Steel Buildings in Europe

Part 7: Fire Engineering 7 - 30 where θ sec, c, E is the characteristic value for the secant modulus of concrete in the fire situation, given by the ration between f c, θ and  cu,  I i is the second moment of area of material i related to the central axis (y or z) of the composite cross-section  a,  (for steel profile),  s,  (for reinforcements) and  c,  (for concrete) are reduction coefficients due to the differential effects of thermal stresses. Detailed information is given in EN 1994-1-2 §4.3.5. Partially encased steel beams The simple design method for partially encased steel beams allows the designer to assess the fire resistance by calculating its bending resistance at the required fire resistance time. It is based on the simple plastic moment theory. The method requires the calculation of the neutral axis and corresponding bending resistance, taking into account temperature distribution through the cross- section and corresponding reduced material strength. Distinction is made between sagging moment capacity (usually at mid-span) and the hogging moment capacity (at the support, if appropriate). If the applied moment is less than the bending resistance of the beam, the member is deemed to have adequate fire resistance. The plastic neutral axis of the beam is determined such that the tensile and compressive forces acting in the section are in equilibrium: 0 1 M,fi,c c, , θ c, 1 M,fi,a y, y, ,                       m j j j j n i i i i f A k f A k    (27) where: f y, i is the nominal yield strength for the elemental steel area A i taken as positive on the compression side of the plastic neutral axis and negative on the tension side f c, j is the nominal compressive strength for the elemental concrete area A j taken as positive on the compression side of the plastic neutral axis and negative on the tension side The design moment resistance fi,t,Rd M may be determined from:                       m j 1 M,fi,c c, j c, , j j j n i 1 M,fi,a y,i y, ,i i i fi,t ,Rd f A z k f A z k M     (28) where: z i , z j are the distances from the plastic neutral axis to the centroid of the elemental area A i and A j