Evaluation Framework for Inter-Module Connections in Steel–Concrete Composite Modular Structures

Abstract

This study presents a structured evaluation framework for inter-module connections in the context of steel–concrete composite modular structures, addressing a gap in existing reviews that have focused almost exclusively on steel modular systems. The paper examines tie-rod (TR), locking mechanism (LM), and bolted inter-module connections, while introducing a new sub-classification of bolted connections into direct bolted (DB) and plug-assisted bolted (PB) types based on assembly methods. A novel four-metric, five-point rating framework is introduced to assess the Composite Compatibility Score (CCS), proposed as a new metric to evaluate the applicability of steel-oriented connections to composite modules; the Validation Evidence Score (VES), which reflects the extent of experimental and numerical validation; the Demountability and Reusability Score (DRS), which measures the ease of assembly and disassembly; and the newly developed Normalised Capacity Index (NCI), which standardises structural capacity assessment across studies reporting different load capacity types. When applied to nearly 50 inter-module connections, the framework reveals that PB connections provide the most well-rounded performance across all evaluation metrics. Overall, the framework establishes a conceptual benchmark for composite modular connection technologies, providing a basis for future research and design practice.

1. Introduction

1.1. Modular Construction Background

Modular construction refers to a building method where individual units, or modules, are prefabricated off-site, typically in a factory setting, before being transported to the construction site for assembly. This process offers several key advantages, such as accelerating construction times by up to 50% [1,2,3], reducing overall costs by up to 10% and up to 25% in on-site labour [1,3]. In addition, modular construction significantly minimises waste, achieving up to a 74% reduction in material waste and a 34% decrease in carbon emissions, contributing to a lower environmental impact [4]. The factory-controlled environment enhances quality control, ensuring consistent standards across modules [5], and promotes safer work conditions, where reportable accidents are reduced by 80% [6]. Furthermore, modular buildings provide flexibility, allowing for easy reconfiguration or expansion, making them adaptable to a wide range of construction needs. Modular construction technologies are gaining traction, especially in sectors that prioritise rapid delivery and high-quality structures. Moreover, the ability to standardise designs and replicate modules makes modular construction highly suitable for high-rise buildings, where repetitive units are commonly used [7].

1.2. Steel–Concrete Composite Modules

Although modular structures can be constructed from various materials, steel is often preferred due to its high strength-to-weight ratio, ductility, robustness, and construction efficiency [8]. In multi-storey buildings, however, hollow steel columns alone present structural limitations, particularly in resisting buckling under heavy loads. To address this challenge, researchers have introduced concrete-filled steel tubes (CFSTs), which effectively combine steel and concrete into composite columns that are highly suited for modular construction applications [9]. These composite modules combine the benefits of both materials: the strength, fire resistance, and durability of concrete, along with the flexibility and efficiency of steel.

The use of CFSTs is especially advantageous in high-rise modular buildings, where the column dimensions are typically kept consistent along the height of the structure to maintain standardised module geometry, thus having identical inter-module connections. In steel modular structures, varying gravity loads between upper and lower storeys often require changes in column size, which complicates fabrication and requires redesigning the inter-module connection geometry at multiple levels. Steel–concrete composite modules with CFST columns overcome this issue by providing substantial increases in axial capacity and stiffness through the concrete infill without altering the dimensions of the steel tube, consistent with extensive CFST research that demonstrates composite interaction across various configurations and confinement effects under monotonic and cyclic axial loading [10,11], while recent studies have also explored CFST beyond structural performance, focusing on reducing CO₂ emissions and cost [12]. Thai et al. [8] highlighted that using different column sizes at different levels, as observed in high-rise steel modular building Croydon Tower, makes the inter-module connection geometry increasingly difficult to standardise.

