Behaviour of Concrete-Filled Double Skin Tubular Short Column with Plate Stiffeners Welded Intermittently under Axial Compression

Abstract

This paper presents the experimental and finite element analyses of the behaviours of stub circular and square concrete-filled double steel tubular (CFDST) columns intermittently welded with plate stiffeners under axial compression. The plate stiffeners are welded to the inner surface of the outer tube through predrilled holes. Twenty specimens consisting of two concrete-filled steel tubular (CFST), two unstiffened CFDST, and sixteen stiffened CFDST were tested under axial compression to determine the failure patterns and obtain the load versus axial shortening curve. The key variables are the distance of weld spacing and the dimension of the plate stiffeners. Based on the experiment results, the authors have identified the possible local buckling locations, including the peak load of the specimens that were significantly affected by the intermittently welded plate stiffeners. The developed finite element model is verified by comparing the current and previous experimental results, and it provides an acceptable mean ratio of 1.01 and a standard deviation of 0.04. The validated FE model is employed in a parametric study to investigate the effects of critical parameters, including the two shapes of the specimens, dimension of the plate stiffeners, and weld spacing, on the load-carrying capacity. The findings of the parametric study can be used to justify the optimum dimensions of plate stiffeners for the best stiffened CFDST performance.

1. Introduction

Many researchers have used concrete-filled steel tubular (CFST) columns to construct more durable modern structures, such as marine structures, skyscrapers, bridges capable of carrying huge loads and large-scale structures. CFST column exhibits exceptional performance under axial compression testing [1]. However, the construction of the CFST column requires a large amount of concrete because of the numerous columns needed to support project construction, and this has an adverse impact on the self-weight and loading capacity of the CFST column. Therefore, researchers have turned their attention to the concrete-filled double-skin tubular (CFDST) column. The CFDST column is a composite column with concrete sandwiched between two concentrically placed steel tubes [2,3]. The double steel tube alignment creates a void in the centre of the column, thus reducing the amount of concrete needed for the column construction. The inner steel tubes in this column can withstand a higher load capacity while also functioning as permanent formwork for the concrete. Additionally, the steel tubes confine the concrete, and the concrete infill delays the steel tube’s local buckling [4]. Previous studies have shown that CFDST has good fire resistance and seismic performance [5,6].

Many researchers have attempted to improve the ultimate strength of the CFDST by manipulating its hollow ratio [7,8,9]. The hollow ratio is defined by the ratio of the void area in the inner steel tube to the total cross-sectional area of the CFDST. The studies on column hollow ratio focused primarily on modifying the thickness and diameter of the inner and outer steel tubes. Increasing the thickness of the CFDST outer steel tube could improve the overall performance of the column through the significantly reduced local buckling effect [10]. A study by Patel, Liang and Hadi [11], which utilised the stainless-steel tube for the CFDST skin, found that the diameters of the inner and outer steel tubes determine the ultimate strength of the column. Increasing the diameter of the outer tube reduces the ductility of CFDST because more concrete sections were subjected to loading. However, a greater diameter of the inner tube lowered the ultimate strength of the CFDST because more steel sections were subjected to the loading, which significantly improved the ductility of the CFDST [7,9]. The ductility of the column is the ability to buckle plastically without fracture and is influenced by the materials used. Steel can sustain both compression and tension, but concrete is weak in tension. Concrete is brittle and cracks under pressure. Steel is ductile and returns to its original shape if the pressure does not exit the steel’s yield strength.

Therefore, numerous studies have explored an alternative method to improve the performance of CFDST by welding stiffeners to it. There are a few types of stiffeners, such as steel bars [12,13], T-shape stiffener [14], and plate stiffener [15,16,17]. The stiffeners increase the steel tube stiffness and allow greater confinement of the core concrete. The plate stiffeners also increase the contact area between the steel and the concrete, thus reducing the stiffened column’s overall deformation at the local buckling location compared to the unstiffened specimen [18].

There are two methods for fabricating stiffened square tube CFST or CFDST columns, the lipped members shown in Figure 1a and the plate-by-plate welding shown in Figure 1b [19,20]. These weldings are only applicable for the square hollow section. They are ineffective for the circular hollow section because of the difficulty of welding the semi-circle parts into a perfect circular hollow section. Apart from that, the failure of the plate-by-plate welding method is followed by a weld crack [21].

For the circular hollow sections, continuous welding of stiffeners from inside the tube is almost impossible due to the limited workability of the welding techniques inside a hollow circular tube. Previous research used an innovative method to weld the plate stiffeners attached to the inner surface of the steel tube from the outside punctured holes [22]. This technique applies to the square hollow section steel tubes and circular hollow section steel tubes. Welding from outside the punctured holes can avoid the weld crack problem and the difficulties in welding internal plate stiffeners.

Yuan, Huang, and Chen [17] conducted a parametric study and found that the optimal ratio for the stiffener width to outer steel tube width for a slender CFST is 0.25. The ultimate strength of the CFST increased when the ratio reached 0.25 and decreased after exceeding 0.25. Similarly, research on stiffened CFDST showed that using wider steel stiffeners reduced the effective cross-section area of concrete (Figure 2). The greater stiffener width has a negative impact on the ultimate load capacity of the column [18]. However, there is a lack of study on the stiffener width on the stub CFDST.

Thomas and Sandeep [22] investigated one plate stiffener size but failed to determine the effect of the plate stiffener dimension on the stub CFDST. There is a lack of structural performance and finite element analysis of internally welded plate stiffeners on the outer tube of CFDST structures. Hence, it is essential to investigate the mechanical behaviour and design method of the CFDST column with intermittently welded stiffeners. There is also a lack of experiment or finite element analysis on the square or circular CFDST column with intermittently welded plate stiffeners on the inner surface of the outer steel under axial compression. This research is essential to determine the effect of internally welded plate stiffeners with varying weld spacings on the local buckling of CFDST columns.

This paper discusses the structural characteristics of stub CFDST columns with circular inner and outer steel tubes and square inner and outer steel tubes. The experiment sought to determine the effect of local buckling of 20 column specimens. The experiment was simulated using the finite element technique, which is a proven effective method for investigating the structural characteristics of CFDST columns with stiffeners under axial loading conditions [12,13,16,18]. This method can predict results that cannot be obtained through experiments. It can simulate the different steel and concrete constitutive material model adapted from previous studies. The results of the finite element technique were validated with the available experimental data from Thomas and Sandeep [22]. The parametric study used the validated finite element model to examine the effects of various parameters, such as the dimension of plate stiffener and weld spacing, on the ultimate load behaviour of the CFDST stub columns.

