TESTS TO EXAMINE THE COMPACT WEB SLENDERNESS OF COLD-FORMED RHS by Tim Wilkinson and Gregory J. Hancock

Transcription

1 TESTS TO EXAMINE THE COMPACT WEB SLENDERNESS OF COLD-FORMED RHS by 1 2 Tim Wilkinson and Gregory J. Hancock Abstract: This paper describes a series of bending tests to examine the influence of web slenderness on the rotation capacity of cold-formed rectangular hollow sections (RHS) for use in plastic design. The results indicate that the plastic web slenderness limits in design standards, which are based on tests of I-sections, are not conservative for RHS. Some sections, which are classified as compact by current steel specifications, do not demonstrate rotation capacity suitable for plastic design. The common approach in which the flange and web slenderness limits are given independently is inappropriate for RHS. There is considerable interaction between the webs and flange which influences the rotation capacity, as shown by approximate iso-rotation curves. A proposal for a bi-linear interaction formula between the web and flange slenderness limits for Compact RHS is given. Keywords: cold-formed steel, hollow sections, plastic design, slenderness ratio, bending, rotation capacity, beams, local buckling. 1 PhD Research Student, Department of Civil Engineering, The University of Sydney, Sydney, 2006, Australia. 2 BHP Steel Professor of Steel Structures, Department of Civil Engineering, The University of Sydney, Sydney, 2006, Australia. Journal of Structural Engineering, American Society of Civil Engineers, Vol 124, No 10, October 1998, pp Note: Page layout and formatting in this pdf version maybe different to the original publication

2 INTRODUCTION Local buckling may affect the bending behaviour of steel sections. Steel design specifications define different classes of cross sections, depending on the point at which local buckling occurs during bending. Sections can be classified as Compact, Non-Compact or Slender (Australian Standard AS 4100 ( Steel 1990) (henceforth referred to as AS 4100 ), AISC LRFD (AISC 1994) (henceforth referred to as AISC LRFD )), or Class 1, 2, 3, or 4 (Eurocode 3 ( Design 1992) (henceforth referred to as Eurocode 3 ), British Standard BS 5950 ( Code 1990), Canadian Standard CANS ( Limit 1994)). A Class 4 or Slender section experiences local buckling before the moment to cause first yield (M ) is reached. Class 3 sections buckle y inelastically at a moment between M yand the fully plastic moment (M p). A Class 2 section can obtain a moment of M but cannot sustain the plastic moment for considerable rotations. Class 2 p and Class 3 are grouped together as Non-Compact sections (in AS 4100 and AISC LRFD). Class 1 or Compact sections can maintain M for sufficiently large rotations to permit plastic p design. Figure 1 illustrates various types of behaviour of different classes of steel beams constructed from cold-formed rectangular hollow sections (RHS). In Figure 1 the moment (M) is nondimensionalised with respect to M p. The curvature () is non-dimensionalised with respect to p, where p= M p/ei and EI is the elastic rigidity. The rotation capacity (R) is a measure of rotation between reaching M and the point where the moment falls below M. R is defined as / - 1, p p p where / p is the dimensionless curvature at which the moment drops below M p. The decrease in moment is usually associated with an inelastic local buckle. There are two important criteria for the suitability of a member for plastic design: Local instability of the plate elements forming the cross section is the major factor affecting rotation capacity. The plate elements must be sufficiently stocky to avoid inelastic local buckling. The width - thickness ratio (b/t) is important in local buckling problems. Width - thickness or slenderness () limits are normally given in design standards to classify the effect of local buckling of sections and to determine suitability for plastic design. There must be sufficient material ductility of the steel to avoid fracture, as a consequence of the high tensile strains caused by the large curvature at a plastic hinge. This paper describes a series of bending tests to examine the influence of web slenderness on the rotation capacity of cold-formed RHS for use in plastic design of tubular structures. Although the research set out to investigate mainly the effect of web slenderness, the interaction between the flange and the web has resulted in the flange slenderness being further investigated, and thus is also included in this paper. PREVIOUS RESEARCH There has been considerable research into plastic design of I-sections over fifty years, including slenderness limits and studies on the rotation capacity required to create a plastic collapse mechanism in various frame types. The background documentation to Eurocode 3 (Sedlacek and Feldmann 1995) summarises previous studies into b/t ratios and rotation capacity of I-sections. More recently the effect of the interaction of the flange and web of I-sections on the moment and rotation capacity has been examined. Daali and Korol (1995) produced flange - web interaction 2