Despite these advantages, steel–concrete composite modular systems have received far less research attention than their steel-only counterparts. Most proposed inter-module connections in the literature are developed for steel modular systems, creating inherent limitations when transferring these solutions into steel–concrete composite settings. CFST columns introduce additional design considerations for inter-module connections, including (i) ensuring that the concrete filling sequence is not obstructed by the inter-module connection layout, (ii) avoiding access obstructions for bolts or plug-in components that may interfere with concrete filling, (iii) accounting for the interaction between the steel tube and the concrete infill, including both global bond behaviour and local shear transfer mechanisms that influence how the forces are introduced into the composite column at the connection, and (iv) addressing the differences in fire performance compared with steel modular structures. These distinctions highlight why an inter-module connection that performs well in steel modular structures may not be directly applicable to steel–concrete composite modular structures. Beyond modular buildings, similar constructability considerations have been observed in prefabricated composite members using permanent (stay-in-place) formwork systems [13,14].

Figure 1 presents the distribution of modular building projects across various continental regions, with a breakdown by material type [15]. Concrete is the most commonly used material in Asian modular construction, while steel is more widely used in Europe, North America, and Oceania. The use of composite materials remains limited globally, with only a small number of projects in Oceania. Although the dataset is not an exhaustive global inventory of modular building projects, it provides a representative indication of current material usage trends across the regions included.

1.3. Inter-Module Connection Importance

The structural behaviour of modular buildings, especially in high-rise applications, is complex and not yet fully understood, in part due to the critical role of inter-module connections. A critical aspect of ensuring stability in modular structures is the design of inter-module connections, which are responsible for transferring loads between prefabricated units. These connections play a key role in determining the overall stiffness of the structure and its ability to withstand both vertical and lateral forces [16,17]. In high-rise modular buildings, inter-module connections must accommodate various load paths and transfer loads between modules without compromising the structural stiffness or flexibility. Typically, connections in modular structures are designed to bear axial loads, bending moments, and shear forces, each of which affects the building’s global stability under different loading conditions, including gravity, wind, and seismic forces. For example, axial load transfer through column-to-column connections is crucial for maintaining vertical stability, while connections at the horizontal plane, such as beam-to-beam joints, ensure lateral load resistance.

1.4. Aim and Scope of the Review

Inter-module connections are crucial to the structural integrity of modular buildings, as they facilitate effective load distribution between units. Researchers consider the lack of suitable inter-module connections to be a significant limitation in the modular construction sector [2,8]. Several review papers have examined these connections, primarily focusing on steel modules, leaving a notable gap in the literature regarding connections for steel–concrete composite modules. The paper addresses a key gap in the literature by presenting a review of current inter-module connection technologies, coupled with a multi-dimensional evaluation framework to assess their performance against four criteria, which include the applicability in steel–concrete composite modular construction. This paper seeks to provide insights into the types of connections designers can use to develop more effective, well-suited designs for steel–concrete composite modular structures. Figure 2 presents a conceptual roadmap of the study, illustrating the progression from context and challenges, through the methodology, to the analysis and key findings.

2. State-of-the-Art Reviews on Inter-Module Connection Technologies

In this section, key literature review papers have been selected to provide an in-depth understanding of advancements in inter-module connection technologies. These specific studies were chosen because they focus extensively on inter-module connections. By concentrating on studies that specifically review inter-module connections, as summarised in

Table 1. Overview of literature review papers on inter-module connections.

Year	Author	Review Title	Material Scope
2022	Corfar et al. [18]	A comprehensive review and classification of inter-module connections for hot-rolled steel modular building systems	Hot-rolled Steel
2019	Srisangeerthanan et al. [17]	Review of performance requirements for inter-module connections in multi-story modular buildings	Steel
2019	Lacey et al. [19]	Review of bolted inter-module connections in modular steel buildings	Steel
2022	Lacey et al. [20]	Experimental methods for inter-module joints in modular building structures—A state-of-the-art review	Steel
2021	Maali et al. [21]	Review of Interconnection in Modular Structures	Steel
2021	Nadeem et al. [22]	Connection design in modular steel construction: A review	Steel
2021	Rajanayagam et al. [23]	A state-of-the-art review on modular building connections	Steel
2023	Yang et al. [24]	Mechanical Behaviors of Inter-Module Connections and Assembled Joints in Modular Steel Buildings: A Comprehensive Review	Steel

, this section provides a comprehensive overview of the current state of research and identifies potential areas for further studies.

