Steel Buildings in Europe

Title A.2 Worked Example – Simply supported beam with intermediate lateral restraints 3 of 7 4 – 66 Second moment of area about the major axis I y = 23130 cm 4 Second moment of area about the minor axis I z = 1318 cm 4 Torsion constant I t = 51,08 cm 4 Warping constant I w = 490 000 cm 6 Elastic section modulus about the major axis W el,y = 1156 cm 3 Plastic section modulus about the major axis W pl,y = 1307 cm 3 Yield strength Steel grade S235 The maximum thickness is 13,5 mm < 40 mm, so: f y = 235 N/mm 2 EN 1993-1-1 Table 3.1 2.5. ULS verification 2.5.1. Actions on the beam Self weight of the beam: (66,3 × 9,81) × 10 -3 = 0,65 kN/m Permanent load: G k = 0,65 + 0,30 × 6,00 = 2,45 kN/m Climatic load: Q s = 0,60 × 6,0 = 3,60 kN/m Q w =  0,50  6,0 =  3,00 kN/m 2.5.2. Effects on the beam due to ULS combinations: Combination 1  G,sup G k +  Q Q s = 1,35  2,45 + 1,50  3,60 = 8,71 kN/m Combination 2  G,inf G k +  Q Q w = 1,00  2,45 - 1,50  3,00 =  2,05 kN/m EN 1990 § 6.4.3.2 Expression 6.10 Bending moment diagram M M y,Ed Maximum moment at mid span: Combination 1 M y,Ed = 8 2 wL = 8 8,71 15 2  = 244,97 kNm Combination 2 M y,Ed = 8 2 wL = 8 2,05 15 2   =  57,66 kNm