350 B. Young and G.J. Hancock formed steel structural members has increased rapidly. Up to the 1980s, the thickness of cold-formed members was limited to 3 mm. This was due to the limitations of the cold-forming technology in the past. In the 1990s, cold-formed members of 12 mm and greater thickness can be produced, and these members are even thicker than some of the hot-rolled members. Therefore, the thicker cold-formed members may be used in place of the thinner hot-rolled members in building construction. The purpose of this paper is first to investigate the use of hot-rolled steel structures standards in the design of thicker cold-formed members. Therefore, a series of tests was conduced on cold-formed unlipped channels subjected to major axis bending (pure flexure in-plane bending upon the application of loads). The test results are compared with the design strengths predicted using the Australian Standard (AS 4100, 1998) for hot-rolled steel structures. The second purpose of this paper is to investigate the appropriateness of the section moment capacity design equations specified in the current cold-formed steel structures standards and specifications for thicker cold-formed members. The test strengths are compared with the design strengths predicted using the Australian/New Zealand Standard (AS/NZS 4600, 1996) and the American Iron and Steel Institute (AISI, 1996) Specification for cold-formed steel structures. Design recommendations are proposed for thicker cold-formed channel members in this paper. In addition, the paper also presents a comparison between the experimental results and the theoretical results of the cold-formed channel members. The theoretical elastic and plastic bending moments were calculated based on the measured material properties and the measured cross-section dimensions. Figure 1" Definition of symbols TABLE 1 MEASURED SPECIMEN DIMENSIONS FOR SERIES S 1 Specimen Web Flanges Thickness Radius Length d t ri L 75x40x4-a 75x40x4-b 100x50x4-a 100x50x4-b 125x65x4-a 125x65x4-b 200x75x5-a 200x75x5-b 250x90x6-a 250x90x6-b 300x90x6-a 300x90x6-b (mm) 74.4 74.4 99.2 99.2 124.9 124.9 198.8 198.8 249.5 249.3 298.5 298.8 bi (mm) 40.3 40.2 50.3 50.4 65.5 65.5 75.9 75.9 90.1 90.0 91.2 91.2 (mm) 3.84 3.85 3.83 3.83 3.84 3.83 4.70 4.69 6.01 6.00 6.00 6.00 (mm) 3.9 3.9 4.1 4.1 3.9 3.9 4.2 4.2 7.9 7.9 8.4 8.4 (mm) 1268.0 1267.8 1269.9 1269.2 1269.2 1269.1 1272.4 1271.3 1269.2 1269.7 1269.8 1271.5 Note: 1 in. = 25.4 mm Section Moment Capacity of Cold-Formed Unlipped Channels TABLE 2 MEASURED SPECIMEN DIMENSIONS FOR SERIES 82 Specimen Web Flanges Thickness Radius Length d t ri L 80x40x4-a 80x40x4-b 140x50x4-a 140x50x4-b 150•215 150•215 (mm) 80.3 80.4 140.0 140.2 149.4 149.3 b: (mm) 39.7 39.6 49.9 50.1 75.6 75.5 (mm) 3.82 3.80 3.86 3.86 3.85 3.84 (mm) 4.0 4.0 4.0 4.0 4.0 4.0 (mm) 1202.0 1201.0 1251.0 1252.0 1050.0 1051.0 Note: 1 in. = 25.4 mm 351 EXPERIMENTAL INVESTIGATION Test Specimens The tests were performed on unlipped channels cold-formed from structural steel coils. Two series of channels were tested, having nominal yield stresses of 450 MPa and 250 MPa for Series S1 and $2 respectively. The test specimens from the test Series S1 (called DuraGal) involve cold-forming of steel sections followed by in-line galvanising. This process considerably enhances the yield stress of the unformed material from 300 MPa to 450 MPa. The specimens were separated into two series of different nominal yield stress. The Series S 1 and $2 consisted of nine different section sizes, having the nominal overall depth of the webs (d) ranged from 75 mm to 300 mm, the nominal overall width of the flanges (by) ranged from 40 mm to 90 mm, and the nominal thicknesses (t) ranged from 4 mm to 6 mm. The length of the specimens was chosen, such that the section moment capacity could be obtained. Tables 1 and 2 show the measured specimen dimensions for the Series S1 and $2 respectively, using the nomenclature defined in Fig. 1. The specimens were labelled according to their cross-section dimensions. For example, the label "75•215 defines the specimen having nominal overall depth of the web of 75 mm, the overall flange width of 40 mm, and the thickness of 4 mm. The last letter "a" indicates that a pair of specimens ("a" and "b") was used in the test to provide symmetric loading for channel sections. The pair of specimens was cut from