1. Introduction
The compressive stability of slender steel columns is one of the main control factors in structural design [
1]. Especially for steel columns with a large slenderness ratio (>150), the strength reduction is even as high as 70% due to stability problems, seriously reducing the strength utilization rate of steel columns in actual engineering [
2,
3]. The research results showed that the strength and stability of steel structures subjected to prestressing can be significantly improved if the prestressing method is reasonable [
4,
5]. The prestressed steel structure can save materials and funds, ensure safety, and reduce deformation [
6,
7]. The prestressed stayed column comprises three parts: the central steel column, which plays a vital role in bearing the upper load. The second part is the prestressed steel cable that can only bear tensile force and apply pre-pressure to the bearing column without increasing excessive weight. The third part is the transverse brace, which acts as a constraint on the central steel column under the action of prestress. Prestressed steel cables limit the deformation of the central steel column and prevent buckling of the central steel column [
8,
9,
10]. However, the research on the structural types of prestressed stayed columns is relatively single, mainly focusing on single and three transverse prestressed beam columns [
11,
12]. The types and theories of new prestressed stayed columns with more reasonable force and higher strength utilization need further study.
The research on the buckling performance of prestressed stayed columns is mainly conducted from theoretical derivation, experimental verification, and numerical simulation. Many scholars have systematically investigated the theory of prestressed stayed columns [
13,
14,
15,
16]. Smith et al. [
13] derived the theoretical buckling solution applicable to the single-transverse prestressed stayed column and applied it to numerical examples. They indicated that the theoretical buckling solution can predict the buckling behavior and bearing capacity of single and multiple transverse prestressed stayed columns.
Temple [
15] proposed a method for calculating the buckling load of multi-transverse prestressed beam columns using the finite element method. The results were very close to the exact solution. Saito and Wadee [
17] employed the Rayleigh–Ritz method to determine the geometric post-buckling behavior of prestressed stayed columns and verified it with numerical approaches. The research showed that the nonlinear behavior was closely related to the initial prestress. Wadee et al. [
18] proposed a simplified theoretical model using discrete rigid connections, which considered the relaxation of prestressed steel cables and the destabilization effect of steel columns. Saito and Wadee [
19] established a nonlinear model considering geometric imperfections utilizing the Rayleigh–Ritz method to compute the buckling behavior of prestressed beam columns. They demonstrated that prestressed columns were very sensitive to defects when bearing critical loads. However, the current theoretical research focuses on improving the bearing capacity of steel columns only by increasing the transverse braces.
Many experimental studies have also been conducted on the buckling behavior of prestressed stayed columns [
10,
20,
21]. Osofero et al. [
20] performed a systematic experimental study on the buckling performance, bearing capacity, and defect sensitivity of prestressed stayed columns. The experimental results verified the existence of symmetric and antisymmetric buckling modes in prestressed stayed columns. Hafez et al. [
10] investigated the effect of the initial prestress on the single-transverse prestressed stayed column. The theoretical and experimental results indicated that the initial prestress greatly affected the buckling performance. De Araujo et al. [
22] employed tests and finite element simulation methods to systematically examine the parameter laws of steel column height, diameter, and prestress size. Martins et al. [
21] conducted experiments on the buckling behavior of prestressed stayed columns using ordinary and high-strength steel, respectively. They reported that high-strength steel has great advantages over prestressed stayed columns. The experimental and numerical results provide a reference for the design of three-dimensional prestressed stayed columns. At present, the research on the test of a prestressed stayed column is relatively few and only concentrates on the study of single transverse prestressed beam columns.
