙√ tins,0,6 ∑5p=1tprot,p* = 0,5 ∙√ 18,6 52+2,5+8,3+7,5= 0,257 kj,6 = 1

tins,6 = (tins,0,6 ∙ kpos,exp,6 + ∆t6) = (18,6 ∙ 0,287 + 0) ∙ 1 = 5,3 min

Insulation time for Calculation II:

t_ins,6* = (t_ins,0,6 ∙ kpos,exp,6* + ∆t6) = (18,6 ∙ 0,257 + 0) ∙ 1 = 4,8 min

Total fire resistance of the structure Calculation I: tins =∑ tprot,i i=n-1 i=1 +tins,n = 24,1+8,8+3,5+11,4+8,6+5,3 = 61,7 min Calculation II:

t_ins* =∑ t_prot,i*

i=1

+t_ins,n* = 52+2,5+8,3+7,5+4,8 = 75,1 min

Table 2 and Figure 27 show the layer-by-layer comparison of the two calculation options versus the results measured in the full-scale test. Calculation I uses only calculated values which are very conservative with respect to the gypsum layers. If the protection time of the gypsum layers is taken from the test report (52 min) and used in the calculation (as is shown in Calculation II) the results are more realistic but still conservative enough. The protection time of the investigated material, Paroc eXtra, is close to the tested value in both options (Calculation I and Calculation II).

Table 2 Comparison of results of full-scale fire tests and calculated results Layer

no Material

tins [min]

Calculation I Calculation II Test

1 Gypsum type A 24,1 - - 2 Gypsum type A 32,9 52 52 3 Paroc eXtra 36,4 54,5 - 4 Paroc eXtra 47,8 62,8 65 5 Gypsum type A 56,4 70,3 - 6 Gypsum type A 61,7 75,1 99

NOTE: Calculation I – tprot for gypsum boards calculated; Calculation II – tprot for gypsum boards taken from test

The calculated fire resistance is conservative compared to full-scale fire test results. This proves that the developed formulas provide safe calculation results.

Figure 27. Comparison of calculations and test data

0 20 40 60 80 100 120 1 2 3 4 5 6 Su m o f p ro tectio n tim es, Σ tprot ,i [ m in ] Layer number i

Generic Stone wool (FSITB) Paroc eXtra, Calculation I Paroc eXtra, Calculation II Test

7.2 Example 2

The second full-scale fire test according to EN 1365-1 [14] used for verification was of one load-bearing external wall element measuring 2.9x2.9 m which included timber studs, boards and Paroc eXtra. The fire exposure was from the external side of the assembly. [15]

The load-bearing elements were timber studs 48x148 mm. The cavities between the studs were completely filled with 150 mm insulation batts with the nominal density of 28 kg/m3_{. Stone wool wind shield board (nominal density 110 kg/m}3_{) was mounted on}

the fire exposed side of the studs and insulation. On the unexposed side was one layer of type A gypsum plasterboard with a thickness of 12,5 mm. On the exposed side were vertical distance battens (22x100 mm) and horizontal wooden cladding (23x120 mm, tongue and groove joint).

The length of the test was 120 minutes. During this time, none of the REI criteria were exceeded.

Layer 1 – Timber (23/2 = 11,5 mm – due to the profile of the cladding boards) t_prot,0,1 = 30 ∙(h1 20) 1,1 = 16,3 min k_pos,exp,1=1 k_pos,unexp,1=0,35 ∙ h₁0,21= 0,35 ∙11,50,21 _{= 0,585} k_j,1=0,4

tprot,1 = (tprot,0,1∙ kpos,exp,1∙ kpos,unexp,1+Δt1) ∙ kj,1 = (16,3 ∙ 1 ∙ 0,585 +0) ∙ 0,4 = 3,8 min

Based on the test report, the protection time of the first layer is: tprot,1* = 10 min

