# Axial Compression Performance of Concrete-Filled Steel Tubular Columns with Different D/t Ratios

Authors: Preetha Achuthan; Ganapathy Ganesh Prabhu; George Gabriel Vimal Arokiaraj; Panneerselvam Arul Sivanantham; Subramanian Suthagar
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

The impacts of three diameter/thickness (D/t) ratios (21.22, 25.46, and 31.83) and concrete strengths (40 N/mm2, 50 N/mm2, and 60 N/mm2) on the strength capabilities of concrete-filled steel tubular (CFST) columns are investigated in this study. The central composite design (CCD) of the response surface methodology (RSM) was used to design the trials in order to complete the tests in a cost-effective manner. 13 (9 distinct tests) columns were evaluated according to the CCD experimental design, and the failure mode of the specimens, load–deformation behavior, and ultimate strength capacity were investigated. Concrete strength improves, resulting in a decrease in steel tube confinement on the core. Because the steel tube longitudinal compressive stress (fsl) increases as the D/t ratio lowers, the confinement is reduced by inhibiting the circumferential tensile stress (fsc). The Reynolds stress model’s, analysis of variance (ANOVA), Pareto chart, and contour plot demonstrated that the column D/t ratio, rather than the in-filled concrete strength, has a considerable impact on the CFST column’s strength capability. The proposed design models in different international codes and literature were evaluated for their effectiveness in predicting the strength capacities of CFST columns subjected to axial compression load. Using regression analysis, a simple design model was suggested to predict the axial strength capacities of CFST short columns, taking into account material strength and column shape. In comparison to other existing and suggested design models, the proposed design model of the present study delivers a more accurate and stable forecast.


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## Body

## 1. Introduction

Concrete-filled steel tubular (CFST) columns are extensively employed in contemporary construction because of their well-known dynamic properties [1–4]. The effect of axial strength on the CFST column in terms of material qualities and applied load has been investigated in several research studies. The research studies [5, 6] investigated the axial load effects on steel–concrete composite sections. Uy et al. [7, 8] studied the behavior of high-strength CFST columns and found that the Eurocode technique for estimating column strength was conservative. The nominal slenderness value and curvature ratio of the column are key characteristics for defining the column’s strength and stiffness capability, according to [9]. Du et al. [10] recently proved that a CFST column’s diameter/thickness ratio (D/t ratio) has the largest impact on its strength. Due to the paucity of confinement pressure from the steel tube, Zhou et al. [11] and Abed et al. [12] found that a high D/t column decreased the CFST’s strength and stiffness. Furthermore, as the in-filled concrete strength grew, the column’s ductility reduced at a higher D/t ratio. Sakino et al. [13] demonstrated that the physical and geometric characteristics of the CFST column have a substantial impact on the column’s structural behavior. Cai and Jiao [14] established a “confinement index (ξ0)” factor to indicate the effects of material strength and the D/t ratio on the CFST column’s strength capability. The effective confinement offered by the steel tube on the concrete core is reduced when the in-filled concrete strength increases, according to Yang et al. [15]. Chang et al. [16] found that concrete strength and steel tube D/t ratio influence the CFST column size effect.The extensive literature review highlights the necessity for more research into the impacts of the D/t ratio and in-filled concrete strength on the axial compression strength capacity of columns. Thus, the current study looked at the CFST column’s strength performance when the D/t ratio and in-filled concrete strength were varied from 20 to 32 and 40 N/mm2 to 60 N/mm2, respectively. The old experimental approach would require 18 tests to achieve findings for D/t ratios ranging from 20 to 32 (with a 3 increment) and concrete strength ranging from 40 N/mm2 to 60 N/mm2 (with a 5 N/mm2 increment). Because steel is costly, the number of tests must be minimized in order to complete the investigation efficiently. Design of experiments (DOE) is a statistical method for comparing experimental results to independent variables. DOE reduces the number of trials required, establishes correlations between independent variables, and offers the best response to experimental data [17]. Response surface methodology (RSM) is a DOE approach that enables researchers to study the impact of independent variables with a minimum of tests [18, 19]. As a result, the trials in this study were designed using RSM’s central composite design (CCD).Several international codes were used to suggest a design model to forecast the strength capabilities of short CFST columns exposed to compression, including EC4 [20], AISC 360–16 [21], and GB50936 [22]. The projection using EC4 [20] was conventional, and the predictions using AISC 360–16 [21] and GB50936 [22] were too conservative because the codes neglected the constrained concrete when calculating strength. The research studies [5, 23–26] have suggested design models to forecast CFST column strength. The column strength capacity projected by these design models, however, is not uniform and is not realistic. As a result, the suitability of design models developed in EC4 [20], AISC 360–16 [21], and GB50936 [22], as well as Aslani et al. [23] and Liang and Fragomeni [6], for forecasting the strength capabilities of columns subjected to axial compression load, was investigated. Based on this study and others [2, 5, 6, 10–13, 26–29], a design model was constructed using regression analysis to estimate column strength during axial compression.


