SHEAR LAG IN SLOTTED GUSSET PLATE CONNECTIONS TO TUBES

Transcription

1 SHEAR LAG IN SLOTTED GUSSET PLATE CONNECTIONS TO TUBES S. Willibald, University of Toronto, Canada J.A. Packer, University of Toronto, Canada G. Martinez Saucedo, University of Toronto, Canada R.S. Puthli, Universität Karlsruhe, Germany ABSTRACT Hollow Structural Sections (HSS) are commonly used as bracing members in steel-framed buildings or as web members in roof trusses. The tubes are frequently slotted onto gusset plates to simplify fabrication and avoid profiling. Under tension loading, these gusset plate connections can be susceptible to shear lag failure of the HSS since only a part of the tube cross-section is connected to the plate. This paper compares current design proposals found in research, design guides and specifications against recent experimental and numerical work by the Authors, which comprised of gusset plate connections for round hollow sections with varying fabrication details. INTRODUCTION Gusset plates can be found in almost any type of steel building. As hollow sections have become more popular due to their exceptional properties in compression and torsion, the combination of both gusset plates and hollow sections can be found in numerous applications. These gusset plate connections can be used to splice hollow section members or to connect web members to the chords in roof trusses (see Figure 1). Three possible fabrication details are shown in Figure 2. Slotting the hollow section (Figures 2 (b) and (c)) is the most common version of this connection type. Various failure modes are possible under tension loading with shear lag being one of them. Shear lag of the hollow section can occur as the circumference of the hollow section is connected to the gusset plate only at two points on opposing sides. The unconnected circumference of the hollow section is not fully engaged and contributes only in part to the resistance of the member. In addition, local stress peaks at the slot ends can cause initiating cracks that may result in an early failure. The presented study focused on shear lag failure for round hollow sections. An experimental study on six connections under tensile loading has been carried out, followed by a numerical analysis, which will be used to substitute for further experimental work. Additionally, recent research and international specifications on this topic are evaluated and "best practice" recommendations are made for application to round hollow section members. Figure 1. Metro Toronto Convention Centre. Connections in Steel Structures V - Amsterdam - June 3-4,

2 (a) (b) (c) Figure 2. Fabrication details of tested gusset plate connections. LITERATURE STUDY Of the failure modes that can occur in gusset plate connections, shear lag is one of the most ill-defined. Shear lag fracture of the hollow section takes place due to the uneven stress distribution around the circumference of the hollow section. The stresses peak at the points 0 where the hollow section is connected to the plate or weld and become less as the distance to the weld increases (see Figure 3). Therefore, the unconnected circumference only contributes in part to the capacity of the member. Strain [µm] International specifications and design guides 500 kn 750 kn 1000 kn 1032 kn Angle θ [ o] For tension loaded connections, Eurocode 3 (1) provides shear lag provisions that are only applicable for bolted connections. For connections with welds, no specific design method is provided in the Eurocode. Otherwise, shear lag is mentioned only in connection with locally introduced shear loads causing bending moments in longitudinally stiffened plated structures. The North American specifications address shear lag for welded connections under tension loading. Unfortunately, the American and Canadian specifications (AISC 2, CSA 3) differ in their design methods for this limit state. In addition, changing formulae in old and new specifications (e.g. AISC 4 versus AISC 5) indicate a lack of certainty with this connection type. The Japanese specification (6) excludes shear lag by providing minimum connection lengths. The following paragraphs briefly introduce the different design methods of the various specifications. 0 θ Figure 3. Strain distribution around circumference of the round hollow section (specimen 1, slotted HSS, no weld return) Connections in Steel Structures V - Amsterdam - June 3-4, 2004