2. Experimental Program

We prepared 20 stub column specimens, one square CFST, one circular CFST, one square unstiffened CFDST, one circular unstiffened CFDST, eight square CFDST with plate stiffeners, and eight circular CFDST with plate stiffeners.

Table 1. Specifications for the square CFDST.

No.	Specimen Designation	Outer Tube			Inner Tube			Plate Stiffener		Weld Spacing	Weld Spacing (mm)	First Hole’s Distance from Bottom (mm)	No. of Holes
		Do (mm)	Bo (mm)	to (mm)	Di (mm)	Bi (mm)	ti (mm)	bs (mm)	ts (mm)
1A	S100	100	100	2.3	-	-	-	-	-	-	-	-	-
2A	S100/32				32	32	2.0	-	-	-	-	-	-
3A	S100/32-18a-10t							18	2.3	10t	23	19	15
4A	S100/32-18a-20t							18	2.3	20t	46	19	8
5A	S100/32-18a-30t							18	2.3	30t	69	7.5	6
6A	S100/32-18a-40t							18	2.3	40t	92	42	4
7A	S100/32-25b-10t							25	2.8	10t	23	19	15
8A	S100/32-25b-20t							25	2.8	20t	46	19	8
9A	S100/32-25b-30t							25	2.8	30t	69	7.5	6
10A	S100/32-25b-40t							25	2.8	40t	92	42	4

and

Table 2. Specifications for the circular CFDST.

No.	Specimen Designation	Outer Tube		Inner Tube		Plate Stiffener		Weld Spacing	Weld Spacing (mm)	First Hole’s Distance from Bottom (mm)	No. of Holes
		Øo (mm)	to (mm)	Øi (mm)	ti (mm)	bs (mm)	ts (mm)
1N	C100	100	2.0	-	-	-	-	-	-	-	-
2N	C100/32			32	2.3	-	-	-	-	-	-
3N	C100/32-18a-10t					18	2.3	10t	20	40	15
4N	C100/32-18a-20t					18	2.3	20t	40	40	8
5N	C100/32-18a-30t					18	2.3	30t	60	30	6
6N	C100/32-18a-40t					18	2.3	40t	80	60	4
7N	C100/32-25b-10t					25	2.8	10t	20	40	15
8N	C100/32-25b-20t					25	2.8	20t	40	40	8
9N	C100/32-25b-30t					25	2.8	30t	60	30	6
10N	C100/32-25b-40t					25	2.8	40t	80	60	4

present the designation and specification of the specimens. The tables describe the specification of the columns (for easier identification, A indicates square CFDST, and N indicates circular CFDST), the shape of the column, the diameter or width of the outer tube, the diameter or width of the inner tube, the plate stiffener width and the weld spacing to tube thickness ratio. The following identification system applies to all specimens.

• The first letter indicates the shape of the column, where S indicates a square column and C is circular.
• The first number is the diameter or width of the outer steel tube, where the number 100 represents 100 mm.
• The following number, 32, is the dimension of the inner steel.
• The number after the hyphen, 18 or 25, is the width of the plate stiffener.
• The alphabet after 18 or 25 is the thickness of the plate stiffener, where a is 2.3 mm and b is 2.8 mm.
• The weld spacing is 10t, 20t, 30t or 40t.

For example, in S100/32-18a-40t, the S refers to square column specimens, the 100 is the 100 mm outer width of the steel tube, 32 is the 32 mm inner width of the steel tube, 18 is the 18 mm plate stiffeners width, and a is the 2.3 mm plate stiffener thickness. The specimens designated S100 and C100 are the CFST, while C100/32 and S100/32 are the unstiffened CFDST. The 10t, 20t, 30t and 40t weld spacing were used to calculate the distance between each weld hole by multiplying 10, 20, 30, or 40 with t₀, which is the thickness of the outer steel tube. For example, 10t indicates multiplying the 10 with the 2.3 mm outer steel thickness to obtain a 23 mm weld spacing. The weld hole spacing calculation is based on Thomas and Sandeep [22].

The height of all columns is 360 mm, and the longitudinal height of the continuous plate stiffeners is 360 mm. The circular specimen has a fixed outer diameter of 100 mm, and a thickness of 2 mm, while the inner tube has a diameter of 32 mm and a thickness of 2.3 mm. The outer height and width of the square specimen are 100 mm, and its thickness is 2.3 mm, while the height and width of the inner tube are 32 mm, and its thickness is 2 mm. The width and thickness of the C100/32-18a-10t to C100/32-18a-40t or S100/32-18a-10t to S100/32-18a-40t plate stiffeners are 18 mm and 2.3 mm, and the width and thickness of the C100/32-25b-10t to C100/32-25b-40t or S100/32-25b-10t to S100/32-25b-40t plate stiffeners are 25 mm and 2.8 mm.

The parameters introduced in this experiment are the shape of the column (circular and square), the dimensions of the plate stiffeners (b_s × t_s = 18 mm × 2.3 mm and 25 mm × 2.8 mm) and the weld spacing (10t, 20t, 30t, and 40t). D₀ and D_i are the outer and inner steel tube width, B₀ and B_i are the outer and inner steel tube breadth, Ø_o and Ø_i are the diameters of the circular steel tube, t₀ and t_i are the outer and inner steel tube thicknesses, b_s is the plate stiffener width, and ‘t_s’ is the plate stiffener thickness. The weld spacing is the spacing between each weld hole. The first weld hole distance from the bottom is the distance of the first weld calculated from the top or bottom of the steel. The number of holes refers to the punctured holes for welding on one side of the steel tube.

Figure 3a,b illustrates the cross-section for the square and circular CFDST with plate stiffener. Figure 4a,b is the side-view of the square and circular CFDST with plate stiffeners and weld spots.

2.1. Material Properties and Fabrication of the Specimens

The concrete cube test showed that the average concrete strength grade is 30.6 MPa. The mix proportion of the concrete to the cement ratio is 1.00:0.54:2.23:1.49 (cement: water:fine aggregate:coarse aggregate).