Compared to theoretical and experimental methods, numerical approaches for prestressed stayed columns have high efficiency, low cost, and broad applicability [
23,
24,
25]. Saito and Wadee [
26] investigated the interactive buckling behavior using numerical analysis methods. They exhibited that interaction buckling behavior can significantly reduce the maximum bearing capacity of prestressed stayed columns. Pichal and Machacek [
27] examined the effect of geometric and material nonlinear imperfections on the post-buckling behavior of prestressed stayed columns using numerical analysis methods. They indicated that the buckling behavior of prestressed columns depends on geometry, material properties, prestressed magnitude, and boundary conditions. Wang et al. [
28] utilized numerical methods to analyze the post-buckling performance of prestressed stayed columns under different cross-brace lengths. The sensitivity analysis of the buckling load was conducted, and an optimization algorithm was applied to obtain the optimal brace length. The research results provide a reference for the design of prestressed columns. Lapira et al. [
29] analytically derived the optimal prestress solution of multi-cross-braced prestressed columns and verified it with the finite element method. The research results can provide a reference for the prestress value of prestressed columns considering geometric nonlinearity. Currently, the research on numerical simulation of prestressed stayed columns primarily focuses on the buckling behavior, post-buckling behavior, and parameter optimization of single-transverse and multi-transverse prestressed beam columns. There are relatively few innovations in the structural forms of prestressed stayed columns.
In summary, numerous scholars have drawn many beneficial conclusions on prestressed stayed columns through large numbers of theories, simulations, and experiments. However, there are few relevant studies on improving the transverse form and increasing the end constraint to enhance the bearing performance of prestressed stayed columns. This study analyzes and compares various prestressed beam-column structures and proposes a new type of prestressed column to enrich and improve the theoretical basis and mechanical performance of prestressed stayed column structures. This research modifies the existing shape from a beam to two steering brace plates to turn the prestressed steel cables. The original prestressed steel cables are divided into two evenly: four prestressed steel cables are divided into four groups of eight, and the prestressed steel cables are turned twice around the compression column through the plate braces. The steel cable can transmit more effective elastic support through supporting plates, while the upper and lower supporting plates are the factors that can make use of the end of the pressure column. Compared to the previous single-point constraints, increasing end constraints can improve the ultimate bearing capacity of the bearing column.
Figure 1 depicts the schematic diagrams of a traditional single-transverse prestressed beam column (
Figure 1a), a three-transverse prestressed beam column (
Figure 1b), and a new double-steering prestressed plate column (
Figure 1c).
The primary contribution novelty of this study is the introduction of a novel double-steering prestressed plate column. Compared to the previous prestressed columns, the design considers both the bending constraint and the two-end constraint. These features significantly enhance the stable bearing capacity and buckling performance of the core steel column. This research investigates the buckling performance of dual steering prestressed brace columns and develops a finite element model. The model considers initial geometric defects and linear contact, analyzing the impact of prestress position distribution and steering plate size. Prestressed columns are widely used in large commercial centers, gymnasiums, terminal buildings, and other long-span structures. The innovative prestressed columns presented in this study offer considerable steel savings.
2. Calculation Model
The research object of this study is a double-steering prestressed plate column. A nonlinear buckling analysis method is selected due to its high nonlinearity of contact. In this section, the calculation model of the double-steering prestressed plate column is developed and calculated.
2.1. Assumptions
- (1)
The steel column and the stayed brace are rigidly connected.
- (2)
The steel column is simplified as isotropic beam elements, and the impact of initial geometrical defects is considered.
- (3)
The prestressed steel cables are simplified as cable elements, which will generate large tensile strains but will not produce any form of compressive and bending strains.
- (4)
The separable motion contact algorithm is used for line-to-surface contact.
- (5)
The lower supporting plate is restrained by fixed constraints, and the upper supporting plate is constrained in a horizontal direction. Vertical loads are imposed on the column’s top along the Z axis.
- (6)
Plane torsional buckling is ignored.
2.2. Initial Prestress
The initial prestress of steel cable is essential for improving the steel column’s bearing capacity.
Figure 2 accurately describes the relationship between the initial prestress value and the critical buckling load of the prestressed stayed column [
10,
11].
Zone one indicates that when the prestress is relatively small (0 ≤
<
), the steel column’s critical bearing capacity is the minimum value of
, and the variation amplitude is small. Zone two demonstrates that when the prestress is moderate (
≤
<
), the steel column’s critical bearing capacity significantly rises with the increase in the initial prestress value, and the maximum value can reach
. Zone three exhibits that when the prestress is too large (
≤
), the steel column’s critical bearing capacity gradually decreases as the initial prestress value grows. When the prestressed value reaches
, the steel column’s critical bearing capacity is 0. The optimal prestress value is at the junction of zones two and three [
30,
31].
