Gusset plate connections under monotonic and cyclic loading

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982 Can. J. Civ. Eng. Vol. 32, 2005 tion potential of the gusset plate was proposed. This approach consists of designing the gusset plate as the weak structural element in the seismic force resisting system rather than the brace member. The following presents an analytical investigation of the behaviour of gusset plates under monotonic tension, monotonic compression, and cyclic loading. The first part looks at the effects of gusset plate support conditions (rigid versus flexible), initial imperfections in the gusset plate, material yielding, and bolt slip. Gusset plate behaviour and energy absorption characteristics are then examined under cyclic loading. In the second part, a brace member is introduced into the model. With the modified model, a parametric study is conducted to examine the interaction between the gusset plate and the brace member and to determine the effect of load sequence on the behaviour of gusset plate – brace member subassemblies. Background Behaviour under monotonic loading Early investigations of the behaviour of gusset plates under monotonic loading in the elastic range were carried out by Whitmore (1952) on a gusset-plate connection detail common to Warren truss-type highway bridges, by Irvan (1957) on a double-gusset-plate Pratt truss connection detail and by Hardin (1958), Davis (1967), and Varsarelyi (1971). These investigations are reviewed in detail in (Walbridge et al. 1998). Chakrabarti and Bjorhovde (1983) and Hardash and Bjorhovde (1985) looked at the inelastic behaviour of gusset plate connections under monotonic loading. From their tests and those of other investigators, a block shear model was proposed to predict the ultimate capacity of gusset plate connections under tensile loading conditions. Thornton (1984), proposed a lower bound approach for determining the compressive strength of steel gusset plate connections, whereby it is assumed that the compressive force in the gusset plate is carried by an equivalent column between the end of the brace member and the edges of the intersecting beam and column members. The method proposed by Thornton for calculating the elastic buckling load was subsequently expanded to include inelastic effects (Williams and Richard 1986). This was achieved by using Thornton’s effective column approach in conjunction with column design equations. The buckling load thus obtained was then limited by the yield load, calculated using the effective width proposed by Whitmore (1952). Hu and Cheng (1987) conducted an experimental and analytical investigation of the buckling behaviour of gusset plate connections loaded monotonically in compression. Their test program focused on the effects of gusset plate thickness, geometry, boundary conditions, eccentricity, and reinforcement. The work of Hu and Cheng showed that thin gusset plates tend to buckle at a load much lower than the yield load predicted using the effective width proposed by Whitmore (1952). In general, either sway or local buckling modes were observed depending on the out-of-plane brace restraint conditions. Further analytical work showed that an increase in the stiffness of the gusset-to-brace splice plate would result in an increase in the buckling strength of the gusset plate up to a splice plate thickness of two to four times the gusset plate thickness. It was recommended that gusset plate connections of this type should be designed so that the distance between the end of the splice plate (or splice member) and the edges of the horizontal and vertical framing members is kept to a minimum. Yam and Cheng (1993) investigated the effects of gusset plate thickness and size, brace angle, out-of-plane brace restraint conditions, bending moments in the framing members, and out-of-plane eccentricity of the brace load on the behaviour and strength of gusset plates loaded in compression. The test specimens used in this investigation were stockier than those of Hu and Cheng, and as a result displayed more inelastic behaviour. Yam and Cheng observed that the compressive capacity of the gusset plate specimens was almost directly proportional to their thickness. The effect of beam and column bending moments on the compressive capacity of the test specimens was found to be small for the bending moment to brace load ratios studied. The method proposed by Thornton (1984) for predicting the compressive capacity of gusset plates was found to be conservative. Some of the test results presented by Yam and Cheng are used later in this paper. These results are summarized in Table 1. Behaviour under cyclic loading Jain et al. (1978) studied the effect of gusset plate bending stiffness and brace member length on the cyclic behaviour of brace members. Although the brace member was the main subject of the investigation, three different gusset plates were tested in conjunction with various brace member lengths. Of the 18 test specimens comprising the test program, none were designed with a gusset plate yield strength lower than that of the brace member. Jain et al. concluded from their investigation that there is no advantage in making the flexural stiffness of the gusset plate greater than that of the brace member. However, they did find that an increase in flexural stiffness of the gusset plate (up to that of the brace member) generally results in a decrease in the effective length of the brace member. This, in turn, tends to improve the cyclic behaviour of the brace member. Astaneh-Asl et al. (1981) studied the cyclic behaviour of brace members composed of back-to-back double angles connected to gusset plates. The focus of their investigation was also the brace member behaviour. In-plane and out-ofplane buckling of the brace members was investigated. Significant deterioration of the gusset plate capacity was observed in some of their test specimens. To avoid this severe strength deterioration, a free buckling length of not more than two times the gusset plate thickness between the end of the brace member and the line marking the points of attachment of the gusset plate to the framing members was proposed. It should be noted that the cyclic loading tests on which Astaneh-Asl et al. based this proposition were not conducted on rectangular-corner gusset plates. Rabinovitch and Cheng (1993) studied the cyclic behaviour of steel gusset plate connections. In their investigation, the effects of gusset plate thickness, geometry, edge stiffeners, and bolt slip were investigated. A series of five tests on full-scale gusset plate specimens showed that cyclic loading causes the compressive strength of the gusset plate to drop © 2005 NRC Canada
