Axial Compression Performance of L-Shaped Partially Encased Steel–Concrete Composite Stub Columns

Abstract

The L-shaped partially encased steel–concrete composite (PEC) stub column, composed of profile steel, concrete, and transverse links, tends to occupy less space than the rectangle-shaped PEC column when used as side or corner columns. In this study, an axial compression test involving three L-shaped PEC stub columns was conducted to investigate the influence of critical factors on axial compression performance. The test results indicated that the axial compression capacity can be effectively enhanced with an increase in material strength. Furthermore, finite element (FE) analysis was carried out with parameters such as material strength, steel thickness, transverse link spacing, transverse link diameter, transverse link distribution, and longitudinal rebar diameter. The results revealed that the primary failure modes of L-shaped PEC columns were concrete spalling and local buckling of the flange. Additionally, it was found that the increase in steel strength, steel thickness, and transverse link diameter, as well as the decrease in transverse link spacing, significantly improved the axial compression capacity and concrete confinement effect. However, an increase in concrete strength diminished the concrete confinement effect. Additionally, the accuracy of the axial compression capacity calculation methods in the Eurocode 4 and T/CECS719-2010 specifications for L-shaped PEC stub columns was verified. Finally, a calculation method based on the superposition principle incorporating the concrete confinement effect was proposed, and validated by comparing with experimental and FE results. Overall, this study could provide a theoretical basis for the engineering application of L-shaped PEC columns.

1. Introduction

Partially encased steel–concrete composite (PEC) structure, one of the innovative composite structures, has been widely used in engineering practice due to its simple construction, excellent material coordination, and diverse forms. As shown in Figure 1, PEC columns and steel cellular beams were used in an office building of Zhejiang University, which makes the structure one of the most prefabricated buildings in China [1]. The PEC components are composed of profile steel, concrete, and transverse links, as displayed in Figure 2. The cross-sectional forms of PEC columns include rectangular sections and special-shaped sections, such as cruciform, T-shaped, L-shaped, and octagonal, which are shown in Figure 3.

A few investigations have been conducted on PEC columns with rectangular sections. Tremblay et al. [2,3] conducted experimental studies, analyzed the failure modes of PEC columns considering parameters such as the steel thickness and material characteristics, and proposed a calculation formula to predict the axial compression capacity. Chicoine et al. [4,5] analyzed the effects of concrete strength and transverse link spacing, revealing that reducing transverse link spacing could prevent local buckling of the flange. Begum et al. [6,7] used finite element analysis to explore various factors that affect axial compression capacity, finding that local defects and residual stress exhibited a minor impact, while transverse links effectively reduce local buckling of the flange. Chen [8] investigated the influence of different reinforcement measures on PEC columns under axial and cyclic horizontal loads. The results showed that PEC columns performed well, and the impact of longitudinal rebars and stirrups on bearing capacity was minimal. Song [9,10] studied the global buckling, local buckling, and post-buckling behavior of PEC columns, finding that the influence of local buckling became insignificant as the slenderness ratio increased. Lin [11] explored the global buckling behavior of PEC columns under axial and eccentric loads, proposing design formulas for global stability. Chuan et al. [12] and Li et al. [13] investigated the effects of various transverse link configurations on PEC components, and the results showed that improved design of transverse links could enhance the constraint on the flange.

Theoretical analysis [14,15,16] demonstrated that steel in PEC columns exerted a constraining effect on the concrete, dividing the constrained area into highly and partially constrained zones. Liu et al. [17] explored the effects of flange width-to-thickness ratio and transverse link spacing on the distribution of constrained concrete areas. Experimental and numerical analysis [18,19,20] assessed the impact of different characteristics on performance and highlighted the suitability of PEC columns in seismic design. Related fire resistance tests were conducted [21,22,23], and the test results exhibited good structural response and economic benefits of PEC columns under fire conditions.

Recent investigations have focused on PEC columns with special cross-sections. Li et al. [24] conducted experiments on cruciform PEC columns, proposing methods to classify confinement regions and determine concrete confinement coefficients. Tao et al. [25] studied the mechanical behavior of T-shaped PEC columns under axial loading, revealing that the steel thickness and transverse link spacing significantly affected the axial compression capacity of the columns. Zhan et al. [26,27] observed that the aspect ratio of the cross-section exhibited a distinct impact on the stability of L-PEC columns. Jamkhaneh [15] explored the behavior of octagonal PEC columns under axial and bending loads through experiments and finite element analysis, showing that stirrups exhibited a limited impact on the flexural strength of the columns.

However, research on the axial compression capacity of L-shaped PEC stub columns remains insufficient. In this study, an axial compression test involving three L-shaped PEC stub columns was conducted, analyzing failure modes and the effects of material strength on axial compression behavior and bearing capacity. Then, finite element modeling was used to further analyze the effects of more parameters. Additionally, based on the experimental and finite element results, this study explored the applicability of axial compression capacity calculation formulas in relevant specifications for L-shaped PEC columns. Eventually, a calculation method based on the superposition principle considering the enhancement of concrete strength is proposed, which can be a theoretical basis for the engineering application of L-shaped PEC columns.

2. Experimental Investigation

2.1. Details of Columns

A total of three L-shaped PEC (LPEC) stub columns were designed and tested, which were composed of profile steel, concrete, transverse links, and internal stiffeners. Detailed information is shown in Figure 4. To ensure uniform stress distribution across the cross-section, 30 mm thick end plates were welded at both ends of the columns, and 10 mm thick internal stiffeners were welded 100 mm away from the ends to prevent end failure of columns. Transverse links, each with a diameter of 8 mm, were arranged at a spacing of 100 mm in the area between the internal stiffeners and were welded on the steel. The thicknesses of the flange and web were both 6 mm. To investigate the influence of material strength on the axial compression performance of LPEC columns, different materials were selected for comparison. The materials of test specimens are shown in

Table 1. Material of test specimens.

Specimen Label	Concrete	Steel
LPEC-1	C25	Q290
LPEC-2	C30	Q290
LPEC-3	C30	Q345

.

2.2. Material Properties

2.2.1. Steel

The profile steel used in test specimens was of two grades: Q290 and Q345, which comply with the requirements of GB/T 228.1-2021 [28]. Samples were taken from the web and flange, respectively, for tensile testing. The average yield strength of the Q290 steel plate was measured to be 295.37 MPa, with an ultimate strength of 478 MPa and an average elastic modulus of 208 GPa. Similarly, the average yield strength of the Q345 steel plate was 355.54 MPa, with an ultimate strength of 563 MPa and an average elastic modulus of 209 GPa. The transverse links were made of HPB300 rebars, and the average yield strength of rebar samples taken from transverse links was measured to be 296.16 MPa, with an ultimate strength of 461 MPa and an average elastic modulus of 208 GPa.