The relationship between initial prestress value and critical buckling load can be described by Equation (1):
The optimum prestress expression of the prestressed stayed column is shown in Equation (2):
where
and
are the coefficients related to the prestressed steel cable and brace parameters;
is the critical bearing capacity of the prestressed stayed column
is the optimum prestress value.
2.3. Geometric Defects
Due to the inevitable existence of certain geometric defects in prestressed stayed columns, the influence of geometric defects is considered in this study, and the application method of geometric defects is consistent with the literature [
32,
33,
34]. Perpendicularity deviation of the main steel structure
is limited by length, as shown in Equation (3):
where
is the height of the prestressed column.
2.4. Line-Surface Contact Algorithm
This study allows the contact between the prestressed cable and the brace to be “hard contact”. The contact algorithm is depicted in the following equation [
35]:
Contact
where
is the contact pressure;
is the gap.
The virtual work of the contact force can be calculated according to the Lagrange principle:
The friction force
can be expressed as
where
is the friction force;
and
are shear stresses;
is the coefficient of friction;
is the equivalent shear stress.
2.5. Force Equation of Double-Steering Prestressed Plate Column
Let and be the horizontal reaction and vertical bending moment at the node of the double-steering prestressed plate column, respectively; and are the horizontal displacement spring coefficient and the vertical rotation spring coefficient at the node, respectively.
The steel column’s lateral displacement at the
node is
The steel column’s angle at the
node is
The elastic buckling equilibrium relationship between the
steel column’s joints is as follows:
where
is the horizontal displacement of
node;
is the horizontal reaction force of the bottom support.
2.6. Calculation Model
The finite element software ANSYS 15.0 is utilized to calculate and analyze the proposed new type of prestressed column. This study compares non-prestressed bearing columns, a traditional single-transverse prestressed beam column, a traditional three-transverse prestressed beam column, and the new double-steering prestressed plate column. The model’s basic mechanical and geometric parameters are as follows.
The elastic modulus of steel is considered 210 GPa, the height of core steel columns is 3 m, the Poisson’s ratio is 0.3, and the column’s section diameter is 50 mm. For a single-transverse prestressed beam column, the length of the brace is set to 150 mm, the cross-sectional diameter is placed to 50 mm, and the prestressed reinforcement is Φ 8. For a three-transverse prestressed beam column, the length of brace one is considered to be 150 mm, the length of brace two is 110 mm, and its cross-sectional diameter is 50 mm; the prestressed reinforcement is Φ 8. For the double-steering prestressed plate column, the thickness of plates () is set to 10 mm, and the hole () radius is 5 mm. The diameter of supporting plates is 330 mm, and the distance from the center of the small hole to the central column is 150 mm. The diameter of steering plates is 220 mm, and the distance from the center of the small hole to the central column is 100 mm. The prestressed reinforcement is Φ 4.
The geometric models of traditional prestressed beam columns and dimensional parameters are illustrated in
Figure 3, and the section parameters are listed in
Table 1.
Figure 4 depicts the mesh convergence results for the supporting plate and steering plate. It indicates that the maximum principal stress converges when the number of elements reaches 50,000. The total number of mesh units used in this study is 53,192, satisfying the required calculation accuracy.
Figure 5a depicts the geometric model and dimensional parameters of a double-steering prestressed plate column, whereas
Figure 5c illustrates the angle diagram, and
Figure 5b displays the mesh model.
Table 2 lists the section parameters. The beam 188 elements are selected for the core steel column and brace. The link ten elements are used for the cable, which can accurately express the mechanical performance model of the material that is only subjected to tensile stress and not compressed. In addition, the input of its mechanical performance can accurately simplify the cable calculation, and the correct results can be determined. This study adopts a sliding form of the connection part. Therefore, Solid185 units are adopted by the plates, which can accurately achieve sliding contact between the lock and steering plates.
Figure 6 shows the element details, including linear and quadratic element, load, and boundary conditions of the new prestressed column.
Load conditions: The buckling analysis consists of two load steps: In the first loading step, static analysis under defect conditions is considered. In this study, the initial strain of the Link 10 element of the prestressed cable must be determined iteratively for the prestressed cable to be prestressed in the static analysis result. The second load step is buckling analysis.