The general principles of using finite element models are described below:

• The structure is transferred into a discrete system by dividing (meshing) the structure into finite elements. The larger the number of finite elements the more accurate the estimate of the structural response, but the analysis time will increase. A balance needs to be made between the number of elements used and the required accuracy. This can only be assessed by carrying out a sensitivity analyses which involves conducting the same structural analysis but increasing the number of finite elements used.
• The type of finite element used to model the structure needs to be defined. The following guidance is offered.
  • Beam elements are line elements, modelling one-dimensional stress state, which include axial and flexural terms. They can be used effectively to model columns and beams. Integrating across the cross-section at several points along the element allows any cross-sectional variation to be included. It is important to ensure that the numerical integration across the cross-section accurately models any variation in material and temperature.
  • Spring elements are elements used to represent the variation of stiffness and strength between two nodal points that are in close proximity. These elements can be used to model connections.
  • Shell and plate elements are planar elements, modelling two-dimensional stress state, which include both membrane and flexural terms. Integrating through the thickness of the element allows the variation of the properties to be included. These elements are typically used to model floor slabs.
• Connecting the finite elements together at nodal points needs careful consideration. It has been shown that the behaviour of structures during fire is predominately governed by restraint to thermal expansion. It is therefore important that the elements are connected at the correct points to ensure accurate representation of thermal restraint.
• Material constitutive models need to be defined. For one-dimensional stress state the stress-strain-temperature relationship given in the codes can be used for steel and concrete. Creep is implicitly included in these models provided the heating rate remains between 2 and 50ºC. Thermal strains for all materials and transient strains for concrete should be included. For two-dimensional stress state a biaxial stress-strain-temperature relationship should be used. Strain reversal during both the heating and cooling stage of the fire should be considered, if it is considered to be detrimental to the structural behaviour.
• Thermal expansion properties of materials need to be defined.
• The boundary conditions should be defined. Due to the effects of restrained thermal expansion the definition of boundary conditions is extremely important. It is typically found that the slightest variation in boundary conditions results in significant changes in the estimated response. Boundary conditions can full into two categories. The first relates to actual boundaries of the structure, which are fairly easy to define. The second relates to boundaries of a sub-model where the fixity at the boundary represents the rest of the structure which is not actually modelled.
• Localised behaviour cannot easily be modelled when considering whole or even sub-structure building behaviour, due to the need to refine the element type and mesh density to adequately model localised behaviour. Areas of particular concern are:
  • Reinforcement fracture (Fig. 1) especially when a smeared cracking model is adopted which is unable to predict localised fracture of reinforcement.
  • Connection fracture (Fig. 2). The forces on the connection will be totally different in a fire condition compared to those used to design the connection cold. The behaviour of the connections during both the heating and cooling stages of the fire should be considered.
    The designer should consider the possibility, and consequence on the overall design strategy, of the possibility of localised behaviour.

    Fig. 1 Reinforcement fracture	Fig. 2 Connection fracture

• The applied static load should comply with the codes assuming fire limit state design. The rise in temperature, together with accurate thermal gradients should be applied in discrete steps to ensure numerical instability does not occur. The range of design fires, encompassing low temperature maximum duration and high temperature minimum duration should be considered to identify the worst case in terms of structural response.
• The effect of possible spalling of concrete should be considered.
• Initial geometric imperfections should be applied to the columns and any laterally unrestrained beams. An initial imperfection of span/1000 is generally adequate. There is no need to provide imperfections if the model provides movement of the members as the temperature is increased.

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