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Structural behavior of tree-like steel columns subjected to combined axial and lateral loads

  • Rabab C. Dekhn EMAIL logo and Khalid K. Shadhan
Published/Copyright: June 13, 2022
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Journal of the Mechanical Behavior of Materials
From the journal Journal of the Mechanical Behavior of Materials Volume 31 Issue 1

Abstract

Few studies have been conducted on the structural behavior of steel columns with branches that are called tree-like columns. These kinds of columns have been used in many structures around the world. The purpose of this study is to investigate the failure load, vertical and lateral displacement, and failure mode of tree-like columns subjected to a combination of axial and lateral loading. The ratio of lateral load to axial load has been selected as the design variable. A finite element model with one branching level and two branches within the level was first developed using ABAQUS/CAE 2017 software. The model was verified with experimental results. The axial failure load and axial and lateral displacement were determined and compared for different loading ratios. The failure mode was also studied for different loading conditions. The results showed that the axial failure load decreased significantly by 54, 42, and 28% when lateral/axial loading ratio increased by 20, 40, and 60%, respectively. There was no significant decrease when lateral/axial loading ratio was more than 60%, while axial and lateral displacements increased significantly by 24% for each 20% increase in the loading ratio. Local buckling was observed as a failure mode when only gravity load is applied, while combined load resulted in lateral buckling.

Keywords: tree-like columns; ABAQUS; steel columns; finite element

1 Introduction

The noticeable ability of trees resisting lateral wind load has inspired several architectural and structural designers to come up with branching structures as a better substitute for traditional structures to provide enhanced resistance to lateral loads [1]. Tree-like columns are providing an efficient and effective way to transfer large space loads to a single point upon the ground. So, they are suitable for public buildings such as airports, sports facilities, railway stations, shopping centers, etc. Tree-like columns appear in many buildings around the world, as their use spread widely in the 1990s of the twentieth century. In the construction of this type of structure, Germany has been seen as one of the first country to feature steel tree-like columns in Stuttgart airport, as shown in Figure 1.

Figure 1 Steel tree-like column in Stuttgart airport [2].
Figure 1

Steel tree-like column in Stuttgart airport [2].

The tree-like column components can be categorized, as shown in Figure 2, in accordance with their trunk position. The first-level branches are sprouts from the trunk; furthermore, the branches sprouting from the first level are the second-level branches. The branch level is categorized by [i + 1], where i refers to the previous branch level that is connected directly. The joint that originates from the first-level branches is termed as the first-branching joint, and so on. A two-branch trunk is the simplest tree-like type of column.

Figure 2 Tree-like column portions.
Figure 2

Tree-like column portions.

Trees are exposed to a variety of internal and external loads, as shown in Figure 3. The most fundamental external load is the wind that the tree can adjust its shape to withstand intense wind power and bending moments. Due to the weight of its trunk and branches, the tree also supported the axial compression load. The stresses propagate from the tensile convex side to the compressive concave side of a part when the tree is exposed to a bending moment. Such internal stresses must be standardized structurally for a uniform distribution of loads and excellent performance [3].

Figure 3 Trees loads types: (a) wind load; (b) gravity load; (c) moment load.
Figure 3

Trees loads types: (a) wind load; (b) gravity load; (c) moment load.

