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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) 664 Worked example The Steel Construction Institute Silwood Park, Ascot, Berks SL5 7QN Therefore Subject Chapter ref. DESIGN OF COMPOSITE COLUMN Design code Made by RML Sheet no. EUROCODE 4 (1990 DRAFT) Checked byGWO tensile force in web depth (225.8 - 2Y) = compressive force in concrete 452 (225.8 - 2Y) ¥ 10.5 ¥ 355 = [(Y + 69.8 + 17.3) ¥ 400 - - 17.3 2 ¥ 225.9 - Y ¥ 10.5] ¥ 0.45 ¥ 30 841.7 ¥ 10 3 - 7.46 ¥ 10 3 Y = 5.4 ¥ 10 3 Y + 470.3 ¥ 10 3 - 3.05 ¥ 10 3 - 52.7 ¥ 10 3 - 0.14 ¥ 10 3 Y or (5.4 + 7.46 - 0.14) Y = 841.7 - 470.3 + 3.05 + 52.7 \ Y = 33.6 mm Hence plastic neutral axis depth from edge of slab is Y p = 33.6 + 69.8 + 17.3 = 120.7 mm Plastic moment of resistance about x-x axis: Take moments about PNA at depth Y p Mpx = 17.3 ¥ 255.9 ¥ 355 ¥ 10-6 ¥ (260.4 - 17.3) + ¥ 0.87 ¥ 460 ¥ 10-6 ¥ (400 - 30 ¥ 2 - 12) + 10.5 ¥ ¥ 355 ¥ 10 -6 + 10.5 ¥ ¥ 355 ¥ 10-6 + (5.4 Y + 470.3 - 3.05 - 52.7 - 0.14 Y) ¥ 10-3 2 Y ( 225. 8 - Y ) 2 ¥ Yp/2 2 452 2 2 Mpx = 382.0 + 29.7 + 2.1 + 68.8 + 35.7 for Y = 33.6 mm Mpx = 518.3 kNm 0.9 Mpx = 466.5 kNm Compressive resistance of column with co-existing moment (equation 22.5) This is equivalent to the resistance of the concrete in compression (see text) P o,x = 148.1 ¥ 10 3 ¥ 0.45 ¥ 30 ¥ 10 -3 = 1999 kN 22 3
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 Moment resistance of column – minor axis Assume PNA at distance X from edge of web. Equating tensile and compressive forces. If Awpy > 0.45fcu ( b2 then PNA lies in web Ar - Af - 2 ) Subject Chapter ref. DESIGN OF COMPOSITE COLUMN Design code Made by RML Sheet no. EUROCODE 4 (1990 DRAFT) Checked byGWO xp 10.5 ¥ 225.8 ¥ 355 ¥ 10 -3 > 0.45 ¥ 30 ¥ (400 2 /2 - 17.3 ¥ 255.9 - 452/2) 841.7 < 1017.2 So PNA lies just outside web Therefore distance X is obtained from: (2X + 10.5) ¥ 2 ¥ 17.3 ¥ 355 ¥ 10 -3 + 10.5 ¥ 225.8 ¥ 355 ¥ 10 -3 x Worked example 665 = 0.45 ¥ 30 ¥ [( 200 - - X) ¥ 400 - - 10. 5 452 255. 9 10. 5 [ - - X] ¥ 17.3] 2 2 2 2 24.6X + 129.0 + 841.7 = 1051.6 - 5.4X - 3.1 - 28.7 + 0.2X X (24.6 + 5.4 - 0.2) = 1051.6 - 841.7 - 129.0 - 3.1 - 28.7 X = 1.7 mm Therefore X p = 200 - 10.5/2 -1.7 = 193.0 mm 22 4
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