Skip to main content
SpringerLink
Log in

Lifetime Cost Optimization for the Structural Fire Resistance of Concrete Slabs

  • Published:
Fire Technology Aims and scope Submit manuscript

Abstract

Contemporary societal concerns emphasize the importance of cost optimization and sustainable constructions. However, with respect to structural fire safety, the application of prescriptive design rules remains common practice and optimization procedures are generally limited to a few examples of performance based design. Both methods consider an explicit or implicit prescribed safety level which is based on societal and empirical considerations. A more rational approach is to take into account the characteristics of the structure and to determine the economic optimum fire safety design. This economic optimum is obtained by minimizing the total costs, explicitly taking into account e.g. the fire ignition frequency, the probability of successful fire suppression and the damage costs due to a fire-induced failure. Applying this methodology to the design of simply supported concrete slabs indicates that in specific situations additional investments beyond the legally required minima constitute a more cost-effective design. It is concluded that the cost optimization of structural fire safety is a powerful tool to assess the utility of additional safety investments beyond the legal requirements.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9

Similar content being viewed by others

Abbreviations

As :

Bottom reinforcement area (mm2/m)

As,ref :

Reference reinforcement area corresponding with cref (mm2/m)

B(p):

Lifetime utility derived from the structure’s existence (Eur)

C(p):

Total construction cost (Eur)

C*(p):

Cost due to a single structural failure (Eur)

C0 :

Construction cost independent of p (Eur)

C1(p):

Construction cost dependent on p (Eur)

D(p):

Lifetime cost due to structural failures (Eur)

MEd :

Design value of the bending moment induced by the design loads for normal design conditions (kNm)

MG :

Bending moment induced by the permanent loads (kNm)

MGk :

Characteristic value of MG (kNm)

MQ :

Bending moment induced by the variable loads (kNm)

MQk :

Characteristic value of MQ (kNm)

MR,fi,t :

Bending moment capacity during fire at t minutes of exposure to the ISO 834 fire (kNm)

MRd :

Design value of the bending moment capacity for normal design conditions (kNm)

Pf,fi,t :

Probability of failure at t minutes of exposure to the ISO 834 fire (–)

Pf,tE :

Probability of failure at tE minutes of exposure to the ISO 834 fire (–)

R:

Structural fire resistance time classification as defined by the Construction Products Regulation (min)

Z(p):

Lifetime utility function (Eur)

a:

Cost of reinforcement per additional mm2 of reinforcement area (Eur/mm2)

b:

Benefit rate (Eur/year)

c:

Nominal concrete cover (mm)

cm :

Probabilistic model of the concrete cover

cref :

Reference concrete cover of 15 mm

f1(t,p):

Probability density function describing the time to the first structural failure

fn(t,p):

Probability density function of the time to the nth structural failure

f*(γ,p):

Laplace transform of f1

fTig :

Probability density function of the time between fire ignitions

fTig,k :

Probability density function of the time to the kth fire ignition

p:

Design parameter

p1 :

Annual fire ignition frequency (1/year) (equal to λ)

psup :

Probability of successful fire suppression (–)

s:

Horizontal spacing of the reinforcement bars (mm)

tE :

Duration of the ISO 834 standard fire (min)

βfi,t :

Reliability index at t minutes of exposure to the ISO 834 fire (–)

γ:

Continuous discount rate (1/year)

ε(p):

Ratio of C1(p) to C0 (–)

λ:

Fire ignition frequency (1/year)

λ*:

Fully-developed fire frequency (1/year) (equal to (1 − psup)λ)

λf,fi :

Fire-induced structural failure frequency (1/year) (equal to Pf,tE λ*)

ξ:

Ratio of the costs due to a single failure to the initial construction costs (–) (C*(p)/C(p))

χ:

Load ratio (–) (MQk/(MQk + MGk))

References

  1. Ceranic B, Fryer C (2000) Sensitivity analysis and optimum design curves for the minimum cost design of singly and doubly reinforced concrete beams. Struct Multidiscipl Optim 20:260–268

    Article  Google Scholar 

  2. Kanagasudaram S, Karihaloo BL (1990) Minimum cost design of reinforced concrete structures. Struct Optim 2:173–184

    Article  Google Scholar 

  3. Barros AFM, Barros MHFM, Ferreira CC (2012) Optimal design of rectangular RC section for ultimate bending strength. Struct Multidiscipl Optim 45:845–860

