12
Purlins
12.1 Introduction Although purlins usually represent a relatively small part of the total mass of a typical steel-framed building, the time taken to erect them could have a significant effect on the completion time of the project. From the point of view of both the ex-works cost and the erection time, the layout and details of the purlin system should be simple and the number of components be kept to a minimum.
12.2 Design of purlins The loading to be used in the design of roof systems as given in the current code SABS 0160-1989 is considerably less severe than in the 1984 edition. For tributary areas from 15,0 m2 upward the nominal live loading has been reduced from 0,5 kPa to 0,3 kPa. For smaller areas the loading increases linearly, reaching a value of 0,5 kPa at 3,0 m2 (see Clause 5.4.3.3 of SABS 0160). Purlins are usually designed as continuous over at least two spans and are assumed to be uniformly loaded. Thus for a span and spacing combination as low as 4,5 m and 1,67 m the minimum value of 0,3 kPa applies. This means that at the ultimate limit state the dead plus live loading combination on the purlins of a typical industrial building with metal cladding is only about two-thirds of what it was prior to 1989. The wind loading in the new code is substantially the same as before, however. Consequently, purlins will tend to be lighter when designed for gravity loading, but the dead load plus wind uplift combination will become more critical; in fact it will often be the governing condition, with lateral-torsional buckling of the bottom flange under negative moment being the main design consideration. The design of purlins, especially of cold-formed section, is dealt with in Chapter 8 of the Steel Construction Handbook (Ref. 5).
12.3 Purlin sections The most commonly used section for purlins is the lipped cold-formed channel. On a strength-to-mass basis this is a very efficient section and the lipping of the flanges adds to its lateral-torsional strength, thus making it more resistant to negative moment when the bottom flange is in compression.
12.1
In the past these sections were rolled almost exclusively from commercial grade steel strip, which does not have a specified yield stress or ultimate strength. It should be noted, however, that clause 3 of SABS 0162-Part 2 requires the use of steel that meets one of the following requirements: a)
It complies with SABS 1431 or one of the other specifications listed in clause 3.1.
b)
If it does not comply with the above, it has specified minimum values of yield stress and ultimate strength as given in the relevant published standard or specification and complies with the ductility requirements of clause 3.2.3.
c)
If it is a so-called 'commercial quality' steel or a steel of unknown origin, it shall be subject to tensile tests in accordance with clause 9.3.1 and the design values of the yield stress and tensile strength shall be taken as not more than 0,8 times the values determined from the tests. Furthermore, the steel shall comply with the ductility requirements of clause 3.2.3.
The random use of commercial quality steel is thus ruled out. If it is used, it must subjected to testing, which would have to be done on samples of the proposed material before the main material order is placed. Cold-formed sections are available on request in Grade 300WA steel, at a price premium of only some 2,5 per cent over commercial grade. It would be advisable for designers to regularly specify this grade, since the greater the demand on the suppliers the more readily available it will become. The advantages from a strength point of view are obvious, although it must be pointed out that the strength ratio, when compared with commercial grade, drops from about 1,33 for members of low slenderness to slightly over 1,00 for members of high slenderness. Grade 300WA steel is thus of somewhat limited advantage for purlins subject to negative moment, but is nevertheless worth using because of the small difference in price. Cold-formed lipped zeds may also be used and have the advantage that their shear centre is located at the centroid of the section. On a sloping roof they are thus less prone to twisting under gravity loading than a channel, whose shear centre is at some distance away from the back of the web (see Fig 12.1). Zeds are, however, about four per cent more expensive than the corresponding channel section and are slightly weaker when laterally unrestrained.