2.2.2. Concrete

The self-compacting concrete had two nominal strengths: 25 MPa and 30 MPa. When casting the concrete of test specimens, six 150 mm × 150 mm × 150 mm cubic test blocks were made for each of the two grades. These test blocks were cured under the same conditions as the columns for 28 days. Then, in accordance with the GB/T 50081-2019 [29], the compressive strength and elastic modulus were tested. The measured average compressive strength of the C25 cubes was 27.10 MPa, with an average elastic modulus of 27.32 GPa. For the C30 cubes, the measured average compressive strength was 29.25 MPa, with an average elastic modulus of 28.69 GPa.

2.3. Setup and Measurement

The YAW-5000F 500 ton loading machine was used to apply vertical loads to the columns for the axial compression test. Four vertical linear variable displacement transducers (LVDTs) were positioned at the four corners of the upper end plate to measure the axial displacement of columns, as specifically displayed in Figure 5. Strain gauges were placed on the surface of the flange at 0.5h of the column to measure the circumferential and tangential strains. For the convenience of description, the flange surfaces and the concrete surfaces were named individually, as illustrated in Figure 6. To avoid the influence of welding residual stress, the strain gauges were positioned at the extended portion of the flange. At each point, they were affixed in both tangential and circumferential orientations. Taking “SG1-1-H&V” as an example, this refers to the circumferential strain gauge “SG1-1-H” and the tangential strain gauge “SG1-1-V”. Before the start of the test, the loading machine was calibrated, and a preload of 0.1 N_u,CECS (N_u,CECS is the axial compression load calculated according to T/CECS 719-2020 [30]) was applied. After that, the formal loading process began. During the formal loading process, a displacement-controlled loading strategy was adopted with a loading rate of 0.005 mm/s. The loading process was stopped either when the load dropped to 80% of the peak load or when significant damage was observed in the column.

2.4. Experimental Results and Analysis

2.4.1. Load Response and Failure Modes

The experimental phenomena observed in all three test specimens were similar, taking the phenomenon of LPEC-2 as an example for analysis. Initially, the axial load was relatively small, and the column was in the elastic stage, without exhibiting significant deformation or concrete cracks. As the load increased to 0.85N_u (N_u refers to the ultimate axial compression load), cracks appeared on the surfaces C1 and C2; upon continued loading, the cracks widened and continued to develop. Approaching N_u, slight bulging occurred on the flange, and gaps appeared between the exposed concrete and the flange, accompanied by minor concrete peeling and slight sounds. After reaching N_u, the local buckling of the flange on surface F2 became evident, and local concrete was crushed and peeled off in large quantities. Loading was stopped when it decreased to 0.8N_u; Figure 7a–c illustrate this failure process. The final failure modes of the column were characterized by concrete spalling and local buckling of the flange, which are shown in Figure 7d.

2.4.2. Axial Load Displacement Curves

As shown in Figure 8a, the axial compression load–displacement curves of LPEC columns can be categorized into three distinct sections. In the initial stage, when the displacement was relatively small, the curve rose linearly, indicating the elastic phase where steel and concrete worked together. As the displacement continued to increase, the load also grew but at a decreased rate, signifying the transition into the elastic–plastic stage. During this stage, the core concrete expanded under compression, and the flange approached yield. Consequently, the slope of the curve gradually decreased until the load reached N_u. After the peak load was attained, the curve went to a descent stage, during which the crushing of the concrete led to a large axial displacement. Then, the descending portion of the curve gradually flattened out.

As displayed in Figure 8b, when comparing the descent segment of the curves, the decline rate of LPEC-1 was significantly slower than that of LPEC-2. This was because the increase in concrete strength led to higher brittleness, resulting in lower ductility for LPEC-2. When comparing LPEC-2 with LPEC-3, it was noted that LPEC-3, which had higher steel strength, exhibited a more gradual descent segment. This was due to the greater bearing capacity of steel in LPEC-3, which caused the load to drop more slowly when concrete failed.

2.4.3. Enhancement Index

The introduction of the bearing capacity enhancement index (I_BCE) can visually reflect the influence of material strength changes on the bearing capacity, as shown in Equation (1):

$$I_{\mathrm{BCE}}={\displaystyle \frac{N_{\mathrm{u}}}{f_{\mathrm{y}}{A}_{\mathrm{s}}+f_{\mathrm{c}}{A}_{\mathrm{c}}+f_{\mathrm{r}}{A}_{\mathrm{r}}}}$$

(1)

where f_y is the yield strength of steel, f_c is the prismatic compressive strength of concrete, and f_r is the yield strength of longitudinal rebars. A_s is the area of steel, A_c is the area of concrete, and A_r is the area of longitudinal rebars.

In addition, a concrete strength enhancement index (I_CSE) was introduced to measure the strength of the concrete confinement effect, which was calculated by the following formula:

$$I_{\mathrm{CSE}}={\displaystyle \frac{N_{\mathrm{u}}-f_{\mathrm{y}}{A}_{\mathrm{s}}-f_{\mathrm{r}}{A}_{\mathrm{r}}}{f_{\mathrm{c}}{A}_{\mathrm{c}}}}$$

(2)

The I_BCE and I_CSE values of each column are shown in

Table 2. I_BCE and I_CSE values of test specimens.

Specimen Label	As (mm2)	Ac (mm2)	Ar (mm2)	Nu (kN)	IBCE	ICSE
LPEC-1	5760	61,776	0	3278.51	1.161	1.4058
LPEC-2	5760	61,776	0	3378.88	1.160	1.3854
LPEC-3	5760	61,776	0	3763.61	1.152	1.4169

, with a comparison presented in Figure 9. The results demonstrated that the I_BCE and I_CSE values for all three stub columns exceeded 1.0. This is attributed to the confinement effect provided by both steel and transverse links, which reinforces the strength of concrete, thereby elevating the bearing capacity. LPEC-1, which had a lower concrete strength compared to LPEC-2, had a larger I_BCE and I_CSE, indicating that the increase in concrete strength would reduce the concrete confinement effect. The I_CSE of LPEC-3 increased by 2.27% compared to the I_CSE of LPEC-2. This is because an increase in steel strength enhances the confinement effect of the concrete. However, as the proportion of the bearing capacity provided by concrete to the total bearing capacity decreased, the I_BCE of LPEC-3 decreased slightly, and the impact of confinement effect on total capacity also diminished simultaneously.

2.4.4. Flange Strain Response

To further investigate the failure mechanism of LPEC stub columns, the strain response analysis of the flange was conducted using LPEC-2 as a typical example. The load–strain relationships for each flange are shown in Figure 10a–c. The strain gauges corresponding to each flange are illustrated in Figure 6.

