Effects of Stress-Strain Characteristics on the Strength Of CHS X Joints

Transcription

1 Effects of Stress-Strain Characteristics on the Strength Of CHS X Joints Seon-H Kim 1), *Cheol-Ho Lee 2), Dong-Hyn Chng 3), Dae-Kyng Kim 4) and Jin-Won Kim 5) 1), 2), 4) Department of Architectre and Architectral Engineering, Seol National University, Seol, Korea 3) Dongyang Strctral Engineers Grop, Seol, Korea 5) Steel Soltion Marketing Department, POSCO, Inchoen, Korea 2) ceholee@sn.ac.kr ABSTRACT Most of crrent steel design standards forbid or limit the se of high strength steels to tblar strctres becase of concerns abot their niqe stress-strain characteristics sch as the absence of yield platea and high yield ratio. The mechanical backgrond of crrent limitations appears nclear and ndly conservative, and their validity needs to be re-evalated. In this stdy, the effects of stress-strain characteristics were systematically investigated based on experimental and testvalidated nmerical analysis of CHS (circlar hollow section) X joints fabricated from different steel grades of SM49, SM57, and HSA8. The strength of high strength steel joints was dominantly governed by the widely-accepted 3% indentation criteria long before reaching the peak strength. The joint strength often exceeded the EC3 nominal strength with sfficient margin, althogh the margin tended to decrease as the yield strength of steel became higher or as the brace to chord diameter ratio became smaller. Overall, the experimental and spplemental nmerical reslts of this stdy indicated that high-strength steel CHS X joints show satisfactory performance, jst slightly inferior to ordinary steels, from the perspective of serviceability, ltimate strength and dctility even when the yield strength of steel is as high as 8MPa. 1. INTRODUCTION The se of circlar hollow sections (CHSs) is being increased more and more in a wide range of strctral applications becase of their many technological advantages over open steel shapes and aesthetic appeal as well. The se of high-strength steel 1), 4) Gradate Stdent 2) Professor 3) Assistant Manager 5) Sr. Researcher

2 tblar members can bring abot frther advantages from design to erection. However, most of crrent internationally representative design standards sch as 28 CIDECT gide (Wardenier et al., 28), 21 AISC Specification (AISC, 21), and EC3 (CEN, 25) forbid or impose restrictions on the se of high strength steels for strctres with hollow sections depending pon steel yield strength and/or yield ratio. The mechanical backgrond of these limitations appears nclear and often ndly conservative, and their validity needs to be frther investigated. As is well-known, crrent design standards for tblar joints were proposed based on the screened test database and extensive test-backed nmerical reslts. Althogh fairly extensive experimental and associated analytical stdies were condcted for CHS X joints in the past (for example, Sammet 1962, JSSC 1972, Gibstein 1973, Boone et. al 1982, Weinstein et al. 1986, Van der Vegte 1995, Kanatani 1996, Noordhoek et al and others), the database on high strength steel joints is still qite limited. In this stdy, the effects of stress-strain characteristics were systematically investigated based on experimental testing and testvalidated nmerical analysis of CHS X joints fabricated from different steel grades of SM49, SM57, and HSA8 in order to agment the database and examine if crrent design standards cold be extrapolated to high strength steels. 2. MATERIAL LIMITATIONS AND JOINT STRENGTH EQUATION The limitations on steel materials and the joint strength eqations for CHS X joints are first briefly smmarized in this section. According to the 21 AISC Specification, the applicable range of hollow section connection configration is limited to steels whose yield strength (F y ) and yield ratio (F ) are within 36 MPa and.8, respectively; the application of high strength steels to tblar strctres is virtally forbidden. The joint resistances given in CIDECT gide are basically for steels with a nominal yield strength p to 355 MPa. For nominal yield strengths greater than this vale, the joint resistances given shold be mltiplied by.9. However, the nominal specified yield strength shold not exceed 46 MPa based on the finished tbe prodct and shold not be taken larger than.8f, where F is the nominal ltimate tensile strength. The redction factor.9 was introdced on one hand de to concerns abot relatively larger deformations in CHS joints with F y appraching 46 MPa and on the other hand probable lower deformation/rotation capacity of other joints with yield strengths exceeding 355 MPa (Wardenier et al., 28). The CIDECT gide is more flexible and generos in that it provides some room for the application of high strength steels to tblar strctres. EC3 (CEN 25) gives additional rles for the se of very high strength steel or S7 whose nominal yield strength is 7 MPa. In this case, a redction factor of.8 to the joint capacity eqations has to be sed instead of the factor.9.