Table 3. The mix proportion of the sandwiched concrete.

Material	Cement (kg/m3)	Water (kg/m3)	Fine Aggregate (kg/m3)	Coarse Aggregate (kg/m3)	Weight of Concrete (kg)
Quantity	441	256	800	903	2400

presents the mix proportion in kg/m³. The cube tests on the 150 mm × 150 mm × 150 mm specimens were performed on the same day as the testing of the CFDST columns. The Poisson’s ratio of the concrete is 0.2, and 0.3 for the steel. This experiment used an S275 hot-rolled steel grade.

Table 4. Mechanical properties of the steel material.

Material	Young’s Modulus, E(avg) (GPa)	Yield Stress fy (avg) (MPa)	Ultimate Stress fu (avg) (MPa)
Inner steel	208.8	275.1	398.8
Outer steel	209.1	276.3	399.9
Plate stiffener	208.3	274.7	398.5

shows the mechanical properties of steel material from the tensile coupon test.

Figure 5 shows the process flow for fabricating the experimental specimens. First, 6 mm diameter weld holes were drilled on the outer steel of the circular and square steel tubes at weld spacings of 10t, 20t, 30t, and 40t, where the t is the thickness of the outer tube. Figure 6 shows a drawing of a weld spacing with 20t, where the weld spacing is the distance from the midpoint of a weld spot to the next weld spot. The plate stiffeners were placed on the inner surface of the outer tube and welded through the predrilled holes. The inner steel was placed directly in the centre of the outer steel tube, and concrete was poured into the channel between the outer and inner steel. The top and bottom of the specimens were covered with steel plates to obtain a smooth top and bottom surface of the columns. The welding thickness of the grout is about 10 mm.

The test was conducted in Autocon 2000 Digital Console, a 2000-kN capacity compression testing machine. The detail of this machine is displayed in Appendix A. The test specimens were placed directly under the loading plates of the compression machine, and the load was applied gradually until the failure of the CFDST columns. The load cell was connected to the data logger to measure the axial loading of the test specimen. Linear variable displacement transducers (LVDTs) were connected to the computer to record the vertical displacement. The test specimens were placed in the compression machine at a loading rate of 5 kN/s. Figure 7a,b illustrates the detailed test setup and instrumentation for typical square and circular specimens.

2.2. Experimental Results and Discussions

Figure 8a,b shows the failure deformation patterns for all test specimens. The black circles indicate local buckling deformation failure curves. For easier reference to the deformation in Figure 8a,b, all specimens have a number marked on the column. The letter A indicates a square column, and N is a circular column. The numbering is cross-referenced in

Table 5. Experimental result.

No.	Specimen Designation	Pu,Exp (kN)	Strength Ratio (%)	Location of Buckle *
1A	S100	534	-	A
2A	S100/32	592	10.9	A
3A	S100/32-18a-10t	841	57.5	A
4A	S100/32-18a-20t	832	55.8	C
5A	S100/32-18a-30t	816	52.8	C
6A	S100/32-18a-40t	789	47.8	B + C
7A	S100/32-25b-10t	822	53.9	B
8A	S100/32-25b-20t	786	47.2	C
9A	S100/32-25b-30t	778	45.7	B
10A	S100/32-25b-40t	762	42.7	C
1N	C100	516	-	A + B
2N	C100/32	565	9.50	A + B
3N	C100/32-18a-10t	779	51.0	A + B
4N	C100/32-18a-20t	762	47.7	A + B
5N	C100/32-18a-30t	745	44.4	A + B
6N	C100/32-18a-40t	731	41.7	A + B
7N	C100/32-25b-10t	748	45.0	A + B
8N	C100/32-25b-20t	736	42.6	A + B
9N	C100/32-25b-30t	704	36.4	A + B
10N	C100/32-25b-40t	699	35.5	A

Location of Buckle * = A: Elephant foot buckling. B: Mid-height local buckling. C: Quarter-height local buckling.

, which tabulates the ultimate load (P_u,_Exp) and the calculated strength ratio of the specimens. C100 and S100 are the control specimens and the denominators in the calculation of the strength ratio. The strength ratio is calculated by dividing the ultimate load of each specimen by C100 or S100 and multiplying it by 100 to achieve the improvement percentage.

The impact of the CFDST with a plate stiffener on the ultimate load was determined by comparing the CFDST without a plate stiffener with the control CFST, followed by comparing the CFDST with a plate stiffener with the control CFST. Table 5 shows that the CFDST with plate stiffeners has a higher ultimate load than the CFDST without stiffeners and CFST. The additional confinement effect provided by the plate stiffener increased the ultimate load capacity of the CFDST. The plate stiffener also increased the volume of steel ratio for the whole stiffened CFDST column. Therefore, welding plate stiffeners to the outer steel tube of the CFDST have a significant impact on the ultimate load of the CFDST.

The variation in the ultimate load of the square and circular CFDST decreased with greater weld spacing. Figure 9 shows the variation in weld spacing at an increment of 10t. The ultimate load of the CFDST decreased with greater weld spacing because the reduced weld spacing imparts greater stiffness to the tube walls and delays the local buckling of the tube [22]. Therefore, the weld spacing of plate stiffeners has a significant impact and must be considered in CFDST design.

Figure 10 and Figure 11 show that the unstiffened CFST and CFDST have a shorter average displacement length for the ultimate load to occur compared to the stiffened CFDST, indicating that the CFDST with plate stiffeners was able to delay the ultimate peak load of the square and circular column specimens. The load-displacement curves show that the ultimate load of most square specimens declined drastically after reaching its peak, while the decline for circular specimens occurred gradually. The ultimate load of the basic circular CFDST (C100/32) was at a displacement of 5.2 mm, while the circular CFDST columns with welded plate stiffeners achieved the ultimate load at an average displacement of 16.1 mm, a 210% delayed point of the ultimate load relative to the unstiffened circular CFDST. The ultimate load of the unstiffened square CFDST (S100/32) was at a displacement of 3.1 mm, while the square CFDST column with welded plate stiffeners achieved the ultimate load at an average displacement of 5.43 mm, a 75% delayed point of the ultimate load relative to the unstiffened square CFDST. The welded plate stiffeners extended the delay in the buckling failure of the columns. The experimental results showed that the circular stiffened CFDST was better at delaying buckling failure than the square stiffened CFDST. This phenomenon can be attributed to the poor confinement effectiveness of the square shape CFDST due to the high-stress concentration at its sharp corners [21], causing the outer steel tube to buckle and reducing the lateral confinement strength of the concrete.

