Numerical Simulation Analysis of the Cast-Steel Joint in a ...

2019 International Conference on Information Technology, Electrical and Electronic Engineering (ITEEE 2019) ISBN: 978-1-60595-606-0

Numerical Simulation Analysis of the Cast-Steel Joint in a Tree-Like

Column Structure

Wen-feng DU, Li-ming ZHU*, Long-xuan WANG and Peng-fei HE

Institute of Steel and Space Structures in Henan University, 475004, Kaifeng, China

*Corresponding author

Keywords: Cast-steel joint, Tree-like column structures, Numerical simulation.

Abstract. The cast-steel joint is often used in a tree-like column structure to achieve smooth

transition. Its performance is critical to ensure the whole structural safety. In this paper, the load

bearing behavior of a cast-steel joint with three branches is investigated. First, a finite element model

of the test joint was established by SolidWorks and analyzed by ANSYS considering the geometric

and material nonlinearity. Then, the calculation formula for load-carrying capacity of the cast-steel

joint with branches was deduced by the method of regression analysis, which is used for estimating

the geometric parameters and load-carrying capacity at the stage of preliminary design of the

cast-steel joint. Comparison analysis shows that there is a good agreement between the experimental

result, the FEM result, and the prediction result from formula.

Introduction

The tree-like column structure has been widely used in engineering practice owing to its beautiful

shape and excellent mechanical performances. Since the tree-like column structure was used at

Germany Stuttgart Airport in 1991 [1] for the first time, a number of representative projects, such as

the ION Orchard shopping center in Singapore (Fig.1), the Stansted Airport in London, the Detroit

Airport in USA, and the Shenzhen cultural center in China, has spread its usage quickly [2].

(a) (b) (c)

Figure 1. Tree-like column structures:(a) Germany Stuttgart Airport; (b) ION Orchard Center; (c) Stansted Airport.

It is obvious that such joints play a critical role in tree-like structures. On the one hand, the whole

upper structure is only supported through a single joint, and the tree-like structure will collapse if the

joint is destroyed. On the other hand, many members including the trunk and branch pipes converge

on the joint with smooth transitions, the force responses of such joints are complicated.

Cast-steel joint with branches is usually adopted in tree-like column structures [3]. Compared with

welded tubular joints, cast-steel joint can avoid the residual stress due to complex welds at junctions,

reduce the construction difficulty, and increase the construction speed of tree-like structures [4-5].

Although the application of casting steel for structures has been attracting continuous interests in

the past decades, the research on the cast-steel joint is still at its early stage [6]. Full-scale experiments

have been the direct and effective method to understand the performances of cast steel joints.

Therefore, several experiments of the cast-steel joint used in important large-span steel roof structures

were carried out, such as Shanghai South Railway Station [7], Beijing national stadium [8], and

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Chongqing Olympic Stadium in China [9]. Numerical analysis has been another approach to obtain

complete map of stresses developed in cast-steel joints. The results of finite element analysis provide

great helps for the design of cast-steel joint, such as the Cycling Gymnasium for Beijing Olympic

Game [10], Guangzhou New Railway Station [11], and Tianjin Convention and Exhibition Center

[12]. Eurocode 3 provided the component method, which allows one to evaluate the stiffness and

resistance characteristic of the joint by assembling those of all the constitutive components [13, 14].

The geometrical configuration of cast-steel joint with branches comprises of one main pipe and

two, three or four branching pipes. It can be foreseen that the application of cast-steel joint with

branches will be more and broader with the development of tree-like column structures. However,

there are no relevant provisions in the existing building standards or codes by far, and the research on

the mechanical performance, calculation theory and structural optimization of the cast-steel joint with

branches is still scarce.

In this paper, a typical numerical simulation analysis of a cast-steel joint with one trunk and three

branches was conducted. The distribution of the stress, the process of plasticity spreading and the

failure mechanism of the joint were calculated by ANSYS. Moreover, the calculation formula for

load-bearing capacity of the cast-steel joint with branches was deduced based on the method of

regression analysis.