Layer 2 – Paroc Cortex, stone wool wind barrier (30 mm)

t_prot,0,2 = 0,3 ∙ h₂(0,75 ∙ log(ρ2) - ρ₂ 400)_{= 0,3 ∙ 30}(0,75 ∙ log(110) - ₄₀₀₎110 = 21,5 min kpos,exp,2 = 1- 0,6 ∙ t_prot,1 t_prot,0,2=1 - 0,6 ∙ 3,8 21,5=0,894

Position coefficient for Calculation II:

kpos,exp,2* = 1- 0,6 ∙

t_prot,1*

tprot,0,2=1 - 0,6 ∙

10

k_pos,unexp,2 = 0,18 ∙ h₂(0,001 ∙ ρ2+0,08) _{= 0,18 ∙ 30}(0,001∙110+0,08)_{= 0,343} k_j,2 = 1

tprot,2 = (tprot,0,2 ∙ kpos,exp,2 ∙ kpos,unexp,2 + ∆t2) ∙ kj,2 = (21,5 ∙ 0,894 ∙ 0,343+ 0) ∙ 1 = 6,6 min

Protection time for Calculation II:

tprot,2* = (tprot,0,2 ∙ kpos,exp,2* ∙ kpos,unexp,2 + ∆t2) ∙ kj,2 = (21,5 ∙ 0,721 ∙ 0,343 + 0) ∙ 1 = 5,3 min

Layer 3 – Paroc eXtra (148 mm)

t_prot,0,3 = 0,45 ∙ h₃ - 1,35 = 0,45 ∙ 148 - 1,35 = 65,3 min k_pos,exp,3 = 1 - 0,55 ∙ t_prot,0,3-0,9 ∙ ∑2 t_prot,p

p=1 = 1- 0,55 ∙ 65,3-0,9 ∙ (3,8+6,6)= 0,867

Position coefficient for Calculation II:

k_pos,exp,3* = 1 - 0,55 ∙ t_prot,0,3-0,9 ∙∑ t_prot,p* 2 p=1

= 1- 0,55 ∙ 65,3-0,9 ∙ (10+5,3)=0,804

k_pos,unexp,3 = 1 kj,3 = 1

t_prot,3 = (t_prot,0,3 ∙ k_pos,exp,3 ∙ k_pos,unexp,3 + ∆t₃) ∙ k_j,3 = (65,3 ∙ 0,867 ∙ 1 + 0) ∙ 1 = 56,6 min

Protection time for Calculation II: t_prot,3* _{= (t}

prot,0,3 ∙ kpos,exp,3* ∙ kpos,unexp,3 + ∆t3) ∙ kj,3 = (28,4 ∙ 0,804 ∙ 1 + 0) ∙ 1 = 52,5 min

Layer 4 – Gypsum plasterboard type A (12,5 mm) t_ins,0,4 = 24 ∙ (h4 15) 1,4 = 24 ∙ (12,5 15 ) 1,4 = 18,6 min kpos,exp,4 = 0,5 ∙√ tins,0,4 ∑3 t_prot,p p=1 = 0,5 ∙√ 18,6 3,8+6,6+56,6= 0,263

kpos,exp,4* = 0,5 ∙√ tins,0,4 ∑3 t_prot,p* p=1 = 0,5 ∙√ 18,6 10+5,3+52,5= 0,262 k_j,4 = 1

tins,4 = (tins,0,4 ∙ kpos,exp,4 + ∆t4) = (18,6 ∙ 0,263 + 0) ∙ 1 = 4,9 min

Insulation time for Calculation II:

t_ins,4* = (t_ins,0,4 ∙ kpos,exp,4* + ∆t4) = (18,6 ∙ 0,262 + 0) ∙ 1 = 4,9 min

Total fire resistance of the structure Calculation I: t_ins =∑ t_prot,i i=n-1 i=1 +t_ins,n = 3,8+6,6+56,6+4,9 = 71,9 min Calculation II: t_ins* =∑ t_prot,i* i=n-1 i=1 +t_ins,n* = 10+5,3+52,5+4,9 = 72,6 min

Table 3 and Figure 28 show the layer-by-layer comparison of the two calculation options versus the results measured in the full-scale test. Calculation I uses only

calculated values which are very conservative with respect to the timber cladding. If the protection time of the timber cladding is taken from the test report (10 min) and used in the calculation (as is shown in Calculation II) the results are more realistic but still conservative.

