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Experimental investigation on bending and shear performance of two-way aluminum alloy gusset joints
Thin-Walled Structures 122 (2018) 124–136
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Full length article
Experimental investigation on bending and shear performance of two-way aluminum alloy gusset joints
MARK
⁎
Mingzhe Shi, Ping Xiang, Minger Wu Tongji University, No. 1239 SiPing Rd., Shanghai, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Aluminum alloy gusset joint Semi-rigid behavior Failure modes Experimental study
Two-way aluminum alloy gusset joints (AAGJs) are considered to be employed in cable-stiffened aluminum alloy single-layer reticulated shell structures meshed with quadrilateral grids. In this study, a series of experiments on six AAGJs with and without shear connectors were conducted to investigate their semi-rigid behavior. Two joints were subjected to pure bending moments and others to shear loads, then their corresponding failure modes were investigated which were mainly beam rupture, beam web buckling, and bolt failure. The moment-rotation curves, shear load-rotation curves, and strain-load curves were also obtained, indicating that AAGJs are typical semi-rigid joints. Shear connectors can optimize the load transferring path and improve ductility under bending moment while enhancing shear performance significantly. A simplified theoretical AAGJ model was also established and parameterized according to the experimental results.
1. Introduction Single-layer reticulated shell structures provide a highly efficient method for building large-span structures. Introducing a tensioning system into a reticulated shell structure can improve the stability of such buildings. There currently exist two kinds of single-layer reticulated shells with tensioning systems: Suspen-domes [1–3] and cable-stiffened shells [4,5]. Both systems can effectively improve the stability of reticulated shells. Suspen-domes are only applicable to domes, however, while cable-stiffened shells can suit almost any curved shape. A cable-stiffened reticulated shell (CSRS) structure is typically comprised of a single-layer quadrilateral-mesh reticulated shell with Xshaped pre-tensioned cables disposed within the grids. The cable can be arranged within the curved surface to improve the in-plane stiffness (Type A) or work with posts externally (Type B) to improve the out-ofplane stiffness of the shell [6]. The Neckarsulm dome (Fig. 1) [7] is a practical application that adopted the Type A cable arrangement; the Kumagaya dome (Fig. 2) [8] adopted the Type B. There have been many studies on the stability of cable-stiffened single-layer reticulated shells. Wu et al. [9] analyzed the introducing process of pre-stress tensile units of a CSRS. Zhang and Fujimoto [10] conducted a numerical study on a series of CSRSs to explore the effect of cable arrangement on linear and nonlinear stability. Feng et al. [11] derived the formula for the linear buckling load of an elliptic paraboloid CSRS with imperfections based on continuum analogy. Li et al. [4,6] performed a series of parametric analysis on the stability behavior ⁎
of cylindrical and elliptic paraboloidal CSRSs with different cable arrangements. Li et al. [12] conducted experimental investigations on two-way single-layer shells with and without cables under different load distributions. Many studies have shown that joint stiffness cannot be ignored in the analysis and design of single-layer reticulated shells, as it significantly affects the global stability behavior [13–17]. There have been extensive numerical and experimental investigations on the semi-rigid behavior of joints in different systems. Feng et al. [18] conducted experiments and numerical analyses including on in-plane and out-ofplane stiffness for bolted joints that are used to constructing CSRSs. Fan et al. [19] and Ma et al. [17] carried out a series of studies on socket joints and bolt-ball joint systems subjected to bending moment, shear force, and axial force to investigate semi-rigid behavior. Han and Liu [20] conducted experiments on twelve welded hollow ball joints subjected to tensile and compress loads. Previous studies and practical engineering projects typically center around steel as the primary material. Aluminum alloy has many notable advantages compared to steel; it is light-weight, cheap to maintain, and has excellent cryogenic properties, among others [21]. It also has some disadvantages, however. Its thermal expansion coefficient is twice as steels, and it has a relatively poorer high temperature material performance than steel. Researches regarding aluminum alloys thermal behavior is fairly limited, however. Chen [22] performed experimental investigation on 114 aluminum alloy coupons to study the influences of temperature, material grade and cooling method on the post-fire mechanical properties. Maljaars [23] carried out investigations on local
Corresponding author.
http://dx.doi.org/10.1016/j.tws.2017.10.002 Received 27 June 2017; Received in revised form 13 September 2017; Accepted 2 October 2017 0263-8231/ © 2017 Elsevier Ltd. All rights reserved.
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(2) Many free-form reticulated shell structures have been built in recent years [35], among which aluminum alloy reticulated shells have been especially popular. Unfortunately, the AAGJ does not readily transfer shear force across the joint due to the lack of connection between beam webs (Fig. 3(a)). Previous research has also indicated that joint shear stiffness affects reticulated shell structures to some extent [34]; the shear stiffness of AAGJ has yet to be fully understood, however. In this study, tests on six full-scale AAGJs were conducted to explore the bending and shear stiffness with and without shear connectors, respectively. The experimental program is introduced below, followed by the results obtained for the failure modes of the joints. Response curves of the joints are then presented and discussed. Finally, the corresponding theoretical AAGJ model is proposed and concluding remarks are provided.
Fig. 1. The Neckarsulm dome.
2. Experimental program 2.1. Materials The material for the beam members and gusset plates used in this study was aluminum alloy 6061-T6 [36]. The bolts were made of austenitic stainless steel and the shear connectors of steel. Though the same raw material was used for the beam members and gusset plates, their mechanical properties may have varied due to differences in processing techniques. Two sets of tension coupon tests were performed to investigate the mechanical properties of the materials: One set contained three coupons cut directly from the unprocessed gusset plates, and the other contained two pairs of coupons cut from the flange and the webs of the I-shaped beam members, respectively. All the seven coupons had the same dimensions except for the thickness, as shown in Fig. 4(a). The chemical composition of the aluminum alloy coupons is in accordance with GB/T 3190-2008 [37] and the shapes and sizes are designed in accordance with GB/T 228.1–2010 [38]. The material properties of the steel components, including the stainless steel bolts type A (connecting beams with plates), stainless steel bolts type B (connecting shear connectors with beams), and steel shear connectors, were provided by the manufacturers. The surface of the aluminum alloy was initially smooth, but became coarse as plastic deformation progressed during the tensile tests (Fig. 4(b)). This phenomenon (plastic texture) can be used to identify regions with high strain concentration among the aluminum alloy components. The stress-strain curves of aluminum alloy coupons are shown in Fig. 5, the results of the tensile coupon tests meet requirements of GB/T 6892-2006 [39]. The mechanical properties of all the materials mentioned above are summarized in Table 1, including the elastic modulus, E, the nominal yield strength, σy , and the ultimate tensile strength, σu .
Fig. 2. The Kumagaya dome.
buckling of aluminum alloy members at elevated temperatures. Maljaars [24] conducted a parametric study on fire exposed aluminum structural members, and proposed a verified model for designing aluminum alloy members at elevated temperatures. Liu [25] measured the solar radiation absorption coefficient of aluminum alloy, and analyzed the temperature distribution and thermal response of aluminum alloy space structures. A considerable number of aluminum alloy single-layer reticulated shells have been constructed since 1950; such structures are widely considered to have attractive appearance and favorable structural features such as easy erection and high durability in moist environments [26]. Building a CSRS using aluminum alloy forms an efficient, economical and elegant structure. Research on the semi-rigid behavior of joint systems of aluminum alloy reticulated shells is fairly limited, however. Sugizaki et al. [27,28] carried out a series of experimental and numerical studies on aluminum insertion joints, and Hiyama et al. [29] performed experimental studies on six aluminum ball joints. Shi et al. [30] investigated the semi-rigid behavior of a novel cast aluminum joint under different loading conditions, and Guo et al. [31–33] derived and experimentally verified a formula for bending stiffness of aluminum alloy gusset joints (AAGJs). Shi et al. [34] investigated the bending and shear stiffness of an AAGJ using FE simulations. This paper also focuses on the AAGJ system, which is one of the most commonly used joint systems in building aluminum alloy reticulated shells, as shown in Fig. 3. There has been very little research to date on combining AAGJ with CSRS, however, leaving the following problems to be solved: (1) As opposed to traditional aluminum alloy reticulated shells, CSRSs usually have quadrilateral meshes rather than triangular meshes; this means that four beam members are connected to a joint instead of six. The semi-rigid behavior of this kind of AAGJ may differ from the traditional joint, but this has yet to be fully confirmed.
