Investigation on Structural Performance of Integral Steel Wall Plate Structure in Cable–Pylon Anchorage Zone

Abstract

To enhance the bearing capacity of cable–pylon anchorage zones in cable-stayed bridges, this paper proposes the integral steel wall plate (IWP) structure and investigates the structural performance of its application in anchorage zones with a steel anchor beam and with a steel anchor box. The proposed structure contains an end plate, a surface plate, and several perforated side plates, forming steel cabins that encase the concrete pylon wall, where the steel and concrete are connected by perfobond connectors on side plates. A half-scaled experiment and a finite element analysis were first conducted on the IWP with the steel anchor beam to study the deformation at the steel–concrete interface, as well as the stress distribution in steel plates and rebars. The results were compared with experimental data of a conventional type of anchorage zone. Then, finite element models of anchorages with steel anchor boxes were established based on the geometries of an as-built bridge, and the performance of the IWP structure was compared with conventional details. Finally, the effects of plate thickness and connector arrangement were investigated. Results show that the proposed IWP structure offers excellent performance when applied with an anchor beam or anchor box, and it can effectively reduce principal tensile stress on the concrete pylon wall compared with conventional anchorage details.

1. Introduction

Cable-stayed bridges have been highly favored in bridge engineering for their exceptional span capabilities, cost efficiency, and elegant design [1]. The anchorage zone of the main pylon in a cable-stayed bridge is a critical structural component that distributes the local concentrated cable forces across the entire cross-section of the pylon. The reliability of these structures directly impacts the safety of the entire bridge. Due to the significant concentrated forces in this region, the anchorage zones of cable-stayed bridge pylons have complex structures and stress states, making them key areas in design.

Cable–pylon anchorage zones can be categorized into prestressed anchorages as in the Helgeland Bridge [2], crossed anchorages as in the Mainbrücke in West Germany [3], and saddle type anchorages as in the Brotonne Bridge in France, as well as U-shaped anchorages [4]. Among these, steel anchor beam or box anchorage belongs to the composite pylon anchorage forms, where the steel structure primarily bears the horizontal tensile forces of the cables, and the concrete pylon takes the vertical forces. This detail leverages the advantages of both materials and is particularly suitable for long-span bridges. Researchers have conducted extensive studies on this form of anchorage. Bayraktar et al. (2017) [5] conducted field tests on installed steel anchor box structures. Lu et al. (2021) [6] built a finite element (FE) model to study the mechanical mechanism of multi-segment exposed steel anchor boxes. Su et al. (2012) [7] investigated the horizontal mechanical behavior of steel–concrete composite cable–pylon anchorage through full-scale tests, finite element analysis, and a simplified deformation-based method. Xu et al. (2023) [8] studied the stress mechanism of exposed steel anchor boxes for small- and medium-span bridges with overly large cable forces. Zhu et al. (2013) [9] established a computational model for the anchorage zone of the steel anchor beam and analyzed its force mechanism.

The steel anchor beam/box anchorage secures the cables to anchor heads at both ends of the steel anchor beam. This beam is positioned longitudinally along the bridge and placed on brackets inside the pylon walls. The web of the anchor beam bears part of the horizontal component of the cable forces, while the unbalanced horizontal forces and the vertical forces are borne by the pylon walls. When the vertical forces are transferred to the pylon walls, early cable-stayed bridges commonly used concrete brackets to connect the steel anchor beam to the pylon walls. However, due to the complex stress distribution in concrete brackets and their protrusion from the pylon walls, which hinders slipform construction, the use of steel brackets has emerged in recent years. Examples include the Jiujiang Yangtze River Highway Bridge [10]. Steel brackets are welded to steel wall plates, which are integrated with the pylon wall using connectors, making the reliability of these connectors a crucial consideration.

Shear studs are a common selection for the connectors between concrete and steel [11,12,13,14], and their shear load capacity has been extensively studied and utilized as shear connectors in composite beams [15,16,17,18]. One of the examples of using shear studs include the Gordie Howe International Bridge [19], and Lu et al. (2021) [6] tested and analyzed the stress state of the shear studs in anchorage zones. Other types of shear connectors include perfobond (PBL) connectors and channel connectors [20,21], and dowel connectors [22,23] were also proposed and investigated with experimental and numerical studies. Perfobond connectors have been shown to effectively transfer loads between concrete and other materials, and studies have been conducted to explore their use as anchorage zone connectors. For instance, Classen and Hegger (2016) [24] studied the anchorage behavior of puzzle-shaped connectors in both cracked and uncracked concrete. Sun et al. (2023) [25] investigated the elastic tensile stiffness of perfobond rib connectors in steel–concrete composite pylons of cable-stayed bridges, proposing predictive equations based on tests, FE analysis, and a spring model. Zou et al. (2020) [26] analyzed the shear behavior of grout-filled perforated plate connectors at the steel–concrete joints of composite bridges. Li et al. (2020) [27] developed a novel PBL anchorage system for the 4th Nanjing Yangtze River Bridge, while Utashev et al. (2021) [28] focused on the pullout behavior of composite structures with perfobond connectors wrapped in carbon fiber-reinforced polymer (CFRP). Li et al. (2024) [29] proposed a novel energy dissipation beam–column joint based on CL composite dowels and low-yield-point steel, and Xiong et al. (2025) [30] identified a new restricted cone failure mode under tensile–shear coupling load for thin-covered composite dowels. These studies indicate that, despite the progress made in applying perfobond connectors in composite beams, their application in cable–pylon anchorage zones remains limited.

