EN 338, Structural timber — Strength classes EN 1194, Timber structures — Glued laminated timber — Strength classes and determination of characteristic values EN 1363-1:1999, Fire resi
General
An extended application analysis is required when the application of a beam is not covered by the field of direct application given in the classification document of the product
The fire tests conducted in accordance with EN 1365-3 are designated as the "reference test" and "reference scenario." The outcome of these tests, specifically the fire resistance related to load-bearing capacity, is denoted as "t ref,fi."
When multiple reference tests are available, they can be utilized for the extended application, provided that all tests share identical mechanical boundary conditions and have been conducted under the same fire curve.
In the classification report, it is possible for all reference beams to be assigned the same classification label "R ref," even though the actual test results (t ref,fi) presented in the test reports may vary.
Basic principles
General
It is assumed that extended application is made by appropriately qualified and experienced persons in the field of structural fire design
The reference test(s) shall be well documented, i.e an insight into the performance of the test specimen(s) and the mode of failure, leading to R ref, are available
Three analyses (described in 4.3, 4.4 and 4.5) should be carried out where appropriate It shall be decided whether:
field of application can be extended, maintaining the classification R ref or changing the classification and if so, by how much;
extension is not possible (new tests are required)
Any predicted increase in fire resistance shall not exceed the lesser of 15 min and 20 % of the target classification
NOTE This is illustrated in A.3.
Basis of the extended application
A comprehensive understanding of structural and thermal performance, along with other relevant features, is essential for the required extended application For minor or straightforward extensions to the reference test, the necessary depth of analysis may be lessened.
Mode of failure
Any evaluation must take into account the potential changes in the mode or cause of failure, such as structural collapse due to bending or the malfunction of a fire protection system Additionally, the significance of a failure mode in a fire test may diminish if certain parameters are altered.
If a change of failure mode is expected, then extended application is not possible unless additional information is available
NOTE For additional information see A.1.
Methods of analysis
When analyzing reference tests, applicable rules from the Eurocodes should be followed, along with additional guidelines provided in this standard for cases where the Eurocodes do not fully address the construction being evaluated Other calculation models and empirical rules must be validated through tests similar to the reference tests, and historic data, as well as ad hoc tests, can be utilized to enhance the information derived from the reference tests.
Basic thermal analysis
For applications involving a cross section that differs in size or shape from the reference tests, or for varying resistance times or nominal fire curves, a thermal assessment is necessary This analysis must provide insights into the temperature distribution and variations in material strength across the beam.
Thermal analysis can be conducted using either finite element or finite difference methods In certain cases, when a dimension is altered, a straightforward calculation may demonstrate that the temperature distribution observed in testing can be conservatively applied to the modified cross section.
For timber beams, analyzing the charring depth can often replace a full thermal analysis When a thermal analysis is performed, the char-line is considered to represent the position of the 300 °C isotherm.
Basic structural analysis
General
The structural behavior of the reference tests and the situation under assessment must be analyzed, with the depth of analysis varying based on the beam's complexity and the proposed extended application Any assessment should take into account the same failure modes that are considered in normal temperature design.
Bending (including lateral torsional buckling)
NOTE 1 It is not normally necessary to consider deformations See A.7
The assessment shall also include:
Connections, either mechanical or glued, between parts of the construction
NOTE 2 As an illustration of the depth of structural analysis required, the report on the analysis for the vertical shear check on a steel beam might simply say, “The shear is low enough to have no influence on the bending strength - no check required”.
Modelling factor
When conducting an assessment, it is crucial to consider the accuracy of the structural model employed If the model overestimates the load resistance of the reference tests, a modeling factor must be applied for any extended application assessments.
In making any assessment, the effective structural resistance shall be determined as follows: eff mf
R eff is the effective structural resistance;
R is the calculated structural resistance; k mf is the modelling factor
For a single reference test, the modelling factor is defined as: mf F k = R but not greater than 1,0 (2) where
F is the applied load or moment in the reference test
For more than one reference test: mf i i
1 F k = n ∑ R but not greater than 1,0 (3) where
F i is the applied load or moment in the reference test I;
R i is the calculated structural resistance of test i calculated using the measured temperature distribution; n is the number of tests and with each individual value:
If the value of (F i / R i) exceeds 1,3 then that test should not be used as part of the assessment of extended application
NOTE 1 If the measured temperature distribution is not sufficiently comprehensive to allow the structural resistance to be adequately predicted then it may be supplemented with computed temperatures
NOTE 2 If the value of (F i / R i) exceeds 1,3, there may be something wrong with the test data or with some aspect of the engineering model being used so the particular test may be considered unreliable.
Material properties
The reference test(s) should be assessed using measured material strength If the actual material strength is not available then the strength should be taken from Table 1
When evaluating extended applications, it is essential to assume mean material properties In cases where the actual mean value is not available, refer to Table 1 for the appropriate mean strength values.
NOTE The values in Table 1 are conservative values for the mean strength
Table 1 — Conservative values for mean strength
Concrete compressive strength f ck + 8 N/mm 2 Reinforcement steel to EN 10080 for concrete f sk × 1,1 Prestressing steel to EN 10138-1 for concrete f pk× 1,1 Hot rolled structural steel to EN 10025 parts 1 and
- Structural timber, strength classes C14 to
- glued laminated timber, all strength classes to EN 1194 f k× 1,3
Other materials to be estimated
(a) f i k and f y are the characteristic strength values (5 % fractile).