2.2. Specimens A series of tests on six specimens were conducted to study the semirigid behavior of AAGJs. A standard AAGJ in a reticulated shell with quadrilateral meshes contains two circular plates and four I-shaped beam members connected by bolts, as shown in Fig. 3. The diameter of the circular plates was 515 mm and the thickness was 12 mm. All the Ishaped beam members had the same cross-sectional dimensions of 350 × 200 × 8 × 12 mm , as shown in Fig. 4(a). The detailed configuration of the beam member is shown in Fig. 6. Each specimen had two long beams and two short ones (Fig. 6(a)). This study focuses on the semi-rigid behavior along principal axis of joints, so the X-direction beams were kept short and with the same length of 300 mm. Each Ishaped beam member was tightly attached to top and bottom plates by 36 stainless steel bolts 10 mm in diameter. The bolts were numbered as shown in Fig. 6(b). As shown in Table 2, two sets of joint specimens were investigated: 125
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Fig. 3. Aluminum alloy gusset joint system.
M series and Q series. The M series specimens were used to study the bending performance of the joint, while the Q series specimens were used to study the shear performance. The length of I-shaped beam members of M series specimens was 2100 mm; that of Q series members was 800 mm. The influence of shear connectors was also investigated. A pair of shear connectors were attached to a beam web on each side via 12 stainless steel bolts with the diameter of 10 mm. The shear connectors had dimensions of 288 × 224 × 5 mm (length × height × thickness), as shown in Fig. 7. As shown in Table 2, M2 and M1 were joints with and without shear connector under bending moments, and Q3 and Q4 were specimens with shear connectors designed for investigating shear performance, while Q1 and Q2 were without.
2.3. Experimental scenario and setup Fig. 5. Material properties of aluminum alloy coupons.
Two experimental scenarios were designed. The test setup of Scenario I, as shown in Fig. 8, was designed to obtain moment-rotation relationship for the joint under pure bending moments. Specimens were simply supported on columns and subjected to two vertical loads at their points of trisection. The load was applied via a load distributing girder with a hydraulic jack located at the midpoint. The total length of each specimen was 4310 mm and the distance between the two supports was 4010 mm. The distances between load points to the midpoint of the specimen was 710 mm. Two anti-torsion bearings were designed to prevent specimens from out-of-plane torsion, as shown in Fig. 8(c). Two anti-torsion columns were also placed at the load points to restrict the out-of-plane displacements of the specimens, as marked in Figs. 8(a) and 8(b). Webs of aluminum alloy I-shaped beam members are prone to local buckling due to their large height-to-thickness ratio. Accordingly, four pairs of steel anti-buckling reinforcements were employed at bearings and load sections where concentrated forces occurred, as marked in Figs. 8(a) and 8(c). Each pair of anti-buckling reinforcements was attached to the beam web via 24 M10 hand-tightened stainless steel bolts. The width of the anti-buckling reinforcements was 100 mm and the height was 324 mm, which was 2 mm less than the distance between the upper and lower flange. Scenario II was designed to study the shear performance of the joint,
Table 1 Joint component material properties. Material Aluminum Alloy
Stainless Steel Steel
Component
E(MPa)
σy (MPa)
σu (MPa)
Plate
6.05 × 10 4
270
315
Flange
6.05 × 10 4
240
270
Web
6.05 × 10 4
240
270
Bolt A
1.95 × 105
515
792
Bolt B
1.95 × 105
300
670
Shear connector
2.06 × 105
235
500
which was described as load-rotation curves. The theoretical model of Scenario II is a short beam fixed on one end and under concentrated force on the other. The test setup shown in Fig. 9 was designed to simulate fixed boundary conditions. It contains two supports: Support A near the center of the joint, which was comprised of a column with an anti-torsion bearing on it, and Support B which was similar to Support A but also included reaction frame on the far-end of the specimen; its beam had the cross-sectional dimension of 400 × 300 × 40 × 40 mm . A Fig. 4. Cross-sectional dimension of the specimen and tensile test coupon.
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Fig. 6. Specimen details.
2.4. Experimental procedure
Table 2 Specimen information. Series
No.
Beam member length (mm)
Shear connector
Failure mode
M
1 2 1 2
2100 2100 800 800
without with without without
3 4
800 800
with with
Beam rupture Beam rupture Bolt failure (1)Bolt failure (2)TB buckling BB buckling Beam rupture
Q
A three-step procedure was adopted for both scenarios. (1) The specimens were subjected to a small load (the smaller one between 1/3 of the linear stage and 10% of the estimated failure load) and then unloaded to check the loading and measuring apparatus. This step also reduced the influence of interspaces between the components. (2) The test was carried out under force control at a relatively swift speed (10 kN/min) during the linear stage. This step ended when the estimated linear stage was covered or nonlinear load-displacement curves were observed. (3) Once the specimens entered the nonlinear stage, the load control method was changed to a displacement control method with a low loading speed (1 mm/min) until failure of the specimens occurred.
3. Failure modes The failure modes are shown in Figs. 10 and 11 and summarized in Table 2. The primary failure modes of the specimens included three types: Beam rupture, beam buckling, and bolt failure. In Scenario I, as shown in Fig. 10, both specimens failed due to rupture of the lower flange near bolts 8 and 9. Introducing the shear connector into the joint system did not interfere with this failure mode under pure bending load. Strengthened by the shear connector, M2 did not rupture entirely, but instead a crack was initiated at the junction of the web and flange. The necking deformation is marked in Fig. 10. The failure modes of specimens in Scenario II are shown in Fig. 11. The loading beam and the bearing beam near the center were divided into four parts for clarity; they are labeled as TL (top of loading beam), BL (bottom of loading beam), TB (top of bearing beam), and BB (bottom of bearing beam) as shown in Fig. 9(a). Q1 and Q2, the specimens without shear connectors, experienced substantial deformation before failure (Fig. 11(a)). The failure mode of Q1 was thread stripping of bolts 1 and 2 of TL and BB (Fig. 11(b)). Q2 had a similar phenomenon as Q1, but the test ended with the buckling of the web at TB (Fig. 11(c)). Q3 and Q4, the specimens with shear connectors, had distinctly less shear deformation compared to Q1 and Q2 (Figs. 11(a) and 11(c)). As shown in Fig. 11(e), stainless steel bolts caused large deformation in the bolt-holes. The failure mode of Q3 was the buckling of the web at BB near the edge of the plate. In this case, the reinforcement was not efficient enough. Although aluminum alloy I-shaped beams are prone to local buckling under concentrated forces, scenario that concentrated forces applied on an aluminum alloy I-shaped beam hardly happens in engineering practices. And the failure mode of Q3 can be avoided at a very low cost. Introducing anti-buckling reinforcements, for instance, can be a feasible and efficient scheme. Thus, in the test of Q4, four pairs of anti-buckling reinforcements with the thickness of 12 mm were employed to determine the joint was well restrained. The failure mode of Q4 was the rupture of the beam web, which occurred in a three-step process (Fig. 11(f)). There were no visible cracks in the first or second step, as cracks were covered by the shear connector. A strip of plastic
Fig. 7. Shear connector.
hydraulic jack was located at the other end of the specimen near the joint plate. The distance between the centers of Support A and the joint plate of the specimen was 358 mm, and the margin between the edges of the support and the plate was 40 mm. The hydraulic jack was placed symmetrically with Support A. A pair of anti-torsion columns were placed at the end of the specimen on the loading side. Three pairs of anti-buckling reinforcements were installed at the support end of the specimen equidistantly, plus one more pair under the hydraulic jack as shown in Fig. 9(a). Displacement transducers (DTs) were installed at several key locations as shown in Figs. 8(a) and 9(a). In Scenario I, DT-S1 and DT-S2 were installed at supports, DT-L1 and DT-L2 loading points, and the DTC plate center. In Scenario II, DT-SA was installed at Support A, DT-SB at Support B, DT-P1 and DT-P2 on the upper plate of the specimen with 300 mm-distance and symmetrical about the center, and DT-L at the loading point. The strain gauges placed on M series specimens are illustrated in Fig. 8(d). M-S-B1 and M-S-B2 were placed at the top and bottom flange of the beam. M-S-P1 and M-S-P2 were placed at the center of the top and bottom plates. Four strain gauges were placed on the shear connector of M2. The strain gauges placed on Q series specimens are shown in Fig. 9(a). Q-S-B1 and Q-S-B2 were placed along the Y-direction near the top and bottom flanges.
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Fig. 8. Setup of Scenario I.
These cracks increased the tensile force in the top flange of the bearing beam, which then ruptured (near bolts 8 and 9) before the crack spread to the bottom flange.
texture can be observed in a similar position as the stress distribution (Fig. 11(e)), which indicated that the first step was horizontal cracking caused by local shear failure; the second step was upright cracking. 128
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Fig. 9. Setup of Scenario II.
4. Response curves and discussion 4.1. Derivation of the response curves The bending behavior of the joint can be described by the relationship between the bending moment M and the corresponding rotation angle ϕ of the joint. The M − ϕ curves in this study were calculated based on the data obtained from the loading apparatus and displacement transducers. The bending moment, M, can be calculated by Eq. (1):
M= Fig. 10. Failure mode of Scenario I.