3 diagrams for different values of rotation capacity for I-sections. Beg and Hladnik (1996) produced a curved limit between Non-Compact and Slender I-sections accounting for flange - web interaction. There has also been research on the flange slenderness limit for rectangular hollow sections and square hollow sections (SHS) (Dwyer and Galambos 1965; Korol and Hudoba 1972; Hasan and Hancock 1988; and Zhao and Hancock 1991a). The flange limit for RHS is different from the flange limit for I-sections since the flange of an RHS is supported on both longitudinal edges, while the flange of an I-section is unsupported on one longitudinal edge. Each web of an RHS has similar support conditions to an I-section web although there are two webs in an RHS. The similar conditions are reflected in the slenderness limits in current design standards, where the web slenderness limits for RHS and I-sections are the same, and are based on tests of I-sections. When an RHS is subjected to major axis bending, the flange is in uniform compression, and the webs are in in-plane bending. Bending is less critical for local buckling than compression for elements with the same b/t ratio, since the plate buckling coefficient (k) and hence the elastic local buckling stress is approximately six times higher for in-plane bending compared to uniform compression. Hence for SHS, and RHS with low aspect ratios (depth/width), flange buckling occurs before the web buckles locally. More recently, RHS have been produced with higher aspect ratios, such as 3.0 (Tubemakers 1994). The webs of these sections are considerably more slender than the flange, and the possibility of web local buckling before flange buckling is increased. Zhao and Hancock (1991b and 1992) observed inelastic web local buckling in some RHS with an aspect ratio of 2.0. The local buckling occurred at low rotation values for specimens with flange and web slenderness values below the limits set in current design standards for plastic design. These results provided the impetus for this series of tests in higher aspect ratio RHS. CURRENT SPECIFICATIONS This paper makes particular reference to three steel design specifications: AISC LRFD, AS 4100 and Eurocode 3. The web and flange slenderness limits for cold-formed RHS bending about the major principal axis are listed in Table 1 and Table 2 respectively for each standard for the RHS shown in Figure 2. Figure 2 defines the dimensions d, b, t and r (depth, width, thickness and e corner radius) of the section. The web ( w) and flange ( f ) slenderness values in Table 1 and Table 2 are independent of each other since no interaction between the webs and flange is considered in current design codes. In AISC LRFD and Eurocode 3, the limits are a function of the yield stress (F ) and the slenderness is a geometric ratio of the width or depth to thickness y only. Hence the limits change for different values of F y. AS 4100 specifies limits which are independent of the yield stress, while the flange and web slenderness values include a term involving F y. For simplicity and consistency, this paper adopts the AS 4100 method, in which the limit is independent of F y, but the slenderness values are a function of the dimensions and F y. Hence, in this paper, the term including F in the limits given in AISC LFRD and Eurocode 3 y have been included in the slenderness term, but not the value of the limit. Table 1 indicates that the AISC LRFD web slenderness limits are significantly higher than AS 4100 and Eurocode 3 web slenderness limits. It can be seen from Table 2 that the flange slenderness limits in the three standards are similar. 3

