Calculul La Actiunea Focului a Structurilor Din Otel

7/27/2019 Calculul La Actiunea Focului a Structurilor Din Otel

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DESIGN OF STEEL STRUCTURES TO FIRE ACTION



DESIGN OF STEEL STRUCTURES TO FIRE ACTION ACCORDING TO ENV 1993-2

Steel structures must be designed to fire according to the following considerations: to maintain their resistance for a certain designed period of time;

to restrain the extension of the fire inside the buildings; to limit the possibility of the fire propagation to other surrounding buildings; to insure the free exit of the inhabitants and their saving; to insure the security of access and operation of the firemen units.

Inside European space, these essential demands are fulfilled in two accepted ways:through conventional scenarios to fire (nominal fire) or by natural scenarios to fire ( parametric fire ).

In the same time, passive protection methods are recommended during the structural

design process, like:- sprinklers;- fire compartments inside buildings;- protection against fire with authorized materials.

Partial safety factors and characteristic values of resistance of materials are probabilistic

determined.











CALCULATION PROCEDURES

Elements for the simplification of the design procedures: tabulated values for the designproposed solutions.

Basic requirements

1. Nominal fire exposure: the structural elements must comply with the R criterion, considering

the resistance (the hydro-carbides curve is defined with HC).

2. Parametric fire exposure: the structure integrity is insured during the whole period of fire

action, including the cooling.

Actions- thermal and mechanical actions;- the emission on the surface of the ordinary steel elements is 0,7 and 0,5 on the surface of

the stainless steel elements (annex C)



Design values of the materials characteristics: ii f M k f d X k X ,0, /γ ⋅=

X k - strength or deformation (characteristic value);

γ M,fi - partial safety factor, equal with 1,0.

The structural model imposed by ENV 1993 is in concordance with the expected behavior against fireaction during the specific period of time, t. The verification is run considering the following relationship:

t fid fid R E ,,,

≤

The structural analysis is according to EN 1990

Methods for verification:- for the analysis of the structural elements at t=0, normal temperature, the combination factors are ψ 1,1

and ψ 2,1;

- for the fundamental group of actions:

d fi fid E E ⋅=η ,

ηfi – reduction factor:

Variation of ηfi with the ratio Qk,1/Gk

Recommended values for η fi : 0,65 excepting live

loads in E category, for which the value is 0,7



Analysis of parts of the structures

As an alternative, for a fire event at t = 0, reactions and sectional efforts at the base of the

structure may be obtained for a normal temperature; the specific part of the structure will be

analyzed for thermal deformations and elongations such as the interaction with the main structure in

order to observe if it is correctly approximated. The end restraints and supports must provide an

independent behavior for the specific part of the structure analyzed. The analysis of this part of structure will take into account the variations of the strength and

stiffness of the materials and the thermal effects of the fire (elongations, deformations) The supports conditions and the efforts at the base of this part of structure must remain constant

during the fire exposure

Structural global analysis

Carbon steel properties of strength and deformation-for rising temperatures with speeds between 2…50 K/min these properties are determined graphically:

(tension, compression, shear);- the tabulated values of the reducing factors of the mechanical characteristics are determined for 20 0

C and defined as it follows:

- the effective yield limit : ky,θ=f y,θ/f y;

- the limit of proportionality (E=ct) : kp,θ=f p,θ/f y;

- the longitudinal elastic module: kE,θ = Ea,θ/Ea

For temperatures up to 4000C the diagram σ-ε may be extended by considering the strain

hardening (annex A) provided the failure will not occur ( local buckling, overall buckling)







REDUCTION FACTORS FOR THE STRESS STRAIN CURVE OF THE CARBON STEEL AT HIGH TEMPERATURES



Relative thermal elongation:

-for 200C≤θa≤7500C:

-for 7500C≤θa≤8600C:

-for 8600C≤θa≤12000C:

Relative elongation of the carbon steel due to increased temperatures

Relative elongation ∆l/l [x10-3 ]

Temperature [0C]



Thermal conductivity of the carbon steel relative to increasing temperature

Thermal conductivity [W/mK]

Temperature [0C]

SPECIFIC HEAT ca

where θa- temperature of the steel [0C]

THERMAL CONDUCTIVITY, λa



DESIGN TO FIRE ACTION OF STEEL STRUCTURES

The methods adopted in the code refer to:- Unprotected elements;- Protected with specific materials;

- Protected with thermal screens.Note: other methods of protection may consist in filling up with water the hollow sections, including the elements in

the area of the floors.

The determination of the strength to fire action may be adopted through three methods:- Simplified design methods;- Advanced design methods;- Experimental tests.

A. Simplified methods t d fid fi R E ,,,

≤

E fi,d - according to ENV 1991-1-2; it represents: NEd, MEd, Ved;

R fi,d,t – Nt,Rd, Mt,Rd, Vt,Rd

Specifications:The design to fire does not include the analysis of the weakened sections in bolted connections; the presence of

mechanical fasteners diminish the local temperature.

The resistance to fire of the connections is not verified if the thermal resistance (d f / λ f ) is ≥ minimum thermal

resistance of any of the parts of the connection.

In the relationship:

df –thickness of the insulation material;

λf – thermal conductivity of the insulation.



Classes of the steel sections

The method of classification is the same as for normal temperatures, excepting the reduced value of

ε:

[ ] 5,0

yf /23585,0 ⋅=ε

Resistance

1.Members in tension

The resistant force Nfi,0,Rd inside of a tensioned element at the time t, exposed to an uniform temperature θa on the

whole cross section is determined with the relationship:

where NRd = Npl,Rd

In the case of an un-uniform exposure in the cross section:

where:

Ai -elementary area of the cross section with a distinct temperature θi ;

θi - the temperature of the elementary area.

