9-3. Structural response

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1 9-3. Structural response in fire František Wald Czech Technical University in Prague

2 Objectives of the lecture The mechanical load in the fire design Response of the structure exposed to fire Levels of accuracy/complexity of fire design Avaliable worked examples and design softwares 2

3 Three steps of fire design Fire design Fire load Fire behaviour Modelling of the gas temparature in the fire compartment Eurocodes EN Thermal response Transfer of heat and development in structure Structural response Design of structure at elevated temparature EN x EN 199x-1-2 3

4 Structural response Global analyses At ambient temparature At elevated temparature The structure Whole structure Part of the structure The structural element (beam, colum, connection) 4

5 at fire situation at fire lower compare to maximum one at ambiet temparature Sorce of safety for structures exposed to fire Described in EN 1990 the load combinations at accidental situation EN procedure to aplly the load EN x particular loading pernament, wind, snow, etc. 5

6 Combination rules for mechanical actions EN 1990: Basis of structural design At fire conditions at the accidental situation E fi,d = G + ψ 1or2,1 Q 1 + ψ Q i>1 1or2,i i E.g. offices area with the imposed load Q, as the leading variable action E fi,d = G + 0,5 Q E.g. offices area with the wind W, as the leading variable action E = G +02W 0,2 W +03Q 0,3 Q E fi,d 6

7 Values of ψ factors for buildings Table A1.11 in EN 1990:2002 Action ψ Imposed loads in buildings, category (see EN ) Category A : domestic, residential areas Category B : office areas Category C : congregation areas Category D : shopping areas Category E : storage areas Category F : traffic area vehicle weight 30kN Category G : traffic area, 30 kn < vehicle weight 160kN 0,7 0,7 0,7 0,7 10 1,0 0,7 ψ 0,5 0,5 0,7 0,7 09 0,9 0,7 0,5 0,3 Category H : roofs Snow loads on buildings (see EN ) Finland, Iceland, Norway, Sweden Remainder of CEN Member States, for sites located at altitude H > 1000 m a.s.l. Remainder of CEN Member States, for sites located at altitude H 1000 m a.s.l. 0,70 0,70 0,7 0,50 0,50 ψ 0,3 0,3 0,6 0,6 08 0,8 0,6 0,20 0,20 0,50 0,20 0 Wind loads on buildings (see EN ) 0,6 0,2 0 Temperature (non-fire) in buildings (see EN ) 0,6 0,5 0 7

8 Reduction factor η fi for load combination The design value at fire situation devided by design value at ultimate limit state at elevated temperature: η fi = G G k γ G k + ψ fi Qk,l + γ Q Q,1 k,1 G k is the characteristic value of a permanent action 0,2 0,0 0,5 1,0 1,5 2,0 2,5 3,0 k p Q k,1 is characteristic value of the leading variable action ψ fi γ G η fi 0,8 0,7 0,6 0,5 0,4 0,3 Q / G k,1 k ψ fi,1 = 0,9 ψ fi,1 = 0,7 ψ fi,1 = 05 0,5 is the combination factor for values, given either by ψ 1,1 or ψ 2,1 (according to relevant National Annexes) is the partial factor for permanent actions γ Q,1 is the partial factor for variable action ψ fi,1 = 0,2 ( 8

9 Material properties at elevated temparature Design values of material properties at elevated temparature for structures exposed to fire are described by reduction factors of properties at ambient temperature X = k d, fi θ Xk /γ M,fi k θ is reduction factor for a mechanical property with respect to temperature X k k is characteristic value of a mechanical property p for ambient temperature design to EN γ M,fi is Partial material safety factor for fire situation; for thermal & mechanical properties recommended 10 1,0 9

10 Material properties Structural steel 1,0 at elevated temperatures, t EN ,8 Reduction factor, k θ strength % of normal value, k θ Effective yield strength Normalised stress for advanced modelling 1 20 C 200 C 400 C 500 C 0,6 0,6 600 C 0,8 0,4 0,2 Elastic modulus Temperature, C 0,4 0, C 800 C Strain, % Yield strength at 600 C reduced by over 50% Elastic modulus at 600 C reduced by about 70% 10