3 The current American Specification for Hollow Structural Sections (AISC 2) uses the concept of "effective net area". The design method provided is based on research carried out by Chesson and Munse (7). An eccentricity factor U is calculated from the connection eccentricity (see Figure 4) and the connection length : with: U = 1- x 0.9 (1) D x = for round hollow sections (2) π The effective net area is then calculated as: A e = A n U (3) D t sl w centre of gravity of top half x t p t w p Figure 4. Parameters of the experimental and numerical study. The current LRFD Specification (AISC 4, Equation B3-2) uses the gross area A g of the member to calculate the effective net area A e (A e = A g U) which can result in considerably different design strengths for gusset plate connections where the hollow section is slotted (A n = A g - 2t p t). In practice, the slot width t sl is usually greater than t p to allow ease of fabrication, and in such cases A n = A g - 2t sl t. Recently, a general examination of the AISC LRFD shear lag design provisions has been made by Kirkham and Miller (8). Based on recent studies, it was concluded that the existing design approaches are overly conservative and further research was necessary. The draft version (5) of the upcoming AISC Specification in 2005 now uses the net area of the member, A n, in its formula but no longer has an upper limit of 0.9 for the eccentricity factor U (see Equation 1). For round HSS with 1.3D, the factor U becomes equal to unity. Connection lengths less than D are not covered. The current Canadian Standard (CSA 3) addresses shear lag in elements connected by a pair of welds parallel to the load by calculating the "effective net area" (Clause ) based on an efficiency factor that depends on the ratio of the distance between the welds around the hollow section perimeter, w, and the connection length, (see Figure 4). The efficiency factor given is: 1.0 for /w 2.0; /w for 2.0 > /w 1.0; 0.75 /w for /w < 1.0. A similar approach based on the former Canadian standard CAN/CSA-S (CSA 9), as well as research done by Korol et al. (10), is given in the design guide for hollow structural sections by Packer and Henderson (11). The recommended efficiency factor there is: 1.0 for /w 2.0; 0.87 for 2.0 > /w 1.5; 0.75 for 1.5 > /w 1.0; 0.62 for 1.0 > /w 0.6. Connections in Steel Structures V - Amsterdam - June 3-4,

4 For values smaller than /w = 0.6 shear rupture of the base metal along the weld line is supposed to govern. As the experimental study by Korol et al. (10) was done with gusset plate connections for square hollow sections, it is possible that the results might not be fully applicable for shear lag in round hollow sections. The Japanese recommendations for the design and fabrication of tubular truss structures in steel (6) exclude shear lag by providing a minimum connection length of 1.2D for gusset plate connections. To account for uncertainties in fabrication of these connections, the connection capacity is restricted to 90% of the unslotted (gross) member strength. Also, AIJ avoid use of the net area of the slotted tube by means of a specific fabrication detail. Table 1 gives an overview of all the above shear lag provisions. Table 1. Shear lag design provisions for round hollow sections. Specification or Effective net Shear lag coefficients design guide area AISC (4) A e = A g U AISC (2) Range of validity x D U = with x = no π restrictions x A e = A n U U = 1- AISC (5) D U = 1 for 1.3D AIJ (6) A e = A g U U = 0.9* 1.2D CSA (3) Packer and Henderson (11) Korol (17) A e = A n α U U = 1.0 for /w 2.0 U = /w for 2.0 > /w 1.0 U = 0.75 /w for /w < 1.0 A e = A n U U = 1.0 for /w 2.0 U = 0.87 for 2.0 > /w 1.5 U = 0.75 for 1.5 > /w 1.0 U = 0.62 for 1.0 > /w 0.6 α = 1.0 for /w 1.2 α = /w for 1.2 > /w 0.6 U = x * ) The factor 0.9 accounts for uncertainties in fabrication. Recent research on shear lag in HSS no restrictions shear lag not critical for < 0.6w shear lag not critical for < 0.6w A number of studies on gusset plate connections have been carried out in the last few years. The latest study, on a special type of gusset plate connection, the so-called hidden joint connection, by Willibald (12) showed that shear lag was not critical for square HSS in this specific connection type but can become critical for rectangular HSS. The results of the parametric study supported the use of the American specifications (2, 4, 5) but indicated a generally overly conservative approach in all current design methods. In an experimental study by British Steel (Swinden Laboratories 13) on slotted end plate connections for circular, square and rectangular hollow sections, 13 of the 24 specimens failed by shear lag. The results of an experimental as well as numerical investigation on shear lag failure for slotted circular hollow sections were given by Cheng et al. (14). Nine tests on gusset plate connections to CHS tension members were performed, but none of the specimens failed by shear lag. However, the experimental and numerical investigations showed that considerable stress concentrations occur at the slot ends. Comparing the results of the study with the then current Canadian (Cheng et al. 15) as well as American specifications (Cheng and Kulak 16), it was shown that neither code accurately represented the behaviour of slotted circular hollow section connections. In contrast to the specifications, Cheng and Kulak (16) concluded that shear lag failure was not critical for round HSS if the connection 448 Connections in Steel Structures V - Amsterdam - June 3-4, 2004

