Elsevier

Structures

Volume 30, April 2021, Pages 11-24
Structures

Behaviors of welded hollow spherical joints strengthened by unidirectional annular ribs

https://doi.org/10.1016/j.istruc.2020.12.080Get rights and content

Abstract

Welded hollow spherical joints are comprehensively used in spatial steel structures. However, the original joints cannot meet the strength requirements in some conditions, such as the corrosion, the fire and the change of structural load. Therefore, it is necessary to explore effective methods of strengthening the joints to maintain the durability and safety of the structures. This paper proposes and investigates the method of strengthening welded hollow spherical joints using unidirectional annular ribs. Experiments were conducted to study the failure modes, axial load–displacement curves and ultimate bearing capacity under axial compressive and tensile load. Nonlinear finite element (FE) model was established and verified to study the failure mechanism and bearing capacity of the test joints using ABAQUS. Based on the accurate FE model, parametric studies were performed to study the influence of the thickness and height of unidirectional annular rib, the dimensions of the steel tubes and the welded hollow spheres on the capacity of the joints. Practical design formulas were proposed based on the test and the FE analysis. The conclusions presented in this study can provide theoretical and numerical basis for the design of welded hollow spheres strengthened with unidirectional annular ribs in spatial steel structures.

Introduction

The spatial grid structure has been extensively used in the large span spatial buildings, such as large-span stadium, airport, etc. The existing research results show that the stiffness of joints plays a crucial role in the overall stability of the structure [1], [2], [3]. Therefore, the study on the stability of spatial grid structure indirectly translates into the study on the stiffness and bearing capacity of joints. The joints used to connect different members in spatial grid structures mainly include socket joints [4] cast steel joints [5], [6] bolt column joints [7], [8] tubular joints [9], [10] bolted spherical joints [11] and welded hollow spherical joints. The welded hollow spherical joints have been comprehensively used in space structure due to its advantages of high stiffness, high strength and low cost.

The spatial grid structures using welded hollow spherical joints may be exposed to some extreme environment such as corrosion, fatigue loading, and high temperatures, as shown in Fig. 1. Zhao et al. [12], [13] studied the influence of corrosion which occurred at different places on the bearing capacity of welded hollow spherical joints. Jiao et al. [14] established fatigue life patterns of three welded spherical joints at variable amplitude. Liu et al. [15] investigated the mechanical behavior of welded hollow spherical joints after exposure to elevated temperatures and proposed a simplified design method to predict the post-fire residual load-bearing capacity and initial axial stiffness of welded hollow spherical joints. Lu et al. [16] focused on the analysis on the behavior of welded hollow spherical joints under the ISO-834 standard fire. The above factors will reduce the bearing capacity of the welded hollow spherical joint in service time; hence, the joints in service needed to be strengthened.

Existing studies on the welded hollow spherical joint mainly focus on the tests and simulation of the bearing capacity under the axial force. Han et al. [17] proposed new formulas of ultimate tensile and compressive bearing capacity of welded hollow spherical joints and proved that the ultimate bearing capacity of the spherical joints is irrelevant with the compression strength of the materials under compressive load. Chen et al. [18] used the punching shear method to deduce the bearing capacity formula of spherical joints under tension and stability failure. Han et al. [19] explored the stiffness degeneration of the joint in the plastic stage which the degeneration would have a negative effect on the stability capacity of single-layer latticed domes. Therefore, based on the stiffness characteristics, Han et al. [20] proposed the formulas to predict the bearing capacity of the joints under combined axial force and bending moment. Liao et al. [21] and Ding et al. [3] conducted finite element (FE) analysis to simulate the failure mode and ultimate bearing capacity of welded hollow spherical joints under tensile load and compressive load. Wang et al. [22] analyzed the axial stiffness and flexural stiffness of welded spherical joint with different types of inner rib stiffeners. Liu et al. [23] investigated the behaviors and proposed the design formula of compressive bearing capacity of welded hollow spherical joint connected with H-beam. Overall, minimal research, except preliminary studies on the bearing capacity and stiffness of original welded hollow spherical joints, has been conducted on unidirectional annular welded hollow spherical joints.

As shown in Fig. 2(a) and (c), a typical welded hollow spherical joint is composed by several tubes and one hollow sphere. In the present study, to resist local buckling and attain high strength, a new method to strengthen the welded hollow spherical joints was proposed using the annular ribs as illustrated in Fig. 2(b) and (d). Besides, to avoid the conflicts of the annular ribs and the tubes, only one pair annular ribs can be welded onto the hollow sphere in some conditions, as shown in Fig. 2(b) and (d).

In this paper, the behaviors of welded hollow spherical joints strengthened by unidirectional annular ribs were investigated through the tests and numerical simulation. The failure modes, axial load–displacement curves, and bearing capacity of joints were initially investigated by four sets of experiments under axial tensile and compressive load. The test results indicated that the unidirectional annular ribs can obviously increase the bearing capacity of the welded hollow spherical joints. Non-linear FE model was developed and verified to study the behaviors and the influence of different parameters on the bearing capacity of strengthened joints. Based on the test and numerical study, design formulas were proposed to design the bearing capacity of strengthened welded hollow spherical joints. Research results provide basic references for the reinforcement of the welded hollow spherical joints in the spatial grid structures.

Section snippets

Specimen design

Twelve welded hollow spherical joints were designed and manufactured in accordance with Technical specification for space frame structures (JGJ 72010) [24] and Technical specification for latticed shells (JGJ 612003) [25] as shown in Table 1. The process of manufacturing includes the hot pressing, trimming, bevel cutting and butt welding of two steel hemispheres. When the welding of the hollow sphere is completed, two annular ribs are welded to the corresponding part. The specimens were

Failure modes

The failure modes of the unreinforced specimens and the reinforced specimens were clearly obtained, as presented in Fig. 5.

The axial tensile failure test of six specimens was accomplished. The phenomena and failure mode of both specimens W235-AT-U and W235-AT-R were basically consistent, which exhibited a similar strength failure in literature [1]. In the early loading stage, no significant changes were discovered. As the loading process continued, the tiny tensile deformation occurred in the

FE model

Behaviors of the welded hollow spherical joints were simulated using software ABAQUS. The elastic perfectly-plastic model and Von-Mises criteria were adopted in analysis for steel. The elastic modulus of steel was taken as 206 GPa and the Poisson’s ratio was 0.3. Mechanical parameters of steel materials were listed in Table 1.

Numerical model was consisted of four parts, including welded hollow spheres, steel tubes, steel plates and annular ribs, as shown in Fig. 9. *TIE option was applied to

Parametric analysis and the proposed design equations

The FE model after verification was used for parametric analysis. Referring to the parameters for the welded sphere joints with H-beam in literature [23] and the formula for the bearing capacity of ordinary welded sphere in literature [24] the influence of the unidirectional annular rib thickness tr, the unidirectional annular rib height b and the ratio of steel tube diameter to hollow sphere diameter on the ultimate bearing capacity were analyzed. Detailed parameter values are listed in Table 4

Conclusion

In this study, the axial performances of welded hollow spherical joints strengthened by unidirectional annular ribs under tension and compression were experimentally and numerically studied. Based on the test and the analysis, the effect of the unidirectional annular ribs on the welded hollow spherical joints is evaluated and calculated using theoretic design formulas. The following conclusions can be drawn based on the obtained results.

  • (1)

    The ultimate bearing capacities of welded hollow spherical

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is supported by the Natural Science Foundation of China under Grant No. 51808182 and the China Postdoctoral Science Foundation (Grant No. 2020M670680).

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