the same long specimen. Therefore, the cross-section dimensions and the material properties of the pair of specimens were nearly the same. Material Properties The material properties of all specimens were determined by tensile coupon tests. The coupons were taken from the centre of the web plate of the finished specimens belonging to the same batches as the bending tests. The coupon dimensions conformed to the Australian Standard AS 1391 (1991) for the tensile testing of metals using 12.5 mm wide coupons of gauge length 50 mm. The longitudinal coupons were also tested according to AS 1391 in a 300 kN capacity MTS displacement controlled testing machine using friction grips. A calibrated extensometer of 50 mm gauge length was used to measure the longitudinal strain. A data acquisition system was used to record the load and the gauge length extensions at regular intervals during the tests. The static load was obtained by pausing the applied straining for one minute near the 0.2% tensile proof stress and the ultimate tensile strength. This allowed the stress relaxation associated with plastic straining to take place. The material properties determined from the coupon tests are summarised in Table 3, namely the nominal and the measured static 0.2% tensile proof stress (or02), the static tensile strength (O'u) and the elongation after fracture (eu) based on a gauge length of 50 mm. The 0.2% proof stresses were used as the corresponding yield stresses (fy). 352 B. Young and G.J. Hancock TABLE 3 NOMINAL AND MEASURED MATERIAL PROPERTIES Test Series Specimen dxbf• 75x40x4 Nominal 0"0.2 =f~ (MPa) 450 0"0. 2 =f~ (SPa) 450 Measured 0-u (MPa) 525 (%) bl 20 S1 100x50x4 450 440 545 20 S1 125x65x4 450 405 510 23 S1 200x75x5 450 415 520 24 S1 250x90x6 450 445 530 21 300x90x6 450 435 535 23 80x40x4 250 280 370 35 140x50x4 250 290 380 39 S1 $2 $2 250 150x75x4 275 375 $2 37 Note: 1 ksi = 6.89 MPa Figure 2: Schematic views of bending test arrangement Section Moment Capacity of Cold-Formed Unlipped Channels 353 Figure 3" Bending test setup of specimens 200•215 354 B. Young and G.J. Hancock Test Rig and Operation The schematic views of the general test arrangement are shown in Figs 2a and 2b for the elevation and sectional view respectively. Two channel specimens were used in the test to provide symmetric loading, and the specimens were bolted to the load transfer blocks at the two loading points and end supports. Hinge and roller supports were simulated by half rounds and Teflon pads. The simply supported specimens were loaded symmetrically at two points to the load transfer blocks within the span using a spreader beam. Half rounds and Teflon pads were also used at the loading points. In this testing arrangement, pure in-plane bending (no shear) of the specimens can be obtained between the two loading points without the presence of axial force. The distance between the two loading points was 480 mm for the Series S 1 and $2, and the distance from the support to the loading point was 350 mm for the Series S1. Two photographs of the test setup of specimens 200x75x5 are shown in Figs 3a and 3b for the elevation and end view respectively. A 2000 kN capacity DARTEC servo-controlled hydraulic testing machine was used to apply a downwards force to the spreader beam. Displacement control was used to drive the hydraulic actuator at a constant speed of 0.8 mm/min and 0.6 mm/min for the Series S1 and $2 respectively. Three displacement transducers were used to measure the vertical deflections and curvature of the specimens. A SPECTRA data acquisition system was used to record the load and the transducer readings at regular intervals during the tests. The static load was recorded by pausing for one minute near the ultimate load. This allowed the stress relaxation associated with plastic straining to take place. TABLE 4 COMPARISON OF EXPERIMENTAL RESULTS WITH THEORETICAL RESULTS FOR SERIES S 1 Specimen dxbfxt 75x40x4 100•215 125•215 200•215 250•215 300•215 Experimental Ult. Moment per Channel M Exp (kNm) 6.44 11.64 16.20 Theoretical Elastic Me (kNm) 5.50 9.53 14.80 Plastic Mp (kNm) 6.52 11.19 17.17 Comparison Elastic M Exp Me Plastic M Exp Mp 1.17 0.99 1.22 1.04 1.09 0.94 1.06 0.90 40.48 38.05 45.10 79.90 77.96 93.10 1.02 0.86 92.89 98.77 119.47 0.94 0.78 Mean COV Note: 1 in. = 25.4 mm; 1 kip = 4.45 kN 1.08 0.92 0.094 0.101 TABLE 5 COMPARISON OF