1 FLl 2
(1)
where F represents the sum of loads acting on both sides of the joint and Ll is the distance between the bearing and the point where the load acts. As shown in Fig. 12, the vertical displacement of the node center, δb, c , obtained from DT-C, can be regarded as the summation of the following two parts: 129
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Fig. 11. Failure modes of Scenario II.
(1) The vertical displacement caused by bending deformation of the beam member, δb, b , is calculated as follows:
δb, b =
FLl (3L2 − Ll2) 12EI
represents the variation of angle caused by the shear deformation and Dc represents the distance between Q-DT-P1 and Q-DT-P2. The shear deformation of the beam is shown in Fig. 11(a). The effect of the bending deformation on the shear angle was neglected because the length of the deformed area was small. The vertical relative displacement between measurement points i and j (δij ) on the specimens can be regarded as the summation of following two parts: (1) The relative displacement caused by rigid body movement of the beam member, δs, r , is calculated by Eq. (5):
(2)
where L denotes the length of a single beam member; E and I are the Young's modulus and moment of inertia of the member, respectively. (2) The vertical displacement caused by rigid body rotation of the beam member, δb, r , is calculated as follows:
δb, r = δb, c − δb, b
(3)
δs, r =
The rotation, ϕ , can be calculated by Eq. (4):
δb, c − δb, b ⎞ δb, r ⎞ ϕ = arctan ⎛ = arctan ⎛ L ⎝ L ⎠ ⎝ ⎠ δ FL , b c l 2 (3L2 − Ll ) ⎤ = arctan ⎡ − ⎢ L ⎥ 12EIL ⎣ ⎦ ⎜
⎟
⎜
Dc (δSA − δSB ) LAB
(5)
where δSA and δSB represent the displacements of Support A and Support B, which can be obtained from DT-SB and DT-SA. LAB denotes the distance between two supports. (2) The relative displacement caused by shear deformation, δs, s , is calculated as follows:
⎟
(4)
In this paper, shear load-rotation (F − θ ) curves are used to describe the shear performance of the joint, where F represents the shear load, θ
δs, s = δij − δs, r = (δP 2 − δP1) − 130
Dc (δSA − δSB ) LAB
(6)
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Fig. 12. Joint deformations.
the webs; and 3) there were gaps between bolts and bolt-holes. When the joint entered the nonlinear stage, the shear connector had greater influence as joint deformation increased; this resulted in an increase in elastic resistance and ultimate load. These results altogether suggest that introducing shear connectors into the joint system does not improve linear bending stiffness to any meaningful extent, but does improve the integrity and ductility of the joint significantly.
where δP1 and δP2 are data obtained from DT-P1 and DT-P2. θ can be calculated by Eq. (7):
δs, s ⎞ δ − δP1 δ − δSB ⎞ θ = arctan ⎛ = arctan ⎛ P 2 − SA Dc LAB ⎠ ⎝ Dc ⎠ ⎝ ⎜
⎟
⎜
⎟
(7)
4.2. Response curves of Scenario I
4.3. Response curves of Scenario II
The load-displacement curves, load-strain curves and M − ϕ curves are shown in Fig. 13. The load-displacement curves of M1-DT-L1 and M1-DT-L2 (DTs of loading points) show good agreement before 260 kN, but separated from each other afterwards as shown in Fig. 13(a). Due to the geometrical imperfections and material uniformity, one side of the joint deformed faster than the other after part of the beam members entered plasticity. A similar phenomenon can be observed for M2 as shown in Fig. 13(b). As shown in Fig. 13(c), the strains on the top and bottom flanges were highly symmetrical. This suggests that the specimens were subjected to a bending moment without axial force. Strains on the top plate grew faster than on the bottom plate, which suggests that the top plate had a larger bending deformation. Strains on the shear connectors were relatively small, indicating that the shear connector made little contribution to the bending stiffness of the joint. The M − ϕ curves shown in Fig. 13(d) are linear in the early stage with subsequent nonlinearity, which exhibits a typical elasto-plastic behavior. At the initial loading stage of the two curves, a slight change in slope occurs due to the slipping between the surfaces of beam flanges and the cover plates. The initial stiffness was provided by the friction between the surfaces due to the pretension of the bolts. When a certain load was reached, the maximum static friction force was exceeded and the surfaces began to slip, leading to a decrease in bending stiffness. The key parameters of the M − ϕ curves are shown in Table 3, including initial bending stiffness (Kini ), elastic moment resistance (My ), plastic bending stiffness (Kp ) and ultimate moment (Mu ). M1 and M2 have almost the same initial bending stiffness (27,308 kN · m/rad and 27,595 kN · m/rad). According to Eurocode 3 [40], the joint is classified semi-rigid joint. The plastic bending stiffness of M2 is 1.1% higher than that of M1 and the elastic moment resistance of M2 is 14.8% higher than that of M1. The ultimate load of M2 is larger than that of M1 by 6.8%. The ultimate rotation of M2 is larger than that of M1 by 31.0%. The shear connector has minor influence on the initial bending stiffness of the joint because 1) in the linear stage, the deformation of the joint was small; 2) the shear connector was installed on the middle part of
The load-strain curves and F − θ curves are shown in Fig. 14. Three stages can be identified from F − θ curves of Q1 and Q2 as shown in Fig. 14(a): The linear stage, the plastic stage, and the failure stage. During the first stage, Q1 and Q2 had almost identical responses. The initial shear stiffness of Q1 and Q2 were 2075 kN/rad and 2229 kN/rad. The elastic load resistance is 112.7 kN and 106.9 kN. The failure stage began with a sudden decrease in load, where the load of Q1 and Q2 were 196.2 kN and 195.5 kN and the rotations were 0.157 rad and 0.153 rad. Though Q1 and Q2 had the same failure mode (bolt thread stripping), their failure stages varied. As marked on Fig. 14(b), the sudden decrease in load was caused by thread stripping followed by four peaks in the Q1 curve but only three in the Q2 curve. The difference is likely attributable to the geometric asymmetry of the specimens or decantation of the loading apparatus. Bolts of Q1 stripped one after another, while the first two peaks of the Q2 curve were four bolts stripped in pairs (bolts 1 and 2) and the third was caused by TB web buckling. According to a former study [31], four stages can be identified from the F − θ curve of the specimen with shear connectors as illustrated in Fig. 14(c): The fixed stage, slipping stage, bolt-hole bearing stage, and failure stage. In the first stage, shear connectors and beam webs were fixed by friction force caused by the pretension of bolts. As the load increased, the sliding force between shear connectors and beam webs exceeded the maximum static friction force leading to slip of the surfaces. The slipping stage ended when the bolts contacted the bolt-hole walls of the beam webs and those of the shear connectors. The specimen then entered the bolt-hole bearing stage followed by the failure stage. As shown in Fig. 14(c), the fixed stages of Q3 and Q4 ended with different loads due to their different preloads; Q3 had a preloading value of 25 kN, during its preloading process, no obvious decrease of slope was observed. Q4 had a preload value of 50 kN, during its preloading process, a decrease of slope was observed around 25–30 kN. The following explanations are made based on the above situation. Q4 131
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Fig. 13. Response curves of Scenario I.
without shear connectors by 60.2% on average. The elastic resistance improved by 136.0%. The ultimate loads improved by 63.1% if the failure mode was cracking and 21.9% if the failure mode was web buckling. As shown in Fig. 14(d), strains of Q3 and Q4 were much smaller compared to those of Q1 and Q2, indicating that the shear connector provided a better load transferring path and greatly improved the integrity of the joint under shear loads.
Table 3 Summary of results (Scenario I). Specimen
Kini (kN · m/rad)
My (kN · m)
Kp (kN · m/rad)
Mu (kN · m)
M1 M2 Comparison (M2/M1)
27,308 27,595 1.011
134.9 154.8 1.148
6375 6459 1.013
213.7 228.2 1.068
4.4. Finite element analysis entered the slipping stage during its preloading process. There was almost no interspace between some of the bolts and their bolt-holes because of the machining error; and these bolts might contact bolt-holes at the very beginning of the slipping stage, which means that by the end of the preloading process of Q4, these bolts had already been in the bearing state. When the specimen was unloaded, the shear connectors did not slide back to its initial position due to the friction force. It should be noticed that the above-mentioned bolts were still in the bearing state when the specimen was completely unloaded. These bolts caused an inversed friction force between the surfaces, and in the following loading procedure, this inversed friction force must be compensated before the surfaces began to slip. Thus, the fixed stage end load of Q4 was improved. As can be seen in Fig. 14(c), despite the difference in end loads of the fixed stage, the two curves had a similar slope under 200 kN in general. A comparison among the initial shear stiffness and critical loads of Q series specimens is shown in Table 4. The initial shear stiffness of specimens with shear connectors was higher than that of specimens
Finite element (FE) simulations offer an intuitional and visualized insight into the component interactions within a semi-rigid joint, which is difficult to acquire by specimen tests. FE models of Scenario II specimens with and without shear connectors were established and analyzed with FE software ABAQUS. Half models were established to reduce calculating time, as shown in Fig. 15(a). The models were meshed with reduced integration elements (C3D8R). Interfaces between two components in the FE model are simulated by creating contact elements. The load is applied to the model by employing a pressure to an area where the hydraulic jack was installed in the experiment. Boundary conditions, as marked in Fig. 15(a), were also set up to simulate the experimental program. Support A was simulated by a rigid surface, and contact elements were created between the rigid surface and the lower surface of the beam member. Support B was simulated by fixing part of the upper flange. Symmetric boundaries were created on the symmetry plane. The friction coefficient for all contact surfaces was 0.3 according to Eurocode 9 [41]. Material properties of the aluminum alloy components used data from the tensile tests. Bilinear models were 132
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Fig. 14. Response curves of Scenario II.