## 2. Design of Experiments

The experiments in this work were designed using the RSM’s CCD fitting approach, using the CFST column strength as the response of modeling. For the CCD model to be created, the number and amount of elements impacting the response must be given. CCD modeling employed the D/t ratio (X1 ranging from 20 to 32) and in-filled concrete strength (X2 ranging from 40 to 60 N/mm2). Table 1 shows the coding and levels of the input factors.Table 1
CCD model Parameters level.
ParametersCodingParameters level−10+1Response 1D/t ratioX121.2225.4631.83In-filled concrete strengthX240 N/mm250 N/mm260 N/mm2The CCD model yielded 13 experiments (9 unique tests) based on these criteria; the specifics of the 13 tests are shown in Table2. All specimens were marked to identify during the discussion, with the labels beginning with CFST and ending with the D/t ratio and in-filled concrete strength. For example, CFST-25.46-50 denotes a D/t ratio of 25.46 and an in-filled concrete strength of 50 N/mm2 for the CFST column.Table 2
Details of DOE (specimen details).
Test no.Specimen designationResponseD/t ratio (X1)Concrete strength (N/mm2) (X2)Actual strength capacityNu, Exp (kN)Predicted strength capacityNu, proposed (kN)(Nu, Exp)/Nu, proposed1CFST-31.83-5031.8350135113341.0452CFST-25.46-5025.4650124911611.0133CFST-25.46-5025.4650124911611.0764CFST-21.22-6021.2260114210701.0765CFST-25.46-5025.4650124911611.0676CFST-25.46-5025.4650124911611.0767CFST-31.83-4031.8340127012381.0768CFST-21.22-5021.2250105710671.0269CFST-25.46-5025.4650124911610.99110CFST-25.46-3525.4635110010311.07611CFST-21.22-4021.2240103710671.06712CFST-31.83-6031.8360145014180.97213CFST-25.46-6025.4660140212561.023Mean1.039Standard deviation (SD)0.031Coefficient of variance (COV)0.029


## 3. Experiments

### 3.1. Materials, Fabrication, and Testing

The column was made from a circular hollow section that met IS 1161–1998 [30] specifications. The column’s external diameter and height were 114.6 and 300 mm, respectively. The study was made up of steel tubes where D/t ratios of 21, 22, 25, 46, and 31, 83 have equivalent yield strength and Poisson’s ratio. The coupon test was used to determine the steel tube’s actual yield strength, following the procedure outlined in IS 1608–2005 [31]. In-filled concrete with 28-day cube strengths of 35 N/mm2 to 60 N/mm2 was employed according to the experimental design. The water/cement ratio was 0.35–0.43, and the concrete mix proportions were designed according to Indian standards. To improve the workability of in-filled concrete, a modified melamine-formaldehyde plasticizer was utilized.The technique reported by Jayaganesh et al. [32] was used to prepare all of the CFST specimens. The leveled cross-sectional surface was achieved by turning the machined steel tube (height, 300 mm). To remove any rubbles, the internal sides of the steel tube were cleaned with a wire brush. Each layer of concrete in the tubes was vibrated to remove air pockets and flaws. The in-filled steel tubes were let to cure for 28 days at room temperature. All of the specimens were tested on a 2000-kN column testing machine. To eliminate uneven surface loading, gypsum mortar was used to cap the ends of the columns, and precautions were made to guarantee that the column aligned properly with the machine’s axis to assure axial loading. To provide flat surface loading, square plates with a size and thickness of 130 mm and 8 mm were used. The 200-ton load cell monitored applied load and all of the specimens were equipped with linear variable displacement transformers (LVDTs) to detect axial and lateral deformation. To collect the results, all of the LVDTs and the load cell were linked to the data acquisition system.


## 3.1. Materials, Fabrication, and Testing

The column was made from a circular hollow section that met IS 1161–1998 [30] specifications. The column’s external diameter and height were 114.6 and 300 mm, respectively. The study was made up of steel tubes where D/t ratios of 21, 22, 25, 46, and 31, 83 have equivalent yield strength and Poisson’s ratio. The coupon test was used to determine the steel tube’s actual yield strength, following the procedure outlined in IS 1608–2005 [31]. In-filled concrete with 28-day cube strengths of 35 N/mm2 to 60 N/mm2 was employed according to the experimental design. The water/cement ratio was 0.35–0.43, and the concrete mix proportions were designed according to Indian standards. To improve the workability of in-filled concrete, a modified melamine-formaldehyde plasticizer was utilized.The technique reported by Jayaganesh et al. [32] was used to prepare all of the CFST specimens. The leveled cross-sectional surface was achieved by turning the machined steel tube (height, 300 mm). To remove any rubbles, the internal sides of the steel tube were cleaned with a wire brush. Each layer of concrete in the tubes was vibrated to remove air pockets and flaws. The in-filled steel tubes were let to cure for 28 days at room temperature. All of the specimens were tested on a 2000-kN column testing machine. To eliminate uneven surface loading, gypsum mortar was used to cap the ends of the columns, and precautions were made to guarantee that the column aligned properly with the machine’s axis to assure axial loading. To provide flat surface loading, square plates with a size and thickness of 130 mm and 8 mm were used. The 200-ton load cell monitored applied load and all of the specimens were equipped with linear variable displacement transformers (LVDTs) to detect axial and lateral deformation. To collect the results, all of the LVDTs and the load cell were linked to the data acquisition system.