With the increase in the span of cable-stayed bridges, the forces on the pylon anchorage zone also increase. This paper draws inspiration from these findings and incorporates transverse steel structure connections into the perforated plate connectors. This has led to the proposal of the integral steel wall plate (IWP) structure, shown in Figure 1a, to further improve the load-bearing performance of cable–pylon anchorage zones. The applications of IWPs along with steel anchor beams and boxes are illustrated in Figure 1b,c, respectively.

The proposed IWP structure contains an end plate inside, a surface plate outside, and several perforated side plates embedded in the pylon wall. The end plate and surface plate are connected via several side plates with perfobond connectors, so that cable forces acting on the steel plates can be transferred into the concrete pylon. Several steel cabins were formed by the steel plates, and the material properties of concrete can be increased from the confining action.

To this end, this paper investigates the performance of the proposed IWP detail with a steel anchor beam and box in the pylon–cable anchorage zone. A half-scaled experiment and a finite element (FE) analysis were first conducted on an IWP with a steel anchor beam, and the stress distribution and the deformation of the steel–concrete interface were obtained and compared with conventional data. Then, finite element models of three types of cable–pylon anchorage zones with a steel anchor box, namely the proposed IWP type, the exposed type, and the internal type, were established and compared.

Finally, a parametric study was conducted to investigate the effects of design parameters such as the thickness of steel plates and the connector arrangement, to provide reference for the future design of IWPs.

2. Performance of IWP with Steel Anchor Beam

2.1. Experimental Program

The performance of the proposed IWP detail with a steel anchor beam was investigated based on an as-built bridge in China, of which the south and north pylons are 234 m and 232 m high, respectively, with 198.2 m above the deck. A standard segment of the cable–pylon anchorage zone was taken for investigation. The geometries of the anchorage zone of the prototype bridge and the selection of the test zone are illustrated in Figure 2. The test zone was selected near one of the cable anchorages. The small asymmetry in the test area was ignored in the model design. Considering the experimental conditions, the test zone was half-scaled.

The layout and geometries of the test model are shown in Figure 3. The test model was composed of a concrete part simulating the 1000 mm thick pylon wall and a steel part with a cantilever steel bracket simulating the IWP detail and for load application. After scaling, as shown in Figure 3a, the concrete part was 2200 mm × 2800 mm × 500 mm, with six circular holes for ground anchors. Other geometric parameters, such as the thickness of the steel plates, the geometries of perfobond connectors, and the diameter and spacing of rebars in the test model were taken as half of the prototype, as summarized in

Table 1. Geometries of test model and prototype (unit: mm).

	Plate Thickness			Perfobond Connector			Rebar
	End Plate	Surface Plate	Side Plate	Circular Hole	Long Hole (Long. × Trans.)	Spacing	Longitudinal	Transverse
Prototype	30	30	20	φ60	60 × 35	300	Φ36@200	Φ28@300
Model	16	16	10	φ30	30 × 17.5	150	Φ18@100	Φ14@150

. Additional rebars were arranged near the anchor holes to prevent local failure. As Figure 3b shows, six narrow perforated side plates and two wide ones were welded on the end plate. Two columns of perfobond connectors, one of which was circular-hole and the other was long-hole, were set on each narrow side plate. For the other two wide ones, four columns of perfobond connectors were set. Perforating bars were set in each long-hole, with a spacing of 150 mm near the anchorage. As for the material characteristics, the values are listed in

Table 2. Material characteristics of test model.

	Concrete	Steel Plate	Rebar
Young’s modulus (MPa)	-	2.0 × 105	1.95 × 105
Compressive strength (MPa)	42.7	-	-
Tensile (yielding) strength (MPa)	3.92	430	335
Ultimate tensile strength (MPa)	-	558	-

.

The selected segment of the steel anchor beam corresponds to a designed cable force of 9182 kN, with a vertical component of 6434 kN. Based on the law of similarity, the load applied to the specimen P = 6434 × 1/4 = 1608 kN. The test setup for the model is shown in Figure 4, which is a self-balancing system. Two 300-ton hydraulic jacks were used to apply horizontal loads to the test model, simulating the vertical force component transferred through the steel anchor beam from the stayed cable. One end of the jacks was pressed against the reaction wall through a spreader beam and a concrete block, while the other end acts on the steel bracket of the test model through another spreader beam. The test model was anchored to the ground with anchors to prevent from being lifted. The reaction beam on the far left was anchored to the reaction wall with eight 40 mm diameter post-tensioning bars. Concrete supports were placed under the test models and the reaction beam to accommodate the height of the hydraulic jacks. The load was increased up to 2.5P (about 4000 kN), when the vicinity of the loading area yielded. During the experiment, no obvious cracks were observed. Only when the load was around the 1.5P, there were a few muffled sounds heard.

As shown in shown in Figure 5, the measurements during the test included strain gauges glued on the steel plates (Figure 5a), embedded rebars and concrete (Figure 5b), as well as linear variable differential transformers (LVDTs) set at the steel–concrete interfaces (Figure 5c). Due to the symmetry of the structure, strain gauges for perforated plates were placed only on the outer side of plates A, B, C, and D, as shown in Figure 5a.

