Fire resistance assessment of steel structures

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1 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Fire resistance assessment of steel structures Basic design methods Worked examples ZHAO Bin CEN/TC250 HG-Fire Convenor CTICM

2 Fire resistance assessment of steel structures Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Basic design methods of EN Fire part of Eurocode 3

3 Fire parts of Eurocodes 2 to 6 and 9 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Following common layout to provide design rules for fire resistance of various types of structures: General Scope, application field, definitions, symbols and units Basic principles Performances requirements, design values of material properties and assessment approaches Material properties Mechanical and thermal properties at elevated temperatures Assessment methods for fire resistance Constructional details Annexes Additional information: common case - more detailed design rules

4 Fire resistance European classes Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Fire resistance is defined in terms of time as follows: Relevant time of fire exposure during which the corresponding fire resistance function of a structure is maintained despite fire actions According to European standard, 3 criteria to define the fire resistance: R E I load bearing function integrity separating function thermal insulating separation function Above criteria may be required individually or in combination: separating only: integrity (criterion E) and, when requested, insulation (criterion I) load bearing only: mechanical resistance (criterion R) separating and load bearing: criteria R, E and, when requested I

5 Fire resistance European classes Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November R load bearing function Capacity of a structure to maintain its required mechanical resistance in case of fire Mechanical loading

6 Fire resistance European classes Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November E integrity separating function Capacity of a structure to maintain its required integrity separating function to hot gases in case of fire With or without additional mechanical loading hot gas 200, 300, 400 C, (no limitation) heat

7 Fire resistance European classes Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November I thermal insulation separating function Capacity of a structure to maintain its required thermal insulation separating function in case of fire With or without additional mechanical loading hot gas Average temperature rise 140 K (under standard fire) Maximum temperature rise 180 K (under standard fire) heat

8 Scope of fire part of Eurocode 3 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Only load bearing function R of steel structures is covered by the design rules of the fire part of Eurocode 3 Load bearing function of a structure is satisfied only if during the relevant duration of fire exposure t E fi,d,t R fi,d,t where E fi,d,t : design effect of actions (Eurocodes 0 and 1) R fi,d,t : corresponding design resistance of the structure at instant t

9 Scope of fire part of Eurocode 3 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Covered field Carbon structural steel: all types of structural members grades in S235, S275, S355, S420 & S460 Cold-formed carbon structural steel: members in accordance with EN Stainless structural steel: 5 commonly used grades for building sector no specific simple design rules Both internal and external steel structures

10 Scope of fire part of Eurocode 3 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Load bearing function R in fire and ambiant temperature design Constant room temperature (20 C) Load increase M r (20 C) Cold design Fire design Constant loading Temperature increase until the collapse at instant t M r ( crit ) M r () M r (20 C)

11 Fire resistance assessment of steel structures according to Eurocode 3 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Eurocodes allow fire resistance to be established in any of 3 domains : Time: Load resistance: Temperature: t fi.d t fi.requ R fi.d.t E fi.d.t cr.d d t fi.d : design fire resistance time t fi.requ : required fire resistance time Usually only directly feasible using advanced calculation models. Feasible by hand calculation. Find reduced resistance at required resistance time. Most usual simple EC3 method. Find critical temperature for loading, compare with design temperature.

12 Application of EC3 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Actions on structures exposed to fire Thermal actions Mechanical actions Load level in fire situation Design approaches Member analysis Analysis of parts of the structure Global structural analysis Material properties at elevated temperatures Thermal properties of steel Eurocodes 0 and 1 Mechanical properties of steel Reduction factors for both strength and stiffness of steel Partial factors for fire design of steel structures

13 Application of EC3 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Different design approaches for mechanical response of structure in fire global structural analysis analysis of parts of the structure member analysis (mainly when verifying standard fire resistance requirements)

14 Application of EC3 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Two types of design methods for assessing mechanical response of steel structures in fire Simple calculation models critical temperature mechanical model of steel structural members Ordinary structural fire design Advanced calculation models all types of steel structures numerical models based on: finite element method finite difference method Advanced and specific structural fire design

15 Application of EC3 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Application domain of different design methods for steel structures under fire situation Thermal action defined under standard fire Type of analysis Member analysis Analysis of parts of the structure Global structural analysis Simple calculation methods Critical temperature Advanced calculation models Yes Yes Yes Not applicable Not applicable Yes Not applicable Not applicable Yes

