Part 3: Mechanical response Part - - PowerPoint PPT Presentation

Part 3: Mechanical response 0 / 43

• Part 3: Mechanical response

Part 3: Mechanical response 1 / 43

• 4: Thermal

response

time

R 5: Mechanical response 6: Possible collapse

Resistance to fire - Chain of events Resistance to fire - Chain of events

time

Θ Θ Θ Θ 2: Thermal action 3: Mechanical actions

Loads

Steel columns

1: Ignition

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• 22 min θ = 720°

C t = 0 θ = 20° C 16 min θ = 620° C 31 min θ = 850° C

Temperature rise

• thermal expansion + loss of both

stiffness and resistance

• additional deformation ⇒

⇒ ⇒ ⇒ eventual collapse

How structures react to fire How structures react to fire

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• Assessment of mechanical response of

structures in fire Assessment of mechanical response of structures in fire

Standard Fire Time Deflection

Design

Fire tests Load-bearing resistance Time P P P Purpose to describe structural behaviour under any type of fire condition Means

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• Basic features related to assessment of

mechanical response of steel structures in fire Basic features related to assessment of 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 5 / 43

• Gk,j : characteristic values of permanent actions

Qk,1 : characteristic leading variable action Qk,i : characteristic values of accompanying variable actions

ψ ψ ψ ψ1,1 : factor for frequent value of a leading variable

action

ψ ψ ψ ψ2,i : factor for quasi-permanent values of accompaning

variable actions

Mechanical loading – combination according to Eurocode (EN1990 and EN1991-1-2) Mechanical loading – combination according to Eurocode (EN1990 and EN1991-1-2)

∑ ∑ ∑ ∑Gk,j + (Ψ

Ψ Ψ Ψ1,1 or Ψ Ψ Ψ Ψ2,1) Qk,1 + ∑

∑ ∑ ∑ Ψ

Ψ Ψ Ψ2,i Qk,i

j ≥ ≥ ≥ ≥ 1 i ≥ ≥ ≥ ≥ 2

Load level: η

η η ηfi,t (see presentation of WP1)

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• Normalised stress

Strain (%) 20° C 200° C 400° C 500° C 600° C 700° C 800° C 0.2 0.4 0.6 0.8 1 5 10 15 20

Mechanical properties of structural steel at elevated temperatures (prEN1993-1-2) Mechanical properties of structural steel at elevated temperatures (prEN1993-1-2)

Elastic modulus at 600°

C reduced by about 70%

Yield strength at 600°

C reduced by over 50% 300 600 900 1200 100 80 60 40 20 % of normal value Temperature (° C) Effective yield strength Elastic modulus Strength

Part 3: Mechanical response 7 / 43

• Mechanical properties of concrete at elevated

temperatures (prEN1994-1-2) Mechanical properties of concrete at elevated temperatures (prEN1994-1-2)

Compressive strength at 600°

C reduced by about 50%

600° C 20° C

Strain (%) Normalised stress

εcu

200° C 400° C 800° C

1 2 3 4 1.0 0.8 0.6 0.4 0.2 Temperature (° C) Strain (%) % of normal value Strain εcu at maximum strength Normal- weight Concrete Strength 6 5 4 3 2 1 100 50 400 800 1200

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• Thermal expansion of steel and concrete

(prEN1993-1-2 and prEN1994-1-2) Thermal expansion of steel and concrete (prEN1993-1-2 and prEN1994-1-2)

5 10 15 20 200 400 600 800 1000 1200

temperature (° C)

steel normal concrete

∆ ∆ ∆ ∆L/L (x103)

Part 3: Mechanical response 9 / 43

• global structural analysis

member analysis (mainly when verifying standard fire resistance requirements) analysis of parts of the structure

Different design approaches for mechanical response of structure in fire Different design approaches for mechanical response of structure in fire

Three different approaches according to Eurocodes

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• interaction effects between

different parts of the structure role of compartment global stability

independent structural element analysis simple to apply generally for nominal fire condition Global structural analysis Member analysis

Different design approaches for mechanical response of structure in fire Different design approaches for mechanical response of structure in fire

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• Advanced

and specific fire design Classic and traditional application Tabulated data composite structural members Simple calculation models critical temperature steel and composite structural members Advanced calculation models all types of structures numerical models based on:

• finite element method
• finite difference method

Three types of design methods for assessing mechannical response of structures in fire Three types of design methods for assessing mechannical response of structures in fire