Analysis of other features
Where relevant phenomena not assessed in 4.3 and 4.4 shall be taken into account
NOTE These may include such things as the stickability of fire protection materials and spalling of concrete
For spalling of concrete, reference should be made to EN 1992-1-2:2004, subclauses 4.5 and 6.2
The adhesion of fire protection materials must be evaluated according to the methods outlined in ENV 13381 or supported by substantial evidence demonstrating the material and fixing system's performance in a minimum of two fire tests.
General
The parameters outlined in sections 5.2 to 5.6 can influence fire performance, particularly the R ref value, and must be considered when preparing an extended application The specific construction parameters differ based on the type of beam under consideration.
NOTE 1 The list in this section is not definitive; in special cases other parameters may also be appropriate
NOTE 2 The review in Annex A of parameters and of corresponding factor and factor influences, is only given for the common thermal, common mechanical and common constructional parameters.
Common thermal parameters
1) Nominal gas temperature time curves
Common mechanical parameters
Common constructional parameters
5) Position and size of holes.
Specific constructional parameters for beams without applied fire protection
Concrete beams
The following specific parameters can be distinguished: a) Concrete specification
NOTE 1 This will normally include:
1) Type of concrete, i.e normal weight or lightweight concrete
2) Type of concrete aggregate, i.e siliceous, calcareous or lightweight
3) Strength of concrete b) Specification of reinforcement
NOTE 2 This will normally include:
1) Type of reinforcement, i.e reinforcing steel, prestressing bars, wires or strands
2) Characteristic strength of the reinforcing or prestressing steel
3) Is the steel hot rolled or cold worked or quenched and tempered?
4) The ductility characteristics of the reinforcing steel c) Degree of any prestressing d) Bond and anchorage properties of the reinforcing or prestressing steel, i.e ribbed or plain surface e) Bonded versus unbonded tendons (post tensioned beams) f) Amount of the main reinforcement and position of the main reinforcement in the cross section g) Concrete cover to reinforcement h) Amount and position of the shear reinforcement i) Minimum dimensions, the level of compressive stresses, moisture content and other parameters possible relevant for spalling j) Other parameters which may effect spalling.
Steel beams
The following specific parameters can be distinguished:
3) Classification of cross section (see EN 1993-1-2)
Composite steel-concrete beams
In addition to the items listed in 5.5.1 and 5.5.2, the following parameters may apply:
NOTE This could include a consideration of whether the slab is flat or composite with profiled steel sheeting
5) Thickness of the concrete slab.
Timber beams
The following parameters apply, where relevant, to timber beams made of solid timber, glued laminated timber and LVL (laminated veneer lumber) or other engineered wood products: a) Timber specification
NOTE This will normally include:
1) Material (timber or wood based materials)
3) Strength class of solid or glued laminated timber (including characteristic values of strength and stiffness parameters and density)
7) Charing rat b) Type of adhesive
The parameters discussed are relevant for beams made of multiple components joined by gluing, including thin-webbed I-beams with solid timber flanges, thin-flanged beams with solid timber webs, and I-beams featuring solid or glued laminated timber flanges and webs Additionally, the materials used for the flanges and webs may also be an important consideration for these types of beams.
Mechanically jointed beams
The parameters outlined in sections 5.5.4.1 and 5.5.4.2 are also applicable to beams with box, I, or T shapes, which consist of multiple components joined by mechanical fasteners These beams may feature flanges and/or webs made from solid or glued laminated timber, wood-based panels, LVL, or other engineered wood products Additionally, other relevant parameters may also be considered.
Specific constructional parameters for beams with applied fire protection
In addition to the parameters given in 5.5, the following parameters may apply:
1) Surface treatment of the beam (i.e grit blasted, primer)
2) Type of protection material (generic or proprietary)
3) Thermal characteristics of the protection (thermal conductivity and specific heat)
6) Number of layers of the applied fire protection
7) Position and geometry of joints in the applied fire protection
8) All details of method of fixing of the fire protection (type of fasteners, spacing and edge distances; including reinforcement where relevant)
9) Surface treatment of the fire protection
10) Position of the fire protection (vertical, horizontal sides; one or more sides may be unprotected)
6 Report of the extended application analysis
The Extended Application report shall be used in conjunction with the classification document as specified in EN 13501-2 and shall contain the following:
2) Name of the expert body which has performed the extended application
3) Date of issue of the report
4) Unique reference number for the report
5) Type of the tested beams This shall include a general description and any trade names of all the products involved
6) Scope of the extended application
7) Summary of the report(s) of the reference test(s) and any previously granted extended applications, if available
This summary is specifically crafted and may differ from the brief summaries typically included in test reports or provided as separate documents It is also permissible to attach complete copies of the relevant reference test reports.
8) Analysis of the extended application, writing including:
Source of any calculation model used
Justification of the use of any calculation model for this particular extended application
List of any assumptions made together with a justification for those assumptions
Supporting information and test references from various fire resistance tests, including those adhering to European Standards, historic tests based on National Standards, and results from ad hoc or small-scale tests, are essential for comprehensive evaluation.
9) Conclusion of the analysis, including the new classification of the fire resistance (R)
Mode of failure
General
When evaluating an extended application, it is crucial to consider any changes in the mode of failure For instance, in a simple beam, the effects of different failure modes, such as bending and shear, are illustrated in Figures A.1 and A.2.
Figure A.1 — Member resistance as a function of time for a single mode of failure
Figure A.2 — Member resistance as a function of time for a changing mode of failure
Other examples of a change in the mode of failure.
