Simplified calculations models for composite mem- 123docz.net

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5.3.5 Simplified calculations models for composite members

The following design methods have been developed to predict the resistance of individual members when exposed to a standard fire curve. Therefore they are not applicable to “natural” fires.

Only the design methods for the most commonly used composite members in single-storey building (composite columns and partially encased concrete beams) are described here.

Composite columns

The simple design methods for columns allow the designer to assess the fire resistance of a composite column by calculating its buckling resistance using the temperature distribution through the cross-section and the corresponding reduced material strength defined at the required fire resistance time. This method is based on the buckling curve concept: the plastic resistance to axial compression Nfi,pl,Rd and the effective flexural stiffness (EI)fi,eff, are used to derive a reduction factor for buckling. The method is applicable to all types of

composite column provide that an appropriate buckling curve is used.

Checking the column consists of proving that the axial compression (for the combination of actions considered in fire situation according to EN 1991-1-2) is less than the buckling resistance of the column.

For a given temperature distribution across the cross-section, the design resistance of a composite column Nfi,Rd can be determined from the appropriate buckling column curve relating the load capacity Nfi,Rd to the plastic load Nfi,pl,Rd and the elastic critical load Nfi,cr as follows:

 θ fi,pl,Rd

fi, .N

N   (22)

 is the reduction factor for flexural buckling depending on the slenderness in fire situation θ.For composite columns, θ may be defined as:

cr fi, R pl, fi,

θ  N /N

 (23)

where:

Nfi, is the Euler buckling load

R pl,

Nfi, is the value of Nfi,pl,Rd according to (24) when the partial security factors M,fi,a, M,fi,s, andM,fi,c,of the materials are taken as 1.0 The reduction factor  is determined as for normal temperature design but using an appropriate buckling curve defined as function of column type (partially encased steel section, filled hollow steel section).

The ultimate plastic load, Nfi,pl,Rd of the cross-section is determined by summing the strengths of every part of the cross-section (yield stress for steel parts, compressive strength for concrete parts) multiplied by the corresponding areas, taking into account the effect of temperature on these elements, without considering their interaction (due to differential thermal stresses), i.e.:



  



m c k

s j

A f A f

A f

N ( . ) ( ) ( )

c fi, M,

θ c, s

fi, M,

θ s, a

fi, M,

θ ay, a Rd

pl,

fi,    (24)

Nfi,cr is the Euler buckling load calculated as a function of the effective flexural stiffness of the cross-section (EI)fi,effand the buckling length  of the column in fire situation, i.e.:

2θ eff 2 fi,

cr fi,

) π (



N  EI (25)

The effective rigidity (EI)fi,eff is determined from:



  



m k

I E I

E I

EI) ( ) ( ) ( )

( fi,eff a,θ a,θ a,θ s,θ s,θ s,θ c,θ c,sec,θ c,θ (26) where:

where Ec,sec,θ is the characteristic value for the secant modulus of concrete in the fire situation, given by the ration between fc,θ and

cu,

Ii is the second moment of area of material i related to the central axis (y or z) of the composite cross-section

a, (for steel profile), s, (for reinforcements) and c, (for concrete) are reduction coefficients due to the differential effects of thermal stresses.

Detailed information is given in EN 1994-1-2 §4.3.5.

Partially encased steel beams

The simple design method for partially encased steel beams allows the designer to assess the fire resistance by calculating its bending resistance at the required fire resistance time. It is based on the simple plastic moment theory. The method requires the calculation of the neutral axis and corresponding bending resistance, taking into account temperature distribution through the cross- section and corresponding reduced material strength. Distinction is made between sagging moment capacity (usually at mid-span) and the hogging moment capacity (at the support, if appropriate). If the applied moment is less than the bending resistance of the beam, the member is deemed to have adequate fire resistance.

The plastic neutral axis of the beam is determined such that the tensile and compressive forces acting in the section are in equilibrium:

1 M,fi,c

, c, θ c,

1 M,fi,a

, , y

y, 









 











 

 

m j

j j j n

i i i

k f f A

A    (27)

where:

fy,i is the nominal yield strength for the elemental steel area Ai taken as positive on the compression side of the plastic neutral axis and negative on the tension side

fc,j is the nominal compressive strength for the elemental concrete area Aj taken as positive on the compression side of the plastic neutral axis and negative on the tension side

The design moment resistance Mfi,t,Rdmay be determined from:



  









 











  m

j M,fi,c

j c, j , c, j j n

i M,fi,a

i, y i, y, i i Rd

, t , fi

k f z f A

k z A

M     (28)

where:

zi, zj are the distances from the plastic neutral axis to the centroid of the elemental area Ai and Aj

For the calculation of the design value of the moment resistance, the cross- section of the beam is divided into various components, namely:

 the flanges of the steel profile

 the web (lower and upper parts) of the steel profile

 the reinforcing bars

 the encased concrete.

To each of these parts of the cross-section, simple rules are given which define the effect of temperatures and allow calculation of the reduced characteristic strength in function of the standard fire resistance R30, R60, R90 or R120.

Detailed information is given in EN 1994-1-2 §4.3.4.