��� ��� Part 3: Mechanical response ��� ��� ��� ��� Part 3: Mechanical response 0 / 43
Resistance to fire - Chain of events Resistance to fire - Chain of events Loads Θ Θ Θ Θ Steel columns time 1: Ignition 2: Thermal action 3: Mechanical actions R time 6: Possible 4: Thermal 5: Mechanical collapse response response ��� ��� ��� ��� Part 3: Mechanical response 1 / 43
How structures react to fire How structures react to fire � Temperature rise � � thermal expansion + loss of both � � � additional deformation ⇒ ⇒ ⇒ ⇒ stiffness and resistance � � � eventual collapse t = 0 θ = 20° 16 min θ = 620° C C 22 min θ = 720° θ = 850° C 31 min C ��� ��� ��� ��� Part 3: Mechanical response 2 / 43
Assessment of mechanical response of Assessment of mechanical response of structures in fire structures in fire � Purpose � to describe structural behaviour under any type of fire condition P � Means Design Fire tests P Load-bearing Deflection resistance P Standard Fire Time Time ��� ��� ��� ��� Part 3: Mechanical response 3 / 43
Basic features related to assessment of Basic features related to assessment of mechanical response of steel structures in fire mechanical response of steel structures in fire � Mechanical loadings under fire situation � specific load combination � Mechanical properties of relevant materials at elevated temperatures � stiffness and resistance varying with temperatures � Assessment methods for structural analysis in fire � different approaches � application domain � Specific consideration in fire design of steel and composite structures � connections, joints, etc ��� ��� ��� ��� Part 3: Mechanical response 4 / 43
Mechanical loading – combination according Mechanical loading – combination according to Eurocode (EN1990 and EN1991-1-2) to Eurocode (EN1990 and EN1991-1-2) ∑ G k,j + ( Ψ ∑ ∑ ∑ Ψ 2,1 ) Q k,1 + ∑ ∑ ∑ Ψ ∑ Ψ 1,1 or Ψ Ψ 2,i Q k,i Ψ Ψ Ψ Ψ Ψ Ψ i ≥ ≥ ≥ 2 ≥ j ≥ ≥ ≥ ≥ 1 G k,j : characteristic values of permanent actions Q k,1 : characteristic leading variable action Q k,i : characteristic values of accompanying variable actions ψ 1,1 : factor for frequent value of a leading variable ψ ψ ψ action ψ 2,i : factor for quasi-permanent values of accompaning ψ ψ ψ variable actions � Load level: η η fi,t (see presentation of WP1) η η ��� ��� ��� ��� Part 3: Mechanical response 5 / 43
Mechanical properties of structural steel at Mechanical properties of structural steel at elevated temperatures (prEN1993-1-2) elevated temperatures (prEN1993-1-2) Strength % of normal value Normalised stress 20° C 200° C 400° C Effective yield 1 100 strength 500° C 0.8 80 0.6 60 600° C 0.4 40 700° C Elastic 0.2 20 800° C modulus 0 0 300 600 900 1200 0 5 10 15 20 Temperature (° C) Strain (%) � Elastic modulus at 600° C � Yield strength at 600° C reduced by about 70% reduced by over 50% ��� ��� ��� ��� Part 3: Mechanical response 6 / 43
Mechanical properties of concrete at elevated Mechanical properties of concrete at elevated temperatures (prEN1994-1-2) temperatures (prEN1994-1-2) Strength Normalised stress % of normal value Strain (%) 1.0 20° C 6 Strain ε cu at 200° C 5 100 maximum 0.8 400° C strength 4 0.6 3 600° C Normal- 50 0.4 weight 2 Concrete 0.2 1 800° C 0 0 1200 400 800 1 2 3 4 Temperature (° C) ε cu Strain (%) � Compressive strength at 600° C reduced by about 50% ��� ��� ��� ��� Part 3: Mechanical response 7 / 43
Thermal expansion of steel and concrete Thermal expansion of steel and concrete (prEN1993-1-2 and prEN1994-1-2) (prEN1993-1-2 and prEN1994-1-2) ∆ L/L (x10 3 ) ∆ ∆ ∆ 20 normal concrete 15 10 steel 5 0 0 200 400 600 800 1000 1200 temperature (° C) ��� ��� ��� ��� Part 3: Mechanical response 8 / 43
Different design approaches for mechanical Different design approaches for mechanical response of structure in fire response of structure in fire � Three different approaches according to Eurocodes global structural analysis analysis of parts of the structure member analysis (mainly when verifying standard fire resistance requirements) ��� ��� ��� ��� Part 3: Mechanical response 9 / 43