S
S
Fig 12.1: Purlin sections - shear centres
12.2
12.4 Spans and spacing As mentioned in Section 6.6 with reference to portal frame buildings, it is necessary to optimise the centre-to-centre distance of the roof principals to achieve the greatest overall economy in the structure. This can only be done by carrying out trial designs to make the necessary cost comparisons between the different schemes, including, of course, the cost of the sheeting. In general it can be said that, within reasonable limits, longer purlin spans, with a reduced number of principals, will be more cost-effective. Regarding the spacing of the purlins themselves, it is usually cheaper on long roof slopes to use wider spacing and deeper profile sheeting than closer spacing and shallow profile sheeting. Comparing two popular sheeting profiles requiring purlin spacings of 1,7 m and 2,2 m respectively it can be shown that the deeper profile sheet together with the larger purlin spacing is only about five per cent more expensive than the alternative combination. This is based on the cost of materials only. When the reduced number of components, i. purlins, sag bars, bolts and sheet fixings, is taken into account it is obvious that there will be a saving in fabrication and erection time that will outweigh the slight additional cost in materials. Before deciding on the purlin spacing, however, the designer should consider the effect that this will have on the truss or rafter supporting the purlins. In the case of a light latticed truss of small to medium span a heavier top chord might be required when a large purlin spacing is used (it being assumed that the purlins are located at the truss panel points). For larger trusses and most portal frame rafters the wider spacing would normally not be detrimental. Another consideration that has a bearing on the spacing is the end-span to interior-span ratio of the sheeting. Roof sheeting has an optimum load resistance when the end spans are about 0,85 times the interior spans. This ratio results in a more uniform distribution of moment in the sheeting and of loading on the purlins. (With uniform purlin spacing the loading on the penultimate purlins, i.e. the first purlin up-slope from the eaves and downslope from the ridge, is nearly 14 per cent higher than on the intermediate purlins.) Closer purlin spacing at the eaves has the added advantage of providing better support to the sheeting in an area that is likely to carry more traffic, both during erection and under subsequent maintenance, e.g. gutter cleaning. On a portal frame rafter the non-uniform spacing would not be of disadvantage; in fact at the eaves it could result in a better location of the penultimate purlin and its fly-brace at or close to the haunch-rafter junction. On a latticed truss with a smaller end the diagonals would be shorter, resulting in a reduction of both member length and force, which would be of benefit if these members were struts. At the ridge the reduction in purlin spacing would be achieved automatically by the down-slope displacement of these purlins; the reduction could be supplemented, if necessary, by a slight reduction in panel length (see Fig 12.2). An even greater reduction in the end spans of the sheeting would help to resist the higher wind suction intensities adjacent to the eaves and ridge specified in SABS 0160, Table 7, Columns 8, 9 and 10.
12.3
X = Flybraces
24 000 span
1 800
4 x 2 120
1 800
200
24 000 span
Fig 12.2: Unequal purlin spacing
12.5
Spanning configurations
The most popular configuration is the two-span continuous arrangement. Single-span purlins are seldom used because of the large deflections – about 2,4 times those of a double-span purlin – although the maximum moment remains the same at WL 8. A further advantage of continuous purlins is that under wind uplift loading a shorter length of the bottom flange is under compression and thus subject to lateral-torsional buckling. Since steel sections can be purchased and transported without undue difficulty in lengths up to 15,0 m, it is common for purlins to be designed as two-span continuous for spans up to 7,5 m. Larger spans, up to say 9,0 m or more, are feasible, but special precautions are necessary both in the transportation and the site handling of such long sections.
12.4
Alternatively, the purlins can be made in single-span lengths (e.g. 9,0 m) and converted to double-span on site by introducing a splice at every second support. In cases where the negative moment at the centre support under downward loading is the critical design moment, the splicing member may be made of a heavier section and a lighter section then be used for the purlin itself. The splice must of course be long enough to extend over the region of high moment. Care must be taken when considering this option because, depending on the ratio of upward to downward loading and the spacing of the sag bars, the design criterion is often negative span moment under upward loading. In this case there is no advantage in using a heavier splice member. A point to be noted with respect to two-span configurations is that the loads imposed on alternate rafters or trusses (at the points of continuity) are 25 per cent higher than in a single-span configuration. This problem can be overcome by staggering the splice positions of alternate purlins in plan, so that each truss is subject to high and low purlin loads at alternate panel points and thus has its overall loading evened out. At the ends of the building each alternate purlin will be simply-supported and should thus be of a thicker section to cater for the increased deflection. A further possibility is to make the purlins fully continuous by splicing purlins of single span length at every support and purlins of double-span length at every alternate support. This enables a lighter section to be used for the interior spans, but a heavier (i.e. thicker) section will be required for the end spans and at penultimate supports because the bending moments at these locations is much higher than in the interior. The disadvantages of this arrangement are the non-uniform purlin section and the additional splices required. The cost of the latter (including not only the splice, but also additional bolts and bolt holes) may well outweigh the saving in purlin material. (See also Section 12.6 below.) For large continuous spans unequal-flanged cold-formed zed sections can be used in order to simplify the splicing, but as already mentioned their availability and higher cost would have to be considered. The splicing member is a short length of zed of the same section as the purlin, but inverted and nested into the purlin to form a splicing sleeve. Another solution for large continuous spans is the overlapped zed system. The purlins are unequal-flanged zeds that are overlapped at each support, the sections in alternate spans being inverted and nested into the adjoining span. The unique feature of this system is that in the regions of high moment over the supports the sections are overlapped, thus providing double the moment resistance. In addition, the splicing of the purlins is automatically catered for. Care should be exercised when considering this solution – where upward loading is critical the narrower bottom flange of the zed in alternate spans could be detrimental because of its reduced resistance to lateral-torsional buckling. In this case no advantage would be gained from the double strength at the overlap.
