Performance study on T-stub connected semi-rigid joint between rectangular tubular columns and H-shaped steel beams

Abstract

This paper investigates the performance of T-stub connected semi-rigid joint of rectangular tubular columns and H-shaped steel beams. The finite element analysis software ABAQUS is used to analyze the nonlinear performance of the joint under monotonic loading. Meanwhile, the dimensions of T-stub, column and beam are considered as analytic parameters to discuss the performance of the joint. The analysis shows that the thickness and the length of T-stub webs, the height of beam section, bolt diameter, shear connector and the preloaded force affect the performance of the joint largely, and the thickness of the steel tube, the thickness and length of T-stub flange, bolt spacing have relatively little influences on the performance of the joint. The research results indicate that this joint is semi-rigid joint.

Keywords

rectangular tubular columns / T-stub / semi-rigid / nonlinear finite element analysis / moment-rotation curves

Introduction

With the increasing development on high-rise steel frame structure in our country, the technological progress on production of the cold bending rectangular tubular, and the better sectional characteristic, the steel tube columns are applied widely. Especially, the application of steel tube column is more mature in Japan. Inventions of both the increasing thickness of columns [1] and the high-strength blind bolts [2] make the steel tube applicable to practical production.

In recent years, foreign professors pay more their attentions on the semi-rigid joint [3] which is materialized mainly by high-strength bolts and weld. Their researches focus on describing the model of the connection, and establish the M-θ_r model by abundant experiments of semi-rigid connection, shown in the references [4-6]. The research on semi-rigid joint of rectangular tubular columns and H-Shaped steel Beams is almost a blank in our country. The main connection types [7] are the inner diaphragm, the through diaphragm and the outer diaphragm. To solve the problem of diaphragm construction, especially for smaller tubular column section, the paper presents a new type of connection style (as shown in Fig. 1). The nonlinear character of the joint is studied by ABAQUS, under monotonic loading.

Establish of the finite element mode

In the joint, T-stub is welded with the rectangular tubular column and connected with the flange of H-shaped steel beam through frictional high-strength bolts. In the finite-element analysis, weld is simulated by “tie”. With the function of “bolt force”, the high strength bolts is preloaded by adjusting the length of bolt. Frictions between bolt cap and T-stub web, between bolt nut and beam flanges, and between beam flange and T-stub web are emulated, where coefficient of friction is 0.4. The “solid” unit is applied to simulate H-shaped beam, rectangular tubular column, T-stub and bolts

Parameters of the joint model

The detailed size of the finite element model is shown in Table 1. Based on this model, parameters are changed to investigate the performance of the joint.

In Table 1, H is length of the rectangular tubular column; L is length of the H-shaped beam. i_b is the linear stiffness of beam; i_c is the linear stiffness of column. i_b = E_bI_b/L, i_c = E_cI_c/H, E is elasticity modulus, I is inertia of the material section to the bending moment neutral axis. Other parameters are shown as Fig. 2.

Material properties of the joint

The steel of square steel tube column, H-shaped beam and T-stub are Q345, whose yield strengths are 310 MPa. The bolt is 10.9 levels of friction-type high strength bolt, whose yield strength is 940 MPa. The elasticity modulus of all steel is 2.06 × 10⁵ MPa. The constitutive relationship of the steel is typical bilinear model and the plastic and hardening stage is simulated by the inclined line. Taking the geometric nonlinearity into consideration, the yield criterion complies with Von Mises yield criterion and the corresponding flow rule.

Finite element models and the hypothesis

Ignoring the component geometry defect and the influence of welding residual stress, it assumes that bolt is not interacted with the wall of bolt hole in the nonlinear finite element analysis. Meshes of the joint are shown as Fig. 3.

Boundary condition and loading of the joint

In the FEA, displacements of all directions and the outer plane rotation are limited in bottom of the column, and out-of-plane displacements and out-of-plane rotations are limited in top of the column. Out-of-plane rotations are limited at the end of beam. The axial compression ratio of the basic joint is 0.2. The load is applied in the end of beam through displacement.

Parametric analyses

Effect of the thickness of column

With other parameter of the basic joint constant, the thickness of the tubular column is changed, including 10, 12 (the basic size), 14, and 16 mm four models. The moment-rotation curves of the FEA are shown as Fig. 4.

As shown in Fig. 4, the curve can be divided into three stages: elastic, elastic-plastic and decline stages. The thickness of the tubular column has little effect on the load-carrying capacity and the stiffness of the joint. The bigger the thickness of column is, the greater the rigidity of joint is and the less obvious the stiffness degradation is during the elastic and elastic-plastic period, but the more obvious the stiffness degradation is during the decline period.

Changing the thickness from 10 to 16 mm, the ultimate bearing capacity ranges from 94.3 to 94.5 kN·m, and the stiffness ranges from 16964 to 20571 kN·m/rad. The ultimate is controlled mainly by the parameter of T-stub, and the failure pattern of basic joint is shown in Fig. 5 (a). When the thickness is 10 mm, the buckling failure of the wall of column happens at the tension area, which is shown in Fig. 5(b).

