Stuck? 
support@mecway.com
support@mecway.com
Mecway
FEA
Eurocode 2 - fire resistance of concrete structures study case
Hi,
I've been trying to advance in some Mecway modelling and I'm trying to analyse concrete beams under fire comparing the EC2 tabular method (dimensions and concrete cover in function of required time) and a simplified approach adapted to brazillian standards design. It's a simply supported beam, 5m span, height 50cm and width 20cm 25MPa, 3 steel rebars 12.5mm 500MPa at the bottom (single reiinforcement). I've checked minium required "concrete cover" (distance measured from the surface to the steel rebar centre of gravity) considering both environmental exposure condition of concrete - class II, and fire design requirements from EC2 tabular method, assuming 60min fire exposure limit, respectively, 40mm and 30 mm. So beam should be designed with 40mm "concrete cover" and "d" would be equal to 46cm.
I want to check fire resistance "real" time for 40mm, and also for 30mm "concrete cover" for assess tabular method accuracy (it is supposed to be conservative). For that I've done: thermal transient analysis in Mecway using convection and radiation exposure to ISO 834 in 3 sides >> temperature distribution assessment in beam cross section at time t >>concrete cross section reduction excluding area above 500C interpolating values in compression zone (bw,fi for 60min=20cm-2x2.2cm=15.6cm) + steel tensile strength reduction due to temperature exposure at time t (considering 40mm "concrete cover", at 60min steel is at 477C and fy,fi=0.83*50kN/cm2) >> calculate neutral axis depth for fire situation at time t (x=4.89cm>> calculate fire resistance bending moment at time t Mrd,fi = 67.26kN.m >> compare to design bending moment at fire situation ant time t Msd,fi
***Design bending moment at room temperature Msd=62.5kN.m and for fire situation, considering EC2, Msd,fi maybe assumed as 0.70*62.5=43.75kN.m.
***No strenght reduction coeficients were used in fire condition and neither 0.85 reduction factor (according to EC2 simplified method).
***First of all, to assess thermal results accuracy, I've checked temperature distribution comparing temperature profiles specified by EC2 for a 30x60cm beam with Mecway results.
If this simple approach is correct then:
1) Mecway thermal results seem to be very closed to EC2 profile temperatures.
2) For 40mm "concrete cover" (environmental exposure condition and fire safety), and bw=200mm, fire safety would be 80min but it is not really an usable value, because fire design time safety must be multiple of 30min;however it shows that beam dimensions could be reduced without compromising safety, and this may be important for countries with less money resources as Brazil.
3) Now here is the catch and I need some help: according to EC2 tabular method, 30mm "concrete cover" and bw=200mm should be more than enough for 60min fire exposure safety; but based on my analisys at 60min steel would be at 602C so fy,fi=0.465*50kN/cm2 >> then neutral axis depth for fire situation x=2.71cm >> ans finally fire resistance bending moment Mrd,fi = 38.86kN.m>> as Msd,fi=43.75kN.m, there would be no safety in fire situation!!!
I must be doing something wrong about the 30mm verification because tabular method should be conservative!!
I've attached the liml file from thermal analisys. Reinforced concrete calculations that I've used are the usual equations for reinforced concrete beams design with some simplifications.
I've been trying to advance in some Mecway modelling and I'm trying to analyse concrete beams under fire comparing the EC2 tabular method (dimensions and concrete cover in function of required time) and a simplified approach adapted to brazillian standards design. It's a simply supported beam, 5m span, height 50cm and width 20cm 25MPa, 3 steel rebars 12.5mm 500MPa at the bottom (single reiinforcement). I've checked minium required "concrete cover" (distance measured from the surface to the steel rebar centre of gravity) considering both environmental exposure condition of concrete - class II, and fire design requirements from EC2 tabular method, assuming 60min fire exposure limit, respectively, 40mm and 30 mm. So beam should be designed with 40mm "concrete cover" and "d" would be equal to 46cm.
I want to check fire resistance "real" time for 40mm, and also for 30mm "concrete cover" for assess tabular method accuracy (it is supposed to be conservative). For that I've done: thermal transient analysis in Mecway using convection and radiation exposure to ISO 834 in 3 sides >> temperature distribution assessment in beam cross section at time t >>concrete cross section reduction excluding area above 500C interpolating values in compression zone (bw,fi for 60min=20cm-2x2.2cm=15.6cm) + steel tensile strength reduction due to temperature exposure at time t (considering 40mm "concrete cover", at 60min steel is at 477C and fy,fi=0.83*50kN/cm2) >> calculate neutral axis depth for fire situation at time t (x=4.89cm>> calculate fire resistance bending moment at time t Mrd,fi = 67.26kN.m >> compare to design bending moment at fire situation ant time t Msd,fi
***Design bending moment at room temperature Msd=62.5kN.m and for fire situation, considering EC2, Msd,fi maybe assumed as 0.70*62.5=43.75kN.m.
