Keywords: structural engineering, semi-rigid behaviour, steel structures, component method, temperature, fire resistance.

Observation of steel structures that suffered fire events has shown that many collapses take place after the fire is extinguished and the steel structural elements start to cool down. On several occasions, the steel joints fail from their tensile components (such as bolts or end-plate), because of high strains induced by the thermal shortening that occurs during cooling.

Most current design codes for the fire resistance of a steel beam [1] are based on tests performed on simply supported beams subjected to the ISO 834 fire curve However these `standard' fire experiments do not represent a real fire. The temperature history during a real fire can be described by three main stages: growth, full development and decay. The high temperatures in the second phase represent the greatest challenge to structural stability, possibly leading to structure collapse. The residual effects in members around the fire zone of a frame after cooling has taken place result from interaction between the thermal effects on these members and restraints from the adjacent structure. During the heating phase, a beam tends to expand due to the thermal expansion and to bend due to the loads applied on a softening material, these actions being partially resisted by the adjacent cooler structure. Additionally, extensive yielding of the beam is usually observed because of the reduction of the yield stress with increasing temperature. If failure does not occur during the heating phase, subsequent cooling causes the beam to re-stiffen and contract. Previous development of yield strains means that elastic unloading leads to residual deformations and a redistribution of internal forces that may induce tensile forces at the supports (joints). These tensile forces may finally lead to failure of the joints from their tensile components (such as bolts or end-plate) and consequently to the failure in the structure.

A methodology for the analysis of steel joints at high temperatures has recently been proposed by some of the authors [2], that enables the evaluation of the moment rotation response under fire loading. In particular, it highlighted the relevance of the combined levels of bending moment and axial force on the failure of the joint. Given the coupled nature of the development of stresses and deformations in a beam-joint substructure, it is the objective of the present paper to analyse the behaviour of that system when subjected to a real fire, including the cooling phase, and to assess the influence of the joint bending and axial flexibility on the overall response of the system. To this purpose, an IPE 200 cross section beam with span 5 m and steel class S275 was chosen and analysed under a representative uniformly distributed load of 14 kN/m and two alternative thermal loads as described above.

The program SAPHIR [3] was chosen to carry out the numerical simulations, which allows for large displacements and the use of non-linear temperature dependent material properties. The parametric study considered variations in the boundary conditions at the left support of the beam, from simply-supported to fixed, with various levels of axial and rotational restraint. It was found that, compared to the usual assumptions of "standard" fire experiments (ISO 834 fire curve and simply-supported boundary conditions), the results are quite distinct. Firstly, even for low axial restraint, an initial increase of bending moment is noted as the temperature increases, that can double the value of the bending moment. This is followed by a reduction of bending moment and axial force, with complete reversal of the bending moment diagram in case of a real fire. Secondly, a parametric variation of the rotational restraint at the beam end reveals the same qualitative behaviour as before, the maximum moment approximately reaching the same value, independently of the level of rotational restraint at the beam end.

The numerical analyses described in this paper thus indicate that strain reversal plays an important role in the behaviour of real structures, being essential to assess the residual safety of fire damaged buildings. Additionally, this strain reversal redistributes high levels of tensile forces to the joints, eventually leading to a tensile failure of the less ductile components such as bolts or welds. This latter issue still remains to be explored. Finally, the possibility of a 3D behaviour of the beam, where lateral-torsional buckling plays a major role, already observed in recent fire tests is an issue being actively explored.

1

CEN, Eurocode 3, Draft prEN - 1993-1-2: 200x, Part 1.2: Structural Fire Design, Eurocode 3: Design of Steel Structures, Stage 34, February 2002, CEN, European Committee for Standardization, Brussels, 2002.

2

L. Simões da Silva, A. Santiago and P. Vila Real, "A component model for the behaviour of steel joints at elevated temperatures", J. of Constructional Steel Research, 57(11), 1169-1195, 2001. doi:10.1016/S0143-974X(01)00039-6

3

J.-M. Franssen, SAFIR. A Thermal/Structural Program Modelling Structures under Fire, Proc. NASCC 2003, A.I.S.C. Inc., Baltimore, April 2-4 (2003)

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