EXPERIMENTAL RESULTS WITH THEORETICAL RESULTS FOR SERIES 82 Specimen dxbfxt 80x40x4 140x50x4 Experimental Ult. Moment per Channel M Exp Theoretical Elastic Me Plastic Mp Comparison Elastic M Exp Me Plastic M Exp M r (kNm) (kNm) (kNm) 5.51 3.72 4.43 1.48 1.24 10.11 14.50 150•215 16.11 Note: 1 in. = 25.4 mm; 1 kip = 4.45 kN 1.20 12.13 16.53 Mean COV 1.43 1.13 0.97 14.28 1.35 1.14 0.141 0.128 Section Moment Capacity of Cold-Formed Unlipped Channels 355 Test Results The experimental ultimate moments per channel (MExp) for bending about the major x-axis are given in Tables 4 and 5 for the Series 1 (nominal yield stress of 450 MPa) and Series $2 (nominal yield stress of 250 MPa) respectively. The moments were obtained using a quarter of the ultimate static applied load from the actuator multiplied by the lever arm (distance from the support to the loading point) of the specimens. Out-of-plane bending was not observed in the tests. COMPARISON OF EXPERIMENTAL RESULTS WITH THEORETICAL RESULTS The experimental ultimate moments per channel (MExp) obtained for the Series S 1 and $2 are compared with the theoretical elastic (Me) and plastic (Mp) bending moments, as shown in Tables 4 and 5. The elastic and plastic bending moments were calculated using the measured yield stress (fy), as listed in Table 3, multiplied by the elastic (Zx) and plastic (Sx) section moduli of the full sections respectively for bending about the major x-axis (Me =fy Zx and Mp = fy Sx). The elastic and plastic section moduli were calculated based on the measured cross-section dimensions as detailed in Tables 1 and 2. The theoretical elastic and plastic bending moments are generally conservative for the Series S 1 and $2, except that the plastic bending moments are unconservative for the Series S1 having the mean value of the experimental to theoretical bending moment (mExp/Mp) ratio of 0.92 and a coefficient of variation (COV) of 0.101, as shown in Table 4. TABLE 6 COMPARISON OF TEST STRENGTHS WITH DESIGN STRENGTHS FOR SERIES S 1 Specimen dxbfxt Experimental 300x90x6 Ult. Moment per Channel Ml,:xp (kNm) 9~., 12.7 16.1 20.5 19.5 18.7 18.7 75x40x4 6.44 100x50x4 11.64 125x65x4 16.20 200x75x5 40.48 250x90x6 79.90 92.89 AS 4100 Section Non-compact Slender Slender Slender Slender Slender Design ( M.,.x ) hot AS/NZS 4600 & AISI ( M.,.x ) cold Comparison AS 4100 M Exp (M.,.x)hol (kNm) 5.50 1.10 8.92 1.31 12.52 1.49 33.32 1.39 70.57 1.28 90.18 1.17 1.29 0.110 Note: 1 in. = 25.4 mm; 1 kip = 4.45 kN (kNm) 5.83 8.87 10.85 29.21 62.62 79.10 Mean COV AS/NZS 4600 & AISI M Exp (M.,.x )c,,la 1.17 1.30 1.29 1.21 1.13 1.03 1.19 0.086 TABLE 7 COMPARISON OF TEST STRENGTHS WITH DESIGN STRENGTHS FOR SERIES 82 Specimen dxbfxt Experimental Ult. Moment per Channel M Exp (kNm) 2~.,. Design 80x40x4 5.51 10.0 140x50x4 14.50 12.9 150x75x4 16.11 19.6 Note: 1 in. = 25.4 mm; 1 kip = 4.45 kN AS 4100 Section Non-compact Non-compact Slender ( M.,. x ) h,,~ (kNm) 4.23 10.72 10.95 AS/NZS 4600 & AISI ( M.,. x ) cold (kNm) Comparison AS 4100 M Exp ( M.,. x ) j,,, 3.72 1.30 10.11 1.35 12.26 1.47 Mean 1.37 COV 0.064 AS/NZS 4600 & AISI M Exp ( M.,. x ) cord 1.48 1.43 1.31 1.41 0.062 356 B. Young and G.J. Hancock COMPARISON OF TEST STRENGTHS WITH DESIGN STRENGTHS The ultimate moments per channel obtained from the tests are compared with the section moment capacity (Msx) for bending about the major x-axis predicted using the AS 4100 for hot-rolled steel structures as well as using the AS/NZS 4600 and AISI Specification for cold-formed steel structures. Tables 6 and 7 show the comparison of the test strengths (mExp) with the unfactored design strengths (Msx)hot and (Msx)cota for hot-rolled and cold-formed steel structures standards respectively. The design strengths were calculated using the measured cross-section dimensions and the measured material properties. The values of the section slendemess ()~) calculated according to the AS 4100 are also given in Tables 6 and 7 for the Series S 1 and $2 respectively. The flanges of all channels were found to be the most slender element of the cross-sections. The design strengths predicted by the hot-rolled and cold-formed steel structures standards are conservative for the Series S 1 and $2. The higher yield stress Series S 1 specimens are predicted less conservatively than the lower yield stress Series $2 specimens. The cold-formed steel structures