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• Yes

Not applicable Not applicable Global structural analysis Yes Yes (if available) Not applicable Analysis of a part of the structure Yes Yes Yes

ISO-834 standard fire

Member analysis Advanced calculation models Simple calculation models Tabulated data Type of analysis

Application domain of different design methods under fire situation Application domain of different design methods under fire situation

Thermal action defined with nominal fires

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• Yes

Not applicable Not applicable Global structural analysis Yes Not applicable Not applicable Analysis of a part of the structure Yes Yes (if available) Not applicable Member analysis Advanced calculation models Simple calculation models Tabulated data Type of analysis

Application domain of different design methods under fire situation Application domain of different design methods under fire situation

Thermal action defined with natural fires

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• Tabulated data

(steel and concrete composite members) Tabulated data (steel and concrete composite members)

Composite columns Composite beams

Concrete for insulation Slab

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• Tabulated data and relevant parameters

(composite columns – prEN1994-1-2) Tabulated data and relevant parameters (composite columns – prEN1994-1-2)

Standard Fire Resistance

c

A s u s

u s w e f e

b

A

h

R30 R60 R90 R120

Minimum ratio of web to flange thickness ew/ef 0,5 1 Minimum cross-sectional dimensions for load level η η η ηfi,t ≤ 0,28 1.1 1.2 1.3 minimum dimensions h and b [mm] minimum axis distance of reinforcing bars us [mm] minimum ratio of reinforcement As/(Ac+As) in % 160

• 200

50 4 300 50 3 400 70 4 2 Minimum cross-sectional dimensions for load level η η η ηfi,t ≤ 0,47 2.1 2.2 2.3 minimum dimensions h and b [mm] minimum axis distance of reinforcing bars us [mm] minimum ratio of reinforcement As/(Ac+As) in % 160

• 300

50 4 400 70 4

• 3

Minimum cross-sectional dimensions for load level η η η ηfi,t ≤ 0,66 3.1 3.2 3.3 minimum dimensions h and b [mm] minimum axis distance of reinforcing bars us [mm] minimum ratio of reinforcement As/(Ac+As) in % 160 40 1 400 70 4

• Standard

fire rating Load level Section dimension Concrete cover Reinforcing steel

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• Section dimension

reinforcing steel concrete cover

η η η ηfi = Efi.d / Rd Efi.d

Rd of θ θ θ θ20°

C

VERIFICATION PRE-DESIGN

How to apply tabulated data in fire design (two different situations) How to apply tabulated data in fire design (two different situations)

Section dimension reinforcing steel concrete cover

η η η ηfi = Efi.d / Ed Efi.d and Ed

Rd ≥ ≥ ≥ ≥ Ed

Standard fire rating

Standard fire rating

Part 3: Mechanical response 17 / 43

• Simple calculation model

(steel and composite members) Simple calculation model (steel and composite members)

Columns Beams (steel or composite)

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• D

F M

t Rd , fi

× × × × = = = =

+ + + +

+ + + +

+ + + +

• Stress

distribution

+

Temperature distibution Section geometry Section S1

Connector S1 Concrete slab Steel section S1 D+ Ft

+

F

c +

Moment resistance

Simple calculation model (composite beam)

• plastic resistance theory

Simple calculation model (composite beam)

• plastic resistance theory

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• Simple calculation model (composite column)
• buckling curve

Simple calculation model (composite column)

• buckling curve

Lfi P Z Y Effective section Aai Acj Ask

Load capacity: Nfi.Rd = χ χ χ χ(λ λ λ λθ

θ θ θ) Nfi.pl.Rd

0.5 1.0 λ λ λ λθ

θ θ θ

Appropriate buckling curve

χ χ χ χ(λ λ λ λθ

θ θ θ)

χ χ χ χ(λ λ λ λθ

θ θ θ) ⇐ strength and rigidity of effective section +

column buckling length Lfi

Part 3: Mechanical response 20 / 43

• Critical temperature method (only steel

members and certain composite beams) Critical temperature method (only steel members and certain composite beams)

Columns Beams (steel and composite)

Part 3: Mechanical response 21 / 43

• Critical temperature method

Critical temperature method

According to simple calculation models, for uniformly heated steel members: Rfi,d,t = ky,θ

θ θ θ Rfi,d,0

On the other hand, fire resistance should satisfy: In particular, when ky,θ

θ θ θ = µ

µ µ µ0 the corresponding temperature is defined as critical temperature θ θ θ θcr θ θ θ θcr = 39.19 ln 0.9674µ µ µ µ0