***No strenght reduction coeficients were used in fire condition and neither 0.85 reduction factor (according to EC2 simplified method).
***First of all, to assess thermal results accuracy, I've checked temperature distribution comparing temperature profiles specified by EC2 for a 30x60cm beam with Mecway results.
If this simple approach is correct then:
1) Mecway thermal results seem to be very closed to EC2 profile temperatures.
2) For 40mm "concrete cover" (environmental exposure condition and fire safety), and bw=200mm, fire safety would be 80min but it is not really an usable value, because fire design time safety must be multiple of 30min;however it shows that beam dimensions could be reduced without compromising safety, and this may be important for countries with less money resources as Brazil.
3) Now here is the catch and I need some help: according to EC2 tabular method, 30mm "concrete cover" and bw=200mm should be more than enough for 60min fire exposure safety; but based on my analisys at 60min steel would be at 602C so fy,fi=0.465*50kN/cm2 >> then neutral axis depth for fire situation x=2.71cm >> ans finally fire resistance bending moment Mrd,fi = 38.86kN.m>> as Msd,fi=43.75kN.m, there would be no safety in fire situation!!!
I must be doing something wrong about the 30mm verification because tabular method should be conservative!!
I've attached the liml file from thermal analisys. Reinforced concrete calculations that I've used are the usual equations for reinforced concrete beams design with some simplifications.
Howdy, Stranger!
It looks like you're new here. If you want to get involved, click one of these buttons!
Comments
For professional proposes, I use the simplify method(which is conservative) of "a_m " based on tables and the virtual thickness between the reinforcement and the outer and closer exposed concrete face. According to the spanish regulation, CTE-DB-SI.
I can provide you my excel spreadsheet(in spanish).
I'd like to see your spreadsheet, yes.
The problem in my case study is that tabular method from EC2 would be unsafe and that seems really strange to me...
P.S.: I'm attaching isothermals from EC2 for a 30x60cm beam and my liml file for validation of thermal analisys in my case study.
Annex A represent the temperature in the crosssection of beams and columns taking symmetry into account.
As it is representing 1/4 of the beam (page 63) it means the simmetry is in both planes. That means the fire could probably have been considered acting from the 4th sides not three as you are imposing in your BC.
Manuel I've checked your excel file. If I understood correctly, for REI120 it's allowed bw inferior to 190mm. I'll check the spanish standard cause it may help reduce dimensions.
Disla, well observed. So if the isothermals are for 4 sides exposure, then my thermal analisys in Mecway for initial validation (viga 300x600) may not be accurate because I simulated 3 sides exposure...I'll try with 4 sides exposure.
My study case is for 3 sides exposure and values from tabular method are valid for 3 sides exposure; considering 60min, bw=200mm and distance from the bottom surface to the centre of the steel rebar=30mm it should be ok...
Probable causes for the strange results:
1) I've considered all the 3 rebars at the worst temperature (equal to corner rebar temperature)...I will redo the analisys considering the temperature in the middle rebar
2) Thermal analisys inaccurate (I've used the formulas from ec2 to modelate thermal properties of concrete and fixed values for convection and radiation parameters so I don't know what's wrong...)
¿What happens with the unaffected face? It should be able to dissipate some heat. Maybe imposing radiation and convection similar to the other faces but with ambient temperature at 20ºC or so. Not sure what the code says about this face, but I would suggest some kind of BC.
The unaffected face (top beam and upper face) at room temperature because it is supposed to be inside a slab...I could have exposed the lateral faces considering that (for example, 40cm of lateral face exposed instead of entire eight) but probably it won't make a substancial difference. I'll give it a try
Your temperatures over time are almost exactly the ones from the EC2-CONCRETE plot. Big accuracy from you.
MANUEL
I want to point out one thing. I recommend you to consider at least 35mm(nominal cover 25mm+increment cover 10mm) of cover (distance from the last molecule of steel rebar until the closest concrete face; do not use the distance from the center of the rebar to the outer face) .
I'll test your suggestions
Meanwhile, I've redone mechanical analisys at 60min for EC2 tabular method, using the already done thermal transient analisys in Mecway.
*Change: I've considered the different temperatures in the 3 rebars (2 corner rebars at 602C and 1 middle rebar at 426C).
Considering concrete section reduction (beam width is equal to region above 500C) and steel strength reduction as function of temperature, I've recalculated new resistance bending moment at fire situation.
NEW RESULTS: Mrd,fi=51,10kN.m > Msd,fi=43,75kN.m; so EC2 values are ok but no so conservative as I'd expected ("Fire safety factor" would be 1,16, although safety fator in fire situation may not have the same meaning as at room temperature).
I'll continue to make some more analisys