Failure of protection system
A beam reached a time of 52 minutes under testing conditions Reducing the applied loading to R60 could be feasible, but significant cracks in the protection system were noted at the test's conclusion, suggesting a potential failure in stickability The stickability of the protection system is crucial, as it influences the beam's heating rate Additionally, any increase in the thickness of fire protection may impact stickability.
Change of structural mode of failure from bending to shear
A fabricated steel beam with a significant service opening was tested, resulting in a load-bearing failure due to mid-span bending Calculations suggest that reducing the web thickness of the beam would minimally impact its bending strength However, a thinner web may compromise shear resistance, potentially leading to shear failure at the opening and increased heat generation.
Change of structure mode of failure from bending to connection failure
The beam test resulted in a time of 79 minutes, suggesting that R90 could be reached with a reduction in applied loading However, the connection between the two parts experienced significant stress and operated at a higher utilization compared to the bending parts It is important to consider the risk of failure occurring before 90 minutes due to the compromised connection, even with decreased loading.
Effect of material strength
Structural designs rely on characteristic material strengths, and fire tests are conducted on test constructions where the material strength of each component typically exceeds the characteristic value In general, increased material strengths contribute to enhanced fire resistance, particularly regarding load-bearing capacity.
When evaluating test results, it's possible to misidentify the reasons behind a specific performance outcome For instance, one might mistakenly believe that a connection is bearing a significant portion of the applied load, while in truth, another component may be responsible for supporting a greater share of the load.
For example, consider a fire test on a reinforced concrete beam which achieves t = 82 min The characteristic and assumed actual material properties are:
The dominant factor in beam strength calculations is often the reinforcement strength, which can lead to misconceptions about the beam's performance in tests The actual bending strength may reach 117% of the strength predicted by characteristic reinforcement values While the average strength loss rate is approximately 1.2% per minute, this loss is not linear during fire resistance tests; in the final 15 minutes, the rate likely increases to around 3% per minute Consequently, the additional 17% of strength could be significant.
6 min A beam with only characteristic material properties might therefore only achieve t = 76 min (= 82 - 6)
To ensure accurate fire resistance assessments, it is essential to measure all material properties as outlined in section 4.4.3 If a test is designated as a reference for extended application, the material properties must be measured; otherwise, mean values should be assumed Future predictions for extended applications should rely on these mean material properties, which are detailed in Table 1 for common structural materials.
Definitive values for mean material strength in structural steel, reinforcement, and concrete cannot be provided, as product standards do not specify these values; thus, the mean strength values in Table 1 are conservative estimates In contrast, product standards for timber do specify mean strength values, which are also included in Table 1 For materials not listed in the table, it is advisable to use a conservative estimate of mean strength.
Extrapolation of fire resistance
In 4.2.1 it is stated that any increase in predicted fire resistance is limited to the minimum of 15 min or
20 % of the target classification fire resistance in any of the reference tests The effect of this is illustrated in Table A.1
Section 4.2.1 outlines the maximum fire resistance extension applicable to extended applications The mode or cause of failure, as detailed in A.1, plays a crucial role in this context This is especially significant when evaluating factors such as timber charring or the adhesion of fire protection materials.
Table A.1 — Maximum increase in fire resistance
Minimum fire resistance required in the longest duration reference test (min)
Accuracy of predictions
The method of conveying the accuracy of predictions significantly influences their numerical values For instance, a 10% error in fire resistance time may not equate to a 10% error in beam strength This is particularly evident with steel, which rapidly loses strength as temperature rises; thus, a mere 5% error in steel temperature can have substantial implications.
600 °C (30 °C) might correspond to a 20 % difference in steel strength However, if the steel reaches
During the test, temperatures reached 600 °C in 60 minutes, with a heating rate of approximately 14 °C per minute towards the end The fire resistance difference observed was around 2 minutes, highlighting the need for caution when comparing test results to predictions It is crucial to focus on any variations in fire resistance, as illustrated in Figure A.3.
Key η Relative resistance t, θ Time or temperature
3 Error in terms of relative resistance
4 Error in terms of time or temperature
Figure A.3 — Illustration of types of error in predictions
Prediction based on material laws
The relationship between load carrying ability and temperature (time) will often be similar to the material law governing the key or critical element This is illustrated in Figure A.4
The material law curve illustrates the strength retention factor in relation to temperature A test point is established by converting the applied load into a fraction of the normal strength at the critical element's temperature, typically positioning this point above the original curve The curve is then adjusted vertically to intersect the test point, allowing for the estimation of the beam's load-carrying capacity in relation to the critical element's temperature, provided that the failure mode remains unchanged.
Key η Relative resistance t, θ Time or temperature
3 Curve drawn by moving the Material Law vertically
Figure A.4 — Illustration of prediction based on material model
Modifying predicted temperatures
Computer modeling of temperature distribution may not always accurately predict the temperatures of critical beam elements, but it can reasonably estimate relative temperature values A practical approach to achieve a reliable temperature distribution for assessment is to adjust the predicted temperatures to align with key measured values This adjusted temperature distribution, as shown in Figure A.5, should consider the impact of errors on structural resistance Notably, the temperature of a reinforcement bar at the bottom of a beam is significantly more critical than that of a concrete element at the top.
Figure A.5 — Illustration of adjusted temperature distribution
Deflection limits
In the EXAP assessment, deformation criteria are typically not assessed separately However, when fire protection enhances the beam's fire resistance, it is essential to ensure that the fire protection maintains its cohesion and coherence under the strain and temperature changes resulting from varying parameters.
