# Load–Displacement Behaviour and a Parametric Study of Hybrid Rubberised Concrete Double-Skin Tubular Columns

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Investigation

## 3. Finite Element Modelling

#### 3.1. Element Type and Meshing

#### 3.2. Material Model

#### 3.2.1. Filament-Wound CFRP Tube

#### 3.2.2. Rubberised Concrete

_{c}

_{,}the ratio of biaxial to uniaxial compression stress $\frac{{f}_{bO}}{{{f}^{\prime}}_{c}}$, dilation angle, eccentricity, viscosity, tension, and compression subroutine with the damage parameter. To allow different yields and triaxial tension and compression stresses, the yield surface of CDPM is noncircular in shape and governed by the ratio of second stresses variant of tension and compression at the same hydrostatic stress denoted by K

_{c}[31], which can be obtained from the following equation [32].

_{c}value is related to the ratio $\frac{{f}_{bo}}{{{f}^{\prime}}_{c}}$, which can be obtained from the following empirical equation by Papanikolaou and Kappos [33].

_{c}is in MPa.

_{co}, the rubber replacement ratio ρvr, aggregate size replaced with rubber particles γ, and the elastic modulus in the equations. The first stage denotes the elastic stage, which showed a linear behaviour up to 30% of the unconfined compressive strength of concrete. The corresponding strain ε

_{rc}

_{,el}can be calculated using the modulus of elasticity E

_{rc}of the concrete. The next stage reflects the elastic–plastic behaviour of concrete for strains ε within the limit of ε < ε

_{rc}

_{,el}< ε

_{rc}

_{,1}, where ε

_{rc}

_{,1}indicates the crushing strain of concrete. The final stage is the post-peak stage for strains ε > ε

_{rc}, which is a function of the post-peak energy and compressive strength f

_{rc}of rubberised concrete. Based on the above discussion, the equations of the model can be summarised as below, where ε

_{rcu}= ultimate strain of unconfined rubberised concrete and f

_{rc}

_{,2}= strength of unconfined rubberised concrete.

_{rc}

_{,el}

_{rc}

_{,el}< ε < ε

_{rc}

_{,l}

_{rcu}

#### 3.2.3. Steel

#### 3.2.4. CFRP Wrapped at the Top and Bottom

#### 3.3. Surface Interaction and Boundary Conditions

## 4. Validation of the Numerical Model

## 5. Parametric Study

_{i}/t

_{o}= 1, 0%, where the first value indicates that the thickness ratio is 1 and the second value indicates the percentage of rubber. The second group comprises specimens with varying hollow ratios (ratio of the inner steel tube diameter to the outer CFRP tube diameter). The specimens in this group are designated by the value of the hollow ratio “HR” followed by the percentage of rubber. For the hybrid column, larger void ratios of 0.7 to 0.8 are desirable for the sustainable use of the void for running pipelines or electrical wirings [11]; however, considering this value, the authors studied the range of 0.3 to 0.8 to obtain an overall picture of the effect of the hollow ratio. The third group examines the effect of steel tube yield strength, as several steel grades are available for construction. The first specimen in this group is designated as f

_{y}= 250, 0%, where the first value indicates the yield strength of the steel tube and the second value indicates the percentage of rubber. The fourth group highlights the effect of variation in the CFRP tube diameter keeping the same thickness and is named O165, 0%, where O165 indicates that the outer CFRP tube of the hybrid column has a diameter of 165 mm and the column is filled with 0% rubberised concrete. Considering the thickness of the CFRP tube as 3 mm, the experimental values of the modulus of elasticity and failure strength of the selected tubes were considered from the study by Li et al. [24].

#### 5.1. Effect of the Thickness Ratio

_{i}/t

_{o}is defined as the ratio of the inner tube thickness t

_{i}to the outer tube thickness t

_{o}. For the parametric study, the outer CFRP tube thickness was kept constant at 2.5 mm, similar to the tube tested by Khusru et al. [19], and the inner steel tube thickness was varied considering 2.5 mm, 5 mm, and 7.5 mm, which gives the range of thickness ratio from 1 to 3 with all other parameters of the column remaining unchanged. The results of the parametric study are presented in Figure 5. Figure 5 depicts that the axial capacity of hybrid RuDSTCs is enhanced with the increase in the steel tube thickness. However, for the same thickness ratio, the axial capacity of the column decreases with the increase in rubber content.