3 Figre 1 shows typical geometrical configration and the symbols of CHS X joints. Eqation (1) below gives the generic form of the CHS X joint strength corresponding to the limit state of chord plastification. It is implied from eqation (1) that the connection geometry and the chord stress are assmed to affect the joint strength in an ncopled manner or in the form of Q Q. Table 1 smmarizes the joint strength eqation and f range of applicability per EC3. Other standards also provide the joint strength provisions similar to EC3. f t 2 y QQ f P sin (1) Figre 1: Geometrical configration and definition of symbols of CHS X joints (see table 1 for the definition of Q and Q f Table 1: Joint strength eqation for CHS X joints: chord plastification limit state per EC3 Strength formla Range of applicability: material Range of applicability: geometry Q (geometry factor) Q f Chord in tension 1. (chord stress factor) Chord in compression 1.3n 1n p 1. a p F Yield ratio 2 y 355MPa b (for 9 ) 4 (for 9 ) 3 9 a n p f p, Ed y f p, Ed y ( : maximm compressive stress in the chord at a joint, : yield strength of a chord member.) b Steels whose yield strength is between 355MPa and 46MPa can be sed with the redction factor of.9, and steels from S46 p to S7 can be sed with the redction factor of.8.

4 3. EXPERIMENTAL PROGRAM In this stdy, a total of 9 CHS X joints fabricated from cold-formed tbes were tested nder axial compression. The key test variables inclded different grades of steels and geometrical configration of the joint. Table 2 smmarizes of the material and geometric properties of the test specimens. In order to investigate the effect of different steel material dimensions on the X joint behavior, one ordinary steel SM49 (F y = 325MPa and F = 49MPa), two high strength steels SM57 (F y = 42MPa and F = 57MPa) and HSA8 (F y = 65MPa and F = 8MPa) were inclded. Especially, HSA8 is a high-strength steel recently developed in Korea throgh the thermomechanical control process (TMCP) for bilding applications. HSA8 has a tighter control on material properties as it specifies an pper limit on the yield ratio (.85) as well as tensile strengths and has lower carbon eqivalent content for improved weldability compared to conventional qenching/tempering high strength steels. Please refer to Lee et al. (213) and Kim et al. (214) for more details of this steel. Note that SM57 and HSA8 are not permitted for tblar strctres according to the 21 AISC Specification. However, these steels may be sed with applying a sitable joint strength redction factor by following the procedre of CIDECT gide or EC3 mentioned in the previos section. Table 2: Smmary of material and geometric properties of test specimens Test Specimen a Chord length l Brace angle (in degrees) Nominal yield strength F y (MPa) Nominal tensile strength F (MPa) d t Geometric parameters d 1 t 1 X X X X X X X X X a In the specimen identification, the first character X represents X joint, and is followed by the brace to chord angle, the 2 nominal yield strength of steel F, the brace to chord diameter ratio, and the chord diameter to thickness ratio 2. y As can be seen in Table 2, the key geometric parameters ( d 1 / d ), 2 ( d / t ), ( t 1 / t ), and are all within the valid ranges of EC3 provisions (see

5 Table 1). The brace to chord diameter ratio was chosen as.62 and.75 to indce chord plastification. The stress-strain diagrams obtained from the copons of each steel plate (or before press bending) are plotted in Figre 2. As expected, Figre 2 shows that SM49, as an ordinary-strength steel, has a stress-strain characteristics desirable for dctile behavior at member and strctral levels; they have a sharp yield point, a distinct yield platea, significant strain-hardening, and a low yield ratio. However, the two high strength steels, SM57 and HSA8, lack these properties. Recently the effects of these different post-elastic properties on the strength and the rotation capacity of I-shaped beams were experimentally and analytically investigated by Lee et al. (213). This stdy may be viewed as an attempt to investigate sch effects on CHS X joints. Figre 2: Measred stress-strain diagrams Figres 3a and 3b show an overall view of typical test setp. A niversal testing machine of 1, kn capacity was sed to apply psedo-static axial compression to the X joint specimens. Both ends of the chord were set free except the lateral restraint provided to prevent ot-of-plane displacement if any. No load was applied to the chord; or all the tests were condcted nder the condition of the chord stress factor (Q f ) of 1.. A total of six LVDTs were attached arond the joint to measre the ot-of-face deformations at the saddle and crown points (see Figre 3c). Additional LVDTs were also provided to measre global displacements of brace and chord members. A lot of strain gages were installed arond the joint to monitor more detailed behavior.