## 4. Discussion

### 4.1. Failure Patterns

A total of 13 tests with two different experimental parameters were performed, and the specimens were tested for failure. Higher D/t ratio specimens were failure with concrete crushing, followed by external buckling of the steel tube at the top and middle of the column (Figure1), whereas lower D/t ratio specimens were failure tested with concrete crushing, followed by outward bulging of the steel tube (Figure 2).Figure 1
Failure shape of CFST-31.83-40, CFST-31.83-50, and CFST-25.46-60.Figure 2
Failure shape of CFST-21.22-40, CFST-21.22-50 and CFST-21.22-60.Regardless of the column D/t ratio, the effect of increased concrete strength on column failure modes was minor. However, the increased concrete strength increased the column’s strength capability. The failure modes of the column change from buckling to bulging as the D/t ratio of the column decreases (Figure2).


### 4.2. Axial Stress–Strain Behavior and Strength Capacity

Figure3 depicts the effects of the D/t ratio and in-filled concrete strength on load-shortening behavior. The load increased rapidly in all of the columns at the start, and the column stiffness decreased at the yield level. Figure 3 indicates that steel tube D/t ratio affects column stress–strain more than concrete strength. As in-filled concrete strength grows, the steel tube’s effective confinement reduces. Furthermore, higher D/t ratio columns buckled, causing a sharp fall in the curve. A sudden dip in the stress–strain curve was observed because the columns with higher D/t ratios were unable to develop their upper yield strength once the concrete crushed. These findings matched those of Zhou et al. [11]. Lower D/t ratio columns showed strain hardening of the steel tube at the peak stage because, although the in-filled concrete crushed, the outside steel tube withstood the load, causing bulging failure. Figure 3 indicates that reducing D/t raises steel tube confinement pressure, improving axial load–deformation behavior. The deformation capacity of the column CFST-21.21-60, for example, was 97.21 percent greater than that of the CFST-31.83-60. The lower the D/t ratio, the greater the confinement pressure provided by the steel tube, and thus the greater the resistance to axial deformation.Figure 3
Comparison of the effects of the D/t ratio and concrete strength on axial stress–strain behavior.The column’s strength capability improves when the D/t ratio drops, as seen in Figure4 and Table 2. Furthermore, increasing the concrete strength improved the CFST column’s strength; however, the effect of the concrete strength on the D/t ratios was minimal. For example, the column CFST-21.21-60 achieved a strength of 1142 kN, which is 10.13 percent greater than the column CFST-21.21-40, and the column CFST-31.83-60 achieved a strength of 1450 kN, which is 26.97 percent greater than the column CFST-21.21-60.Figure 4
Comparison of the effects of the D/t ratio and concrete strength on the ultimate strength of a column.


## 4.1. Failure Patterns

A total of 13 tests with two different experimental parameters were performed, and the specimens were tested for failure. Higher D/t ratio specimens were failure with concrete crushing, followed by external buckling of the steel tube at the top and middle of the column (Figure1), whereas lower D/t ratio specimens were failure tested with concrete crushing, followed by outward bulging of the steel tube (Figure 2).Figure 1
Failure shape of CFST-31.83-40, CFST-31.83-50, and CFST-25.46-60.Figure 2
Failure shape of CFST-21.22-40, CFST-21.22-50 and CFST-21.22-60.Regardless of the column D/t ratio, the effect of increased concrete strength on column failure modes was minor. However, the increased concrete strength increased the column’s strength capability. The failure modes of the column change from buckling to bulging as the D/t ratio of the column decreases (Figure2).


## 4.2. Axial Stress–Strain Behavior and Strength Capacity

Figure3 depicts the effects of the D/t ratio and in-filled concrete strength on load-shortening behavior. The load increased rapidly in all of the columns at the start, and the column stiffness decreased at the yield level. Figure 3 indicates that steel tube D/t ratio affects column stress–strain more than concrete strength. As in-filled concrete strength grows, the steel tube’s effective confinement reduces. Furthermore, higher D/t ratio columns buckled, causing a sharp fall in the curve. A sudden dip in the stress–strain curve was observed because the columns with higher D/t ratios were unable to develop their upper yield strength once the concrete crushed. These findings matched those of Zhou et al. [11]. Lower D/t ratio columns showed strain hardening of the steel tube at the peak stage because, although the in-filled concrete crushed, the outside steel tube withstood the load, causing bulging failure. Figure 3 indicates that reducing D/t raises steel tube confinement pressure, improving axial load–deformation behavior. The deformation capacity of the column CFST-21.21-60, for example, was 97.21 percent greater than that of the CFST-31.83-60. The lower the D/t ratio, the greater the confinement pressure provided by the steel tube, and thus the greater the resistance to axial deformation.Figure 3
Comparison of the effects of the D/t ratio and concrete strength on axial stress–strain behavior.The column’s strength capability improves when the D/t ratio drops, as seen in Figure4 and Table 2. Furthermore, increasing the concrete strength improved the CFST column’s strength; however, the effect of the concrete strength on the D/t ratios was minimal. For example, the column CFST-21.21-60 achieved a strength of 1142 kN, which is 10.13 percent greater than the column CFST-21.21-40, and the column CFST-31.83-60 achieved a strength of 1450 kN, which is 26.97 percent greater than the column CFST-21.21-60.Figure 4
Comparison of the effects of the D/t ratio and concrete strength on the ultimate strength of a column.


