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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) 644 Worked examples The Steel Construction Institute Silwood Park, Ascot, Berks SL5 7QN Composite condition – service loading Subject Chapter ref. DESIGN OF CONTINUOUS COMPOSITE BEAM Design code Made by RML Sheet no. BS 5950: Parts 1 & 3 Checked by TCC Determine elastic section properties under positive moment Elastic neutral axis depth x Take ae = 15 for LWC r x Second moment of area of section (equation 21.2) I Elastic section modulus – steel flange (equation 21.3) Z e e c t = = = = D D r D s - p + a Ê e + D ˆ s 2 Ë 2 ¯ 1 + a r A 7650 + ( D - D ) B ( 130 - 50) 2100 s p e È80 + ¥ ¥ Ê 406. 4 0. 045 15 Ë + 130 ˆ ˘ ÎÍ 2 2 ¯ ˚˙ ( 1 + 0. 045 ¥ 15) 158. 1mm = 2 3 AD ( + Ds + Dp) Be( Ds - Dp) + + I x 41 ( + aer) 12ae = È7650( 406. 4 + 130 + 50) Í Î 4( 1 + 0. 045 ¥ 15) 2100 ¥ ( 130 -50) + 12 ¥ 15 = 6 ( 393. 0 + 6. 0 + 216) ¥ 10 = 6 4 615 ¥ 10 mm 6 615 ¥ 10 = ( 406. 4 + 130 -158. 1) 6 3 = 162 . ¥ 10 mm e = 0. 045 2 3 ˘ + ˙ ˚ ¥ 216 10 6 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 Service load on composite section = (5.0 + 1.0 + 0.5) ¥ 3 = 19.5 kN/m Worked examples 645 Subject Chapter ref. DESIGN OF CONTINUOUS COMPOSITE BEAM Design code Made by RML Sheet no. BS 5950: Parts 1 & 3 Checked by TCC Mid-span moment for serviceability conditions should take into account ‘shakedown effects’ as degree of moment redistribution at ultimate loads exceeds 30%. Shakedown load = Dead load + 80% Imposed load ws = [ 20 . + 05 . + 08 . ¥ ( 50 . + 10 . ) ]¥ 3+ 06 . = 22. 5 kN/ m Shakedown moment (elastic negative (hogging) moment) = 0.125wsL 2 = 0.125 ¥ 22.5 ¥ 12 2 = 405 kNm This is less than the plastic moment resistance of the beam (= 426 kNm), so no plastification occurs at working load. Service moment under imposed loading on all spans (allowing for 30% redistribution of negative moment) = (0.0703 + 0.15 ¥ 0.125) ¥ 19.5 ¥ 12 2 = 250.0 kNm Steel stress (lower flange) = Additional stress in steel beam arising from self weight of floor = 63 N/mm2 Total stress = 63 + 154 = 217 N/mm 2 < py Concrete stress = 250. 0 ¥ 10 6 162 . ¥ 10 250 ¥ 10 615 ¥ 10 6 6 6 = 154 Nmm / 2 158. 1 2 ¥ = 43 . N/ mm < 05 . fcu 15 21 9
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