Numerical Simulation Analysis

Analysis Model

In order to understand the performance of the test joint comprehensively, the corresponding finite

element model was established. As shown in Fig.2 (a), the model of the joint was established by using

the default ANSYS preprocessor at first. However, it is difficult to achieve a smooth transition

between the main pipe and the branches. So the joint was modeled by the 3D modeling software

SolidWorks to ensure that the established joint model is consistent with the actual joint, as shown in

Fig.2 (b).

(a) (b) (c)

Figure 2. The comparison of models: (a)The model established by ANSY; (b) The model established by SolidWorks;

(c) Finite element meshes.

The established joint model was imported into the finite element software ANSYS for analysis.

The material properties of the model were obtained from the material test. The elastic modulus of the

material (E) is 2.0×105 N/mm2, the yield strength (fy) is 235MPa, and the Poisson's ratio (μ) is 0.3.

The constitutive behavior of the material was chosen to be the ideal elastic-plastic model. The

Von-Mises yield criterion and associated flow rule were used for the elastic-plastic analysis. To

ensure the model boundary conditions capture the actual situation, the boundary conditions of the

joint were set as following: the end part of the main pipe is fixed, and the ends of the branch pipes are

fixed vertically. The load was applied to the end of the branch pipes in a manner of surface pressure.

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After research and comparison, the three-dimensional solid element Solid65 was chosen from the

ANSYS element type library. The element type has a quadratic displacement and it is suitable for

irregular grid division. The finite element mesh of the joint is shown in Fig.2(c).

Analysis Results of the Joint

The finite element analysis was conducted for the case of the test joint. Fig.3 shows the stress contours

of the joint when the load reaches 1000 kN, 2000 kN, 3000 kN, 4000 kN, 5000 kN respectively. From

Fig.3, it can be seen that the overall stress level of the joint under the 1000 kN load is low, and the

maximum stress value is mainly distributed in the vicinity of the joint core area. The stress in the main

pipe and the branch pipes is obviously less than the stress at the core area of the joint. The former is

only 11.5% of the later.

(a) (b) (c)

(d) (e)

Figure 3. Stress contours of the joint: (a) The stress contour of the joint under 1000 kN; (b)The stress contour of the joint

under 2000 kN; (c)The stress contour of the joint under 3000 kN; (d)The stress contour of the joint under 4000 kN;

(e)The stress contour of the joint under 5000kN.

When the load reaches 2000 kN, the stress level of the joint gradually increases with the increasing

load. It shows a linear increasing trend, and the maximum stress value is 219 MPa. When the load

reaches 3000 kN, the yielding of the steel appears. However the yield region is only concentrated on

three points in the chamfer between the branch pipe and the branch pipe. When the load increases to

4000 kN, the yield region expands outward. On the one hand, the plastic region becomes larger. On

the other hand, the chamfer between the main pipe and the branch pipes also enters the plastic zone.

When the load reaches 5000 kN, the expansion of the plastic zone on the joint is further increased, but

it is still mainly concentrated in the vicinity of the joint core area. At this load stage, almost the whole

core area of the joint enters the yield state. It can be concluded that the plastic hinge has been formed,

and the load-displacement curve enters stage Ⅲ (Fig.4). While the stresses at the main pipe and

branch pipes are still relatively small, which are about 106 MPa. It indicates that stress is concentrated

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on the core region for the cast-steel joint with branches, which has a great influence on the ultimate

load-carrying capacity of the joint.

Figure 4. Load-displacement curves of specimens. Figure 5. The vertical displacement contours of joint.

Fig.4 shows the vertical displacement of the joint under the maximum load 5000 kN. From Fig.5, it

can be seen that the maximum vertical displacement (4.366mm) is smaller than that (8.064mm)

obtained from the test. It is mainly due to the non-tight contact between the joint and the test

equipment piston.