Literature reviews on inter-module connections for modular structures have had some significant advancements in recent years. Corfar et al. [18] provided a comprehensive review and classification of inter-module connections for steel modular buildings. They identified key gaps in the field, such as inconsistent nomenclature and the need for a unified classification system. The study also proposed future research directions, such as inter-module connections with enhanced demountability and reuse without compromising strength and stiffness. Srisangeerthanan et al. [17] reviewed performance requirements for inter-module connections in multi-storey modular buildings. They assessed structural, manufacturing, and construction aspects, identified challenges in achieving effective lateral load transfer and high-performing connections, and emphasised the need for high-performance, standardised connections to advance modular construction.

Lacey et al. [19] focused specifically on bolted inter-module connections in modular steel buildings. Their review assessed the mechanical performance and design considerations of bolted joints, highlighting their advantages, such as ease of assembly and disassembly, and estimating the stiffness properties of these bolted connections. In a follow-up paper, Lacey et al. [20] reviewed experimental methods for studying inter-module connections. They provided an overview of testing protocols and measurement techniques. They concluded that standardised testing methods are crucial for accurately evaluating the structural behaviour of these joints and improving connection designs.

Maali et al. [21] offered a broad overview of inter-module connections in modular structures and classified the connections. Their review underlined the critical role of inter-module connections in ensuring stability, load transfer, and overall structural performance while pointing out the need for further research to improve connection design. Nadeem et al. [22] examined various inter-module connection designs in modular steel buildings; their study focused on structural performance and implementation. They underscored the need for standardised design guidelines and highlighted the need for simple, efficient connection designs, especially for high-rise applications.

Rajanayagam et al. [23] provided a comprehensive review of modular building connections, including inter-module, intra-module, and module-to-foundation connection types. They examined various design approaches for inter-module connections, focusing on features such as vertical and horizontal connectivity, as well as the mechanical behaviour of different connection types. Yang et al. [24] conducted a comprehensive review of the mechanical behaviours of inter-module connections in modular steel buildings. Their study focused on the mechanical complexities and load transfer paths. The authors highlighted the need for further research on self-locking connections to improve the integrity of modular buildings.

After reviewing the literature on inter-module connections, it is evident that existing studies primarily focus on steel modules, with little to no consideration of steel–concrete composite modules. This gap is addressed in the present review by providing a structured classification of inter-module connection types and a comprehensive performance-based evaluation to guide their application and development for composite modular construction. Furthermore, in this study, a comparative evaluation framework is introduced, assessing inter-module connections based on key criteria, including composite compatibility, validation evidence, demountability, and structural capacity. Through this approach, this review delivers a focused analysis of inter-module connections for composite modular buildings, identifying inter-module connection designs that are potentially transferable to composite modules and highlighting those that exhibit limitations.

Figure 3 provides a visual summary of the gap highlighted in this section, contrasting the focus on steel modules in existing reviews with the limited attention to steel–concrete composite modules.

3. Overview and Classification of Modular Connections

This section provides an overview of how modular buildings are structurally connected, outlining the main connection types and establishing the context for the detailed classification of inter-module connections that follows.

3.1. Classification and Types of Modular Connections

In modular structures, connections can be generally categorised into three main types: intra-module, inter-module, and module-to-foundation connections. Intra-module connections refer to the joints within a single module, connecting elements such as beams and columns. These connections are typically assembled in the factory using traditional methods like bolting or welding. Inter-module connections link individual modules together onsite, forming a larger structure. These types of connections facilitate the load transfer between the different modules, which contribute to the overall stability of the modular structure. These connections play a critical role in preventing progressive collapse and maintaining the structural integrity of the modular building. Lastly, module-to-foundation connections anchor the entire modular building to its foundation, which provides a secure base for the structure. These connection types are summarised in Figure 4, which synthesises classifications commonly reported in the literature.

Rajanayagam et al. [23], Srisangeerthanan et al. [17,25], Lacey et al. [26], and Maali et al. [21] classified modular connections into the aforementioned three types. However, Chen et al. [27] introduced a fourth type: modules-to-frame/core connections, which transfer loads between the modular units and the primary frame or core.

