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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) 434 Beams In building design when using hot-rolled sections, for which relevant properties are tabulated, 2 it will normally be sufficient to ascertain a section’s classification and moment capacity simply by referring to the appropriate table. An example illustrates the point. Example Using BS 5950: Part 1 1 determine the section classification and moment capacity for a 533 ¥ 210 UB82 when used as a beam in (1) S275 steel and (2) S355 steel. (1) From Reference 2, p. 129, section is ‘plastic’ and Mcx = 566 kN m Alternatively, from Reference 2, p. 26, b/T = 7.91, d/t = 49.6 Since T = 13.2 mm from Reference 1, Table 9, py = 275 N/mm 2 and e = (275/py) 1 – 2 = 1.0 From Reference 1, Table 11, limits for plastic section are b/t � 9e, d/t � 80e; actual b/t and d/t are within these limits and section is plastic. From Reference 1, clause 4.2.5, Mc = py S = 275 ¥ 2060 ¥ 10 -3 = 566.5 kNm (2) From Reference 2, p. 303, section is compact and Mcx = 731 kN m Alternatively, from Reference 2, p. 26, b/T = 7.91, d/t = 49.6 Since T = 13.2 mm from Reference 1, Table 9, py = 355 N/mm 2 and e = (275/py) 1 – 2 = 0.88 From Reference 1, Table 11, limits for plastic section are b/T � 9e, d/t = 80e, which give b/T � 7.9, d/t � 72; actual b/T of 7.91 exceeds 7.9 so check compact limits of b/T � 10e, which gives b/T � 9; actual b/T of 7.91 meets this and section is compact From Reference 1, clause 4.2.5, Mc = py S = 355 ¥ 2060 ¥ 10 -3 = 731.3 kN m Thus whichever grade of steel is being used, the moment capacity, Mc, will be the maximum attainable value corresponding to the section’s full plastic moment capacity, Mp. Provided that S275 material is used, the beam is capable of redistributing moments, since the plastic cross section behaves as illustrated in Fig. 13.4(a) and so could be used in a plastically designed frame. Use of the higher strength S355 material, while not affecting the beam’s ability to attain Mp, precludes the use of plastic design since redistribution of moments cannot occur due to the lack of rotation capacity implied by the behaviour illustrated in Fig. 13.4(b). For a continuous structure designed on the basis of elastic analysis to determine the distribution of internal forces and moments or for simple construction, the question of rotation capacity is not relevant and in both cases moment capacity should be taken as Mp. The fact that the section is plastic for S275 material is then of no particular relevance; a more appropriate classification would be to regard the section as compact or better.
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) Inspection of the relevant tables in Reference 2 shows that when used as beams: S275 steel all UBs are plastic all but 4 UCs are plastic (2 are semi-compact) S355 steel all but 7 UBs are plastic (1 is semi-compact) all but 9 UCs are plastic (6 are semi-compact) Cross-section classification and moment capacity, Mc Table 16.2 Non-plastic UBs and UCs in bending Compact Semi-compact S275 UC 305 ¥ 305 ¥ 97 356 ¥ 368 ¥ 129 203 ¥ 203 ¥ 46 152 ¥ 152 ¥ 23 S355 UB 762 ¥ 267 ¥ 134 406 ¥ 178 ¥ 54 406 ¥ 140 ¥ 39 305 ¥ 165 ¥ 40 254 ¥ 146 ¥ 31 203 ¥ 133 ¥ 25 356 ¥ 171 ¥ 45 UC 305 ¥ 305 ¥ 118 356 ¥ 368 ¥ 153 203 ¥ 203 ¥ 52 356 ¥ 368 ¥ 129 152 ¥ 152 ¥ 30 305 ¥ 305 ¥ 97 254 ¥ 254 ¥ 73 203 ¥ 203 ¥ 46 152 ¥ 152 ¥ 23 In those cases of semi-compact sections, moment capacities based on My are listed. The full list of non-plastic beam sections is given as Table 16.2. When using fabricated sections individual checks on the web and compression flange using the actual dimensions of the trial section must be made. It normally proves much simpler if proportions are selected so as to ensure that the section is compact or better since the resulting calculations need not then involve the various complications associated with the use of non-compact sections. This point is particularly noticeable when designing bridge beams to BS 5400: Part 3. When slender sections are used the amount of calculation increases considerably due to the need to consider loss of effectiveness of some parts of the cross section due to local buckling when determining Mc. Probably the most frequent use of slender sections involves cold-formed shapes used for example as roof purlins. Because of their 435
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