4.5. Discussion
Table 4 Summary of results (Scenario II). Specimen
Kini (kN/rad)
Fy (kN)
Kp (kN/rad)
Fu (kN)
Q1 Q2 Q3 Q4
2075 2229 3275 3620
112.7 106.9 / 259.1
768 783 / 1573
198.9 210.1 238.4 318.8
Specimens without shear connectors have an indirect shear load transmission path. The path can be described as web-flange-plateflange-web. Key components that transfer the shear load are gusset plates which were attached on beam flanges by bolts. X-direction beams participate in transferring the shear load by restricting out-of-plane deformation of the plates, in other words, improving the stiffness of the plates. Shear connectors provide a more direct shear load transmission path which is web-connector-web. Shear connectors have the most contribution among the three components in general, especially in the fixed stage. To use shear connectors efficiently, it is recommended by the authors that high-strength bolts should be used to connect shear connectors and beam webs in engineering practice.
employed to model material properties of all steel components. F − θ curves of test and finite element analysis (FEA) are plotted in Figs. 14(a) and 14(c). Both for joints with and without shear connectors, test and FEA curves have good accordance in the linear range, but have some discrepancies among the nonlinear range, which may be induced by simplifications that introduced in the FE modeling, such as the bilinear model adopted as the material property of bolts, and fabrication errors of the specimens. The FE model in this paper was established aiming at simulating a well restrained joint, such as Q4. Q3 was not well restrained leading to a failure mode of beam web buckling, which explains the discrepancies in the nonlinear range between curves of Q3 and FEA. Stress distributions of the models under the same load value of 150 kN, are plotted in Fig. 15(b). It can be seen that, the stresses on the plates and the X-direction beams of model with the shear connector are much lower than those of the model without the shear connector, indicating that shear connectors optimize the load transferring path.
5. Theoretical model As a highly modularized joint system, AAGJs consist of similar Ishaped beams and plates with different dimensions. Most deformation in the AAGJ is composed of both joint rotation and shear deformation. A theoretical model of AAGJ considering both bending and shear deformation is proposed in this paper. The theoretical model is comprised of several beam and spring elements. The model along the Z-direction is shown in Fig. 16, where Sb denotes the bending stiffness of the joint, Ss, p denotes the shear stiffness provided by top and bottom plates, 133
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Fig. 17. Parameter naming rules.
Table 5 Naming rules. Parameter K M
Slope of the line Moment value of the point
Component p bx sc
Plate Beams in the X-direction Shear connector
connector on Sb was omitted. Rotational springs were employed to simulate the shear stiffness of the joint, so the F − θ curves were converted into M − θ curves. M can be calculated as follows: (8)
M = F ·Dc
Test data of Q4 are more available for reference than those of Q3 because that, as stated in Section 3, scenario that concentrated forces applied on an aluminum alloy I-shaped beam hardly happens in engineering practices and the failure mode of Q3 can be avoided at a very low cost. The converted curves of Q4 and Q2 are shown in Fig. 18. Curves were linearized as marked on the figure and the corresponding parameters are listed in Table 6. The shear stiffness provided by plates was obtained via FE simulation. An FE model without X-direction beams using the same modeling method stated in Part 4.4 was established and analyzed. The M − θ curve and the linearized curve are shown in Fig. 18; the parameters are listed in Table 6. The shear stiffness provided by the shear connector was obtained per the shear stiffness of Q4 minus the shear stiffness of Q2. The shear stiffness provided by beams in the X-direction was obtained by the shear stiffness of Q2 minus the shear stiffness of the FE simulation results. The M − θ curves of components, i.e., the plates, Xdirection beams, and shear connectors are plotted in Fig. 19. Over 40% of the total shear stiffness is provided by the shear connectors when deformation is smaller than 0.02 rad or larger than 0.06 rad. The beams in the X-direction also provided over 35% of the total shear stiffness on average, and the contribution of the plates to shear stiffness of the joint was about 20%. In the future, this theoretical model may be used to
Fig. 15. Finite element analysis.
Fig. 16. Theoretical model.
Ss, bx denotes the shear stiffness provided by beams along the X-direction, Ss, sc denotes the shear stiffness provided by the shear connector, and Dc is the node region of the joint. All beam elements in the node region of the model are considered to be rigid. The value of Dc was determined by the experiments. In regards to bending deformation (Fig. 10), cracking occurred near bolt 8 which suggests that rotation occurred nearby. For the shear deformation (Fig. 11(a)), bolt 3 was less deformed than bolts 1 and 2 suggesting that shear deformation occurred between bolt 3 s of the opposite beams. Most of the joint deformation occurred between bolts 3 and 8, so Dc can be considered as the distance between middle points of the bolts 3 s and 8 s where bolt 5 s were located. Sb can be described by a bilinear curve, the parameters of which are determined by the M − ϕ curve of M1. The naming rule of the parameters are detailed in Fig. 17 and Table 5. The influence of the shear
Fig. 18. M − θ curves.
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Table 6 M − θ curve parameters. Specimen No.
1 2 3 4
Component
M1
Q3
Q2
p
bx
sc
K
M
K
M
K
M
K
M
K
M
K
M
27,308 6581
134.9 213.7
718 244
32.1 58.7
2141 880 424
14.3 77.7 95.6
303 106
9.4 22.4
415 612 138
12.9 21.2 36.3
1423 162 636 180
9.5 15.6 37.3 44.9
Units: K (kN · m/rad), M (kN · m).
rotation of the joint by over 30%. For specimens under shear loads, shear connectors improved the initial shear stiffness by over 60%, the elastic resistance by over 130%, and the ultimate load by over 60% in the case of beam rupture failure mode. Shear connectors also remarkablely reduced strain on the beam flange. (4) The shear connectors and X-direction beams provided over 80% of the total shear stiffness of the joint. The contribution of the shear connectors to the shear stiffness of the joint exceeded that of the Xdirection beams in the fixed and bolt-hole bearing stages. The contribution of the plates was about 20%. (5) FE models established in this paper can simulate specimens with and without shear connectors under shear loads with acceptable accuracy. After further research to confirm its feasibility and effectiveness, the proposed joint model may be used to directly evaluate AAGJ mechanical properties and employed in the stability analysis of cable-stiffened aluminum alloy single-layer reticulated shell structures.
Fig. 19. M − θ curves of components.
Acknowledgements
directly evaluate mechanical properties of AAGJs given the dimensions of all components.
This study is supported by National Natural Science Foundation of China (Project no. 51178331).
6. Conclusions
References
Six full-scale specimens of aluminum alloy gusset joints and corresponding beam members were tested under pure bending and shear load in this study. FE models of Q series specimens with and without shear connectors were established and analyzed. A theoretical AAGJ model was established accordingly and parameterized based on the experimental data. Main findings of this study can be summarized as follows. (1) The failure mode of joints under pure bending loads was lower beam flange rupture. Under shear loads, joints without any shear connectors showed bolt thread stripping followed by beam web buckling, while joints with shear connectors experienced beam web buckling if the constraint was weak and beam web rupture if the constraint was strong. The weak sections of the AAGJ system included flanges near the outermost row of bolts and beam webs near the joint center. The former occurred because bolt-holes reduced the sectional area; the latter is attributable to the large height-to-thickness ratio of the web and deformation of the plate under shear loads. (2) The M − ϕ and F − θ curves suggest that AAGJs are typical semi-rigid joints. The joints exhibited nonlinear bending and shear stiffness which decreased beyond the elastic stage. Four stages can be identified from the F − θ curves of specimens with shear connectors: The linear stage, the sliding stage, the bolt bearing stage, and the failure stage. The second and the third stages may merge into one if the machining error of the shear connectors is considerable. (3) For AAGJs under only bending loads, shear connectors did not influence the failure mode, initial bending stiffness, or subsequent bending stiffness in the nonlinear stage, but slightly improved the ultimate load (less than 7%). Shear connectors improved the ultimate
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Full length article
Experimental investigation on bending and shear performance of two-way aluminum alloy gusset joints
MARK
⁎
Mingzhe Shi, Ping Xiang, Minger Wu Tongji University, No. 1239 SiPing Rd., Shanghai, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Aluminum alloy gusset joint Semi-rigid behavior Failure modes Experimental study
Two-way aluminum alloy gusset joints (AAGJs) are considered to be employed in cable-stiffened aluminum alloy single-layer reticulated shell structures meshed with quadrilateral grids. In this study, a series of experiments on six AAGJs with and without shear connectors were conducted to investigate their semi-rigid behavior. Two joints were subjected to pure bending moments and others to shear loads, then their corresponding failure modes were investigated which were mainly beam rupture, beam web buckling, and bolt failure. The moment-rotation curves, shear load-rotation curves, and strain-load curves were also obtained, indicating that AAGJs are typical semi-rigid joints. Shear connectors can optimize the load transferring path and improve ductility under bending moment while enhancing shear performance significantly. A simplified theoretical AAGJ model was also established and parameterized according to the experimental results.
