Mechanical Behavior and Parametric Analysis of Socket-Type Disc-Lock Full-Hall Scaffold System for Long-Span Transfer Beams in Metro Depot Over-Track Development

Abstract

Taking the over-track development project of a metro depot in Chongqing as the engineering background, this study investigates the socket-type disc-lock full-hall scaffold system beneath the long-span transfer beam of Tower 9. A finite element model was established using MIDAS Civil to analyze the stress distribution and deformation characteristics of the scaffold system under construction loads, and the model was validated through field monitoring. On this basis, a parametric analysis was conducted to investigate the effects of erection height, step spacing of vertical standards, spacing between vertical standards, sweeping rod height, and joint stiffness on the overall stability of the scaffold system. A fitted analytical model for the buckling eigenvalue was further established. The results show that the scaffold system was mainly subjected to compression during construction. The measured maximum compressive stress of the vertical standards was 90.92 MPa, with an error of 12.50% compared with the finite element result of 80.82 MPa. The measured maximum tensile stress was 22.37 MPa, which was close to the calculated value of 21.96 MPa. The measured maximum average cumulative vertical displacement of the scaffold was 1.69 mm, which did not exceed the allowable deformation range during construction. The parametric analysis indicates that increases in erection height, step spacing of vertical standards, spacing between vertical standards, and sweeping rod height reduce the overall stability of the scaffold system, among which the step spacing of vertical standards has the most significant influence. In contrast, increasing joint stiffness is beneficial for enhancing the stability reserve. In this study, the overall stability of the scaffold system is characterized by the buckling eigenvalue obtained from linear eigenvalue buckling analysis. These findings can provide a reference for parameter selection, scheme comparison, and construction control of similar disc-lock high-formwork support systems for heavily loaded transfer beams. However, the conclusions of this study are mainly based on linear eigenvalue buckling analysis and single-factor parametric investigation, without further consideration of material nonlinearity and multi-parameter interaction effects.

1. Introduction

With the continuous expansion of urban rail transit networks and the increasing demand for intensive land use, over-track development of metro depots has become an important mode of integrated urban construction [1,2,3,4]. Such projects usually require residential and ancillary buildings to be arranged above existing metro depot structures, while the transfer floor plays a key role in transforming the upper structural system and redistributing construction-stage loads. Owing to the effects of building function, structural transformation, and construction conditions, transfer beams are often characterized by long spans, large cross-sections, concentrated construction loads, and large support heights [5,6,7]. Consequently, their formwork support systems face more prominent stability and safety control issues during construction. Socket-type disc-lock full-hall scaffold systems have been widely used in high-formwork support projects because of their high bearing capacity, high assembly efficiency, and favorable structural integrity [8,9]. However, in over-track development of metro depots, the scaffold system not only bears the construction loads of heavily loaded transfer beams, but is also constrained by the bearing conditions and spatial arrangement of the underlying existing floor-slab structure. Therefore, its stress distribution and deformation characteristics are more complex than those under conventional high-formwork support conditions, and the current understanding remains insufficient [10,11].

Regarding formwork support systems, extensive studies have been conducted both domestically and internationally on the load-bearing performance, semi-rigid joint characteristics, overall stability, and construction-stage response of disc-lock or bowl-lock scaffold systems, mainly through experimental tests, finite element analysis, and field monitoring [12,13,14]. These studies have provided a foundation for the design analysis and construction safety control of scaffold systems, and have also accumulated engineering experience in the selection and arrangement of support systems for heavily loaded members such as transfer beams, prestressed beams, and cast-in-place box girders. However, most existing studies have focused on conventional building structures, cast-in-place bridge members, or general high-formwork support conditions, while relatively limited attention has been given to full-hall disc-lock scaffold systems beneath long-span transfer beams in metro depot over-track development projects [15]. In particular, under the bearing constraints imposed by the underlying existing floor-slab structure, the distribution characteristics of controlling members, the response evolution of key positions, and the mechanisms influencing the overall stability of the scaffold system have not yet been systematically analyzed.

From a methodological perspective, finite element analysis can effectively reveal the overall mechanical state of a scaffold system, field monitoring can reflect its actual response during construction, and parametric analysis can help identify the dominant factors affecting structural stability [10,16]. However, in existing studies, these three methods are often used separately for safety checking, engineering monitoring, or discussion of local behavior, with insufficient integration among them. As a result, several key issues have not been fully addressed [17,18,19,20]. For example, whether the stress and displacement evolution of the scaffold system during construction can be reliably characterized by a numerical model, whether parameters such as erection height, step spacing of vertical standards, spacing between vertical standards, sweeping rod height, and joint stiffness have significantly different effects on overall stability, and whether these analytical results can be further transformed into simplified tools for scheme comparison and construction control still require further investigation.

Overall, existing studies have laid a foundation for establishing analytical methods for scaffold systems. However, they have mainly focused on conventional building structures, cast-in-place box girders, or general high-formwork support conditions, while insufficient attention has been paid to the composite load-bearing scenario involving “long-span transfer beam, disc-lock full-hall scaffold system, and underlying existing floor-slab structure” in metro depot over-track development projects. In particular, under the construction conditions of heavily loaded transfer beams, systematic research remains lacking on the response characteristics of key load-bearing members in socket-type disc-lock full-hall scaffold systems, the consistency between numerical models with semi-rigid joints and full-process monitoring results, and the quantitative influence of key erection parameters on overall stability.

Based on this background, this study takes the over-track development project of a metro depot in Chongqing as the engineering context and selects the socket-type disc-lock full-hall scaffold system beneath the transfer beam of Tower 9 as the research object. By combining finite element analysis, field monitoring, and parametric analysis, this study focuses on the mechanical and deformation characteristics of the scaffold system during construction, the consistency between numerical calculations and field-measured responses, and the effects of erection height, step spacing of vertical standards, spacing between vertical standards, sweeping rod height, and joint stiffness on the overall stability of the scaffold system. A fitted analytical model for the buckling eigenvalue is also established. The research framework is shown in Figure 1. The selected project has typical characteristics, including a long-span transfer beam, high-formwork support erection, and bearing constraints from the underlying existing structure, and can therefore reflect a representative problem in the construction of heavily loaded transfer members in metro depot over-track development projects. The findings can provide a reference for parameter selection, scheme comparison, and construction control of similar disc-lock high-formwork support systems for heavily loaded transfer beams.

2. Project Profile

The Chongqing metro depot over-track development project is located in Nan’an District, Chongqing. The project consists of Towers 1 to 12 and a kindergarten, with residential use as its primary function. The site area is 65,873 m², and the total building area is 244,639.73 m², including 180,372.9 m² above ground and 64,266.9 m² underground. Finite element numerical analysis and field monitoring were carried out for the disc-lock scaffold system used in the high-formwork support of the transfer beam in Tower 9. The main structure of Tower 9 is a fully frame-supported shear wall structure, with a total building height of 50.25 m, two underground floors, and fifteen above-ground floors. The first basement level serves as the transfer floor. The maximum beam cross-section in the transfer floor is 1600 mm × 2000 mm, and the maximum span is 12.85 m. The transfer beam is made of C60 concrete. The slab thickness is 200 mm, the elevation of the slab top is 9.4 m, and the erection height of the scaffold system is 9.2 m. Converted from the self-weight of the transfer beam with the maximum cross-section, the line load is 82.08 kN/m [21], which classifies this system as a high-formwork support project with a line load greater than 20 kN/m. Considering factors such as quality controllability, ease of erection, safety, and economy, a socket-type disc-lock full-hall scaffold system was adopted for the high-formwork support of the transfer beam in this project [10].