16 Application of EC3 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Application domain of different design methods for steel structures under fire situation Thermal action defined under natural fire Type of analysis Simple calculation methods Critical temperature Advanced calculation models Member analysis Yes (if available) Yes (if available) Yes Analysis of parts of the structure Global structural analysis Not applicable Not applicable Yes Not applicable Not applicable Yes

17 Application of EC3 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Thermal properties of steel at elevated temperatures Thermal conductivity (W/m K) Specific Heat (J/kg K) l a = 45 W/m K (EC simple calculation model) 4000 c a = 600 J/kg K 3000 (EC4 simple calculation model) Temperature ( C) Temperature ( C) Density of steel: 7850 kg/m 3

18 Application of EC3 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Thermal properties of steel at elevated temperatures 20 Thermal expansion of steel L/L (x10 3 ) Temperature ( C)

19 Application of EC3 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Mechanical properties of steel at elevated temperatures Reduction factors Elastic modulus k E, Effective yield strength k y, obtained with 2% strain Temperature ( C) Elastic modulus at 600 C reduced by about 70% Normalised stress 20 C 200 C 400 C 500 C 600 C 700 C 800 C % Strain (%) Yield strength at 600 C reduced by over 50%

20 Application of EC3 for fire resistance assessment basic knowledge Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Partial factors of steel at elevated temperatures Type of members Ambient temperature design Fire design Cross-sections M0 = 1.0 M,fi = 1.0 Members with instability Tension members to fracture M1 = 1.0 M,fi = 1.0 M2 = 1.25 M,fi = 1.0 Joints M2 = 1.25 M,fi = 1.0

21 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November FIRE RESISTANCE STEEL TEMPERATURE Action in fire situation E fi.d.t Building regulations t fi.requ

22 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Design load in fire situation Either.. E fi,d,t = G k,j + 2,1 Q k,1 + 2,i Q k,i j 1 i 2 Reduction factor Recommended, for practical application refer to each National Annex Or more usefully.. E fi.d.t fi E d relative to ambienttemperature design load On the other hand, load level fi,t E fi,d,t R d relative to ambienttemperature design resistance

23 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Reduction factor for design load in fire situation fi GA G G G k k y 2.1 Q.1 Q Q k.1 k.1 G Q.1 Ambient temperature strength design = 1.35 Permanent loads; = 1.50 Combination factor; variable loads In structural fire design GA = 1.0 Permanent loads; accidental design situations y 2.1 = 0.3 Combination factor; variable loads, offices Q k,1 /G k fi

24 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November FIRE RESISTANCE STEEL TEMPERATURE Action in fire situation E fi.d.t Classify member Building regulations t fi.requ

25 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Classification of steel members in fire C1: M M C2: M M C3: M M C4: M pl pl el M eff, el f > f f < f req req classified as at ambient temperature however, different value of to take account of temperature influence Temperature induced f y

26 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November FIRE RESISTANCE STEEL TEMPERATURE Action in fire situation E fi.d.t Classify member Resistance at 20 C by fire rules R fi.d.20 Degree of utilisation m 0 Building regulations t fi.requ

27 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November The Degree of Utilisation is the design loading of a member in fire, as a proportion of its design resistance at ambient temperature (t = 0) but including material partial factors for fire design. m 0 E R fi.d fi.d.0 A simple version of Degree of Utilisation: m 0 fi,t M,fi M0 can be used when no risk of overall or lateral-torsional buckling conservative if fi,t calculated as proportion of design loading at ambient temperature.

28 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November FIRE RESISTANCE STEEL TEMPERATURE Action in fire situation E fi.d.t Classify member Resistance at 20 C by fire rules R fi.d.20 Degree of utilisation m 0 Critical temperature cr Building regulations t fi.requ

29 Temperature ( C) Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Critical temperature of steel members Basic assumption: uniform temperature of steel member 1000 Stable structure Time Standard fire Strength reduction of steel member cr µ Uniform heating of 200 steel member 0.2 t fi.d Designed collapse Degree of utilisation

30 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Critical temperature of steel members Critical Temperature ( C) Based on standard fire tests. Simple members only. Non-slender sections without instability (Classes 1, 2, 3) treated the same. Slender (Class 4) sections treated conservatively (350 C) or Annex E for more detailed design rules cr 1.19ln m Class 4 sections Class 1, 2, 3 sections Degree of Utilisation m 0

31 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Critical temperature of steel members under instability using specific tabulated data based on: non-dimensional slenderness at instant 0 l fi,0 and a specific load level m 0 = N fi,d,t / N pl,fi,0 each steel grade has its own tabulated data l fi, m