3.2. Classification and Types of Inter-Module Connections

This subsection outlines the classification of inter-module connections identified in the literature. Farajian et al. [28] classified inter-module connections based on stiffness and strength. They proposed criteria for buckling (ultimate limit state) and displacement/drift (serviceability limit state). This classification was developed to simplify design and ensure structural stability for modular buildings, whilst He et al. [29] focused on a more detailed classification system that incorporates both inter-module and intra-module connections. They identified critical stiffness parameters and derived boundary limits to define the rigidity, ensuring a clear distinction between rigid and non-rigid connections.

In classifying the different types of proposed designs for inter-module connections, Thai et al. [8] presented three main types. First, there are tie-rod connections, which are used to connect vertical elements like columns from the lower module to the upper module, ensuring strong column-to-column load transfer. These connections use tie rods, plugin bars, or threaded rods to join the modules vertically. Second, there are plug-in connectors, which are prefabricated and pre-welded onto the modules for quick and easy on-site assembly by slotting or locking modules together using these connectors. Third, there are bolted connections, where plates or components from adjacent modules are joined using bolts.

Corfar et al. [18] proposed a classification of inter-module connections similar to that of Thai et al. [8], grouping them into three main types. The first category is post-tension connections, equivalent to the tie-rod connections described by Thai et al. The second category includes locking device connections, aligning with Thai et al.’s plug-in connectors classification. The third category consists of bolted connections, which are also emphasised in Thai et al.’s classification. This study adopts a similar high-level classification approach.

Furthermore, Corfar et al. [18] further sub-classified bolted inter-module connections according to their geometric location, such as column-to-column, beam-to-beam, and fitting-to-fitting. While this approach provides a clear spatial understanding of connection types, it offers limited insight into aspects such as constructability, particularly how the connection is installed and handled during onsite assembly and disassembly. To complement this perspective, the present study introduces a novel sub-classification based on assembly method, aimed at highlighting factors relevant to installation procedures and modularity characteristics.

3.3. Sub-Classification of Bolted Inter-Module Connections

Building on the classifications reported in the literature, this subsection introduces an additional sub-classification of bolted inter-module connections based on their assembly method, as shown in Figure 5. Direct bolted connections refer to those in which bolts are accessible and installed entirely from the exterior of the modules, without requiring access to enclosed hollow sections or internal compartments. In contrast, plug-assisted bolted connections involve systems that integrate plug-in components, such as tenons, sleeves, or locating pins, to assist alignment or load transfer, in combination with bolting.

To highlight the implications of this sub-classification,

Table 2. Comparative assessment of direct bolted and plug-assisted bolted inter-module connections.

Feature	Direct Bolted Connections	Plug-Assisted Bolted Connections
Assembly Method	Bolts are inserted and tightened directly from the module exterior without any assistive alignment components	Combination of plug-in alignment components (e.g., tenons or sleeves) followed by bolting
Access Required	Typically require full exterior access for bolt placement and tightening	Typically require only partial interior or limited exposed access
Ease of Assembly and Disassembly	Moderate; depends on bolt locations and module layout	High; plug-in components reduce alignment time and simplify removal process
Alignment Precision	Manual alignment typically required during installation	Improved with the use of plug-in components like tenons and sleeves
Composite Compatibility	Often slightly lower due to bolt access needs	Often higher due to pre-configured geometry
Structural Capacity	Usually higher due to direct bolt force transfer	May be slightly reduced depending on plug geometry or load eccentricity
Manufacturing Simplicity	Often uses typical components such as plates and bolts, making it easier to manufacture	Typically requires specially fabricated plug-in parts such as sleeves or tenons

compares these subtypes across key characteristics.

In the literature, bolted inter-module connections are the most commonly proposed type for steel modules due to their comparatively well-understood mechanical behaviour. Bolt-related load transfer mechanisms are well established in steel construction, providing a clearer basis for assessing these inter-module connections.

3.4. Excluded Connection Types and Alternative Designs

There are other methods used for connecting modules, which include wet grouting, welding, or adhesive bonds. While these types of connections effectively meet the structural requirements by providing enough strength and stability, their main drawback is the lack of demountability. This characteristic goes against one of the core advantages of modular construction, which is flexibility and ease of assembly and disassembly. Although welded, grouted, and adhesive connections offer structural performance, they limit the modularity of the building, as they are difficult, if not impossible, to dismantle once assembled. Hence, these types of connections were omitted from consideration in this study. Examples of excluded inter-module connections include shear-keyed grouted sleeve connections [30] and welded connections [31].