Branch diameter is a critical parameter in the design of branching structures and has a crucial relationship with further design parameters [4]. Da Vinci suggested that the sum of the branches cross-sectional areas must be equal to the trunk cross-sectional area [5]. Tan has investigated the construction of the tree-like column structure on a joint using SolidWorks and ANSYS models and has determined the mechanical responses of the joint under axial loads [6]. Minggui and Feng explained how to design, manufacture, and install tree-like columns made of steel pipes. The goal of the study was to share the experience of employing tree-like columns with steel tubes in large-scale projects and in creative steel structure architecture, in order to improve tree-like column with steel tube design processes. They used the SAP 2000 program to examine a park pavilion construction with a long corridor made up of single row of trees. The tree’s height, length, and width are 10, 20, and 10 m, respectively. The wind load was added to the self-weight load by the tree-like column. These studies concentrated on the foundations of tree-like structures exposed to a constant wind load and did not look into the arrangement of branches or form in general. According to the study’s findings, failure in this kind of column, which is exposed to wind load, occurs first in the foundation. They concluded that to prevent collapse, the foundation for single-row or single-root tree-like columns must be stable and “deep-rooted,” and also to prevent over-rising, a separate column base should be used, which should be enlarged in the direction of bending moments [7]. Investigated the ultimate strength, shape, durability, and materials used to construct tree-like steel columns. The results of an actual project (Golden Tree of Shenzhen Cultural Center) study were compared to the design details using ANSYS software. The researchers also planned a series of trials to determine the effect of the joint. They came to the conclusion that the tree-like steel column is ideal for usage in many places because of its attractive appearance, lightweight, and high bearing strength. In addition, the branching junction is critical because it serves as a turning point in the failure stage [8].

Zhao et al. employed a systematic method for analyzing and designing tree-like steel columns. This method includes all stages of designing the tree-like columns, starting from establishing the topology to defining the cross-sectional area. First, a topological technique based on existing finite element codes was introduced, and then it was used to do a form-finding study. After optimizing the shape, GA was used to create the cross-section area. The GA may be used to determine optimized area ratios at various levels. The conclusion was that even when the maximum permitted change happened, the optimal area proportions of the components of different levels remained consistent, and the square of a cross-section area was computed to be the buckling load factor ratio of a distinct case. According to the requirement for buckling capacity, the maximum area of the components can be established [9]. Khamees and Shadhan found that increasing the ratio of an experimental column specimen width to total width under static loading, resulted in reducing the failure load and buckling load and increasing maximum vertical displacement. They also found that failure and buckling loads are directly proportional to the ratio of branch height to total height up to a ratio of 100%. However, beyond a ratio of 100%, the failure and buckling loads were noticed to decline [10].

Khamees and Shadhan have investigated the effect of the branch horizontal spacing and the number of branches and branching levels on failure and bucking loads and vertical displacement. They have found that failure and buckling loads decreased by increasing the branch horizontal spacing, but those loads were found to be directly proportional to the increase in both the number of branches and branching levels. In all cases, they found that the vertical displacement was also directly proportional to the increase in the mentioned parameters [11]. Almost all studies of tree-like columns were conducted under the influence of vertical loads only. In general, there are few studies of the effect of lateral loads on structures. Lateral loads are the live loads applied parallel to the ground due to the horizontal forces acting on the structure. Those lateral loads are different from gravity loads which are applied vertically as downward forces. Typical lateral loads include wind loads, seismic loads, and water and earth pressures. Among those loads, wind loads are considered as the most important in the design of slender structures [12].

2 Study description

This research mainly aims to study the structural performance of branching steel columns exposed to axial and lateral loads. A finite element model with one branching level and two branches within the level was first developed using ABAQUS/CAE 2017 software. The model was verified first using the experimental results obtained by Khamees and Shadhan [10]. The experimental specimen has a rectangular cross-sectional trunk with an area of 480 mm2 and two branches. The cross-sectional area of each of the two branches is 240 mm2, which is equivalent to half of the trunk’s cross-sectional area, as illustrated in Figure 4. The specimen’s width to the maximum width ratio (W/WT) and the branch’s height to total height ratio (HB/HT) was 50%. The dimensions and the laboratory testing results of the selected specimen are listed in Table 1.

Figure 4 Tree-like column specimen parameters [10].
Figure 4

Tree-like column specimen parameters [10].

Table 1

Specimen dimensions and laboratory testing results [10]

Specimen label HB (mm) W (mm) Trunk length (mm) Failure load (kN) Buckling load (kN) Vertical displacement (mm)
T–50–100 175 350 175 53.0 36.5 1.215

After verification, the model was exposed to an axial load only, with a value of 228 kN applied as pressure to the loading plate, then the lateral load was increased as a percent from the axial load starting with 0 to 20, 40, 60, 80, and 100% respectively, the last case was loaded with lateral load with a value of 228 kN applied as concentrated forces on the nodes. The maximum failure load, maximum displacement, and failure mode for both axial and lateral loading were determined and represented.