## 5. RSM Modeling and Discussion

### 5.1. Importance of Response-Influencing Process Variables

Statistical models and estimation procedures (analysis of variance (ANOVA)) may be used to analyze the connection between process variables and responsesP values (P-lack of fit) in ANOVA were used to determine the influence of independent factors on the response (Table 3).Table 3
Regression model’s analysis of variance (ANOVA) for experimental outcomes.
SourceResponses (Yfck − t)DFF-valueP valueModel556.960.000Linear2138.330.000X1198.620.000X21178.040.000Square22.970.116X1210.000.004X2215.820.9752-Way interaction12.190.183X1X212.190.183Variables were deemed important or highly significant to the answer when theP values were less than 0.005 or 0.001. P values greater than 0.05 were deemed insignificant and eliminated from the model or process. With a P value less than 0.001, it is clear from Table 3 that the linear parameters X1 and X2 have an effect on column strength. An example of a bar graph is the Pareto chart, which illustrates the relative importance of various process variables in shaping the results. As can be seen in Figure 5, a Pareto chart displays the responses. Pareto’s graphic illustrates that the D/t ratio is the essential parameter in decisive the column’s strength capacity since the D/t ratio had a bigger normalized effect on CFST column strength capacity than did the in-filled concrete strength. As a result, in-filled concrete’s compressive strength may not affect the CFST column’s strength capacity since D/t is more relevant.Figure 5
Pareto chart examination of the effect of D/t ratio and concrete strength on column strength.


### 5.2. Surface and Contour Plot Analysis

Response surface plots were generated to describe the regression RSM for each pair of independent variables in order to better understand the influence of each variable. Figure6 shows the surface plot derived by plotting the response (Z direction) versus the two independent variables (X and Y direction). As the D/t ratio and in-fill concrete strength grew, so too did column strength (Figure 6). A lower D/t ratio and a higher in-filled concrete strength are necessary to achieve maximum strength. Increasing the in-fill concrete strength moderately increased the column strength, but decreasing the D/t ratio significantly improved the column strength (Figure 6). Stronger columns are achieved by reducing the D/t ratio, which increases the steel tube confinement. Figure 7 displays the response’s contour plot. The D/t ratio of 21.2 to 31.83 and the concrete strength of 35 to 60 N/mm2 were used to plot the contour. Column strength is shown in the contour plot by the pink and green colors, which indicate the average and highest levels of strength. Figure 7 shows that as the concrete strength grows, so does the column’s strength capability. However, the D/t ratio had a substantial impact on column strength (the contour color changed from pink to green when the steel tube D/t ratio was lower than 21.22). Even though there was an increase in concrete strength, it had no effect on the column’s strength (the color did not change to green as a result of the increase in concrete strength). There may be little to no effect on CFST column strength from increasing the compressive strength of in-fill concrete.Figure 6
Surface plot examination of the effect of D/t ratio and concrete strength on column strength.Figure 7
Contour plot examination of the effect of D/t ratio and concrete strength on column strength.


## 5.1. Importance of Response-Influencing Process Variables

Statistical models and estimation procedures (analysis of variance (ANOVA)) may be used to analyze the connection between process variables and responsesP values (P-lack of fit) in ANOVA were used to determine the influence of independent factors on the response (Table 3).Table 3
Regression model’s analysis of variance (ANOVA) for experimental outcomes.
SourceResponses (Yfck − t)DFF-valueP valueModel556.960.000Linear2138.330.000X1198.620.000X21178.040.000Square22.970.116X1210.000.004X2215.820.9752-Way interaction12.190.183X1X212.190.183Variables were deemed important or highly significant to the answer when theP values were less than 0.005 or 0.001. P values greater than 0.05 were deemed insignificant and eliminated from the model or process. With a P value less than 0.001, it is clear from Table 3 that the linear parameters X1 and X2 have an effect on column strength. An example of a bar graph is the Pareto chart, which illustrates the relative importance of various process variables in shaping the results. As can be seen in Figure 5, a Pareto chart displays the responses. Pareto’s graphic illustrates that the D/t ratio is the essential parameter in decisive the column’s strength capacity since the D/t ratio had a bigger normalized effect on CFST column strength capacity than did the in-filled concrete strength. As a result, in-filled concrete’s compressive strength may not affect the CFST column’s strength capacity since D/t is more relevant.Figure 5
Pareto chart examination of the effect of D/t ratio and concrete strength on column strength.