The introduction of deformation limits in EN 1365-3 primarily aims to safeguard individuals conducting fire tests from the risks associated with sudden beam collapses into the furnace, while also minimizing potential damage to the furnace itself This approach aligns with the fire-related sections of the Eurocodes, such as Eurocode 3: Design of Steel Structures, Part 1.2, which outlines general rules for structural fire design.
In fire scenarios, it is essential that steel structures are designed and constructed to retain their load-bearing capabilities throughout the duration of the fire exposure.
(2) Deformation criteria shall be applied where the protection aims, or the design criteria for separating elements, require consideration of the deformation of the load bearing structure
(3) Except from (2) consideration of the deformation of the load bearing structure is not necessary in the following cases, as relevant:
- the efficiency of the means of protection has been evaluated according to section 3.4.3; and
- the separating elements have to fulfil requirements according to a nominal fire exposure.
The Extended Application Of Steel Beams
Introduction
This annex illustrates the use of extended applications of the results of two reference tests on fire protected steel beams
The reference tests were conducted following EN 1365-3 standards, resulting in bending failure A lightweight insulation material was utilized, and evidence confirms that the fire protection system meets ENV 13381-4 requirements No steel temperatures were recorded, and aside from the load level, both reference tests are identical.
In both reference tests, mechanical loading remained constant until failure was reached The degree of utilization, denoted as à0, represents the ratio of the applied load to the failure load at room temperature, based on the actual yield stress of the steel The results showed that for reference test 1, à0 was 0.60, while for reference test 2, à0 was 0.70.
The reference tests resulted in the following times of fire resistance with respect to the load bearing capacity: reference test 1: t ref, fi = 86 min; reference test 2; t ref, fi = 75 min
During the tests, the insulation material remained coherent and adhesive during the full duration of the tests Directly after reaching the performance criteria, the tests were terminated
The client aims to achieve a fire resistance rating of 90 minutes and seeks to determine the necessary load reduction to meet this standard To accomplish this, an extended application is performed based on the outcomes of two reference tests, incorporating semi-empirical rules from existing literature regarding the heating behavior of insulated steel members.
Analysis of reference tests
Thermal performance
Analogous to the assumptions in EN 1993-1-2, a uniform temperature distribution across and along the steel beams is assumed
The time \( t \) required for a steel profile to attain a temperature of \( \theta_a \) ºC is determined using a semi-empirical equation outlined in the Design Manual on the European standards.
Recommendations for the Fire Safety of Steel Structures, (published by ECCS, see bibliography):
A is exposed surface of the steel member;
V is volume of the steel member; d is thickness of the applied insulation material; λ is thermal conductivity of the applied insulation material
The factor [d/λ*V/A] reflects the combined effect of the section factor (A/V) and the insulation parameter (d/λ) on the heating rate and is called the Heating Rate Parameter (HRP)
The application range for the model on which Equation (B.1) is based, is specified as follows:
Mechanical performance
The mechanical performance is based on the EN 1993-1-2, in which the relation between the degree of utilisation and the critical steel temperature of a steel beam is given by: a,cr n 3,833
(B.3) where θa,cr is the critical steel temperature of the beam; à0 I s the degree of utilisation of the steel beam
Substituting Equation (B.1) into Equation (B.3) allows us to express the time required to reach the critical steel temperature under standard fire conditions as a function of the degree of utilization This time is recognized as the fire resistance concerning the load-bearing capacity of a steel beam, denoted as \( t_{fi} (à0) \).
The quantity t fi (à0) is measured in the reference tests for two values of the degree of utilisation à0
The Heating Rate Parameter (HRP) is assumed to be consistent across both tests, as they were conducted on identical test specimens, including beams and insulation systems.
Figure B.1 presents a graphical representation of the reference test results in the load domain, alongside calculated values for different HRP levels, illustrating the application range accordingly.
NOTE Note in this respect that - by using Equation (B.3) - condition (B.2c) is transferred from the temperature domain into the load domain, as follows:
Figure B.1 — Relation between the fire resistance and the degree of utilisation in the reference
Other features
The stickability of the fire protection system is a crucial feature, rated at 4.5, with two reference tests confirming no failures The extrapolated extension of 4 minutes, from 86 to 90 minutes, indicates that stickability does not limit the extended application This 4-minute extension complies with the requirements of 4.2.1, as it is less than 15 minutes and under 20% of the target fire resistance of 90 minutes.
Model for extended application
By systematically adjusting the Heating Rate Parameter (HRP), the optimal value for HRP can be identified, as illustrated in Figure B.2 For the reference tests analyzed, this optimal value has been established.
In general, the use of numerical tools to identify the best-fit value (e.g method of least squares) is recommended
Using this value of HRP, interpolation of the results of the reference tests is feasible The limits specified in Equations B.2 (a through d) are all met
The predicted results show discrepancies when compared to the outcomes of the reference tests, as illustrated in Table B.1 for the load domain To address these discrepancies, a modeling factor \( k_{mf} \) has been introduced, calculated according to the method outlined in section 4.4.2.
Hence, for a certain fire resistance, the value of utilisation predicted using this method can be accepted without any reduction
Table B.1 — Discrepancy between the applied and predicted outcomes (load domain)
Fire resistance achieved in reference test Degree of utilisation àààà 0 applied in ref test predicted as best fit test 1: 86 min 0,60 0,54 test 2: 75 min 0,70 0,73
Figure B.2 — Relation between the fire resistance and the degree of utilisation, to be used in the EXAP
Figure B.2 illustrates the connection between the utilisation factor à0 and fire resistance For a fire resistance classification of R90, the utilisation factor must be decreased to 0.459, which remains within the specified field of application.