5 length was longer than 1.3 times the diameter of the circular hollow section (U = 1.0), however all their tests but one were performed with the slot end welded. The results of this research will be incorporated in the upcoming AISC (5) specification (see Table 1). A study on shear lag in slotted square and rectangular hollow sections has been performed by Korol et al. (10). A total of 18 specimens was tested under tensile loading with seven specimens failing by shear lag. The authors concluded that for six of the seven specimens that failed by shear lag, all with /w 1.0, the connection capacity was nearly equal to the tensile capacity of the hollow section, N u = A n F u. One specimen, where /w = 0.61, failed very prematurely due to shear lag. For specimens with /w-ratios smaller than 0.6, base metal shear failure of the hollow section governed. The influence of the eccentricity x on the connection capacity was found to be only minor. Based on the results of the earlier study, Korol (17) proposed a slightly modified approach for the calculation of the effective shear lag net section area. Instead of using the efficiency factors as given in the Canadian or American specifications, less conservative formulae were provided: α = 1.0 for /w 1.2 (net/gross section failure governs) (4a) α = /w for 1.2 > /w 0.6 (shear lag failure governs) (4b) non-applicable for /w < 0.6 (block shear tear-out governs). The eccentricity factor U was then calculated by: x U = The effective shear lag net section was then given by: A e = A n α U (6) (5) EXPERIMENTAL STUDY Scope of testing The experimental study comprised of six gusset plate connections for round hollow sections. The specimens had varying fabrication details (see Figure 2): slotted versus unslotted HSS, slot end welded versus no weld return. A further parameter in the test series was the weld or connection length with the /w-ratio varying between 0.66 and 0.88 (with w = 0.5 π D - t sl or w = 0.5 π D t p ). Standard cold-formed 168 x 4.8 mm Class C hollow sections with a specified yield stress of 350 MPa (CSA 18) were used. The gusset plate was made out of 1" (25.4 mm) Grade 300W steel. Table 2 shows the dimensional, and Table 3 the material, properties of the tested specimens. The welds connecting the hollow section and the gusset plate were standard 10 mm fillet welds using E480XX electrodes (CSA 19). Each specimen was equipped with 10 linear strain gauges measuring the longitudinal strain distribution on the hollow section (see Figure 5). The displacement of the connection was measured by four LVDTs (Linear Variable Differential Transformers). The results of these measurements were later on used to verify the numerical models of the tested specimens o 22.5 o 22.5 o 22.5 o Figure 5. Strain gauge locations on tested specimens. Connections in Steel Structures V - Amsterdam - June 3-4,