During construction, to ensure the mechanical safety of the scaffold system and the underlying existing structure, I16 distribution beams were installed at the bottom of the scaffold, and two layers of 15-mm-thick composite plywood were placed beneath the I-beams to improve the support conditions and disperse local load effects. During construction of the transfer beam, the upper loads were transferred through the formwork, square steel tubes, and channel steel to the vertical standards of the disc-lock scaffold system, then from the vertical standards to the bottom distribution beams, and finally from the distribution beams to the existing floor-slab structure, as shown in Figure 2. The vertical standards of the disc-lock scaffold were Q355 steel tubes with a specification of φ48 × 3.25 mm and an elastic modulus of 190 GPa. The horizontal ledgers were Q235 steel tubes with a specification of φ48 × 2.75 mm and an elastic modulus of 190 GPa. The diagonal braces were Q235 steel tubes with a specification of φ48 × 2.75 mm and an elastic modulus of 190 GPa. Their technical performance and structural detailing requirements comply with the relevant provisions of the Technical Standard for Safety of Socket-type Disc-lock Steel Tubular Scaffolds in Construction (JGJ/T 231—2021) [22] and the Technical Code for Temporary Support Structures in Construction (JGJ 300—2013) [23]. The technical performance and structural requirements of these components comply with the relevant codes specified in these documents. The socket-type disc-lock full-hall scaffold systems features a longitudinal spacing of 600 mm, a transverse spacing of 600 mm, and a horizontal ledger step distance of 1500 mm. At the top of the vertical standard, Q235 grade channel steel is laid perpendicular to the beam span direction as the main beam to transfer upper loads, spaced at 600 mm. On the channel steel, 40 mm × 40 mm square steel tubes are laid at 70 mm intervals as secondary beams to transfer upper loads. On top of the square steel tube is 15 mm thick composite plywood. The layout of the full socket-type disc-lock full-hall scaffold systems for the transfer beam is illustrated in Figure 3.

To enhance the overall stability and robustness of the socket-type disc-lock full-hall scaffold system, the diagonal braces within the support system are installed in the manner of “lattice columns.” Specifically, every four vertical standards and diagonal braces form a single lattice column unit. During construction, all diagonal braces of each lattice column are assembled in a clockwise direction. According to the relevant code, the diagonal braces within each lattice column unit are arranged in a “one-on, one-off” pattern both longitudinally and transversely along the horizontal direction. The arrangement of the diagonal braces in the scaffold system is shown in Figure 4.

3. Finite Element Modeling Method

3.1. Model Assumptions and Limitations

(1)

The scaffold system was treated as a spatial frame structure. The vertical standards, horizontal ledgers, and diagonal braces were all simulated using beam elements, mainly to reflect the overall mechanical behavior, deformation characteristics, and stability features of the scaffold system during construction.

(2)

The disc-lock joints were modeled as equivalent semi-rigid connections. A unified rotational stiffness was used to characterize the restraining effect of the joints, thereby reflecting the actual mechanical behavior of the joints, which lies between ideal hinged and fully rigid connections.

(3)

The construction loads were treated as equivalent static loads at key construction stages. The loads from fresh concrete, reinforcement, formwork, and construction activities were converted and applied according to the corresponding tributary widths. The wind load was transferred through an auxiliary “virtual surface”, with emphasis placed on capturing the overall response of the scaffold system at each construction stage.

(4)

Erection imperfections, such as initial inclination of vertical standards, installation eccentricity, assembly gaps at joints, and compressive deformation of the screw jacks and base plates, were not explicitly considered in this study. The stiffness development of concrete with age during staged pouring, the migration of local construction surcharge, and second-order geometric nonlinear effects were also not further simulated. Therefore, the proposed model is more suitable for analyzing the overall mechanical behavior of the scaffold system during construction, comparing controlling responses, and investigating the influence patterns of key parameters.

3.2. Model Establishment

The socket-type disc-lock full-hall scaffold system beneath the transfer beam was selected as the research object, and a three-dimensional spatial finite element model was established using MIDAS Civil. Based on the symmetry of the transfer beam and scaffold arrangement, and considering the maximum span of 12.85 m as the controlling condition, the most unfavorable scaffold system beneath the transfer beam was selected for analysis. The modeling range extended from the bottom distribution beams to the channel steel at the top of the scaffold, including the full-hall scaffold beneath the transfer beam and the 1-m-wide slab strips on both sides.

The rotational restraint of disc-lock joints is mainly provided by the interlocking action between the rosette plates of the vertical standards and the plug-in heads of the horizontal ledgers and diagonal braces. Their actual mechanical behavior lies between that of ideal hinged connections and fully rigid connections. Based on the recommended reference value for the linear rotational stiffness of disc-lock joints in the Technical Standard for Safety of Socket-type Disc-lock Steel Tubular Scaffolds in Construction (JGJ/T 231—2021) [22], and with reference to finite element studies on similar high-formwork support systems, the rotational stiffness of the horizontal ledger and diagonal brace joints was uniformly taken as 20 kN·m/rad in this study [10]. This value was adopted in a conservative manner to represent the reduction effect of semi-rigid joints on the overall stiffness of the scaffold system. Considering that on-site joint assembly quality, the seating condition of locking pins, and connection gaps may lead to a certain degree of dispersion in joint stiffness, the joint stiffness was further varied from 20 to 60 kN·m/rad in the subsequent parametric analysis to investigate the influence of connection stiffness on the overall stability reserve.

When applying the wind load, an auxiliary “virtual surface” was established between the horizontal ledger and vertical standard joints to serve as the load-transfer medium for the wind load. This “virtual surface” was simulated using 1-mm-thick plate elements, with the unit weight set to 0, Poisson’s ratio set to 0.30, and the elastic modulus assigned a value of 1 kPa, which is far smaller than that of steel. A sensitivity check confirmed that variations in the auxiliary plate parameters cause only minor changes in key structural responses, verifying that the virtual surface serves solely as a load-transfer medium without introducing unintended stiffness into the global model. This ensured that the auxiliary surface only functioned as a load-transfer medium and did not contribute to the stiffness of the main scaffold structure.

A sensitivity check was conducted for the parameters of the auxiliary “virtual surface” and the member discretization scheme. The results show that, with the boundary conditions, load values, and material parameters kept unchanged, variations in the auxiliary plate parameters or appropriate refinement of member discretization caused only minor changes in the key stresses, maximum vertical displacement, and buckling eigenvalue of the scaffold system. This indicates that the proposed model is not sensitive to element discretization or auxiliary load-transfer parameters, and that the adopted discretization accuracy can satisfy the requirements for overall mechanical behavior and stability analysis. The stress and displacement responses of the scaffold system were analyzed using first-order linear elastic finite element analysis, without further considering second-order geometric nonlinear analysis involving P-Δ and P-δ effects. The overall stability was evaluated using linear eigenvalue buckling analysis. The obtained buckling eigenvalue, $\lambda$, represents the load amplification factor under the reference load pattern. That is, when the current load distribution remains unchanged, the ideal elastic structure reaches the critical bifurcation buckling state when the load is increased to $\lambda$ times the reference load.

Therefore, the buckling eigenvalue used in this study is mainly intended to characterize the relative variation in the overall stability reserve of the scaffold system under different parameter conditions. It is not directly equivalent to the actual ultimate bearing capacity after considering material plasticity, initial geometric imperfections, and joint slip. In this model, steel material nonlinearity, initial geometric imperfections of members, and joint slip were not explicitly considered. Instead, the semi-rigid restraint characteristics of disc-lock joints were represented through joint rotational stiffness.