standards are more accurate for predicting the section moment capacity for the Series S 1 having the mean value of the test strength to design strength (MExp / (Msx)cold) ratio of 1.19 and a coefficient of variation of 0.086, as shown in Table 6. CONCLUSIONS AND DESIGN RECOMMENDATIONS An experimental investigation of cold-formed unlipped channels subjected to major axis bending has been presented. The tests were conducted on channel members having plate thickness up to 6 mm. The test specimens have thicker plates than the traditional cold-formed thin gauge members. Two series of channels having nominal yield stresses of 450 MPa and 250 MPa were tested. The experimental results were compared with the theoretical elastic and plastic bending moments. It has been shown that the theoretical bending moments are generally conservative for all channels, except that the plastic bending moments are unconservative for channels having nominal yield stress of 450 MPa. The test strengths were also compared with the design strengths obtained using the Australian Standard (AS 4100, 1998) for hot-rolled steel structures as well as using the Australian/New Zealand Standard (AS/NZS 4600, 1996) and the American Iron and Steel Institute (AISI, 1996) Specification for cold- formed steel structures. It is demonstrated that the design strengths predicted by the hot-rolled and the cold-formed steel structures standards and specifications are conservative for all tested channels. Therefore, it is recommended that the section moment capacity design equations specified in the AS 4100, AS/NZS 4600 and the AISI Specification can be used for cold-formed channel members having plate thickness up to 6 mm. The higher yield stress specimens are predicted less conservatively than the lower yield stress specimens. REFERENCES American Iron and Steel Institute (1996). Specification for the Design of Cold-Formed Steel Structural Members, AISI, Washington, DC. Australian Standard (1991). Methods for Tensile Testing of Metals, AS 1391, Standards Association of Australia, Sydney, Australia. Australian Standard (1998). Steel Structures, AS 4100, Standards Association of Australia, Sydney, Australia. Australian/New Zealand Standard (1996). Cold-Formed Steel Structures, AS/NZS 4600:1996, Standards Australia, Sydney, Australia. Hancock, G.J., (1998). Design of Cold-Formed Steel Structures (To Australian/New Zealand Standard AS/NZS 4600:1996), 3rd Edition, Australian Institute of Steel Construction, Sydney, Australia. WEB CRIPPLING TESTS OF HIGH STRENGTH COLD-FORMED CHANNELS B. Young ~ and G.J. Hancock 2 School of Civil and Structural Engineering, Nanyang Technological University, Singapore 639798 (Formerly, Department of Civil Engineering, University of Sydney, Sydney, NSW 2006, Australia) 2 Department of Civil Engineering, University of Sydney, Sydney, NSW 2006, Australia ABSTRACT The paper presents a series of web crippling tests of high strength cold-formed unlipped channels subjected to the four ioading conditions specified in the Australian/New Zealand Standard (AS/NZS 4600, 1996) and the American Iron and Steel Institute (AISI, 1996) Specification for cold-formed steel structures. The four specified loading conditions are the End-One-Flange (EOF), Interior-One-Flange (IOF), End-Two-Flange (ETF) and Interior,Two-Flange (ITF) loading. The web slenderness values of the channel sections ranged from 15.3 to 45. The test strengths are compared with the design strengths obtained using the AS/NZS 4600 and the AISI Specification. It is demonstrated that the design strengths predicted by the standard and the specification are generally unconservative for unlipped channels. Test strengths as low as 43% of the design strengths were obtained. For this reason, new web crippling design equations for unlipped channels are proposed in this paper. The proposed design equations are derived based on a simple plastic mechanism model, and the web crippling strength is obtained by dispersing the bearing load through the web. The proposed design equations are calibrated with the test results. It is shown that the web crippling strengths predicted by the proposed design equations are generally conservative for unlipped channels with web slenderness values of less than or equal to 45. The reliability of the current design rules and the proposed design equations used in the prediction of web crippling strength of cold-formed channels are evaluated using reliability analysis. The safety indices of the current design rules for different loading conditions are generally found to be lower than the target safety index specified in the AISI Specification, while the safety indices of the proposed design equations are higher than the target value. KEYWORDS Bearing capacity, Cold-formed channels, Design strength, High strength steel, Plastic mechanism model, Reliability analysis, Steel structures, Structural design, Test program, Test strength, Web crippling, Web slenderness. 