Effect of Joint Parameters on Compression Behavior of the Cast-Steel Joint

In order to investigate the influence of different parameters on the ultimate load-carrying capacity of

the joint, a parametric study of controlling variables is conducted. The variable is changed one by one

while other variables remain constant.

Table 1. Comparison between finite element analysis and experimental results.

Load/kN

Stress/MPa 1000 2000 3000 4000 5000

A2

Calculation results 24.8 49.6 79.4 106.8 132.2

Experimental results 23.2 51.3 78.6 109.3 126.3

Error analysis 6.89% 3.42% 1.01% 2.34% 4.67%

B12



Error analysis 5.69% 3.17% 8.45% 6.67% 5.24%

B22



Error analysis 6.64% 4.23% 4.27% 3.76% 1.50%

C12



Error analysis 9.02% 2.97% 4.07% 2.06% 5.68%

C22



Error analysis 8.39% 6.03% 1.40% 2.72% 4.77%

C32



Error analysis 5.18% 5.89% 5.64% 3.17% 4.97%

The modeling results are shown in Table 1, which could be summarized as:

1) Under compression, the ultimate load-carrying capacity of the fifth joint (J5) is the largest,

reaching 5720.7 kN. The ultimate load-carrying capacity of the eighth joint (J8) is the least, reaching

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1334.73kN. J8 and J5 have the same geometrical parameters, but the diameter thickness ratio (γ) of J8

is the largest, and that of J5 is the smallest. So the effect of the diameter thickness ratio (γ) on the

ultimate carrying-load capacity of joints is the most significant.

2) When only θ increases while other variables remain unchanged, the ultimate carry-loading

capacity of the joint is largely reduced. It shows that θ has a great influence on the ultimate

load-carrying capacity of the joint.

3) When β and R3 gradually increase and other variables remain unchanged, the ultimate

load-carrying capacity of the joint is greatly increased. It shows that β and R3 have a large influence

on the ultimate load-carrying capacity of the joint too.

4) When L, R1 and R2 gradually increase and other variables remain unchanged, the ultimate

carry-loading capacity of the joint is nearly unchanged. The largest amount of change is less than 5%.

It shows that L, R1 and R2 have almost no influence on the ultimate load-carrying capacity of the

joint.

5) According to the finite element modeling results, it is concluded that the influence of the

geometric parameters should be fully considered when the load-carrying capacity of the cast-steel

joint with branches is analyzed. The dimension parameter of the joint should be carefully selected to

ensure the safety and reliability of the structure.

Load-Carrying Capacity Estimation of the Three-Branch Cast-Steel Joint

It is found in literatures the load-carrying capacity formulas for the welded tubular T-joints, the steel

tubular XK-joints, the multi-planar KX-and KT-joints under axial load are all expressed as the

product of the material yield strength and square of the pipe wall thickness. Therefore, the estimation

of the cast-steel joint with branches can be expressed similarly as:

2

u yF KT f (1)

where Fu is load-carrying capacity of the joint; K is a parameter that contains the geometric

parameters such as θ, γ and β of the joint; T is the pipe wall thickness; and fy is the material yield

strength of the joint.

In Eq. (1), expression of K is the research focus for different type joints. Since K is a

comprehensive index reflecting the influence of various geometric parameters on the joint

load-carrying capacity, it is no longer a single study of the relationship between K and Fu, but a

multiple study of the relationship between each parameter and K.

Results of the finite element analysis show that L, R1 and R2 of the joint have little influences on

the joint ultimate load-carrying capacity, so these three parameters are ignored during the analysis of

comprehensive index K. According to the line charts between θ, γ, β and R3 and K respectively, as

shown in Fig.6, a regression analysis is conducted.

(a) (b)

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(c) (d)

Figure 6. The relationship line chart between geometric parameters (θ, γ, β, R3) of the joint and the K: (a) Relationship line

chart between θ and Kθ; (b) Relationship line chart between γ and Kγ; (c) Relationship line chart between β and Kβ;

(d) Relationship line chart between R3 and KR3.