The resistant force of a tensioned member at time t having an un-uniform distribution of the temperature on the

cross section, may be considered equal with the resistant force N fi, t, Rd developed for a member exposed to constant

temperature θ a equal with the maximum temperature of the steel reached in the time t.



2. Members in compression- class 1, 2 and 3

where:

χb – buckling reduction factor in the design to fire; it is taken

the minimum between χy, fi and χz ,fi and is determined with:

Reduced slenderness θ λ for temperature θ a :

The effective length lfi of column exposed to fire is determined identically as for normal conditions; allowances are

made for the situations in which fixing points are considered in the plane of the fire compartments.

In the case of a rigid connected frame for which every storey is considered separately as resistant to fire l fi=0,5L,

excepting the last storey where lfi=0,7L.

If a nominal fire effect is considered, axial buckling resistance N b,fi,t,Rd, of the compressed member un-uniformly

exposed to fire may be equalized with the resistance of a member uniformly exposed, N b,fi,θ,Rd, considering θmax the

temperature reached on the surface of the steel



Beams with cross sections in class 1 or 2

Moment resistance of a beam exposed to a constant temperature θa is determined with the relationship:

MRd is determined at normal temperature, according to ENV 1993-1-1;

ky,θ factor of reducing the yield limit of steel for the temperature θa

Moment resistance of a beam exposed to a constant temperature θa is determined with the relationship:

zi-distance from the neutral axis in plastic distribution of the stresses on the whole cross section of an

elementary area Ai ;

f y,i- yield limit for the elementary area; it is considered positive in the compressed area and negative in the

tensioned area with respect to the neutral axis in plastic.



As an alternative the moment resistance Mfi,,Rd for a section in class 1 and 2 of an element with an un-uniform

distribution of the temperature may be determined with the relationship:

M fi,θ,Rd/k1k2 moment resistance of a cross section subjected to an uniform θa, equal to an uniform temperature

temperature at the time t, thermally non-affected by the supports;k1- factor of adapting the cross section to un-uniform temperature;

k2- factor of adapting the un-uniform temperature of the steel on the length of the beam

Moment resistance to flexural-torsional buckling M b,fi,t,Rd for an element with the cross section in class 1 and 2 is

determined with the relationship:

χLT, fi- reduction factor due to lateral buckling (torsional) for an element in bending exposed to fire;

k y, θ, com - reduction factor of the yield limit of steel for the maximum temperature θa,com, reached at the time t in the

compressed flange; θa,com may be conservatively considered uniform on the whole cross section.

χLT, fi- is determined with the relationship:

where:

K,E,θ,com - the reduction factor for the part of the cross section having an linear elastic behaviour at maximum temperature

θa,com in the flange in compression at the time t.



The resistance to shear Vfi, t, Rd of a transversal section in class 1 or 2 is determined with the relationship:

V Rd - shear resistance of a cross section at normal temperature, according to EN 1993-1-1;

θweb – averaged temperature on the cross section;

ky,θ,web – reduction factor of the yield limit of the steel for the temperature θweb

The value of the coefficient k1 of adapting the un-uniform temperature of the steel on the cross section is

considered as it follows:- A beam equally exposed to fire all around its four faces: k1= 1,0;

- A beam un-protected and exposed to fire on three faces, the fourth being in contact with the floor: k1= 0,7;- A beam protected and exposed to fire on three faces, the fourth being in contact with the floor: k1=0,85;

A non uniform distribution of the temperature along the beam the adapting factor k2 must be considered as it

follows:

-the supports of static un-determined beams: k2=0,85;

-for the other cases: k2=1,0



Beams in class 3

The moment resistance in the case of an uniform distribution of temperature is determined with the relationship:

MRd -plastic moment resistance of the cross section, M pl,Rd for normal temperature, respectively, according to

EN 1993-1-1;

K y,θ - reduction factor of the yield limit for the temperature θa

In the case of an un-uniform distribution of the temperature the moment resistance Mfi,t,Rd, is determined with

the relationship:

MRd-plastic moment resistance of the cross section for the design according to EN 1993-1-1;

Ky,θ,max – reduction factor of the yield limit;

K1 –factor of adapting the transversal section to un-uniform temperature;

K2 – factor of adapting the steel element to un-uniform temperature longitudinally.

Moment resistance to lateral buckling, Mb,fi,t,Rd for a class 3 beam considering the torsional buckling is determined

with the relationship:

Shear resistance Vfi,t,Rd for a class 3 beam is determined with the relationship:

VRd- shear resistance for a class 3 beam according to EN 1993-1-1



Members in class 1, 2 and 3 subjected to bending and compression





The evolution of the temperature of the steel

I- Steel structure un protected to fire, placed inside the building

the increment of the temperature ∆θa,1 on the cross section in the case of a uniform distribution of this temperature is

determined with the relationship:

Ksh – correction factor for shadowing; Am/V – factor of section for un-protected elements [1/m];

Am – area of the surface exposed to fire of the element of the unit length [m2/m];

Ca – specific heat of the steel [J/kgK]

- design value of the thermal net flux on the unit surface [W/m 2];

∆t – time interval of fire exposure [s];

ρa – the density of the steel [kg/m3]

The correction factor for shadowing effects to a I shape exposed to a nominal fire is determined with:

[ Am/V]b- the value of the convex contour section factor

For the general cases, the value of ksh is determined with:

Neglecting the shadowing effect may reach to similar results.

The value of is determined according to EN 1991-1-2, considering εt and εmd net

h ,

∆t is considered at most 5 sec.; Am/V is inferior limited to a value of 10 m -1



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Calculul La Actiunea Focului a Structurilor Din Otel