32 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November FIRE RESISTANCE Action in fire situation E fi.d.t Classify member STEEL TEMPERATURE (UNPROTECTED) Find Section Factor A m /V and k sh Resistance at 20 C by fire rules R fi.d.20 Degree of utilisation m 0 Critical temperature cr Building regulations t fi.requ

33 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Section factor: bare steel members insulated steel members Definition: ratio between perimeter through which heat is transferred to steel and steel volume

34 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Section factor A m /V - unprotected steel members b h perimeter c/s area exposed perimeter c/s area 2(b+h) c/s area

35 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Temperature increase of unprotected steel shadow effect k sh : shadow effect caused by local shielding of radiative heat transfer, due to shape of steel profile, i.e.: profiles, shadow effect: yes profiles, shadow effect: no < 180 (reduced radiation) Thermal radiation already taken into account, no shadow effect; hence: Insulated steel members, shadow effect: no Calculation of shadow effect k sh A 0.9 V m A V m b = 180 full radiation A m V Am V b

36 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November FIRE RESISTANCE Action in fire situation E fi.d.t Classify member Resistance at 20 C by fire rules R fi.d.20 STEEL TEMPERATURE (UNPROTECTED) Find Section Factor A m /V and k sh Step by step calculation until fi,d = cr Degree of utilisation m 0 Critical temperature cr at t fi.d Building regulations t fi.requ

37 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Temperature increase of unprotected steel Temperature increase in time step t ( 5 seconds) : a.t c k a sh a A V m h net.d t Fire temperature Steel temperature Heat flux h net.d has 2 parts: Radiation: h net,r res g m 273 Steel 4 Convection: hnet,c c g m Under standard fire situation res = f x m =0.7 and f = 1.0 c = 25 W/m²K

38 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Steel temperature as function of Section Factor value Bare steel profiles Temperature [ C] minutes 15 minutes k sh A m /V (m -1 )

39 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November FIRE RESISTANCE Action in fire situation E fi.d.t Classify member Resistance at 20 C by fire rules R fi.d.20 STEEL TEMPERATURE (UNPROTECTED) Find Section Factor A m /V and k sh Step by step calculation until fi,d = cr Degree of utilisation m 0 Critical temperature cr Is at t fi.d t fi.d t fi.requ?? Building regulations t fi.requ

40 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November FIRE RESISTANCE Action in fire situation E fi.d.t Classify member STEEL TEMPERATURE (PROTECTED) Find Section Factor A p /V Resistance at 20 C by fire rules R fi.d.20 Degree of utilisation m 0 Critical temperature cr Building regulations t fi.requ

41 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Section factor A p /V - protected steel members b h Steel perimeter steel c/s area inner perimeter of board steel c/s area 2(b+h) c/s area

42 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November FIRE RESISTANCE Action in fire situation E fi.d.t Classify member Resistance at 20 C by fire rules R fi.d.20 STEEL TEMPERATURE (PROTECTED) Find Section Factor A p /V Step by step calculation until fi,d = cr Degree of utilisation m 0 Critical temperature cr at t fi.d Building regulations t fi.requ

43 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Temperature increase of protected steel members Some heat stored in protection layer. Heat stored in protection layer relative to heat stored in steel Fire temperature Steel temperature f c c p a p a d p A / d p V Temperature rise of steel in time d p increment t ( 30 seconds) l A 1 Steel Protection f /10 g,t a,t t e g, t p p p a.t 1 caa V 1 f/ 3

44 Temperature [ o C] Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Examples of protected steel members Time [min] Standard fire curve A m / V = 100 [m -1 ] A p /V = 100 [m -1 ] + insulation

45 Establishing fire resistance of steel structures using simple process Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November FIRE RESISTANCE Action in fire situation E fi.d.t Classify member STEEL TEMPERATURE (PROTECTED) Find Section Factor A p /V Resistance at 20 C by fire rules R fi.d.20 Degree of utilisation m 0 Critical temperature cr Iterate temp./time until fi,d > cr Is at t fi.d t fi.d > t fi.requ?? Building regulations t fi.requ

46 Simple load-bearing design rules Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Tension, simple bending and members under compression without instability behaviour (classes 1 to 3) classes 1 and f y, class F c F t D M fi,t,rd F t D Simple bending A t Cross section Temperature Distibution + - f fi,t,rd t y, Stress N A Tension or compression Load bearing capacity

47 Simple load-bearing design rules Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Adaptation factors - beam with concrete slab on top flange Adaptation factors used to allow for nonuniform temperature distribution for both Temp Moment Resistance: M fi,t,rd M Rd k y. Shear Resistance: V fi,t,rd V Rd k y..max M,1 M,fi 1 1 M,1 M,fi 2 1 =1.0 for uniform c/s temperature, 0.7 or 0.85 for slab on top flange. 2 =0.85 at supports of statically indeterminate beam, 1.0 for all other cases (temperature distribution along beam).