11 Material properties Concrete at elevated temperatures, EN Reduction factor, k θ strength % of normal value 1,0 0,5 Normalweight Concrete Strain, % Strain ε cu at maximum strength Normalised stress for advanced modelling 1,0 0,8 0,6 0,4 0,2 20 C 200 C 800 C 400 C 600 C 0, Temperature, C Strain, % ε cu Compressive strength at 600 C reduced by about 50 % 11

12 Formative assessment question 1 Where are formulated the combination rules for mechanical actions? How is defined the redaction factor for load combinations? How is reduced the yield strength of structural steel at 600 C? How is reduced the compressive strength of concrete at 600 C? How is defined the reduction of the material properties at elevated temperature during fire in standards? 12

13 Procedure for assessing mechanical response in fire Tabulated data Composite structural members Simple models Critical temperature method Steel and composite structural members models All types of structures Numerical models based FE Classic and traditional fire design fire design 13

14 Tabulated data for steel and concrete composite members Composite beams Slab Composite columns Concrete for insulation 14

15 Tabulated data parameters for composite columns EN e f A A c s h Standard Fire Resistance ew b u s u s R30 R60 R90 R120 Minimum ratio of web to flange thickness e w /e f 05 0,5 1 Minimum cross-sectional dimensions for load level η fi,t 0, minimum dimensions h and b [mm] minimum axis distance of reinforcing bars us [mm] minimum ratio of reinforcement A s /(A c +A s )in% Minimum cross-sectional dimensions for load level η fi,t 0, minimum dimensions h and b [mm] minimum axis distance of reinforcing bars us [mm] minimum ratio of reinforcement A s /(A c +A s ) in % 3 Minimum cross-sectional dimensions for load level η fi,t 0, minimum dimensions h and b [mm] minimum axis distance of reinforcing bars us [mm] minimum ratio of reinforcement A s /(A c +A s ) in % Standard fire rating Load level Section dimension Reinforcing steel Concrete cover 15

16 Application of tabulated data Design resitance at ambient temparaturet Acting forces at elevated temparature Reduction factor for load combination Verification R d E fi,d η fi = E fi,d / R d Section dimension Reinforcing steel Concrete cover Rating for nominal standard fire curve Acording to DIFISEK + 16

17 Simple s models The Eurocode for fire design of steel structures EN based on global analyses at ambient temperature: Limits of use Classification of sections Procedure for evaluation of member resistance for evaluation of the members in time or resistance domain Beams Columns Critical temperature procedure for evaluation of the members in temperature domain 17

18 s Classification of cross-sectionssections For the purpose of the simplified rules the cross-sections sections may be classified as for ambient temperature design with a reduced value for 235 ε = 0,85 where: f f y is the yield strength at ambient temperature y 1,2 Ration k E, θ k y, θ 1 0,8 0,6 About 0,85 k E, θ k y,θ 0,4 0, Temparature, C 18

19 s Beams Class 1 and 2, laterally restrained The design moment resistance of a Class 1 or Class 2 cross-section with a uniform temperature θ a should be determined from where: M fi,θ,rd = k y,θ [γ M,0 / γ M,fi ] M Rd k y,θ is the reduction factor for the effective yield strength of steel at temperature θ a M Rd is the plastic moment resistance of the cross-section M pl,rd for ambient temperature design γ M,0 / γ M,fi is the ratio of partial safety factors at ambient and fire situation 19

20 Beams Non-uniform temperature distribution solution The design moment resistance at time t of a Class 1 or 2 cross-section in a member with a non-uniform temperature distribution s M fi,t,rd = M fi,θ,rd /(κ 1 κ 2 ) where: M fi,θ,rd is the design moment resistance of the cross-section for a uniform temperature θ a κ 1 and κ 2 are the adaptation factors of non-uniform temperature distribution p a Complex solution Based on reduction of material properties along the cross-section hight and distance from the plastic neutral axis 20