NOTE Further information is available in item 5 of the Bibliography
The Extended Application Of Timber Beams
Introduction
This annex gives guidance to extended application of the results of one or more reference test(s) on timber beams with or without applied fire protection
The rules apply where reference tests have been performed in accordance with EN 1365-3 and a client may wish to do one of the following:
increase the load-bearing capacity by increasing strength and stiffness properties by choosing timber of a higher strength class;
increase the load-bearing capacity by increasing the dimensions of the beam;
increase the load-bearing capacity of the beam for a smaller fire resistance time than tested;
increase the fire resistance by applying fire protection
The reference tests are conducted until the beam is on the verge of collapse at time \$t_{ref,fi}\$ If a reference test is stopped at a designated time, typically aligned with the desired fire resistance rating, and no failure has been observed, it is prudent to assume that failure has occurred at the moment the test was terminated.
A thermal analysis is normally not necessary if the charring depth can be determined, see C.2, or the effect of charring is included in the model used, see C.2.2.
Extended application in the load domain (increase of load-bearing capacity)
Increasing of load-bearing capacity by higher strength class
This example applies to beams where the failure mode in the reference test is by bending failure that is failure due to lateral torsional buckling is excluded
When the strength class of the beam being evaluated, as per EN 338 or EN 1194, exceeds that of the reference beam, the bending moment capacity of the assessed beam should be considered as \( m_{\text{mean}} \).
M 1 is themoment resistance of the beam to be assessed;
The moment resistance of the reference beam, denoted as \$M_{ref}\$, is compared to the mean bending strength of the timber beam being assessed, represented as \$f_{m,mean}\$ This assessment also considers the mean bending strength of the timber beam from the reference test, indicated as \$f_{m,mean,ref}\$.
NOTE For mean properties of timber and LVL, see Table 1.
Increasing of load-bearing capacity by increasing beam dimensions (braced beams) 25
When assessing a beam with increased dimensions, it is essential to measure and record the charring depths of the reference beam after heating The resulting increase in the bending moment capacity of the beam should be considered as ef,1.
M 1 is thebendingmoment capacity of the beam to be assessed;
M ref is thebending moment capacity of the reference beam;
W ef,ref is the section modulus of the effective rectangular residual cross section of the reference beam, see below;
W ef,1 is the section modulus of the effective rectangular residual cross section of the beam to be assessed, see below ref 0,1 h ( / ) min 1,2 h h k =
In the assessment of beam dimensions, the reference beam's width (\$b_{ref}\$) and depth (\$h_{ref}\$) are crucial For beams with a depth greater than 600 mm, it is important to limit the depth considered for evaluation to a maximum of 600 mm.
The depth factor k h given by expression (C.3) should only be applied for rectangular glued laminated beams; for other beams they may be taken equal to unity
NOTE The factor k h, derived from the depth factor given in EN 1995-1-1:2004 subclause 3.3, takes into account the effect of beam size on bending strength
The section moduli W ef,ref of the reference beam and W ef,1 of the beam to be assessed should be determined following the following steps:
1) Determine the section modulus W ef,ref of the residual cross section from the recorded shape of the residual cross-section of the reference beam
2) Determine the notional charring depth d char,n,ref of the reference beam by replacing the recorded residual cross-section by a rectangular residual cross-section such that the following expression is satisfied:
3) W ef,ref = 1 6 ( b ref − 2 d char,n,ref ) ( h ref − nd char,n,ref ) 2 (C.4) where n = 1 in case of charring of the sides and bottom only (3-sided fire exposure); n = 2 in case of charring of all sides
4) As an alternative to the procedure in step 2, the notional charring depth of the reference beam may be determined as: char,ref char,n,ref char,ref
1,23 for solid timber 1,08 for glued laminated timber d d d
(C.5) where d char,ref is the charring depth measured on the wide side of the reference beam
Determine the section moduli W ef,ref and W ef,1 as (see EN 1995-1-2:2004 subclause 4.2):
2 ef,ref ref char,n,ref ref char, n, ref
W =6 b − d + h −n d + (C.6) ef,1 1 char,n,ref 1 char, n,ref 2
The formula for assessing the width and depth of a beam is given by \$W = 6b - d + h - nd + (C.7)\$, where \$b\$ represents the beam's width and \$h\$ denotes its depth The variable \$n\$ takes the value of 1 for charring on the sides and bottom only, indicating a 3-sided fire exposure, and 2 when charring occurs on all sides.
Increasing of load-bearing capacity by decreasing the fire resistance
The guidelines outlined in C.2.3 are applicable solely for establishing a higher load level when a lower fire resistance time is involved, based on one or more reference tests, without any restrictions on failure modes.
NOTE 1 This implies that extrapolation in the time domain is not permitted, since it cannot be excluded that other more unfavourable failure modes could occur, or charring could increase at a considerably higher rate
The relationship η between load ratio and time to failure t may be taken as: e 1 fi η = − k t (C.8) where k 1 is a parameter; t fi is the time to failure
NOTE 2 In Figures C.1 and C.2, a justification is given for the use of the exponential model given by expression (C.8) Figure C.1 shows the calculated relationship of load-bearing capacity and time for a glued laminated beam of dimensions 140 mm × 600 mm exposed on three sides (the upper side is assumed to be protected by a slab) according to EN 1995-1-2 The exponential model has been determined for the value at
60 min and gives conservative results
Figure C.2 illustrates the relationships for a beam covered with a 12.5 mm thick layer of gypsum plasterboard type F, secured with 41 mm long screws Point A indicates the onset of charring, while point B marks the failure time of the gypsum plasterboards caused by the pull-out failure of the screws It is assumed in Figure C.2 that the mechanical degradation of the gypsum plasterboard occurs after the time indicated by point B.