Effect of the height of H-shaped beam

With other parameters of the basic joint constant, the height of H-shaped beam is changed in the paper, including 200 (the basic size), 250, and 300 mm three models. The moment-rotation curves of the FEA are shown as Fig. 6.

As shown in Fig. 6, the height of beam has considerable effects on the ultimate bearing capacity of the joint and little effects on the rotational stiffness. While the stiffness only increase 4.5% and 2%, the height increases 25% and 20%, and the ultimate bearing capacities increase 16% and 25%. It results from the decrease of the tension and stress under the same moment as the height of beam increases.

Effect of thickness of T-stub flange

With other parameters of the basic joint constant, the thickness of T-stub flange is changed in the paper, including 10, 12, 14 (the basic size), and 16 mm four models. The moment-rotation curves of the FEA are shown as Fig. 7.

As shown in Fig. 7, the curve can be divided into three stages: elastic, elastic-plastic and decline stages. The thickness of T-stub flange has little effect on the ultimate bearing capacity and rotational stiffness, which are controlled mainly by the parameter of T-stub web. Changing the thickness from 10 to 16 mm, the ultimate bearing capacity ranges from 93.6 to 94.6 kN·m, the stiffness ranges from 18507 to 20260 kN·m/rad. The failure type of joint is tensile failure in the root of T-stub web.

Comparing with the elastic-plastic period of curves in Fig. 7, the thicker the thickness is, the less obvious the stiffness degradation is. On the contrary, the stiffness is more obvious in the decline period. Through FEA, the increase of the rotational stiffness of the joint is due to welding the T-stub flange with column.

Effect of the length of T-stub flange

With other parameters of the basic joint constant, the thickness of T-stub flange is changed in the paper, including 120, 135, 150 (the basic size), 165 and 180 mm five models. The moment-rotation curves of the FEA are shown as Fig. 8.

As shown in Fig. 8, as the length of T-stub flange ranges from 120 to 180 mm, the ultimate bearing capacity ranges from 92.6 to 94.3 kN·m. The reason is that height of T-stub flange has almost no effect on the ultimate bearing capacity. The rotational stiffness is 21816 kN·m/rad, when the height of T-stub flange is 165 mm. When the length is bigger or smaller than 165 mm, the rotational stiffness decreases, the yield rotation becomes larger and the ductility of joint is worse.

Effect of the thickness of T-stub web

With other parameters of the basic joint constant, the thickness of T-stub web is changed in the paper, including 8, 10, 12, 14 (the basic size) and 16mm five models. The moment-rotation curves are shown as Fig. 9.

As shown in Fig. 9, the thickness of T-stub web has an effect on both ultimate bearing capacity and rotational stiffness. The buckling failure of the web of T-stub appears in three joint models, including 8, 10 and 12 m, which fail to achieve their bearing capacity, as shown in Fig. 5(c). When the thickness is bigger than 14 mm, joint bearing capacity hardly increases. But rotational stiffness increases largely. When the thickness increases by 14%, the increase of the bearing capacity is less than 6%, and the increase of the stiffness is less than 20%. It concludes that the thickness of T-stub web contributes to the increase of the bearing capacity and, especially, to the increase of the rotational stiffness.

Effect of the length of T-stub web

With other parameters of the basic joint constant (bolt spacing 80 mm), the thickness of T-stub web is changed in the paper, including 100, 160 and 240 mm three models. The moment-rotation curves of the FEA are shown as Fig. 10.

As shown in Fig. 10, the length of T-stub web has a significant effect on the ultimate bearing capacity and rotational stiffness. In certain range, the bearing capacity and stiffness increase as the length of T-stub web increases. The bearing capacity increases by 72% and the increase of the rotational stiffness is double when length increases by 60%.

The rotational stiffness of the joint with the length of T-stub web 240 mm is 147245 kN·m/rad, which belongs to rigid joint according to Eurocode3. It concludes that the length of T-stub web contributes to the increase of the joint bearing capacity and stiffness considerably.

Effect of the diameter of high-strength bolts

With other parameters of the basic joint constant, the diameter of high-strength bolts is changed in the paper, including M16, M20 and M24 three models. The moment-rotation curves of the FEA are shown as Fig. 11.

As shown in Fig. 11, the diameter of high-strength bolt has a significant effect on the bearing capacity and rotational stiffness of the joint. The bearing capacity and stiffness increase as the diameter of bolt increasing. As the diameter changes from 16 to 20 mm and from 20 to 24 mm, the bearing capacity increases 52% and 16% respectively, and stiffness increases 67% and 14% separately.

Effect of the bolt pre-tightening force

With other parameters of the basic joint constant, the bolt pre-tightening force is changed in the paper, including 125, 140 and 155 kN (the basic size) three models. The moment-rotation curves of the FEA are shown as Fig. 12.

