RF-/STEEL EC3 - Online Manual Version 5/8

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RF-/STEEL EC3 - Online Manual Version 5/8

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8.2 Fire Resistance

This example describes the fire resistance design for a steel column, using the National Annex of Germany.

System and loads
Table 8.5 System and loads
Figure 8.3

Column cross-section: HE-B 300, steel S 235
System: hinged column, β = 1.0
System height: 3 m
Loading: GK = 1200 kN, QK = 600 kN

Ultimate limit state design for room temperature
Flexural buckling about minor axis (⊥ to z-z axis)

Ncr,z=21000·8560.00·π2300.002=19712.90 kN 

λ¯z=A·fyNcr,z=149.0·23.519712.90=0.422>0.2 

→ Design for flexural buckling must be performed.

cross-sectional geometry: h/b = 1.00 ≤ 1.2; structural steel S 235; t ≤ 100 mm

  • [1] Table 6.2, row 3, column 4: buckling curve c
  • ⇒ αz = 0.49   ([1] Table 6.1)

Φ=0.5·[1+0.49·(0.422-0.2)+0.4222]=0.643 

χz=10.643+0.6432-0.4222=0.886 

NEd=1.35·GK+1.5·QK=1.35·1200+1.5·600=2520 kN 

Design ratio

NEdχz·A·fy/γM1=25200.886·149.0·23.5/1.1=0.8941.0 

Results of RF-/STEEL EC3 calculation
Table 8.6 Results of RF-/STEEL EC3 calculation

Iz

8560.00

cm4

Effective member length

Lcr,z

3.000

m

Elastic flexural buckling force

Ncr,z

19712.9

kN

Slenderness

λz

0.4215

> 0.2

6.3.1.2(4)

Buckling curve

BCz

c

Tab. 6.2

Imperfection factor

αz

0.490

Tab. 6.1

Auxiliary factor

Φz

0.643

6.3.1.2(1)

Reduction factor

χz 

0.886

Eq. (6.49)

Flexural buckling resistance

Nb,z,Rd

2821.80

kN

Eq. (6.47)

Design ratio

η

0.893

≤ 1.0

Eq. (6.46)

Fire resistance design

After a fire exposure of 90 minutes according to the standard temperature-time curve, the mean steel temperature is 524 ℃.

A box-shaped GRP encasement (glass-reinforced plastic) is used as fire resistance material, having the following properties:

Table 8.6

Specific weight:

ρp = 945 kg/m3

Thermal conductivity:

λp = 0.2 W/K

Specific heat capacity:

cp = 1700 J/kgK

Thickness:

dp = 18 mm

Determination of reduction factors
Table 8.6

ky,Θ = 0.704

[10] Table 3.1

kE,Θ = 0.528

[10] Table 3.1

Design in fire situation according to [2] clause 4.2.3.2

Imperfection factor α:

α=0.65·235fy=0.65·235235=0.65 

Non-dimensional relative slenderness ƛΘ:

λ¯Θ=λ¯·ky,ΘkE,Θ0.5=0.422·0.7040.5280.5=0.486 

Auxiliary factor:

Φθ=12·[1+α·λ¯θ+λ¯θ2]=12·[1+0.65·0.486+0.4862]=0.776 

Reduction factor for flexural buckling in fire situation:

χfi=1φθ+φθ2-λ¯θ2=10.776+0.7762-0.4862=0.724 

Buckling resistance of structural component subjected to compression:

Nb,fi,Rd=χfi·A·ky,θ·fyγM,fi=0.724·149.0·0.704·23.51.0=1784.7 kN 

Loading in case of fire:

Nfi,Ed=1.0·Gk+0.9·Qk=1.0·1200+0.9·600=1740 kN 

Design ratio

η=Nfi,EdNb,fi,Rd=17401784.7=0.9751.0 

Results of RF-/STEEL EC3 calculation
Table 8.7 Results of RF-/STEEL EC3 calculation

Reduction factor

ky,θ

0.704

[2], Tab. 3.1

Reduction factor

kE,θ

0.528

[2], Tab. 3.1

Slenderness

λz,θ

0.486

[2], Eq. (4.7)

Imperfection factor

α

0.650

[2], 4.2.3.2(2)

Auxiliary factor

Φz,Θ

0.776

[2], 4.2.3.2(2)

Reduction factor

χz,fi

0.724

[2], Eq. (4.6)

Partial safety factor

γM,fi

1.000

[2], 2.3 (1)

Flexural buckling resistance

Nb,fi,z,Θ,Rd

1784.4

kN

[2], Eq. (4.5)

Design ratio

η

0.975

≤ 1.0

[2], Eq. (4.1)

Literatur
[1] Eurocode 3: Design of steel structures - Part 1‑1: General rules and rules for buildings; EN 1993‑1‑1:2010‑12
[2] EN 1993-1-2 (2005): Eurocode 3: Design of steel structures - Part 1-2: General rules - Structural fire design [Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC]
[10] Kindmann, R.; Frickel, J.: Elastische und plastische Querschnittstragfähigkeit. Berlin: Ernst & Sohn, 2002