Table 3 Comparison of results of full-scale fire tests and calculated results Layer

no Material

tins [min]

Calculation I Calculation II Test

1 Timber 3,8 10 10

2 Cortex 10,4 15,3 23

3 Paroc eXtra 67,0 67,8 -

4 Gypsum type A 71,9 72,6 120

The calculated fire resistance is conservative compared to full-scale fire test results. This proves that the developed formulas provide safe calculation results.

Figure 28. Comparison of calculations and test data 0 20 40 60 80 100 120 1 2 3 4 Su m o f p ro tectio n tim es, Σ tprot ,i [ m in ] Layer number i

Generic Stone wool (FSITB) Paroc eXtra, Calculation I Paroc eXtra, Calculation II Test

8 Conclusions

The generally accepted procedure for the development and verification of the design equations [3] is applied to Paroc eXtra in this report. The steps taken have been described.

The design equations developed within this work showed conservative and therefore acceptable results in comparison with full-scale fire test results used for the verification of the equations.

The equations for Paroc eXtra, as shown in this report, are fully compatible with other materials and material groups in the improved component additive method. These equations can be used in calculations with any combination of materials and layers to calculate the fire separating function of timber structures.

References

[1] Eurocode 5: Design of timber structures - Part 1-2: General - Structural fire design,

CEN, 2004.

[2] V. Schleifer, Zum Verhalten von raumabschliessenden mehrschichtigen

Holzbauteilen im Brandfall, Zürich, Switzerland, 2009.

[3] K. N. Mäger, A. Just, J. Schmid, N. Werther, M. Klippel, D. Brandon and A. Frangi,

“Procedure for implementing new materials to the component additive method,”

Fire Safety Journal, 2017.

[4] K. N. Mäger, Implementation of New Materials to the Improved Component

Additive Methof for Fire Design of Timber Structures, Tallinn, Estonia, 2016.

[5] Östman B. et al, Fire safety in timber buildings. Technical guideline for Europe,

Stockholm, Sweden: SP Technical Research Institute of Sweden, 2010.

[6] “PAROC eXtra,” [Online]. Available:

http://www.paroc.com/Products/Building-Insulations/BI-General-Insulations/PAROC-eXtra.

[7] CEN, EN 1363-1: Fire resistance tests, Brussels: CEN, 1999.

[8] “Sciences

Appliquées-

SAFIR,”

[Online].

Available:

http://www.facsa.ulg.ac.be/cms/c_1584029/en/safir. [Accessed 13 April 2016].

[9] J. M. Franssen, User's manual for SAFIR 2013b2, Liège, Belgium: University of Liège

Department ArGEnCO Service Structural Engineering, 2012.

[10] SAFIR Technical documentation, 2011.

[11] Eurocode 1: Actions on structures - Part 1-2: General actions - Actions on

structures exposed to fire, CEN, 2002.

[12] CEN, EN 1364-1: Fire resistance tests for non-loadbearing elements - Part 1: Walls,

Brussels, 2001.

2005.

[14] CEN, EN 1365-1: Fire resistance tests of loadbearing elements - Part 1: Walls,

Brussels, 1999.

[15] VTT Expert Services Ltd, „Test report no. VTT-S-08833-13. Fire resistance test on a

loadbearing external timber wall covered with Paroc Cortex 30 wind shield board

and wooden panels on the exposed side and GN 13 gypsum plasterboards on the

unexposed side,“ Espoo, Finland, 2013.

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Fire Research RISE Report 2017:68 ISBN: 978-91-88695-37-6