The model consists of a total of 1783 nodes and 4426 beam elements. The finite element model of the socket-type disc-lock full-hall scaffold system for the transfer beam is shown in Figure 5.

The load design for the scaffold system model is as follows:

(1)

This study mainly focuses on the socket-type disc-lock scaffold system. Considering the layout and mechanical characteristics of the full-hall scaffold beneath the transfer beam, the transfer beam and the 1-m-wide slab strips on both sides were selected to establish the scaffold model. The modeling range extended from the bottom distribution beams to the channel steel at the top of the scaffold, including the full-hall scaffold beneath the transfer beam and the slab strips on both sides. During load application, the permanent loads of fresh concrete, reinforcement, formwork, and square steel tubes in the beam region and slab-strip regions were calculated separately. These loads were then converted into equivalent line loads according to the tributary width of the channel steel at the top of the scaffold and applied to the channel steel. The converted area load of the permanent load in the beam region was 52.73 kN/m², corresponding to an equivalent line load of 31.64 kN/m. The converted area load of the permanent load in the slab-strip regions was 9.80 kN/m², corresponding to an equivalent line load of 5.88 kN/m. Therefore, 82.08 kN/m corresponds to the self-weight line load of the transfer beam member, while 31.64 kN/m and 5.88 kN/m correspond to the equivalent permanent line loads applied to the channel steel in the beam region and slab-strip regions, respectively, in the finite element model [24].

(2)

The construction personnel and equipment load was taken as 2.5 kN/m² according to the relevant code provisions. This construction live load was converted into an equivalent line load and applied to the channel steel at the top of the disc-lock scaffold system. Since the channel steel at the top of the scaffold was arranged along the top surfaces of the vertical standards at a spacing of 600 mm, the construction live load was converted according to the tributary width of 0.60 m for a single channel steel member. The corresponding equivalent line load was therefore 1.5 kN/m.

(3)

Considering the influence of wind load, the wind load was calculated according to the relevant code provisions and taken as 0.17 kN/m². In the finite element model, the wind load was applied by establishing a “virtual surface” between the vertical standard and horizontal ledger joints along the span direction of the transfer beam and imposing surface pressure on this surface, so as to reflect the overall mechanical behavior of the scaffold system under wind action. When converted using the same tributary width of 0.60 m as that of the top channel steel, the corresponding equivalent line load is 0.102 kN/m. However, in the finite element implementation, the wind load was still directly applied to the “virtual surface” as a surface pressure of 0.17 kN/m², rather than being simplified as a line load acting on the top members.

For the loads acting on the socket-type disc-lock full-hall scaffold system, load combinations were determined according to the relevant provisions on load-effect combinations and stability calculation in the Technical Code for Temporary Support Structures in Construction (JGJ 300—2013) [25]. The wind load was determined in accordance with the Load Code for the Design of Building Structures (GB 50009—2012) [23]. The ultimate limit state combination was adopted for strength checking, while the serviceability limit state combination was adopted for stiffness checking. In this study, the wind load was considered separately as an independent variable load and was included together with the construction live load in the most unfavorable load combination. In the finite element model, the wind load was applied as surface pressure through the “virtual surface”. For strength checking, the load combination was taken as 1.2 × permanent load + 1.4 × (variable load + wind load). For stiffness checking, the load combination was taken as 1.0 × permanent load + 1.0 × variable load + 1.0 × wind load.

4. Finite Element Numerical Analysis of Stress and Deformation

4.1. Stress Analysis

In this study, the stress sign convention is defined as positive for tension and negative for compression. In the finite element results, positive values denote tensile stress, whereas negative values denote compressive stress. For ease of comparison, the terms maximum compressive stress and maximum tensile stress used in this paper refer to the corresponding extreme stress magnitudes.

Numerical analysis was conducted on the scaffold system, and the stress contour diagram and corresponding stress values of the support system under load combinations are shown in Figure 6 and

Table 1. Finite element numerical analysis stress calculation values of the scaffold system under combined loads.

Member Type	Maximum Compressive Stress/MPa	Maximum Tensile Stress/MPa
vertical standard	80.82	—
horizontal ledger	11.52	9.11
diagonal brace	74.58	21.96

. Analysis of the stress contour diagram and Table 1 indicates that all vertical standards in the scaffold system are subjected to compressive forces and mainly bear compressive stress under the combined loads. As shown in Figure 6a, the maximum compressive stress in the vertical standards of the support system is 80.82 MPa, located at the mid-span of the transfer beam. As shown in Figure 6b, the minimum compressive stress is 3.04 MPa, mainly located under the slab strips on both sides of the transfer beam. The reason for this is that the vertical standards under the slab strips, when subjected to wind load, experience greater tensile stress on the side facing the wind load. Under the combined loads, the compressive stress of the vertical standards near the windward side is relatively small [26].

As shown in Figure 6c,d, the maximum compressive stress of the horizontal ledgers was 11.52 MPa, occurring in the first-layer horizontal ledger on the windward side beneath the transfer beam. The maximum tensile stress was 9.11 MPa, occurring in the second-layer horizontal ledger beneath the mid-span. Overall, the stress level of the horizontal ledgers was relatively low, indicating that their main function was not to directly carry the primary vertical load, but to participate in the overall load-bearing behavior by restraining the lateral displacement of the vertical standards, coordinating joint deformation, and transferring local horizontal effects. After the wind load was included in the load combination, local compression in the windward horizontal ledgers and tensile stress in some horizontal ledgers near the mid-span became more evident. However, their stress levels remained far below the yield strength of Q235 steel.

As shown in Figure 6e,f, the maximum compressive stress of the diagonal braces was 74.58 MPa, occurring in the middle diagonal braces beneath the transfer beam. The maximum tensile stress was 21.96 MPa, occurring in the diagonal braces on the leeward side. Diagonal braces play an important role in resisting lateral displacement and redistributing internal forces in the spatial working behavior of the scaffold system. Under the combined action of the upper heavy load and wind load, the diagonal braces in the middle region not only restrain the lateral deformation of the vertical standards, but also bear additional axial forces induced by joint rotation and spatial geometric coordination. Therefore, both their compressive and tensile stresses were more significant than those of the horizontal ledgers. When normalized by the yield strength, the stress ratio corresponding to the maximum compressive stress of the diagonal braces was 0.317, which represents a relatively critical control value among the Q235 members. This indicates that diagonal braces should be given particular attention in the overall stability assessment and local strength checking of the scaffold system.

Under the combined loads, the maximum combined compressive stress and maximum combined tensile stress in the scaffold system are 80.82 MPa and 21.96 MPa, respectively, both of which do not exceed the standard strength values of Q355 and Q235 steel. Therefore, the system meets the requirements of the relevant codes.

Further analysis of

Table 2. Controlling Check Items and Stress Ratios of the Disc-Lock Scaffold System.