6 (a) (b) (c) Figre 3: Typical test setp and LVDT arrangement: (a) X ; (b) X ; (c) LVDT arrangement 4. SUPPLEMENTAL NUMERICAL ANALYSIS PROGRAM In order to spplement the limited test database of this stdy, test-validated FE (finite element) nmerical analyses were also condcted. With the same steel grades sed in the test (SM49, SM57 and HSA8), and by varying (.2,.4,.62, and.8 ), a total of 12 nmerical models with 9 were created and analyzed. Table 3 smmarizes the material and geometric information of the nmerical models investigated. Especially, the three models with.62, X9-325/42/ (N) in Table 3 were sed in validating the accracy of FE nmerical modeling of this stdy. Note that the chord geometries and the brace thicknesses are all kept identical.

7 Table 3. Material properties and geometric dimensions for FE nmerical analysis models Nmerical model a X (N) Chord length l Brace angle (in degrees) Nominal yield strength F y (MPa) Nominal tensile strength F (MPa) X (N) X (N) 65 8 X (N) X (N) X (N) X (N) X (N) X (N) 65 8 X (N) X (N) X (N) 65 8 d t Geometric parameters d 1 t a The same naming rle sed for the specimen identification in Table 2 was again applied for the nmerical model.; the last character N in the parenthesis stands for nmerical analysis Nmerical analysis was done sing the commercial FE software ABAQUS (Simlia, 214). First, validation of FE nmerical model was carried ot by sing experimental reslts obtained from the three test specimens X9-325/42/ (see Table 2). For the material option, the von Mises yield criterion with isotropic hardening was assmed and the 2-node solid elements with redced integration (C3D2R in ABAQUS) were sed to ensre a sfficient degree of accracy, rather than more cheap 8-node solid element or shell element. RIKS algorithm was employed as static analysis option in order to trace nstable behavior if any. The weldment as fabricated was reflected in the FE modeling. Bt geometric imperfection was not considered becase the behavior of CHS X-joints were shown to be geometricimperfection insensitive. Mesh sensitivity stdy was also condcted to assre convergence. The load-indentation deformation responses predicted by the FE modeling scheme described above showed excellent correlation with experimental reslts of the three CHS X joints with.62 (see Figre 6c). 5. DISCUSSIONS OF EXPERIMENTAL AND NUMERICAL RESULTS 2.1 Joint strength criteria and joint dctility Before presenting the reslts, the joint strength criteria is briefly reviewed first.

8 The joint strength in many design standards (e.g., CIDECT gide) is based on the ltimate limit state and is defined by the lower of the ltimate strength of the joint and the load corresponding to an ltimate deformation limit. An ot-of-plane deformation of the connecting face, eqal to 3% of the CHS face diameter ( 3%d ) is generally sed as the ltimate deformation limit by following the recommendation by L et al. (1994). This serves to control joint deformations at both the factored and service load level, which is necessary de to concerns abot some highly flexible CHS joints. This ltimate deformation limit implicitly aims at restricting joint deformation at service load less than 1%d. In proposing this ltimate deformation limit by L et al (1994), the factored to service load ratio was assmed to be 1.5. In crrent steel design practice, this ratio is sally taken as 1.67 or 1.7 (e.g., AISC 21). It seems that the 3%d ltimate deformation limit is widely adopted among researchers for all types of welded tblar joints. Figre 4: Definition of connection dctility ( ) proposed based on eqal energy criteria The joint dctility ( ) or energy absorption capacity is crcially important nder extreme loading events for a strctre to srvive throgh redistribtion of forces. The joint dctility may be defined in a somewhat varied manner depending pon joint type and application prposes. Within the athors knowledge, a niversally accepted definition for the dctility of tblar joints appears not available. In order to appraise the joint dctility on a common basis, the definition of dctility for CHS X joints is temporarily proposed in this stdy. Since the load-deformation relation of CHS X joints is geometrically nonlinear from the beginning, the definition is proposed based on the initial tangent and the eqal energy criteria as illstrated in Figre 4. Defining the dctility in this manner is a bit arbitrary, bt it is believed that the joint dctility can be compared in a consistent manner from this definition.