_{i}/t

_{o}= 2, the transition between the stages appeared at 1239 kN, which reduced to 40.5% and 51.5% when incorporating 15% and 30% rubber, respectively.

#### 5.2. Effect of the Hollow Ratio

#### 5.3. Effect of Steel Tube Yield Strength

#### 5.4. Effect of the Diameter of the CFRP Tube

## 6. Comparison with Existing Design Guideline

_{cc}′ = compressive strength of confined concrete;

_{c}

_{0}′ = compressive strength of unconfined concrete;

_{k}= confinement stiffness ratio of the FRP tube;

_{ε}= strain ratio of the FRP tube;

_{c}

_{0}′ in Equation (9). The remaining parameters of Equation (9) were calculated as per Zhang et.al. [11]. To calculate the confined concrete strength (f

_{cc}′) of the hybrid RuDSTCs, the individual axial capacity of the exterior and interior parts, namely, the filament-wound CFRP tube and the interior steel tube, respectively, was deducted from the overall capacity of the column, and the calculated axial load carried by confined concrete was then converted into the confined stress using the cross-sectional area of the concrete infill.

_{cc}′ from FE and those calculated using Yu et al.’s [11] model are presented in Table 3.

## 7. Conclusions

- i.
- The axial load capacity of the hybrid RuDSTCs is enhanced with an increase in the tube thickness, yield strength of steel, and inner steel tube diameter and a decrease in the hollow ratio. Increasing the rubber content results in a flatter second stage of the load–displacement curve, indicating ductile behaviour compared with the non-rubberised columns.
- ii.
- For the same thickness ratio, the axial capacity of the column decreases with the increase in the rubber content. Again, for the same strength of the inner tube steel, increasing the percentage of rubber resulted in a smoother transition from the first stage to the second stage of the load–displacement curve. A higher grade of steel also showed a greater stiffness of the hybrid column.
- iii.
- A larger outer diameter of the CFRP tube resulted in a stiffer second stage of the column. The yielding of steel tubes occurred at a similar displacement, but the axial load value varied significantly for the non-rubberised columns.
- iv.
- The strength and stiffness of the hybrid columns decreased with the increasing rubber content. A gradual and smooth transition of the load–displacement curve was observed for the 30% rubberised concrete compared with the 15% non-rubberised concrete.
- v.
- The confined concrete strength of the hybrid RuDSTCs obtained from the parametric study was compared with the results obtained from the modified Yu et al. model using rubberised concrete properties. A good correlation was achieved, which indicated that the modified Yu et al.’s model can be used to predict the capacity of hybrid RuDSTCs.
- vi.
- Further exploration of hybrid columns under varying loading conditions, including long-term cyclic loading, environmental influences, and impact loading, will present an opportunity to deepen our understanding of their structural behaviour and accommodation for practical use.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Comparison of axial load–axial displacement curves obtained from experiments and FE simulations of 0%, 15%, and 30% RuDSTCs: (

**a**) 0% RuDSTCs, (

**b**) 15% RuDSTCs, and (

**c**) 30% RuDSTCs.

**Figure 6.**Effect of the hollow ratio: (

**a**) 0% RuDSTC, hollow ratio = 0.80, (

**b**) 15% RuDSTC, hollow ratio = 0.50, and (

**c**) 30% RuDSTC, hollow ratio = 0.30.

**Figure 7.**Effect of the steel tube yield strength: (

**a**) f

_{y}= 250 MPa, (

**b**) f

_{y}= 350 MPa, and (

**c**) f

_{y}= 450 MPa.

**Figure 9.**Comparison of confined concrete strength (f

_{cc}′) from modified Yu et al.’s model [13] against the FE results.

