# THREE-DIMENSIONAL FE ANALYSIS OF HEADED STUD ANCHORS EXPOSED TO FIRE

## **Abstract**

In the present paper a transient three-dimensional thermo-mechanical model for concrete is presented. For given boundary conditions, temperature distribution is calculated by employing a three-dimensional transient thermal finite element analysis. Thermal properties of concrete are assumed to be constant and independent of the stress-strain distribution. In the thermo-mechanical model for concrete the total strain tensor is decomposed into pure mechanical strain, free thermal strain and load induced thermal strain. The mechanical strain is calculated by using temperature dependent microplane model for concrete (Ožbolt et al., 2001). The dependency of the macroscopic concrete properties (Young’s modulus, tensile and compressive strengths and fracture energy) on temperature is based on the available experimental database. The stress independent free thermal strain is calculated according to the proposal of Nielsen et al. (2001). The load induced thermal strain is obtained by employing the bi-parabolic model, which was recently proposed by Nielsen et al. (2004). It is assumed that the total load induced thermal strain is irrecoverable, i.e. creep component is neglected. The model is implemented into a three-dimensional FE code. The performance of headed stud anchors exposed to fire was studied. Three-dimensional transient thermal FE analysis was carried out for three embedment depths and for four thermal loading histories. The results of the analysis show that the resistance of anchors can be significantly reduced if they are exposed to fire. The largest reduction of the load capacity was obtained for anchors with relatively small embedment depths. The numerical results agree well with the available experimental evidence.

## Keywords

Thermal Strain Concrete Member Embedment Depth Microplane Model Solid Finite Element## Preview