4 Steel design specifications have varying rotation capacity requirements for plastic design. The wide variety of loading patterns and structural frame shapes results in a large range of required plastic rotations. However, it is appropriate to adopt a representative value of rotation capacity which is satisfactory for most practical situations. Korol and Hudoba (1972) put forward a recommendation of R = 4. Eurocode 3 Class 1 and AISC LRFD Compact limits are based on a rotation capacity of R = 3. However AISC LRFD states that greater rotation capacity may be required in seismic regions. A value of R = 4 was adopted in the determination of the RHS flange slenderness limit in AS 4100 (Hasan and Hancock 1988, Zhao and Hancock 1991a) as appropriate for plastic design. R = 4 is used to formulate recommendations in this paper. Large rotations and consequently large strains are required from sections in a plastically designed frame in order to form a plastic collapse mechanism. Hence design standards have material ductility requirements for the suitability of sections for plastic design. Clause of Eurocode 3 has the following criteria: F u /F y 1.2 e 15% f e u/e y 20 where F is the yield stress, F is the tensile strength, e is the yield strain, e is the strain at the y u y u ultimate tensile strength, and e is the percentage strain (elongation) after failure measured across f the fracture surface of a tensile coupon on a gauge length of 5.65 S o where S o is the cross sectional area of the undeformed tensile coupon. Clause of AS 4100 specifies the following for plastic design: F u /F y 1.2 e f 15% the length of the yield plateau is greater than 6e y the steel exhibits strain-hardening and specifically excludes cold-formed steel, only permitting hot-formed, doubly symmetric I- sections to be used in plastic design. The only material requirement for plastic design in AISC LRFD is that F 450 MPa y (Clause A5.1). However cold-formed tubes must satisfy the requirements of ASTM A500 ( Standard 1993) to be considered an approved steel by Clause A3.1.1a of AISC LRFD. Table 2 of ASTM A500 specifies: e 21% 50 for Grade C steels (and slightly higher values for other steel grades), where e is the elongation 50 on a 2 inch (50.8 mm) gauge length. TEST SPECIMENS A variety of cold-formed RHS was chosen for the test series. The RHS were manufactured by Tubemakers of Australia Limited (now known as BHP Structural and Pipeline Products). Two strength grades were selected, Grade C350L0 and C450L0 (nominal yield stress (F ) of 350 MPa yn and 450 MPa respectively and nominal tensile strength (F ) of 430 MPa and 500 MPa un respectively), manufactured to Australian Standard AS 1163 ( Structural 1991). The Grade C450 specimens are known as DuraGal sections, produced using a proprietary cold-forming and in-line galvanizing process. In-line galvanizing provides strength enhancement and corrosion protection. The samples were artificially strain aged in a furnace at 170 C for 20 minutes to avoid strain ageing with time during the test program. 4

5 Figure 2 shows the names given to each of the faces of the RHS: weld, opposite, adjacent 1, and adjacent 2. For most RHS, the longitudinal weld was located on one of the shorter faces (the flange). Since the weld was normally slightly off-centre, the adjacent face of the RHS which was closer to the weld is labelled adjacent 1". In one case (S01) the weld was located on the longer side (the web). This was an exception to the usual situation and was probably caused by twisting of the coil during the forming process. TENSILE COUPON TESTS Three coupons were taken from the centre of the flats of each tube. One was cut from the face opposite the weld, and one from each of the sides adjacent to the weld. Corner coupons were cut from selected RHS. The coupons were prepared and tested in accordance with AS 1391 ( Methods 1991) in a 250 kn capacity INSTRON Universal Testing Machine. Since the steel was cold-formed, the yielding was gradual, so that the yield stress used was the 0.2% proof stress. The average of the yield stress from both of the adjacent faces was used in the determination of plastic moment and slenderness values. The average of the Young s modulus of elasticity from both of the adjacent faces was used in stiffness calculations. The yield stress of the opposite face was on average 10% higher than that of the adjacent faces. This was a result of the cold-forming process and has been identified previously (CASE 1990). The yield stress obtained from the corner coupons was on average 10% higher than that of the opposite face. Values of F y, F u and e f are included in Table 3 and are the mean of the values obtained from the adjacent faces of the RHS. All measured yield stresses and ultimate strengths values are static values obtained by stopping the test for approximately one minute near the yield and ultimate loads. These values are often considerably lower than commercial test values which are usually dynamic. Full details on the tensile coupon tests are given in Wilkinson and Hancock (1997). PLASTIC BENDING TESTS Procedure The bending tests were performed in a 2000 kn capacity DARTEC testing machine, using a servo-controlled hydraulic ram. A diagram of the test set-up is shown in Figure 3. The four point bending arrangement provided a central region of uniform bending moment and zero shear force. Specimens were supported on half rounds resting on greased Teflon pads which simulated a set of simple supports. The members were loaded symmetrically at two points via a centrally loaded spreader beam. Three methods of transferring the force from the spreader beam to the RHS were employed. The initial loading method (called the parallel plate method) adopted is one that has been used previously (Hasan and Hancock 1988, Zhao and Hancock 1991a) and involved welding plates parallel to the webs of the RHS beam as shown in Figure 3. A greased teflon pad was placed between the bottom of the spreader beam and the half round, allowing for the half rounds to move due to the axial shortening of the beam caused by curvature, without inducing axial strain into the RHS. The half round bore upon a thick load transfer plate, which in turn transmitted the force to the loading plates. The loading plates and the load transfer plate were connected by bolts and 5