The stress distribution in the perforated plates is a key focus of this experiment. Generally, the shear force on individual connectors can be calculated by placing strain gauges between adjacent holes. However, due to the small spacing between the holes in the test model’s perforated plate and the significant stress variation between them, it is not possible to accurately measure the forces on the connectors. Therefore, triaxial strain gauges shown in Figure 6 were placed in the central area between four adjacent holes to measure the stress distribution and principal stress direction of the perforated plate.

Taking the strain readings from the three gauges as ${\epsilon }_A$, ${\epsilon }_B$, and ${\epsilon }_C$, the maximum stress principal (${\sigma }_1$) and the minimum stress principal (${\sigma }_3$) can be calculated from the following equation:

$${\sigma }_1={\displaystyle \frac{E}{2}}\left[{\displaystyle \frac{{\epsilon }_A+{\epsilon }_C}{1-\nu }}+{\displaystyle \frac{1}{1+\nu }}\sqrt{{\left({\epsilon }_A-{\epsilon }_C\right)}^2+{\left(2{\epsilon }_B-{\epsilon }_A-{\epsilon }_C\right)}^2}\right]$$

(1)

$${\sigma }_3={\displaystyle \frac{E}{2}}\left[{\displaystyle \frac{{\epsilon }_A+{\epsilon }_C}{1-\nu }}-{\displaystyle \frac{1}{1+\nu }}\sqrt{{\left({\epsilon }_A-{\epsilon }_C\right)}^2+{\left(2{\epsilon }_B-{\epsilon }_A-{\epsilon }_C\right)}^2}\right]$$

(2)

Then, the Von Mises stress can be calculated with

$${\sigma }_{mises}={\displaystyle \frac{1}{\sqrt{2}}}\sqrt{{\left({\sigma }_1-{\sigma }_2\right)}^2+{\left({\sigma }_2-{\sigma }_3\right)}^2+{\left({\sigma }_3-{\sigma }_1\right)}^2}$$

(3)

where ${\sigma }_2$ = 0 for plane stress state.

2.2. Experimental Results

2.2.1. Stress of the Steel Plate

To study the stress distribution in the steel structure, the stress state of the concrete, and the load transfer mechanism at the steel–concrete interface in the pylon anchorage zone, stress and strain measurement points were arranged at key positions on the expected load path from the stay cable through the concrete to the IWP components to capture the local stress response during loading. The vertical stress on the end plates reflects the transfer pattern of the vertical component of the cable force at the interface. Figure 7 shows the variation in Y-direction stress at certain measurement points on the end plate with increasing load. At points p-10, p-18, and p-22—located near the connection between the end plate and the steel bracket—the Y-direction stress increases linearly with the applied load before entering the plastic stage. These points exhibit consistently higher stress levels throughout the loading process compared to other locations. The top plate of the bracket is subjected to tensile stress, while the lower part of the support plate experiences concentrated compressive stress.

Figure 8 show the measured Mises stress distribution on the perforated plate under a 2.5P load. From these figures, the Mises stress at the measurement points on the perforated plate varies significantly with height. From the first row of holes downwards, the Mises stress gradually increases, reaching a maximum near the sixth row of holes; further down, the Mises stress decreases and then increases again, with a second peak near the twelfth row of holes, and then it decreases again. Under the 2.5P load, the maximum Mises stress at effective measurement points on the perforated plate is 406.9 MPa, occurring between the 12th and 13th rows of holes on plate C. Comparing the different plates, plate C experiences the highest stress, while plate A experiences the lowest stress.

Figure 9 shows the relationship of Mises stress with load at certain measurement points on the perforated plate. The Mises stress at these measurement points increases as the load increases. At measurement point C-13, the Mises stress reaches 430 MPa at approximately 1.8P, indicating that the local steel plate has yielded.

2.2.2. Stress of the Rebar

Due to the bond between rebars and surrounding concrete, before cracking, the strains in the rebars and the concrete were consistent. However, when the concrete cracks, the tensile forces were transferred to the rebars. Based on this principle, strain gauges were placed on the rebars at locations where the concrete tensile stress was high to determine whether the concrete at those positions was cracked, as shown in Figure 10. Figure 10a shows the relationship of axial stress with load at certain measurement points on the rebar between the plates. When the load is below 1.2P, the slope of the curves at each measurement point remains almost unchanged, indicating that the local area near the measurement points is in the elastic stage. When the load exceeds 1.2P, the slope of the curve corresponding to measurement point V-3 starts to increase significantly, indicating that the concrete near this measurement point has entered the plastic stage, and the proportion of load borne by the rebar begins to increase. For the other three measurement points, the slope of their corresponding curves begins to increase when the load exceeds approximately 1.7P, but the increase is not significant. Figure 10b shows the relationship of axial stress with load at the measurement points on the transverse perforating rebar. The overall stress level on the transverse rebar is relatively low, and it mainly exhibits a compressed state. The maximum tensile stress is 13.4 MPa, and the maximum compressive stress is 60.2 MPa.

2.2.3. Deformation at Steel–Concrete Interface

To measure the relative horizontal and pull-out slip between steel and concrete under load, LVDTs were placed at key positions on the test model. A total of 6 displacement gauges were used, with WY-1 to WY-5 measuring the relative slip between the end plate and concrete and WY-6 measuring the separation between the top of the end plate and the concrete. Figure 11a shows the relative slip between the end plate and concrete as the load changes, with the results from symmetrical measurement points averaged. It can be observed that when the load is below 1.0P, the relative slip between steel and concrete increases linearly with the load; however, when the load exceeds 1.0P, the relative slip increases more rapidly. Figure 11b shows the relative separation between the end plate and concrete as the load changes. It can be observed that at lower loads, the separation increases linearly with the load; when the load exceeds 1.4P, the slope of the curve starts to increase continuously.