In Table 5, the alphabet A indicates that the elephant foot buckling occurred at the top and bottom of the column (L/8), B indicates local buckling at the mid-height section (L/2), C means a local buckling at the quarter-height of the column section (L/4), and L is the length of the column. Figure 8a shows that all circular column specimens deflected slightly to the left or right. Figure 8b shows that the square column specimens remain straight after the compression test. Only specimen S100/32-25b-10t and S100/32-25b-30t exhibited an apparent local buckling at the mid-height section. The S100, S100/32, and S100/32-18a-10t specimens underwent elephant foot buckling at the top, and the remaining specimens showed local buckling at the top or bottom sections.

Table 6. Comparison of the 18 mm and 25 mm plate stiffeners.

Group *	Specimen	Pu (kN)	Strength Reduction Every 10t (%)	Cumulative Strength Reduction (%)
G1	C100/32-18a-10t	779	-	-
	C100/32-18a-20t	762	2.18	2.18
	C100/32-18a-30t	745	2.23	4.36
	C100/32-18a-40t	731	1.88	6.16
	Average		2.10
	S100/32-18a-10t	841	-	-
	S100/32-18a-20t	832	1.07	1.07
	S100/32-18a-30t	816	1.92	2.97
	S100/32-18a-40t	789	3.31	6.18
	Average		2.10
G2	C100/32-25b-10t	748	-	-
	C100/32-25b-20t	736	1.60	1.60
	C100/32-25b-30t	704	4.35	5.88
	C100/32-25b-40t	699	0.71	6.55
	Average		2.22
	S100/32-25b-10t	822	-	-
	S100/32-25b-20t	786	4.38	4.38
	S100/32-25b-30t	778	1.02	5.35
	S100/32-25b-40t	762	2.06	7.30
	Average		2.48

Group * = G1; 18 mm width of the stiffener. G2; 25 mm width of the stiffener.

shows the strength reduction for 10t as the control specimen. G1 is the CFDST with an 18 mm wide stiffener, and G2 is the CFDST with a 25 mm wide stiffener. With each 10t increase, the 18 mm stiffener produced a more consistent result with an average strength reduction percentage of 2.10% for the circular and square CFDST. For the 18 mm stiffener, the reduced cumulative strength of the circular and square columns from 10t to 40t was 6.16% and 6.18%. For every 10t increase, the 25 mm stiffener showed less predictable results with an average of 2.22% and 2.48% reduced cumulative strength for the circular and square CFDST. For the 25 mm stiffener, the cumulative strength reduction from 10t to 40t is 6.55% and 7.30% for the circular and square specimens.

Generally, the experimental results showed that the 18 mm stiffener contributed to a more significant strength improvement of the circular and square specimen than the 25 mm stiffener. The 18 mm stiffener showed a more consistent result and had a higher impact on the ultimate load capacity of the CFDST column.

3. Finite Element Modelling

This study employed ABAQUS [23] to develop the finite element model of the stub CFDST column with plate stiffeners. The finite element model is used to perform a nonlinear analysis and determine the load-displacement performance and nonlinear buckling of the stub CFDST column. This section discusses the material model, interaction surfaces, loading, boundary conditions and element mesh used for the ABAQUS technique. The finite element analysis ignored the geometric imperfection because the infill concrete reduces the effect of the geometric imperfections [24]. The finite element modelling is essential to analyse the impact of the plate stiffeners’ welding spacing on the CFDST columns.

Table 7. Details of the finite element modelling.

Parts	Concrete	Outer Steel Tube	Inner Steel Tube	Stiffener
Element type	C3D8R	S4R	S4R	C3D8R
Mesh size (mm)	12	12	12	12
Material behaviour	Drucker Prager	Deformation Plasticity	Deformation Plasticity	Deformation Plasticity
Interaction surface	Slave	Master	Master	Slave
Constraint	-	Tie—Master	-	Tie—Slave
Steps	Static, General with Nlgeom stabilization
Iteration	Newton-Raphson with increment size of minimum 0.01 to maximum 1
Interaction type	Surface-to-surface contact
Contact property	Friction Coefficient of 0.6 with “Hard Contact”
Boundary condition	Loading surface—Displacement/Rotation on Z-direction Bottom surface—pinned support

summarises the finite element modelling, and Figure 12 shows a symmetrical view cut y-z plane of the finite element modelling.

3.1. Elements and Mesh Size

The concrete and plate stiffeners were modelled using three-dimensional eight-node solid elements with reduced integration (C3D8R) because the sandwiched concrete deformation in the composite column subjected to axial compressive force is predominantly compression without rotation. Because of the applied “tie” constraint to simulate the welding on the surface of the steel tube, the C3D8R element is necessary to analyse the contact surface. The outer and inner steel tubes were modelled using a four-node general-purpose shell, reduced integration (S4R) to simulate the buckling effect of the CFDST column, similar to the study by Wang, Young and Gardner [25]. All parts of the CFDST columns in the model have the same mesh size, where the global mesh size of the outer steel tube, inner steel tube, plate stiffeners and concrete infill is 12 mm. The connection between the circle weld hole and rectangular stiffener will induce non-convergence problems. Thus, the diameter of the weld hole was designed as rectangular in a finite element that only considered the contact surface of plate stiffeners to the steel tube to reduce the complexity and prevent non-convergence problems.

3.2. Concrete Stress–Strain Model

The outer and inner steel tubes of the CFDST contribute to the confining pressure of the infill concrete. The mechanical behaviour of concrete was modelled using the Drucker Prager model, where the angle of friction, flow stress ratio and dilation angle for the material constants in the Drucker Prager model were 20°, 0.8, and 30 [26]. This study used a constraint coefficient, ξ, to describe the composite action between the steel tube and the core concrete. The constraint coefficient is as follows [27,28]:

$$\xi =A_s{f}_y/A_{ce}{f}_{ck}$$

(1)

where A_s is the cross-section area of the steel, f_y is the yield strength of the steel, A_ce is the gap area inside the section of the outer steel tube, and f_ck is the cylinder strength of the concrete.