Member Type	Material	Maximum Combined Stress/MPa		Design Strength/MPa	Stress Ratio		Controlling Load Case	Critical Location
		Compressive Stress	Tensile Stress		Compressive Stress	Tensile Stress
Vertical standard	Q355	80.82	/	305	0.265	/	1.2 × permanent load + 1.4 × live load + 1.4 × 0.6 × wind load	bottom vertical standard at the mid-span of the transfer beam
Horizontal ledger	Q235	11.52	9.11	205	0.056	0.044	1.2 × permanent load + 1.4 × live load + 1.4 × 0.6 × wind load	first-layer horizontal ledger on the windward side
Diagonal brace	Q235	74.58	21.96	205	0.364	0.107	1.2 × permanent load + 1.4 × live load + 1.4 × 0.6 × wind load	diagonal brace beneath the beam at mid-span

shows that, within the disc-lock scaffold system, the diagonal braces had the highest compressive stress ratio, followed by the vertical standards, while the horizontal ledgers had the lowest value. This indicates that, under the ultimate limit state for strength, the diagonal braces had the relatively smallest safety reserve, but they still remained within the elastic stress range and satisfied the code requirements. The compressive stress ratio of the vertical standards was approximately 73% of that of the diagonal braces. However, as the primary compression-bearing members, their load-bearing area and overall stability still play a controlling role in the overall safety of the scaffold system. The stress ratio of the horizontal ledgers was much lower than those of the other two member types, indicating that they mainly functioned to transfer horizontal loads and restrain the lateral displacement of the vertical standards. The stress ratios of all members were less than 0.4, demonstrating that the scaffold system had sufficient safety reserve in terms of strength.

4.2. Numerical Simulation Displacement Analysis

Displacement analysis was conducted on the finite element model of the scaffold system, and the deformation contour diagram of the scaffold system under the stiffness load combination was obtained, as shown in Figure 7. As shown in Figure 7b, the maximum vertical displacement of the scaffold system under the stiffness load combination is 1.35 mm, which occurs at the top of the vertical rod located beneath the mid-span of the transfer beam.

As shown in Figure 7c, the maximum displacement perpendicular to the beam span direction occurs at the top of the vertical rod under the slab strip on the windward side of the transfer beam, with a maximum value of 2.43 mm. As shown in Figure 7d, the maximum displacement in the beam span direction is 0.11 mm, which is located on the horizontal ledger near the end of the transfer beam.

The maximum combined displacement of the transfer beam occurs at the top of the vertical rod at the mid-span position under the slab strip on the windward side, with a value of 2.45 mm, as shown in the deformation contour diagram in Figure 7e. Although the maximum displacement of the scaffold system perpendicular to the beam span direction is greater than the vertical displacement and the displacement in the beam span direction, the calculation and analysis in this model consider a 1 m wide slab strip on each side of the transfer beam and take into account the influence of the full hall support under the slab. Therefore, during the displacement monitoring of the scaffold system, the vertical displacement is taken as the main control target for on-site monitoring.

5. Stress and Deformation Monitoring Analysis

In order to study the influence of the transfer beam during construction on the stress and deformation of the socket-type disc-lock full-hall scaffold system below, ensure the safety and stability of the support, and verify the accuracy of the finite element model of the socket-type disc-lock full-hall scaffold system, on-site dynamic monitoring of the stress and deformation of the support system at key sections of the transfer beam was carried out during construction. According to the construction plan and relevant code requirements for the scaffold system of the transfer beam, one monitoring section (D1) was set at the mid-span position of the transfer beam, and one monitoring section was set on each side of D1, near the beam ends (D2 and D3), resulting in a total of three monitoring sections on the transfer beam, as shown in Figure 8. Monitoring of the scaffold system started from the beginning of the construction of the bottom formwork and beam reinforcement of the transfer beam, and ended when the bottom scaffold system was removed after the concrete of the transfer beam reached the design strength requirements. To ensure the accuracy and reliability of the monitoring data, the specifications of the sensors used in this study are as follows: the Intelligent String-type Formwork Axial Force Meter for vertical rod axial force has a precision of ±1% Full Scale (FS) and a sampling frequency of 1 sample/minute; the Steel Structure Surface Strain Gauge for measuring the stress of horizontal ledgers and diagonal braces has a precision of ±2% of the reading, with a sampling frequency of 1 sample/minute; the Wire-type Displacement Meter for vertical displacement has a precision of ±0.1 mm and a sampling frequency of 1 sample/minute. All sensors were continuously recorded via automated data acquisition instruments.

5.1. Stress Monitoring Analysis

According to the actual site conditions, stress monitoring was conducted at three monitoring sections, namely D1, D2, and D3. For the stress monitoring of vertical standards, intelligent vibrating-wire formwork-support axial force meters were installed on the screw jacks of the vertical standards at the stress measurement points of the three monitoring sections, as shown in Figure 9. The axial forces of the vertical standards in the disc-lock scaffold system under loading were collected using an automated data acquisition instrument, and the corresponding stresses of the vertical standards were then calculated from the field-monitored axial forces. For the stress monitoring of horizontal ledgers and diagonal braces, steel-structure surface strain gauges were welded onto the horizontal ledgers and diagonal braces at the corresponding measurement points of each monitoring section. The strain values of the horizontal ledgers and diagonal braces in the disc-lock scaffold system under loading were collected using an intelligent reading instrument, and the corresponding stresses were subsequently calculated. These results were compared with the finite element numerical results to verify the accuracy of the numerical simulation. Before installation, all sensors were subjected to zero-point inspection and functional calibration according to the instrument manuals. After installation, the initial values were rechecked to ensure stable and reliable signal acquisition. During sensor installation, special attention was paid to the measurement-point locations, installation directions, and cable fixation quality, so as to avoid abnormal readings caused by installation deviation, local loosening, or construction disturbance. After data acquisition, individual spike values and interference values were identified, and the original time-history data were smoothed in combination with the construction stages. This ensured that the monitoring curves could accurately reflect the stress evolution of the scaffold system at each construction stage. The stress monitoring results and finite element results adopted the same sign convention, namely positive for tension and negative for compression.

Based on the principle of symmetry in the arrangement of the transfer beam and scaffold system, and with reference to the results of finite element numerical calculations, six stress observation points were arranged at each stress monitoring section: two vertical rod axial force monitoring points (numbered Di-Z1 and Di-Z2), two horizontal ledger stress monitoring points (numbered Di-H1 and Di-H2), and two diagonal brace stress monitoring points (numbered Di-X1 and Di-X2) (i = 1, 2, 3). The arrangement of stress measurement points for the transfer beam is shown in Figure 10.

Monitoring began after the scaffold system was erected and the construction of the upper transfer beam formwork and reinforcement started, and ended when the bottom scaffold system was removed after the concrete of the transfer beam reached the design strength requirements. During the entire construction monitoring process, the maximum stress values and their locations at the stress measurement points of the scaffold system are shown in

Table 3. Maximum Stress Values and Their Locations from On-site Monitoring of the Scaffold system.

Measurement Point Number	Maximum Compressive Stress/MPa	Location of Occurrence	Maximum Tensile Stress/MPa	Location of Occurrence
Z1	−90.92	Section D1	—	—
Z2	−77.24	Section D3	—	—
H1	−5.60	Section D2	7.78	Section D3
H2	−13.58	Section D3	22.37	Section D1
X1	−68.75	Section D1	14.59	Section D3
X2	−56.17	Section D2	6.46	Section D1

.

As shown in Table 2, the vertical standards in the scaffold system mainly bear compressive stress and are all compression members, indicating that the support system primarily withstands compressive forces. During actual construction, some horizontal ledgers and diagonal braces may experience varying degrees of tensile force, and installing stress gauges on these tension members will record tensile stress values; however, the overall tensile stress values are relatively small. As shown in Figure 11a, the maximum tensile stress measured at point D1-H2 is 22.37 MPa, while the maximum tensile stress of the support system under combined load is 21.96 MPa, with an error of 1.83%, which has little impact on the safety and stability of the scaffold system. Figure 8 also shows that the maximum compressive stress of the vertical rod measured at D1-Z1 is 90.92 MPa, and the maximum compressive stress of the diagonal brace measured at D1-X1 is 68.75 MPa. As shown in Figure 11b, the maximum compressive stress of the horizontal ledger measured at D3-H2 is 13.58 MPa.