2.2.4. Comparison Between IWP Specimen and PBL Specimen

The experimental results of the IWP specimen were compared with the PBL specimen reported in the literature (Liu et al., 2024) [31]. The geometries and loading scheme were identical with the IWP specimen, except for the anchorage detail. It can be observed that the stress distribution patterns on the steel plates are similar under both structural forms. Taking plate A as an example, the Mises stress increases from measurement point A-1 to A-3, and then exhibited a very similar stress distribution from A-3 to A-7.

Figure 12a compares the stress measurements at the same positions on the perforated plates of the two specimens. The Mises stress values on the measurement points of the PBL specimen begin to decrease after the load exceeds 1.9P. For the IWP specimen, the Mises stress curve at measurement point A-3 shows a plateau when the load reaches 1.7P and then begins to increase after the load reaches about 2.4P. The Mises stress at measurement point A-3 increases linearly in two segments, with the slope change occurring around 0.9P. After 1.9P, the stress on the IWP specimen remains unchanged or continues to increase, demonstrating higher load-bearing capacity compared to the PBL specimen.

Figure 12b shows the relationship of axial stress with load at measurement point V-3 on the main reinforcing bars between the plates of the two specimens. It can be observed that for the PBL specimen, the slope of the curve starts to increase after the load exceeds 0.8P, indicating that the proportion of force borne by the reinforcing bars is increasing, and the concrete near the measurement point has started to exhibit non-linear behavior. In contrast, the slope of the curve for the IWP specimen only starts to increase after the load exceeds 1.2P. Moreover, when the load exceeds 1.7P, there is a sudden increase in the stress value at the measurement point on the PBL specimen, indicating that cracks perpendicular to the strain measurement direction have appeared near the measurement point in the concrete. However, this phenomenon is not observed at the measurement points on the IWP specimen.

Figure 13a compares the relative slip between the end plate and concrete for the two specimens. In the initial loading phase, both specimens have almost identical shear stiffness, and the steel–concrete relative slip is also quite similar. However, at load levels of 1.6P and 1.9P, the slope of the curve for the PBL specimen increases significantly twice, indicating a notable change in structural stiffness. This results in the steel–concrete relative slip of the PBL specimen being significantly greater than that of IWP specimen. Figure 13b compares the separation between the end plate and concrete for the two specimens. The slope of the separation curve for the PBL specimen is greater, indicating that the IWP specimen has higher pull-out stiffness than the PBL specimen. The slope of the separation curve for the IWP specimen increases more gradually, whereas the corresponding curve for the PBL specimen shows noticeable increases in slope at 1.7P and 2.7P.

2.3. FE Analysis and Results

It is hard to observe the damage pattern inside the specimen during the loading process, and the number of measurement points is limited by the actual space and equipment, so the data obtained through the model test is limited. Thus, a nonlinear finite element model of the test model is established in this section.

2.3.1. FE Model of the IWP Test Model

General FE software ABAQUS 2020 was utilized to analyze the test model. To simulate the stress distribution of the structure accurately, the steel plate, concrete, and plate-perforating rebar were modeled by C3D8R, 8-node linear hexahedral solid elements with reduced integration, with at least four layers of element in the thickness direction, as shown in Figure 14. As Figure 14a shows, two rigid plates were established under the test model to simulate the supporting beam, the reference points of which are constrained in all degrees of freedom (DOFs). The translational DOFs along the X- and Z-axes of the nodes inside six square regions (shown in red) are constrained to simulate the ground anchors. The end of the test model was constrained in the Y-axis to simulate the effect of the reaction beam. The nodes on the loading surface are coupled to a reference point RP-1, on which an imposed displacement was introduced to apply the load. The loading speed was controlled to be 0.02 mm/s, and the ratio of kinematic to internal energy was controlled under 5%. Hard contact with penalty frictional formulation was adopted to simulate the interaction between the supporting beam and the test model and all steel–concrete interfaces, with the friction coefficient assumed as 0.5. The mesh sizes of the concrete and steel parts were determined based on mesh sensitivity checks shown in

Table 3. Element sizes in mesh sensitivity test.

	Steel		Concrete
	Global Size (mm)	Layer Through Thickness	Global Size (mm)	Local Size at Steel–Concrete Interface (mm)
Coarse mesh	30	3	60	30
Regular mesh	20	4	40	20
Fine mesh	15	6	25	15

and Figure 15, and the regular mesh with less than 5% of error compared to fine mesh is utilized in the following analysis. Figure 14b,c shows the finite element models of the steel part. Besides the perforating bars, the rest of the rebars were modeled by TRUSS elements.