21 Beams Adaptation factor for non-uniform temperature distribution across For non-uniform temperature distribution across a crosssection s - for a beam exposed on all four sides κ 1 = 1,0 - for an unprotected beam exposed on three sides, with a composite or concrete slab on side four κ 1 =0,70 - for an protected beam exposed on three sides, with a composite or concrete slab on side four κ 1 = 0,85 Temperature Stresses κ 1 = 0,7 21

22 s Beams Adaptation factor for non-uniform temperature distribution along For a non-uniform temperature distribution along a - at the supports of a statically indeterminate beam κ 2 =0,85 2, - in all other cases κ 2 =1,0 κ 2 = 1,00 2, κ 2 = 0,85 22

23 s Critical temperature method According to simple models, for uniformly heated steel members R fi,d,t = k y,θ R fi,d,0 On the other hand, fire resistance should satisfy: E fi,d R fi,d,t E fi,d = R fi,d,0 = μ 0 R fi,d,0 k y,θ μ 0 R fi,d,0 In particular, when k y,θ = μ 0 the corresponding temperature is defined as critical temperature θ cr In EN a formula is given to determine critical temperature 1 θ a,cr = 39,19 ln ,9674 μ 3,

24 Verification in the time domain The metod is handly for stress driven resistance, e.g. bending For stability problem is more efficient i to check the resistance at certain level of temperature Stress, MPa Element resistance 1,0 Utilisation level at fire situation Collapse 08 0,8 0,6 Resource of resistance 04 0,4 0,2 Critical temperature 0,0 Critical temperature Temperature, C Temperature, C 24

25 Application of critical temperature method Action in fire E fi,d Design resistance at ambient temperature R d or design action at ambient temperature E d Load level in fire η fi,t = E fi,d R d Utilisation level μ 0 = η fi,t γ M,fi γ M Critical temperature θ cr 25

26 d l model Example composite cellular beam n, mm Deflectio Test Calculation Tested failure mode Time, min Calculation vs test Simulated failure mode Acording to DIFISEK + O. Vassart, ArcelorMittal 26

27 Examples of the tools General / Commerical codes Examples Abaqus Ansys Others Dedicated Codes Examples Vulcan Adaptic Safir Others 27

28 Pros and Cons of the tools General/Commerical codes Pros Fast Reliable Very general Support Cons (Very) expensive Black-box Dedicated codes Pros Good price Access to source Focussed on fire Cons Struggle with large problems Not support Credibility 28

29 Formative assessment question 2 What is the difference of classification of cross-sections at ambient and elevated temperatures? Describe the evaluation of the design moment resistance of a beam of a Class 1 or Class 2 cross-section at elevated temperature with a uniform temperature? How may be treated the non-uniform temperature of a cross-section? What is the principle of the critical temperature method? Pros of dedicated codes for advanced fire design? 29

30 Fire design of an unprotected beam using graphs This worked example covers the fire design of a hot-rolled IPE section forming gpart of floor structure of an office building. The beam is uniformly loaded and restrained against lateral torsional buckling by the presents of a concrete slab on the top flange. The beam is to be designed to achieve R15 fire resistance without the use of fire protection material. q g l = 7,4 m 30

31 Basic data Steel grade S 275 Yield stress f y = 275 N/mm² Density: ρ a = 7850 kg/m³ Loads Permanent action: g =4,8 knm -1 k Variable action: q k = 78kNm 7,8-1 q k l = 7,4 m q g 31

32 Mechanical actions at ambient temperature t l = 7,4 m The characteristic value of the load is v k = g k + q k = 4,8 +7,2 = 12,6 kn/m The design value of the load is v d = g k γ G + q k γ Q = 4,8 1,35 + 7,2 1,5 = 18,18 kn/m The applied bending moment is given by M Ed = v d l = 18,18 7,4 2 = 124, 4 knm 8 8 q g 32

33 Design at ambient temperature The IPE 300 section is a Class 1 section in bending. t w =7,1 r=15 t f h=300 b=150 t f =10,7 The section is checked at ULS at ambient temperature. The concrete slab is assumed to provide full lateral restraint to the beam; therefore, lateral-torsional instability does not need to be taken into account. 33