12.6 Continuous purlins with reduced end spans When purlins are used in the fully-continuous configuration as discussed above, two drawbacks become apparent. The first is that the bending moments in the end span and over the penultimate support are greater than at the intermediate locations, thus requiring a heavier section in the end and penultimate spans, and the second is that the load imposed on the penultimate truss or portal rafter is greater than on the typical intermediate ones.
12.5
Both of these disadvantages can be overcome by the simple expedient of slightly reducing the end spans of the purlins in relation to the intermediate ones, i.e. by making the end bays of the building shorter than the interior bays. Fig 12.3 shows the values of the moments and end reactions for ratios of end span to intermediate spans of 1,0, 0,95, 0,9, 0,85 and 0,8. The values given are for a seven-span fully-continuous purlin and are intended to give a general indication of the reductions that are possible. For spans separate analyses would be necessary. In the case depicted in Fig 12.3 it will be seen that the optimum end-span length is 0,85 times the intermediate span length; at this ratio the maximum moments over the supports are all nearly equal.
M1
RA
M2
RB
M1
M6
M4
RC
L1
L1 L
M5
M3
RD
L
L
M2
M3
M4
M5
M6
RA
RB
L
RC
RD
1,0
0,0762
-0,1056
0,0335
-0,0775
0,0440
-0,0845
0,394
1,134
0,965
1,01
0,95
0,0674
-0,0991
0,0359
-0,0792
0,0433
-0.0842
0,371
1,10
0,976
1,01
0,9
0,0586
-0,0925
0,0383
-0,0809
0,0426
-0,0838
0,347
1,06
0,986
1,00
0,85
0,0505
-0,0871
0,0403
-0,0824
0,0421
-0,0835
0,333
1,03
0,995
1,00
0,8
0,0424
-0,0817
0,0423
-0,0838
0,0415
-0,0832
0,298
1,00
0,003
1,00
Fig 12.3: Moment diagram - purlins with reduced end spans
Further benefits that would accrue from reducing the end spans would be that the high wind suction loading on the roof adjacent to the gables (see SABS 0160, Table 7, Column 7) would be more easily catered for and that the end-bay purlins, if designed to act as struts in the rafter bracing systems, would be able to participate more effectively because of their shorter length. Shorter end bays would also be beneficial to the girts and vertical bracing in the sides of the building.
12.7 Sag bars For purlin spans over 4,5 m, sag bars are generally used, with one per span for spans up to 7,5 m and two per span up to 12,0 m. However, for spans somewhat in excess of 7,5 m and 12,0 m the number of sag bars can be reduced to zero and one respectively, provided a thorough analysis of the purlin is made. This should include an accurate assessment of loading, careful consideration of the bending moment distribution and allowance for lateral-torsional buckling of the bottom flange. A heavier section of purlin will be required, but this will in most cases be offset by the saving in the sag bars. It must be remembered that the labour-to-mass ratio of sag bars, including the extra holes required
12.6
in the purlins, is very high and that the elimination or reduction of sag bars will represent a significant saving.
12.8 Summary •
Purlins designed to the current loading code SABS 0160-1989 are subject to less severe gravity loading, but the dead load plus wind load combination is more critical. Special care is needed to ensure resistance to lateral-torsional buckling of the bottom flanges when in compression.
•
Although cold-formed purlins can be made from commercial quality steel, provided it is tested for compliance with the current code, consideration should be given to using steel with known strength values, which is available at only a small increase in price.
•
It is important to optimise truss or rafter spacing, i.e. the purlin spans, in order to achieve the right balance between purlin and roof principal costs. Generally, larger purlins spans are favoured.
•
The spacing of the purlins adjacent to the eaves and the ridge of a roof may be reduced to give a more uniform moment distribution in the roof sheets.
•
Purlins may be of double-span or multi-span configuration, the latter requiring a smaller purlin section, but needing additional splice material, which tends to be expensive, especially in erection.
•
The end spans of multi-span purlins require a heavier section than interior spans.
•
For very long spans unequal-flanged zed sections may be used, with sleeves or overlaps at the splices to provide full continuity.
•
For fully-continuous purlin configurations the larger bending moments and truss loading in the end spans and at the penultimate trusses can be reduced by making the end spans (i.e. the end bays of the building) smaller than the interior ones.
•
For purlin spans above 4,5 m, sag bars are generally used, one per span up to 7,5 m and two per span up to 12,0 m. The number of sag bars may be reduced for spans in excess of these limits if a careful analysis of the lateral-torsional buckling of the purlin is made.
12.7
