Section and Design Strength for Negative Moment Resistance in Fire-Resistant Conditions of Composite Beams Partially Encased in Concrete [13]

Table 2.10: Hfi values ​​corresponding to fire resistance levels [13]

Fire resistance level

Assuming that the axial force is neglected, the limiting moment in both positive and negative moment cases is calculated simply by summing the partial stresses corresponding to the load-bearing members as considered above. For the structure to satisfy the durability condition, this moment value must be greater than the calculated value according to the fire load, that is:

M



fi,Sd

  fi M Sd



 M

fi,Rd



M

and

fi,Sd

  fi M Sd



 M

fi,Rd

Table 2.11: bfi values ​​corresponding to fire resistance levels [13]

Fire resistance level

2.1.5. Steel-concrete composite columns

The process of temperature propagation in the section of a partially concrete-encased composite column is explained similarly to that in the section of a partially concrete-encased composite beam. In fire-resistant conditions, the flange of the steel column will heat up directly, while the web will be protected by a layer of concrete cover. This concrete layer not only reduces the slenderness of the steel column section but also acts together with the steel column to bear the load. To determine the bearing capacity of the column in this case, the temperature of the cross-sectional parts (two flanges, web, concrete cover and reinforcement) is considered to be uniformly distributed or linearly varying, the section can be calculated with attenuation or fully calculated but the strength and elastic modulus are weakened.

a. Fire resistance calculation cross section and strength:

- The flange part of the steel section: because it is completely exposed in the fire, it often reaches the highest temperature. In the calculation, this temperature is evenly distributed over the entire flange area, determined by the formula:

  

 k  Am 

f , t

o,t

 

t  V 

o,t and kt are temperature and time coefficient, depending on the fire resistance level as consulted in the table.

bc,fi

hw,fi

bc,fi

Z

u2

ef

hw

h

ef

u1

ew

Y

b

Figure 2.8: Design cross-section under fire resistance conditions of partially concrete-encased composite columns [13]

Table 2.12: Values ​​of o,t and kt corresponding to fire resistance level [13]

Fire resistance level

Because the bearing area of ​​the flange is not weakened, the strength and elastic modulus are reduced through coefficients k depending on the temperature of the flange:

f a max, f ,  kmax, . f ay , f ,200 C

Ea, f , t

 k E , .E a , f ,200 C

Table 2.13: Values ​​of kE,, kmax, corresponding to temperature  [13]

Flange temperature 

(0C)

- The web part: because it is near the position of the flange, it is also affected by the process of temperature spread in the steel material, so it also has a high temperature. Therefore, when included in the calculation formula, this part has a partially reduced cross-section, corresponding to the size hw,fi determined by the formula:

 H 

hw, fi

 0.5 h  2 e f 1  1  0.16 

t

In there:

 h 

h: is cross-section height; ef: is flange thickness

Ht: is a parameter depending on the fire resistance level

Table 2.14: Values ​​of Ht corresponding to fire resistance levels [13]

Fire resistance level

Residual strength of web:

fa max,,w,

 fay,,w,200 C

1  0.16 H t

h

The elastic modulus of the web is still calculated with the value of the steel material in

normal working conditions

- The concrete part covering the web: is also calculated to be fire-resistant according to the reduced cross-section, with the two-way dimensions narrowed compared to the actual cross-section by an amount bc, fi depending on the fire resistance level.

Table 2.15: Values ​​of bc,fi corresponding to fire resistance levels [13]

Fire resistance level

depends on the fire resistance class and section coefficient of the structure under consideration.

Table 2.16: c,t values ​​corresponding to fire resistance level [13]

R30

Similar to the flange portion of the steel section, the strength and modulus of elasticity of the concrete are reduced at a rate that depends on the temperature reached in the concrete during the fire.

Ec,sec,  k

c,

. fc,200 C

/ cu,

f c ,  k c , . f c ,200 C

Table 2.17: Values ​​of kE,, kmax, corresponding to temperature  [13]

Concrete temperature c (0C)

800

- For steel in concrete: the process of reducing strength

ry ,20 C

fry ,t  ky ,t . f 0

and elastic modulus

Er ,t

 k E ,t . E 0

determined by

u1u2

r, 20 C

The distance from the center of gravity of the steel bar to the edge of the concrete is expressed by the parameter u 

Table 2.18: Ky,t values ​​corresponding to fire resistance level [13]

Fire resistance level

Table 2.19: Values ​​of kE,t corresponding to fire resistance level[13]

Fire resistance level