Steel Buildings in Europe

Part 7: Fire Engineering 7 - 52 is modelled by use of step-by-step iterative solution procedures, rather than a steady state analysis. This Section outlines some of the primary considerations in modelling the behaviour of single-storey buildings with steel or composite frames in the fire situation, notably features related to material models, computation procedure, structural modelling, etc. Advanced calculation models can be used in association with any heating curve, provided that the material properties are known for the relevant temperature range and that material models are representative of real behaviour. At elevated temperature, the stress-strain curve of steel is based on a linear-elliptic-plastic model, in contrast to the elasto-plastic model adopted for normal temperature design. The steel and concrete stress-strain relationships given in EN 1993-1-2 and EN 1994-1-2 are commonly used. In the fire situation, the temperature field of structural members varies with time. As stress-strain relationships of materials are non-linear and temperature dependant, an appropriate material model has to be adopted in advanced numerical modelling to allow the shift from one behaviour curve to another, at each step of time (and thus of temperature). The so-called kinematical material model is usually used for steel structures, assuming that the shift from one stress-strain curve to another one due to the change of temperature is made by staying at a constant plastic strain value (see Figure 6.3). This model can be used at any stress state of steel (tension or compression). For concrete, it is much more complicated, since the material has a different behaviour in tension and in compression. Therefore, different shift rules are needed for when the material is in tension or in compression. Generally, this kinematic model is used in most advanced calculation models for fire safety engineering applications. Behaviour of steel is often modelled with a Von Mises yield contour including hardening. Behaviour of concrete in compression is modelled with a Drucker-Prager yield contour, including hardening.  ) , ε ( θ d ε d σ 1 0        θ (t) θ  1 Δ t) θ (t θ   2 a) Behaviour law of structural steel Parallel to 2 0)        , ε ( θ d ε d σ Parallel to  Compression b) Behaviour law of concrete   θ (t) θ  1 Δ t) θ (t θ   2 tensi le Figure 6.3 Kinematic material models for steel and concrete Another aspect to be noted in the application of advanced calculation models for steel and composite structures under natural fire conditions is the material behaviour during cooling phase. It is well known that for commonly used steel grades, the variation of mechanical properties with temperature are considered