To more intuitively analyze the stress behavior of the scaffold system throughout the construction process and to verify the capability of the finite element model to characterize the response variation trends at key construction stages, the stress time-history curves of representative monitoring sections were selected for comparative analysis, as shown in Figure 11. Considering the mechanical characteristics of the transfer beam and the arrangement of the monitoring sections, section D1 was located at the mid-span region and could reflect the controlling response of the scaffold system under the most concentrated upper load. Section D3 was located near the beam end and could reflect the stress level in the edge region and its difference from the mid-span region. Therefore, D1 and D3 were selected as representative sections in Figure 11 to highlight the response variation characteristics of the scaffold system from the controlling region to the edge region along the beam span direction. Section D2 was located between D1 and D3 and served as a transition section. The stress histories of its measurement points were generally consistent with those of D1 and D3, while the response amplitudes were generally between the two. It mainly served to verify the transition pattern between the mid-span and edge regions. Accordingly, the monitoring results of section D2 are described in this study by combining tabulated statistics with integrated textual analysis.

As shown in Figure 11, the concrete for the transfer beam was poured in layers, and the stress variation at each measurement point during the two concrete pours was basically linear. The rate of stress increase in the scaffold system during the first concrete pour was greater than that during the second pour. The stress in the vertical standards, horizontal ledgers, and diagonal braces of the support system reached their extreme values at the end of the first concrete pour, and reached their maximum values after the second pour was completed. The second concrete pour for the transfer beam was carried out when the concrete from the first pour reached a strength of 35 MPa. During the curing process of both pours, as the strength of the transfer beam concrete gradually increased, the stress in the scaffold system decreased. Once the concrete reached the required strength and curing was completed, the stress dropped to zero after the support system was dismantled. The underlying reason can be explained as follows. When the newly poured concrete is in a plastic state, its elastic modulus is extremely low, and it can hardly bear any structural load. At this stage, the entire construction load is solely supported by the scaffolding system, resulting in a more pronounced stress response. The structural system at this point functions purely as a support-bearing system. During the second stage of construction, the concrete from the first pour had reached a strength of 35 MPa, and its elastic modulus had increased significantly, enabling it to share part of the applied load. Consequently, a composite load-bearing system comprising both the scaffolding and the hardened concrete was formed. In this phase, the support system only needed to bear the newly added load from the second pour and a portion of the load transferred from the first-stage concrete. As the hardened concrete beam participated in load sharing, the incremental load borne by the support system was reduced, leading to a slower rate of stress increase.

The maximum compressive stresses of the vertical standards, horizontal ledgers, and diagonal braces calculated using the finite element model were 80.82 MPa, 11.52 MPa, and 74.58 MPa, respectively. The errors between the numerical simulation results and the field-measured values were 12.50%, 17.88%, and 7.82%, respectively. These discrepancies can be attributed to the fact that the finite element model was established based on ideal geometric conditions, without explicitly considering actual imperfections such as initial member curvature, installation eccentricity, joint assembly gaps, and local contact deformation. In addition, the loads induced by the concrete placing boom, material stacking, and construction personnel activities on site were staged and discrete, making it difficult for the actual load distribution to be fully consistent with the uniformly distributed loads adopted in the model. Meanwhile, during the layered pouring of concrete, differences in pouring sequence, casting rate, and local concrete accumulation could also cause fluctuations in the internal forces of the scaffold system in local regions. Nevertheless, the calculated and measured stresses of all types of members remained within a reasonable error range, and the controlling stress levels did not exceed the warning stress values of the corresponding steel grades. This indicates that the model can be used for the overall mechanical analysis and safety assessment of the scaffold system. Further analysis shows that, according to the relevant provisions on the safety reserve of temporary support structures in the Technical Code for Temporary Support Structures in Construction (JGJ 300—2013) [25], together with the recommended construction monitoring warning thresholds in the Technical Standard for Safety of Socket-type Disc-lock Steel Tubular Scaffolds in Construction (JGJ/T 231—2021) [22], both the monitoring data and numerical simulation results were lower than the warning stress values of Q355 and Q235 steel when the safety factor k was taken as 3.0, namely [σ₁] = 118 MPa and [σ₂] = 78 MPa, where [σ] = f_y/k. This demonstrates that the disc-lock scaffold system exhibited favorable mechanical performance, safety, and reliability during construction, and could meet the requirements of on-site construction.

To further quantify the overall predictive accuracy of the finite element model at different construction stages, a statistical error analysis was performed on the stress time-history data of each measurement point. The comparison between the finite element results and field-measured values at the vertical standard stress measurement points during key construction stages is summarized in

Table 4. Comparison between Finite Element and Field-Measured Stress Values at Vertical Standard Measurement Points during Key Construction Stages.

Construction Stage	Measurement Point Number	Finite Element Value/MPa	Field-Measured Value/MPa	Absolute Error/MPa
Completion of formwork and reinforcement installation	D1-Z1	41.26	45.83	4.57
	D1-Z2	38.94	43.12	4.18
	D3-Z1	39.58	44.37	4.79
	D3-Z2	37.82	42.05	4.23
Completion of the first concrete pouring	D1-Z1	68.35	75.48	7.13
	D1-Z2	64.71	71.93	7.22
	D3-Z1	65.42	72.86	7.44
	D3-Z2	62.18	69.31	7.13
Completion of the second concrete pouring	D1-Z1	80.82	90.92	10.10
	D1-Z2	76.55	85.47	8.92
	D3-Z1	77.43	86.81	9.38
	D3-Z2	73.29	82.56	9.27

. The mean absolute error and root-mean-square error are calculated using Equations (1) and (2), respectively:

$$MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|{\sigma }_{\mathrm{FEM},i}-{\sigma }_{\mathrm{EXP},i}\right|}$$

(1)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left({\sigma }_{\mathrm{FEM},i}-{\sigma }_{\mathrm{EXP},i}\right)}^2}}$$

(2)

where ${\sigma }_{\mathrm{FEM},i}$ is the finite element calculated stress value at the $i$-th measurement point, ${\sigma }_{\mathrm{EXP},i}$ is the field-measured stress value at the $i$-th measurement point, and n is the total number of measurement points.

As shown in Table 4, during the three key construction stages, namely completion of formwork and reinforcement installation, completion of the first concrete pouring, and completion of the second concrete pouring, the finite element calculated values and field-measured values exhibited consistent variation trends, both increasing gradually with the increase in load. The MAE values at the three stages were 4.44 MPa, 7.23 MPa, and 9.42 MPa, respectively. The absolute error increased with the load level, which was closely related to the increasing discreteness of actual construction loads during concrete pouring. For all 12 groups of data, the MAE was 6.78 MPa and the RMSE was 7.32 MPa, both of which remained at relatively low levels. This indicates that the finite element model has good overall predictive accuracy for the stress time history and can reliably reflect the stress evolution characteristics of the scaffold system at different construction stages.

5.2. Vertical Displacement Monitoring Analysis of Support System

In this study, a wire-type displacement meter (Figure 12) was used to monitor the vertical displacement of the scaffold system. The displacement meter was installed on the vertical standards of the support system. Its working principle is as follows: during construction, the vertical standards undergo vertical displacement under load, causing the wire of the displacement meter to stretch or contract. The sensor outputs an electrical signal proportional to the movement distance of the wire. By using an automated data acquisition instrument to collect the output signal, the vertical displacement of the rods can be obtained. For this study, a negative displacement value indicates downward vertical deformation, consistent with the sign convention used for compressive stress.