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## References

- Abrams, M.S. (1971), “Compressive strength of concrete at temperatures to 1600F”,
*ACI SP 25, Temperature and Concrete*, American Concrete Institute, Detroit.Google Scholar - Batdorf, S.B. and Budianski, B. (1949), “A mathematical theory of plasticity based on the concept of slip”,
*Technical Note No. 1871*, National Advisory Committee for Aeronautics, Washington D.C.Google Scholar - Bažant, Z.P. and Chern, J.C. (1987), “Stress-induced thermal and shrinkage strains in Concrete”,
*J. of Eng. Mech.*,**113**(10), 1493–1511.Google Scholar - Bažant, Z.P. and Prat, P.C. (1988), “Microplane model for brittle-plastic material - parts I and II”,
*J. of Eng. Mech.*,**114**(10), 1672–1702.Google Scholar - Bažant, Z.P. and Ožbolt, J. (1990), “Nonlocal microplane model for fracture, damage and size effect in structures”,
*J. of Eng. Mech.*,**116**(11), 2485–2504.Google Scholar - Bažant, Z.P. and Kaplan, M.F. (1996),
*Concrete at High Temperatures: Material Properties and Mathematical Models*, Harlow, Longman.Google Scholar - Carol, I., Jirásek, M., and Bažant, Z.P. (2001), “New thermodynamically consistent approach to microplane theory: Part I - Free energy and consistent microplane stress”,
*Int. J. of Sol. and Struct.*,**38**(17), 2921–2931.zbMATHCrossRefGoogle Scholar - Belytschko, T., Liu, W.K. and Moran, B. (2001),
*Nonlinear Finite Elements for Continua and Structures*, John Wiley & Sons Ltd.Google Scholar - Cook, R.D., Malkus, D.S., Plesha, M.E. and Witt, R.J. (2002),
*Concepts and Applications of Finite Element Analysis*, 4th edition, John Wiley & Sons Inc.Google Scholar - Ehm, C. (1986), “Versuche zur Festigkeit und Verformung von Beton unter zweiaxialer Beanspruchung und hohen Temperaturen”,
*PhD thesis*, Heft 71, TU Braunschweig, Braunschweig.Google Scholar - Gawin, D., Majorana, C.E. and Schrefler, B.A. (1999), “Numerical Analisys of hygro-thermal behaviour and damage of concrete at high temperatures”,
*Mech. Cohes.-Frict. Mater.*,**4**(1), 37–74.CrossRefGoogle Scholar - Khoury, G.A.,Grainger, B.N. and Sullivan, P.J.E. (1985a), “Transient thermal strain of concrete: literature review, conditions within specimens and behaviour of individual constituents”,
*Mag. of Conc. Res.*,**37**(132), 131–144.Google Scholar - Khoury, G.A., Grainger, B.N. and Sullivan, P.J.E. (1985b), “Strain of concrete during first heating to 600°C under load”,
*Mag. of Conc. Res.*,**37**(133), 195–215.CrossRefGoogle Scholar - Nielsen, C.V., Pearce, C.J. and Biani, N. (2001), “Theoretical model of high temperature effects on uniaxial concrete member under elastic restraint”,
*Mag. of Conc. Res.*,**54**(4), 239–249CrossRefGoogle Scholar - Nielsen, C.V., Pearce, C.J. and Biani, N. (2004), “Improved phenomenological modelling of transient thermal strains for concrete at high temperatures”,
*Computers and Concrete*, in press.Google Scholar - Ožbolt, J., Li, Y.-J. and Kožar, I. (2001), “Microplane model for concrete with relaxed kinematic constraint”,
*Int. J. of Sol. and Struct.*,**38(**16), 2683–2711.CrossRefzbMATHGoogle Scholar - Pearce, C.J., Bićanić, N. and Nielsen, C.V. (2003), “A transient thermal creep model for concrete”,
*Computational Modeling of Concrete Structures*, Sweets & Zeitlinger, Lisse.Google Scholar - Reick, M. (2001), “Brandverhalten von Befestigungen mit großem Randabstand in Beton bei zentrischer Zugbeanspruchung”,
*Mitteilungen des Institut für Werkstoffe im Bauwesen*, Band 2001/4, IWB, Universität Stuttgart, Stuttgart.Google Scholar - Schneider, U. (1986),
*Properties of Materials at High Temperatures, Concrete*, 2nd. Edition, RILEM Technical Comitee 44-PHT, Technical University of Kassel, Kassel.Google Scholar - Schneider, U. (1988), “Concrete at High Temperatures – A General Review”,
*Fire Safety Journal*,**13**(1), 55–68CrossRefGoogle Scholar - Stabler, J. (2000), “Computational modelling of thermomechanical damage and plasticity in concrete”,
*PhD thesis*, The University of Queensland, Brisbane.Google Scholar - Taylor, G.I. (1938), “Plastic strain in metals”,
*J. of the Inst. of Metals.*,**62**, 307–324.Google Scholar - Terro, M.J. (1998), “Numerical modelling of the behaviour of concrete structures in fire”,
*ACI Struct. J.*,**95**(2), 183–193.Google Scholar - Thelandersson, S. (1983), “On the multiaxial behaviour of concrete exposed to high temperature”,
*Nucl. Eng. and Design*,**75**(2), 271–282.CrossRefGoogle Scholar - Thelandersson, S. (1987), “Modelling of combined thermal and mechanical action in concrete”,
*J. of Eng. Mech.*,**113**(6), 893–906.CrossRefGoogle Scholar - Thienel, K.-C. (1993), “Festigkeit und Verformung von Beton bei hoher Temperatur und biaxialer Beanspruchung - Versuche und Modellbildung”,
*PhD thesis*, Heft 10, IBMB, TU Braunschweig, Braunschweig.Google Scholar - Thienel, K.-C. and Rostassy, F.S. (1996), “Transient creep of concrete under biaxial stress and high temperature”,
*Cem. and Conc. Res.*,**26**(9), 1409–1422.CrossRefGoogle Scholar - Zhang, B. and Bićanić, N. (2002), “Residual Fracture Toughness of Normal- and High-Strength Gravel Concrete after Heating to 600°C”,
*ACI Mat. J.*,**99**(3), 217–226.Google Scholar