1. Introduction Single-layer reticulated shell structures provide a highly efficient method for building large-span structures. Introducing a tensioning system into a reticulated shell structure can improve the stability of such buildings. There currently exist two kinds of single-layer reticulated shells with tensioning systems: Suspen-domes [1–3] and cable-stiffened shells [4,5]. Both systems can effectively improve the stability of reticulated shells. Suspen-domes are only applicable to domes, however, while cable-stiffened shells can suit almost any curved shape. A cable-stiffened reticulated shell (CSRS) structure is typically comprised of a single-layer quadrilateral-mesh reticulated shell with Xshaped pre-tensioned cables disposed within the grids. The cable can be arranged within the curved surface to improve the in-plane stiffness (Type A) or work with posts externally (Type B) to improve the out-ofplane stiffness of the shell [6]. The Neckarsulm dome (Fig. 1) [7] is a practical application that adopted the Type A cable arrangement; the Kumagaya dome (Fig. 2) [8] adopted the Type B. There have been many studies on the stability of cable-stiffened single-layer reticulated shells. Wu et al. [9] analyzed the introducing process of pre-stress tensile units of a CSRS. Zhang and Fujimoto [10] conducted a numerical study on a series of CSRSs to explore the effect of cable arrangement on linear and nonlinear stability. Feng et al. [11] derived the formula for the linear buckling load of an elliptic paraboloid CSRS with imperfections based on continuum analogy. Li et al. [4,6] performed a series of parametric analysis on the stability behavior ⁎
of cylindrical and elliptic paraboloidal CSRSs with different cable arrangements. Li et al. [12] conducted experimental investigations on two-way single-layer shells with and without cables under different load distributions. Many studies have shown that joint stiffness cannot be ignored in the analysis and design of single-layer reticulated shells, as it significantly affects the global stability behavior [13–17]. There have been extensive numerical and experimental investigations on the semi-rigid behavior of joints in different systems. Feng et al. [18] conducted experiments and numerical analyses including on in-plane and out-ofplane stiffness for bolted joints that are used to constructing CSRSs. Fan et al. [19] and Ma et al. [17] carried out a series of studies on socket joints and bolt-ball joint systems subjected to bending moment, shear force, and axial force to investigate semi-rigid behavior. Han and Liu [20] conducted experiments on twelve welded hollow ball joints subjected to tensile and compress loads. Previous studies and practical engineering projects typically center around steel as the primary material. Aluminum alloy has many notable advantages compared to steel; it is light-weight, cheap to maintain, and has excellent cryogenic properties, among others [21]. It also has some disadvantages, however. Its thermal expansion coefficient is twice as steels, and it has a relatively poorer high temperature material performance than steel. Researches regarding aluminum alloys thermal behavior is fairly limited, however. Chen [22] performed experimental investigation on 114 aluminum alloy coupons to study the influences of temperature, material grade and cooling method on the post-fire mechanical properties. Maljaars [23] carried out investigations on local
Corresponding author.
http://dx.doi.org/10.1016/j.tws.2017.10.002 Received 27 June 2017; Received in revised form 13 September 2017; Accepted 2 October 2017 0263-8231/ © 2017 Elsevier Ltd. All rights reserved.
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(2) Many free-form reticulated shell structures have been built in recent years [35], among which aluminum alloy reticulated shells have been especially popular. Unfortunately, the AAGJ does not readily transfer shear force across the joint due to the lack of connection between beam webs (Fig. 3(a)). Previous research has also indicated that joint shear stiffness affects reticulated shell structures to some extent [34]; the shear stiffness of AAGJ has yet to be fully understood, however. In this study, tests on six full-scale AAGJs were conducted to explore the bending and shear stiffness with and without shear connectors, respectively. The experimental program is introduced below, followed by the results obtained for the failure modes of the joints. Response curves of the joints are then presented and discussed. Finally, the corresponding theoretical AAGJ model is proposed and concluding remarks are provided.
Fig. 1. The Neckarsulm dome.
2. Experimental program 2.1. Materials The material for the beam members and gusset plates used in this study was aluminum alloy 6061-T6 [36]. The bolts were made of austenitic stainless steel and the shear connectors of steel. Though the same raw material was used for the beam members and gusset plates, their mechanical properties may have varied due to differences in processing techniques. Two sets of tension coupon tests were performed to investigate the mechanical properties of the materials: One set contained three coupons cut directly from the unprocessed gusset plates, and the other contained two pairs of coupons cut from the flange and the webs of the I-shaped beam members, respectively. All the seven coupons had the same dimensions except for the thickness, as shown in Fig. 4(a). The chemical composition of the aluminum alloy coupons is in accordance with GB/T 3190-2008 [37] and the shapes and sizes are designed in accordance with GB/T 228.1–2010 [38]. The material properties of the steel components, including the stainless steel bolts type A (connecting beams with plates), stainless steel bolts type B (connecting shear connectors with beams), and steel shear connectors, were provided by the manufacturers. The surface of the aluminum alloy was initially smooth, but became coarse as plastic deformation progressed during the tensile tests (Fig. 4(b)). This phenomenon (plastic texture) can be used to identify regions with high strain concentration among the aluminum alloy components. The stress-strain curves of aluminum alloy coupons are shown in Fig. 5, the results of the tensile coupon tests meet requirements of GB/T 6892-2006 [39]. The mechanical properties of all the materials mentioned above are summarized in Table 1, including the elastic modulus, E, the nominal yield strength, σy , and the ultimate tensile strength, σu .
Fig. 2. The Kumagaya dome.
buckling of aluminum alloy members at elevated temperatures. Maljaars [24] conducted a parametric study on fire exposed aluminum structural members, and proposed a verified model for designing aluminum alloy members at elevated temperatures. Liu [25] measured the solar radiation absorption coefficient of aluminum alloy, and analyzed the temperature distribution and thermal response of aluminum alloy space structures. A considerable number of aluminum alloy single-layer reticulated shells have been constructed since 1950; such structures are widely considered to have attractive appearance and favorable structural features such as easy erection and high durability in moist environments [26]. Building a CSRS using aluminum alloy forms an efficient, economical and elegant structure. Research on the semi-rigid behavior of joint systems of aluminum alloy reticulated shells is fairly limited, however. Sugizaki et al. [27,28] carried out a series of experimental and numerical studies on aluminum insertion joints, and Hiyama et al. [29] performed experimental studies on six aluminum ball joints. Shi et al. [30] investigated the semi-rigid behavior of a novel cast aluminum joint under different loading conditions, and Guo et al. [31–33] derived and experimentally verified a formula for bending stiffness of aluminum alloy gusset joints (AAGJs). Shi et al. [34] investigated the bending and shear stiffness of an AAGJ using FE simulations. This paper also focuses on the AAGJ system, which is one of the most commonly used joint systems in building aluminum alloy reticulated shells, as shown in Fig. 3. There has been very little research to date on combining AAGJ with CSRS, however, leaving the following problems to be solved: (1) As opposed to traditional aluminum alloy reticulated shells, CSRSs usually have quadrilateral meshes rather than triangular meshes; this means that four beam members are connected to a joint instead of six. The semi-rigid behavior of this kind of AAGJ may differ from the traditional joint, but this has yet to be fully confirmed.