In this study, the vertical displacement of the vertical standards at three monitoring sections—D1, D2, and D3—was monitored. Considering the principle of symmetry, three vertical displacement measurement points were arranged at each monitoring section, symmetrically installed on the vertical standards beneath the beam (numbered Dj-Y1, Dj-Y2, Dj-Y3, where j = 1, 2, 3). The arrangement of vertical displacement measurement points for the scaffold system is shown in Figure 13. During on-site monitoring, attention should be paid to properly protecting the installation and fixation positions of the wire-type displacement meters.

After the entire scaffold system was erected, wire-type displacement meters were installed on the vertical standards to measure the vertical displacement of the support system. Once the instruments were installed and connected to the data acquisition box, instrument debugging was performed. After successful debugging, the deformation value was set as the initial displacement value. The difference between the measured displacement at a monitoring point during a specific construction stage and the initial displacement value is the cumulative vertical displacement at that point for that stage. The average cumulative vertical displacement values at the three monitoring sections of the transfer beam, after the completion of beam formwork and beam reinforcement construction, as well as after the first and second concrete pours, are shown in Figure 14.

As shown in Figure 14, the cumulative vertical deformation of the transfer beam after completion of the beam formwork and reinforcement, and after the first and second concrete pours, all exhibited a parabolic distribution. This conforms to the general deformation law of beams under load, where the deformation at the mid-span is greater and the deformation at both ends is smaller. This trend is consistent with the cumulative vertical displacement of the support system, demonstrating the reliability of the monitoring data from the scaffold system.

As shown in Figure 14, after the first concrete pour of the transfer beam, the average cumulative vertical displacement at sections D1 and D2 was relatively large, located at the mid-span and the left side of the mid-span, with average cumulative vertical displacements of −0.94 mm and −1.21 mm, respectively. After the second concrete pour and once the concrete reached the design strength, the maximum average cumulative vertical displacement was −1.69 mm, located at the mid-span of the transfer beam (i.e., section D3). According to finite element calculations, the maximum vertical deformation was −1.35 mm. The on-site measured values of vertical deformation for the scaffold system were slightly larger than the finite element calculated values (

Table 5. Vertical Deformation Observations of Scaffold system Sections (mm).

Monitoring Point	D1	D2	D3
Y1	−0.72	−0.95	−1.35
Y2	−1.27	−1.64	−2.04
Y3	−0.83	−1.03	−1.69
average value	−0.94	−1.21	−1.69

). The reason for this difference is that the numerical model was based on an ideal erection condition and did not fully account for site-related factors, such as the initial out-of-plumbness of vertical standards, slight compression of screw jacks, assembly gaps at joints, and contact compression deformation between the bottom distribution beams and base plates. In addition, during construction, the arrangement of the concrete placing boom on the beam, local material stacking, and personnel operation loads could further amplify the vertical deformation response in the mid-span region. Therefore, the displacement difference does not indicate model failure, but rather reflects the discrepancy between idealized calculation conditions and actual construction conditions. Considering that the finite element results could accurately identify the deformation control section, and that the measured vertical displacement did not exceed the allowable deformation range during construction, the model demonstrates good applicability for analyzing the overall deformation behavior of the scaffold system and assessing construction safety. Further analysis shows that both the field-measured values and finite element calculated values were within the allowable displacement deformation range during construction. This indicates that the disc-lock scaffold system adopted for transfer beam construction was appropriate, safe, and reliable, and could meet the actual requirements of on-site construction.

Furthermore, according to Equations (1) and (2), combined with Table 5 and the finite element calculated data of the corresponding measurement points, the MAE and RMSE of section D1 were 1.13 mm and 1.20 mm, respectively. The MAE and RMSE of section D2 were 1.24 mm and 1.33 mm, respectively, while those of section D3 were 1.05 mm and 1.10 mm, respectively. The overall MAE was 1.14 mm, and the overall RMSE was 1.21 mm. The magnitude of the errors was far smaller than the deformation limit allowed by the relevant code, indicating that the finite element model has high predictive accuracy for the vertical displacement time history of the scaffold system.

6. Parametric Influence Effect Analysis

6.1. Parametric Analysis Scheme

To investigate the influence of different erection parameters on the overall stability of the disc-lock scaffold system, parametric numerical analysis was conducted based on the established finite element model. The parameter values were determined with reference to the Technical Standard for Safety of Socket-type Disc-lock Steel Tubular Scaffolds in Construction (JGJ/T 231—2021) [22], the Technical Code for Temporary Support Structures in Construction (JGJ 300—2013) [25], and the Load Code for the Design of Building Structures (GB 50009—2012) [23], while also considering the actual erection conditions of the high-formwork support system for the transfer beam in this project.

In the background project, the actual erection height of the scaffold was 9.2 m, the step spacing of vertical standards was 1.5 m, the longitudinal and transverse spacing of vertical standards was 0.6 m, and the reference value of joint rotational stiffness was 20 kN·m/rad. Therefore, the parametric analysis was based on the measured and designed values of the project and was appropriately extended within the ranges permitted by the relevant codes and commonly used in engineering practice, so as to analyze the influence of different parameter variations on the overall stability reserve of the scaffold system.

The erection heights were set to 8 m, 12 m, 16 m, 19 m, 22 m, and 26 m, respectively. The step spacing of vertical standards was taken as 0.5 m, 1.0 m, 1.5 m, 2.0 m, 2.5 m, and 3.0 m. The spacing between vertical standards was selected as 0.6 m, 0.8 m, 1.1 m, 1.4 m, 1.7 m, and 2.0 m. The sweeping rod heights were set to 0.10 m, 0.15 m, 0.20 m, 0.25 m, 0.30 m, and 0.35 m. The joint stiffness values were set as 20 kN·m/rad, 30 kN·m/rad, 40 kN·m/rad, 50 kN·m/rad, and 60 kN·m/rad. Among them, 20 kN·m/rad is the reference value for the linear rotational stiffness of socket-type joints specified in (JGJ 300—2013) [25], and was therefore adopted as the baseline condition. A total of 28 groups of numerical simulation tests were completed. Through a comprehensive analysis of the results under multiple parameter combinations, the specific influence patterns of different factors on the disc-lock scaffold system were clarified.

6.2. Multiple Linear Regression Analysis

In this study, multiple linear regression was used to establish a relationship model between the buckling eigenvalue of the scaffold system and the main erection parameters. Considering that the buckling eigenvalue obtained from linear eigenvalue buckling analysis can reflect variations in the overall stability reserve of the scaffold system under the reference load pattern, the buckling eigenvalue was selected as the stability evaluation index to quantitatively analyze the overall stability of the scaffold system under different parameter conditions. By establishing a linear combination equation of the independent variables, the influence degree of each design and construction parameter on scaffold stability can be evaluated. Its general form can be expressed as follows:

$$\lambda ={\beta }_0+{\beta }_{1}H+{\beta }_{2}S+{\beta }_{3}L+{\beta }_{4}D+{\beta }_5\mathrm{K}+\epsilon$$

(3)

where H denotes the erection height (m); S denotes the step spacing of vertical standards (m); L denotes the longitudinal and transverse spacing of vertical standards (m); K denotes the joint rotational stiffness (kN·m/rad); $\lambda$ denotes the buckling eigenvalue (dimensionless); D denotes the sweeping rod height (m); and $\epsilon$ denotes the error term.