48 Simple load-bearing design rules Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Members under bending or/and compression with instability behaviour (classes 1 to 3) P 1.0 (l ) L fi 0.5 Section and temperature 0 l Specific buckling curve Load bearing capacity: N fi,t,rd = (l ) N fi,pl,rd (l ) resistance and stiffness of cross section + buckling length L fi and a specific buckling curve

49 Simple load-bearing design rules Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Design buckling length of steel columns in fire situation Braced structures Continued or ends maintained columns Same fire resistance R between columns and floor members L fi =0.7L 2 L 2 Bracing system L fi =0.5L 1 L 1

50 Simple load-bearing design rules Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Design recommendations for steel joints Check of thermal resistance of steel joints d f of steel jo int min imum value of lf c of any of the connected members d l f f m Check of utilisation of steel joints c,fi of steel joint maximum value of m,fi of any of the connected members More detailed simple design rules for steel joints Annex D

51 Column Flame Simple load-bearing design rules Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Design rules for external steel works Facade wall Partition wall Beam Floor Opening Fire in one compartment Corridor Simple design rules Thermal action: annex B of EC1 Heating of steel: annex B of EC3

52 Advanced fire resistance design tools Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Application example of advanced thermal analysis Heating of fire insulated steel joint for R90 Main beam Secondary beam Numerical model of fire insulated joint Temperature field of fire insulated joint Temperature field of steel parts of the joint

53 Advanced fire resistance design tools Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Application example of advanced structural analysis failure mode of bare steel structures exposed to fire Fire wall

54 Fire resistance assessment of steel structures Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Worked examples according to fire part of Eurocode 3

55 3.4 m 3.4x6 = 20.4 m Building in steel structure Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Office building with 6 levels of floor Standard fire resistance requirement: R60 Composite slab Bracing system

56 7 m 14 m S2 - S2 7 m Bracing system Bracing system Structure grid of the steel building Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Plan view of the steel structure two span continuous composite slab S m 6 m 6 m 6 m 6 m A 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m Bracing system B S1 S1 C Bracing system S2 S1 - S1

57 Sizes of the structural members Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Structural members Composite slab: Total thickness: 12 cm Steel deck: COFRAPLUS60 Thickness of steel deck: 0.75 mm Continuous slab over 2 spans Common secondary beams: IPE360 with steel grade of S275 Internal main beams: HEA360 with steel grade of S275 Columns for ground level: Edge columns (ground level): HEA300 with steel grade of S275 Central columns (ground level): HEB300 with steel grade of S275

58 Design loads of the steel structure Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Actions (for all floor levels) Self weight G1: composite slab unit weight: steel structural members: Permanent load G2: finishing, embedded services, partitions: Permanent load G3: Façade cladding load: Characteristic values of variable loads and y factors 2.12 kn/m² according to their sizes 1.50 kn/m² 2.00 kn/m Type q k y 1 y 2 Live load on floors 4.0 kn/m² Snow on roof 1.7 kn/m²

59 7 m 14 m S2 - S2 7 m Bracing system Bracing system Selected worked examples Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Secondary beams under end support of the continuous slabs 2. Secondary beams under central support of the continuous slabs 3. Simply supported central main beams 4. Central columns at ground level S m 6 m 6 m 6 m 6 m A 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m Bracing system B S1 4 3 S1 C 2 Bracing system S2 1 S1 - S1

60 7 m 14 m S2 - S2 7 m Bracing system Bracing system Worked example 1 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Secondary beams under end support of the continuous slabs S m 6 m 6 m 6 m 6 m A 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m Bracing system B S1 S1 C Bracing system S2 1 S1 - S1

61 1. Secondary beams under end support of the continuous slabs Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 1: Design mechanical action in fire design Summary of input data Office q s (G k = 3.62 kn/m²; Q k = 4.0 kn/m²) two span continuous slab Studied system End support of the slab = 0.75 q s x l Self weight of IPE360 = 0.56 kn/m q b (G k = kn/m; Q k =9.0 kn/m) 7 m