3 Numerical simulation analysis

3.1 Analysis model

The model of the tree-column was established by using ABAQUS/CAE 2017 program as shown in Figure 5. The material properties were obtained from material test by Khamees and Shadhan [10]. The modulus of elasticity is 200,000 MPa, the yield strength f y is 426 MPa, tensile strength is 666 MPa, and the Poisson’s ratio (μ) is 0.3. The model is provided with steel bases and loading plate connected to the tree-column using tie constraint. The boundary conditions of the model were set according to the following cases:

Figure 5 (a) Tree-like column model by ABAQUS. (b) Finite element meshes.
Figure 5

(a) Tree-like column model by ABAQUS. (b) Finite element meshes.

Case 1: when axial load only is applied, models’ movements are restricted at the bottom and top but are allowed to move vertically only at the top.

Case 2: when axial load as well as lateral load are applied, model movement is restricted at the bottom and allowed to move vertically and horizontally at the top.

Case 3: when lateral load only is applied, models’ movements are restricted at the bottom and top but are allowed to move horizontally only at the top.

The load was applied to the loading plate in a manner of surface pressure; lateral loads acted as concentrated forces at a set of nodes on the loading plate as shown in Figure 6.

Figure 6 Loading way of the model.
Figure 6

Loading way of the model.

In this study, the element size of meshing was taken 8 and with tetrahedron element type.

3.2 Model calibration

For load deflection performance, maximum strength capacity, and failure mode, the finite element model was calibrated by using the experimental results obtained by Khamees and Shadhan [10]. The load-deflection curve for the tree-column that was obtained by the finite element analysis and experimental work is shown in Figure 7. The difference between the FE simulation and experimental failure load is (–5.6%) and correlation coefficient R 2 between load points for both the experimental and FE results is 0.94 as shown in Figure 8. Both results of the experiments and corresponding FE simulation were identified as the same mode of failure as shown in Figure 9.

Figure 7 Load deflection curve of TR–1–2–0:100 for experimental specimen [10] versus calibrated finite element model.
Figure 7

Load deflection curve of TR–1–2–0:100 for experimental specimen [10] versus calibrated finite element model.

Figure 8 Correlation between experimental load and finite element load for TR–1–2–0:100.
Figure 8

Correlation between experimental load and finite element load for TR–1–2–0:100.

Figure 9 Mode of failure for experimental specimen [10] versus calibrated FE mode.
Figure 9

Mode of failure for experimental specimen [10] versus calibrated FE mode.

4 Results

4.1 Load-displacement results

The results of the tree column models under variety of lateral to axial load ratios are shown in Table 2. Each model is named with a label as TR–1–2–X:Y, where TR refers to the tree-like column with rectangular cross section, the first number (1) represents the number of branching levels, the second number (2) represents the number of branches, and X:Y stands for the lateral to axial load ratio.

Table 2

Results of rectangular tree like column (TR–1–2) with different loading conditions

Specimen symbol Axial load at failure (kN) Axial displacement at failure (mm) Lateral load at failure (kN) Lateral displacement at failure (mm)
TR–1–2–0:100 50 1.28 0 0
TR–1–2–20:100 22.7 7.90 4.54 15.37
TR–1–2–40:100 13.2 11.58 5.26 23.04
TR–1–2–60:100 9.5 18.54 5.70 35.77
TR–1–2–80:100 7.5 28.67 6.03 52.54
TR–1–2–100:100 6.8 37.38 6.87 64.49
TR–1–2–100:0 0 0 34.15 87.96

The axial load deflection curves for this column is shown in Figure 10. The curves became very close after applying 60% of lateral to axial load ratio which means the failure loads are almost the same after this ratio.

Figure 10 Axial load-displacement response for TR–1–2 model at different loading ratios.
Figure 10

Axial load-displacement response for TR–1–2 model at different loading ratios.

