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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) 634 Worked examples The Steel Construction Institute Silwood Park, Ascot, Berks SL5 7QN Composite condition – service load Determine elastic section properties Subject Chapter ref. DESIGN OF SIMPLY SUPPORTED COMPOSITE BEAM Modular ratio a e = 15 for LWC (see Table 21.3) Elastic neutral axis depth (equation 21.1): x where r = x Second moment of area (equation 21.2): I e e c = = = D D r D s - p + a Ê e + D ˆ s 2 Ë 2 ¯ ( 1 + aer ) A 8540 = = 0. 0355 ( Ds - Dp) Be 80 ¥ 3000 80 + ¥ ¥ Ê 453. 6 0. 0355 15 Ë + 130 ˆ 2 2 ¯ ( 1 + 0. 0355 ¥ 15) 150. 1mm below top of slab = 2 3 AD ( + Ds + Dp) Be( Ds - Dp) + + Is 41 ( + aer) 12ae = 8540( 453. 6 + 130 + 50) 4( 1 + 0. 0355 ¥ 15) 3000 ¥ 80 + 12 ¥ 15 = 6 4 861. 8 ¥ 10 mm Elastic section modulus – steel flange (equation 21.3) 6 861. 8 ¥ 10 Zt = = 198 . ¥ 10 mm ( 453. 6 + 130 -150. 1) Elastic section modulus – concrete (equation 21.4) 6 861. 8 ¥ 10 Zc = ¥ 15 = 86. 1 ¥ 10 mm 150. 1 Design code Made by RML Sheet no. BS 5950: Part 3 Checked by GWO 2 3 6 3 + 294 ¥ 10 6 3 6 21 6
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) ¥ 3.0 = 19.5 kN/m Service moment = 19.5 ¥ 12 2 /8 = 351 kNm Worked examples 635 Subject Chapter ref. DESIGN OF SIMPLY SUPPORTED COMPOSITE BEAM Design code Made by RML Sheet no. BS 5950: Part 3 Checked by GWO Stress in steel = = 177 N/mm2 6 351 ¥ 10 6 198 . ¥ 10 Additional stress on non-composite section = 92 N/mm 2 Total serviceability stress = 177 + 92 = 269 N/mm 2 < p y Stress in concrete Deflection – imposed load Imposed load = (5.0 + 1.0) ¥ 3.0 = 18.0 kN/m Deflection Additional deflection from partial shear-connection (equation 21.18) d s d d c c 6 351 ¥ 10 = 6 86. 1 ¥ 10 2 = 41 . Nmm / < 05 . fcu 4 -3 5 18. 0 ¥ 12000 ¥ 10 = ¥ 384 205 ¥ 10 ¥ 861. 8 ¥ 10 = 27. 5 mm 861. 8 = ¥ 27. 5 = 80. 6 mm 294. 0 dcd d d I = c + 031 . ( - K) ( s - c) = 27. 5 + 0. 3( 1 -0. 76) ( 80. 6 - 27. 5) = 31. 3 mm ( span/ 383) 3 6 Deflection is the limiting criterion. It would be possible to show that the imposed load could be increased to 6 kN/m 2 for the same beam size. 21 7
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