62 1. Secondary beams under end support of the continuous slabs Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 1: Design mechanical action in fire situation Design load in fire situation qfi,d,t Gb 0.75 k,1 2,1 k, 1 M V E fi,d,t = G k,j + 2,1 Q k,1 + 2,i Q k,i j 1 i 2 fi,d,t fi,d,t q q fi,d,t 8 L fi,d,t 2 L 2 G y Q l kn/ m end support of 2 span slab knm kn 0.6 (meeting area) kn/m

63 1. Secondary beams under end support of the continuous slabs Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 2: Classify member Bending member (IPE360) Relation 4.2 of Eurocode 3 part f y S275 Table 5.2 of Eurocode 3 part 1-1 M Rd c t w 72 Web class 1 Pure bending - + c t f = = 56.6 Flange class 1 Section class 1 = 4.96 = 7.07

64 1. Secondary beams under end support of the continuous slabs Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 3: Design resistance at ambient temperature Design resistance at ambient temperature according to and of Eurocode 3 part 1-1 Moment resistance (relation 6.13) M Rd M pl,rd W pl,y M0 f y knm kn/m W pl,y (cm 3 ) IPE A v (cm²) Vertical shear resistance (relation 6.18) V Rd V pl,rd A v f y M kn M0 = 1

65 1. Secondary beams under end support of the continuous slabs Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 4: Degree of utilisation with respect to two resistances without consideration of adaptation factors 1 and kn/m Relative to moment resistance (relation 4.24) m M M0 fi,d,t M0 0,M fi,m M,fi MRd M,fi Relative to vertical shear resistance (relation 4.24) m V M0 fi,d,t M0 0,V fi,v M,fi VRd M,fi M0 = M,fi = 1

66 1. Secondary beams under end support of the continuous slabs Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 4: Degree of utilisation (bare beam) modification with consideration of adaptation factors 1 and 2 for bare steel beams kn/m On the basis of relation four sides exposed (see 4.1(16) of EN ) m m m m m 0 = max(m 0,M,, m 0,V, ) = ,M, 0,M 1 2 0,V, 0,V Design value of degree of utilisation no adaptation factors for vertical shear

67 1. Secondary beams under end support of the continuous slabs Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 5: Critical temperature (bare beam) with simple calculation rule with accurate reduction factor table kn/m Simple calculation rule (relation 4.22) cr 1.19ln m C Linear interpolation of the reduction factor k y, (table 3.1) at 600 C: k y, = 0.47 at 700 C: k y, = 0.23 cr 667 C

68 1. Secondary beams under end support of the continuous slabs Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 4b: Degree of utilisation (insulated beam) modification with consideration of adaptation factors 1 and 2 for insulated steel beams kn/m On the basis of relation three sides exposed (insulated) m m m m m 0 = max(m 0,M,, m 0,V, ) = ,M, 0,M 1 2 0,V, 0,V Design value of degree of utilisation no adaptation factors for vertical shear

69 1. Secondary beams under end support of the continuous slabs Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 5b: Critical temperature (insulated beam) with simple calculation rule with accurate reduction factor table kn/m Simple calculation rule (relation 4.22) cr 1.19ln m C Linear interpolation of the reduction factor k y, (table 3.1) at 600 C: k y, = 0.47 at 700 C: k y, = 0.23 cr 687 C

70 7 m 14 m S2 - S2 7 m Bracing system Bracing system Worked example 2 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Secondary beams under central support of the continuous slabs S m 6 m 6 m 6 m 6 m A 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m Bracing system B S1 S1 C 2 Bracing system S2 S1 - S1

71 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 1: Design mechanical action in fire design Summary of input data Office q s (G k = 3.62 kn/m²; Q k = 4.0 kn/m²) two span continuous slab Studied system Central support of slab = 1.25 q s x l Self weight of IPE360 = 0.56 kn/m q b (G k = kn/m; Q k =15.0 kn/m) 7 m 7 m

72 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 1: Design mechanical action in fire situation Design load in fire situation E fi,d,t = G k,j + 2,1 Q k,1 + 2,i Q k,i j 1 i 2 G y Q l kn/ m qfi,d,t 1.25 k,1 2,1 k, 1 central support of 2 span slab 0.6 Two span continuous beam P fi,d,t = kn/m

73 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 2: Classify member Bending member (IPE360) Relation 4.2 of Eurocode 3 part f y Table 5.2 of Eurocode 3 part 1-1 c t w 72 Web class 1 M Rd - + Pure bending M Rd - + c t f = = 56.6 Flange class 1 Section class 1 = 4.96 = 7.07