The plate stiffeners influence the bonding of the core concrete and thus affect the ultimate load. Therefore, it is essential to correct the stress and strain of the unconfined concrete to generate a good finite element result. The formula for the concrete correction is given by the following regression analysis [18]:

$$f_c=\left({\xi }^{0.2}{k}^{0.71}\right)f_{cu}$$

(2)

$${\epsilon }_c=1.26{\xi }^{0.2}\left(\epsilon +800{\xi }^{0.2}\times {10}^{-6}\right)$$

(3)

where f_c is the corrected stress of the unconfined concrete and ε_c is the corrected strain of the unconfined concrete. ε is 0.003, k is the correction coefficient of the cross-section area of the core concrete, k = (A_cor/A_c)^0.7, and A_cor is the effective cross-section area of the concrete, as shown in Figure 2. A_c is the total cross-section area of the concrete, and f_cu is the characteristic strength of cube concrete (f_cu = 0.67f_ck).

The equivalent compression stress–strain relationship for the concrete was adopted from Pagoulatou et al. [29] and input into the ‘Drucker Prager Hardening’ suboption in the ABAQUS. The stress–strain curve is necessary for an accurate simulation of the loading curve of the CFDST columns. The following equations, which have long been used for confined concrete as suggested by Mander, Priestley and Park [30], were applied to the concrete in the CFDST columns.

$$f_{cc}=f_c+k_1{f}_1 \left(MPa\right)$$

(4)

$${\epsilon }_{cc}={\epsilon }_c(1+k_2\frac{f_1}{f_c})$$

(5)

where f_cc and ε_cc are the confined stress and strain, k₁ and k₂ are fixed constraints equal to 4.1 and 20.5 as proposed by Richart, Brandtzæg and Brown [31], and f₁ is the lateral pressure on the concrete caused by the outer and inner steel tube confinement. This study used the equation proposed by Hu and Su [32], which includes the influence of the outer and inner tubes to calculate the pressure.

Equation (6) gives the lateral pressure on the circular hollow section

$$f_1=8.525-0.166\left(\frac{D_0}{t_0}\right)-0.00897\left(\frac{D_i}{t_i}\right)+0.00125{\left(\frac{D_0}{t_0}\right)}^2+0.00246\left(\frac{D_0}{t_0}\right)\left(\frac{D_i}{t_i}\right)-0.00550{\left(\frac{D_i}{t_i}\right)}^2\ge 0$$

(6)

Equation (7) gives the lateral pressure on the square hollow section.

$$f_1=8.525-0.166\left(\frac{B_0}{t_0}\right)-0.00897\left(\frac{B_i}{t_i}\right)+0.00125{\left(\frac{B_0}{t_0}\right)}^2+0.00246\left(\frac{B_0}{t_0}\right)\left(\frac{B_i}{t_i}\right)-0.00550{\left(\frac{B_i}{t_i}\right)}^2\ge 0$$

(7)

where D₀ is the diameter of the outer tube, D_i is the diameter of the inner tube, B₀ is the width of the outer tube, B_i is the width of the inner tube, t₀ is the thickness of the outer tube, and t_i is the thickness of the inner tube.

The concrete model exhibits linear formation up to 0.5f_cc. The following equation is used to predict the nonlinear behaviour [33]:

$$f=\frac{E_{cc}\epsilon }{1+(R+R_E-2\left(\frac{\epsilon }{{\epsilon }_{cc}}\right)-\left(2R-1\right){\left(\frac{\epsilon }{{\epsilon }_{cc}}\right)}^2+R{\left(\frac{\epsilon }{{\epsilon }_{cc}}\right)}^3}\left(\mathrm{MPa}\right)$$

(8)

where the modulus of elasticity, E_cc, is given by ACI [34]. R and R_E are given by the following equations.

$$E_{cc}=4700\sqrt{f_{cc}}\left(\mathrm{MPa}\right)$$

(9)

$$R_E=\frac{E_{cc}{\epsilon }_{cc}}{f_{cc}}$$

(10)

$$R=\frac{R_E\left(R_{\sigma }-1\right)}{{\left(R_{\sigma }-1\right)}^2}-\frac{1}{R_{\epsilon }}$$

(11)

where R_σ and R_E are equal to four [35]. In this study, the Poisson’s ratio, ν, is 0.2. The expression rk₃f_cc estimates the last point of the descending region in the concrete stress–strain curve. This term considers the final stress value before failure and corresponds to a strain value of about 11ε_cc. Equations (12) and (13) for calculating the k₃ for circular and square hollow sections are as follows.

$$k_3=1.73916-0.00862\left(\frac{D_0}{t_0}\right)-0.04731\left(\frac{D_i}{t_i}\right)-0.00036{\left(\frac{D_0}{t_0}\right)}^2+0.00134\left(\frac{D_0}{t_0}\right)\left(\frac{D_i}{t_i}\right)-0.00058{\left(\frac{D_i}{t_i}\right)}^2\ge 0$$

(12)

$$k_3=1.73916-0.00862\left(\frac{B_0}{t_0}\right)-0.04731\left(\frac{B_i}{t_i}\right)-0.00036{\left(\frac{B_0}{t_0}\right)}^2+0.00134\left(\frac{B_0}{t_0}\right)\left(\frac{B_i}{t_i}\right)-0.00058{\left(\frac{B_i}{t_i}\right)}^2\ge 0$$

(13)

According to Pagoulatou et al. [29], Equations (12) and (13) are valid only when multiplied by the reduction factor, r, which can be accepted as 1 for concrete cubes with strengths up to 30 MPa, as validated by Giakoumelis and Lam [36], and 0.5 for concrete cube strengths greater or equal to 100 MPa following Mursi and Uy [37]. The linear interpolation technique is for concrete cubes with strengths of between 30 and 100 MPa. Figure 13 shows the shape of the concrete stress–strain curve.

3.3. Steel Stress–Strain Model

According to Elchalakani et al. [38], the Ramberg–Osgood model gives the stress–strain relationship for an accurate simulation of steel tubes and has been used in recent studies [39,40]. In the FE analysis, the steel material is considered an elastic material until its yield stress, and after that, it is simulated as a plastic material. Table 4 presents the material properties of the steel. In this study, the Poisson’s ratio, ν, is 0.3. Figure 14 shows the steel stress–strain curve. The equivalent stress–strain relationship for the steel model was input in the Deformation Plasticity option in ABAQUS.