The regression analysis is first conducted on the relationship between θ and Kθ. Through the

regression analysis, the relationship between the sine value of θ and Kθ can be given as:

2 30.60022 2.5311sin 6.59681sin 5.07388sinK (2)

For the relationship between γ and Kγ, it could be expressed as a power function:

0.662424.3725K (3)

A linear relationship could be observed between the β and Kβ from Fig.7 which could be expressed

as:

1 0.58856K (4)

At last the regression analysis is conducted between R3 and KR3. According to the principle of

dimensional analysis, it is required that the item of R3 contained in the formula is dimensionless. A

dimensionless chamfer coefficient ρ is defined to consider the influence of R3, which is shown as:

3R

dt

(5)

where d is the outer diameter of the branch pipe; t is the wall thickness of the branch pipe. The finite

element model shows that the joint ultimate load-carrying capacity is very small when R3 is greater

than or equal to 100mm. So R3 is limited less than or equal to 100mm on the ultimate load-carrying

capacity calculation formula for the cast-steel joint with three branches. Through regression analysis,

the relationship between the chamfer coefficient ρ and KR3 follows a linear relation, which is

expressed:

3

31 0.33738R

RK

dt

(6)

Because these four parameters are independent of each other, the overall formula for the joint

load-carrying capacity can be obtained by multiplying them, following the method of establishing the

load-carrying capacity of joints in the existing standards, which is expressed as:

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0.66242 3

2 3 2

4.37251 (1 0.58856 )(1 0.33738 )(0.60022

2.5311sin 6.59681sin 5.07388sin ) y

RF

dt

f T

(7)

In order to validate the accuracy of Eq. (7), the results of finite element modeling and those of

regression formula are compared. The comparison results are shown in Table 2. It can be found that

the error between the calculation formula and the finite element calculation is very small, and the

maximum error is 1.9%. It can be concluded that this suggested formula can predict the ultimate

load-carrying capacity of the cast-steel joint with three branches accurately.

Table 2. Calculation formula error table.

Joint

number

θ

(o)

γ β R3

(mm) F/(fyo*T²)

Regression formula

results Difference percentage(%)

J5 30 10 0.7 0 9.74 9.92 1.90

J6 30 15.2 0.7 0 13.07 13.09 0.19

J2 30 20 0.7 0 15.67 15.70 0.21

J7 30 25 0.7 0 18.14 18.21 0.37

J8 30 29.9 0.7 0 20.37 20.50 0.65

J1 20 20 0.7 0 13.62 13.62 0.00

J3 40 20 0.7 0 15.78 15.78 0.00

J4 50 20 0.7 0 11.30 11.30 0.00

J18 30 20 0.6 0 15.14 15.05 -0.61

J19 30 20 0.66 0 15.54 15.44 -0.61

J20 30 20 0.74 0 16.02 15.97 -0.32

J21 30 20 0.8 0 16.47 16.36 -0.66

J15 30 20 0.7 50 19.23 19.09 -0.75

J16 30 20 0.7 100 22.40 22.47 0.32

Conclusions

The numerical simulation and experimental investigation of a full-scale cast-steel joint with three

branches are presented. A typical full-scale model of cast-steel joint was established by SolidWorks

and analyzed by ANSYS considering the geometric and material nonlinearity. The corresponding

verification experiment was carried out to confirm the numerical simulation. Moreover, the formula

for calculating the load-carrying capacity of the cast-steel joint with three branches was presented,

which could satisfy the requirement of engineering design. Through the research of this paper, the

investigation yields the following conclusions:

1) Through the analysis of the full-scale joint experimental results, the stress distribution of the

joint under compression was obtained. Large stresses are mainly concentrated on the core area of the

joint, and the stresses in the main pipe and the branch pipes are small. It provides a basis of evaluating

the strength and stiffness of joint to meet design requirements.

2) SolidWorks is applicable to establish the model of cast-steel joint with branches. It solved the

problem of modeling the joint of tube and tube intersection with smooth transition to be consistent

with the actual joint.

