Keywords: fire resistance, non-linear planar frames, strain-based finite element method, heat conduction, reinforced concrete, creep, thermal strain, transient strain.

Fire resistance presents an important part of the safety of structures. It is well known that the temperature increase in fire conditions decreases load-carrying capacity of concrete, and increases its deformability. Due to the structural and chemical changes in material, caused by the elevated temperature, due to the internal stresses implied by the temperature gradient, and due to high pore pressures caused by the evaporation of the unbound pore water, internal microcracks or damages appear in concrete. Further on, at the elevated temperature, the decomposition process of cement stone in concrete begins, which is the consequence of the dehydration of cement binder. Physical-chemical changes appear also in the stoneware, which leads to the decomposition of aggregate grains. For this reason the decrease of compressive strength in concrete at the elevated temperature depends also on the type of aggregate used. Abrams [1] discovered that compressive strength of concrete made of limestone aggregate is at approximately , and at only of its strength at room temperature. The decrease of compressive strength of concrete made of siliceous aggregate at elevated temperature is even more pronounced. At such concrete the strength at is only of its room temperature strength. According to the European prenorm Eurocode 2 ENV 1992-1-2, the compressive strength of concrete made from limestone aggregate is slightly less than that determined by Abrams [1]. The elasticity and shear moduli of concrete decrease nearly linearly with the increase of temperature in contrast to the thermal extension coefficient of concrete which increases non-linearly with the increase of temperature [5]. Due to stresses in concrete caused by the temperature gradient, due to the increase of pore pressures [3,4], and due to the fact that the thermal extension coefficient of steel reinforcement increases with elevated temperature much faster than that of concrete, a concrete splitting appears. The strength of reinforcing steel starts decreasing from upwards. At about - although the precise data depend on the type of steel - it is still to of its strength at room temperature, and at higher temperatures it decreases even more rapidly.

The magnitude of concrete creep at elevated temperatures is much bigger than at room temperature. According to the experimental research [2], the concrete creep at is 3.2-times, at 6.4-times, at 14.9-times, and at even 32.6-times larger than at . It is well known that the effect of creep of a steel onto stress and strain state in reinforced concrete frames subjected to fire is very important, especially when the temperature in reinforcement bars exceeds [7].

The paper presents a computational model and a computer program developed for the non-linear analysis of the response of plane reinforced concrete frames simultaneously exposed to fire and external mechanical loads up to the failure. The analysis takes into account the geometrical and material non-linearities of the structure and includes the influence of elevated temperature on the mechanical and rheological properties of materials. The time response of a structure exposed to fire and mechanical external loads is obtained by the finite element method. Here we use an original beam finite element. The element is based on Reissner's theory of beams and is designed in such a way that only deformation variables of the centroidal axis of the beam need to be interpolated [6]. In numerical examples, a special attention is paid to the influence of creep in concrete and steel reinforcement onto the behaviour of the structure. With the help of the developed computational model and the related computer program, we analyse a number of reinforced concrete frames in fire. We compare our numerical results to the ones obtained in experiments in a fire laboratory, and prove that the effect of creep in concrete can not be neglected in the fire analysis of structures.

1

M.S. Abrams, "Compressive strength of concrete at temperatures to 1600 F", ACI, Special Publication SP-25, Temperature and Concrete, SP-25, 1971.

2

C.R. Cruz, "Apparatus for measuring creep of concrete at high temperatures", Journal of the PCA Research and Development Laboratories, 10(3), 36-42, 1968.

3

N.A. Gamal, J.P. Hurst, "Coupled heat and mass transport phenomena in siliceous aggregate concrete slabs subjected to fire", Fire and Materials, 21, 161-168, 1997. doi:10.1002/(SICI)1099-1018(199707/08)21:4<161::AID-FAM602>3.0.CO;2-R

4

P. Kalifa, F.-D. Menneteau, D. Quenard, "Spalling and pore pressure in HPC at high temperatures", Cement and Concrete Research, 30, 1915-1927, 2000. doi:10.1016/S0008-8846(00)00384-7

5

T.D. Lin, B. Ellingwood, O. Piet, "Flexural and shear behaviour of reinforced concrete beams during fire tests", PCA, Research and Development Bulletin, Report No. NBS-GCR-87-536, Center for Fire Research, National Bureau of Standards, Washington, 1988.

6

I. Planinc, M. Saje, B. Cas, "On the local stability condition in the planar beam finite element", Structural Engineering and Mechanics, 12(5), 507-526, 2001.

7

G. Williams-Leir, "Creep of structural steel in fire: Analytical expressions", Fire and Materials, 7(2), 73-78, 1983. doi:10.1002/fam.810070205

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