Walbridge et al. 983 Table 1. Partial summary of Yam and Cheng (1993) gusset plate test specimens. Specimen Plate size (mm) to a stable post-buckling level after several load cycles, but it has little effect on the tensile strength. Although the addition of edge stiffeners was seen to have little effect on the initial compressive strength, this addition was shown to significantly improve the post-buckling compressive strength as well as the energy dissipation characteristics of the gusset plates tested. As in the tests by Hu and Cheng (1987), and Yam and Cheng (1993), the tests by Rabinovitch and Cheng used test specimens with strong splice and brace members. The behaviour of the gusset plate was investigated without considering the interaction of the gusset plate and the brace member. Test results from Rabinovitch and Cheng will be used to validate the finite element model developed for the parametric study presented herein. These results are summarized in Table 2 and Fig. 1. Finite element modelling of gusset plates To predict gusset plate behaviour under monotonic and cyclic loading, a model was developed using the finite element program ABAQUS (1995). The model was validated with data from the experimental investigations of Yam and Cheng (1993) for gusset plates loaded monotonically in compression, and Rabinovitch and Cheng (1993) for gusset plates under cyclic loading. The following procedure was adopted to develop the model: (1) A study of inelastic tensile gusset plate behaviour was performed to investigate the effects of mesh refinement, strain hardening, and framing member stiffness. The modelled gusset plates were all loaded beyond their peak tensile capacities. Since tensile test results were not available, peak tensile loads from the cyclic tests conducted by Rabinovitch and Cheng (1993) were used for validation purposes at this stage. (2) Initial imperfections were subsequently incorporated into the model developed in step (1). The modified model was then used to investigate gusset plate response under monotonic compressive loading with different imperfection shapes and magnitudes. The results of this investigation were compared with some of the test results of Yam and Cheng (1993). (3) Finally, the finite element model developed in step (2) was used to simulate gusset plate behaviour under cyclic loading. At this stage, a fastener model was developed to model the bolt slip that was observed for some of the specimens tested by Rabinovitch and Cheng (1993) (Fig. 1). The results of this investigation were compared with the test results from this same reference. The following presents the details and results of the above-mentioned process. Material properties Performance Young’s modulus (MPa) Yield strength (MPa) Ultimate strength (MPa) Monotonic tension loading Ultimate tensile load (kN) GP1 500 × 400 × 13.3 207 600 295 501 — 1956 GP2 500 × 400 × 9.8 210 200 305 465 — 1356 GP3 500 × 400 × 6.5 196 000 275 467 — 742 Ultimate compressive load (kN) Modelling Four finite element meshes were used to model specimen A2 from Rabinovitch and Cheng (1993) (Fig. 1 and Table 2), each with an increasing level of refinement. ABAQUS shell element S4R was used to model the gusset plate and the T-shaped splice members. Two different material models were investigated: an elasto-plastic model and an isotropic strain-hardening model. The adopted material properties were based on the materials test results reported by Rabinovitch and Cheng (1993), summarized in Table 2. The particulars of the two models can be summarized as follows: The elasto-plastic model assumes linear elastic behaviour (with a Young’s modulus of 206 000 MPa) until the yield stress, after which perfect plastic behaviour is assumed. The isotropic strain hardening model assumes linear elastic behaviour (again, with a Young’s modulus of 206 000 MPa) until the yield stress. The strain hardening curve is then defined in terms of true stress versus plastic strain. The strain hardening curve assumes perfect plastic behaviour until a plastic strain of 0.025. The true stress then increases to the ultimate true stress at a plastic strain of 0.18 (Walbridge et al. 1998). The bolts were modelled as rigid links between the gusset plate and the splice members. The displacement and rotation of the nodes along the connected edges of the gusset plate were fully restrained, thereby simulating rigid framing members. The models were loaded by displacing the nodes along the loaded edge of each splice member (Fig. 2). The four meshes are shown in Fig. 3. They are numbered from 1 to 4, and contain 206, 336, 454, and 596 elements, respectively. The mesh refinement study indicated that with a mesh consisting of 454 shell elements in the gusset plate, convergence of the load-displacement behaviour was achieved (Walbridge et al. 1998). This mesh was thus adopted for subsequent analyses. A more realistic model of the actual boundary (support) conditions was obtained by modelling the beam and column (framing members), as shown in Fig. 4. The beam and column were modelled using ABAQUS S4R shell elements with linear elastic material properties. A more realistic bolt model was developed using ABAQUS SPRING2 elements. The SPRING2 element links a global degree of freedom at one node with a global degree of freedom at another node. For this model, two springs were required (one for each inplane displacement degree of freedom) to link each of the two splice members to the gusset plate at each bolt location. The stiffness assigned to the SPRING2 elements for this step was taken from a double shear load test presented by Wallaert and Fisher (1965). The stiffness value was taken as the initial slope of the load versus displacement curve for a © 2005 NRC Canada
Page 1: Introduction Gusset plate connectio
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Page 7 and 8: Walbridge et al. 987 Fig. 9. Spring
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Page 11 and 12: Walbridge et al. 991 Table 4. Gusse
Page 13 and 14: Walbridge et al. 993 Fig. 17. Effec
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Gusset plate connections under monotonic and cyclic loading

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