Specimen | P_{FE} | P_{EXP} | P_{EXP}/P_{FE} |
---|---|---|---|

kN | kN | ||

C-I60-00-I | 1792 | 1671 | 0.93 |

C-I60-00-II | 1792 | 1692 | 0.94 |

C-I60-15-I | 1329 | 1314 | 0.98 |

C-I60-15-II | 1329 | 1286 | 0.97 |

C-I60-30-I | 1034 | 987 | 0.95 |

C-I60-30-II | 1034 | 888 | 0.86 |

Specimen ID | % Rubber | FRP Tube | Steel Tube | Control Concrete Strength | |||
---|---|---|---|---|---|---|---|

D_{o} (mm) | t_{o} (mm) | D_{i} (mm) | t_{i} (mm) | f_{y} (mm) | f′_{c} (MPa) | ||

Group 1, thickness ratio | |||||||

t_{i}/t_{o} = 1, 0% | 0% | 200 | 2.5 | 101.6 | 2.5 | 250 | 50 |

t_{i}/t_{o} = 1, 15% | 15% | 200 | 2.5 | 101.6 | 2.5 | 250 | |

t_{i}/t_{o} = 1, 30% | 30% | 200 | 2.5 | 101.6 | 2.5 | 250 | |

t_{i}/t_{o} = 2, 0% | 0% | 200 | 2.5 | 101.6 | 5.0 | 250 | 50 |

t_{i}/t_{o} = 2, 15% | 15% | 200 | 2.5 | 101.6 | 5.0 | 250 | |

t_{i}/t_{o} = 2, 30% | 30% | 200 | 2.5 | 101.6 | 5.0 | 250 | |

t_{i}/t_{o} = 3, 0% | 0% | 200 | 2.5 | 101.6 | 7.5 | 250 | 50 |

t_{i}/t_{o} = 3, 15% | 15% | 200 | 2.5 | 101.6 | 7.5 | 250 | |

t_{i}/t_{o} = 3, 30% | 30% | 200 | 2.5 | 101.6 | 7.5 | 250 | |

Group 2, hollow ratio | |||||||

HR = 0.30, 0% | 0% | 200 | 2.5 | 60.3 | 5.0 | 250 | 50 |

HR = 0.30, 15% | 15% | 200 | 2.5 | 60.3 | 5.0 | 250 | |

HR = 0.30, 30% | 30% | 200 | 2.5 | 60.3 | 5.0 | 250 | |

HR = 0.50, 0% | 0% | 200 | 2.5 | 101.6 | 5.0 | 250 | 50 |

HR = 0.50, 15% | 15% | 200 | 2.5 | 101.6 | 5.0 | 250 | |

HR = 0.50, 30% | 30% | 200 | 2.5 | 101.6 | 5.0 | 250 | |

HR = 0.80, 0% | 0% | 200 | 2.5 | 159 | 5.0 | 250 | 50 |

HR = 0.80, 15% | 15% | 200 | 2.5 | 159 | 5.0 | 250 | |

HR = 0.80, 30% | 30% | 200 | 2.5 | 159 | 5.0 | 250 | |

Group 3, steel tube yield strength | |||||||

f_{y} = 250, 0% | 0% | 152 | 2.5 | 60.3 | 3.6 | 250 | 50 |

f_{y} = 250, 15% | 15% | 152 | 2.5 | 60.3 | 3.6 | 250 | |

f_{y} = 250, 30% | 30% | 152 | 2.5 | 60.3 | 3.6 | 250 | |

f_{y} = 350, 0% | 0% | 152 | 2.5 | 60.3 | 3.6 | 350 | 50 |

f_{y} = 350, 15% | 15% | 152 | 2.5 | 60.3 | 3.6 | 350 | |

f_{y} = 350, 30% | 30% | 152 | 2.5 | 60.3 | 3.6 | 350 | |

f_{y} = 450, 0% | 0% | 152 | 2.5 | 60.3 | 3.6 | 450 | 50 |

f_{y} = 450, 15% | 15% | 152 | 2.5 | 60.3 | 3.6 | 450 | |

f_{y} = 450, 30% | 30% | 152 | 2.5 | 60.3 | 3.6 | 450 | |

Group 4, diameter of CFRP tube | |||||||

O114, 0% | 0% | 114 | 3.0 | 60.3 | 3.6 | 250 | 50 |

O114, 15% | 15% | 114 | 3.0 | 60.3 | 3.6 | 250 | |

O114, 30% | 30% | 114 | 3.0 | 60.3 | 3.6 | 250 | |

O165, 0% | 0% | 165 | 3.0 | 60.3 | 3.6 | 250 | 50 |

O165, 15% | 15% | 165 | 3.0 | 60.3 | 3.6 | 250 | |

O165, 30% | 30% | 165 | 3.0 | 60.3 | 3.6 | 250 |

**Table 3.**Comparison of the confined concrete strength of the hybrid columns with the existing design model.

Specimen ID | f_{cc}′_{(FE)} MPa | f_{cc}′_{(Yu)} MPa | Ratio of f_{cc}′_{(FE)} f_{cc}′_{(Yu)} |
---|---|---|---|

