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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) 640 Worked examples The Steel Construction Institute Silwood Park, Ascot, Berks SL5 7QN A/O.125 wL2 wuI + + + + + w + + Wu\N/// 0.0625 wL2 Subject Chapter ref. DESIGN OF CONTINUOUS COMPOSITE BEAM Design code Made by RML Sheet no. BS 5950: Parts 1 & 3 Checked by TCC The section is ‘plastic’ when grade S355 steel is used. According to Table 21.1, 50% redistribution of the negative (hogging) moment can be made provided the slab has nominal reinforcement. Negative moment = 0.0625 ¥ 40.1 ¥ 12 2 = 360.9 kNm Positive moment = 0.096 ¥ 40.1 ¥ 12 2 = 554.3 kNm (50% redistribution) Alternatively, single-span loading gives: Positive (sagging) moment = {0.096 ¥ 1.6 ¥ (5.0 + 1.0) ¥ 3.0 + 0.070 ¥ 1.4 ¥ [(2.0 + 0.5) ¥ 3.0 + 0.6]} ¥ 12 2 = 512.4 kNm 21 4 No redistribution 50% redistribution (0.0703 + 0.032) wuL 2 = 0.103 wuL 2 (accurate value = 0.096 wuL 2 ) Imposed load on one span; dead load on both spans
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 Plastic moment resistance of steel section = 355 ¥ 1200 ¥ 10 3 ¥ 10 -6 = 426 kNm > 360.9 kNm Worked examples 641 Subject Chapter ref. DESIGN OF CONTINUOUS COMPOSITE BEAM Design code Made by RML Sheet no. BS 5950: Parts 1 & 3 Checked by TCC This exceeds the design moment. It may be shown that 42% redistribution of moment is adequate. Check moment resistance of composite section. Moment resistance of composite section Effective breadth of slab (for internal span) B e = 0.7 ¥ 12000/4 = 2100 mm � beam spacing (note 0.7 has been used for internal span, rather than 0.8 for external span) Resistance of slab in compression Rc = 045 . fcuBe( Ds - Dp) = 0. 45 ¥ 30 ¥ 2100 ¥ ( 130 -50) ¥ 10 = 2268 kN Resistance of steel section in tension R s = Ap y = 7650 ¥ 355 ¥ 10 -3 = 2715 kN As R s > R c, plastic neutral axis lies in steel flange Plastic moment resistance of composite section M R D 2 ( Ds + Dp) È( Rs - Rc) T ˘ pc = s + Rc - ¥ 2 2 Í Î R ˙ f 4˚ where R f = 12.8 ¥ 177.9 ¥ 355 ¥ 10 -3 = 808 kN -3 21 5
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