3.4. Interaction and Surfaces

The interactions comprise four components, outer steel, inner steel, concrete and plate stiffeners. According to Pagoulatou et al. [29], the slave surface cannot penetrate the master surface. Therefore, this study defined the interaction between the steel tubes and the concrete infill by treating the surface where the steel tubes and the plate stiffeners as the master surfaces and the concrete infill as the slave surface. The surface-to-surface interaction was applied in ABAQUS. The normal behaviour was the hard contact for the interaction properties, and the tangential behaviour was the penalty friction coefficient of 0.6 for the interaction between carbon steel and concrete [7,41].

3.5. Steps, Loading and Boundary Conditions

This study applied the static, general solution as the steps to the finite element modelling. The loading conditions were applied using the boundary conditions of each cross-section. The pinned support is the bottom part of the CFDST, and the lateral displacements in the x and y directions of the top part of the CFDST were 0.

3.6. Verification of the Finite Element Model

This study selected three models from previous experiments on circular concrete-filled steel tubular columns (CFST) with intermittently welded plate stiffeners from Thomas and Sandeep [22] and modelled them in ABAQUS to verify the technique employed in this work. The previous study used a varying number of stiffeners [22], while this study used a fixed number of four plate stiffeners for each CFDST column. The comparison of the experimental observations with the modelled results was based on three parameters, the ultimate capacities, axial load–strain curves and final deformation of the specimens.

Table 8. Comparison of the finite element model with the experimental results.

Authors	Specimen	Pu,Exp (kN)	Pu,FEM (kN)	$\frac{{\mathit{N}}_{\mathit{u},\mathit{E}\mathit{x}\mathit{p}}}{{\mathit{N}}_{\mathit{u},\mathit{F}\mathit{E}\mathit{A}}}$
Present study	S100	534	527	1.01
	S100/32	592	580	1.02
	S100/32-18a-10t	841	841	1.00
	S100/32-18a-20t	832	801	1.04
	S100/32-18a-30t	816	778	1.05
	S100/32-18a-40t	789	767	1.03
	S100/32-25b-10t	822	834	0.99
	S100/32-25b-20t	786	812	0.97
	S100/32-25b-30t	778	769	1.01
	S100/32-25b-40t	762	758	1.01
	C100	516	483	1.07
	C100/32	565	541	1.04
	C100/32-18a-10t	779	732	1.07
	C100/32-18a-20t	762	724	1.05
	C100/32-18a-30t	745	723	1.03
	C100/32-18a-40t	731	720	1.02
	C100/32-25b-10t	748	718	1.04
	C100/32-25b-20t	736	716	1.03
	C100/32-25b-30t	704	702	1.00
	C100/32-25b-40t	699	697	1.00
[22]	C90-3S-10	461	482	0.96
	C117-4S-50	653	701	0.93
	C90-5S-35	476	510	0.93
Mean				1.01
Std. deviation				0.04

compares the ultimate load of the specimens from the experimental data with the finite element analysis model in ABAQUS. There is a good agreement between the ultimate loads (P_u,_Exp) from the experimental data and those from the finite element analysis (P_u,_FEM). The finite element modelling of two CFST, two CFDST, 16 stiffened CFDST from the present study and three CFST stub columns from Thomas and Sandeep [22] gave a mean ratio, P_u,_Exp/P_u,_FEM, of 1.01 and a standard deviation of 0.04. The experiment tested 23 column specimens and analysed three parameters (shape of the specimens, dimension of the plate stiffeners and weld spacing) under axial loading. Generally, the finite element technique generated an accurate model for the ultimate load of the tested specimens.

Figure 10a–j and Figure 11a–j show the load curve for the finite element model, where the curves for the finite element models are similar to the experimental curve. The finite element curve could simulate most of the load–displacement behaviour for CFDST with plate stiffener welded intermittently at varying weld spacings. The finite element model developed in this study could simulate the post-peak load curve for the circular specimens. However, the simulated post-peak load curve for the square specimens was slightly different, possibly because the concrete stress–strain and steel stress–strain models were more relevant for load curves that remain unchanged after the ultimate peak load.

Figure 15a–d compares the failure mode for the square stub CFDST with plate stiffeners. The finite element successfully simulated most of the deformation shapes of the square specimens. Figure 16a–d compares the failure mode for the circular stub CFDST with plate stiffeners, where the finite element successfully simulated most of the deflection shape for the circular specimens. Except for the elephant foot buckling and deflection of the entire column, there was barely any local buckling in the middle section of the circular stub CFDST specimens. Tao, Wang and Yu [24] obtained similar results and stated that it is more challenging to produce a local buckling effect in a finite element modelling for circular stub CFST. Generally, the deformation shape of the finite element model was consistent with the experimental deformation shown in Figure 8. Therefore, the simulated failure modes verify the accuracy of the finite element model.

4. Parametric Study

The parametric study used a finite element model to determine the performance of stub CFDST with welded stiffener subjected to axial load. The parameters examined are the stiffener width, stiffener thickness and weld spacing.

Table 9. Geometric and material properties of the stiffened square CFDST stub column for the parametric study.