9 Table 4: Smmary of experimental and spplemental nmerical analysis reslts ( 9 ) Nmerical model or test specimen a X (N) Tensile mechanical properties after press bending Measred yield strength (MPa) Measred tensile strength (MPa) YR Experimental or nmerical joint strength (kn) Standard-nominal joint strength based on measred yield strength (kn) 3% d Peak AISC CIDECT EC3 Joint strength normalized by EC3 formla % (3.3% b ) % 3.49 X (N) % (3.7%) NA NA % 2.23 X (N) % (4.8%) NA NA % 1.98 X (N) % (3.6%) % 3.34 X (N) % (4.%) NA NA % 2.8 X (N) % (5.1%) NA NA % 2.52 X (N) (3.5%) 26% % X (E) (4.%) 25% 3.88 X (N) (3.7%) 52% % NA NA 2497 X (E) (4.2%) 51% 3.21 X (N) (4.8%) 35% % NA NA 4166 X (E) (4.9%) 35% 2.7 X (N) % (3.2%) % 4.29 X (N) % (2.9%) NA NA % 3.63 X (N) % (3.7%) NA NA % 3.47 a E = experimental, N = nmerical. b The ot-of-plane deformation of the crown in terms of %d at peak load. c Joint dctility. See Figre 4 for the definition. c 5.2 Discssions Experimental and nmerical reslts of this stdy were evalated according to the joint strength criteria proposed by L et al (1994) discssed above. The joint strengths and joint dctility obtained from both test and nmerical reslts are smmarized in Table 4. In preparing Table 4, following aspects were considered. The AISC and CIDECT nominal strengths for SM57 and HSA8 specimens were not provided since their yield strengths all violated the pper limits of the yield strength; 355MPa (AISC) and 46MPa (CIDECT). The nominal joint strengths for SM57 and HSA8 specimens were calclated with inclding the redction factor of.8 according to the additional rles for steels with grades higher than S46 and p to S7 in EC3, since their measred yield strengths ranged from 478 to 798MPa (see Table 4). All the nominal joint strengths were compted by sing the measred yield strength reported in Table 4. It is noted that all the three standards specify similar joint strengths. The joint strengths in this stdy was mostly governed by the 3%d criteria except X (N) with.8.

10 (a) 9,.75 (b) 9,.62 (c) 6,.62 (d) 45,.62 Figre 5: Load verss ot-of-deformation relationships obtained from experiments (a).2 ( 2 26, 9) (b).4 ( 2 26, 9) (c).6 ( 2 26, 9) (d).8 ( 2 26, 9) Figre 6: Load verss ot-of-deformation relationships obtained from nmerical analysis

11 Figre 5 and Figre 6 respectively show the axial compression verss ot-ofdeformation crves obtained from test and nmerical analysis. As can be observed in Figre 5, EC3 nominal strength eqation still nderestimates the experimental strengths of HSA8 specimens even when the redction factor.8 is not applied. Table 4 indicates that all the joint strengths exceed the EC3 nominal strength, often with sfficient margin, althogh the margin tended to decrease as the yield strength of steel became higher or as the brace to chord diameter ratio became smaller. This may be explained in terms of more localized ot of bending deformation of the chord face and redced force transfer to the side wall of the chord when brace to diameter ratio becomes smaller (say,.2 is involved). It is interesting to note that the strength margin for test specimens and nmerical models with SM57 is particlarly high. It seems that this conspicos conservatism is jst artificial becase the measred yield strength of SM57 (478MPa) is jst slightly above the threshold strength (46MPa) for which the highest redction factor.8 shold be applied. Table 4 also shows the joint dctility of all models. Overall, it may be said that each joint exhibits comparable order of dctility ranging from 2 and 4. However, srely the joints with high strength steels (SM57 and HSA8) show smaller dctility compared to ordinary steel (SM49). For SM49, the joint dctility ranges from 3.5 to 4.3. For SM57 and HSA8, it is in the order of 2.2 to 3.6 and 2. to 3.5, respectively. Table 5: Ot-of-plane deformation (%d ) corresponding to service load level Ns N a 1.5 or Ns N a 1.7 Steel grade SM49 SM57 HSA8 Nmerical model or test specimen s %d N N 1.5 N 1.7 X (N).89%.74% X (N).78%.66% X (N).59%.48% X (E).53%.41% X (N).38%.3% X (N) 1.17%.98% X (N) 1.8%.91% X (N).82%.68% X (E).84%.67% X (N).5%.4% X (N) 1.51% 1.29% X (N) 1.48% 1.26% X (N) 1.15%.96% X (E) 1.16%.98% X (N).71%.59% a N is experimental or nmerical joint strength reported in Table 4