The stress–strain relationships for steel plates and rebars were assumed as a perfectly elastic–plastic model, with the yield strength being 430 MPa and 335 MPa and the modulus of elasticity being 200 GPa and 195 GPa, respectively. The material properties for concrete were determined based on material tests of three cubic and six cylindrical specimens. A concrete damaged plasticity model was assumed for concrete. The elastic modulus, Poisson ratio, dilation angle, eccentricity, f_b0/f_c0, K, and the viscosity parameter were taken to be 34.4 GPa, 0.2, 30°, 0.1, 1.16, 0.67, and 0.0, respectively. The material nonlinearity of the concrete was considered in the stress–strain relationship under compression with the following relationship [32]:

$${\sigma }_c/f_c={\displaystyle \frac{\gamma \left({\epsilon }_c/{\epsilon }_c^{\prime }\right)}{\gamma -1+{\left({\epsilon }_c/{\epsilon }_c^{\prime }\right)}^{\gamma }}}$$

(4)

$$\gamma ={\left(f_c/32.4\right)}^3+1.55$$

(5)

where σ_c stands for the compressive stress of concrete (MPa); ε_c stands for the compressive strain; ε_c′ is the peak strain of concrete; f_c is the compressive strength of concrete (MPa), taken as 44.3 MPa based on material tests; and γ is an undermined coefficient. The stress–strain relationship of concrete under tension before cracking was assumed to be linear, and the relationship between the tensile stress and crack width after cracking was calculated based on the following [33]:

$${\sigma }_t/f_t=f\left(\omega \right)-\left(\omega /{\omega }_c\right)f\left({\omega }_c\right)$$

(6)

$$f\left(\omega \right)=\left[1+{\left(c_1\omega /{\omega }_c\right)}^3\right]\exp \left(-c_2\omega /{\omega }_c\right)$$

(7)

$$G_f=73f_c^{0.18}$$

(8)

where ω is the crack width (mm); ω_c is the crack width at the complete release of tensile stress, and ${\omega }_c$ = 5.14G_f; c₁ and c₂ are coefficients and can be taken as 3.0 and 6.93, respectively; G_f is the fracture energy required to create a unit area of stress-free crack (N/m); f_t is the tensile strength of the concrete (MPa), taken as 3.92 MPa based on material tests.

2.3.2. Model Validation

Figure 16a compares the experimental and FEM Mises stress values on plate D under a 2.5P load (only the first row of measurement points on plate D is listed). Figure 16b and Figure 16c show the comparison of experimental and finite element-calculated stress at measurement points p-10 and p-15 and relative slip at measurement point WY-3. The experimental stress and relative slip values show good agreement with the FE results. The slight difference in these curves can be attributed to the fact that bond strength was not considered in the FE model and that small gaps or imperfect contact likely existed at the steel–concrete interface in the physical test, causing the stress to increase gradually at the beginning. These results indicate that the FE model can accurately reflect the experimental results.

2.3.3. Results and Discussion

Figure 17 shows the Mises stress distribution on the end plate and surface plate under a 2.5P load. At 2.5P, the maximum Mises stress on the end plate is 429.9 MPa. The overall stress level of the steel plate is within a reasonable range, with larger Mises stress in the area contacting the steel bracket, while the Mises stress in other areas does not exceed 50 MPa. The maximum Mises stress on the surface plate is 106.3 MPa. The highest stress occurs in the upper region where the surface plate connects to the plate C, due to localized pressure.

Figure 18 illustrates the Mises stress distribution on the perforated plates under a 2.5P load. For plate A, the maximum Mises stress is 202.9 MPa, and the overall stress level is low, with most areas experiencing stress below 30 MPa. Plate B shows a maximum Mises stress of 425.4 MPa, but the overall stress remains low, with most of the plate under 70 MPa. On plate C, the maximum Mises stress reaches 430 MPa, with two regions of higher stress: one at the upper connection to the bracket support plate, experiencing concentrated tensile stress, and another at the lower connection, experiencing concentrated compressive stress. Plate D exhibits a maximum Mises stress of 417.3 MPa, and like the other plates, the overall stress level is low, with most areas under 80 MPa. In summary, while certain regions on the plates exhibit higher stress concentrations, the overall stress levels across all plates remain relatively low.

Figure 19 shows the principal tensile stress distribution in the concrete under a 2.5P load. Under this load, the maximum principal tensile stress reaches 4.3 MPa, occurring primarily in the Y-direction in the local concrete region beneath the upper part of the end plate. The area near the lower edge of the bracket web experiences significant local compressive stress, while the principal compressive stress in other regions is relatively small. Overall, under 2.5P load, the principal compressive stress in most areas of the concrete does not exceed 20 MPa.

3. Performance of IWP with Steel Anchor Box

3.1. FE Analysis Results and Performance Comparison

The performance of the proposed IWP detail with steel anchor box was investigated and compared with two conventional types of cable–pylon anchorage zone, namely the internal type and the exposed type, as shown in Figure 20. The steel plates of the proposed IWP type wrap the whole concrete pylon wall, while the internal type is totally inside the pylon walls, and the exposed type exposes the end plates to the outside. The IWP type uses perfobond connectors for load transferring, while the internal and exposed type relate to a concrete pylon wall with studs.

3.1.1. FE Model

As shown in Figure 20, three FE models were established in ANSYS 14.5 for the anchoring zone of the cable pylons with internal, exposed, and IWP details with a steel anchor box, based on the geometries of an actual bridge. The model encompasses the top six segments of the cable pylon anchoring zone, numbered sequentially from 1 to 6 from top to bottom. The bottom of the pylon wall is fully constrained in the vertical direction, and symmetry constraints are applied along the longitudinal and transverse symmetry axes. In the model, concrete is simulated using Solid65 elements; steel plates are simulated using Shell63 elements; anchor bearing plates are simulated using Solid45 elements; prestressed tendons are simulated using Link8 elements. Connectors are simulated using three-directional spring elements, and contact elements are established at the steel–concrete interface to account for pressure transfer effects at the interface. The material properties and connector properties are listed in

Table 4. Material properties and connector properties in FEM analysis.