Different design approaches for mechanical Different design approaches for mechanical response of structure in fire response of structure in fire Member analysis Global structural analysis � interaction effects between � independent structural � element analysis � different parts of the structure � simple to apply � role of compartment � generally for nominal � global stability � fire condition ��� ��� ��� ��� Part 3: Mechanical response 10 / 43
Three types of design methods for assessing Three types of design methods for assessing mechannical response of structures in fire mechannical response of structures in fire � Tabulated data � composite structural members Classic and � Simple calculation models traditional application � critical temperature � steel and composite structural members � Advanced calculation models � all types of structures Advanced � numerical models based on: and specific fire design • finite element method • finite difference method ��� ��� ��� ��� Part 3: Mechanical response 11 / 43
Application domain of different design Application domain of different design methods under fire situation methods under fire situation � Thermal action defined with nominal fires Simple Advanced Tabulated data Type of calculation calculation analysis models models Member Yes Yes Yes analysis ISO-834 standard fire Analysis of a Yes part of the Not applicable Yes (if available) structure Global Not Yes structural Not applicable applicable analysis ��� ��� ��� ��� Part 3: Mechanical response 12 / 43
Application domain of different design Application domain of different design methods under fire situation methods under fire situation � Thermal action defined with natural fires Simple Advanced Tabulated Type of calculation calculation data analysis models models Member Not Yes Yes analysis applicable (if available) Analysis of a Not Not part of the Yes applicable applicable structure Global Not Not Yes structural applicable applicable analysis ��� ��� ��� ��� Part 3: Mechanical response 13 / 43
Tabulated data Tabulated data (steel and concrete composite members) (steel and concrete composite members) Composite Composite columns beams Slab Concrete for insulation ��� ��� ��� ��� Part 3: Mechanical response 14 / 43
Tabulated data and relevant parameters Tabulated data and relevant parameters (composite columns – prEN1994-1-2) (composite columns – prEN1994-1-2) e f Standard A A s c Standard Fire h fire rating Resistance u s e Load level w u s b R30 R60 R90 R120 Minimum ratio of web to flange thickness e w /e f 0,5 Section η η η η fi,t ≤ 0,28 1 Minimum cross-sectional dimensions for load level dimension minimum dimensions h and b [mm] 1.1 160 200 300 400 minimum axis distance of reinforcing bars us [mm] 1.2 - 50 50 70 1.3 - 4 3 4 minimum ratio of reinforcement A s /(A c +A s ) in % η fi,t ≤ 0,47 η 2 Minimum cross-sectional dimensions for load level η η Reinforcing minimum dimensions h and b [mm] 2.1 160 300 400 - minimum axis distance of reinforcing bars us [mm] 2.2 - 50 70 - steel 2.3 minimum ratio of reinforcement A s /(A c +A s ) in % - 4 4 - 3 Minimum cross-sectional dimensions for load level η η η η fi,t ≤ 0,66 Concrete minimum dimensions h and b [mm] - - 3.1 160 400 - - 3.2 minimum axis distance of reinforcing bars us [mm] 40 70 cover - - 3.3 1 4 minimum ratio of reinforcement A s /(A c +A s ) in % ��� ��� ��� ��� Part 3: Mechanical response 15 / 43
How to apply tabulated data in fire design How to apply tabulated data in fire design (two different situations) (two different situations) VERIFICATION PRE-DESIGN R d of θ θ 20° θ θ E fi.d and E d C η fi = E fi.d / E d η η η E fi.d η η η η fi = E fi.d / R d Standard fire rating Section dimension Section dimension reinforcing steel reinforcing steel concrete cover concrete cover R d ≥ ≥ E d ≥ ≥ Standard fire rating ��� ��� ��� ��� Part 3: Mechanical response 16 / 43
Simple calculation model Simple calculation model (steel and composite members) (steel and composite members) Beams (steel or composite) Columns ��� ��� ��� ��� Part 3: Mechanical response 17 / 43
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