12 As mentioned previosly, the 3%d ltimate deformation limit proposed by L et al. (1994) also aims at restricting the joint deformation at service load less than 1%d. In proposing this ltimate deformation limit, the factored to service load ratio was assmed to be 1.5. In crrent steel design practice, this ratio is sally taken as 1.67 or 1.7 (e.g., AISC 21). Table 5 smmarizes the ot-of-plane deformation (%d ) corresponding to service load level N N 1.5 or N 1.7. Table 5 shows that as the s strength of steel becomes higher, the deformation level tends to increase. For the factored to service load ratio of 1.5, some of SM57 joints and most of HSA8 joints violated the 1%d deformation criteria at service load. However, for the ratio of 1.7, most of the joints satisfy the deformation criteria for serviceability except HSA8 joints with.2 and.4. Althogh HSA8 joints with small do not meet the serviceability criteria, considering that the vale of is sally larger than.5~.6 in practice, this slight violation appears a minor isse sbjected to engineering jdgement. Considering all these, it may be said that both test specimens and spplementary nmerical models with high strength steels in this stdy exhibit acceptable in terms of serviceability, strength, and dctility. 6. SUMMARY AND CONCLUSIONS In this stdy, the effects of different stress-strain characteristics on the strctral performance of CHS X joints investigated experimentally and nmerically by sing typical ordinary and high strength steels. The primary objective was to explore the possibility of extrapolating crrent ordinary-steel based design standards to high strength steels. The reslts of this stdy can be smmarized as follows. i) The benchmark steel, SM49, showed a stress-strain characteristics typical of an ordinary-strength steel with a sharp yield point, a distinct yield platea, and a yield ratio as low as.62. Whereas the two high strength steels, SM57 and HSA8, lacked sch properties and had the yield strength of 478 and 798MPa respectively, ths falling into the category for which the joint strength redction factor.8 shold be applied according to the EC3 rle. ii) All of the high-strength steel X joints exceeded the EC3 nominal strength, often with sfficient margin, althogh the yield strength of steel was as high as 8MPa. Generally, the margin was higher for high strength steels as a reslt of applying the joint strength redction factor.8 according to the EC3 rle, except the case where the brace to chord diameter ratio ( ) approached the lower limit.2.

13 iii) Particlarly high conservatism observed in SM57 joint models is jst artificial becase the measred yield strength of SM57 (478MPa) is jst slightly above the threshold strength (46MPa) from which the highest redction factor.8 shold be applied. More smooth variation of the joint strength redction factor from.9 to.8, depending pon the yield strength of steel, wold lead to more niformity in conservatism. iv) As the yield strength of steel becomes higher, the deformation at service load level tends to increase. For the factored to service load ratio of 1.5, HSA8 joints violates the 1%d deformation criteria by abot 5% when is less than.4. However, for the ratio of 1.7, almost all of the high-strength steel joints satisfy the deformation criteria for serviceability except HSA8 joints with less than.4. Considering that the vale of is sally higher than.5~.6 in practice, this slight violation appears as a minor isse sbjected to engineering jdgements. v) Based on the definition of joint dctility proposed in this paper for a consistent comparison, the dctility of CHS X joints with SM49, SM57 and HSA8 was respectively 3.76, 3.2, and 2.69 on average. Althogh the dctility tends to decrease as the yield strength of steel becomes higher, high strength steel CHS X joints seem to have still acceptable order of dctility. Considering all these, it may be said that the high strength steel CHS X joints of this stdy showed an acceptable performance in terms of serviceability, strength, and dctility, althogh frther test and spplemental nmerical stdies are needed to draw more general conclsions. ACKNOWLEDGEMENT This research was spported by a grant from High-Tech Urban Development Program (29 A1) fnded by Ministry of Land, Infrastrctre and Transport of Korea. Additional spport to this stdy by the POSCO Affiliated Research Professor Program is also grateflly acknowledged. REFERENCES [1] Wardenier, J., Krobane, Y., Packer, J.A., Vegte, G.J. van der, & Zhao, X.-L.

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