	Concrete	Steel	Prestress Tendon		Stud	PBL Connector
Modulus of elasticity	34.5 GPa	210.0 GPa	195.0 GPa	Diameter	22 mm	70 mm
Poisson ratio	0.2	0.3	0.3	Shear Stiffness	302 kN/mm	543 kN/mm

. The design cable force is applied, with a maximum force per cable of 8528 kN, as a surface load on the anchor bearing plates. No prestressing is applied for internal and IWP type models, while two bundles of circumferential prestressed tendons are applied for the exposed type in every segment. The tendons were modeled as truss elements and were embedded in the concrete elements. The prestress was introduced by the cooling method, and the temperature change was calculated based on the defined thermal expansion coefficient.

3.1.2. Utilization Rate of Steel Anchor Box

Here, the horizontal cable force refers to the sum of the horizontal forces of two cables on a single end of the segment, and the utilization rate is defined as the proportion of horizontal cable force borne by the steel anchor box.

Table 5. Utilization rate of horizontal cable force by different types of steel anchor box.

Section Number	Horizontal Cable Force/kN	Horizontal Load/kN			Proportion/%
		Internal	Exposed	IWP	Internal	Exposed	IWP
1	14,678	7045	7339	7045	48	50	48
2	14,678	10,715	9247	10,568	73	63	72
3	13,272	11,148	9158	11,016	84	69	83
4	13,272	11,016	9025	11,016	83	68	83
5	13,272	11,281	8892	11,281	85	67	85
Average	13,834	10,376	8715	10,237	75	63	74

presents the utilization rates of the internal, exposed, and IWP structures for each segment. To eliminate the influence of the bottom boundary of the models, the top 1–5 segments of the steel anchor boxes were selected for comparative analysis. As shown in Table 1, the proportion of horizontal cable force taken by the exposed steel anchor boxes is approximately 50–70%. The IWP and internal steel anchor boxes have similar capacities for bearing horizontal cable forces, with utilization rates exceeding 83% for all but the top two segments. This indicates that the addition of fixed ends to the IWP detail only enhances the local stiffness of the pylon wall, with minimal impact on the overall longitudinal stiffness of the pylon wall. As a result, the IWP type achieves a high utilization rate similar to that of the internal type.

3.1.3. Maximum Principal Stress Distribution in Pylon Wall

Figure 21 shows the distribution of principal tensile stress in the outer concrete of the pylon wall at the anchoring zones for the internal, exposed, and IWP designs. Figure 21a illustrates the outer surface of the pylon wall at Segment 3, with the origin of the coordinates located at the center of the outer surface of the pylon wall. For the exposed type, the principal tensile stress along the Y- and Z-axes is taken at x = 1.2 m on the pylon wall. Along the surface of the pylon wall, the principal tensile stress in the middle of the concrete’s outer pylon wall for the IWP design is reduced by 1.5 MPa compared to the internal type, because of the fixed ends. For the exposed type, the maximum principal tensile stress on the pylon wall is maintained below 3.0 MPa due to the application of prestressing. Through the thickness direction of the pylon wall, for the IWP type, principal tensile stress no longer occurs beyond a depth of 0.6 m from the wall surface. For the internal type, principal tensile stress of approximately 1.0 MPa still appears on the inner side of the pylon wall. For the exposed type, principal tensile stress persists throughout the thickness of the pylon wall. This indicates that the IWP design, even without applying prestressing, can still improve the crack resistance of the concrete in the anchoring zone.

3.1.4. Stress State at the Steel–Concrete Interface

Figure 22 illustrates the force distribution of the studs in Segment 3 of the anchoring zone for the internal steel anchor box. The studs are numbered sequentially as N-1 to N-8 along the transverse direction from the center of the end plate to both sides and as 1–15 along the vertical direction from the bottom to the top of the segment. The overall shear force distribution of the connectors is smaller in the middle and larger on both sides along the transverse direction of the bridge, due to the shear lag effect. In the vertical direction, the shear forces are slightly larger at the bottom and the top and smaller at the mid-height. This is in accordance with the typical distribution for a column of studs under shear, which is due to the axial deformation of the end plate. In the horizontal direction, the studs are subjected to compressive forces from the cable. Therefore, the compressive forces are larger for rows 3–6. For the N-7 column, the ratio between average transverse compressive force to vertical shear force reaches 0.50, with the maximum ratio for an individual stud being 0.63. The ratio of the maximum vertical shear force to the average force for each column ranges from 1.04 to 1.11. The ratio of the maximum horizontal compressive force to the average force ranges from 1.35 to 1.65.