t_{i}/t_{o} = 1, 0% | 107.46 | 94.78 | 1.13 |

t_{i}/t_{o} = 1, 15% | 78.33 | 76.01 | 1.03 |

t_{i}/t_{o} = 1, 30% | 65.90 | 61.97 | 1.06 |

t_{i}/t_{o} = 2, 0% | 93.47 | 94.78 | 0.99 |

t_{i}/t_{o} = 2, 15% | 76.90 | 76.01 | 1.01 |

t_{i}/t_{o} = 2, 30% | 60.90 | 61.97 | 0.98 |

t_{i}/t_{o} = 3, 0% | 118.32 | 94.78 | 1.25 |

t_{i}/t_{o} = 3, 15% | 92.34 | 76.01 | 1.21 |

t_{i}/t_{o} = 3, 30% | 79.20 | 61.97 | 1.28 |

HR = 0.30, 0% | 78.29 | 94.78 | 0.83 |

HR = 0.30, 15% | 75.15 | 76.01 | 0.99 |

HR = 0.30, 30% | 65.40 | 61.97 | 1.06 |

HR = 0.50, 0% | 107.85 | 94.78 | 1.14 |

HR = 0.50, 15% | 79.12 | 76.01 | 1.04 |

HR = 0.50, 30% | 69.12 | 61.97 | 1.12 |

HR = 0.80, 0% | 136.73 | 94.78 | 1.44 |

HR = 0.80, 15% | 77.73 | 76.01 | 1.02 |

HR = 0.80, 30% | 61.26 | 61.97 | 0.99 |

f_{y} = 250, 0% | 117.69 | 111.36 | 1.06 |

f_{y} = 250, 15% | 92.38 | 92.60 | 1.00 |

f_{y} = 250, 30% | 47.81 | 78.56 | 0.61 |

f_{y} = 350, 0% | 122.21 | 111.36 | 1.10 |

f_{y} = 350, 15% | 94.88 | 92.60 | 1.02 |

f_{y} = 350, 30% | 89.52 | 78.56 | 1.14 |

f_{y} = 450, 0% | 124.90 | 111.36 | 1.12 |

f_{y} = 450, 15% | 99.72 | 92.60 | 1.08 |

f_{y} = 450, 30% | 69.32 | 78.56 | 0.88 |

O114, 0% | 176.65 | 134.40 | 1.31 |

O114, 15% | 145.20 | 115.64 | 1.26 |

O114, 30% | 130.66 | 101.59 | 1.29 |

O165, 0% | 148.10 | 105.92 | 1.40 |

O165, 15% | 101.21 | 87.15 | 1.16 |

O165, 30% | 91.12 | 73.11 | 1.25 |

Mean | 1.09 | ||

CV | 0.12 |

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## Share and Cite

**MDPI and ACS Style**

Khusru, S.; Thambiratnam, D.P.; Elchalakani, M.; Fawzia, S.
Load–Displacement Behaviour and a Parametric Study of Hybrid Rubberised Concrete Double-Skin Tubular Columns. *Buildings* **2023**, *13*, 3131.
https://doi.org/10.3390/buildings13123131

**AMA Style**

Khusru S, Thambiratnam DP, Elchalakani M, Fawzia S.
Load–Displacement Behaviour and a Parametric Study of Hybrid Rubberised Concrete Double-Skin Tubular Columns. *Buildings*. 2023; 13(12):3131.
https://doi.org/10.3390/buildings13123131

**Chicago/Turabian Style**

Khusru, Shovona, David P. Thambiratnam, Mohamed Elchalakani, and Sabrina Fawzia.
2023. "Load–Displacement Behaviour and a Parametric Study of Hybrid Rubberised Concrete Double-Skin Tubular Columns" *Buildings* 13, no. 12: 3131.
https://doi.org/10.3390/buildings13123131