6 an angle section, but this connection did not transfer load and was for safety only. For the perpendicular plate loading method, the loading plates were welded perpendicular to the web of the RHS as shown in Figure 4. Two plates were welded on each web at each loading point. Care was taken to ensure full contact for the bearing between these plates and the load transfer plate. In all other respects the loading mechanism is the same as the first. This method was used to see whether the parallel plate method inadvertently strengthened the section. The pin loading system involved a steel pin through the neutral axis of the RHS. A hole was drilled through the RHS and short channel sections either side of the RHS and a pin inserted as shown in Figure 5. Load was transferred by bearing from the spreader beam to the channel sections, and in turn from the channel to the pin and the bending specimen. The pin allowed rotation of the beam. Teflon pads between the spreader beam and the channels allowed longitudinal movement. The webs of both the RHS and the channels were reinforced with additional plates to avoid local bearing failure. Longitudinal strain gauges were placed midspan on each flange, and linear displacement transducers were positioned midspan and directly below the loading plates. This enabled the curvature to be calculated from both the strain gauge and displacement measurements (Hasan and Hancock 1988). For some of the later tests, curvature was determined from the displacements only. Load, deflection and strain measurements were recorded by a SPECTRA data acquisition system. The lengths of the specimens were chosen to avoid lateral buckling (Zhao, Hancock and Trahair 1995), and shear failure in the end spans. For RHS with depth d 100 mm, the length between the loading points (L 1) was 800 mm, and the distance between the supports (L 2) was 1700 mm. For sections with d 75 mm, L 1 was 500 mm, and L 2 was 1300 mm. Results The results of the plastic bending tests are presented in Table 3. Table 3 lists the nominal section size, the measured dimensions and measured yield stress, the ratio M max/m p, and R. M max is the maximum static moment reached during the test and M is the plastic moment of the section based p on the measured dimensions and the mean measured yield stress of the adjacent faces. The static moment was obtained when the test machine was halted for approximately one minute in the vicinity of the ultimate load. The nominal plastic moment (M ) (based on nominal properties) pn is also listed. R is the rotation capacity as defined in the Introduction. All specimens, except the two C450 specimens (BS01B and BS01C) and the C450 (BS19A, BS19B and BS19C) samples, experienced web local buckling which produced a rapid shedding of load with increased deflection. Each web buckled and compatibility of rotation at the corner caused deformation of the flange. In all cases, the buckle formed adjacent to one of the loading plates. BS01B and BS01C exhibited large deflections and an inelastic lateral deformation was observed at high curvatures (/ p) greater than 6. There was no sudden unloading associated with the lateral deflection. BS19A, BS19B and BS19C were SHS and, as expected, failed by flange local buckling. Specimen BS08C was not loaded to failure. No specimen failed due to insufficient material ductility. Four typical non-dimensional moment-curvature curves are shown in Figure 1, and are 6