6.3. Stability Analysis of the Support System Under Different Parameters

6.3.1. Effect of Different Erection Heights

The variation in the buckling eigenvalue of the scaffold system and the stress responses of key members when the erection height increased from 8 m to 26 m are shown in Figure 15. As shown in Figure 15, with the increase in erection height, the buckling eigenvalue of the scaffold system generally exhibited a decreasing trend. This indicates that, under the modeling conditions adopted in this study, the overall stability reserve of the scaffold system gradually decreased as the erection height increased. Within the height range of 8–16 m, the eigenvalue decreased from 12.42 to 11.61, showing a relatively moderate variation. When the height increased from 16 m to 19 m, the decrease in the eigenvalue became more pronounced, indicating that the sensitivity of the overall stability of the scaffold system to height variation increased. Meanwhile, the tensile and compressive stresses of the members generally increased. Under the 26 m condition, the maximum compressive stress reached 199.057 MPa, indicating that the internal force level of the members increased significantly under a larger erection height. Although this value did not nominally exceed the yield strength of the corresponding steel, it approached the yield strength level of Q235 steel, indicating that the strength reserve of the members under this condition was significantly reduced. For high-formwork support scaffold systems, engineering acceptability should not be judged solely based on whether the stress is lower than the yield strength. Instead, it should be comprehensively evaluated in accordance with the requirements for overall stability, structural detailing, joint connection, allowable deviation, and construction control specified in the Technical Standard for Safety of Socket-type Disc-lock Steel Tubular Scaffolds in Construction (JGJ/T 231—2021) [22] and the Technical Code for Temporary Support Structures in Construction (JGJ 300—2013) [25]. In particular, under larger erection heights, initial imperfections, installation deviations, joint semi-rigidity, and construction disturbances may further amplify adverse responses. Therefore, under conditions of larger erection height, greater attention should be paid to the overall stability reserve of the scaffold system and the stress levels of key members.

6.3.2. Effect of Different Step Spacings of Vertical Standards

Figure 16 shows the variation in the buckling eigenvalue of the scaffold system and the stresses of key members under different step spacings of vertical standards. The results indicate that, as the step spacing of vertical standards increased, the buckling eigenvalue of the scaffold system continuously decreased, and the overall stability reserve showed a decreasing trend. When the step spacing increased from 0.5 m to 1.5 m, the eigenvalue decreased from 18.35 to 10.24. When the step spacing further increased from 1.5 m to 2.0 m, the eigenvalue decreased to 7.04, with a more pronounced reduction than in the previous stage. This suggests that, within the parameter range considered in this study, the overall stability of the scaffold system was relatively sensitive to increases in the step spacing of vertical standards. When the step spacing increased to 3.0 m, the eigenvalue decreased to 4.26, indicating that the stability reserve under this condition had been significantly reduced. Meanwhile, the stress levels of the members generally increased with the increase in step spacing, with tensile stress showing a more pronounced increase.

6.3.3. Effect of Different Spacings Between Vertical Standards

Figure 17 presents the variation curve of the buckling eigenvalue of the scaffold system under different spacings between vertical standards. As the spacing between vertical standards increased, the buckling eigenvalue of the scaffold system showed an overall decreasing trend, indicating that the overall stability reserve decreased with increasing spacing. When the spacing increased from 0.6 m to 0.9 m, the eigenvalue decreased from 18.94 to 13.42, showing a relatively significant reduction. With further increases in spacing, the eigenvalue continued to decrease, but the rate of variation gradually slowed. Correspondingly, the internal force level of the members generally increased, especially the maximum compressive stress of the vertical standards, which showed a more pronounced increase. This indicates that, as the spacing between vertical standards increases, the tributary load-bearing range of a single vertical standard also increases, making the overall mechanical behavior and stability of the scaffold system more sensitive to spacing variation. Therefore, in practical engineering scheme design, the spacing between vertical standards should not be excessively large.

6.3.4. Effect of Different Sweeping Rod Heights

The variations in the buckling eigenvalue and the maximum tensile and compressive stresses of the scaffold system with increasing sweeping rod height are shown in Figure 18. As shown in Figure 18, when the sweeping rod height increased from 0.10 m to 0.35 m, the buckling eigenvalue decreased from 14.24 to 9.16, indicating a continuous reduction in the overall stability reserve of the scaffold system. Meanwhile, the stress levels of the members generally increased, and the increase in tensile stress was particularly evident in the sweeping rods and adjacent horizontal members. These results indicate that variations in sweeping rod height have a noticeable influence on the bottom restraint characteristics and overall mechanical state of the scaffold system. This may be because, as the sweeping rod position rises, the effective restraint region at the bottom shifts upward, and the unfavorable effective length of the lower vertical standards increases accordingly, thereby affecting the overall stability. Therefore, the sweeping rod height should be reasonably controlled in combination with structural detailing requirements and site conditions.

6.3.5. Effect of Different Joint Stiffnesses

As shown in Figure 19, with the increase in joint stiffness, the buckling eigenvalue of the scaffold system generally showed an upward trend. When the joint stiffness increased from 20 kN·m/rad to 60 kN·m/rad, the buckling eigenvalue increased from 13.98 to 17.35. This indicates that, under the modeling conditions adopted in this study, enhancing the rotational restraint of joints is beneficial for improving the overall stability reserve of the scaffold system. Meanwhile, the variation in member stress levels was relatively limited, suggesting that changes in joint stiffness had a more pronounced influence on overall stability than on stress redistribution. It should be noted that even when the joint stiffness was increased to 60 kN·m/rad, the corresponding buckling eigenvalue still differed from that of the ideal rigid-connection model. This indicates that directly simplifying disc-lock joints as fully rigid connections may overestimate the overall structural stiffness. Therefore, it is more reasonable to characterize the joint behavior using semi-rigid connections in numerical analysis.

6.4. Regression Analysis Results

To quantitatively evaluate the combined effects of various design and construction parameters on the overall stability of the disc-lock scaffold system, and to establish an analytical model applicable to preliminary design and construction control, statistical analysis was conducted in this section using multiple linear regression based on 28 sets of numerical simulation results obtained from the parametric analysis.

The buckling eigenvalue of the scaffold system was selected as the dependent variable, while erection height, step spacing of vertical standards, spacing between vertical standards, sweeping rod height, and joint stiffness were chosen as the five independent variables. The regression analysis was performed using the least squares fitting method, and the significance of the equation, the contribution of each independent variable, and potential multicollinearity were examined.

The analysis results show that the overall regression model was highly significant, and all influencing factors passed the statistical significance tests. Among them, erection height, step spacing of vertical standards, spacing between vertical standards, and sweeping rod height generally showed negative correlations with the buckling eigenvalue, with the standardized influence of the step spacing of vertical standards being relatively higher. In contrast, joint stiffness showed a positive correlation with the buckling eigenvalue. These results indicate that, within the parameter range and modeling conditions considered in this study, the step spacing of vertical standards is one of the sensitive factors affecting the overall stability reserve of the scaffold system, while increasing the joint rotational stiffness is beneficial for improving the overall stability performance of the scaffold system. Based on the regression results, the prediction formula for the buckling eigenvalue was obtained, as shown in Equation (4).

$$\lambda =35.769-5.219H-6.215S-0.399L-22.051D+0.194K$$

(4)

where H denotes the erection height (m); S denotes the step spacing of vertical standards (m); L denotes the longitudinal and transverse spacing of vertical standards (m); K denotes the joint rotational stiffness (kN·m/rad); $\lambda$ denotes the buckling eigenvalue (dimensionless); D denotes the sweeping rod height (m); and $\epsilon$ denotes the error term.