3.833

1

• 1 +482

Rfi,d,t ≥ ≥ ≥ ≥ Efi,d = Rfi,d,0 Efi,d Rfi,d,0 = µ µ µ µ0Rfi,d,0 ky,θ

θ θ θ ≥

≥ ≥ ≥ µ µ µ µ0 In EN1993-1-2, a simple formula is given to determine critical temperature θ θ θ θcr

Part 3: Mechanical response 22 / 43

• Design resistance at 20°

C: Rd

• r design action at 20°

C: Ed Action in fire Efi.d

How to apply critical temperature method How to apply critical temperature method

Critical temperature: θ θ θ θcr

• direct method
• iterative method

Load level in fire: η η η ηfi,t = Efi,d Rd Utilisation level: µ µ µ µ0

0 = η

η η ηfi,t γ γ γ γM,fi γ γ γ γM

Part 3: Mechanical response 23 / 43

• Why direct and iterative critical temperature

method (case of steel column) Why direct and iterative critical temperature method (case of steel column)

• Short column

without instability

Nb,fi,t,Rd = A ky,θ

θ θ θmax fy

1 γ γ γ γM,fi

• Column with risk
• f buckling

Nb,fi,t,Rd=χ χ χ χ(λ λ λ λθ

θ θ θ)Aky,θ θ θ θmaxfy

1 γ γ γ γM,fi

Strength reduction factor ky.θ

θ θ θ.max at θ

θ θ θa,max Reduction factor of buckling χ χ χ χ(λ λ λ λθ

θ θ θ) depends on:

• strength
• stiffness
• As a consequence, simple iterative procedure is needed

to find the accurate θ θ θ θa,max in case of instability problem

Part 3: Mechanical response 24 / 43

• Simulated failure mode

Tested failure mode

50 100 150 200 250 300 20 40 60 80 100 120 140

time (min) Deflection (mm)

test calculation

Calculation vs test

Advanced calculation model for any case (steel and concrete composite cellular beam) Advanced calculation model for any case (steel and concrete composite cellular beam)

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• necessary to use advanced

calculation model choice of appropriate structural modeling existing boundary conditions loading conditions appropriate material models restrained condition in relation with unmodeled parts of the structure

Fire design by global structural analysis Fire design by global structural analysis

analysis of results and check on failure criteria review of untreated features in direct analysis (consistency between numerical model and constructional details) General rules

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• Application requirement of advanced calculation models

requirement on material models

• strain composition
• kinematical material model
• strength during cooling phase

step by step iterative solution procedure check of possible failure untreated in direct analysis

• rupture due to excessive steel elongation
• cracking and crushing of concrete

Fire design by global structural analysis Fire design by global structural analysis

Part 3: Mechanical response 27 / 43

• εt: total strain

εt: strain due to thermal elongation εσ: strain due to stress tensor εr: strain due to residual stress (if appropriate) εc: strain due to creep

Requirement on material model Requirement on material model

z y G

ε ε ε εth ε ε ε εc ε ε ε εt ε ε ε εr

θ θ θ θ

ε ε ε εσ

σ σ σ

Temperature distribution z = constant Unitary strain Section

εt = εth + (εσ + εc)+ εr

Strain composition

Part 3: Mechanical response 28 / 43

• ε

ε ε ε

parallel to (θ θ θ θ2, ε ε ε ε = 0) dε ε ε ε dσ σ σ σ                         θ θ θ θ2 = θ θ θ θ (t+∆ ∆ ∆ ∆t) parallel to (θ θ θ θ1, ε ε ε ε = 0) dε ε ε ε dσ σ σ σ                         θ θ θ θ1 = θ θ θ θ (t)

ε ε ε ε σ σ σ σ

Compression Tension θ θ θ θ2 = θ θ θ θ (t+∆ ∆ ∆ ∆t) θ θ θ θ1 = θ θ θ θ (t)

Concrete (compression-tension anisotropic material) Steel (isotropic material)

Requirement on material model Requirement on material model

kinematical material model

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• t0 = 0

θ0 = 20° C t1 = 20 min θ1 = 710° C t2 = 27 min θ2 = 760° C

t0= 0 θ θ θ θ0 t1 θ θ θ θ1 t 2 θ θ θ θ2

Loading

Pfi

Displacement U

Step by step iterative solution procedure Step by step iterative solution procedure