6 1400 Shear lag Tear-out Figure 6. Specimen 1 at failure. Connection Load [kn] Sp. 1 Sp. 2 Sp. 3 Sp. 4 Sp. 10 Sp Displacement [mm] Figure 7. Load versus Displacement curves of the tested specimens. Table 2. Measured dimensional properties of test specimens. Specimen HSS t sl [mm] w [mm] [mm] t p [mm] w p [mm] x A g = 2513 mm with x = 53.6 mm x x 75.5 Connection type Slotted tube, slot end not filled Slotted tube, slot end filled Slotted tube, slot end not filled Slotted plate Table 3. Measured material properties of test specimens. E [MPa] F y [MPa] F u [MPa] ε u [%] HSS * Plate * ) Using the 0.2% offset method, as material was cold-formed. Test results Failure of all six specimens was caused by either shear lag (specimens 3, 4, 10, 11)), tearout of the HSS base material along the weld (specimen 2) or both failures taking place at the same time (specimen 1, see Figure 6). Shear lag failure causes the HSS to fail circumferentially while block shear tear-out happens along the weld. Table 4 shows the ultimate connection strength, the failure mode as well as the predicted failure loads according to current design methods. Generally, the specimens with the shorter connection lengths (specimens 1, 2 and 10) had a reduced connection capacity. Before failure, all specimens showed ovalization in the hollow section, especially pronounced in the specimens with the unslotted tube and the slotted plate (see Figure 2 (a)). In all specimens, the strain gauge readings showed very high stresses at the strain gauges closest to the weld at the beginning of the connection (strain gauge 5, see Figures 3 and 5). The strain gauge furthest away from the weld (strain gauge 8) reported either negligible or even negative strains (specimens 10 and 11) at ultimate load. The strain distribution along the weld and beyond could be 450 Connections in Steel Structures V - Amsterdam - June 3-4, 2004

7 observed by comparing strain gauges 1, 3, 5 and 10. Again, strain gauge 5 had the highest strain levels in each specimen. Considerable displacement took place in all tested specimens (see Figure 7). The specimens having an unslotted tube and a slotted plate showed the largest deformation before reaching their ultimate loads. Considering these sizable displacements, it might be necessary to define a deformation limit which, for some connections, will then govern their capacity. Having comparable connection lengths, specimens 1,2 and 10 as well as specimens 3, 4 and 11 have only slightly different capacities. This indicates that the fabrication detail only has a little influence on the connection strength. Currently most codes do not specify the use of a certain detail but provide one design method to cover all three cases. However, with increasing gusset plate thickness, the difference in connection strength between the various fabrication details might be more pronounced. Generally, the design methods found in the American specifications (AISC 4,5) show the best agreement with the tests but further research seems necessary. Table 4. Actual and predicted connection strength of test specimens Specimen Test Failure Mode* N ux /A n F u N ux /A g F u AISC (4) AISC (5) CSA (3) Packer and Henderson (11) Korol (17) N ux or N u [kn] 1032 SL, N ux /N u - TO N ux or N u [kn] TO 0.89** 0.80 N ux /N u N ux or N u [kn] SL 1.00** 0.89 N ux /N u N ux or N u [kn] SL N ux /N u N ux or N u [kn] SL 0.81 N ux /N u N ux or N u [kn] SL 0.88 N ux /N u * ) SL stands for shear lag failure and TO stands for block shear tear-out failure along the weld; ** ) As slot end was welded, it might be also appropriate to assume A n = A g ; N u = A e F u. NUMERICAL STUDY For further study of gusset plate connections, a numerical study has been started. The final goal of this numerical study will be a parametric study concentrating on the influences of several variables: weld length, hollow section diameter, hollow section wall thickness, the eccentricity of the top or bottom part of the HSS, and fabrication details. The Finite Element program ANSYS 5.7 (Swanson Analysis System Inc. 20) has been used for the numerical study. A geometric and material non-linear analysis was performed for all specimens. 8-noded, large strain solid elements (solid45) with reduced integration and hourglass control were used throughout. The material properties were input as a multi-linear curve with the engineering stress and strain converted to the true stress and strain values. To simulate cracking in the models, a maximum equivalent plastic strain limit was used. The so-called "birth and death" elements allow the user to significantly reduce the stiffness of the elements, or "kill them", if an equivalent plastic strain is reached. Due to the symmetry of the connection it was only necessary to model an eighth of the connection (see Figure 8). The welds were fully modelled. A gap between the gusset plate Connections in Steel Structures V - Amsterdam - June 3-4,