74 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 3: Design resistance at ambient temperature two equal span continuous beam Plastic load-bearing capacity Moment resistance ratio n q fi,0,rd M fi M,0,Rd fi,0, Rd Plastic hinge position 1 n 1 n Load-bearing capacity 2M fi,0,rd 2 L L L M fi,0,rd M fi,0,rd Necessary vertical shear resistance at central support ( V n) fi,0,rd q fi,0,rd L 2 M fi,0, Rd L

75 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 3: Design resistance at ambient temperature Design resistance at ambient temperature according to Eurocode 3 part 1-1 Moment resistance (relation 6.13) M Rd M pl,rd W pl,y M knm Vertical shear resistance (relation 6.18) f y W pl,y (cm 3 ) IPE A v (cm²) V Rd A v fy 3 Vpl,Rd kn M0 = 1 M0

76 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 3a: Design resistance at ambient temperature (bare beam and four sides exposed) P fi,d,t = kn/m Modify sagging moment resistance at 20 C (relation 4.10) refer to Step 3 for M Rd M 2 0 fi,0,rd M Rd knm Modify hogging moment resistance at 20 C (relation 4.10) M fi,0,rd M Rd 1 2 M0 M,fi M0 M,fi knm

77 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 3a: Design resistance at ambient temperature (bare beam) two equal span continuous beam and four sides exposed section Plastic load-bearing capacity n MRd MRd n 1 n q fi,0,rd 2M Rd 2 L 70.1 kn/ m Step 4a: Degree of utilisation (bare beam) m0 qfi,d,t qfi,0, Rd 0.330

78 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 4a: Degree of utilisation (bare beam) two equal spans continuous beam and four sides exposed section Check of vertical shear resistance at central support Necessary vertical shear resistance at central support ( V n) fi,0,rd q fi,0,rd Vertical shear resistance of the beam at central support no adaptation factors for vertical shear ( n) As no further calculation is needed to modify the degree of utilisation L 2 M fi,0, Rd M0 V fi,0,rd VRd kn > M,fi V > fi,0,rd V fi,0,rd L V ( n) fi,0,rd kn

79 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 5a: Critical temperature (bare beam) with simple calculation rule (relation 4.22) with accurate reduction factor table (Table 3.1) Simple calculation rule (relation 4.22) cr 1.19ln m C Linear interpolation of the reduction factor k y, (Table 3.1) at 600 C: k y, = 0.47 at 700 C: k y, = 0.23 cr 658 C

80 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 3b: Design resistance at ambient temperature (insulated beam 3 sides exposed) P fi,d,t = kn/m Modify sagging moment resistance at 20 C (relation 4.10) refer to Step 3 for M Rd M 2 0 fi,0,rd M Rd knm Modify hogging moment resistance at 20 C (relation 4.10) M fi,0,rd M Rd 1 2 M0 M,fi M0 M,fi knm

81 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 3a: Design resistance at ambient temperature (insulated beam 3 sides exposed) Plastic load-bearing capacity n MRd MRd n 1 n q fi,0,rd 2M Rd 2 L 82.5 kn/ m Step 4b: Degree of utilisation (insulated beam 3 sides exposed) m0 qfi,d,t qfi,0, Rd 0.281

82 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 4b: Degree of utilisation (insulated beam 3 sides exposed) Two equal spans continuous beam Check of vertical shear resistance at central support Necessary vertical shear resistance at central support ( V n) fi,0,rd q fi,0,rd Vertical shear resistance of the beam at central support no adaptation factors for vertical shear ( n) As no further calculation is needed to modify the degree of utilisation L 2 M fi,0, Rd M0 V fi,0,rd VRd kn > M,fi V > fi,0,rd V fi,0,rd L V ( n) fi,0,rd kn

83 2. Secondary beams under central support of the continuous slab Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 5b: Critical temperature (insulated beam 3 sides exposed) with simple calculation rule (relation 4.22) with accurate reduction factor table (Table 3.1) Simple calculation rule (relation 4.22) cr 1.19ln m C Linear interpolation of the reduction factor k y, (Table 3.1) at 600 C: k y, = 0.47 at 700 C: k y, = 0.23 cr 679 C

84 7 m 14 m S2 - S2 7 m Bracing system Bracing system Worked example 3 Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Simply supported central main beams S m 6 m 6 m 6 m 6 m A 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m Bracing system B S1 3 S1 C Bracing system S2 S1 - S1

85 3. Simply supported central main beams Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 1: Design mechanical action in fire design Summary of input data Design load in fire situation Design load in fire situation two span continuous beam Studied system Central support of secondary beam = 1.25 q x L Self weight of HEA360 = 1.12 kn/m q b (G k = 1.12 kn/m; 3 m 6 m P fi,d,t Q k =0.0 kn/m)