4. Evaluation and Classification of Existing Inter-Module Connections

This section presents a comprehensive review of 47 inter-module connections identified in existing literature. The inter-module connections have been classified, and the findings are categorised across four detailed tables:

Table 3. Summary of tie-rod inter-module connections and their applicability to steel–concrete composite modular systems.

Connection ID. Author and Year	Steel–Concrete Composite Module Applicability
TR01 [32] Chen et al. 2017	The connection was designed with CFST in consideration. The connection is directly applicable.
TR02 [33,34] Sanches et al. 2018	In this design, filling the columns with concrete is not feasible due to the position of the threaded rod running through the column.
TR03 [35] Lacey et al. 2019	In this design, filling the columns with concrete is not feasible due to the position of the tie rod running through the column. In addition to the access openings on the side of the columns.
TR04 [36] Han et al. 2024	In this design, filling the columns with concrete is not feasible due to the position of the rod running through the column, as well as the roof and floor nodes at the ends of the columns.

for tie-rod (TR) inter-module connections,

Table 4. Summary of locking mechanism inter-module connections and their applicability to steel–concrete composite modular systems.

Connection ID. Author and Year	Steel–Concrete Composite Module Applicability
LM01 [37,38] Chen et al. 2021	Applicability may be possible for this connection by pouring the concrete off-site, as the corner fittings are pre-welded to the columns.
LM02 [39,40,41] Chen et al. 2019	Applicability may be possible for this connection by pouring the concrete off-site, as the connectors are pre-welded to the columns.
LM03 [42] Dai et al. 2019	Applicability may be possible for this connection by pouring the concrete off-site, as the connectors are pre-welded to the columns.
LM04 [43] Yang et al. 2023	In this design, columns may only be pre-filled with concrete in the factory to create CFST, as the inner insert plate is pre-welded onto the lower columns.
LM05 [44,45] Nadeem et al. 2022	In this design, concrete can be filled into the steel columns before installing the adapters and centre plates.
LM06 [46,47] Srisangeerthanan et al. 2022	In this design, columns may only be pre-filled with concrete in the factory to create CFST, as the internal and external units are pre-welded onto the ends of the columns.
LM07 [48] Sharafi et al. 2017	In this design, concrete can be filled into the steel columns after the assembly is complete, as it does not interfere with the columns.

for locking mechanism (LM) inter-module connections,

Table 5. Summary of direct bolted inter-module connections and their applicability to steel–concrete composite modular systems.