357 358 INTRODUCTION B. Young and G.J. Hancock Web crippling is a form of localized buckling that occurs at points of transverse concentrated loading or supports. Cold-formed channels that are unstiffened against this type of loading are susceptible to structural failure caused by web crippling. The computation of the web crippling strength by means of theoretical analysis is quite a complex process as it involves a large number of variables. Hence, the current design rules found in most specifications for cold-formed steel structures are empirical in nature. The empirical design rules used in the Australia/New Zealand Standard (AS/NZS 4600, 1996) and the American Iron and Steel Institute (AISI, 1996) Specification for cold-formed steel structures were based on the experimental findings of Winter & Pian (1946), Zetlin (1955) and Hetrakul & Yu (1978) for sections with slender webs. The four loading conditions that are of prime interest are namely the End-One-Flange (EOF), Interior-One-Flange (IOF), End-Two-Flange (ETF) and Interior- Two-Flange (ITF) loading. Although, according to Nash & Rhodes (1998), the computation of web crippling strength obtained using empirical methods is relatively rapid and safe within their range of application, this does not imply that empirical methods are without drawbacks. The equations, derived through empirical methods, are only applicable for a specific range and it may be difficult to ascertain the underlying engineering principles in parts of the complex equations. Therefore, there is a need to determine the appropriateness of the current design rules on the various types of steel members and to propose some design equations that are derived through a combination of both empirical and theoretical analyses. In this paper, the appropriateness of the current design rules in the AS/NZS 4600 and the AISI Specification for unlipped channels subjected to web crippling is investigated. A series of tests was conducted under the four loading conditions specified in the AISI Specification. The web crippling test strengths are compared with the design strengths obtained using the AS/NZS 4600 and the AISI Specification. A set of equations to predict the web crippling strengths of unlipped channels with web slenderness (depth of the flat portion of the web to thickness ratio, h/t) values less than or equal to 45 is proposed. The proposed design equations are derived based on a simple plastic mechanism model, and these equations are calibrated with the test results. The proposed design equations are derived through a combination of theoretical and empirical analyses. Factors to account for the variation of the web slenderness of the channel sections have also been incorporated in the proposed design equations. In addition, the current design rules and the proposed design equations used in the prediction of web crippling strength are evaluated using reliability analysis. The safety indices of the current design rules and the proposed design equations are compared with the target safety index specified in the AISI Specification. TEST PROGRAM A series of tests was performed on cold-formed unlipped channels subjected to web crippling. The specimens were rolled from structural steel sheets having nominal yield stress of 450 MPa. The sections (called DuraGal) have in-line galvanising which increases the nominal yield stress from 300 MPa to 450 MPa when combined with roll-forming. The test specimens consisted of six different cross-section sizes, having a nominal thicknesses ranged from 4 mm to 6 mm, a nominal depth of the webs ranged from 75 mm to 300 mm, and a nominal flange widths ranged from 40 mm to 90 mm. The web slenderness (h/t): values ranged from 15.3 to 45.0, and these values were obtained using the