86 3. Simply supported central main beams Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 1: Design mechanical action in fire situation Design load in fire situation E fi,d,t = G k,j + 2,1 Q k,1 + 2,i Q k,i j 1 i 2 Uniformely distributed load qfi,d,t Gk,1 y2,1q k, 1 Self weight kn/m Concentrated load from continuous secondary beam Pfi,d,t 1.25 Gk,1 y2,1q k, 1 L kn/ m design load of secondary beam in fire situation

87 3. Simply supported central main beams Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 1: Design mechanical action in fire situation both uniform and concentrated loads Design loading conditions in fire situation 1.12 kn/m kn Applied bending moment and vertical shear 2 qfi,d,tl Pfi,d,tl Mfi,d,t knm 2 2 P l fi,d,t Vfi,d,t qfi,d,tl kn 2 3 m

88 3. Simply supported central main beams Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 2: Classify member Bending member (HEA360) Relation 4.2 of Eurocode 3 part f y S275 Table 5.2 of Eurocode 3 part kn/m kn c t w 72 Web class 1 Pure bending - + c t f = = 56.6 Flange class 1 Section class 1 = 6.74 = 7.07

89 3. Simply supported central main beams Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 3: Design resistance at ambient temperature Design resistance at ambient temperature according to Eurocode 3 part 1-1 Moment resistance (relation 6.13) M Rd M pl,rd W pl,y M0 f y kn/m kn knm W pl,y (cm 3 ) HEA A v (cm²) Vertical shear resistance (relation 6.18) M0 = 1 V Rd V pl,rd A v f y M kn

90 3. Simply supported central main beams Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 4: Degree of utilisation with respect to two resistance forces without consideration of adaptation factors 1 and kn/m kn Relative to moment resistance (relation 4.24) m M M0 fi,d,t M0 0,M fi,m M,fi MRd M,fi Relative to vertical shear resistance (relation 4.24) m V M0 fi,d,t M0 0,V fi,v M,fi VRd M,fi M0 = M,fi = 1

91 3. Simply supported central main beams Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 4: Degree of utilisation modification with consideration of adaptation factors 1 and 2 for bare steel beams 1.12 kn/m kn On the basis of relation three sides exposed (bare) m m 134 m 0 = max(m 0,M,, m 0,V, ) = ,M, m0,m 1 2 0,V, m0,v 0. Design value of degree of utilisation no adaptation factors for vertical shear

92 3. Simply supported central main beams Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 5: Critical temperature (bare beams) with simple calculation rule with accurate reduction factor table 1.12 kn/m kn Simple calculation rule (relation 4.22) cr 1.19ln m C Linear interpolation of the reduction factor k y, (table 3.1) at 600 C: k y, = 0.47 at 700 C: k y, = 0.23 cr 639 C

93 3. Simply supported central main beams Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 4b: Degree of utilisation modification with consideration of adaptation factors 1 and 2 for insulated steel beams 1.12 kn/m kn On the basis of relation three sides exposed (insulated) m m m 134 m 0 = max(m 0,M,, m 0,V, ) = ,M, 0,M 1 2 0,V, m0,v 0. Design value of degree of utilisation no adaptation factors for vertical shear

94 3. Simply supported central main beams Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 5b: Critical temperature (insulated beam) with simple calculation rule with accurate reduction factor table 1.12 kn/m kn Simple calculation rule (relation 4.22) cr 1.19ln m C Linear interpolation of the reduction factor k y, (table 3.1) at 600 C: k y, = 0.47 at 700 C: k y, = 0.23 cr 606 C

95 7 m 14 m S2 - S2 7 m Bracing system Bracing system Worked examples Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Central columns at ground level S m 6 m 6 m 6 m 6 m A 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m 3 m Bracing system B S1 4 S1 C Bracing system S2 S1 - S1

96 4. Central column at ground level Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 1: Design mechanical action in fire design Summary of input data kn 311.8x5 kn Design load in fire situation kn Design load in fire situation 3.4 m Studied system Design load per level from secondary beam: 98.7 kn Design load per level from main beam: kn Self weight of HE300 = 1.15 kn/m

97 4. Central column at ground level Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 1: Design mechanical action in fire situation Design load in fire situation E fi,d,t = G k,j + 2,1 Q k,1 + 2,i Q k,i j 1 i 2 Self weight of the column q fi,d, t kN/ m Total concentrated axial load from steel beams Pfi,d,t Gk,1 y2,1q k, kn secondary beam main beam