Figure 23 shows the force distribution of the studs in Segment 3 of the anchoring zone for the exposed-type steel anchor box. The studs are sequentially numbered as W-1 to W-8 from the inner side of the pylon wall outward and as 1–15 from the bottom to the top of the segment. Along the longitudinal direction of the bridge, the forces are larger on the inner side of the pylon wall and smaller on the outer side. This is because the cable force is applied on the inner side of the pylon; therefore, the slips at inner studs are larger. In the vertical direction, the forces are larger in the middle and smaller at both ends, and the location of the peak force moves downwards from column W-1 to W-8. The reason for this phenomenon is that the cable force is gradually transferred sloping downwards to the concrete, from the inner to the outer side. Both the vertical and longitudinal directions are the primary shear directions for the connectors. For Row 7, the ratio of average transverse shear force to average vertical shear force reaches 0.94, with the maximum ratio for an individual stud being 1.3. The ratio of the maximum vertical shear force to the average vertical shear force for each column ranges from 1.27 to 1.36, and the ratio of the maximum longitudinal shear force to the average longitudinal shear force ranges from 1.75 to 2.47.

Figure 24 shows the force distribution of the perfobond connectors in Segment 3 of the anchoring zone for the IWP detail with a steel anchor box. The perforations on the side plate are sequentially numbered as C-1 to C-5 from the inner side to the outer side of the pylon wall, whereas the perforations on the end plate are labeled as Column D-1, and those on the surface plate are numbered as Columns M-1 and M-2, from both sides inward. The rows are sequentially numbered 1–10 from the bottom to the top of the segment. In the vertical direction, the forces are almost uniform in the vertical direction, and gradually decrease from the inner to the outer side, due to the bending of pylon wall. Along the longitudinal direction of the bridge, the forces are larger on the inner side of the pylon wall and smaller on the outer side, due to the differences in the slip of perfobond connectors. The primary shear direction for the connectors is vertical. The maximum ratio of longitudinal shear force to vertical shear force for an individual perforation is 0.21, indicating minimal longitudinal shear forces. The ratio of the maximum vertical shear force to the average vertical shear force for each column ranges from 1.04 to 1.14.

From the above comparisons, it can be observed that the connectors of the internal and exposed steel anchor boxes experience a relatively uneven force distribution across the columns. In contrast, the connectors of the IWP detail mainly experience vertical shear, and the force distribution across the columns is more uniform, with the maximum force not exceeding 1.14 times the average force. This indicates that the steel–concrete interface in the IWP detail transfers force in a more uniform and smooth manner.

Table 6. Proportion of vertical cable force carried by different plates of steel anchor box.

Section Number	Internal	Exposed	IWP
	End Plate	Side Plate	Side Plate	End Plate	Surface Plate
1	100	100	68	23	9
2	100	100	71	25	4
3	100	100	72	25	3
4	100	100	72	24	4
5	100	100	71	24	5

shows the proportion involved in vertical force transfer at the steel–concrete interface for the three types of steel anchor boxes and the corresponding proportions they bear. For the internal type, the entire vertical force transferred to the pylon wall is borne by the end plate; for the exposed type, the entire vertical force is borne by the side plates; for the IWP type, the vertical force transferred to the pylon wall is approximately 70%, 25%, and 5% borne by the perforated side plates, end plate, and surface plate, respectively. Compared to the internal and exposed types, where a single component transfers the entire load, the IWP type transfers the vertical force through the combined effort of the side plates, end plate, and surface plate, offering higher reliability in force transfer.

3.2. Parametric Study

To study the pylon wall stresses, steel anchor box utilization, and the force characteristics at the steel–concrete interface for the IWP detail, parameters such as the thickness of the perforated side plates, end plate, and surface plate; the diameter of perforations on the perforated plates; and the arrangement of connectors are varied to observe the performance of the IWP with a steel anchor box as a parametric study.

3.2.1. Effect of Perforated Side Plate Thickness

Figure 25 shows the influence of the thickness of the perforated side plate on the shear force of the connectors and the vertical force distribution ratio. When the thickness of the perforated side plates increases from 15 mm to 30 mm, the maximum shear force on the connectors of the perforated side plates, the average shear force on the connectors of the end plate, and the maximum shear force all decrease by more than 24 kN. The proportion of vertical force borne by the end plate decreases from 27.5% to 21.1%, while that borne by the surface plate increases from 1.3% to 5.1%. This indicates that the increase in the thickness of the perforated side plates leads to an increase in their stiffness, enhancing the overall interaction between the surface plate and side plates. As a result, the force on the C-1 row perforations of the side plates decreases, while that on the C-5 row increases, and the proportion of vertical force transferred by the surface plate also rises. In addition, the principal tensile stress of the concrete on the outer side of the pylon wall ranges between 5.57 MPa and 5.48 MPa, and the utilization rate of the steel anchor box remains at 83%, indicating that the stress on the pylon wall and the utilization rate of the steel anchor box are essentially unaffected by the thickness of the side plates.

3.2.2. Effect of End Plate Thickness

Figure 26 shows the influence of end plate thickness on the shear force of the connectors and the utilization rate of the steel anchor box. When the thickness of the end plate increases from 15 mm to 30 mm, the shear force of the connectors changes slightly: the average shear force on the connectors of the end plate increases by 5.4 kN, while the average shear force on the connectors of the perforated side plates decreases by 1.7 kN. The utilization rate of the steel anchor box decreases by 0.7%. This indicates that the thickening of the end plate increases the local stiffness of the pylon wall, resulting in a slight reduction in the utilization rate of the anchor box. On the other hand, the thickening of the end plate enhances its ability to bear vertical forces, leading to a slight increase in the shear force of its connectors. In addition, the principal tensile stress of the concrete on the outer side of the pylon wall remains at 5.55 MPa, and the vertical force borne by the end plate increases by approximately 1.6%.