7 representative of the performance of the test specimens. Compact and Non-Compact behaviour, as shown in Figure 1, was observed. No specimen behaved as a Slender section, but the behaviour of a typical slender member is included in Figure 1 for completeness. The web slenderness is calculated slightly differently in AS 4100, Eurocode 3, and AISC LRFD as demonstrated in Table 1. Figures 6 displays the rotation capacity versus web slenderness for AISC LRFD and differentiates between the different loading methods. Figure 7 graphs the results with respect to AS 4100, and distinguishes the different aspect ratios of the specimens. The results calculated according to Eurocode 3 are shown in Figure 8, which also compares the results of the different steel grades. In each figure, the slenderness is calculated with the measured dimensions and yield stress. DISCUSSION The results in Figures 6, 7 and 8 clearly indicate that the current web slenderness limits in AISC LRFD, AS 4100 and Eurocode 3 respectively for Compact or Class 1 sections are nonconservative. There is a large number of sections which are currently classified as Compact or Class 1 which demonstrate insufficient rotation capacity for plastic design. The Compact limit for the AISC LRFD specification appears to be the most unconservative. Many of the sections classified by AS 4100 and Eurocode 3 as Compact or Class 1 failed to reach the required rotations of R = 3 or R = 4 as shown in Figures 7 and 8. As indicated in Figure 7, several of the sections ( C450, C450, and C450) have Non-Compact flanges according to the AS 4100 flange limit. However, these sections have Compact or Class 1 flanges with respect to the AISC LRFD and Eurocode 3 limits. The sections just exceed the Compact flange limit ( = 30 defined in AS 4100) and it is reasonable to expect that they would behave almost identically to sections with Compact flanges. Figure 6 also distinguishes between the loading methods. There is a column in Table 3, called the Rotation ratio. The rotation ratio is defined as the rotation capacity using either the perpendicular or pin method divided by the average rotation capacity achieved in the parallel plate tests for that section size and grade. On average the perpendicular plate method gave an extra 16% rotation capacity. The pin loading method produced, on average, an extra 19% rotation capacity. However these averages have been boosted by three tests (BS04A C450 - perpendicular, BS06A C450 - perpendicular, and BS17A C450 - pin) which had rotation ratios of 1.69, 1.63, and 2.0 respectively. For all the other tests, there was no significant effect on the rotation capacity. These three specimens exhibit Non-Compact or Class 2 behaviour (M is reached but the rotation capacity is insufficient). p The loading method did not change the classification of the behaviour from Non-Compact to Compact. M was barely affected by altering the loading arrangement. No specific trends can max be derived from Figure 6 for the three loading methods. Figure 7 also compares the different aspect ratios (b/d) of the RHS with respect to web slenderness and rotation capacity. The majority of sections, which had an aspect ratio of 3, exhibit a close to linear increase of rotation capacity with respect to web slenderness. For sections with the same web slenderness, the RHS with higher aspect ratios (which corresponds to a lower flange slenderness) exhibit higher rotation capacities. For example, one may compare in Table 3 the C450 RHS (d/t = 3, b/t = 17, d/b = 3, R 2.5), with the

8 C450 RHS (d/t = 3, b/t = 25, d/b = 2, R 1.0). This suggests that flange - web interaction may affect the rotation capacity of RHS. Figure 8 also distinguishes between the different steel grades. Separate linear regression lines for the Grade C350 and Grade C450 are plotted in Figure 8. It can be seen that to achieve a rotation capacity of approximately R = 4, a similar web slenderness is required from both Grade C350 and Grade C450 RHS. At higher web slenderness, less rotation capacity is available from the Grade C450 RHS compared to the Grade C350 specimens of the same slenderness. Zhao and Hancock (1991a) also observed this behaviour with respect to the flange slenderness of RHS. The most appropriate way to illustrate the interaction between the flange and the web is with iso-rotation curves, which plot contours of equal rotation capacity against the flange and web slenderness of each section. Figure 9 shows approximate iso-rotation curves for the RHS tested. Since some tests were repeated, the rotation capacity shown in Figure 9 is the average rotation from the two (or three) tests performed on a given RHS size. Only the results of sections tested by the parallel plate method are shown in Figure 9. To incorporate the effects of flange buckling, the results of Hasan and Hancock (1988) and Zhao and Hancock (1991a) are included in Figure 9. Most of the tests by Hasan and Hancock, and Zhao and Hancock were performed on SHS, with an aspect ratio of 1.0 (or close to 1.0), and several RHS with an aspect ratio of 2.0 were also tested. All tests used the parallel plate method of loading. Figure 9 distinguishes the two steel grades. It can be seen that near the contour R = 4, there is not much difference between the two steel grades. However, in the higher contour regions, the Grade C350 RHS achieve a higher rotation than the Grade C450 RHS of similar flange and web slenderness. Hence for most stocky sections, steel grade does appear to affect the rotation capacity, but in the vicinity of R = 4, the steel grade does not have considerable effect on R. The iso-rotation curves in Figure 9 give the best indication of the relationship between the flange and web slenderness, and rotation capacity. The nature of the rotation contours highlight the interaction of flange and web slenderness. The sections with higher aspect ratio have a relatively stiffer flange which provides restraint against web local buckling. A section with a similar web but having a less stiff flange has less resistance against local buckling and hence a lower rotation capacity. The current rectangular independent flange and web limits, which assume no interaction, are inappropriate for this type of behaviour. Figure 9 indicates that the Compact flange limit accurately models the behaviour for RHS and SHS with stocky webs which buckle predominately in the flange. However there is a significant region for members with more slender webs in which AS 4100 is non-conservative. A simple bilinear interaction formula may be appropriate and is shown in Figure 10 and Equation 1 for AS Similar proposals may be suitable for Eurocode 3 and the AISC LRFD. Since the proposed limit is based on a rotation capacity of R = 4, then the effect of steel grade (detailed above) has no notable impact on the value of the compact limit. The bi-linear curve has been chosen initially due to its simplicity, while still accounting for the flange web interaction. A multi-linear curve or an elliptical compact limit may also be appropriate, and could be less conservative than the proposed bi-linear limit. w 70 5 f 6, f 30 (1) 8