98 4. Central column at ground level Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 1: Design mechanical action in fire situation Total design loading conditions in fire situation kn N fi,d, t kn Buckling length in fire situation pinned column base L fi 0.7L m

99 4. Central column at ground level Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 2: Classify member Bending member Relation 4.2 of Eurocode 3 part f y c t w S275 Table 5.2 of Eurocode 3 part 1-1 Web class 1 HEB300 - Compression c t f = = 25.9 Flange class 1 Section class 1 = 6.2 = 7.07

100 4. Central column at ground level Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 3: Design resistance at instant 0 (ambient temperature) Design resistance at instant 0 (ambient temperature) according to Eurocode 3 part 1-2 Plastic axial resistance N pl,fi,0 A f y M, fi Non-dimensional slenderness knm A (cm²) HEB i z (cm) 7.58 l fi,0 Af N y cr L i z fi

101 4. Central column at ground level Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 4: Degree of utilisation for tabulated data m Step 5: Critical temperature With N fi,d,t 0 N pl,fi, l fi and linear interpolation of tabulated data,0 l fi, m cr 560 C

102 Summary of critical temperatures Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Critical temperatures of all calculated steel members Bare and insulated Steel members Secondary beams under end support of continuous slab Secondary beams under central support of continuous slab Simply supported central main beam Critical temperatures ( C) Bare Insulated Central column at ground level

103 1. Secondary beams under end support of the continuous slabs Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 6: Heating of bare steel members under standard fire Change of steel temperature in time t (Section of EN ): a.t = k sh / (c a a ) A m /V h net.d t Four sides exposed: 800 cr = 667 C Section factor: A m /V = 186 m -1 (IPE360) 600 k sh = 0.9 x146/186 = (relation 4.26a) Net heat flux/unit area h net.d for ISO834 Standard Fire (EN ): Using f = 1.0 et m = 0.7 (Section 3.1) Using c = 25 W/m²K (Section 3.2.1) By calculation using Excel sheet with t = 5 seconds. ( (5) of EN ) 1000 Temperature ( C) ISO834 Bare Time (min) Time for bare steel to reach critical temperature = 17 min 00 sec

104 2. Secondary beams under central support of the continuous slabs Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 6: Heating of bare steel members under standard fire Change of steel temperature in time t (Section of EN ): a.t = k sh / (c a a ) A m /V h net.d t Four sides exposed: 800 cr = 658 C Section factor: A m /V = 186 m -1 (IPE360) 600 k sh = 0.9 x146/186 = (relation 4.26a) Net heat flux/unit area h net.d for ISO834 Standard Fire (EN ): Using f = 1.0 et m = 0.7 (Section 3.1) Using c = 25 W/m²K (Section 3.2.1) By calculation using Excel sheet with t = 5 seconds. ( (5) of EN ) 1000 Temperature ( C) Bare Time (min) Time for bare steel to reach critical temperature = 16 min 30 sec ISO834

105 3. Simply supported central main beams Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 6: Heating of bare steel members under standard fire Change of steel temperature in time t (Section of EN ): a.t = k sh / (c a a ) A m /V h net.d t Three sides exposed: cr = 639 C Section factor: A m /V = 107 m -1 (HEA360) k sh = 0.9 x70/107 = (relation 4.26a) Net heat flux/unit area h net.d for ISO834 Standard Fire (EN ): Using f = 1.0 et m = 0.7 (Section 3.1) Using c = 25 W/m²K (Section 3.2.1) By calculation using Excel sheet with t = 5 seconds. ( (5) of EN ) 1000 Temperature ( C) Bare Time (min) Time for bare steel to reach critical temperature = 23 min 10 sec ISO834

106 4. Central columns at ground level Workshop Structural Fire Design of Buildings according to the Eurocodes Brussels, November Step 6: Heating of bare steel members under standard fire Change of steel temperature in time t (Section of EN ): a.t = k sh / (c a a ) A m /V h net.d t Four sides exposed: cr = 560 C Section factor: A m /V = 116 m -1 (HEB300) k sh = 0.9 x 80/116 = (relation 4.26a) Net heat flux/unit area h net.d for ISO834 Standard Fire (EN ): Using f = 1.0 et m = 0.7 (Section 3.1) Using c = 25 W/m²K (Section 3.2.1) By calculation using Excel sheet with t = 5 seconds. ( (5) of EN ) 1000 Temperature ( C) Bare Time (min) Time for bare steel to reach critical temperature = 17 min 50 sec ISO834

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