Connection No. Author and Year	Steel–Concrete Composite Module Applicability
DB01 [49] Kandel et al. 2023	The connection was designed with CFST in consideration. The connection is directly applicable to steel–concrete composite modules.
DB02 [50] Liu et al. 2023	Pouring concrete in the columns on-site is not possible. However, applicability may be possible for this connection by pouring the concrete off-site, as the top plates are pre-welded to the columns.
DB03 [51] Sendanayake et al. 2019	In this design, columns may only be pre-filled with concrete in the factory to create CFST, as the endplates are pre-welded onto the columns before onsite assembly.
DB04 [52,53] Deng et al. 2018	In this design, concrete can be filled into the steel tubes after bolting is completed, and the cover plate is welded.
DB05 [54] Yang et al. 2020	This connection is feasible for CFSTs, with concrete filling up to the column plates, leaving a small area near the connection unfilled.
DB06 [55] Park et al. 2015	In this design, concrete can be filled into the steel tubes after the cross-shaped plate and bolts are installed.
DB07 [56] Styles et al. 2016	This connection is feasible for CFSTs, with concrete filling the column without affecting the splice connections.
DB08 [57] Gunawardena 2016	This connection is feasible for CFSTs, with concrete filling the column without affecting the bolting of the plates.
DB09 [58] Zhai et al. 2023	In this design, concrete can be filled into the steel tubes after the connection has been assembled for designs without strengthening stiffening ribs. However, if the stiffening ribs are pre-welded, the concrete would need to be pre-filled.
DB10 [59,60] Qin et al. 2023 & Tan et al. 2024	The design of this connection does not incorporate hollow steel sections for the columns, making the application of CFST unsuitable for this design.
DB11 [61] Hu et al. 2020	In this design, columns may only be pre-filled with concrete in the factory to create CFST. The positioning plates are pre-welded onto the lower columns before onsite assembly.
DB12 [62] Lee et al. 2018	In this design, the connection requires certain adjustments or off-site modifications to facilitate concrete filling, as the ceiling bracket blocks the top of the column.
DB13 [63] Liu et al. 2015	This connection is suitable for CFSTs, allowing concrete to fill the steel columns without obstructing the bolted splicing of the connection.
DB14 [64] Wang et al. 2019	In this design, columns may only be pre-filled with concrete in the factory to create CFST. The locating tubes and end plates are pre-welded onto the columns before assembly.
DB15 [65] Cho et al. 2019	In this design, concrete can be filled into the steel tubes after the blind bolts are installed to avoid affecting the installation.
DB16 [66] Lyu et al. 2021	In this design, concrete can be filled into the steel tubes before the splice connection is installed.
DB17 [67,68] Deng et al. 2023	Applicability may be possible for this connection by pouring the concrete off-site, as the corner fittings are pre-welded to the columns.
DB18 [69] Shi et al. 2023	In this design, columns may only be pre-filled with concrete in the factory to create CFST, as the ceiling-cast steel connectors are pre-welded onto the columns before onsite assembly.
DB19 [70,71] Dhanapal et al. 2019 and Vectorbloc Corp.	In this design, columns may only be pre-filled with concrete in the factory to create CFST, as the upper bloc is pre-welded onto the columns before onsite assembly.
DB20 [72] Lee et al. 2021	In this design, columns may only be pre-filled with concrete in the factory to create CFST. The bottom blocks are pre-welded onto the lower columns.
DB21 [73,74] Liu et al. 2024 and Zhang et al. 2024	Applicability may be possible for this connection by pouring the concrete off-site, as the corner fittings are pre-welded to the columns.
DB22 [75] Chen et al. 2014	Columns may only be pre-filled with concrete in the factory to create CFST. The down joint is pre-welded onto the columns before assembly.

for direct bolted (DB) inter-module connections, and

Table 6. Summary of plug-assisted bolted inter-module connections and their applicability to steel–concrete composite modular systems.

Connection No. Author and Year	Steel–Concrete Composite Module Applicability
PB01 [76,77] Peng et al. 2021	The connection was designed with CFST in consideration. The connection is directly applicable.
PB02 [78] Han et al. 2023	Applying CFST to Type A is feasible since the top opening for the shear key can be used to fill the column with concrete. However, for Type B, adding concrete is challenging due to the side opening needed for tightening the nut.
PB03 [79] Ma et al. 2023	In this design, concrete can be filled into the steel tubes after the one-sided bolts are installed to avoid affecting the bolts.
PB04 [80] Shi et al. 2023	In this design, concrete can be filled into the steel tubes after the bolts are installed to avoid affecting the bolts.
PB05 [81] Zhang et al. 2021	In this design, concrete can be filled into the steel tubes after the plug-in connector is installed.
PB06 [82] Khan et al. 2020	In this design, concrete can be filled into the steel tubes after tenon and bolts are installed. The upper connection is designed to be hollow for tenon insertion, allowing for CFST application in the columns.
PB07 [83,84,85] Chen et al. 2017	In this design, concrete can be filled into the steel tubes, specifically after the plug-in devices have been installed.
PB08 [86,87] Lacey et al. 2019	This connection is feasible for CFSTs, as the concrete can fill the steel columns without interfering with the bolts positioned outside the tubes.
PB09 [88] Bazarchi et al. 2023	In this design, columns may only be pre-filled with concrete in the factory to create CFST, as the cap plates are pre-welded onto the columns before onsite assembly.
PB10 [89] Yang et al. 2023	In this design, concrete can be filled into the steel tubes after the connection has been assembled.
PB11 [90,91] Corfar et al. 2023	In this design, columns may only be pre-filled with concrete in the factory to create CFST. The corner steel boxes are pre-welded onto the columns before onsite assembly.
PB12 [92] Deng et al. 2017	In this design, concrete can be filled into the steel tubes after the connection has been assembled.
PB13 [93] Ma et al. 2021	In this design, concrete can be filled into the steel tubes during the assembly.
PB14 [94] Zhai et al. 2023	Pouring concrete in the columns on-site is not possible. However, applicability may be possible for this connection by pouring the concrete off-site, as in this design, a connection plate is pre-welded atop the SHS columns.

for plug-assisted (PB) bolted inter-module connections. By systematically comparing these designs, which are primarily intended for steel modules, this chapter highlights advancements, challenges, and practical considerations related to their application in composite modules.