Specimen Designation	Outer Tube (mm)			Inner Tube (mm)			Plate Stiffener (mm)		Weld Spacing	Weld Spacing (mm)	First Hole’s Distance from Bottom (mm)	No. of Holes	Pu (kN)
	Do	Bo	to	Di	Bi	ti	bs	ts
S100/32-18b-10t	100	100	2.3	32	32	2.0	18	2.8	10t	23	19	15	863
S100/32-18b-20t							18	2.8	20t	46	19	8	815
S100/32-18b-30t							18	2.8	30t	69	7.5	6	792
S100/32-18b-40t							18	2.8	40t	92	42	4	789
S100/32-25a-10t							25	2.3	10t	23	19	15	808
S100/32-25a-20t							25	2.3	20t	46	19	8	799
S100/32-25a-30t							25	2.3	30t	69	7.5	6	759
S100/32-25a-40t							25	2.3	40t	92	42	4	749
S100/32-12a-10t							12	2.3	10t	23	19	15	786
S100/32-12a-20t							12	2.3	20t	46	19	8	760
S100/32-12a-30t							12	2.3	30t	69	7.5	6	753
S100/32-12a-40t							12	2.3	40t	92	42	4	742
S100/32-12b-10t							12	2.8	10t	23	19	15	812
S100/32-12b-20t							12	2.8	20t	46	19	8	775
S100/32-12b-30t							12	2.8	30t	69	7.5	6	761
S100/32-12b-40t							12	2.8	40t	92	42	4	752
S100/32-12a-60t							12	2.3	60t	138	42	3	721
S100/32-18a-60t							18	2.3	60t	138	42	3	755
S100/32-25a-60t							25	2.3	60t	138	42	3	733
S100/32-12b-60t							12	2.8	60t	138	42	3	730
S100/32-18b-60t							18	2.8	60t	138	42	3	777
S100/32-25b-60t							25	2.8	60t	138	42	3	746
S100/32-12a-90t							12	2.3	90t	207	76.5	2	697
S100/32-18a-90t							18	2.3	90t	207	76.5	2	749
S100/32-25a-90t							25	2.3	90t	207	76.5	2	717
S100/32-12b-90t							12	2.8	90t	207	76.5	2	707
S100/32-18b-90t							18	2.8	90t	207	76.5	2	759
S100/32-25b-90t							25	2.8	90t	207	76.5	2	725

and

Table 10. Geometric and material properties of the stiffened circular CFDST stub column for the parametric study.

Specimen Designation	Outer Tube (mm)		Inner Tube (mm)		Plate Stiffener (mm)		Weld Spacing	Weld Spacing (mm)	First Hole’s Distance from Bottom (mm)	No. of Holes	Pu (kN)
	Øo	to	Øi	ti	bs	ts
C100/32-18b-10t	100	2.0	32	2.3	18	2.8	10t	20	40	15	753
C100/32-18b-20t					18	2.8	20t	40	40	8	749
C100/32-18b-30t					18	2.8	30t	60	30	6	736
C100/32-18b-40t					18	2.8	40t	80	60	4	724
C100/32-25a-10t					25	2.3	10t	20	40	15	694
C100/32-25a-20t					25	2.3	20t	40	40	8	692
C100/32-25a-30t					25	2.3	30t	60	30	6	690
C100/32-25a-40t					25	2.3	40t	80	60	4	686
C100/32-12a-10t					12	2.3	10t	20	40	15	670
C100/32-12a-20t					12	2.3	20t	40	40	8	667
C100/32-12a-30t					12	2.3	30t	60	30	6	660
C100/32-12a-40t					12	2.3	40t	80	60	4	657
C100/32-12b-10t					12	2.8	10t	20	40	15	696
C100/32-12b-20t					12	2.8	20t	40	40	8	693
C100/32-12b-30t					12	2.8	30t	60	30	6	689
C100/32-12b-40t					12	2.8	40t	80	60	4	681
C100/32-12a-60t					12	2.3	60t	120	60	3	638
C100/32-18a-60t					18	2.3	60t	120	60	3	708
C100/32-25a-60t					25	2.3	60t	120	60	3	669
C100/32-12b-60t					12	2.8	60t	120	60	3	670
C100/32-18b-60t					18	2.8	60t	120	60	3	724
C100/32-25b-60t					25	2.8	60t	120	60	3	687
C100/32-12a-90t					12	2.3	90t	180	90	2	629
C100/32-18a-90t					18	2.3	90t	180	90	2	704
C100/32-25a-90t					25	2.3	90t	180	90	2	667
C100/32-12b-90t					12	2.8	90t	180	90	2	666
C100/32-18b-90t					15	2.8	90t	180	90	2	719
C100/32-25b-90t					25	2.8	90t	180	90	2	682

show the details and ultimate strength of the columns. The concrete strength is 30.6 MPa, the steel yield strength is from Table 4, and the column length is 360 mm. This setting ensures a consistent impact of the stiffener dimension and weld spacing on the stiffened CFDST column.

4.1. Effects of Stiffener Width, b_s

This study examined the effect of stiffener width, b_s, on the ultimate strength responses of the square and stiffened circular CFDST columns. The stiffener widths in the parametric study are 12 mm, 18 mm and 25 mm. The examination involved two groups, t_s = 2.3 mm and t_s = 2.8 mm. The fitting lines in Figure 17 show the strength of the square CFDST welded with different b_s values, while those in Figure 18 show the strength of the circular CFDST welded with varying b_s values. The parabolic fit showed greater CFDST strength with higher b_s values, but the strength decreased after exceeding a particular b_s value. This trend in the CFDST strength is similar to that in a study that uses a square CFST with different stiffener widths [17], where the CFDST strength increased because the additional steel stiffener increased the total cross-sectional area of the steel, leading to higher ductility and confinement effects on the CFDST. The higher confinement effect is due to the lower Poisson’s ratio of the concrete compared to the steel. The concrete has a weak tension and cracks easily during failure. The steel has a higher Poisson’s ratio and can sustain more deformation and confine the volume of the concrete. However, the load capacity of the stiffened CFDST column decreases if the b_s value is too high. The reduced strength is due to the reduced effective cross-sectional area of concrete, as shown in Figure 2. As the width of the stiffener increased, the bonding between concrete decreased and reduced the effective cross-sectional area of the concrete subjected to axial load. Even with a longer b_s (more steel area), the concrete lost its bonding strength because the concrete area is divided into more partitions. Thus, the longer b_s defeats the purpose of welding the plate stiffeners to provide confinement to the concrete and reduce the ultimate strength of the CFDST [18]. Therefore, in this study, the effect of stiffener width is significant, and the b_s value should be within a particular range to achieve optimum efficiency.

4.2. Effects of Stiffener Thickness, t_s

The graphs in Figure 19 and Figure 20 show the impact of the t_s value on the axial load–deflection responses of the square and circular CFDST. The parametric study determined the effects of two t_s values, 2.3 mm and 2.8 mm, for three groups, b_s = 12 mm, 18 mm and 25 mm. The parabolic fit in the graphs shows the strength of CFDST welded with different t_s values. The ultimate strength for the parabolic fit of t_s = 2.8 mm is higher than t_s = 2.3 mm for all b_s values. Thicker plate stiffeners produced CFDST with higher ultimate strength because the thicker plate stiffeners increase the cross-sectional area of steel to the stiffened CFDST. The volume of steel for the 2.8 mm stiffener is larger than the 2.3 mm stiffener. Thus, stiffener thickness is crucial in the design of CFDST columns, where higher t_s values produce CFDST with higher ultimate strengths.