Calculation procedure must take account of temperature dependance of both stiffness and strength of the structure

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• For example if θ

θ θ θmax ≥ ≥ ≥ ≥ 300 ° C fc,θ,20°

C = 0.9 fc,θ max

Linear interpolation applies to fc,θ for θ θ θ θ between θ θ θ θmax and 20° C

Material strength during cooling phase Material strength during cooling phase

Steel recovers its initial strength during cooling phase Concrete during cooling phase 20 300 Time θ θ θ θmax Temperature of concrete tmax Time 1.0 Strength fc,θ max 0.9 fc,θ max tmax

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• Standard part of the

floor system Composite slab 15 m 15 m 15 m 10 m 10 m 10 m 3.2 m 4.2 m

Global analysis of steel and concrete composite floor under localised fire Global analysis of steel and concrete composite floor under localised fire

Steel deck: 0.75 mm

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• Choice of structural model

Choice of structural model

Two different structural models may be adopted 2D composite frame model (beam elements)

• membrane effect is limited to one direction due to

1D effect slab model

• load redistribution is not possible between parallel

beams 3D composite floor model (multi-type element)

• membrane effect over whole floor area
• load redistribution becoming possible with help of

shell elements More realistic to apply 3D composite floor model

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• Validity of 3D composite floor model

Validity of 3D composite floor model

• 200
• 160
• 120
• 80
• 40

15 30 45 60 75

Time (min)

• Vert. Disp. (mm)

Test

• Cal. 3D
• Cal. 2D

20 40 60 20 40 60 80

Time (min)

• Hori. Disp. (mm)

Test 3D calculation model

Part 3: Mechanical response 34 / 43

• Strategy of 3D composite floor modelling

Strategy of 3D composite floor modelling

Global structure without composite slab Fire area Detail of numerical modelling

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• θ = 0

θ = 0

Continuity condition

• f concrete slab

Continuity condition of columns

Mechanical loading and boundary conditions Mechanical loading and boundary conditions

Uniformly distributed load: G + Ψ

Ψ Ψ Ψ1,1Q

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• 20 min

140 mm 40 min 310 mm

Mechanical response of the structure Mechanical response of the structure

Total deflection of the floor and check of the corresponding failure criteria

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• 60 min

230 mm 110 mm ≤ L/20 = 500 mm 280 mm ≤ L/20 = 750 mm

Mechanical response of the structure Mechanical response of the structure

Total deflection of the floor and check of the corresponding failure criteria

• 300
• 250
• 200
• 150
• 100
• 50

10 20 30 40 50 60

Time (min) Deflection (mm) Secondary beam Main beam

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• Check of failure criteria: elongation of reinforcing steel

Strain of reinforcing steel // slab span 1.4 % ≤ 5 % Strain of reinforcing steel ⊥ ⊥ ⊥ ⊥ slab span 1.3 % ≤ 5 %

Mechanical response of the structure Mechanical response of the structure

Part 3: Mechanical response

• Maximum gap of 15

mm between beam and column and between lower flange of the beam gap gap ≤ 15 mm

Construction details shall be respected in prder to consistent with numerical models Construction details shall be respected in prder to consistent with numerical models

Reinforcing bars between slab and edge columns φ φ φ φ12 in S500

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• Real building with bare steel frames based on

global structural analysis Real building with bare steel frames based on global structural analysis

During construction Finished

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• Constructional details

Joint details (steel and composite) Connection between steel and concrete

• Connectors
• Reinforcing steel

Behaviour during cooling phase under natural fire Joint

Specific consideration in fire design of steel and composite structures Specific consideration in fire design of steel and composite structures

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• Join detail - Example

gap Continuous reinforcing bar Sections with infilled concrete studs

A limited gap allowing to develop a hogging moment in the fire situation

Construction details to get hogging moment resistance in fire situation (prEN1994-1-2) Construction details to get hogging moment resistance in fire situation (prEN1994-1-2)

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• Connection between steel profile and encased concrete

Construction details for connection between concrete and steel (prEN1994-1-2) Construction details for connection between concrete and steel (prEN1994-1-2)

Welding of stirrups to the web

welding

φr ≥ 8 mm aw ≥ 0,5 φs lw ≥ 4 φs φr ≥ 8 mm φs ≥ 6 mm Welding of studs to the web

studs

d ≥ 10 mm hν ≥ 0,3b b hν

Part 3: Mechanical response 44 / 43