During the initial loading stage, the strain growth rate on each flange was relatively stable, indicating that the flanges were in the elastic stage and the components were working together. As loading continued, the tangential strain on surface F3 reached the yield strain (ε_y = −1644) at 0.8N_u. With further loading, the strain growth rate slowed down, and surfaces F1 and F2 reached the yield strain when the load reached N_u, indicating that the performance of the flanges can be fully utilized. As the load approached its peak, the tangential strain of surfaces F1 and F2 abruptly mutated, indicating that local buckling occurred on the flange of surfaces F1 and F2, which was identical to the observed experimental phenomenon displayed in Figure 7. During the load descending stage, the tangential strain continued to increase, but the growth rate significantly decreased, indicating that all flange surfaces remained in a compression state until the column was destroyed.

3. Finite Element Parametric Analysis

3.1. Finite Element Modeling

The CAE software Abaqus 2020 was utilized to establish LPEC models, which consist of profile steel, concrete, transverse links, internal stiffeners, and end plates. The profile steel was represented using the four-node reduced integration shell element (S4R), while the concrete and internal stiffeners were modeled with the eight-node reduced integration brick element (C3D8R). The transverse links were represented using the truss element (T3D2), and the end plates were designated as rigid bodies.

There was relative slippage between the flange and the concrete, whereas no slippage occurred between the web and the concrete according to experimental observations. Therefore, a “surface-to-surface contact” was employed to simulate the interaction between the flange and the concrete surface. This contact definition incorporated a tangential friction coefficient of 0.3 [31] and a normal hard contact behavior. Further, a tie connection [32] was used to simulate the interaction between the web and the concrete surface. Both ends of the transverse links and internal stiffeners were tied to surfaces of profile steel, and other parts of transverse links and internal stiffeners were embedded into the overall model. Additionally, the tie connection was also set along the end plate interface. Local imperfections were deemed negligible in this analysis considering their minimal influence on the bearing capacity [7].

The vertical mesh size was set to h/15, namely a mesh size of 50 mm. Horizontally, the mesh size was set to b/15, equivalent to 20 mm for a size of 300 mm × 300 mm × 150 mm (a × b × b_f) cross-section. Similarly, the internal stiffeners and transverse links were meshed with a size of 20 mm to ensure accurate representation.

To simulate loading and boundary conditions, a reference point was established at the centroid of the L-shaped section, corresponding to the end plate. This reference point served as the application point for the axial displacement load, which was applied to the upper end plate. Figure 11 provides detailed information of the FE model.

3.2. Material Model

Steel materials, including profile steel, transverse links, and internal stiffeners utilized a five-stage linear constitutive model [33] that takes secondary flow plasticity into account. The stress–strain curve is shown in Figure 12 and the related formulas are shown as follows:

$$\sigma =\left\{\begin{array}{cc}{E}_{\mathrm{s}}\epsilon \hfill & \hfill \epsilon \le {\epsilon }_{\mathrm{e}}\\ -A{\epsilon }^2+B\epsilon +C\hfill & \hfill {\epsilon }_{\mathrm{e}}<\epsilon \le {\epsilon }_{\mathrm{e}1}\\ f_{\mathrm{y}}\hfill & \hfill {\epsilon }_{\mathrm{e}1}<\epsilon \le {\epsilon }_{\mathrm{e}2}\\ f_{\mathrm{y}}\left(1+0.6{\displaystyle \frac{\epsilon -{\epsilon }_{\mathrm{e}2}}{{\epsilon }_{\mathrm{e}3}-{\epsilon }_{\mathrm{e}2}}}\right)\hfill & \hfill {\epsilon }_{\mathrm{e}2}<\epsilon \le {\epsilon }_{\mathrm{e}3}\\ 1.6f_{\mathrm{y}}\hfill & \hfill \epsilon >{\epsilon }_{\mathrm{e}3}\end{array}\right.$$

(3)

$${\epsilon }_{\mathrm{e}}=0.8f_{\mathrm{y}}/E_{\mathrm{s}}$$

(4)

$${\epsilon }_{\mathrm{e}1}=1.5{\epsilon }_{\mathrm{e}}$$

(5)

$${\epsilon }_{\mathrm{e}2}=10{\epsilon }_{\mathrm{e}1}$$

(6)

$${\epsilon }_{\mathrm{e}3}=1000{\epsilon }_{\mathrm{e}1}$$

(7)

To simulate the diverse structural responses of concrete, the plastic damage model in Abaqus was selected to represent the constitutive behavior of concrete. The stress–strain relationship was established according to the Chinese design code of concrete [34].

3.3. Validation of FE Models

As shown in

Table 3. Material properties of FE models for validation.

Specimen Label	Concrete Strength (MPa)	Steel Strength (MPa)
LPEC-M1	18.16	295.37
LPEC-M2	19.60	295.37
LPEC-M3	19.60	355.54

, three refined FE models with identical geometric dimensions and material properties as those of test specimens were established. A comparative analysis was conducted between the FE model and the experimental results to verify the accuracy of the FE model. As shown in Figure 13a–c, the comparison of load–displacement curves revealed that the development and variation trends of the two curves were similar. The peak load calculated by the FE model matched well with the experimental results. However, the post-yielding plateau in the experimental results was lower than that of the FE model, which resulted from the brittle failure of concrete after reaching the peak load. Figure 14 displays a consistent local buckling failure mode of the flange with the experimental results. Therefore, the FE simulation is relatively accurate and suitable for further analysis of relevant parameters.

3.4. Parametric Study

Relevant FE models were established to investigate the axial compression performance of LPEC stub columns, considering the influence of parameters including material strength, steel thickness (flange thickness and web thickness), transverse link spacing, transverse link diameter, and transverse link distribution which refers to the distance from the center axis of the transverse link to the end of the flange, expressed as a multiple of i, where i equals 12 mm, as shown in Figure 15a. When calculating the axial compression capacity of PEC stub columns, the confinement effect of longitudinal rebars on concrete is limited [35]. To investigate the impact of longitudinal rebars, this paper adopted the diameter of the longitudinal rebar as a parameter, a total of four longitudinal rebars using the truss element (T3D2) with a yield strength of 300 MPa were embedded in the FE model, and the schematic diagram of the arrangement is shown in Figure 15b. All the FE models have a height of 750 mm and a cross-section with dimensions a and b, both of which are equal to 300 mm, and the specific parameters of the models are shown in

Table 4. FE models for parametric analysis.