According to EN 1995-1-2, gypsum plasterboard B does not specify failure times for mechanical failure, which necessitates testing for accurate determination Additionally, the exponential model is considered more conservative for protected beams.
Figure C.1 — Comparison of relationships for load ratio vs time for a glued laminated beam of dimensions 140 mm × 600 mm exposed to fire on three sides
Figure C.2 — Comparison of relationships for load ratio vs time for a glued laminated beam of dimensions 140 mm × 600 mm and applied protection exposed to fire on three sides C.2.3.2 Single reference test
Where only one reference test has been performed, the coefficient k 1 should be taken as:
1 lnη k t (C.9) where t fi,ref is the time to failure in the reference test, in min; η ref should be taken as: ref ref
M ref is the bending moment in the reference beam in the fire situation;
M 20 is the mean moment capacity of the reference beam at normal temperature (20 °C)
The mean bending moment capacity of the reference beam at normal temperature should be calculated as:
M f W (C.11) where f mean is the mean value bending strength of the reference beam given in Table.1;
W 20 is the section modulus of the original cross section in the reference test
For a fire resistance time of t fi,ref with t fi,1 ≤ t fi,ref, the load-bearing capacity of the beam should be taken as:
1 e η = − k t (C.13) t fi,1 is the time to failure (fire resistance) of the beam to be assessed
Where more than one reference test has been performed, expression (C.12) is replaced by
The modeling factor determination, as outlined in clause 4.4.2, is demonstrated through a practical example involving three reference tests These tests were performed under varying applied loads, resulting in relative action effects denoted as \$\eta_{ref}\$ (refer to expression (C.10)) and corresponding times to failure, \$t_{fi}\$, as shown in Table C.1 and Figure C.3.
Table C.1 — Test data ηref t fi min η k mf,i k mf,I,adj
The trendline expression for the exponential model is given by the equation \( t = e^{-0.0181 \eta} \) The modeling factor \( k_{mf,i} \) is computed for each reference test, considering all three tests since none exceed the value of 1.4 Adjustments are made to ensure that no individual modeling factor surpasses 1.2 The total modeling factor is then calculated as \( mf = 1 \).
Since it is greater than unity, the value to be used is: mf 1 k 80 70 60
Figure C.3 — Reference test results and exponential model
Extended application in the time domain: Increasing fire resistance by applied fire
To enhance fire resistance, a beam previously tested without protection will be fitted with 12.5 mm thick gypsum plasterboard type A, as per EN 520 standards The charring depth of the reference beam was measured and documented at the end of the heating test.
The extended application should include the following steps:
1) Determine the notional charring depth of the reference beam, d char,n,ref, as shown in C.2.2;
2) Determine the notional charring rate of the reference beam, β n,ref, as:
3) n,ref char,n,ref fi,ref β =d t (C.17) where t fi,ref is the time to failure in the reference test
5) Determine the time of start of charring, t ch, of the beam as (see EN 1995-1-2:2004 clause 3.4.3.3):
6) t ch =2,8h p −14 (C.19) where h p is the thickness of the cladding, in mm
7) Determine the notional charring rate of the beam to be assessed, β n,1, as (see EN 1995-1- 2:2004, clause 3.4.3.2):
9) Determine the fire resistance of the beam to be assessed as: char,n,1 fi,1 ch βn,1
= +d t t for d char,n,1 ≤ 25 mm (C.21) and, taking account of expression (C.22), char,n,1 fi,1 ch n n
For applied fire protection using materials not specified in EN 1995-1-2, the charring time (\$t_{ch}\$) must be established through tests as per ENV 13381-7 When fire protection remains effective after the beam begins to char, a reduced notional charring rate (\$k_{2} \beta_{n}\$) should be calculated, applicable until the protection's failure time (\$t_{f}\$) The values for \$k_{2}\$ and \$t_{f}\$ can be sourced from EN 1995-1-2:2004, clauses 3.4.3.2 and 3.4.3.4, or determined through testing in accordance with ENV 13381-7.
The Extended Application of a Composite Steel Concrete Beam
Introduction
General
This section demonstrates a beam composed of two distinct materials, steel and concrete, highlighting the application of calibration adjustments for both thermal and structural analyses.
Two reference beam fire tests were conducted on steel beams of slightly varying sizes These unprotected beams, made from three welded plates, are embedded in the concrete floor slab, with nominal reinforcement extending over the top flanges.
1 Top flange Test 1 15 mm Test 2 12 mm
2 Bottom flange Test 1 25 mm Test 2 18 mm
Figure D.1 — Cross-section through test specimens
Reference test 1
Applied loading four loads of 120 kN
Mode of failure Overall bending
Reference test 2
Applied loading four loads of 115 kN
Mode of failure Overall bending
Figure D.2 — Thermocouple numbers and positions
The client requires a beam to carry normal floor loading of 5 kN/m 2 with a span of 10 m and a spacing to the next beams of 6 m The required fire resistance is 60 min.