9 The cold-formed RHS do not satisfy the material ductility requirements of AS 4100 (Clause 4.5.2) or Eurocode 3 (Clause ) for plastic design. However local instability (web buckling) was the failure mode of most of the sections, not material failure. Section BS01B, which did not experience local buckling, exhibited large rotations and strains, indicating that ductility may not present a problem. Hence the limitation on cold-formed RHS for plastic design on reduced material ductility may be incorrectly based. CONCLUSIONS The results of the plastic bending tests on a range of cold-formed RHS with different web and flange slenderness, aspect ratio and yield stress grade have been presented. The major finding of the study is that the Compact (or Class 1) web slenderness limits for RHS, which were based on tests of I-section beams, are non-conservative for RHS. The three methods of loading the RHS did not have a considerable effect on the rotation or moment capacity of the sections. Many Compact or Class 1 sections which satisfy the plastic slenderness limits of AS 4100, Eurocode 3 and AISC LRFD do not exhibit the rotation capacity suitable for plastic design. There is interaction between the flange and the web in the failure mode so that the flange and web slenderness limits must be related. This has been identified in the iso-rotation plot from which a simple bi-linear interaction curve for the Compact limits of RHS has been proposed. The bi-linear interaction curve has been drawn at a rotation capacity of R = 4, where it has been shown that the effect of steel grade is not significant. ACKNOWLEDGEMENTS This research project is funded by CIDECT (Comité International pour le Developpement et l Étude de la Construction Tubulaire). Tube specimens were provided by BHP Structural and Pipeline Products (formerly Tubemakers of Australia Limited). The experiments were carried out in the J. W. Roderick Laboratory for Materials and Structures, Department of Civil Engineering, The University of Sydney. The first author is funded by an Australian Postgraduate Award from the Commonwealth of Australia Department of Employment, Education, Training and Youth Affairs, supplemented by the Centre for Advanced Structural Engineering and The University of Sydney. 9

