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This material is copyright - all rights reserved. Reproduced under licence from The Steel Construction Institute on 12/2/2007 To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ Steel Designers' Manual - 6th Edition (2003) 636 Worked examples The Steel Construction Institute Silwood Park, Ascot, Berks SL5 7QN Check natural frequency of beam Subject Chapter ref. DESIGN OF SIMPLY SUPPORTED COMPOSITE BEAM Design code Made by RML Sheet no. BS 5950: Part 3 Checked by GWO Consider weight of floor in dynamic calculations to include: self weight of slab and beam + 10% imposed load + ceiling load but excluding partitions = (2.0 + 0.1 ¥ 5.0 + 0.5) ¥ 3.0 + 0.67 = 9.67 kN/m Accurate calculations show that the ratio of the dynamic to static stiffness of a composite beam used in deflection calculations is 1.1 to 1.15. Consider deflection reduction of 1.1 for the same section properties as calculated under imposed load. Deflection of composite beam, when subject to instantaneously applied self weight (as above) d sw = = 4 3 5 ¥ 9. 67 ¥ 12 ¥ 10 384 ¥ 205 ¥ 10 ¥ 1. 1 ¥ 861. 8 ¥ 10 13. 4 mm Natural frequency of beam f � 18 d = 18 13. 4 = 4. 91 Hz Satisfactory sw 6 -6 (A detailed check to Reference 21.14 demonstrates that this floor is satisfactory for general office use). 21 8
This material is copyright - all rights reserved. Reproduced under licence from The Steel Construction Institute on 12/2/2007 To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.org/ Steel Designers' Manual - 6th Edition (2003) The Steel Construction Institute Silwood Park, Ascot, Berks SL5 7QN wu /M = 0.0625 li/a L2 Worked examples 637 Subject Chapter ref. DESIGN OF CONTINUOUS COMPOSITE BEAM Design code Made by RML Sheet no. BS 5950: Parts 1 & 3 Checked by TCC Use same design data as for simply-supported composite beams. Choose 406 ¥ 178 ¥ 60 kg/m UB grade S355 N.B. Section is plastic. (span/depth ratio = 22, and 12% weight saving). Construction condition Design load in construction condition wu = ( 16 . ¥ 05 . + 14 . ¥ 20 . ) ¥ 30 . + 060 . ¥ 14 . = 116 . kN/ m Check stability of bottom flange under worst combination of loading M = 0.0625 ¥ 11.6 ¥ 12 2 Slenderness l = 12000/39.7 = 302 = 104.4 kNm From SCI publication ‘Steelwork Design: Guide to BS 5950: Part 1: Volume 1’ (page B5) u = 0.880 x = 33.8 Assume top flange is laterally restrained by the decking. Use design formula for equivalent slenderness in BS 5950: Part 1 (Annex G.2.4.1). l = n uv l where v = TB t t t a hs a l + h x Ê ˆ Ë ¯ + È 4 Í Í Í 2 1 1 Ê ˆ ÎÍ 20 Ë ¯ and a = distance of restraint above shear centre of beam (= hs/2 in this case) hs = distance between shear centre of flanges s 2 2 ˘ ˙ ˙ ˙ ˚˙ 05 . 21 1
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