## 5.2. Surface and Contour Plot Analysis

Response surface plots were generated to describe the regression RSM for each pair of independent variables in order to better understand the influence of each variable. Figure6 shows the surface plot derived by plotting the response (Z direction) versus the two independent variables (X and Y direction). As the D/t ratio and in-fill concrete strength grew, so too did column strength (Figure 6). A lower D/t ratio and a higher in-filled concrete strength are necessary to achieve maximum strength. Increasing the in-fill concrete strength moderately increased the column strength, but decreasing the D/t ratio significantly improved the column strength (Figure 6). Stronger columns are achieved by reducing the D/t ratio, which increases the steel tube confinement. Figure 7 displays the response’s contour plot. The D/t ratio of 21.2 to 31.83 and the concrete strength of 35 to 60 N/mm2 were used to plot the contour. Column strength is shown in the contour plot by the pink and green colors, which indicate the average and highest levels of strength. Figure 7 shows that as the concrete strength grows, so does the column’s strength capability. However, the D/t ratio had a substantial impact on column strength (the contour color changed from pink to green when the steel tube D/t ratio was lower than 21.22). Even though there was an increase in concrete strength, it had no effect on the column’s strength (the color did not change to green as a result of the increase in concrete strength). There may be little to no effect on CFST column strength from increasing the compressive strength of in-fill concrete.Figure 6
Surface plot examination of the effect of D/t ratio and concrete strength on column strength.Figure 7
Contour plot examination of the effect of D/t ratio and concrete strength on column strength.


## 6. Validation Models Presented in Many International Standards and Literature

Axial compression of the CFST column can be predicted using a number of different design models. However, despite the fact that the design models are proposed in international codes based on various test results, the accuracy of the anticipated outcomes may vary with respect to the variations in concrete strength and steel tube thickness. Results from this investigation were compared to those predicted using EC4 [20], GB50936, AISC 360–16 [21], and GB50936 [22] and by Farhad et al. [23], Liang and Fragomeni [6], and Farhad et al. [23]. For equations (1) to (6), it is assumed that the steel tube confinement (increased concrete strength) predicts the column strength capacity in EC4 [20]. It can be used for columns with an in-filled concrete strength of at least 80 MPa, a steel yield strength of no more than 460 MPa, and an overall strength of no more than 1,200 MPa [20].(1)Nu,full=ηsfyAs+1+ηc×tD×fyfcfck′Ac,(2)ηsteel=0.25×3+2λ¯,(3)ηconcrete=4.9−18.5λ¯+17λ¯2,(4)λ=NNE,(5)N=fyAs+fck′Ac,(6)NE=π2×EsIs+0.6EcIcL2where Ec is 5000fck and Es is 200000 MPa.The AISC [21] design model for CFST column strength prediction is quite similar to the design model for steel column strength prediction. To establish the nominal strength capacity of the CFST member, AISC [21] uses the plastic stress distribution method and confines the yield stress of steel and concrete strength to not more than 525 MPa and 70 MPa, respectively. In AISC [21], equations (7) and (8) were recommended for forecasting the strength of the compact section if D/t≤λr.(7)Nu,full=As+Ac×1.212+Bξ+Cξ2fck,prism,(8)Nu,full=As+Ac×1.212+Bξ+Cξ2fck,prism,where Es and Ec are the steel and concrete Young’s moduli, respectively. In GB50936 [22], the steel tube confinement to the concrete core and its confinement factor were used to develop the design model. Equations (9)–(13) can predict the strength.