8 Figure 8. Numerical model of specimen 2. Table 5. Comparison between test and numerical results. Specimen N ux [kn] N FE [kn] N ux / N FE Connection Load [kn] Spec. 2 FE Spec. 2 Spec. 3 FE Spec. 3 Connection Load [kn] Strain Gauge 5 Spec. 2 FE Spec. 2 Spec. 3 FE Spec Displacement [mm] Strain [µm] Figures 9a and 9b. Comparison between test and numerical results. and the hollow section was modelled to prohibit any direct stress transfer between the plate and the hollow section thus forcing load transfer to occur only via the welds. Symmetry boundary conditions were employed along the planes of symmetry (translations normal to the plane of symmetry were fixed) and the nodes at the HSS end were fixed. The finite element models were then loaded by displacing the nodes at the end of the gusset plate. Specimens 2 and 3, which have a slotted HSS with the slot end welded (fabrication detail (c), see Figure 2) have been numerically modelled and show very good agreement with the tests. The predicted ultimate loads for these two specimens are both within 2% of the actual ultimate loads for each test (see Table 5). Figure 9a compares the load-displacement curves for specimens 2 and 3 with the respective results of the numerical models. For both specimens the agreement is very good up to peak load. Unfortunately, the numerical models had problems converging beyond a certain point. At this load step, a high number of elements are killed which causes a sudden change in stiffness thus causing severe convergence problems. Yet, due to the high number of lost elements it is safe to assume that the ultimate load of the FE-model has been reached and subsequent calculation steps would result in a lower connection load. The comparison of the most critical strain gauge (strain gauge 5, see Figure 5) also shows good agreement between test and FE model (see 452 Connections in Steel Structures V - Amsterdam - June 3-4, 2004

9 Figure 9b). For the future, it is planned to have comparable models for the other two fabrication details and to use these finite element models in a parametric study. CONCLUSIONS An experimental, numerical as well as literature study on shear lag in round hollow section gusset plate connections under tension loading has been carried out. The experimental study showed that shear lag can indeed become critical in gusset plate connections. The connection length had the largest effect on the connection capacity, whereas the fabrication detail of the connection (see Figure 2) only had a minor influence on the capacity. For some specimens, large displacements could be observed before failure, which could become critical if deformations are restricted by a deformation limit. The numerical study showed that it is possible to generate very good finite element models of these connections. The numerical study will soon be extended to do further parametric studies to finally provide suitable design methods against shear lag failure. The design methods that can be found in current international specifications have been introduced in the literature study and have been evaluated against the experimental research carried out. At present, the American specification (AISC 5) seems to be best suited to design against shear lag failure under quasi-static tension loading, but all design methods are overly conservative and additional research is still necessary. For the future, further research is currently planned on shear lag in gusset plate connections under cyclic loading, as can be found in earthquake situations. With these connections, special attention will be paid to the fabrication and refined connection details will be considered. ACKNOWLEDGEMENTS Financial support for this project has been provided by CIDECT (Comité International pour le Développement et l Etude de la Construction Tubulaire) Programme 8G and NSERC (Natural Sciences and Engineering Research Council of Canada). IPSCO Inc. and Walters Inc. (Hamilton, Canada) generously donated steel material and fabrication services, respectively. NOTATION A g = gross cross-sectional area of hollow section A e = effective net cross-sectional area of hollow section A n = net cross-sectional area of hollow section D = outside diameter of round hollow section E = modulus of elasticity F y = yield tensile stress F u = ultimate tensile stress = weld length N FE = connection strength as predicted by numerical model N u = calculated connection strength N ux = measured connection strength U = coefficient for shear lag net section fracture calculation t = wall thickness of hollow section t p = thickness of gusset plate t sl = width of slot in hollow section Connections in Steel Structures V - Amsterdam - June 3-4,

10 w p = width of gusset plate w = distance between the welds, measured around the perimeter of the HSS x = eccentricity ratio α = coefficient for shear lag net section failure calculation ε u = ultimate strain at rupture θ = angle between gusset plate centre line and radial line of hollow section REFERENCES (1) Eurocode 3, (1993). Design of steel structures - General rules - Part 1-8: Design of joints. Draft version. British Standards Institute, London, England. (2) AISC, (2000). Load and Resistance Factor Design Specification for Steel Hollow Structural Sections. American Institute of Steel Construction, Chicago, USA. (3) CSA, (2001). Limit States Design of Steel Structures. CAN/CSA-S Canadian Standards Association, Toronto, Canada. (4) AISC, (1999). Load and Resistance Factor Design Specification for Structural Steel Buildings. American Institute of Steel Construction, Chicago, USA. (5) AISC, (2003). Specification for Structural Steel Buildings. Draft (December 1, 2003) version of the forthcoming (2005) Specification. American Institute of Steel Construction, Chicago, USA. (6) AIJ, (2002). Recommendations for the Design and Fabrication of Tubular Truss Structures in Steel. (in Japanese) Architectural Institute of Japan, Japan. (7) Chesson E., Jr., and Munse, W.H. (1963). Riveted and bolted joints: Truss type tensile connections. Journal of the Structural Division, ASCE, 89(1), (8) Kirkham, W.J., and Miller, T.H. (2000). Examination of AISC LRFD shear lag design provisions. Engineering. Journal, AISC, 3 rd Quarter, (9) CSA, (1994). Limit States Design of Steel Structures. CAN/CSA-S Canadian Standards Association, Toronto, Canada. (10) Korol, R.M., Mirza, F.A., and Mirza, M.Y. (1994). Investigation of shear lag in slotted HSS tension members. Proceedings, 6 th International Symposium on Tubular Structures, Melbourne, Australia, (11) Packer, J. A., and Henderson, J. E. (1997). Hollow structural section connections and trusses - A design guide. 2 nd Ed., Canadian Institute of Steel Construction, Toronto, Canada. ISBN: (12) Willibald, S. (2003). Bolted Connections for rectangular hollow sections under tensile loading. PhD thesis, University of Karlsruhe, Germany. (13) Swinden Laboratories, (1992). Slotted end plate connections. Report No. SL/HED/TN/22/-/92/D. British Steel Technical, Rotherham, England. (14) Cheng, J.J.R., Kulak, G.L., and Khoo, H. (1996). Shear lag effect in slotted tubular tension members. Proceedings, 1 st CSCE Structural Specialty Conference, Edmonton, Alberta, Canada, (15) Cheng, J.J.R., Kulak, G.L., and Khoo, H. (1998). Strength of slotted tubular tension members. Canadian Journal of Civil Engineering, Vol. 25, (16) Cheng, J.J.R., and Kulak, G.L. (2000). Gusset plate connection to round HSS tension members. Engineering Journal, AISC, 4 th Quarter, (17) Korol, R.M. (1996). Shear lag in slotted HSS tension members. Canadian Journal of Civil Engineering, Vol. 23, Connections in Steel Structures V - Amsterdam - June 3-4, 2004

11 (18) CSA, (1998). General Requirements for Rolled or Welded Structural Quality Steel/ Structural Quality Steel. CAN/CSA-G40.20/G Canadian Standards Association, Toronto, Canada. (19) CSA, (2003). Welded Steel Construction (Metal Arc Welding). CAN/CSA-W Canadian Standards Association, Toronto, Canada. (20) ANSYS Release 5.7. (2000). Swanson Analysis System Inc., Houston, USA. Connections in Steel Structures V - Amsterdam - June 3-4,

12 456 Connections in Steel Structures V - Amsterdam - June 3-4, 2004