2.2. Specimens A series of tests on six specimens were conducted to study the semirigid behavior of AAGJs. A standard AAGJ in a reticulated shell with quadrilateral meshes contains two circular plates and four I-shaped beam members connected by bolts, as shown in Fig. 3. The diameter of the circular plates was 515 mm and the thickness was 12 mm. All the Ishaped beam members had the same cross-sectional dimensions of 350 × 200 × 8 × 12 mm , as shown in Fig. 4(a). The detailed configuration of the beam member is shown in Fig. 6. Each specimen had two long beams and two short ones (Fig. 6(a)). This study focuses on the semi-rigid behavior along principal axis of joints, so the X-direction beams were kept short and with the same length of 300 mm. Each Ishaped beam member was tightly attached to top and bottom plates by 36 stainless steel bolts 10 mm in diameter. The bolts were numbered as shown in Fig. 6(b). As shown in Table 2, two sets of joint specimens were investigated: 125
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Fig. 3. Aluminum alloy gusset joint system.
M series and Q series. The M series specimens were used to study the bending performance of the joint, while the Q series specimens were used to study the shear performance. The length of I-shaped beam members of M series specimens was 2100 mm; that of Q series members was 800 mm. The influence of shear connectors was also investigated. A pair of shear connectors were attached to a beam web on each side via 12 stainless steel bolts with the diameter of 10 mm. The shear connectors had dimensions of 288 × 224 × 5 mm (length × height × thickness), as shown in Fig. 7. As shown in Table 2, M2 and M1 were joints with and without shear connector under bending moments, and Q3 and Q4 were specimens with shear connectors designed for investigating shear performance, while Q1 and Q2 were without.
2.3. Experimental scenario and setup Fig. 5. Material properties of aluminum alloy coupons.
Two experimental scenarios were designed. The test setup of Scenario I, as shown in Fig. 8, was designed to obtain moment-rotation relationship for the joint under pure bending moments. Specimens were simply supported on columns and subjected to two vertical loads at their points of trisection. The load was applied via a load distributing girder with a hydraulic jack located at the midpoint. The total length of each specimen was 4310 mm and the distance between the two supports was 4010 mm. The distances between load points to the midpoint of the specimen was 710 mm. Two anti-torsion bearings were designed to prevent specimens from out-of-plane torsion, as shown in Fig. 8(c). Two anti-torsion columns were also placed at the load points to restrict the out-of-plane displacements of the specimens, as marked in Figs. 8(a) and 8(b). Webs of aluminum alloy I-shaped beam members are prone to local buckling due to their large height-to-thickness ratio. Accordingly, four pairs of steel anti-buckling reinforcements were employed at bearings and load sections where concentrated forces occurred, as marked in Figs. 8(a) and 8(c). Each pair of anti-buckling reinforcements was attached to the beam web via 24 M10 hand-tightened stainless steel bolts. The width of the anti-buckling reinforcements was 100 mm and the height was 324 mm, which was 2 mm less than the distance between the upper and lower flange. Scenario II was designed to study the shear performance of the joint,
Table 1 Joint component material properties. Material Aluminum Alloy
Stainless Steel Steel
Component
E(MPa)
σy (MPa)
σu (MPa)
Plate
6.05 × 10 4
270
315
Flange
6.05 × 10 4
240
270
Web
6.05 × 10 4
240
270
Bolt A
1.95 × 105
515
792
Bolt B
1.95 × 105
300
670
Shear connector
2.06 × 105
235
500
which was described as load-rotation curves. The theoretical model of Scenario II is a short beam fixed on one end and under concentrated force on the other. The test setup shown in Fig. 9 was designed to simulate fixed boundary conditions. It contains two supports: Support A near the center of the joint, which was comprised of a column with an anti-torsion bearing on it, and Support B which was similar to Support A but also included reaction frame on the far-end of the specimen; its beam had the cross-sectional dimension of 400 × 300 × 40 × 40 mm . A Fig. 4. Cross-sectional dimension of the specimen and tensile test coupon.
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Fig. 6. Specimen details.
2.4. Experimental procedure
Table 2 Specimen information. Series
No.
Beam member length (mm)
Shear connector
Failure mode
M
1 2 1 2
2100 2100 800 800
without with without without
3 4
800 800
with with
Beam rupture Beam rupture Bolt failure (1)Bolt failure (2)TB buckling BB buckling Beam rupture
Q
A three-step procedure was adopted for both scenarios. (1) The specimens were subjected to a small load (the smaller one between 1/3 of the linear stage and 10% of the estimated failure load) and then unloaded to check the loading and measuring apparatus. This step also reduced the influence of interspaces between the components. (2) The test was carried out under force control at a relatively swift speed (10 kN/min) during the linear stage. This step ended when the estimated linear stage was covered or nonlinear load-displacement curves were observed. (3) Once the specimens entered the nonlinear stage, the load control method was changed to a displacement control method with a low loading speed (1 mm/min) until failure of the specimens occurred.
3. Failure modes The failure modes are shown in Figs. 10 and 11 and summarized in Table 2. The primary failure modes of the specimens included three types: Beam rupture, beam buckling, and bolt failure. In Scenario I, as shown in Fig. 10, both specimens failed due to rupture of the lower flange near bolts 8 and 9. Introducing the shear connector into the joint system did not interfere with this failure mode under pure bending load. Strengthened by the shear connector, M2 did not rupture entirely, but instead a crack was initiated at the junction of the web and flange. The necking deformation is marked in Fig. 10. The failure modes of specimens in Scenario II are shown in Fig. 11. The loading beam and the bearing beam near the center were divided into four parts for clarity; they are labeled as TL (top of loading beam), BL (bottom of loading beam), TB (top of bearing beam), and BB (bottom of bearing beam) as shown in Fig. 9(a). Q1 and Q2, the specimens without shear connectors, experienced substantial deformation before failure (Fig. 11(a)). The failure mode of Q1 was thread stripping of bolts 1 and 2 of TL and BB (Fig. 11(b)). Q2 had a similar phenomenon as Q1, but the test ended with the buckling of the web at TB (Fig. 11(c)). Q3 and Q4, the specimens with shear connectors, had distinctly less shear deformation compared to Q1 and Q2 (Figs. 11(a) and 11(c)). As shown in Fig. 11(e), stainless steel bolts caused large deformation in the bolt-holes. The failure mode of Q3 was the buckling of the web at BB near the edge of the plate. In this case, the reinforcement was not efficient enough. Although aluminum alloy I-shaped beams are prone to local buckling under concentrated forces, scenario that concentrated forces applied on an aluminum alloy I-shaped beam hardly happens in engineering practices. And the failure mode of Q3 can be avoided at a very low cost. Introducing anti-buckling reinforcements, for instance, can be a feasible and efficient scheme. Thus, in the test of Q4, four pairs of anti-buckling reinforcements with the thickness of 12 mm were employed to determine the joint was well restrained. The failure mode of Q4 was the rupture of the beam web, which occurred in a three-step process (Fig. 11(f)). There were no visible cracks in the first or second step, as cracks were covered by the shear connector. A strip of plastic
Fig. 7. Shear connector.
hydraulic jack was located at the other end of the specimen near the joint plate. The distance between the centers of Support A and the joint plate of the specimen was 358 mm, and the margin between the edges of the support and the plate was 40 mm. The hydraulic jack was placed symmetrically with Support A. A pair of anti-torsion columns were placed at the end of the specimen on the loading side. Three pairs of anti-buckling reinforcements were installed at the support end of the specimen equidistantly, plus one more pair under the hydraulic jack as shown in Fig. 9(a). Displacement transducers (DTs) were installed at several key locations as shown in Figs. 8(a) and 9(a). In Scenario I, DT-S1 and DT-S2 were installed at supports, DT-L1 and DT-L2 loading points, and the DTC plate center. In Scenario II, DT-SA was installed at Support A, DT-SB at Support B, DT-P1 and DT-P2 on the upper plate of the specimen with 300 mm-distance and symmetrical about the center, and DT-L at the loading point. The strain gauges placed on M series specimens are illustrated in Fig. 8(d). M-S-B1 and M-S-B2 were placed at the top and bottom flange of the beam. M-S-P1 and M-S-P2 were placed at the center of the top and bottom plates. Four strain gauges were placed on the shear connector of M2. The strain gauges placed on Q series specimens are shown in Fig. 9(a). Q-S-B1 and Q-S-B2 were placed along the Y-direction near the top and bottom flanges.
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Fig. 8. Setup of Scenario I.
These cracks increased the tensile force in the top flange of the bearing beam, which then ruptured (near bolts 8 and 9) before the crack spread to the bottom flange.
texture can be observed in a similar position as the stress distribution (Fig. 11(e)), which indicated that the first step was horizontal cracking caused by local shear failure; the second step was upright cracking. 128
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Fig. 9. Setup of Scenario II.
4. Response curves and discussion 4.1. Derivation of the response curves The bending behavior of the joint can be described by the relationship between the bending moment M and the corresponding rotation angle ϕ of the joint. The M − ϕ curves in this study were calculated based on the data obtained from the loading apparatus and displacement transducers. The bending moment, M, can be calculated by Eq. (1):
M= Fig. 10. Failure mode of Scenario I.