3.2.3. Effect of Surface Plate Thickness

Figure 27 shows the impact of the surface plate thickness on the principal tensile stress on the outer side of the pylon wall and the utilization rate of the steel anchor box. As the surface plate thickness increases from 15 mm to 30 mm, the principal tensile stress of the concrete on the outer side of the pylon wall decreases by approximately 0.4 MPa, and the utilization rate of the steel anchor box decreases by about 0.5%. This indicates that increasing the surface plate thickness enhances the local stiffness of the pylon wall, thereby improving the principal tensile stress of the pylon wall to a certain extent while slightly reducing the utilization rate of the steel anchor box. In addition, the variation in the shear force of the connectors does not exceed 1.6 kN; the vertical force distributed to the surface plate decreases from 3.3% to 1.8%, while the end plate and perforated side plate remain essentially unchanged. This indicates that the surface plate thickness does not have a significant impact on the shear force of the connectors and the distribution of vertical forces.

3.2.4. Effect of Hole Diameter of Perfobond Connector

Figure 28 shows the effect of the hole diameter of the perforated plate connectors on the load of the connectors and the principal tensile stress on the outer side of the concrete pylon wall. As the hole diameter increases from 50 mm to 80 mm, the maximum shear force of the connectors in the perforated side plate increases by 27 kN, and both the maximum and average values of the end plate connectors also increase; the principal tensile stress in the concrete pylon wall increases by about 0.2 MPa. This indicates that increasing the hole diameter enhances the shear stiffness of the connectors, causing the connectors closer to the inside of the pylon wall to bear more shear force. In addition, the utilization rate of the steel anchor box remains essentially unchanged; the vertical force borne by the end plate and perforated side plate slightly increases, while the vertical force borne by the surface plate decreases from 5.4% to 1.9%. This indicates that increasing the hole diameter on the side plate also weakens the overall integrity of the IWP structure, leading to a reduction in the vertical force transferred by the surface plate.

3.2.5. Effect of Shear Connector Arrangement

Figure 29 shows the effect of connector arrangement on the shear force of the steel–concrete interface connectors. The connector arrangement considered the increase in perforated side plate connectors from four columns to seven columns, and end plate connectors from two columns to five columns. When the perforated side plate connectors are increased from four columns to seven columns, the maximum shear force of the perforated side plate connectors decreases by about 24.5 kN; the maximum shear force of the end plate connectors decreases by about 10 kN. When the end plate connectors are increased from two columns to five columns, the maximum shear force of the perforated side plate connectors decreases by about 28 kN; the maximum shear force of the end plate connectors decreases by about 30 kN.

Figure 30 shows the effect of connector arrangement on the vertical force distribution of the steel–concrete interface, where the slip stiffness of the perforated side plate or end plate is set as the total vertical slip stiffness of the connectors on it. As shown in the figure, when the slip stiffness ratio of the perforated side plate to end plate reaches 2, the perforated side plate transfers more than 50% of the vertical force, which is 1.4 times that of the end plate. When the slip stiffness ratio between the two reaches 6, the vertical force borne by the perforated side plate begins to level off, and further increases in the stiffness ratio cannot effectively enable the perforated side plate to bear more vertical force. The vertical force borne by the surface plate remains basically below 5%. This indicates that changes in the connector arrangement alter the slip stiffness ratio between the perforated side plate and the surface plate, thereby causing a redistribution of the vertical force and simultaneously changing the forces acting on the connectors. In addition, the principal tensile stress on the outer side of the pylon wall and the utilization rate of the steel anchor box are basically unaffected by changes in the connector arrangement. The maximum stress difference does not exceed 0.1 MPa, and the difference in utilization rate does not exceed 0.2%.

4. Conclusions

This study proposes an integral wall plate (IWP) structure to connect the steel anchor beam/box to the concrete pylon wall in the cable–pylon anchorage zone. The performance of the IWP was analyzed through half-scaled model tests and FE analysis of the composite pylon anchorage zone. The following conclusions have been drawn:

• The IWP exhibits excellent stiffness and pull-out resistance, with significant tensile forces observed in the perfobond connectors. For the steel anchor beam configuration, relative deformation between the end plate and the pylon wall increased linearly with load up to 1.2 times the design load P, with no visible cracking observed below 2.5P. FE results confirm that stress levels in both the steel and concrete components remain within allowable limits. In the steel anchor box configuration, the IWP secures the steel anchor box utilization at 74% and reduces the principal tensile stress on the outer pylon wall by approximately 1.5 MPa, with stresses vanishing beyond 0.6 times the wall thickness—unlike conventional internal or exposed types.
• The IWP design promotes consistent and efficient force transfer through the combined action of end, side, and surface plates. Perfobond connectors primarily experience unidirectional shear, with longitudinal-to-vertical shear ratios remaining below 0.21. Parametric studies reveal that connector arrangement, perforated hole diameter, and side plate thickness significantly affect the distribution of vertical and shear forces. Increasing end or surface plate thickness slightly reduces anchor box utilization and tensile stress in the pylon wall, which can be beneficial for optimizing design against fatigue effects in long-term service.
• This study is based on a down-scale model experiment. Scaling effects and simplified boundary conditions may influence accuracy in real applications. Future work should include FE simulations incorporating detailed wall reinforcement, dynamic loading, and long-term fatigue and creep effects. These would offer more comprehensive guidance for practical design standards, especially for large-scale bridge pylons subjected to high cable forces.