Parameter	Specimen Label	Steel Thickness	Concrete Strength (MPa)	Steel Strength (MPa)	Transverse Link Spacing (mm)	Transverse Link Diameter (mm)	Transverse Link Distribution	Longitudinal Rebar Diameter (mm)
		tw × tf (mm)
Flange	LPEC-F1	6 × 4	19.6	295.37	100	8	3i	/
	LPEC-F2	6 × 8	19.6	295.37	100	8	3i	/
	LPEC-F3	6 × 10	19.6	295.37	100	8	3i	/
	LPEC-F4	6 × 12	19.6	295.37	100	8	3i	/
Web	LPEC-W1	4 × 6	19.6	295.37	100	8	3i	/
	LPEC-W2	8 × 6	19.6	295.37	100	8	3i	/
	LPEC-W3	10 × 6	19.6	295.37	100	8	3i	/
	LPEC-W4	12 × 6	19.6	295.37	100	8	3i	/
Concrete	LPEC-C1	6 × 6	20.1	345	100	8	3i	/
	LPEC-C2	6 × 6	26.8	345	100	8	3i	/
	LPEC-C3	6 × 6	32.4	345	100	8	3i	/
Steel	LPEC-S1	6 × 6	26.8	235	100	8	3i	/
	LPEC-S2	6 × 6	26.8	460	100	8	3i	/
Transverse link	LPEC-L1	6 × 6	19.6	295.37	50	8	3i	/
	LPEC-L2	6 × 6	19.6	295.37	150	8	3i	/
	LPEC-L3	6 × 6	19.6	295.37	200	8	3i	/
	LPEC-L4	6 × 6	19.6	295.37	/	/	/	/
	LPEC-L5	6 × 6	19.6	295.37	100	6	3i	/
	LPEC-L6	6 × 6	19.6	295.37	100	10	3i	/
	LPEC-L7	6 × 6	19.6	295.37	100	12	3i	/
	LPEC-L8	6 × 6	19.6	295.37	100	8	5i	/
	LPEC-L9	6 × 6	19.6	295.37	100	8	4i	/
	LPEC-L10	6 × 6	19.6	295.37	100	8	2i	/
	LPEC-L11	6 × 6	19.6	295.37	100	8	i	/
Longitudinal rebar	LPEC-R1	6 × 6	19.6	295.37	100	8	3i	6
	LPEC-R2	6 × 6	19.6	295.37	100	8	3i	8
	LPEC-R3	6 × 6	19.6	295.37	100	8	3i	10
	LPEC-R4	6 × 6	19.6	295.37	100	8	3i	12

Note: i refers to the distance from the center axis of the transverse link to the end of the flange; i = 12 mm.

. The axial load–displacement curves and I_CSE value of each FE model are shown in Figure 16 and Figure 17, respectively. The simulation results of FE models are shown in

Table 5. Simulation results of FE models in parametric analysis.

Parameters	Specimen Label	As (mm2)	Ac (mm2)	Ar (mm2)	Nu (kN)	Nu-fyAs-frAr (kN)	fcAc (kN)	ICSE
Validation	LPEC-M1	5760	61,776	0	3320.20	1618.86	1121.85	1.4430
	LPEC-M2	5760	61,776	0	3439.86	1738.52	1210.81	1.4358
	LPEC-M3	5760	61,776	0	3789.75	1741.83	1210.81	1.4385
Flange	LPEC-F1	4884	62,652	0	3201.30	1758.71	1227.97	1.4322
	LPEC-F2	6636	60,900	0	3679.62	1719.54	1193.64	1.4405
	LPEC-F3	7512	60,024	0	3918.13	1699.31	1176.47	1.4444
	LPEC-F4	8388	59,148	0	4156.52	1678.95	1159.30	1.4482
Web	LPEC-W1	4774	62,762	0	3163.49	1753.39	1230.48	1.4249
	LPEC-W2	6772	60,764	0	3718.31	1718.06	1191.21	1.4422
	LPEC-W3	7780	59,756	0	3996.93	1698.95	1171.68	1.4500
	LPEC-W4	8784	58,752	0	4276.66	1682.12	1152.24	1.4598
Concrete	LPEC-C1	5760	61,776	0	3759.04	1771.84	1241.69	1.4269
	LPEC-C2	5760	61,776	0	4188.92	2201.72	1655.59	1.3298
	LPEC-C3	5760	61,776	0	4556.98	2569.78	2001.54	1.2839
Steel	LPEC-S1	5760	61,776	0	3526.69	2173.09	1655.59	1.3125
	LPEC-S2	5760	61,776	0	4864.61	2215.01	1655.59	1.3378
Transverse link	LPEC-L1	5760	61,776	0	3484.29	1782.95	1210.81	1.4725
	LPEC-L2	5760	61,776	0	3421.20	1719.86	1210.81	1.4204
	LPEC-L3	5760	61,776	0	3407.93	1706.59	1210.81	1.4094
	LPEC-L4	5760	61,776	0	3369.39	1668.05	1210.81	1.3776
	LPEC-L5	5760	61,776	0	3415.72	1714.38	1210.81	1.4159
	LPEC-L6	5760	61,776	0	3464.01	1762.67	1210.81	1.4557
	LPEC-L7	5760	61,776	0	3487.44	1786.10	1210.81	1.4751
	LPEC-L8	5760	61,776	0	3440.79	1618.31	1210.81	1.4366
	LPEC-L9	5760	61,776	0	3444.88	1623.00	1210.81	1.4399
	LPEC-L10	5760	61,776	0	3442.58	1622.72	1210.81	1.4380
	LPEC-L11	5760	61,776	0	3438.61	1615.88	1210.81	1.4348
Longitudinal rebar	LPEC-R1	5760	61,662	114	3473.41	1738.15	1208.59	1.4381
	LPEC-R2	5760	61,574	202	3499.15	1737.50	1206.86	1.4396
	LPEC-R3	5760	61,461	315	3532.78	1737.20	1204.65	1.4420
	LPEC-R4	5760	61,323	454	3573.60	1736.55	1201.94	1.4447

.

3.4.1. Effect of Material Strength

Figure 16a indicates that when the compressive strength of concrete increased from 30 MPa to 40 MPa and 50 MPa, the axial compression capacity of LPEC stub columns increased by 11.44% and 19.05% respectively, with an accompanying increase in initial stiffness. However, the ductility decreased, and the residual strength did not improve noticeably. Figure 16b shows that when the yield strength of steel increased from 235 MPa to 345 MPa and 460 MPa, the axial compression capacity of the stub columns increased by 18.78% and 37.94%, respectively. Additionally, both ductility and ultimate strength were enhanced. The above results suggested that increasing the material strength can effectively improve the axial compression capacity of LPEC stub columns.

