Steel Buildings in Europe

Part 7: Fire Engineering 7 - 35 Maximum lateral displacements δ i ( i = 1, 2) induced at the top of columns located at the compartment ends can be obtained using the following expression (see Figure 5.11):               building of the middle fire is in the when the ; Max building end of the fire is at the when the th t th t i i i i K c nl F K K c nl K K  (30) where: n is the number of heated bays K i is the equivalent lateral stiffness of the considered part i of the structure [N/m] K t is the equivalent stiffness (depending on equivalent stiffnesses 1 K and 2 K ) given by: 1 2 1 2 t K K K K K    is the span of one heated bay connected to the column [m] F is the tensile force [N] c th is an empirical coefficient (dependent on the slope of the roof and the type of steel structure)          Frames Lattice for Frames Portal for 0,009 slope for 10% 0,015 slope for 5% 0,011 slope for 0% 0,01 th c Lateral stiffness K for fire in the middle of a frame If the fire compartment is in the middle of the frame as illustrated in Figure 5.11 , K 1 and K 2 should be calculated by an elastic method. 1  2  m 1 = 1 m 2 = 2 n = 1 K 2  K 1 Figure 5.11 Fire located in a cell at the middle of the building However, for usual steel frames (constant range, even standard steel profiles from one span to another), the equivalent lateral stiffness i K on either side of the fire can be calculated approximately according to the number of cold spans on that side ( m i ) using the following relationships: