Experimental and Analytical Investigations of Net Section Fracture in Brace-Gusset Plate Connections

Transcription

1 Experimental and Analytical Investigations of Net Section Fracture in Brace-Gusset Plate Connections AUTHORS Xiangyang Fu, Graduate Research Assistant, Civil and Environmental Engineering, University of California at Davis, Benjamin V. Fell, Graduate Research Assitant, Civil and Environmental Engineering, University of California at Davis, Amit M. Kanvinde, Assistant Professor, Civil and Environmental Engineering, University of California at Davis, Andrew T. Myers, Graduate Research Assistant, Civil and Environmental Engineering, Stanford University, ABSTRACT In recent years, braced-frame construction has gained considerable popularity for lateral load resisting systems in regions of high seismic activity. Concentrically Braced Frames (CBFs) have been one of the more prominent systems in this classification, relying on the inelastic cyclic buckling and yielding to resist seismic loads and dissipate energy. During tensile cycles, the brace places large demands on the brace-gusset plate, and in turn the gusset plate-beam or column, connections. While failures in this region have not been observed in previous earthquakes, studies suggest that net-section fracture may be a potential mode of failure in these connections. This paper focuses on investigating the inelastic seismic response of typical slotted net section connections of hollow structural sections (HSS) and round pipe under earthquake type monotonic and cyclic loads. Specifically, experimental observations from a Network for Earthquake Engineering Simulation and Research (NEESR) project on nineteen large-scale bracing members in the context of net section performance are presented. In addition to providing insights into behavior, the experiments also serve to validate micromechanics-based modeling approaches that predict ductile fracture. One such approach, utilizing the Void Growth Model (VGM) is discussed and presented as an analytical and general alternative to costly experimentation. INTRODUCTION The widespread use of braced-frame construction since the 1994 Northridge earthquake has brought noteworthy attention to the behavior of these systems during seismic loading [6, 7]. Concentrically Braced Frames (CBFs) are recognized as an efficient system for resisting lateral forces and minimizing building drifts primarily due to the large axial stiffness of the bracing members prior to brace buckling and the economy of the overall system [7]. The predominant mode of seismic energy dissipation in CBFs is the inelastic response of these bracing members through cyclic buckling in compression and tensile

2 yielding. Consequently, the braces are susceptible to buckling induced fatigue-fracture failure at brace plastic hinge locations (at the center of the braces) and fracture at bracegusset plate connections during brace tensile actions [4]. This paper is focused on the latter issue, specifically the evaluation of large-scale experimental results and micromechanical-based fracture model predictions in the context of seismic performance of typical slotted net section connections in bracing elements for CBFs. Two commonly used brace cross-sections used in CBF construction are hollow structural sections (HSS) and round pipe which are commonly slotted at each end for attachment to the gusset plate [7]. This results in a reduced area at the tip of the gusset plate where strains may concentrate to trigger net-section type fracture [14]. While encountered commonly in construction, AISC [2] does not permit the use of details in CBF systems that might trigger net-section type fracture. Recent studies [14] have suggested adding reinforcement plates at the reduced section to prevent fracture of this type. While Yang and Mahin [14] conducted multiple tests to establish that the reinforcement plates relieved the net-section fracture problem for HSS tubes, data to verify this is somewhat sparse for other types of cross sections, most notably pipe sections. In fact only one such test exists for pipe sections, and no data exists for connections involving wide-flange braces. To provide further data in this regard, the study described in this paper investigates reinforced and unreinforced end details for HSS and pipe braces to examine the issue of net section fracture during earthquake loading. To address the concerns of connection performance of bracing systems during severe ground shaking, this paper includes experimental performance results of nineteen largescale bracing members that were tested as part of a comprehensive NEESR project which aims to validate new modeling approaches to predict fatigue and fracture in full-scale steel components [8, 9]. The experimental specimens, representing several types of CBF braces were tested under a variety of reversed-cyclic loading histories to investigate fracture initiation at the reduced section in HSS and round pipe bracing members. The reversed cyclic loading protocols were designed with an objective to impose deformation demands on the specimens consistent with earthquake loading and to interpret the results in a performance context [12]. In addition to the experimental data, which is of practical significance, another focus of this paper is to examine the validity of micromechanics-based fracture models to predict fracture in full-scale details. Connection details such as those described in this paper typically exhibit large scale yielding prior to fracture, and moreover do not contain a sharp crack, thereby invalidating traditional fracture mechanics approaches (e.g. the J- Integral or Crack Tip Opening Displacement CTOD) [1, 10, 11]. Thus, design considerations for these and similar connections rely on experimental approaches, which are often expensive and cannot be generalized reliably. To expand on the experimental results, the Finite Element Model (FEM) simulation program ABAQUS is used to simulate the seismic response of the braces to validate the micromechanics-based models and explain localized fracture effect that may impact CBF design. The application of these models to the experiments described in this paper will serve to demonstrate and examine this modeling approach for full-scale structural details.

3 EXPERIMENTAL SETUP The experiments were conducted at the UC Berkeley NEES facility located at the Richmond Field Station. As shown in Figure 1, the experimental setup consisted of the brace specimen installed in a test rig with two actuators. The test rig applied a fixed-fixed boundary condition to the braces; one end was bolted directly to the reaction block and the other attached to moving cross-beam that was constrained to prevent out-of-plane motion. The gusset plates of the braces were oriented so that buckling occurred in the horizontal plane. The tests were performed in displacement control and the actuators were set in a master-slave relationship to minimize the rotation of the cross-beam, thereby, maintaining the fixed-fixed boundary condition at the translating end. Cyclic loading FIGURE 1 TOP VIEW OF TEST SETUP Specimen Actuator Brace buckling Reaction Block Figure 2 shows the fabrication drawings of a typical HSS or PipeSTD brace specimen (see Table 1 for dimensions of each brace). A total of nineteen brace specimens were tested as part of the experimental program (the reader is referred to Fell et al, 2006, for the complete testing matrix). The test matrix features two HSS cross-sections (6- HSS4x4x1/4 and 2-HSS4x4x3/8), two Pipe sections (4-Pipe3STD and 4-Pipe5STD), and one wide-flanged shape (W12x16). Of these, all the HSS sections were reinforced with reinforcing plates at the net sections. Of the Pipe sections, two each of the Pipe3STD and Pipe5STD were unreinforced, whereas no reinforcement plates were provided for the W- section. Table 2 lists the brace and material properties for each of the cross-sectional shapes. All the members and connections, including welds were designed as per the Seismic Provisions [2]. The connections were detailed to prevent weld rupture under the maximum tensile strength based on the expected yield strength of the bracing member, R y F y A g [2, 3] where R y is the ratio of the expected to minimum specified yield stress, F y, and A g is the gross cross-sectional area. Figure 2b illustrates the net section details of each type of connection. Net-section reinforcement was examined for the pipe specimens by placing reinforcing plates on two of the four PipeSTD (of each diameter) braces at the slotted net section connection. For each section, the slenderness (KL B /r), and compactness (b/t or D/t) ratios were varied to examine effects on fracture behavior. Other variables included the type of

4 loading history (far-field versus near-fault), and loading rates (quasi-static versus earthquake rate). The reader is referred to [9] for a detailed discussion of these parameters (i.e., the influence of brace slenderness and compactness on cyclic ductility) in relation to CBF performance; the main intent of this paper is to focus on monotonic net section behavior. FIGURE 2 FABRICATION DRAWING OF HSS AND PIPESTD BRACES (A) AND CONNECTION DETAILS (B) Cross-Section QTY BWL ET EW GW GL GWT RL RW RT HSS4x4x1/4 6* ½ 5/ ¼ HSS4x4x3/8 2* ½ 7/ /8 Pipe3STD 4** 6 ½ 1 ½ 14 5 ½ 8 5/ ¼ Pipe5STD 4** 12 1 ½ 14 7 ½ 13 ½ 3/ ¼ TABLE 1 D ESIGN VARIABLES OF BRACES. *ALL NET SECTIONS REINFORCED; **TWO BRACES FABRICATED WITHOUT REINFORCING PLATES Bracing b/t or D/t KL B /r F y F u Member (AISC Limit) (AISC Limit) (ksi) (ksi) R y R t H SS4x4x1/ (16.1) 77 (100) H SS4x4x3/ (16.1) 83 (100) Pipe3STD 16.2 (36.5) 103 (115) Pipe5STD 21.6 (36.5) 64 (115) W12x (7.2)* 155 (96)* TABLE 2 BRACE AND MATERIAL PROPERTIES [2, 3] (*EXCEEDS THE LIMITS OF THE AISC SEISMIC PROVISIONS) A variety of loading histories were applied to the specimens. Shown in Figures 3 and 4, these are (1) a modified ATC/SAC [5, 12] protocol (2) A tension dominated near fault loading history, Figure 4a and (3) A compression dominated near fault loading history, Figure 4b, based on the ATC/SAC protocol. Referring to Figures 3 and 4, the loading protocols are expressed in terms of drift amplitudes that can easily be converted to axial brace deformations based on a simple kinematic relationship Δ a = 59.θ, where θ is the

5 inter-story drift angle (expressed in radians), and Δ a is the corresponding axial deformation in the brace. FIGURE 3 MODIFIED ATC/SAC FAR-FIELD LOADING PROTOCOL FOR CBFS SHOWN WITH ORIGINAL SAC/ATC PROTOCOL FOR MRFS The tension dominated history (Figure 4a) consists of a large monotonic pull followed by subsequent cycles. This protocol was designed as a worst-case scenario for tensionsensitive details such as un-reinforced net-section connections at slotted ends of the brace. A similar approach was adopted by Yang and Mahin [14]. The tension history is similar to the near fault compression history, except that to ensure that the brace would not buckle before the main tension pull, the tension history does not include any large compression cycles before the first tension pull. Additionally, to ensure significant inelastic tensile demands during its initial loading excursion, the amplitude of the initial tension pull is 8% drift, which is larger than the 6% drift used in the compression history. (a) (b) FIGURE 4 ASYMMETRIC TENSION (A) AND COMPRESSION (B) NEAR-FAULT HISTORY

6 SUMMARY OF EXPERIMENTAL RESULTS Four tests (Test # 8, 9, 10, and 11) were designed specifically to examine the seismic performance and fracture at the net section of round pipe braces. The tension dominated near-fault history (introduced in the preceding section) was applied to each of these specimens. As discussed previously, this loading history was based on the SAC near fault loading protocol, and consisted of a large tension pulse followed by smaller cycles. The main intent of using the tension dominated near-fault history was to subject the connection region to the worst-case scenario. It was anticipated that other typical loading histories would localize damage due to buckling at the center of the brace, protecting the net section from fracture. Applying the tension pulse at the beginning of the loading history would ensure significant tensile deformations at the connections. If the brace survived the first tension pulse, it would fracture in the center on subsequent cycles (Test # 9 and 11). Figure 5 show the Pipe3STD with and without reinforcement at the end of the experiments. The reinforced section shows appreciable yielding without fracture, whereas the unreinforced net section fractures completely for Test # 8 and 10. The results of these four tests are summarized in Table 3 which list the deformation capacity of each brace, and the maximum experimental force, P u, compared to the current code-based expected yield force estimation, R y F y A g, the net-section capacity formula, FuUA n and the expected tensile strength estimation RtFuA g where Rt is the expected to minimum specified ultimate tensile capacity, F u. Fracture/ Pu Pu Pu Test Cross Pu Maximum RyFA y g FUA u n RFA # Section (kips) Drift * ** 8 P ipe3std 5.0% Pipe3STD # 8.0% # Pipe5STD 6.4% Pipe5STD # 8.0% # TABLE 3 E XPERIMENTAL RESULTS OF BRACING CONNECTIONS (# DENOTES REINFORCED NET SECTION AND MAXIMUM DRIFT SUSTAINED WITHOUT NET-SECTION FRACTURE FAILURE OCCURRED DURING SUBSEQUENT CYCLIC t u g LOADING IN BRACE PLASTIC HINGE; * R Y = 1.6, **RT = 1.2 FOR PIPE SECTIONS FROM AISC, 2005) FIGURE 5 PIPE3STD CONNECTION PERFORMANCE AFTER TENSILE EXCURSION OF UNREINFORCED (A) AND REINFORCED (B) NET SECTIONS

7 Referring to Table 3 and Figure 5, one can readily observe that the unreinforced pipe sections exhibited net section type fracture, whereas all the reinforced pipe sections survived deformations corresponding to drifts as large as 8.0% before fracturing at the center. The unreinforced pipe sections fractured at deformations corresponding to drifts as large as 5.0% and 6.4% for the Pipe3STD and Pipe5STD, respectively. Furthermore, during loading, a stress concentration occurred at the end of slot and localized ductile yielding in this area. The yielding zone then propagated along a 45 degree line from the slotted hole and forming an X-shaped yielding region at the net section. Beyond the five tests described in this section, it is relevant to note that the eight reinforced HSS tests (subjected to regular far-field or near-fault histories) did not exhibit any distress at their connections. The maximum tensile forces predicted by the R y F y A g formula are, on average, 20% lower than the experimentally observed values, indicating that the R y F y A g formulas are somewhat un-conservative when predicting demands on connections. The welds in the tests were designed based on these values, and likely did not fracture due to residual capacity afforded by the φ -factor. Using the RtFuAg, formula, based on the ultimate strength of the material provides fairly accurate and slightly conservative estimates of the maximum tensile capacity of the bracing members. The net-section formula FuUAn is conservative by approximately 40% while predicting the tensile load capacity of the member. This is consistent with the use of the φ -factor = 0.75 for net section failure. MICROMECHANICAL SIMULATION OF NET-SECTION FRACTURE IN BRACE- GUSSET CONNECTIONS This section describes the various aspects of applying micromechanics-based models to predict fracture in the brace-gusset connections. As discussed earlier, traditional fracture mechanics methods depend on several assumptions and may not be suitable for predicting fracture in common structural details where large-scale yielding is present in the absence of a sharp crack or flaw. In contrast, micromechanics-based models simulate the underlying physics of ductile crack initiation, and can be applied in a general sense to a wide variety of structural details. One such model is the Void Growth Model (VGM) that has been recently validated for small and medium scale experiments for a wide variety of structural steels [11]. The Void Growth Model (VGM), based on derivations by Rice and Tracey [13] is based on the concept of tracking microvoid growth and coalescence. The model assumes void growth to be the defining step in the fracture process, and does not explicitly model void nucleation and coalescence. The PipeSTD net section fracture experiments described in the previous section present an ideal opportunity to validate the micromechanics-based modeling approach, because (1) The brace-gusset connections provide a situation (large scale yielding and the absence of a sharp crack) where traditional fracture mechanics may not be reliable and (2) Relevant material properties, such as toughness parameters (for the Void Growth Model), and other constitutive properties have been calibrated for this steel as part of a larger NEESR project. As per the VGM, the extent of void growth is dependent on two quantities: (1) the equ ivalent plastic strain (ε P ) and (2) the stress triaxiality, T = σ m /σ e. The equivalent plastic strain quantifies the deformation in the material, while the triaxiality is a convenient measure of the ratio between the hydrostatic (dilational) stress σ m to the von

8 Mises (distortional) stress σ e. Mathematically, the extent of void growth can be conveniently expressed in terms of the Void Growth Index (VGI) a normalized measure of the void growth demand that can be determined as a function of the stress triaxiality and plastic strain histories as follows ε p Fracture Index ( FI) = VGI VGI critica = exp(1.5 T). dε VGI (1) l p critical 0 To predict fracture, the void growth demand can be compared to a void growth capacity, VGI critical, which is assumed to be a material property based on the notion of a critical void size. Thus, a Fracture Index (FI) can describe be used to describe the relative size of the void growth within the material ( demand ) to the critical void size. Fracture initiation is predicted the instant that any point within the FEM mesh records a stress and cumulative strain state that drives the Fracture Index to unity. Shown in Fig. 6 is a FEM model for typical brace-gusset connection detail. In order to accurately predict fracture initiation, continuum based models are needed to provide reliable approaches that model localized effects, such as small imperfections at the slotted brace connection and the spatial variability of different material properties for base metal and weld metal. The general-purpose finite element analysis program ABAQUS was used to perform nonlinear finite element simulation of the bracing member using continuum three-dimensional brick elements and multi-axial plasticity with large deformations. Each bracing member was modeled from the dimensions and calibrated material properties of the experimental specimens. Symmetry was used for computational efficiency by only constructing a quarter of each cross-sectional brace. CONTINUUM-BASED FRACTURE PREDICTION RESULTS AND DISCUSSION Figure 6 demonstrates the ability of the FEM analyses to simulate the localized yielding effects at the slotted net section connection that was observed in the full-scale experiments shown in Figure 5 (also note the X-shaped high strain region in Figure 6, similar to the experimental observations). The comparison illustrates the ability of FEM analyses to model regions of high stresses and strains where fracture is likely to initiate. The strain gradients of Figure 6 further support the need for reinforcing plates which shift the high strain region away from the critical net section and into the body of the bracing member. (a) (b) FIGURE 6 EQUIVALENT PLASTIC STRAIN CONTOURS FOR UNREINFORCED (A) AND REINFORCED (B) PIPE3STD SLOTTED NET SECTION CONNECTION

9 Referring to Table 4, the model predictions are within approximately 0.6% story drift of the experimental results for the unreinforced PipeSTD specimens and confirm that net section fracture is prevented for the reinforced specimens. In addition, the experimental and analytical maximum forces are comparable, supporting the validity of the material models used for the base and weld metal. Test Cross Test Results Model Predictions # Section Fracture/ P u Fracture/ P u Maxi mum Drift (kips) M aximum Drift (kips) 8 Pi pe3std 5.0% % Pi pe3std # 8.0% # % # Pipe5STD 6.4% % Pipe5STD # 8.0% # % # 266 TABLE 4 COMPARISON OF TEST RESULTS AND MODEL PREDICTIONS SUMMARY This paper reviews experimental performance results of nineteen large-scale bracing members that were tested as part of a larger Network for Earthquake Engineering Simulation and Research (NEESR) project which aims to validate new modeling approaches to predict fatigue and fracture in full-scale steel components. Connection performance regarding net section fracture was investigated by subjecting the bracing members to tension dominated near-fault loading histories with a large initial pulse. These tests, and later the analytical results, confirmed previous findings that net section reinforcement substantially increases ductility (up to an 8% story drift) and prevents fracture at the net section. In fact, for the pipe specimens, the large difference between yield and ultimate strengths resulted in large ductilities even for unreinforced connections, which fracture at 5.0% and 6.4% for the Pipe3STD and Pipe5STD, respectively. Furthermore, the test data did confirm that the expected yield strength (R y F y A g ) and the expected ultimate strength (R t F u A g ) tend to bracket the maximum measured strength fairly well. Finally, the representative brace-gusset plate connections are investigated to validate micromechanical based fatigue-fracture models at the slotted net section regions of CBF construction. Finite element analyses are used to simulate localized stress and strain demands which are used in a void growth failure criterion to predict fracture initiation at the net section. The results are encouraging in that the methodology predicts fracture initiation fairly close to the experimental fracture deformations and locations. This can be extended to generate parametric studies or perhaps more complex, connection details with a high degree of confidence. ACKNOWLEDGEMENTS This research is supported by the National Science Foundation (NSF), the George E. Brown Jr. Network for Earthquake Engineering Simulation (NEES), and the Structural

10 Steel Educational Counsel (SSEC). The advice and guidance of Helmut Krawinkler (Stanford University), Steve Mahin (UC Berkeley), Charles Roeder (Univ. Washington), Walterio Lopéz and Mark Saunders (Rutherford and Chekene) is greatly appreciated. In addition, the knowledgeable support of the UC Berkeley NEES lab personnel is acknowledged. REFERENCES [1] An derson, T.L., Fracture Mechanics, [2] AISC, Load and Resistance Factor Design Specification for Structural Steel Buildings, 3 rd ed. American Institute of Steel Construction, Chicago, IL, [3] AISC, Seismic Provisions for Structural Steel Buildings, American Institute of Steel Construction, Chicago, IL, [4] Astaneh-Asl, A., Seismic Behavior and Design of Gusset Plates, Steel Tips Technical Information and Product Service, Structural Steel Education Council, [5] ATC. ATC-24, Guidelines for Cyclic Seismic Testing of Components of Steel Structures, Applied Technology Council, 1992 [6] Becker, R., and Ishler, M., Seismic Design Practice for Eccentrically Braced Frames, Steel Tips Technical Information and Product Service, Structural Steel Education Council, [7] Cochran, M. L., and Honeck, W. C., Design of Special Concentric Braced Frames, Steel Tips Technical Information and Product Service, Structural Steel Education Council, [8] Fell, B.V., Myers, A.T., Deierlein, G.G., Kanvinde, A.M., Testing and Simulation of Ultra Low Cycle Fatigue and Fracture in Steel Braces, Proceeding of the 8th National Conference on Earthquake Engineering, San Francisco, CA, [9] Fell, B.V., Kanvinde, A.M., Deierlein, G.G., Myers, A.T., Fu, X., Buckling and Fracture of Concentric Braces under Inelastic Cyclic Loading, Steel Tips Technical Information and Product Service, Structural Steel Education Council, [10] Hancock, J.W., and Mackenzie, A.C., On the Mechanics of Ductile Failure in High-strength Steel Subjected to Multi-axial Stress-states, Journal of Mechanics and Physics of Solids, 24, 1976, [11] Kanvinde, A.M., and Deierlein, G.G., Micromechanical Simulation of Earthquake Induced Fractures in Steel Structures, Blume Center TR145, Stanford University, Stanford, CA, [12] Krawinkler, H., Gupta, A., Median, R., and Luco N., Loading Histories for Seismic Performance Testing of SMRF Components and Assemblies, SAC Joint Venture, Report No. SAC/BD-00/10, [13] Rice, J.R., and Tracey, D.M., On the Ductile Enlargement of Voids in Triaxial Stress Fields, Journal of the Mechanics and Physics of Solids 17, 1969, [14] Yang, F., and Mahin, S.A., Limiting Net Section Fracture in Slotted Tube Braces. Steel Tips Series, Structural Steel Education Council, Moraga, CA, 2005.