As shown in Figure 17a, as the compressive strength of concrete increased from 30 MPa to 40 MPa and 50 MPa, the I_CSE decreased by 6.80% and 10.02%, indicating that increasing the concrete strength significantly reduced the confinement effect. On the other hand, as the yield strength of steel increased from 235 MPa to 345 MPa and 460 MPa, the I_CSE increased by 1.32% and 1.93%, suggesting that increasing the steel strength influenced the confinement effect slightly.

3.4.2. Effect of Steel Thickness

Figure 16c indicates that when the flange thickness increased from 4 mm to 6 mm, 8 mm, 10 mm, and 12 mm, the axial compression capacity of the column increased by 8.36%, 15.07%, 22.58%, and 30.09%, respectively; a significant improvement in initial stiffness was also observed. Similarly, Figure 16d shows that when the web thickness increased from 4 mm to 6 mm, 8 mm, 10 mm, and 12 mm, the axial compression capacity of the LPEC stub column increased by 8.74%, 17.54%, 26.35%, and 35.19%, accompanied by a notable improvement in both initial stiffness and ductility. This demonstrated that increasing the steel thickness can significantly improve the axial compression performance of LPEC stub columns.

As shown in Figure 17b, when the flange thickness increased from 4 mm to 6 mm, 8 mm, 10 mm, and 12 mm, the I_CSE increased by 0.25%, 0.58%, 0.85%, and 1.12%, respectively. Meanwhile, when the web thickness increased from 4 mm to 6 mm, 8 mm, 10 mm, and 12 mm, the I_CSE increased by 0.73%, 1.20%, 1.76%, and 2.48%, respectively. It indicated that increasing the flange thickness can slightly enhance the confinement strength of concrete, but the effect was limited, and increasing the web thickness had a significant effect on enhancing the concrete confinement.

3.4.3. Effect of Transverse Link Parameters

Figure 16e illustrates that when the transverse link spacing dropped from 200 mm to 150 mm, 100 mm, and 50 mm, the axial compression capacity of the stub column increased by 0.39%, 0.94%, and 2.24%, respectively. Similarly, Figure 16f shows that when the transverse link diameter increased from 6 mm to 8 mm, 10 mm, and 12 mm, the axial compression capacity of the stub column increased by 0.71%, 1.41%, and 2.10%, respectively. However, Figure 16g shows that when the transverse link distribution changed, the ultimate axial compression capacity did not vary significantly.

As shown in Figure 17c, when the transverse link spacing dropped from 200 mm to 150 mm, 100 mm, and 50 mm, the I_CSE increased by 0.77%, 1.87%, and 4.47%, respectively; when the transverse link diameter increased from 6 mm to 8 mm, 10 mm, and 12 mm, the I_CSE increased by 1.40%, 2.81%, and 4.18%, respectively.

The results above indicated that reducing the transverse link spacing and increasing its diameter can notably improve both the axial compression capacity and the concrete confinement effect of LPEC stub columns. However, the transverse link distribution had a relatively minor impact on both the ultimate axial compression capacity and the concrete confinement effect of the column, making it negligible.

3.4.4. Effect of Longitudinal Rebar Diameter

Figure 16h illustrates that when the longitudinal rebar diameter increased from 6 mm to 8 mm, 10 mm, and 12 mm, the axial compression capacity of the stub column increased by 0.74%, 1.70%, and 2.88%, respectively. This indicated that increasing the longitudinal rebar diameter can improve the column’s bearing capacity. As shown in Figure 17d, compared to the column without longitudinal rebars which can be considered as having a longitudinal rebar diameter of 0 mm, the I_CSE values for columns with longitudinal rebar diameters of 6 mm, 8 mm, 10 mm, and 12 mm increased by 0.16%, 0.26%, 0.43%, and 0.62%, respectively. This indicated that longitudinal rebar had a limited effect on enhancing the concrete confinement.

4. Discussion on Calculation Methods in Specifications

Currently, there is no existing method for calculating the axial compression capacity of LPEC stub columns. Therefore, two calculation methods in specifications (T/CECS719-2020 [30] and EC4 [36]) were selected to calculate the axial compression capacity of LPEC stub columns in the aforementioned experiments and FE parametric analysis, in order to verify the accuracy of these two specifications.

4.1. Eurocode 4

According to specification EC4, the calculation formula for the axial compression capacity of PEC stub columns is shown in Equation (8):

$$N_{\mathrm{u},\mathrm{EC}4}=f_{\mathrm{ys}}{A}_{\mathrm{s}}+f_{\mathrm{c}}^{\prime }{A}_{\mathrm{c}}+f_{\mathrm{yr}}{A}_{\mathrm{r}}$$

(8)

where N_u,EC4 represents the axial compression capacity of the PEC column; A_s represents the area of steel; A_c represents the area of concrete; A_r represents the area of longitudinal rebars; f_ys represents the yield strength of steel; f_c′ represents the cylinder compressive strength of concrete; and f_r represents the yield strength of longitudinal rebar.

4.2. T/CECS 719-2020

According to specification T/CECS719-2020, the calculation formula for the axial compression capacity of PEC stub columns is shown in Equation (9):

$$N_{\mathrm{u},\mathrm{CECS}}=f_{\mathrm{ys}}{A}_{\mathrm{s}}+f_{\mathrm{c}}{A}_{\mathrm{c}}+f_{\mathrm{yr}}{A}_{\mathrm{r}}$$

(9)

where N_u,CECS represents the axial compression capacity of the PEC column; A_s represents the area of steel; A_c represents the area of concrete; A_r represents the area of longitudinal rebars; f_ys represents the yield strength of steel; f_c represents the prismatic compressive strength of concrete; and f_r represents the yield strength of longitudinal rebar.

4.3. Comparison of Different Specifications

By comparing the experimental and FE calculation results with those calculated from the specifications, as detailed in

Table 6. Comparison between experimental, FE analysis and specifications.