(9)Nu,full=As+Ac×1.212+Bξ+Cξ2fck,prism,(10)ξ=AsfyAcfc,(11)B=0.131fy213+0.723,(12)C=−0.07fc14.4+0.026,(13)fck,prism=0.67×fck,cube,where ξ is the confinement factor of the column. Based on the design model proposed in AS (AS5100.6 2004) [33], Farhad et al. [23] proposed determining the strength capacity of a column exposed to axial compression, and equation (14) was used.(14)Nu=Asfy+0.82Acfc′.Liang and Fragomeni [6] presented a design model (equations (15)–(18)) to anticipate the CFST column’s strength capacity based on the test results:(15)Nu,full=γcfck′+4.1frpAc+γsfyAs,(16)γc=1.85Dc−0.135,(17)γs=1.458Dt−0.1(18)frp=0.7υe−υs2tD−2tfyforDt≤47,0.006241−0.0000357Dtfyfor47<Dt≤150,where υe and υs are Poisson’s ratio of the steel tube with and without in-filled concrete, respectively. Poisson’s ratio of the steel υs was 0.5, and Tang et al. proposed equation (19) to predict υe as follows:(19)υe=0.2312+0.358υe′−0.1524fck′fy+4.843υe′fck′fy−9.169fck′fy2,(20)υe′=0.881×10−6Dt3−2.58×10−4Dt2+1.953×10−2Dt+0.4011.Table4 shows the mean, standard deviation (SD), and coefficient of variance for the anticipated strength capabilities of columns using various codes. Figure 8 shows a comparison of the findings of several international codes with the models suggested by Farhad et al. [23] and Liang and Fragomeni [6].Table 4
Validation of test results with various International codes and model proposed in [6, 23].
Column designationExp. (kN),Nu, ExpPredicted strength using various international codes and model proposed by Liang and Fragomeni [16]Nu, EC4 (kN)Nu, Exp/Nu, EC4Nu, AISC (kN)Nu, Exp/Nu, AISCNu, GB50936 (kN)Nu, Exp/Nu, GB50936Nu, Farhad (kN)Nu, Exp/Nu, FarhadNu, Liang (kN)Nu, Exp/Nu, LiangCFST-31.83-5013511288.601.0481073.111.259815.461.597946.961.2821284.761.052CFST-25.46-5012491155.671.081975.611.280756.701.540845.221.2711174.241.064CFST-25.46-5012491155.671.079975.611.280756.701.540845.221.2711174.241.064CFST-21.22-6011421081.671.056967.871.180778.191.423806.781.2361165.030.980CFST-25.46-5012491155.671.081975.611.280756.701.540845.221.2711174.241.064CFST-25.46-5012491153.811.083975.611.280756.701.540845.221.2711174.241.064CFST-31.83-4012701228.741.034992.911.279737.441.675891.581.3041170.871.085CFST-21.22-5010571016.501.040881.861.199695.971.487747.391.2591056.781.000CFST-25.46-5012491155.671.083975.611.280756.701.540845.221.2711174.241.064CFST-25.46-3511001060.711.037850.871.293637.431.663759.081.310998.611.102CFST-21.22-401037953.361.088795.851.303614.491.566687.991.287941.731.101CFST-31.83-6014501350.971.0731153.311.257895.381.5301002.341.2621388.801.044CFST-25.46-6014021222.581.1471092.041.284870.691.451925.611.2421321.201.061Mean1.0711.2661.5451.2721.057Standard deviation (SD)0.0250.0360.0720.0210.032Coefficient of variance (COV)0.0240.0290.0460.0170.032Figure 8
Validation of test results with various International codes and model proposed in [6, 23]: comparison.Forecasts made with AISC [21], GB50936 [22], and Farhad et al. [23] are conservative and underestimate the column’s strength capacity (Table 4 and Figure 8), but the means of predictions made with AISC [21] and GB50936 [22] are 1.266 and 1.545, respectively, which are relatively high (see Figure 9). The forecasts made by EC 4 [20] and Liang and Fragomeni [6] were, on the other hand, fairly accurate, with averages of 1.071 and 1.057, respectively, which are acceptable (see Figure 9). The forecast made with Liang and Fragomeni’s model [6] was quite near to the straight line, indicating that the predictions were more reliable.Figure 9
Validation of test results with various International codes and model proposed in-Histogram approach.The model suggested by Liang and Fragomeni [6] was also proven as dependable and accurate by Shiming Zhou et al. [6, 11, 23].