4.1. Review of Tie-Rod Inter-Module Connections

The reviewed TR connections commonly employ post-tensioned rods combined with shear keys or plates to enhance lateral performance. However, a key limitation is their compatibility with steel–concrete composite modules; only TR01 was explicitly designed to support composite module integration.

4.2. Review of Locking Mechanism Inter-Module Connections

LM connections utilise self-locking features such as tabs, rotary parts, and interlocking latches to enable efficient assembly and load transfer. Several designs may be compatible with steel–concrete composite modules if concrete filling is carried out off-site before LM part installation, though this compatibility is not universal.

4.3. Review of Direct Bolted Inter-Module Connections

DB connections primarily use bolted plates, splice joints, or gusset components to form reliable connections between modules. Most designs demonstrate good compatibility with steel–concrete composite modules, typically allowing concrete filling either before or after assembly, depending on the configuration. This makes DB connections generally well-suited for composite modular systems.

4.4. Review of Plug-Assisted Bolted Inter-Module Connection

PB connections integrate plug-in mechanisms with bolted assemblies to achieve both vertical alignment and structural continuity between modules. Most designs show potential compatibility with steel–concrete composite modules, though the construction sequence varies, where in some cases concrete can be filled after plug-in installation, while in others it can only be completed beforehand.

5. Evaluation Framework

In order to facilitate comparative analysis of inter-module connection performance, four metrics were formed and used to measure every connection: Composite Compatibility Score (CCS), Validation Evidence Score (VES), Demountability and Reusability Score (DRS), and Normalised Capacity Index (NCI). Each of these metrics is defined below and used to measure every connection that is summarised above in Table 3, Table 4, Table 5 and Table 6.

5.1. Composite Compatibility Score (CCS)

The Composite Compatibility Score (CCS) evaluates the extent to which each inter-module connection can be integrated in a composite module system, considering both design feasibility and constructability. The scoring criteria are presented in

Table 7. Composite Compatibility Score (CCS) rating criteria for inter-module connections.

Composite Compatibility Score (CCS) Rating	Description
CCS 5 Directly applicable	The connection design explicitly supports concrete filling in steel tubes without complications, making it fully optimised for CFST modules and highly suitable for composite structures.
CCS 4 Suitable for on-site concrete filling	The connection design allows for concrete to be filled into the steel tubes during or after assembly with minimal challenges, effectively accommodating CFST for steel–composite modules.
CCS 3 Moderately applicable	The connection design offers partial compatibility with CFST, requiring certain adjustments or off-site modifications to facilitate concrete filling.
CCS 2 Limited to factory pre-filling	Concrete filling is only feasible in a controlled factory environment, as specific design elements obstruct the top of the column, preventing onsite pouring.
CCS 1 Not applicable	The connection design is incompatible with steel–concrete module application, as concrete filling is not feasible due to inherent design features.

.

5.2. Validation Evidence Score (VES)

The Validation Evidence Score (VES) captures how rigorously each connection has been evaluated across experimental testing and numerical analysis. The scoring criteria are presented in

Table 8. Validation Evidence Score (VES) rating criteria for inter-module connections.

Validation Evidence Score (VES) Rating	Description
VES 5	Comprehensive validation including experimental testing, validated numerical simulation (e.g., FEM), and additional mathematical modelling or parametric studies.
VES 4	Both experimental testing and numerical simulation were performed.
VES 3	Experimental testing only, without any supporting simulations or modelling.
VES 2	Numerical modelling only, without experimental validation.
VES 1	Conceptual only; no experimental testing or numerical simulation.

.

5.3. Demountability and Reusability Score (DRS)

The Demountability and Reusability Score (DRS) evaluates the extent to which each inter-module connection supports ease of assembly and disassembly. The scoring criteria are presented in

Table 9. Demountability and Reusability Score (DRS) rating criteria for inter-module connections.

