Steel Buildings in Europe

Part 7: Fire Engineering 7 - 53 as reversible, which means that once they cool down they will recover their initial mechanical properties. However, this phenomenon is not true with concrete, whose composition will be totally modified when heated to an elevated temperature. After cooling down, it cannot recover its initial strength. Indeed, its strength might even be less after cooling than at maximum temperature. The effects of thermal expansion should be taken into account. This is done by assuming that the total deformation of structural members is described by the sum of independent terms: r tr c σ th t ) (            (30) where th  , σ  , r  and c  are the strains due to thermal expansion, stress, residual stress and creep, respectively. tr  is the strain due to transient and non uniform heating regime for concrete (usually neglected). In Eurocodes, the creep strain is considered to be included implicitly in stress-strain relationships of steel and concrete. The residual stress is usually neglected except for some special structural analysis. The thermal strain is the thermal expansion (  L / L ) that occurs when most materials are heated. Thermal strains are not important for fire design of simply supported steel members, but they must be considered for composite members, frames and complex structural systems, especially where members are restrained by other parts of the structure (as for single-storey building divided into cells separated from one another by fire walls) since thermally induced strains, both due to temperature rise and temperature differential, can generate significant additional internal forces. Distribution of temperature for z = cte Unit strain Cross-section (x = cte) z y G  c  th    t  r  Figure 6.4 Strain composition of material in advanced numerical modelling In general, the structural analysis in the fire situation is based on ultimate limit state analysis, at which there is equilibrium of the structure between its resistance and its applied loading. However, significant displacement of the structure will inevitably occur, due to both material softening and thermal expansion, leading to large material plastification. Therefore, advanced fire analysis is a non-linear elasto-plastic calculation in which both strength and stiffness vary non-linearly. From a mathematical point of view, the solution of such analysis cannot be obtained directly and has to be achieved using an iterative procedure:  A step-by-step analysis is carried out in order to find the equilibrium state of the structure at various instants (at different temperature fields).  Within each time step, an iterative solution procedure is carried out to find the equilibrium state of the structure behaving in elasto-plastic way.