	Specimen Label	Nu (kN)	Nu,CECS (kN)	Nu,EC4 (kN)	Nu/Nu,CECS	Nu/Nu,EC4
Test	LPEC-1	3278.51	2823.18	2825.69	1.161	1.160
	LPEC-2	3378.88	2912.14	2914.85	1.160	1.159
	LPEC-3	3753.62	3258.72	3261.43	1.152	1.151
FE models	LPEC-M1	3320.20	2823.18	2825.69	1.176	1.175
	LPEC-M2	3439.86	2912.14	2914.85	1.181	1.180
	LPEC-M3	3789.75	3258.72	3261.43	1.163	1.162
	LPEC-F1	3174.40	2670.33	2673.08	1.189	1.188
	LPEC-F2	3652.72	3153.95	3156.62	1.158	1.157
	LPEC-F3	3891.23	3395.76	3398.40	1.146	1.145
	LPEC-F4	4129.62	3637.57	3640.17	1.135	1.134
	LPEC-W1	3163.49	2640.58	2643.34	1.198	1.197
	LPEC-W2	3718.31	3191.46	3194.12	1.165	1.164
	LPEC-W3	3996.93	3469.67	3472.29	1.152	1.151
	LPEC-W4	4276.66	3746.77	3749.35	1.141	1.141
	LPEC-C1	3759.04	3228.90	3231.68	1.164	1.163
	LPEC-C2	4188.92	3642.80	3646.50	1.150	1.149
	LPEC-C3	4556.98	3988.74	3993.22	1.142	1.141
	LPEC-S1	3526.69	3009.20	3012.90	1.172	1.171
	LPEC-S2	4864.61	4305.20	4308.90	1.130	1.129
	LPEC-L1	3484.29	2912.14	2914.85	1.196	1.195
	LPEC-L2	3421.20	2912.14	2914.85	1.175	1.174
	LPEC-L3	3407.93	2912.14	2914.85	1.170	1.169
	LPEC-L4	3369.39	2912.14	2914.85	1.157	1.156
	LPEC-L5	3415.72	2912.14	2914.85	1.173	1.172
	LPEC-L6	3464.01	2912.14	2914.85	1.190	1.188
	LPEC-L7	3487.44	2912.14	2914.85	1.198	1.196
	LPEC-L8	3440.79	2912.14	2914.85	1.182	1.180
	LPEC-L9	3444.88	2912.14	2914.85	1.183	1.182
	LPEC-L10	3442.58	2912.14	2914.85	1.182	1.181
	LPEC-L11	3438.61	2912.14	2914.85	1.181	1.180
Average					1.167	1.166
Standard deviation					0.018	0.018

, the results show that the ratios of N_u to N_u,CECS range from 1.13 to 1.198, with an average value of 1.167. Similarly, the ratios of N_u and N_u,EC4 range from 1.129 to 1.196, with an average ratio of 1.166. The comparison results indicate that both specifications underestimate the axial compression capacity of LPEC stub columns. These underestimated results arise from the fact that both methods rely primarily on the integration of material strengths, and the enhanced concrete strength resulting from the concrete confinement effect is ignored.

5. Proposed Calculation Method Considering Strength Enhancement of Concrete

To precisely calculate the axial compression capacity of LPEC stub columns, a calculation method based on the superposition principle incorporating the concrete confinement effect is proposed. By dividing the concrete into zones and calculating the concrete strength separately in each zone, this method considers the differences in the constrained strength of concrete in various regions, each represented by a specific enhancement coefficient. Considering the varying degrees of constrained strength provided by steel, the concrete is divided into highly constrained regions and partially constrained regions. The regions covered by webs on both sides are defined as highly constrained regions, and the regions covered by only one web or no web are classified as partially constrained regions, as shown in Figure 18.

The formula for calculating the bearing capacity of LPEC stub columns can be expressed as Equation (10), where N_u,p represents the axial compression capacity calculated by the proposed calculation formula; K_chi represents the enhancement coefficient for concrete in highly constrained regions calculated by Equations (19) and (20); and K_cpi represents the enhancement coefficient for concrete in partially constrained regions calculated by Equation (25). In addition, the influence of transverse links on the bearing capacity is represented by an enhancement coefficient K_link calculated by Equation (26). A_chi represents the area of the highly constrained region as expressed in Equation (11); D_i represents the width of the highly constrained region as expressed in Equations (12) and (13); A_cpi represents the area of the partially constrained region as expressed from Equation (14) to (17); A_s represents the area of steel as expressed in Equation (18); A_r represents the area of longitudinal rebars; f_c represents the prismatic compressive strength of concrete; f_y represents the yield strength of steel; and f_r represents the yield strength of longitudinal rebar.

$$N_{\mathrm{u},\mathrm{p}}=K_{\mathrm{link}}\cdot \left({\displaystyle \sum _{\mathrm{i}=1}^2{K}_{\mathrm{chi}}{f}_{\mathrm{c}}{A}_{\mathrm{chi}}}+{\displaystyle \sum _{\mathrm{i}=1}^4{K}_{\mathrm{cpi}}{f}_{\mathrm{c}}{A}_{\mathrm{cpi}}}\right)+f_{\mathrm{y}}{A}_{\mathrm{s}}+\left(f_{\mathrm{r}}-f_{\mathrm{c}}\right)\cdot A_{\mathrm{r}}$$

(10)

$$A_{\mathrm{chi}}=D_{\mathrm{i}}^2$$

(11)

$$D_1={\displaystyle \frac{b_{\mathrm{f}}-t_{\mathrm{w}}}{2}}$$

(12)

$$D_2={\displaystyle \frac{b_{\mathrm{f}}-t_{\mathrm{w}}}{2}}-t_{\mathrm{f}}$$

(13)

$$A_{\mathrm{cp}1}=2\left(b-b_{\mathrm{f}}-t_{\mathrm{f}}\right)\cdot \left({\displaystyle \frac{b_{\mathrm{f}}-t_{\mathrm{w}}}{2}}\right)+\left({\displaystyle \frac{b_{\mathrm{f}}-t_{\mathrm{w}}}{2}}-t_{\mathrm{f}}\right)\cdot t_{\mathrm{f}}$$

(14)

$$A_{\mathrm{cp}2}={\displaystyle \frac{1}{2}}\left(b_{\mathrm{f}}-t_{\mathrm{w}}\right)\cdot \left(a-b_{\mathrm{f}}-t_{\mathrm{f}}\right)$$

(15)

$$A_{\mathrm{cp}3}={\displaystyle \frac{1}{2}}\left(b_{\mathrm{f}}-t_{\mathrm{w}}\right)\cdot \left(a-2t_{\mathrm{f}}\right)$$

(16)

$$A_{\mathrm{cp}4}=\left[{\displaystyle \frac{1}{2}}\left(b_{\mathrm{f}}-t_{\mathrm{w}}\right)-t_{\mathrm{f}}\right]\cdot t_{\mathrm{f}}$$

(17)

$$A_{\mathrm{s}}=3b_{\mathrm{f}}{t}_{\mathrm{f}}+\left(a-2t_{\mathrm{f}}\right)\cdot t_{\mathrm{w}}+\left(b+{\displaystyle \frac{t_{\mathrm{w}}-b_{\mathrm{f}}}{2}}\right)\cdot t_{\mathrm{w}}$$

(18)

5.1. Enhancement Coefficient for Concrete in Highly Constrained Regions

Based on the results from the experiments and FE analysis, no local buckling phenomenon was observed on the web plate when the column broke. The confinement state of concrete in highly constrained regions can be considered similar to that in a square steel tube of the same size [37]. The enhancement coefficient for the strength of constrained concrete is calculated according to the formula put forward by Yu et al. [38], specifically detailed in Equations (19) and (20).