34 Mechanical actions for the fire design situation ti The reduction factor for the design load level is equal to η G η gk + ψ1,1 qk 4,8 + 0, 3 7,8 = g γ + q γ 4,8 1,35 + 7, 8 1,5 fi = = k k Q 0,393 where for office buildings is taken the ψ factor as ψ 1,1 =0,3 34

35 Design at ambient temperature Bending moment resistance 3 Wpl,y fy 628, M pl, Rd = = = 172,8 knm > 124,4 knm = γ 1,0 M0 M Sd Serviceability Limit State Deflection limits are given either in a national annex or in other national documents. This limit is a typical value. δ = vk l E I 4 y = , , = 28,0 mm < 29,6 mm OK = l 250 OK The section is satisfactory at ambient temperature. 35

36 Design in the fire situation Section factor The section factor for the hot-rolled section is taken from tables. The box section factor for an unprotected beam exposed on three sides is equal to A V m b = 139 m 1 The exposed perimeter is indicated d by the dashed d line on figure. The shadow effect is considered by modifying the section factor as follows. A V m A = 0,9 V m sh b = 0,9 139 = 125 m 1 36

37 Degree of utilization The adaptation factor κ 1 = 0,7 is used for an unprotected beam exposed to fire on three sides The adaptation factor κ 2 = 1,0 is used for simply supported beam. The degree of utilization for the beam with non-uniform temparature distruibution is given by μ 0 = η fi κ 1 κ 2 = 0,393 0,7 1,0 = 0,275 37

38 Critical temparature The critical temparature can be evaluated for the degree of utilization θ a,cr 1 = 39,19 ln = 3, 833 0,9674 μ0 1 = 39,19 ln = 677 C 3, 833 0,9674 0,275 38

39 Transfer of heat by graph The step-by-step procedure may be replaced by reading on the Steel temperature θ a,cr [ C] Am / V, ( Am/V) [m ] b graph, 400 as reproduced 300 in Figure Fire duration t [min]

40 Verification in the time domain The fire resistance period predicted using Figure is equal to 17 min. This exceeds the required fire resistance R15. Therefore, the fire resistance of the section is satisfactory without t applied protection. ti For detailed explanation and another worked examples with more precised procedure see worked examples in steel com 40

41 Assessment What is the difference between the load level and the utilisation level? For what cases is useful the critical temperature method? In which domain is recommended to evaluate the resistance in case of stability? 41

42 There are tree levels of accuracy/complexity of fire design For simple worked examples please consult AcceesSteel For complex worked examples and software please consult DIFISEK + New models for composite slab, connections and coldformed elements are finalised 42

43 Thank you for your attention 43

44 to users of the lecture This session is a basic information about the mechanical load of structures exposed to fire and its modeling requires about 60 min lecturing and 60 min for tutorial session. Further readings on the relevant documents from website of and The use of relevant standards of national standard institutions are recommended. Formative questions should be well answered before the summative questions completed within the tutorial session. Keywords for the lecture: fire design, mechanical loading, mechanical response at elevated temperature, simple methods, Eurocodes. 44

45 to users of the lecture s for mechanical response The application of the graph is in AccessSteel example Fire design of an unprotected beam using graphs The description of step by step procedure for heat transfer is in AccessSteel examples Fire design of an unprotected IPE section beam exposed to the standard time temperature curve Fire design of a protected HEB section column exposed to the standard temperature time curve 45

46 for lecturers Subject: Fire modelling and transfer of heat to structure. Lecture duration: 60 min plus 60 min tutorial Keywords: fire design, mechanical loading, mechanical response at elevated temperature, simple methods, Eurocodes. Aspects to be discussed: recources of fire safety at fire, start of reduction of material properties, advanced models. Within the lecturing, the procedure of Eurocode fire design is explained. Further reading: relevant documents from website of and 46

Fire resistance assessment of composite steel-concrete structures

Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, 78 November 0 Fire resistance assessment of composite steelconcrete structures Basic design methods Worked examples CAJOT