10 APPENDIX I. REFERENCES AISC, (1994), Load and Resistance Factor Design Specification for Structural Steel Buildings, (Metric edition), American Institute of Steel Construction, Chicago, Il. Beg D. and Hladnik L., (1996), Slenderness Limit of Class 3 I Cross-sections Made of High Strength Steel, Journal of Constructional Steel Research, 38(3), pp Code of Practice for Design in Simple and Continuous Construction: hot-rolled sections, Structural use of Steelwork in Building, (1990), BS 5950 Part 1, British Standards Institute London, United Kingdom. Limit States Design of Steel Structures, (1994), S , Canadian Standards Association, Etobicoke, Ontario, Canada. CASE, (1992), Tests on Rectangular Hollow Sections to Investigate the Effect of Variation of Yield Stress Around a Section, Investigation Report, No. S885, Centre for Advanced Structural Engineering, School of Civil and Mining Engineering, University of Sydney, Sydney, Australia. Daali M. L. and Korol R. M., (1995), Prediction of Local Buckling and Rotation Capacity at Maximum Moment, Journal of Constructional Steel Research, 32(1), pp Dwyer T. J., and Galambos T.V., (1965), Plastic Behaviour of Tubular Beam-Columns, Journal of the Structural Division, ASCE, 91(4), pp Design of Steel Structures: Part General Rules and Rules for Buildings, (1992), DD ENV , European Committee for Standardisation, Eurocode 3 Editorial Group, Brussels, Belgium. Hasan S. W., and Hancock G. J., (1988), Plastic Bending Tests of Cold-Formed Rectangular Hollow Sections, Research Report, No. R586, School of Civil and Mining Engineering, The University of Sydney, Sydney, Australia. Korol R. M., and Hudoba J., (1972), Plastic Behaviour of Hollow Structural Sections, Journal of the Structural Division, ASCE, 98(5), pp Standard Specification for Cold-Formed Welded and Seamless Carbon Steel Structural Tubing in Rounds and Shapes, (1993), A500, ASTM, Philadelphia, Pa. Steel Structures, (1990), AS 4100, Standards Australia, Sydney, Australia. Structural Steel Hollow Sections, (1991), AS 1163, Standards Australia, Sydney, Australia. Methods for Tensile Testing of Metals, (1991), AS 1391, Standards Australia, Sydney, Australia. Sedlacek G. And Feldmann M., (1995), The b/t ratios Controlling the Applicability of Analysis models in Eurocode 3, Part 1.1, Background Document 5.09 for Chapter 5 of Eurocode 3, Part 1.1, Aachen, Germany. Tubemakers, (1994), Design Capacity Tables for DuraGal Steel Hollow Sections, Tubemakers of Australia Limited, Structural Products Division, Newcastle, Australia. Wilkinson T., and Hancock G. J., (1997), Tests for the Compact Web Slenderness Limits of Cold-Formed Rectangular Hollow Sections, Research Report, No. R744, Department of Civil Engineering, The University of Sydney, Sydney, Australia. Zhao X. L. and Hancock G. J. (1991a), Tests to Determine Plate Slenderness Limits for Cold- Formed Rectangular Hollow Sections of Grade C450, Steel Construction, Journal of Australian Institute of Steel Construction, 25 (4), pp Zhao X. L. and Hancock G. J., (1991b), T-Joints in Rectangular Hollow Sections Subject to Combined Actions, Journal of Structural Engineering, ASCE, 117(8), pp Zhao X. L. and Hancock G. J., (1992), Square and Rectangular Hollow Sections Subject to Combined Actions, Journal of Structural Engineering, ASCE, 118(3), pp Zhao X. L., Hancock G. J., and Trahair N. S., (1995), Lateral Buckling Tests of Cold-Formed RHS Beams, Journal of Structural Engineering, ASCE, 121(11), pp

11 APPENDIX II. NOTATION b d E ey e u Width of RHS Depth of RHS Young s modulus of elasticity Yield strain Strain at the ultimate tensile strength e Strain over a gauge length of f e50 Fu Fun Fy Fyn I k L1 L2 M M Mp M My R So re t p f max pn w 5.65 S o Strain over 2 in. (50.8 mm) gauge length Ultimate tensile strength Nominal ultimate tensile strength Yield stress Nominal yield stress Second moment of area Elastic plate buckling coefficient Length between loading plates Length between supports Bending moment Maximum bending moment Plastic bending moment Nominal plastic bending moment Bending moment at first yield Rotation capacity Cross sectional area of a tensile coupon External radius of RHS Thickness of RHS Curvature Plastic curvature (= M p/ei) Slenderness Flange slenderness Web slenderness 11

12 Specification Web Web slenderness limits slenderness ( w ) Class 1 Class 2 Class 3 Non- Compact Compact F y AS 4100 d 2t t 250 F y Eurocode 3 d 3t t 235 d 2r e F y AISC LRFD - - t E (106)* (161)* Notes: Sections exceeding the Class 3 or Non-Compact limit are Class 4 or Slender respectively. * Applies to F y = 250 MPa for comparison with the AS 4100 limits. Table 1: Summary of RHS Web Slenderness Limits Specification Flange Flange slenderness limits slenderness ( f ) Class 1 Class 2 Class 3 Non- Compact Compact F y AS 4100 b 2t t 250 F y Eurocode 3 b 3t t 235 b 2r e F y AISC LRFD - - t E (31.7)* (39.6)* Notes: Sections exceeding the Class 3 or Non-Compact limit are Class 4 or Slender respectively. * Applies to F y = 250 MPa for comparison with the AS 4100 limits. Table 2: Summary of RHS Flange Slenderness Limits 12