$$K_{\mathrm{chi}}=\left\{\begin{array}{ll}1+17\alpha \hfill & \hfill \alpha <{\displaystyle \frac{5}{34}}\\ 3.5\hfill & \hfill \alpha \ge {\displaystyle \frac{5}{34}}\end{array}\right.$$

(19)

$$\alpha =\left({\displaystyle \frac{D_{\mathrm{i}}+2t_{\mathrm{w}}}{t_{\mathrm{w}}}}\right)\cdot \left({\displaystyle \frac{f_{\mathrm{y}}}{f_{\mathrm{c}}}}\right)$$

(20)

5.2. Enhancement Coefficient for Concrete in Partially Constrained Regions

Based on the observed experimental phenomena, local buckling occurred on the flange when the column reached the axial compression capacity, the out-of-plane bending deformation of the flange’s extended portion exerted a confining effect on the concrete in partially constrained areas. Therefore, the flange’s extended portion can be viewed as a cantilever beam, and the effective lateral stress distribution can be simplified as a rectangular distribution [39]; it is assumed that at the ultimate load, the internal moment resisted by the flange’s extended portion is equal to the bending moment generated by the lateral stress on the flange, as shown in Figure 19. The effective lateral confining stress exerted by the flange’s extended portion on the concrete can be expressed by Equation (21), where f_lyi is flange effective lateral constraint stress. When local buckling occurs on the flange, the effective partially constrained area is considered as the area enclosed by two parabolas with a terminal angle of 45 degrees and profile steel [40].

The effective partially constrained area is denoted as A_ecpi, as shown in Figure 20; since A_cp4 is relatively small, to facilitate calculations, A_ecp4 and A_cp4 are considered to be approximately equal. K_ei represents the effective confinement coefficient for concrete in the partially constrained region, as expressed in Equation (22).

$$f_{\mathrm{lyi}}={\displaystyle \frac{K_{\mathrm{ei}}{t}_{\mathrm{f}}^2{f}_{\mathrm{y}}}{3{\left(\frac{b_{\mathrm{f}}-t_{\mathrm{w}}}{2}\right)}^2}}$$

(21)

$$K_{\mathrm{ei}}={\displaystyle \frac{A_{\mathrm{ecpi}}}{A_{\mathrm{cpi}}}}$$

(22)

Incorporating the mathematical expression introduced by EI-Tawil [41], which correlates confining stress with the strength improvement coefficient of concrete, upper and lower bounds for the strength enhancement coefficient of constrained concrete are considered in this study. These bounds are contingent upon the magnitude of lateral stresses exerted on the concrete in two directions. When f_lxi ≤ f_lyi = 0.3f_c′, the upper bound k_h is expressed as follows:

$$k_{\mathrm{h}}=1.3+5.55{\displaystyle \frac{f_{\mathrm{lxi}}}{f_{\mathrm{c}}^{\prime }}}-7.5{\left({\displaystyle \frac{f_{\mathrm{lxi}}}{f_{\mathrm{c}}^{\prime }}}\right)}^2$$

(23)

When f_lxi = f_lyi, the lower bound k_l is expressed as:

$$k_1=-1.254+2.254\sqrt{1+{\displaystyle \frac{7.94f_{\mathrm{lxi}}}{f_{\mathrm{c}}^{\prime }}}}-2{\displaystyle \frac{f_{\mathrm{lxi}}}{f_{\mathrm{c}}^{\prime }}}$$

(24)

where f_lxi represents the effective lateral constraint stress in the horizontal direction orthogonal to f_lyi, and considering only the confining effect of the flange on the concrete in the partially constrained areas, f_lxi is deemed to be zero [39]; f_c′ is the strength of cylindrical concrete.

By considering both cases, the expression of the enhancement coefficient for concrete in partially constrained regions (K_cpi) is given in Equation (25):

$$K_{\mathrm{cpi}}=k_1+\left(k_{\mathrm{h}}-k_1\right)\cdot \sqrt{{\displaystyle \frac{f_{\mathrm{lyi}}}{3f_{\mathrm{c}}^{\prime }}}}$$

(25)

5.3. Enhancement Coefficient Provided by the Transverse Links

As analyzed in Section 3.4.4, the transverse link spacing and diameter have a significant impact on the axial compression capacity, while the transverse link distribution has a relatively minor effect. Therefore, the enhancement coefficient provided by the transverse links is expressed as a function of the transverse link spacing and diameter. Through the calculation results of a few FE models with transverse link diameter from 4 mm to 20 mm and transverse link spacing from 50 mm to 200 mm, the expression for the enhancement coefficient provided by the transverse links is fitted as shown in Equation (26), where d represents the transverse link diameter and s represents the transverse link spacing.

$$K_{\mathrm{link}}={\left(1+{\displaystyle \frac{d^2}{0.53s}}\right)}^{0.08}$$

(26)

5.4. Verification of the Proposed Calculation Method

A total of 27 FE models were established for further analysis. The materials (f_y and f_c), steel thickness (t_w and t_f), transverse link spacing (s) and diameter (d), and the size of the shape (a and b) were considered parameters. All the FE models had a height of 750 mm, and the detailed parameters of the models are shown in

Table 7. Supplementary FE models.

Specimen Label	Steel Dimension	Concrete Strength (MPa)	Steel Strength (MPa)	Transverse Link Spacing (mm)	Transverse Link Diameter (mm)
	a × b × bf × tw × tf (mm)
LPEC-F6	300 × 300 × 150 × 6 × 8	19.6	295.37	/	/
LPEC-F7	300 × 300 × 150 × 6 × 10	19.6	295.37	/	/
LPEC-F8	300 × 300 × 150 × 6 × 12	19.6	295.37	/	/
LPEC-W6	300 × 300 × 150 × 8 × 6	19.6	295.37	/	/
LPEC-W7	300 × 300 × 150 × 10 × 6	19.6	295.37	/	/
LPEC-W8	300 × 300 × 150 × 12 × 6	19.6	295.37	/	/
LPEC-L12	300 × 300 × 150 × 6 × 6	26.8	345	100	6
LPEC-L13	300 × 300 × 150 × 6 × 6	26.8	345	100	10
LPEC-L14	300 × 300 × 150 × 6 × 6	26.8	345	100	12
LPEC-L15	300 × 300 × 150 × 6 × 6	32.4	345	100	6
LPEC-L16	300 × 300 × 150 × 6 × 6	32.4	345	100	10
LPEC-L17	300 × 300 × 150 × 6 × 6	32.4	345	100	12
LPEC-L18	300 × 300 × 150 × 6 × 6	26.8	345	50	8
LPEC-L19	300 × 300 × 150 × 6 × 6	26.8	345	150	8
LPEC-L20	300 × 300 × 150 × 6 × 6	26.8	345	200	8
LPEC-L21	300 × 300 × 150 × 6 × 6	32.4	345	50	8
LPEC-L22	300 × 300 × 150 × 6 × 6	32.4	345	150	8
LPEC-L23	300 × 300 × 150 × 6 × 6	32.4	345	200	8
LPEC-UN1	300 × 400 × 150 × 6 × 6	26.8	345	100	8
LPEC-UN2	300 × 450 × 150 × 6 × 6	26.8	345	100	8
LPEC-UN3	300 × 500 × 150 × 6 × 6	26.8	345	100	8
LPEC-UN4	400 × 300 × 150 × 6 × 6	26.8	345	100	8
LPEC-UN5	450 × 300 × 150 × 6 × 6	26.8	345	100	8
LPEC-UN6	500 × 300 × 150 × 6 × 6	26.8	345	100	8
LPEC-FW2	300 × 300 × 150 × 8 × 8	19.6	295.37	100	8
LPEC-FW3	300 × 300 × 150 × 10 × 10	19.6	295.37	100	8
LPEC-FW4	300 × 300 × 150 × 12 × 12	19.6	295.37	100	8