1 FLl 2
(1)
where F represents the sum of loads acting on both sides of the joint and Ll is the distance between the bearing and the point where the load acts. As shown in Fig. 12, the vertical displacement of the node center, δb, c , obtained from DT-C, can be regarded as the summation of the following two parts: 129
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Fig. 11. Failure modes of Scenario II.
(1) The vertical displacement caused by bending deformation of the beam member, δb, b , is calculated as follows:
δb, b =
FLl (3L2 − Ll2) 12EI
represents the variation of angle caused by the shear deformation and Dc represents the distance between Q-DT-P1 and Q-DT-P2. The shear deformation of the beam is shown in Fig. 11(a). The effect of the bending deformation on the shear angle was neglected because the length of the deformed area was small. The vertical relative displacement between measurement points i and j (δij ) on the specimens can be regarded as the summation of following two parts: (1) The relative displacement caused by rigid body movement of the beam member, δs, r , is calculated by Eq. (5):
(2)
where L denotes the length of a single beam member; E and I are the Young's modulus and moment of inertia of the member, respectively. (2) The vertical displacement caused by rigid body rotation of the beam member, δb, r , is calculated as follows:
δb, r = δb, c − δb, b
(3)
δs, r =
The rotation, ϕ , can be calculated by Eq. (4):
δb, c − δb, b ⎞ δb, r ⎞ ϕ = arctan ⎛ = arctan ⎛ L ⎝ L ⎠ ⎝ ⎠ δ FL , b c l 2 (3L2 − Ll ) ⎤ = arctan ⎡ − ⎢ L ⎥ 12EIL ⎣ ⎦ ⎜
⎟
⎜
Dc (δSA − δSB ) LAB
(5)
where δSA and δSB represent the displacements of Support A and Support B, which can be obtained from DT-SB and DT-SA. LAB denotes the distance between two supports. (2) The relative displacement caused by shear deformation, δs, s , is calculated as follows:
⎟
(4)
In this paper, shear load-rotation (F − θ ) curves are used to describe the shear performance of the joint, where F represents the shear load, θ
δs, s = δij − δs, r = (δP 2 − δP1) − 130
Dc (δSA − δSB ) LAB
(6)
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Fig. 12. Joint deformations.
the webs; and 3) there were gaps between bolts and bolt-holes. When the joint entered the nonlinear stage, the shear connector had greater influence as joint deformation increased; this resulted in an increase in elastic resistance and ultimate load. These results altogether suggest that introducing shear connectors into the joint system does not improve linear bending stiffness to any meaningful extent, but does improve the integrity and ductility of the joint significantly.
where δP1 and δP2 are data obtained from DT-P1 and DT-P2. θ can be calculated by Eq. (7):
δs, s ⎞ δ − δP1 δ − δSB ⎞ θ = arctan ⎛ = arctan ⎛ P 2 − SA Dc LAB ⎠ ⎝ Dc ⎠ ⎝ ⎜
⎟
⎜
⎟
(7)
4.2. Response curves of Scenario I
4.3. Response curves of Scenario II
The load-displacement curves, load-strain curves and M − ϕ curves are shown in Fig. 13. The load-displacement curves of M1-DT-L1 and M1-DT-L2 (DTs of loading points) show good agreement before 260 kN, but separated from each other afterwards as shown in Fig. 13(a). Due to the geometrical imperfections and material uniformity, one side of the joint deformed faster than the other after part of the beam members entered plasticity. A similar phenomenon can be observed for M2 as shown in Fig. 13(b). As shown in Fig. 13(c), the strains on the top and bottom flanges were highly symmetrical. This suggests that the specimens were subjected to a bending moment without axial force. Strains on the top plate grew faster than on the bottom plate, which suggests that the top plate had a larger bending deformation. Strains on the shear connectors were relatively small, indicating that the shear connector made little contribution to the bending stiffness of the joint. The M − ϕ curves shown in Fig. 13(d) are linear in the early stage with subsequent nonlinearity, which exhibits a typical elasto-plastic behavior. At the initial loading stage of the two curves, a slight change in slope occurs due to the slipping between the surfaces of beam flanges and the cover plates. The initial stiffness was provided by the friction between the surfaces due to the pretension of the bolts. When a certain load was reached, the maximum static friction force was exceeded and the surfaces began to slip, leading to a decrease in bending stiffness. The key parameters of the M − ϕ curves are shown in Table 3, including initial bending stiffness (Kini ), elastic moment resistance (My ), plastic bending stiffness (Kp ) and ultimate moment (Mu ). M1 and M2 have almost the same initial bending stiffness (27,308 kN · m/rad and 27,595 kN · m/rad). According to Eurocode 3 [40], the joint is classified semi-rigid joint. The plastic bending stiffness of M2 is 1.1% higher than that of M1 and the elastic moment resistance of M2 is 14.8% higher than that of M1. The ultimate load of M2 is larger than that of M1 by 6.8%. The ultimate rotation of M2 is larger than that of M1 by 31.0%. The shear connector has minor influence on the initial bending stiffness of the joint because 1) in the linear stage, the deformation of the joint was small; 2) the shear connector was installed on the middle part of
The load-strain curves and F − θ curves are shown in Fig. 14. Three stages can be identified from F − θ curves of Q1 and Q2 as shown in Fig. 14(a): The linear stage, the plastic stage, and the failure stage. During the first stage, Q1 and Q2 had almost identical responses. The initial shear stiffness of Q1 and Q2 were 2075 kN/rad and 2229 kN/rad. The elastic load resistance is 112.7 kN and 106.9 kN. The failure stage began with a sudden decrease in load, where the load of Q1 and Q2 were 196.2 kN and 195.5 kN and the rotations were 0.157 rad and 0.153 rad. Though Q1 and Q2 had the same failure mode (bolt thread stripping), their failure stages varied. As marked on Fig. 14(b), the sudden decrease in load was caused by thread stripping followed by four peaks in the Q1 curve but only three in the Q2 curve. The difference is likely attributable to the geometric asymmetry of the specimens or decantation of the loading apparatus. Bolts of Q1 stripped one after another, while the first two peaks of the Q2 curve were four bolts stripped in pairs (bolts 1 and 2) and the third was caused by TB web buckling. According to a former study [31], four stages can be identified from the F − θ curve of the specimen with shear connectors as illustrated in Fig. 14(c): The fixed stage, slipping stage, bolt-hole bearing stage, and failure stage. In the first stage, shear connectors and beam webs were fixed by friction force caused by the pretension of bolts. As the load increased, the sliding force between shear connectors and beam webs exceeded the maximum static friction force leading to slip of the surfaces. The slipping stage ended when the bolts contacted the bolt-hole walls of the beam webs and those of the shear connectors. The specimen then entered the bolt-hole bearing stage followed by the failure stage. As shown in Fig. 14(c), the fixed stages of Q3 and Q4 ended with different loads due to their different preloads; Q3 had a preloading value of 25 kN, during its preloading process, no obvious decrease of slope was observed. Q4 had a preload value of 50 kN, during its preloading process, a decrease of slope was observed around 25–30 kN. The following explanations are made based on the above situation. Q4 131
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Fig. 13. Response curves of Scenario I.
without shear connectors by 60.2% on average. The elastic resistance improved by 136.0%. The ultimate loads improved by 63.1% if the failure mode was cracking and 21.9% if the failure mode was web buckling. As shown in Fig. 14(d), strains of Q3 and Q4 were much smaller compared to those of Q1 and Q2, indicating that the shear connector provided a better load transferring path and greatly improved the integrity of the joint under shear loads.
Table 3 Summary of results (Scenario I). Specimen
Kini (kN · m/rad)
My (kN · m)
Kp (kN · m/rad)
Mu (kN · m)
M1 M2 Comparison (M2/M1)
27,308 27,595 1.011
134.9 154.8 1.148
6375 6459 1.013
213.7 228.2 1.068
4.4. Finite element analysis entered the slipping stage during its preloading process. There was almost no interspace between some of the bolts and their bolt-holes because of the machining error; and these bolts might contact bolt-holes at the very beginning of the slipping stage, which means that by the end of the preloading process of Q4, these bolts had already been in the bearing state. When the specimen was unloaded, the shear connectors did not slide back to its initial position due to the friction force. It should be noticed that the above-mentioned bolts were still in the bearing state when the specimen was completely unloaded. These bolts caused an inversed friction force between the surfaces, and in the following loading procedure, this inversed friction force must be compensated before the surfaces began to slip. Thus, the fixed stage end load of Q4 was improved. As can be seen in Fig. 14(c), despite the difference in end loads of the fixed stage, the two curves had a similar slope under 200 kN in general. A comparison among the initial shear stiffness and critical loads of Q series specimens is shown in Table 4. The initial shear stiffness of specimens with shear connectors was higher than that of specimens
Finite element (FE) simulations offer an intuitional and visualized insight into the component interactions within a semi-rigid joint, which is difficult to acquire by specimen tests. FE models of Scenario II specimens with and without shear connectors were established and analyzed with FE software ABAQUS. Half models were established to reduce calculating time, as shown in Fig. 15(a). The models were meshed with reduced integration elements (C3D8R). Interfaces between two components in the FE model are simulated by creating contact elements. The load is applied to the model by employing a pressure to an area where the hydraulic jack was installed in the experiment. Boundary conditions, as marked in Fig. 15(a), were also set up to simulate the experimental program. Support A was simulated by a rigid surface, and contact elements were created between the rigid surface and the lower surface of the beam member. Support B was simulated by fixing part of the upper flange. Symmetric boundaries were created on the symmetry plane. The friction coefficient for all contact surfaces was 0.3 according to Eurocode 9 [41]. Material properties of the aluminum alloy components used data from the tensile tests. Bilinear models were 132
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Fig. 14. Response curves of Scenario II.