13 Specimen Cut from Loading d b t r d 2r e b 2r e Fy Fu ef M M M M max R Rotation e pn p max section method (mm) (mm) (mm) (mm) t t (MPa) (MPa) (%) (knm) (knm) (knm) M p ratio BS01B C450 Parallel >13.0 BS01C C450 Parallel >9.0 BS02B C450 Parallel BS02C C450 Parallel BS02A C450 Pin BF C450 Parallel BS03A C450 Parallel BS03B C450 Parallel BS03C C450 Parallel BS04B C450 Parallel BS04C C450 Parallel BS04A C450 Perp BS16A C450 Pin BS05A C450 Parallel BS05B C450 Parallel BS05C C450 Parallel BS06B C450 Parallel BS06C C450 Parallel BS06A C450 Perp BS17A C450 Pin BS07B C450 Parallel BS07C C450 Parallel BS08B C450 Parallel BS08C C450 Parallel * BS09B C450 Parallel BS09C C450 Parallel BS09A C450 Perp BS10B C350 Parallel BS10C C350 Parallel BS11B C350 Parallel BS11C C350 Parallel BS20A C350 Perp BS20B C350 Pin BS12B C350 Parallel BS12C C350 Parallel BS13B C350 Parallel BS13C C350 Parallel BS13A C350 Perp BS21A C350 Pin BS19A C450 Parallel BS19B C450 Pin BS19C C450 Perp BJ C350 Parallel BF C350 Parallel Mean 1.09 Standard deviation Notes: For Grade C350, nominal yield stress (F yn) = 350 MPa, nominal tensile strength (F un) = 430 MPa. For Grade C450, nominal yield stress (F yn) = 450 MPa, nominal tensile strength (F un) = 500 MPa. * Specimen BS08C not tested to failure. Table 3: Summary of Results of Plastic Bending Tests 13

14 1.4 Non Dimensional Moment ( M /M p ) Slender (Class 4) Behaviour: M max < M y (not observed in this test series) Non-Compact (Class 2) Behaviour: M max > M p, R < 4 Compact (Class 1) Behaviour: M max > M p, R > 4 Non-Compact (Class 3) Behaviour: M y < M max < M p R = / p Non Dimensional Curvature (/ p) Figure 1: Types of Bending Behaviour of Steel Beams Opposite t Flange Corner Web d Adjacent 1 Adjacent 2 r e Weld b Figure 2: RHS Section Notation 14

15 Spherical head Loading ram Spreader beam Half rounds Load transfer plate A Teflon pads RHS A Parallel loading plate Transducers L 1 L2 Spreader beam RHS Half round Load transfer plate Parallel loading plate Section A-A RHS Figure 3: The Parallel Plate Loading Method for Plastic Bending Tests 15

16 Spreader beam RHS Half round Load transfer plate Section A-A Perpendicular loading plate Fillet weld (both sides) RHS Figure 4: The Perpendicular Plate Loading Method Spreader beam Teflon pad Web stiffening plates Fillet weld 20 mm (approx.) Pin Channel Section A-A RHS Figure 5: The Pin Loading Method 16

17 14 12 Rotation Capacity R AISC LRFD Compact Limit Parallel Perpendicular Pin Web Slenderness (AISC LRFD) w Figure 6: Web Slenderness - Rotation Capacity Curve (AISC LRFD) with respect to Loading Method Rotation Capacity R d/b = 3 d/b = 2 d/b = 1.66 d/b = 1.5 AS 4100 Compact Limit 2 0 These sections have noncompact flanges, but only just exceed the AS 4100 flange compact limit = Web Slenderness (AS 4100) w Figure 7: Web Slenderness - Rotation Capacity Curve (AS 4100) with respect to Aspect Ratio 17

18 14 12 Linear Regression Grade C350 Rotation Capacity R Eurocode 3 Class 1 Limit Linear Regression Grade C Grade C450 Grade C Web Slenderness (Eurocode 3) w Figure 8: Web Slenderness - Rotation Capacity Curve (Eurocode 3) with respect to Steel Grade Flange Slenderness (AISC LRFD) f R = R = 2 This Paper Grade C This Paper Grade C R = 4 Zhao & Hancock (1991) Grade C450 R = 6 Hasan & Hancock (1988) Grade C Web Slenderness (AISC LRFD) w AISC LRFD Compact Limit Figure 9: Iso-Rotation Curves (AISC LRFD) 18

19 50 Flange Slenderness (AS 4100) f Possible new Compact Limit w < 70-5 f /6 f < 30 R = 4 AS 4100 Compact Limit R = 2 R = 1 5 R = Web Slenderness (AS 4100) w Figure 10: Proposal for New Compact Limits for RHS (AS 4100) 19