Depending on the finite element results, the axial failure load reaches its maximum value which is 50 kN if the applied load is axial load only because it represents the minimum applied loading condition to the model. The presence of lateral load in combination with axial loading influences the axial response of the tree-column. When the lateral to axial load ratio increases by 20, 40, 60, 80, and 100%, respectively, the axial failure load decreases by (54.5, 73.6, 81, 85, and 86)%, respectively, as shown in Figure 11. While the vertical displacement increase by 517, 804, 1,348, 2,139, and 2,820%, respectively as shown in Figure 12.

Figure 11 Axial failure load versus load ratio for TR–1–2 model.
Figure 11

Axial failure load versus load ratio for TR–1–2 model.

Figure 12 Axial failure displacement versus load ratio for TR–1–2 model.
Figure 12

Axial failure displacement versus load ratio for TR–1–2 model.

Figure 13 represents the lateral load-displacement curve for different loading conditions by increasing the lateral to vertical loading ratio. It is obvious that load-diplacement curves are almost the same when increasing the lateral/axial loading ratios. There is a significant difference when the model was loaded with lateral load only.

Figure 13 Lateral load-displacement response for TR–1–2 model at different loading ratios.
Figure 13

Lateral load-displacement response for TR–1–2 model at different loading ratios.

The lateral failure load was also presented graphically for different ratios of lateral to axial load as shown in Figure 14. It can be noticed that when the lateral/axial load ratio increases by about 40, 60, 80, and 100%, respectively, the lateral failure load increase by 15.6, 25.5, 32.8, and 51. However, the maximum lateral failure load is 34 kN when no axial load was applied. While the lateral displacement at failure increases significantly by 50, 133, 242, and 320% as shown in Figure 15.

Figure 14 Lateral failure load versus load ratio for TR–1–2 model.
Figure 14

Lateral failure load versus load ratio for TR–1–2 model.

Figure 15 Lateral failure displacement versus load ratio for TR–1–2 model.
Figure 15

Lateral failure displacement versus load ratio for TR–1–2 model.

When the column is subjected to lateral loading only, the lateral displacement is high, while it reduced by 27% if the column is exposed to combined loading, this reduction in lateral displacement may possibly be due to the increase in column axial weight that directly influences the lateral displacement.

4.2 Failure mode results

The failure modes for the tree-like column TR–1–2 are shown in Figure 16. When the lateral load ratio is zero (axial load is the only load applied to the column), the failure mode is local buckling. The buckling starts from the branches and extends towards the trunk because each branch is half the trunk’s cross-sectional area. The presence of lateral load makes the column buckle laterally. Since the joint is the most critical part in a tree-like column, buckling occurs at the branching area, and trunk buckling appears with the advancement of loading. The stress is high in branches as compared with other parts.

Figure 16 Failure modes for TR–1–2 column. (a) R–1–2–0:100 (b) R–1–2–20:100 (c) R–1–2–40:100 (d) R–1–2–60:100 (e) R–1–2–80:100 (f) R–1–2–100:100 and (g) R–1–2–100:0.
Figure 16

Failure modes for TR–1–2 column. (a) R–1–2–0:100 (b) R–1–2–20:100 (c) R–1–2–40:100 (d) R–1–2–60:100 (e) R–1–2–80:100 (f) R–1–2–100:100 and (g) R–1–2–100:0.

5 Summary

This study numerically examined the behavior of tree-like column structures under combined axial and lateral loads and the results are summarized as follows:

  1. At combined loading cases, the axial failure load is decreased by the increase in the lateral load to axial load ratio, this increasing is accompanied by increase in the axial displacement at failure.

  2. The presence of axial load in combination with lateral load works on decreasing the lateral displacement of the tree-like column structures.

  3. The axial failure load decreased significantly by 54, 42, and 28% when lateral/axial loading ratio increased by 20, 40, and 60%, respectively. There was no significant decrease when lateral/axial loading ratio was more than 60%.

  4. The failure mode is local buckling at trunk and branches when the applied load is axial load only, while the failure mode is lateral buckling at combined loading cases.