3) The finite element model of the test joint was imported into ANSYS for analysis. The finite

element results are compared with the experimental results, and the analysis results are consistent

with the experimental results. The verified finite element model could be confidently adopted for

evaluating effects of joint geometry parameters on the behavior of the three-branch cast-steel joint.

4) Finite element analysis of the joints with different geometric parameters was conducted. The

ultimate load-carrying capacity of the joints was obtained. The error analysis between the prediction

results and the finite element results of the joint showed the maximum error was 1.9%. Therefore the

suggested formula can predict ultimate load-carrying capacity of the joints accurately to meet the

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requirement of engineering design. It will be an available tool for the geometry parameter selections

in the structural design of the joint.

5) The stress level in the branch pipes of the cast-steel joint is low overall. It indicates the wall

thicknesses or diameters of the branch pipes could be reduced for optimal designs.

Acknowledgement

The authors gratefully acknowledge the support of the National Natural Science Foundation of China

for this work (U1704141).

References

[1] L.W. Tong, Y.Z. Chen, Y.Y. Chen, C. Fang. Cyclic behavior of beam-to-column joints with cast

steel connectors, J. Journal of Constructional Steel Research.116 (2016) 114-130.

[2] I. M. Rian, M. Sassone. Tree-inspired dendriforms and fractal-like branching structures in

architecture: A brief historical overview, J. Frontiers of Architectural Research. 3(3) (2014) 298-323.

[3] X.L. Zhao, L.W. Tong. New development in steel tubular Joints, J. Advances in Structural

Engineering. 14(4) (2011) 699-715.

[4] C. Fang, B.A. Izzuddin, A.Y. Elghazouli. Modeling of semi-rigid beam-to-column steel joints

under extreme loading, J. Frontiers of Structural and Civil Engineering. 7(3) (2013) 245–263.

[5] C. Brett, Y. Lu. Assessment of robustness of structures: current state of research, J. Frontiers of

Structural and Civil Engineering. 7(4) (2013) 356–368.

[6] M.S. Aziz, Y.A.E. Sheriff. Biomimicry as an approach for bio-inspired structure with the aid of

computation, J. Alexandria Engineering Journal. 55(1) (2016) 707-714.

[7] Z. Wang, X. Zhao, Y. Chen, Z.Y. Shen. Experimental study on cast steel joint of South Railway

Station in Shanghai, J. Advances in steel structures.1 (2005) 887-892.

[8] H. Schober. Steel castings in architecture and engineering, J. Modern Steel Construction. 43(4)

(2003) 65-72.

[9] J.C. Oliveira, S. Willibald, J.A. Packer, C. Christopoulos, T. Verhey. Cast steel nodes in tubular

construction—Canadian experience, C. Proceedings of the 11th International Symposium and IIW

International Conference on Tubular Structures, Quebec City, Canada, (2006) 523–529.

[10] L.B Wang, H. Jin, H.W. Dong, J. Li. Balance fatigue design of cast steel nodes in tubular steel

structures, J. The Scientific World Journal. 2013(1) (2013) 14-24.

[11] J. G. Cai, J. Feng, J. Wang. Numerical analysis of Y-type cast-steel joint for Guangzhou New

Railway Station, C. 2nd IEEE International Conference on Computer Science and Information

Technology, (2009) 39-42.

[12] F. Bouafia, S. Boualem, MME. Amin, B. Benali. 3-D finite element analysis of stress

concentration factor in spot-welded joints of steel: The effect of process-induced porosity, J.

Computational Materials Science, 50(4) (2011) 1450-1459.

[13] Eurocode 3: Design of steel structures. Part 1.8 (design of joints) [S]. 2005.

[14] A. Loureiro, R Gutierrez, JM Reinosa, A Moreno. Axial stiffness prediction of non-preloaded

T-stubs: an analytical frame approach, J. Journal of Construction Steel Research, 66(12) (2011)

613-622.

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Numerical Simulation Analysis of the Cast-Steel Joint in a ...

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