4.5. Discussion
Table 4 Summary of results (Scenario II). Specimen
Kini (kN/rad)
Fy (kN)
Kp (kN/rad)
Fu (kN)
Q1 Q2 Q3 Q4
2075 2229 3275 3620
112.7 106.9 / 259.1
768 783 / 1573
198.9 210.1 238.4 318.8
Specimens without shear connectors have an indirect shear load transmission path. The path can be described as web-flange-plateflange-web. Key components that transfer the shear load are gusset plates which were attached on beam flanges by bolts. X-direction beams participate in transferring the shear load by restricting out-of-plane deformation of the plates, in other words, improving the stiffness of the plates. Shear connectors provide a more direct shear load transmission path which is web-connector-web. Shear connectors have the most contribution among the three components in general, especially in the fixed stage. To use shear connectors efficiently, it is recommended by the authors that high-strength bolts should be used to connect shear connectors and beam webs in engineering practice.
employed to model material properties of all steel components. F − θ curves of test and finite element analysis (FEA) are plotted in Figs. 14(a) and 14(c). Both for joints with and without shear connectors, test and FEA curves have good accordance in the linear range, but have some discrepancies among the nonlinear range, which may be induced by simplifications that introduced in the FE modeling, such as the bilinear model adopted as the material property of bolts, and fabrication errors of the specimens. The FE model in this paper was established aiming at simulating a well restrained joint, such as Q4. Q3 was not well restrained leading to a failure mode of beam web buckling, which explains the discrepancies in the nonlinear range between curves of Q3 and FEA. Stress distributions of the models under the same load value of 150 kN, are plotted in Fig. 15(b). It can be seen that, the stresses on the plates and the X-direction beams of model with the shear connector are much lower than those of the model without the shear connector, indicating that shear connectors optimize the load transferring path.
5. Theoretical model As a highly modularized joint system, AAGJs consist of similar Ishaped beams and plates with different dimensions. Most deformation in the AAGJ is composed of both joint rotation and shear deformation. A theoretical model of AAGJ considering both bending and shear deformation is proposed in this paper. The theoretical model is comprised of several beam and spring elements. The model along the Z-direction is shown in Fig. 16, where Sb denotes the bending stiffness of the joint, Ss, p denotes the shear stiffness provided by top and bottom plates, 133
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Fig. 17. Parameter naming rules.
Table 5 Naming rules. Parameter K M
Slope of the line Moment value of the point
Component p bx sc
Plate Beams in the X-direction Shear connector
connector on Sb was omitted. Rotational springs were employed to simulate the shear stiffness of the joint, so the F − θ curves were converted into M − θ curves. M can be calculated as follows: (8)
M = F ·Dc
Test data of Q4 are more available for reference than those of Q3 because that, as stated in Section 3, scenario that concentrated forces applied on an aluminum alloy I-shaped beam hardly happens in engineering practices and the failure mode of Q3 can be avoided at a very low cost. The converted curves of Q4 and Q2 are shown in Fig. 18. Curves were linearized as marked on the figure and the corresponding parameters are listed in Table 6. The shear stiffness provided by plates was obtained via FE simulation. An FE model without X-direction beams using the same modeling method stated in Part 4.4 was established and analyzed. The M − θ curve and the linearized curve are shown in Fig. 18; the parameters are listed in Table 6. The shear stiffness provided by the shear connector was obtained per the shear stiffness of Q4 minus the shear stiffness of Q2. The shear stiffness provided by beams in the X-direction was obtained by the shear stiffness of Q2 minus the shear stiffness of the FE simulation results. The M − θ curves of components, i.e., the plates, Xdirection beams, and shear connectors are plotted in Fig. 19. Over 40% of the total shear stiffness is provided by the shear connectors when deformation is smaller than 0.02 rad or larger than 0.06 rad. The beams in the X-direction also provided over 35% of the total shear stiffness on average, and the contribution of the plates to shear stiffness of the joint was about 20%. In the future, this theoretical model may be used to
Fig. 15. Finite element analysis.
Fig. 16. Theoretical model.
Ss, bx denotes the shear stiffness provided by beams along the X-direction, Ss, sc denotes the shear stiffness provided by the shear connector, and Dc is the node region of the joint. All beam elements in the node region of the model are considered to be rigid. The value of Dc was determined by the experiments. In regards to bending deformation (Fig. 10), cracking occurred near bolt 8 which suggests that rotation occurred nearby. For the shear deformation (Fig. 11(a)), bolt 3 was less deformed than bolts 1 and 2 suggesting that shear deformation occurred between bolt 3 s of the opposite beams. Most of the joint deformation occurred between bolts 3 and 8, so Dc can be considered as the distance between middle points of the bolts 3 s and 8 s where bolt 5 s were located. Sb can be described by a bilinear curve, the parameters of which are determined by the M − ϕ curve of M1. The naming rule of the parameters are detailed in Fig. 17 and Table 5. The influence of the shear
Fig. 18. M − θ curves.
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Table 6 M − θ curve parameters. Specimen No.
1 2 3 4
Component
M1
Q3
Q2
p
bx
sc
K
M
K
M
K
M
K
M
K
M
K
M
27,308 6581
134.9 213.7
718 244
32.1 58.7
2141 880 424
14.3 77.7 95.6
303 106
9.4 22.4
415 612 138
12.9 21.2 36.3
1423 162 636 180
9.5 15.6 37.3 44.9
Units: K (kN · m/rad), M (kN · m).
rotation of the joint by over 30%. For specimens under shear loads, shear connectors improved the initial shear stiffness by over 60%, the elastic resistance by over 130%, and the ultimate load by over 60% in the case of beam rupture failure mode. Shear connectors also remarkablely reduced strain on the beam flange. (4) The shear connectors and X-direction beams provided over 80% of the total shear stiffness of the joint. The contribution of the shear connectors to the shear stiffness of the joint exceeded that of the Xdirection beams in the fixed and bolt-hole bearing stages. The contribution of the plates was about 20%. (5) FE models established in this paper can simulate specimens with and without shear connectors under shear loads with acceptable accuracy. After further research to confirm its feasibility and effectiveness, the proposed joint model may be used to directly evaluate AAGJ mechanical properties and employed in the stability analysis of cable-stiffened aluminum alloy single-layer reticulated shell structures.
Fig. 19. M − θ curves of components.
Acknowledgements
directly evaluate mechanical properties of AAGJs given the dimensions of all components.
This study is supported by National Natural Science Foundation of China (Project no. 51178331).
6. Conclusions
References
Six full-scale specimens of aluminum alloy gusset joints and corresponding beam members were tested under pure bending and shear load in this study. FE models of Q series specimens with and without shear connectors were established and analyzed. A theoretical AAGJ model was established accordingly and parameterized based on the experimental data. Main findings of this study can be summarized as follows. (1) The failure mode of joints under pure bending loads was lower beam flange rupture. Under shear loads, joints without any shear connectors showed bolt thread stripping followed by beam web buckling, while joints with shear connectors experienced beam web buckling if the constraint was weak and beam web rupture if the constraint was strong. The weak sections of the AAGJ system included flanges near the outermost row of bolts and beam webs near the joint center. The former occurred because bolt-holes reduced the sectional area; the latter is attributable to the large height-to-thickness ratio of the web and deformation of the plate under shear loads. (2) The M − ϕ and F − θ curves suggest that AAGJs are typical semi-rigid joints. The joints exhibited nonlinear bending and shear stiffness which decreased beyond the elastic stage. Four stages can be identified from the F − θ curves of specimens with shear connectors: The linear stage, the sliding stage, the bolt bearing stage, and the failure stage. The second and the third stages may merge into one if the machining error of the shear connectors is considerable. (3) For AAGJs under only bending loads, shear connectors did not influence the failure mode, initial bending stiffness, or subsequent bending stiffness in the nonlinear stage, but slightly improved the ultimate load (less than 7%). Shear connectors improved the ultimate
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