## 7. Proposed Design Model for Circular Short CFST Columns under Axial Compression

The codes AISC [21] and GB50936 [22] underestimated the strength of the CFST column, as seen in Figure 8 and Table 4. Because the models of EC4 [20] and Liang and Fragomeni [6] provided somewhat good predictions, the correctness and reliability of the design model were confirmed using test results from 105 specimens [2, 4–6, 11–13, 26–29, 34–39]. Although the EC4 [20] and Liang and Fragomeni [6] models were relatively accurate for a few specimens, they deviated by 15% in many specimens (see Table 4). Furthermore, EC4’s design model limits material strength and shape [20] (Table 4). Predicting column strength needs a simplified model. Using experimental data from this work and others [2, 5, 6, 10–13, 26–29], a simple design model was created to estimate column strength under axial compression. This model determines the column’s strength capacity based on the column geometry and material properties. Parameters are given in (21)180≤fy≤750Nu,full=As+Acfck′0.9944+1.070ξ+0.1025ξ2−0.03127ξ320≤fc′≤9020≤Dt≤170.Figure10 shows linear regression’s normal probability map. Figure 10’s regression analysis findings indicate a fair distribution of points. Furthermore, the design model’s anticipated R2 was 98.6, with a difference of 0.01 between the predicted and adjusted R2. As a result, the constructed model accurately predicted the short column strength under axial compression.Figure 10
Normal probability plots.The proposed model (equation (21)) was compared to the test results of the 105 specimens available in the literature to verify its accuracy in predicting the axial strength of the circular CFST column with higher material strength (fy > 450 N/mm2 and fck′ > 60 N/mm2), the high-strength steel tube filled with high-strength concrete, and the low-strength steel tube filled with high-strength concrete. Figure 11 shows the comparison between the expected and test findings for 105 specimens. Table 5 shows the 105 column strength values predicted using the proposed model, as well as the mean of Nu, test/Nu, Proposed, SD, and COV. Table 5 and Figure 11 indicate that the anticipated strength values match the actual results. Furthermore, with a COV of 0.0341, the mean value of Nu, test/Nu, Proposed, was 0.997, showing that the proposed model (equation (21)) produced reasonably accurate predictions. It is commonly known that a model is considered good if the Nu, test/Nu, Proposed, ratio is near to or equal to 1.0. Figure 12 shows the contrast between the suggested model and Liang and Fragomeni’s [6] design model. The histogram shows that the majority of Nu, test/Nu, Proposed, results (almost 85%) fell in the 0.95–1.05 range. As a result, the proposed model is more precise than Liang and Fragomeni’s design models [6].Figure 11
Validation of proposed model with 105 column test results available in various literature.Table 5
Verification of proposed model results with test results available from the literature.
LiteraturesSpecimen designationD (mm)t (mm)fy (N/mm2)fc (N/mm2)D/tL (mm)Nu, testNu, proposedNu, test/Nu, proposedNu, LiangNu, test/Nu, LiangNu, EC4Nu, test/Nu, EC4Wang et al. [26]CFST-MA-11572.5032685.463314211721051.0062242.470.944NANACFST-MA-21572.5032685.463314205821050.9782242.470.918NANACFST-MA-31572.5032685.463314206821050.9832242.470.922NANACFST-HA-11533.6032085.443306226422181.0212454.720.922NANACFST-HA-21533.6032085.443306227422181.0252454.720.926NANACFST-HA-31533.6032085.443306220522180.9942280.360.967NANAChen et al. [40]LS-21832.00312.857.692549188919120.9882041.810.925NANALS-31832.00312.859.392549192419560.9842094.620.919NANAHS-11872.90353.561.564561227223760.9562490.260.912NANAHS-21872.90353.561.164561228723650.9672478.910.923NANAHS-31872.90353.560.564561223723490.9532461.900.909NANAHM-12473.90362.561.563741407142010.9694285.420.950NANAHM-22473.80362.561.165741412541470.9954237.810.973NANAHM-32473.80362.560.565741416641191.0124209.210.990NANAAbed et al. [12]CFSTf44D167t3.11673.103004454351171015341.1151731.520.9881644.981.040CFSTf60D114t5.61145.603006020251136514150.9651275.541.0701349.591.011CFSTf60D114t3.61143.60300603225193410890.8581088.760.8581104.610.846CFSTf60D167t3.11673.103006054351187318770.9982126.900.8811948.640.961Yu et al. [27]SZ5S3A12194.8035042.646657315029921.0532979.881.0573087.731.020SZ5S4A1a2194.8035050.546657340032791.0373610.200.9423337.891.019SZ5S4A1b2194.7035050.547657335032471.0323578.520.9363326.041.007SZ3S6A11652.7035077.261512208022060.9432482.810.838NANASZ3S6B1652.8035077.259495216022290.9692512.510.860NANASZ3S6C1652.8035077.259495209522290.9402349.970.892NANASZ3S4A11652.703505761512175017820.9822013.670.8691803.690.970SZ3C4A11652.8035046.359512156015810.9871773.140.8801614.980.966Sakino and Hayashi [38]CC4-A-21493.0028325.4504478909220.966947.060.940990.780.898CC4-A-4-11493.0028340.750447106411790.9031338.830.7951217.560.874CC4-A-4-32374.702844150711332029791.1143271.591.0153100.291.071CC4-A-81493.0028378.150447178118180.9801908.080.933NANAGiakoumelis and Lam [5]C91155.0036557.623299132414640.9041346.350.9831403.190.944C10a1143.7034357.631296103811550.8991139.580.9111153.150.900Han and Yao [35]scv2–12003.00303.558.567600238324850.9592594.100.9192512.520.948Zhang and Wang [36]L-B-1-85h1393.30331.744.642417114012530.9091408.360.8091280.590.890L-B-2-88h1393.30331.744.642417122012530.9731278.700.9541280.590.953L-B-3-89h1403.40331.744.641420118012870.9171441.580.8191319.720.894M-A-1-97h1673.4035470.649501207522820.9092584.530.803NANAM-A-2-100h1673.3035470.651501210522580.9322558.770.823NANAM-A-3-95h1683.3035470.651504205522800.9012583.000.796NANAM-B-1-20h1393.30331.762.542417148015170.9761561.450.948NANAM-B-2-26h1393.40331.762.541417152015360.9901574.600.965NANAM-B-3-90h1393.30331.762.542417150015170.9891561.450.961NANAM-C-1-120h1403.60325.361.439420158215641.0121767.960.895NANAM-C-3-86h1403.60325.361.439420154015640.9851767.960.871NANAM-E-1-21h1335.2035170.626399181019540.9262040.260.887NANAM-E-2-27h1335.0035170.627399177019100.9272015.610.878NANAM-E-3-23h1335.1035170.626399183519320.9502028.000.905NANAH-B-1-310h1393.30331.777.142417168817330.9741961.040.861NANAH-B-2-309h1393.30331.777.142417168017330.9691961.040.857NANAH-D-1-311h1595.40356.377.129477248027250.9102900.700.855NANAH-D-2-308h1605.00356.377.132480244026480.9212588.810.943NANAH-D-3-324h1595.10356.377.131477246026480.9292578.110.954NANAH-E-1-322h1335.1035177.126399193020190.9561923.401.003NANAH-E-2-306h1335.2035177.126399195520410.9581935.931.010NANAH-E-3-323h1335.0035177.127399195519970.9791910.871.023NANATan et al. [37]A2-21272.0025884.764445133913021.0291436.790.932NANAA3-11333.5035284.738466199517901.1151832.921.088NANAA3-21333.5035284.738466199117901.1122003.990.994NANAA4-11334.7035284.728466227320371.1162155.001.055NANAA4-21334.7035284.728466215820371.0602155.001.001NANAB-21084.5035877.424378142314131.0071339.411.062NANAB-31084.5035877.424378151814131.0751462.021.038NANAC-11334.7035274.528466185419000.9762031.990.912NANAC-21334.7035274.528466193319001.0172031.990.951NANAGardener and Jacobson [28]3101.703.07650.1034.1033203111210661.0431037.621.072NANA4101.703.07650.1031.2033203106710321.034999.861.067NANASchneider [2]C3140.006.58537.0028.2021616201021550.9332148.250.936NANASaisho et al. [29]H60.1139.802.37462.6059.9059419155814801.0531679.260.928NANAH60.2139.802.37462.6068.0059419157716010.9851831.140.861NANAH60.3139.802.37462.6068.0059419157716010.9851831.140.861NANAH60.4139.802.37462.6068.0059419162616011.0151708.310.952NANAL60.1139.802.37462.6026.605941910989881.1111007.561.090NANAL60.2139.802.37462.6026.605941911079881.1201029.641.075NANAL60.3139.802.37462.6026.605941910789881.0911029.641.047NANASakino and Hayashi [38]CC6-A-2122.004.54576.0025.4027366150914311.0551411.411.069NANACC6-A-4–1122.004.54576.0040.5027366165717500.9471691.780.979NANACC6-A-4–2122.004.54576.0040.5027366166317500.9501691.780.983NANACC6-A-8122.004.54576.0077.0027366210021890.9602065.611.017NANAZhou et al. [11]C140-1141.422.05724.0042.4069525181014491.0491479.661.223NANAC150-1151.052.98691.0042.4051563196519501.0081987.910.988NANALiang and Fragomeni [6]CC4-A-2149.002.96308.0025.40505599419580.9821023.950.919996.260.945CC4-A-4-2149.002.96308.0040.5050559118012110.9741259.460.9371227.600.961CC4-A-8149.002.96308.0077.0050559178118340.9711925.760.925NANACC6-A-2122.004.54576.0025.4027458150914311.0551459.871.034NANACC6-A-4-1122.004.54576.0040.5027458165717500.9471637.131.012NANACC6-A-4-2122.004.54576.0040.5027458166317500.9501691.780.983NANACC6-A-8122.004.54576.0077.0027458210021890.9602286.380.918NANAC3114.433.98343.0026.69294299489021.051894.241.060895.791.058C8115.044.92365.0089.1623431178717621.0141662.101.075NANAC9115.025.02365.0048.9623431141313821.0231260.571.1211254.431.126C11114.293.75343.0048.9630429106710830.9851058.301.0081037.921.028C14114.543.84343.0084.1030430135914510.9371568.840.866NANAYu et al. [27]SC2-1120.001.48307.0042.60813606106750.904747.860.816NANASC3-1180.001.48307.0042.60122540138413651.0141404.190.986NANAO’Shea and Bridge [4]S30CS50B165.002.82363.3048.3059563166216511.0071732.310.959NANAS20CS50A190.001.94256.4041.0098658167814911.1261573.521.066NANAS16CS50B190.001.52306.1048.30125658169516711.0141773.270.956NANAS12CS50A190.001.13185.7041.00168658137712931.0651356.911.015NANAS10CS50A190.000.86210.7041.00221658135012741.0601292.831.044NANASuliman Abdalla et al. [39]CFST f60 D167 t3.1167.003.10300.0060.0054350187318770.9982126.900.8811954.240.958CFST f60 D114 t3.6114.003.60300.0060.0032250109510891.0051088.761.0061104.970.991CFST f60 D114 t5.6114.005.60300.0060.0020250136514150.9651275.541.0701347.991.013CFST f44 D167 t3.1167.003.10300.0044.0054350171015341.1151731.520.9881640.821.042CFST f44 D114 t3.6114.003.60300.0044.003225010429321.1181023.701.018968.871.075CFST f44 D114 t5.6114.005.60300.0044.0020250131412581.0451117.891.1751224.821.073Mean0.9970.957—Standard deviation (SD)0.0340.083—Coefficient of variance (COV)0.0340.087—Figure 12
Validation of proposed model with 105 column test results available in various studies: Histogram approach.


## 8. Conclusion

The impacts of three D/t ratios and three concrete strengths on CFST column strength capabilities were examined in this work. Cost-effective tests were designed using the CCD model of RSM. Thirteen columns were examined for specimen failure mode and other parameters according to the CCD model design. Regardless of the column D/t ratio, the impact of increased concrete strength on the column’s strength was minor. A drop in the D/t ratio, on the other hand, improved the column’s strength regardless of concrete strength, and the effective confinement given by the steel tube on the concrete core was substantial with a higher D/t ratio. Furthermore, when the in-filled concrete strength increased, the steel tube on the concrete core’s effective confinement decreased. The D/t ratio of the column was more important than the in-filled concrete strength in enhancing the strength capacity of the CFST column, according to the ANOVA, Pareto chart, and contour plot of RSM. The appropriateness of design models offered in standards and literature for calculating CFST columns’ axial compression strength was also studied. Furthermore, based on this study and earlier research, a simple design model was built utilizing regression analysis to anticipate column strength during axial compression. The model’s accuracy was verified.



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*Source: 9170525-2022-07-12.xml*