  5. The stresses at branching joint are increased with the increase in the lateral load ratio.

  1. Funding information: The authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

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Received: 2022-03-16
Revised: 2022-04-04
Accepted: 2022-04-10
Published Online: 2022-06-13

© 2022 Rabab C. Dekhn and Khalid K. Shadhan, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/jmbm-2022-0030
Keywords for this article
tree-like columns; ABAQUS; steel columns; finite element
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  45. Sustainability in the design of liquefied petroleum gas systems used in buildings
  46. Utilization of serial tendering to reduce the value project
  47. Time and finance optimization model for multiple construction projects using genetic algorithm
  48. Identification of the main causes of risks in engineering procurement construction projects
  49. Identifying the selection criteria of design consultant for Iraqi construction projects
  50. Calibration and analysis of the potable water network in the Al-Yarmouk region employing WaterGEMS and GIS
  51. Enhancing gypseous soil behavior using casein from milk wastes
  52. Structural behavior of tree-like steel columns subjected to combined axial and lateral loads
  53. Prospect of using geotextile reinforcement within flexible pavement layers to reduce the effects of rutting in the middle and southern parts of Iraq
  54. Ultimate bearing capacity of eccentrically loaded square footing over geogrid-reinforced cohesive soil
  55. Influence of water-absorbent polymer balls on the structural performance of reinforced concrete beam: An experimental investigation
  56. A spherical fuzzy AHP model for contractor assessment during project life cycle
  57. Performance of reinforced concrete non-prismatic beams having multiple openings configurations
  58. Finite element analysis of the soil and foundations of the Al-Kufa Mosque
  59. Flexural behavior of concrete beams with horizontal and vertical openings reinforced by glass-fiber-reinforced polymer (GFRP) bars
  60. Studying the effect of shear stud distribution on the behavior of steel–reactive powder concrete composite beams using ABAQUS software
  61. The behavior of piled rafts in soft clay: Numerical investigation
  62. The impact of evaluation and qualification criteria on Iraqi electromechanical power plants in construction contracts
  63. Performance of concrete thrust block at several burial conditions under the influence of thrust forces generated in the water distribution networks
  64. Geotechnical characterization of sustainable geopolymer improved soil
  65. Effect of the covariance matrix type on the CPT based soil stratification utilizing the Gaussian mixture model
  66. Impact of eccentricity and depth-to-breadth ratio on the behavior of skirt foundation rested on dry gypseous soil
  67. Concrete strength development by using magnetized water in normal and self-compacted concrete
  68. The effect of dosage nanosilica and the particle size of porcelanite aggregate concrete on mechanical and microstructure properties
  69. Comparison of time extension provisions between the Joint Contracts Tribunal and Iraqi Standard Bidding Document
  70. Numerical modeling of single closed and open-ended pipe pile embedded in dry soil layers under coupled static and dynamic loadings
  71. Mechanical properties of sustainable reactive powder concrete made with low cement content and high amount of fly ash and silica fume
  72. Deformation of unsaturated collapsible soils under suction control
  73. Mitigation of collapse characteristics of gypseous soils by activated carbon, sodium metasilicate, and cement dust: An experimental study
  74. Behavior of group piles under combined loadings after improvement of liquefiable soil with nanomaterials
  75. Using papyrus fiber ash as a sustainable filler modifier in preparing low moisture sensitivity HMA mixtures
  76. Study of some properties of colored geopolymer concrete consisting of slag
  77. GIS implementation and statistical analysis for significant characteristics of Kirkuk soil
  78. Improving the flexural behavior of RC beams strengthening by near-surface mounting
  79. The effect of materials and curing system on the behavior of self-compacting geopolymer concrete
  80. The temporal rhythm of scenes and the safety in educational space
  81. Numerical simulation to the effect of applying rationing system on the stability of the Earth canal: Birmana canal in Iraq as a case study
  82. Assessing the vibration response of foundation embedment in gypseous soil
  83. Analysis of concrete beams reinforced by GFRP bars with varying parameters
  84. One dimensional normal consolidation line equation
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