Analysis of reference tests
Reference test 1
The measured temperatures at failure and at 60 min The mean temperature is shown The thermocouple numbers and positions are shown in Figure D.2 No temperatures were measured in the concrete
Table D.1 — Measured temperatures in reference test 1
(30 mm up from top of flange
The temperature distribution in the reference test was predicted using a finite difference thermal analysis program, which has demonstrated reasonable accuracy in similar beams and complies with the advanced calculation model criteria outlined in EN 1994-1-2 For analysis, the beam is segmented into rectangular elements, allowing the program to compute heat flow between adjacent elements at short time intervals A comparison of predicted and measured temperatures is presented in Table D.2.
Table D.2 — Comparison of measured and predicted temperatures in reference test 1
NOTE The measured weighted mean = (2 × TC1 + TC2)/3
The predicted weighted mean is the mean of 5 elements used in the thermal modelling
The predicted temperatures align closely with the measured values; however, the program underestimates the temperature for TC2, located at the center of the bottom flange Overall, the mean temperature of the bottom flange is accurately predicted, while the prediction for TC3 is deemed unconservative.
On the basis of Reference Test 1, some modification to the predicted temperatures may be required when predicting other cases for 60 min fire resistance.
Reference test 2
The measured temperatures at failure and at 60 min are shown in Table D.3 No temperatures were measured in the concrete
Table D.3 — Measured temperature in reference test 2
Thermocouple Temperature at 60 min Temperature at 66 min
The predictions and measured temperatures are compared in Table D.4
Table D.4 — Comparison of measured and predicted temperatures in reference test 2
The forecasted temperatures align closely with the observed values; however, the program underestimates the temperature for TC2, located at the center of the bottom flange The average temperature of the bottom flange is predicted accurately, while the prediction for TC3 is deemed unconservative.
The thermal analysis program is effective for modeling this type of composite beam; however, minor calibration adjustments are necessary to refine the results.
In Reference Test 1, the discrepancy between measured and predicted temperatures was most significant, indicating that the predictions were unconservative for both tests Consequently, for a duration of 60 minutes, it is recommended to increase any predicted temperatures by 12 °C, which reflects the difference in weighted mean temperatures.
700 °C, this correction could affect the flange strength by 6 %
The difference between the measured and predicted temperatures was at greatest 18 °C in
Reference Test 1 and 17°C in Test 2 For 60 min, therefore, any predicted temperatures should be increased by 18°C.
Structural performance
Eurocode 4, EN 1994-1-2, does not cover this exact type of structure although it gives methods of computing the moment resistance of composite sections
A torsionally stable beam can only fail due to bending or shear According to EN 1994-1-2, there is no requirement to check the shear resistance of such beams in fire conditions.
Bending resistance
In Reference Test 1, the applied bending moment was 267.8 kNm, while Reference Test 2 recorded a moment of 257.3 kNm, with no material strengths measured According to section 4.4.3, the mean properties of steel and concrete should be utilized for evaluating the Reference Tests and making predictions Material strengths at elevated temperatures are referenced from EN 1994-1-2.
Assume that for S275 steel the mean strength is 110 % of the characteristic value i.e 302,5 N/mm 2
(275 × 1,1) and that for concrete the mean strength is 38 (30 + 8)
NOTE In this example, for simplicity, the shear connection between the concrete and steel is not considered A full analysis should include this effect.
Assessment of reference test 1
The structural model used is a simple plastic analysis of the cross-section as specified in
EN 1994-1-2 The cross-section is divided into 5 elements:
2) Top flange of steel web of welded steel section
3) Upper 150 mm of steel web of welded steel section
4) Lower 70 mm of web of welded steel section
5) Bottom flange of welded steel section
A material strength and temperature are assigned to each element The plastic moment resistance may be calculated by hand but, here, Excel based calculations are presented in Table D.5 and Table D.6
Table D.5 — Calculation of moment resistance in reference test 1
Width Depth Material Cold Temp Centroid Hot Force Moment strength strength contribution
(mm) (mm) (N/mm²) (°C) (mm) (N/mm²) (kN) (kNm)
Compressive force in concrete (kN) 1 900,0 Compressive force in steel (kN) 223,7 Tensile force in steel (kN) 2 123,7
The plastic neutral axis of the welded steel section is located in the top flange, dividing the element into two parts: the upper section experiences compression while the lower section is subjected to tension.
The calculated moment resistance is 293,7 kNm This is 9,7 % greater than the applied moment in the test (267,8 kNm) This difference is reasonable for this type of calculation.
Assessment of reference test 2
Table D.6 — Calculation of moment resistance in reference test 2
Width Depth Material Cold Temp Centroid Hot Force Moment strength strength contribution
(mm) (mm) (N/mm²) (°C) (mm) (N/mm²) (kN) (kNm)
The moment resistance is measured at 281.3 kNm, with a compressive force in concrete of 1900.0 kN and a compressive force in steel of 137.8 kN Additionally, the tensile force in steel reaches 2037.8 kN It is important to note that the plastic neutral axis is located in the top flange of the welded steel section, which is divided into two elements: the upper part experiences compression while the lower part is under tension.
The calculated moment resistance is 281,3 kNm This is 14 % greater than the applied moment in the test (246,8 kNm).
Conclusions of structural performance
The EN 1994-1-2 method for calculating moment resistance predicted strengths that were 9.7% and 14% higher than those measured in tests These discrepancies may be attributed to inaccuracies in the assumed material properties, inadequate temperature data, or other unidentified factors Consequently, the modelling factor (k mf) is relevant for further analysis.