measured cross-sectional dimensions. The specimens are considered to have stocky webs. The specimen lengths were determined according to the AS/NZS 4600 and the AISI Specification. Table 1 shows the nominal specimen dimensions, using the nomenclature defined in Fig. 1, where d is the overall depth of web, bf is the overall width of flange and t is the thickness of the channels. Young and Web Crippling Tests of High Strength Cold-Formed Channels 359 Hancock (1998) also performed similar tests on cold-formed channels having different web slendemess and material properties. The web slenderness values ranged from 16.2 to 62.7, and had nominal yield stress values of 250 MPa and 450 MPa. The material properties of the test specimens were determined by tensile coupon tests. The coupons were taken from the centre of the web plate of the finished specimens. The tensile coupons were prepared and tested according to the Australian Standard AS1391 (1991) using 12.5 mm wide coupons of gauge length 50 mm. The static load was obtained by pausing the applied straining for one minute near the 0.2% tensile proof stresses and the ultimate tensile strength. This allowed the stress relaxation associated with plastic straining to take place. Table 1 summarises the material properties determined from the coupon tests, namely the nominal and the measured static 0.2% tensile proof stress (o02), the static tensile strength (ou) and the elongation after fracture (cu) based on a gauge length of 50 mm. The 0.2% proof stresses were used as the corresponding yield stresses. The load or reaction forces were applied by means of bearing plates. The bearing plates were fabricated using high strength steel having a nominal yield stress of 690 MPa. All bearing plates were designed to act across the full flange widths of the channels excluding the rounded comer. The length of bearing (N) was chosen to be the full and half flange width of the channels. The channel specimens were tested using the four loading conditions according to the AISI Specification. These loading conditions are EOF, IOF, ETF and ITF as described earlier. Displacement control was used to drive the hydraulic actuator at a constant speed of 0.8 mm/min. The static load was recorded by pausing for one minute near the ultimate load. Details of the test set-up and test rig are given in Young and Hancock (1998). The experimental ultimate web crippling loads per web (PExp) are given in Tables 2 and 3. Two tests were repeated for 125x65x4 channel subjected to ITF loading condition, and the test results for the repeated tests are very close to their first test values, with a maximum difference of 1.5%. The small difference between the repeated tests demonstrated the reliability of the test results. For 75x40x4 channel (stockier web having h/t = 15.3) subjected to EOF loading condition, web crippling was not observed at ultimate load during testing, but specimens failed in overall twisting of the sections. t_. ~X /ri !-~ bs Figure 1" Definition of symbols TABLE 1 NOMINAL AND MEASURED MATERIAL PROPERTIES Channel dx bfx t (mm) 75x40x4 100x50x4 125x65x4 200x75x5 Nominal 0"0. 2 0"0. 2 (MPa) (MPa) 450 450 450 450 450 440 405 415 Measured O'u ~'u (%) (MPa) 525 545 510 520 20 20 23 24 250x90x6 450 445 530 21 300x90x6 450 435 535 23 Note:lin. =25.4 mm; 1 ksi = 6.89MPa COMPARISON OF TEST STRENGTHS WITH CURRENT DESIGN STRENGTHS The web crippling loads per web obtained from the tests are compared with the nominal web crippling strengths predicted using the AS/NZS 4600 and the AISI Specification for cold-formed steel structures. Table 2 shows the comparison of the test strengths (PExp) with the unfactored design strengths (Pn). The current design strengths were calculated using the average measured cross-section dimensions and . loading conditions that are of prime interest are namely the End-One-Flange (EOF), Interior-One-Flange (IOF), End-Two-Flange (ETF) and Interior- Two-Flange (ITF) loading. Although, according. structures. The four specified loading conditions are the End-One-Flange (EOF), Interior-One-Flange (IOF), End-Two-Flange (ETF) and Interior,Two-Flange (ITF) loading. The web slenderness values. may be used in place of the thinner hot-rolled members in building construction. The purpose of this paper is first to investigate the use of hot-rolled steel structures standards in the design