The above regression model can be used for rapid estimation and parameter comparison during the scheme design stage of disc-lock scaffold systems. Its applicability corresponds to the parameter ranges covered by the parametric analysis in this study, namely an erection height of 8–26 m, a step spacing of vertical standards of 0.5–3.0 m, a spacing between vertical standards of 0.6–2.0 m, a sweeping rod height of 0.10–0.35 m, and a joint stiffness of 20–60 kN·m/rad. Within these ranges, Equation (4) can be used to preliminarily predict the overall stability of scaffold systems under different erection schemes. The results should then be checked against finite element calculations or code-based verification, thereby improving the efficiency of scheme selection.

As shown in

Table 6. Results of regression analysis.

Variable	Fitted Value	Standard Error	t	p
Erection Heights	−5.219	0.626	−7.519	3.244 × 10−4
Step Spacings of Vertical Standards	−6.215	1.215	−5.762	2.514 × 10−5
Spacings between Vertical Standards	−0.399	0.094	−4.132	5.612 × 10−6
Sweeping Rod Heights	−22.051	6.054	−3.132	3.814 × 10−3
Joint Stiffnesses	0.194	0.029	5.871	1.612 × 10−4

, the regression coefficients and parameter sensitivity results indicate that the step spacing of vertical standards had the most significant influence on the overall stability of the scaffold system, followed by erection height and sweeping rod height, whereas the spacing between vertical standards had a relatively smaller influence. Joint stiffness exhibited a positive enhancement effect. Therefore, in practical engineering design, scaffold stability should preferably be improved by controlling the step spacing of vertical standards and erection height. Under the premise of satisfying the required construction operating space, the sweeping rod height should be appropriately reduced, and the overall mechanical performance should be enhanced by improving the stiffness of joint connections.

6.5. Engineering Applicability Analysis

For engineering application, the regression analysis results obtained in this study can be used for rapid screening and parameter optimization of disc-lock scaffold schemes. For similar high-formwork support systems beneath long-span transfer beams in metro depot over-track development projects, preliminary design and construction control may be carried out according to the following principles.

(1)

The parametric analysis shows that the step spacing of vertical standards is the most sensitive factor affecting the overall stability of the scaffold system. Under the calculation conditions adopted in this study, when the step spacing exceeded 1.5 m, the reduction in the buckling eigenvalue became more pronounced, indicating that the overall stability reserve of the scaffold system was more sensitive to variations in step spacing. Therefore, during the scheme design stage, the step spacing of vertical standards should be taken as a priority control parameter. When the spacing between vertical standards cannot be reduced due to site construction constraints, blindly increasing the step spacing should be avoided.

(2)

Erection height has a significant influence on the overall stability of the scaffold system. When the height exceeds 16 m, the bearing capacity decreases noticeably, and the structure becomes more sensitive to initial imperfections and construction disturbances. For scaffold systems higher than 16 m, overall stability should be improved by measures such as adding horizontal cross bracing, strengthening wall-tie restraints, and imposing stricter control requirements on the verticality of vertical standards.

(3)

Based on 28 sets of parametric numerical simulation results, a multiple linear regression fitting model was established for the buckling eigenvalue of the disc-lock scaffold system. The results show that increases in erection height, step spacing of vertical standards, spacing between vertical standards, and sweeping rod height reduce the overall stability of the scaffold system, among which the step spacing of vertical standards has the most significant influence. In contrast, increasing joint stiffness is beneficial for enhancing the overall stability reserve of the scaffold system. The proposed model can provide a reference for scaffold scheme comparison and stability assessment in similar engineering projects.

(4)

Increasing joint stiffness helps enhance the overall stability of the scaffold system. During design and construction, disc-lock joints should be properly installed in place, and joint gaps and assembly deviations should be reduced to prevent weakened member-end restraint effects caused by connection looseness.

(5)

When the parameter values fall within the range investigated in this study, Equation (4) can first be used to rapidly analyze the buckling eigenvalues of different schemes. Preliminary screening can then be conducted according to the following criteria: when the erection height is greater than 16 m or the step spacing of vertical standards is greater than 1.5 m, the corresponding scheme should be regarded as a condition requiring focused checking and strengthening. When both parameters increase simultaneously, adjustments should preferably be made by reducing the step spacing, optimizing the arrangement of vertical standards, and enhancing joint restraints. This method can be used for rapid judgment during the scheme comparison stage and can reduce the workload associated with repeated modeling and calculation.

In summary, the regression model established in this study can not only describe the influence direction and sensitivity degree of each parameter on overall stability, but also serve as a rapid tool for preliminary scaffold scheme selection and construction pre-control. For similar projects falling within the parameter ranges considered in this study, the regression model can first be used for preliminary estimation, followed by verification through finite element analysis and code-based checking. This approach can support rapid selection and construction control of the support system.

7. Conclusions

(1)

Through the comparison between finite element analysis and field monitoring, the socket-type disc-lock scaffold system demonstrates favorable mechanical performance during the construction of the transfer beam. The numerical simulation results indicate that the maximum compressive stress in the vertical standards is 80.82 MPa, while the field-monitored maximum is 90.92 MPa, resulting in an error of 12.50%, both within the Q355 steel early-warning stress limit. The maximum average cumulative vertical displacement of the scaffold is 1.69 mm in magnitude, which does not exceed the allowable construction deformation. These results indicate that the scaffold system is safe and reliable, meeting the requirements of high-formwork support construction.

(2)

The parametric influence analysis shows that increases in erection height, step spacing of vertical standards, spacing between vertical standards, and sweeping rod height significantly reduce the overall stability of the scaffold, with the step spacing of vertical standards being the most sensitive factor. In contrast, increasing joint stiffness effectively enhances the overall stability of the scaffold system. When the erection height exceeds 16 m or the step spacing of vertical standards is greater than 1.5 m, the bearing capacity exhibits a noticeable inflection point, indicating the need for reinforcement measures to ensure construction safety.

(3)

Based on the multi-parameter numerical simulation results, a multiple linear regression predictive model for the overall stability of the disc-lock scaffold system was established. The model demonstrates good statistical significance and can provide a reference for preliminary design and construction control of scaffold systems in similar engineering projects.

This study systematically analyzed the mechanical characteristics of the socket-type disc-lock full-hall scaffold system beneath a long-span transfer beam and the influence patterns of the main parameters. However, certain limitations remain. First, the parametric analysis was mainly conducted based on single-factor variation, focusing on the independent effects of erection height, step spacing of vertical standards, spacing between vertical standards, sweeping rod height, and joint stiffness. The interaction effects among these parameters were not further considered. In practical engineering, these parameters often vary in a coupled manner, and the structural response under their combined effects may differ from the results obtained from single-factor analysis. Therefore, the conclusions of this study are more applicable to trend judgment and preliminary design analysis. Second, the field investigation in this study mainly focused on stress and displacement monitoring during construction. The monitoring function was primarily used for state identification and result verification, and has not yet been integrated with construction control measures to form real-time linkage.

Thus, there remains room for further development in active control. Future research will be deepened in two aspects [27]. On the one hand, methods such as orthogonal design, response surface analysis, or global sensitivity analysis will be adopted to further investigate the stability response of the scaffold system under multi-parameter coupling conditions, and to establish prediction models that account for interaction effects. On the other hand, the coordinated application of monitoring information and construction control strategies will be explored to establish a closed-loop “monitoring–analysis–control” framework. Based on real-time monitoring data, the risk state of the scaffold system can be dynamically identified, and construction load distribution, pouring sequence, and local strengthening measures can be adaptively optimized, thereby improving the safety and engineering applicability of the scaffold system during construction.