NOTE As the ratio F/R for each test is less than 1,2, the actual values do not have to be limited to 1,2.
Model for extended application
The thermal and structural models utilized for analyzing the reference tests can be applied with specific corrections Based on the data provided in this example, any extended application is limited to a duration of 60 minutes.
Extended application
It is assumed that, for normal conditions, the design conforms to EN 1994-1-2
The loads are factored using factors from EN 1991-1:
To ensure accurate bending resistance, it is essential to incorporate the Modelling factor According to the plastic bending resistance model, the required bending resistance is calculated to be 478.2 (derived from 427.5 divided by 0.894) Additionally, as per the guidelines in section A.7, deflection calculations are not necessary.
The proposed beam cross-section, illustrated in Figure D.3, features a deeper section size and an increased web thickness compared to the reference tests Additionally, the slab width has been adjusted.
2 500 mm is based on 25 % of the 10 m span (EN 1994-1-1)
The predicted temperatures and corrected temperatures are shown in Table D.7 and the calculation of moment resistance is shown in Table D.8
The calculated bending resistance is 503,9 kN so the design is adequate, based on the extended application analysis
Figure D.3 — Cross-section through required design
Table D.7 — Predicted temperatures and corrected temperatures
Table D.8 — Calculation of moment resistance in design example
Width Depth Material Cold Temp Centroid Hot Force Moment strength strength contribution
(mm) (mm) (N/mm²) (°C) (mm) (N/mm²) (kN) (kNm)
The compressive force in concrete is 3,328.4 kN, while the compressive force in steel is zero Conversely, the tensile force in steel also measures 3,328.4 kN It is important to note that the plastic neutral axis is located in the top flange of the welded steel section, which is divided into two elements: the upper part experiences compression, while the lower part is under tension.
The extended application of concrete beams
Introduction
This annex gives some examples for extended application of the results of one or more reference test(s) concrete beams
In most cases extended application of concrete beams can be carried out by using design rules of
Failure modes
Failure modes of reinforced or prestressed concrete beams exposed to fire may be: a) Tension failure of the reinforcement in bending
This is the most common type of failure and can be predicted by rapid increase of deflection b) Compression failure of concrete in bending
Possible, if the compression side of the cross section is exposed to fire, like continuous beams near the supports, or thin beams c) Shear failure
Possible for beams with thin webs, like I-beams d) Anchorage failure
Could be possible for prestressed beams, but normally prevented by stirrups in the anchorage zone e) Spalling
EN 1992-1-2 includes design rules to prevent spalling.
Examples
Possible change of failure mode
A typical resistance curve for a concrete beam with a constant cross-section is illustrated in Figure N.1 In the event of bending failure during a fire test, the findings can be applied to longer spans without the concern of shear failure.
Change of cross section
If the average distance of the main reinforcement remains constant, modifications can be made to the cross-section dimensions, load, span, and quantity of reinforcement, provided that calculations confirm that the tensile stress in the reinforcement does not increase.
NOTE When the load level in the test has been chosen to give maximum steel stress, this verification is automatically covered by normal temperature design
However, decrease of the width may increase temperature in the critical areas of the cross section, and should not be done without more detailed calculations
Ratio V fi/f cdbd should not increase and average axis distance of stirrups should not decrease.
Change of material strength
Test results are applicable to all classes of normal strength concrete (≤ C50/60) using the same type of aggregates, whether siliceous, calcareous, or lightweight, provided that the load level remains constant Additionally, the type of reinforcement can include reinforcing steel, prestressing bars, wires, or strands.
The results cannot be applied to other types of reinforcement without accounting for the differences in thermal and mechanical properties, as outlined in ENV 1992-1-2 Additionally, the strength of reinforcing or prestressing steel must be taken into consideration.
Change of strength has no influence on fire resistance assuming that load level is kept unchanged.
Axial and rotational restraint
Concrete beams are normally tested as simply supported These results are on the safe side for the other cases because axial and rotational restraint increases the fire resistance
NOTE Axial restraint may decrease fire resistance if it is situated above the centroid axis of the beam This should be prevented by design rules
[1] EN 1992-1-1, Eurocode 2 Design of concrete structures — Part 1-1: General rules and rules for buildings
[2] EN 1993-1-1, Eurocode 3 Design of steel structures — Part 1-1: General rules and rules for buildings
[3] EN 1994-1-1, Eurocode 4 Design of composite steel and concrete structures — Part 1-1: General rules and rules for buildings
[4] EN 1999-1-1, Eurocode 9 Design of aluminium structures — Part 1-1: General rules and rules for buildings
[5] ECCS-TC3: Design Manual on the European Recommendations for the Fire Safety of Steel Structures, 1985
[6] EN 1363-2, Fire resistance tests — Part 2: Alternative and additional procedures
[7] EN 1992-1-2:2004, Eurocode 2: Design of concrete structures — Part 1-2: General rules — Structural fire design
[8] EN 1993-1-2, Eurocode 3: Design of steel structures — Part 1-2: General rules - Structural fire design
[9] EN 1994-1-2, Eurocode 4 - Design of composite steel and concrete structures - Part 1-2: General rules - Structural fire design
[10] EN 1995-1-2:2004, Eurocode 5: Design of timber structures - Part 1-2: General - Structural fire design
[11] EN 1995-1-1:2004, Eurocode 5: Design of timber structures - Part 1-1: General - Common rules and rules for buildings
[12] ENV 13381-7, Test methods for determining the contribution to the fire resistance of structural members - Part 7: Applied protection to timber members