As shown in Fig. 12, the pre-tightening force of high-strength bolt has an effect on the joint performance. Once the force increases 15 kN twice, the stiffness increases 15% and 4%, and the bearing capacity increases 9% and 15% respectively. It concludes that the pre-tightening force of bolts influences the performance of joint, which should be controlled accurately during the construction.

Effect of the bolts spacing

With other parameters of the basic joint constant, the bolt pre-tightening force is changed in the paper, including 100, 110, 120 (the basic size) and 130 mm four models. The moment-rotation curves of the FEA are shown as Fig. 13.

As shown in Fig. 13, the bolts spacing has an effect on the performance of the joint. As the bolting spacing changes from 100 to130 mm, the bearing capacity ranges from 84.9 to 94.7 kN, and the stiffness ranges from 16197 to 18644 kN·m/rad. To joints with the bolt spacing 100 and 110 mm, the curves decline owing to the separation of T-stub web from beam flange, as shown in Fig. 5(d). It concludes that the distance between the first bolt hole and the root of T-stub web should be controlled.

Effect of shear connectors

To research the joint performance affected by shear connectors, three joints are designed, namely, the upper shear connector, the nether shear connector and both shear connectors. The shear connector [8] is designed to triangle, whose right sides are 50 and 98 mm, and the thickness 14 mm. The failure pattern of the joint with both connectors is shown in Fig. 5(e). The moment-rotation curves of the FEA are shown as Fig. 14.

As shown in Fig. 14, the bearing capacity and stiffness of the joint increase by setting bolting shear connectors. Compared the joint installed two shear connectors with the basic joint, the bearing capacity increases by 8%, and the rotational stiffness increases by 23%. Compared joints installed upper or nether shear connectors with the basic joint, the bearing capacities increase by 5.7% and 2.6%, respectively, and the rotational stiffness increase by 7.3% and 20% respectively. It concludes that the upper shear connector mainly affects the bearing capacity, and the nether shear connector mainly affects the rotational stiffness of the joint. Because the bearing capacity of the joint is mainly controlled by the upper T-stub which bear the tensile, and the rotational stiffness is mainly controlled by the lower T-stub which is easy to take on the buckling failure.

The failure pattern of joins

The FEA results show that the bearing capacity and rotational stiffness mainly are affected by height of H-shaped beam, the length and thickness of T-stub web, diameter of the bolt, pre-tightening force of the bolt. By changing parameters of the joints, the failure patterns are the yield failure of T-stub web under the tensile force (Fig. 5(a)), the buckling of the wall of rectangular tubular column (Fig. 5(b)) and the buckling of T-stub web under the compress force (Fig. 5(c)). As shown in Fig. 5, failure pattern (a) is resulted from the stress concentration in the crossed weld under the bending moment. Failure pattern (b) is caused by the insufficient out-of-plane stiffness when the thickness of the tubular column is thin. Failure pattern (c) is caused by the insufficient stiffness when the thickness of the T-stub web is thin, which is key factor for the joint performance. The failure pattern (d) shows that the distance between the first bolt hole and the root of T-stub web affected the performance of joint. By setting t shear connectors upper and nether, the force transferring of joint is uniform, which is shown in Fig. 5(e).

Semi-rigid joints judgment

The definition of the semi-rigid joint provided by Eurocode3 (EC3) [9] is based on the deformability and bending bearing capacity.

By deformability

Semi-rigid joints: 0.5EI_b/L_b<S_{j ini}<8EI_b/L_b

Where EI_b/L_b is the stiffness ratio of beam which connected to the joint; S_{j ini} is initial rotational stiffness of the joint.

By bending bearing capacity

Partial strength joints: 0.25M_pl,Rd<M_j,Rd<M_pl,Rd

Where M_j.Rd is the plastic bending bearing capacity of the joint. M_pl,Rd is the plastic bending bearing capacity of the beam connected with the joint

Through the finite element calculation, excepting for the joint with the high-strength bolt M24 and the joint with 240 mm-T-stub-web, the ultimate bearing capacity of all joints range from 51.16 to 100.6 kN·m, and the rotational stiffness range from 12375 to 24577 kN·m/rad. It concludes that this joint belongs to semi-rigid joint according to Eurocode3.

Conclusions

1) The thickness and length of T-stub webs, the height of beam section, bolt diameter, shear connector and preloaded force affect the performance of the joint largely, and the thickness of the steel tube, the thickness and length of T-stub flange, bolt arrangement spacing have little effect on the performance of the joint.

2) The failure pattern of the joint is mainly yield failure of T-stub web under the tensile force at the root of the web. When designing the joint, the shear connectors should be applied to enhance the stiffness and bearing capacity of the joint.

3) Since the initial stiffness and plastic bearing capacity of the joint meets the regulation of Eurocode3, which defines the semi-rigid connection, the joint designed in the paper is semi-rigid joint. The influence of semi-rigid in steel frame should be considered when designing.

References

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[9] CEN (Commission of the European Communities). Euro code3: Design of Steel Structures: Part1.1 General Rules and Rules for Building. Belgium: Bruxelles, 1993

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