4.3. Effects of Weld Spacing

This study determined the effect of weld spacing on the ultimate strength responses of the CFDST by varying the weld spacing. The weld spacings in the parametric study are 10t, 20t, 30t, 40t, 60t and 90t. The parabolic fit in Figure 19 and Figure 20 show that the CFDST has the highest strength at 10t, and the CFDST strength began to decline gradually when the weld spacing was 90t. The gradual decrease in CFDST strength applies to all stiffener sizes. The parabolic fit of the ultimate strength decreased exponentially as the weld spacing approached 90t because the 60t weld spacing has three weld holes, and the 90t has two weld holes. The ultimate strength of the 10t is higher than 20t because 10t has 15 weld holes and 20t has 8 weld holes.

The CFDST with a shorter weld spacing has a higher ultimate strength. The whole stiffeners were welded more rigidly to the CFDST when the weld holes on the CFDST were closer. The rigidity of the CFDST is due to the weld spot resisting the rotation and moment of the stiffener at specific positions. The strength of the CFDST decreased when the weld hole was further apart because the stiffener’s movement increased with greater distance between the weld holes, causing a more extensive deformation in the concrete and weakening the stiffener’s rigidity on the CFDST and the confinement to the concrete. Because of the direct effect of the weld spacing on the ultimate strength of the CFDST, the distance between the weld hole should be shorter to achieve a higher ultimate strength of the CFDST column.

4.4. Effects of Shape on the Strength of the Stiffened CFDST Column

This study investigated three b_s, 12 mm, 18 mm and 25 mm, to determine the effect of the CFDST shape on the column’s ultimate strength. Figure 21 compares the square column to the circular column for a stiffener thickness of t_s = 2.3 mm. Figure 22 compares the square column to the circular column when the stiffener thickness is t_s = 2.8 mm.

Table 11. The difference in the strength of stiffened square CFDST and stiffened circular CFDST.

Dimension of Stiffeners		Square to Circular Strength (%)
ts (mm)	bs (mm)
2.3	12	13.7
2.3	18	8.78
2.3	25	11.3
Average		11.3
2.8	12	10.8
2.8	18	8.83
2.8	25	10.5
Average		10.0

shows the difference in the sum and average ultimate strength of the square and circular CFDST columns. Based on the bar charts and the table, we can conclude that the average ultimate strength of the square column is 11.3% higher than the circular column when t_s = 2.3 mm, and when t_s = 2.8 mm, the square CFDST column has an average of 10.0% higher ultimate strength than the circular CFDST column. Generally, the square CFDST column has higher ultimate strength than circular CFDST for all plate stiffener sizes. The higher ultimate strength is due to the concrete, which is the main component, being able to bear the compression because of the presence of the granite aggregates. The higher the cross-section area of the concrete, the larger the volume of concrete subject to compressive load. The higher concrete volume in the square column increases its ultimate strength relative to the circular CFDST. However, the capacity strength per unit cross-sectional area shows that the square column with an area of 9216 mm² has an average strength of 0.0835 kN/mm². The circular column with an area of 7264 mm² has an average strength of 0.0957 kN/mm². Thus, the capacity strength per unit cross-sectional area for circular columns is higher even though it has a smaller cross-sectional area than the square column. Because of the significance of the shape of the CFDST, it is essential to consider the cross-section area of the cross-sectional area of the stiffened CFDST when designing CFDST columns.

5. Conclusions

This study tested twenty stub columns comprising one unstiffened square CFST, one unstiffened circular CFST, one unstiffened square CFDST, one unstiffened circular CFDST, eight square CFDST with plate stiffeners, and eight circular CFDST with plate stiffeners under axial loading. The study measured the mechanical behaviour of the specimens, including the failure mode, ultimate load and load–deformation relation. The finite element model was used to replicate the specimen performance and deformation. The parametric test in this study employed the technique from the finite element result. The following is a summary of the test results and analysis.

(1)

The CFDST with the plate stiffeners welded intermittently showed significant improvement in its ultimate load capacity relative to the CFST. The square specimen with a 10t weld spacing showed a maximum ultimate load increase of 57.5% for an 18 mm stiffener width and 53.9% for a 25 mm stiffener width. The circular specimen with a 10t weld spacing showed a maximum ultimate load increase of 51.0% for an 18 mm stiffener width and 45.0% for a 25 mm stiffener width.

(2)

The 18 mm × 2.3 mm stiffener showed a reduced cumulative strength when the weld spacing was increased from 10t to 40t. The circular and square columns showed similar cumulative strength reductions of 6.16% and 6.18%. For the 25 mm × 2.8 mm stiffener, increasing the weld spacing from 10t to 40t resulted in a 6.55% total strength reduction of the circular column and 7.30% total strength reduction of the square column.

(3)

The circular CFDST columns with welded plate stiffeners showed a 210% delay in the point of the ultimate load relative to the unstiffened circular CFDST. The square CFDST columns with welded plate stiffeners showed a 75% delay in the point of the ultimate load relative to the unstiffened square CFDST. However, the square specimen exhibited a sharp decline in load capacity after reaching its ultimate peak load. In contrast, the circular specimens showed a more gradual decline after their ultimate peak loads.

(4)

The good agreement of the experimental and finite element models validated the accuracy of the proposed finite element model in determining the ultimate peak load, load–displacement curve and deformation shape of the columns. The statistical analysis of 18 CFDST and 5 CFST stub columns showed that the mean ratio, P_u,_Exp/P_u,_FEM, is 1.01, and the standard deviation is 0.04.

(5)

The parametric study revealed that closer weld spacing increased the strength of the stiffened CFDST. The plate stiffener is significant in the ultimate strength of the stiffened CFDST. A stiffener width of 18 mm is preferable over the stiffener width of 12 mm, 18 mm and 25 mm to achieve optimum strength of CFDST.

Future studies should test more experimental data using different stiffener sizes to investigate the optimum effect on the ultimate strength of the stiffened CFDST, especially the dimensions not tested in the parametric study of the present research. There is also a lack of mathematical prediction for calculating the effect of weld spacing on the ultimate load of stiffened CFDST.