Steel Buildings in Europe

Title A.4 Worked Example – Simply supported, primary composite beam 13 of 13 4 – 93 Deflection in the final stage F G + F Q = 62,78 + 45,0 = 107,78 kN q G = 0,65 kN/m EN 1990 § 6.5.3 Deflection at the final stage: I y is calculated for the equivalent section, by calculating an effective equivalent steel area of the concrete effective area. b equ = b eff / n 0 n 0 is the modular ratio for primary effects ( Q k ) = E a / E cm = 210000 / 31000 = 6,77  b eq = 2,25 / 6,77 = 0,332 m Using the parallel axis theorem the second moment of area is obtained: I y = 82458 cm 4 EN 1994-1-1 § 5.4.2.2 For the permanent action: n = 2 E a / E cm = 20,31 for permanent loads ( G k )  b equ = 2,25 / 20,31 = 0,111 m The second moment of area is calculated as: I y = 62919 cm 4 EN 1994-1-1 § 5.4.2.2(11) The deflection can be obtained by combining the second moment of area for the variable and the permanent actions as follows: w G = 27,3 mm 2,6 mm 13500 10 62919 210000 24 ) - 4 3000 (3 9000 3000 4 2 2 partitions          w 45000 10 82458 210000 24 ) - 4 3000 (3 9000 3000 4 2 2 Q         w = 6,7 mm So, w = w G + w partitions + w Q = 27,3 + 2,6 + 6,7 = 36,6 mm The deflection under ( G + Q ) is L /246 EN 1994-1-1 § 7.3.1 Note 1: The deflection limits should be specified by the client and the National Annex may specify some limits. Note 2: The National Annex may specify frequency limits. EN 1993-1-1 § 7.2.3