    Article  MATH  MathSciNet  Google Scholar 

  4. Han SH, Adamu A, Karihaloo BL (1996) Minimum cost design of multispan partially prestressed concrete T-beams using DCOC. Struct Optim 12:75–86

    Article  Google Scholar 

  5. Kanda J, Shah H (1997) Engineering role in failure cost evaluation for buildings. Struct Saf 19:79–90

    Article  Google Scholar 

  6. Elms DG (1997) Risk balancing in structural problems. Struct Saf 19:67–77

    Article  Google Scholar 

  7. Cohen L, Noll R (1981) The economics of building codes to resist seismic shocks. Public Policy 29:1–29

    MATH  Google Scholar 

  8. Kunreuther H (2001) Incentives for mitigation investment and more effective risk management: the need for public–private partnerships. J Hazard Mater 86:171–185

    Article  Google Scholar 

  9. Rosenblueth E, Mendoza E (1971) Reliability optimization in isostatic structures. J Eng Mech Div 97:1625–1642

    Google Scholar 

  10. Rackwitz R (2000) Optimization—the basis of code-making and reliability verification. Struct Saf 22:27–60

    Article  Google Scholar 

  11. Rackwitz R (2001) Optimizing systematically renewed structures. Reliab Eng Syst Saf 73:269–280

    Article  Google Scholar 

  12. Rackwitz R (2002) Optimization and risk acceptability based on the life quality index. Struct Saf 24:297–331

    Article  Google Scholar 

  13. Rackwitz R, Lentz A, Faber M (2005) Socio-economically sustainable civil engineering infrastructures by optimization. Struct Saf 27:187–229

    Article  Google Scholar 

  14. Graubner C-A, Brehm E, Glowienka S (2007) Economic potentials of probabilistic optimization methods. In: Proceedings of the 5th international probabilistic workshop, Ghent (28-29/11), pp 219–231

  15. Lentz A (2007) Acceptability of civil engineering decisions involving human consequences. Doctoral thesis, Technical University of Munich

  16. Cornell M, Daniels P, Kirkland J, Wolff A (1976) A survey of methods for estimating the cost value of a human life. Report No. CG-D-66-76, US Coast Guard. http://hdl.handle.net/2027/ien.35556021299177

  17. Nathwani JS, Lind NC, Pandey MD (1997) Affordable safety by choice: the life quality method. Institute for Risk Research, University of Waterloo, Waterloo

    Google Scholar 

  18. Proske D (2008) Catalogue of risks: natural, technical, social and health risks. Springer, Berlin

    Google Scholar 

  19. Adey B, Hajdin R, Brühwiler E (2004) Effect of common cause failures on indirect costs. J Bridge Eng 9:200–208

    Article  Google Scholar 

  20. Van Coile R, Caspeele R, Taerwe L (2012) Global resistance factor for concrete slabs exposed to fire. In: Proceedings of the 7th international conference on structures in fire, Zürich (6-8/6), pp 775–784

  21. Eamon CD, Jensen E (2012) Reliability analysis of prestressed concrete beams exposed to fire. Eng Struct 43:69–77

    Article  Google Scholar 

  22. Sidibé K, Duprat F, Pinglot M, Bourret B (2000) Fire safety of reinforced concrete columns. ACI Struct J 97(10):642–647

    Google Scholar 

  23. CEN (2002) EN 1990: basis of structural design. European Standard

  24. CEN (2004) EN 1992-1-1: design of concrete structures: part 1-1: general rules and rules for buildings. European Standard

  25. NBN (2010) NBN EN 1992-1-1-ANB: Eurocode 2: ontwerp en berekening van betonconstructies—Deel 1-1: algemene regels en regels voor gebouwen. Belgian National Annex to EN 1991-1-1

  26. Holický M, Sýkora M (2010) Stochastic models in analysis of structural reliability. In: Proceedings of the international symposium on stochastic models in reliability engineering, life sciences and operation management, Beer Sheva (08-11/02)

  27. JCSS (2001) Probabilistic model code. The Joint Committee on Structural Safety. www.jcss.byg.dtu.dk

  28. CEN (2004) CEN, EN 1992-1-2: design of concrete structures: part 1-2: structural fire design. European Standard

  29. Annerel E (2010) Assessment of the residual strength of concrete structures after fire exposure. Doctoral thesis, Ghent University, Ghent

  30. Holický M, Retief JV, Dunaiski PE (2007) The reliability basis of design for structural resistance. In: Proceedings of the third international conference on structural engineering, mechanics and computation (SEMC), Cape Town

  31. Gulvanessian H, Calgaro J-A, Holický M (2002) Designers’ guide to EN 1990: Eurocode 0: basis for structural design. Thomas Telford, London

    Book  Google Scholar 

  32. Torrent RJ (1978) The log-normal distribution: a better fitness for the results of mechanical testing of materials. Matér Constr 11:235–245

    Article  Google Scholar 

  33. Van Coile R, Caspeele R, Taerwe L (2012) Quantifying the structural safety of concrete slabs subjected to the ISO 834 standard fire curve using full-probabilistic FEM. In: Proceedings of the 10th international probabilistic workshop, Stuttgart (15-16/11), pp 313–330

  34. European Union (2011) Regulation (EU) No 305/2011 laying down harmonized conditions for the marketing of construction products and repealing Council Directive 89/106/EC. Off J Eur Union 54(88):5–43

  35. Ang AH-S, Tang WH (2007) Probability concepts in engineering, 2nd edn. Wiley, New York

    Google Scholar 

  36. Albrecht C, Hosser D (2010) Risk-informed framework for performance-based structural fire protection according to the Eurocode fire parts. In: Proceedings of the 12th interflam conference, Nottingham (5-7/07), pp 1031–1042

  37. Rahikainen J, Keski-Rahkonen O (2004) Statistical determination of ignition frequency of structural fires in different premises in Finland. Fire Technol 40:335–353

    Article  Google Scholar 

  38. Sandberg M (2004) Statistical determination of ignition frequency. Master Dissertation, Lund University, Sweden

  39. Sleich J-B, Cajor L-G, Pierre M, Joyeux D, Aurtenetxe G, Unanua J, Pustorino S, Heise F-J, Salomon R, Twilt L, Van Oerle J (2002) Competitive steel buildings through natural fire safety concepts—final report. European Communities, London

  40. Fontana M, Favre JP, Fetz C (1999) A survey of 40000 building fires in Switzerland. Fire Saf J 32:137–158

    Article  Google Scholar 

  41. Belgisch Staatsblad (1994) Koninklijk Besluit tot vaststelling van de basisnormen voor de preventie van brand en ontploffing waaraan nieuwe gebouwen moeten voldoen, Belgisch Staatsblad, 26/05/1995, p 11036

  42. National Building Specification (2013) Approved document B—fire safety, vol 2. Buildings other than dwelling houses

  43. Bouwbesluit (2012) Staatsblad van het Koninkrijk der Nederlanden, p 416

  44. Holický M (2009) Probabilistic risk optimization of road tunnels. Struct Saf 31:260–266

    Article  Google Scholar 

  45. Holický M (2013) Optimisation of the target reliability for temporary structures. Civil Eng Environ Syst 30:87–96. doi:10.1080/10286608.2012.733373

Download references

Acknowledgments

The authors wish to thank the FWO for the financial support on the research project “Probabilistic formulation of the structural reliability of concrete structures subjected to fire in relation to risk-based decision making and risk-transfer mechanisms”.

Author information

Authors and Affiliations

  1. Magnel Laboratory for Concrete Research, Department of Structural Engineering, Faculty of Engineering and Architecture, Ghent University, Technologiepark Zwijnaarde 904, 9052, Ghent, Belgium

    Ruben Van Coile, Robby Caspeele & Luc Taerwe

Authors
  1. Ruben Van Coile
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robby Caspeele
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luc Taerwe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ruben Van Coile.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Van Coile, R., Caspeele, R. & Taerwe, L. Lifetime Cost Optimization for the Structural Fire Resistance of Concrete Slabs. Fire Technol 50, 1201–1227 (2014). https://doi.org/10.1007/s10694-013-0350-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10694-013-0350-9

Keywords

Search

Navigation