.

When comparing the experimental and FE analysis results with the calculating results, the ratio of N_u to N_u,p was mostly between 0.97 and 1.03, with an average value of 1.024 and a standard deviation of 0.02. The detailed results are shown in

Table 8. Comparison between experimental, FE analysis and proposed calculation method.

	Specimen Label	Nu (kN)	Nu,p (kN)	Nu/Nu,p
Test	LPEC-1	3278.51	3187.81	1.028
	LPEC-2	3378.88	3283.38	1.029
	LPEC-3	3753.62	3687.19	1.018
FE models	LPEC-M1	3320.20	3187.81	1.042
	LPEC-M2	3439.86	3283.38	1.048
	LPEC-M3	3789.75	3687.19	1.028
	LPEC-F1	3174.40	3036.93	1.045
	LPEC-F2	3652.72	3529.62	1.035
	LPEC-F3	3891.23	3775.63	1.031
	LPEC-F4	4129.62	4021.41	1.027
	LPEC-W1	3163.49	2868.16	1.103
	LPEC-W2	3718.31	3726.65	0.998
	LPEC-W3	3996.93	4185.48	0.990
	LPEC-W4	4276.66	4651.62	0.995
	LPEC-C1	3759.04	3649.67	1.030
	LPEC-C2	4188.92	4094.24	1.023
	LPEC-C3	4556.98	4465.48	1.020
	LPEC-S1	3526.69	3355.10	1.051
	LPEC-S2	4864.61	4866.23	1.000
	LPEC-L1	3484.29	3339.58	1.043
	LPEC-L2	3421.20	3258.11	1.050
	LPEC-L3	3407.93	3243.46	1.051
	LPEC-L4	3369.39	3186.27	1.057
	LPEC-L5	3415.72	3249.14	1.051
	LPEC-L6	3464.01	3317.70	1.044
	LPEC-L7	3487.44	3350.72	1.041
	LPEC-L8	3319.65	3440.79	1.048
	LPEC-L9	3324.34	3444.88	1.049
	LPEC-L10	3324.06	3442.58	1.048
	LPEC-L11	3317.22	3438.61	1.047
	LPEC-F6	3579.79	3433.28	1.043
	LPEC-F7	3819.44	3680.07	1.038
	LPEC-F8	4058.79	3926.64	1.034
	LPEC-W6	3649.10	3620.67	1.008
	LPEC-W7	3929.97	4069.61	1.000
	LPEC-W8	4210.60	4525.35	1.004
	LPEC-L12	4164.89	4048.63	1.029
	LPEC-L13	4213.03	4139.95	1.018
	LPEC-L14	4243.23	4183.92	1.014
	LPEC-L15	4525.29	4411.84	1.026
	LPEC-L16	4589.00	4519.25	1.015
	LPEC-L17	4619.05	4570.97	1.011
	LPEC-L18	4240.32	4169.09	1.017
	LPEC-L19	4173.40	4060.58	1.028
	LPEC-L20	4160.10	4041.06	1.029
	LPEC-L21	4618.16	4553.52	1.014
	LPEC-L22	4545.29	4425.89	1.027
	LPEC-L23	4515.54	4402.94	1.026
	LPEC-UN1	5598.07	5579.38	1.003
	LPEC-UN2	5997.42	5924.84	1.012
	LPEC-UN3	6401.77	6270.29	1.021
	LPEC-UN4	5606.12	5581.42	1.004
	LPEC-UN5	5992.22	5927.89	1.011
	LPEC-UN6	6386.36	6274.35	1.018
	LPEC-FW2	3968.41	3966.01	1.001
	LPEC-FW3	4503.83	4499.16	1.001
	LPEC-FW4	5039.28	4986.27	1.011
Average				1.027
Standard deviation				0.020

and the error graph is shown in Figure 21. This indicates that the experimental and FE analysis results are in good agreement with the formula results. The calculation method based on the superposition principle considering the concrete confinement effect is suitable for calculating the axial compression capacity of LPEC stub columns.

6. Conclusions

This study conducted experiments and finite element parametric analysis on the axial compression capacity of L-shaped PEC stub columns. The experimental phenomena, mechanical properties, and calculation methods for axial compression capacity were studied separately. The main conclusions are summarized as follows:

• The primary failure modes observed in the experiments were concrete spalling and local buckling of the flange. The load–displacement curve of an L-shaped PEC stub column under axial compression exhibited distinct phases: an initial elastic stage, followed by an elastic–plastic stage, and ultimately a load-decreasing stage.
• Experimental results demonstrated that the bearing capacity enhancement index (I_BCE) value of L-shaped PEC columns exceeded 1.0, and the confinement effect significantly improved the bearing capacity of the concrete. Additionally, the decrease in the concrete strength or the increase in steel strength leads to an increase in the concrete strength enhancement index (I_CSE) value.
• The finite element models were validated to be accurate. According to the FE parametric analysis, the axial compression capacity of the L-shaped PEC stub column improved with increases in concrete strength, steel strength, steel thickness, transverse link diameter, and longitudinal rebar diameter, as well as a decrease in transverse link spacing. Furthermore, the concrete confinement effect was enhanced with increases in steel strength, steel thickness, and transverse link diameter, as well as a decrease in transverse link spacing.
• The current calculation methods in relevant specifications (T/CECS719-2020 and EC4) do not consider the concrete confinement effect, which leads to an underestimation of the calculation results. A calculation method based on the superposition principle considering the concrete confinement effect is proposed. By comparing the results with experimental and FE parametric analysis, it can be considered that this calculation method has high accuracy.