VE1026 | Fire Resistance: Calculating Reinforced Concrete Column According to Simplified Method A DIN EN 1992-1-2, 5.3.2

An inner column in the first floor of a three-story building is designed. The column is monolithic connected with the top and bottom beams. The fire design simplified method A for columns according to DIN EN 1992-1-2 is than proofed and the results compared to [1].

Material	Concrete C35/45	Design value of concrete compressive strength	fcd	19.900	N/mm2
	Reinforcing Steel B500S(B)	Design yield strength	fyd	434.783	N/mm2
Geometry	Structure	Column length	lcolumn	4.200	m
	Cross-section	Height	h	200	mm
		Width	b	200	mm
		Cross-section area	Ac	400	mm2
Loads	Permanant Loads	LC1	Gk	363.000	kN
		LC2	Sk	30.000	kN
		LC3	Qk	150.000	kN

RFEM Settings

• The simplified method according to chapter 5 is activated as the method for fire design.
• Permanent and transient for normal temperature acc. to 2.4.2(2) is the design situation type for fire loads.
• The reduction factor fo the design load level η_fi is set to 0,61.
• The flexural buckling k_y for the fire design is set to 0.5.

Results

1. Inner forces
   The governing load combination: 1.35·LC1 + 0.75·LC2 + 1.5·LC3
   

   Normal force NEd [kN]
   RFEM	Analytical solution	Ratio
   737.550	738.000	1.00

   

   Column Normal Force due to Governing Load Combination
   
   
2. Effective length and slenderness
   

   'Effective length and slenderness
   Parameter	Description	Unit	RFEM	Analytical solution	Ratio
   ky	Effective length factor	–	1.000	1.000	1.00
   l0	Effective length	m	4.200	4.200	1.00
   l0	Effective length	m	4.200	4.200	1.00
   n	Relative normal force	–	0.930	0.932	1.00
   iy	Radius of gyration	–	57.700	57.700	1.00
   λ	Slenderness	–	72.746	73.000	0.99

   
   
3. Required reinforcement
   

   Parameter	Description	Unit	RFEM	Analytical solution	Ratio
   As,min	Minimum longitudinal reinforcement area	cm2	2.540	2.540	1.00
   As,req	required reinforcement	cm2	12.480	12.400	1.00

   
   
4. Fire design
   The building where the column is located, is considered as building class 4. The requirement for the column is therefore a fire resistance duration of at least R60. First, the minimum section dimension according to the simplified method A for columns acc. to 5.3.2(1), table 5.2(a):
   

   Minimum section dimension and rebar axis distance acc. to 5.3.2(1) table 5.2a
   Parameter	Description	Unit	RFEM	Analytical solution	Ratio
   ηfi	Reduction factor design load level for fire situation	–	0.610	0.614	1.00
   NEd,fi	Axial force in section due to loading for fire design	kN	452.856	453.000	1.00
   NRd	Column capacity	kN	798.835	800.000	1.00
   μfi	Degree of utilization in the fire situation	kN	0.570	0.566	1.00
   bmin,req	Required minimum cross-sectional dimension	mm	216.7	217.0	1.00
   am,req	Required minimum distance	mm	39.3	39.3	1.00

   
   

Furthermore, the minimum fire duration R is determined. it is calculated as following:

The following equation is used to calculate the fire resistance determined on basis of bearing capacity R_η,fi:


For simplification purposes, the literature assumes that μ_fi = η_fi. Therefore it is necessary to recalculate R_η,fi using the actual μ_fi to be able to compare it with the results of RFEM:

Minimum fire duration acc. to Eq. 5.7
Parameter	Description	Unit	RFEM	Analytical solution	Ratio
μfi	Degree of utilization in the fire situation	kN	0.570	0.570	1.00
ω	Mechanical reinforcement ratio	–	0.689	0.690	1.00
Rη,fi	Fire resistance determined on basis of bearing capacity	–	35.948	35.690	1.00
Ra	Fire resistance determined on basis of reinforcement cover	–	16.000	16.000	1.00
Ri	Fire resistance determined on basis of buckling length	–	27.840	27.800	1.00
Rb	Fire resistance determined on basis of cross-sectional dimension	–	18.000	18.000	1.00
Rn	Fire resistance determined on basis of number of bars	–	0	0	1.00
R	Time of fire resistance	min	83	82	1.01