Demountability and Reusability Score (DRS) Rating	Description
DRS 5 Highly optimised demountability	Specifically designed for repeated assembly and disassembly. The connection enables rapid, intuitive installation and removal with minimal manual intervention.
DRS 4 Efficient demountability	The connection is designed for fast installation. Assembly and disassembly involve minimal manual adjustment, with features that streamline alignment and reduce reinstallation steps.
DRS 3 Reliable demountability	The connection supports predictable and consistent assembly and disassembly. The design allows clear access and tolerates minor misalignments, reducing the risk of error during reinstallation.
DRS 2 Conventional demountability	Fully demountable using standard tools and procedures. Reuse is practical but typically requires sequencing, manual realignment, or skilled labour.
DRS 1 Demountable with significant effort	Disassembly is possible but difficult. It may require internal access or tight working conditions. Reuse is feasible but time consuming and labour intensive.

.

5.4. Normalised Capacity Index (NCI)

To enable a systematic comparison of the structural capacity of the various inter-module connections, this study introduces the Normalised Capacity Index (NCI), a dimensionless metric that evaluates the relative structural capacity of each connection based on reported structural capacities. Given that inter-module connections are tested under a variety of load types, connecting members with different sectional properties, the NCI is formulated to provide a standardised scale from 0 to 1 that facilitates comparative assessment without unit dependencies.

5.4.1. Capacity Adjustment Factor

Before computing the NCI, each reported capacity is first converted into an adjusted capacity C_i,adj, to minimise the influence of column section size and material strength, allowing the capacities to more accurately reflect the intrinsic behaviour of the inter-module connection rather than the stiffness or strength of the supporting column. Two adjustment considerations were applied to account for differences in column characteristics: one related to the sectional properties and another related to the material strength.

To streamline the adjustment process, the section-based and material-based modifiers were combined into a single Capacity Adjustment Factor (F), defined according to the relevant structural action. The specific form of F varies by action and is denoted as F_A, F_h, F_Z, or F_I depending on whether the reported capacity is axial/shear, lateral load, moment, or rotational stiffness, respectively. The adjustment factors for the different structural actions are defined as follows:

For axial and shear capacities, the governing section property is the column cross-sectional area. The combined adjustment factor F_A is defined as

$$F_A={\displaystyle \frac{A_0}{A_i}}\times {\displaystyle \frac{f_{y0}}{f_{yi}}}$$

(1)

For lateral load capacities, additional adjustments were required to account for differences in both the height at which the lateral load was applied and the number of columns participating in resisting the load. The combined adjustment factor F_h is defined as

$$F_h={\displaystyle \frac{A_0}{A_i}}\times {\displaystyle \frac{f_{y0}}{f_{yi}}}\times {\displaystyle \frac{h_i}{h_0\times n_{col,i}}}$$

(2)

For moment capacity, which depends on the plastic section modulus, the combined adjustment factor F_Z is defined as

$$F_Z={\displaystyle \frac{Z_{p0}}{Z_{pi}}}\times {\displaystyle \frac{f_{y0}}{f_{yi}}}$$

(3)

For rotational stiffness, which is governed by flexural rigidity, variations in Young’s modulus were negligible across all tests; therefore, the material adjustment is omitted. Accordingly, only the section-based adjustment is applied using the second moment of area, and the combined adjustment factor F_I is defined as

$$F_I={\displaystyle \frac{I_0}{I_i}}$$

(4)

Slip resistance capacities did not receive a section or material adjustment and are assigned F = 1. This is because slip behaviour is governed primarily by the connector’s geometric design, along with its clamping and frictional mechanisms, rather than the column’s sectional properties. Applying section-based or material-based adjustments would introduce scaling unrelated to the actual slip behaviour.

Where A_i, Z_pi, and I_i are the cross-sectional area, plastic section modulus, and second moment of area of the inter-module connection’s column, respectively, and A₀, Z_p0, and I₀ are the corresponding properties of the reference section. Likewise, f_yi and f_y0 denote the yield strengths of the specimen and reference steels, respectively. h_i is the effective column height for inter-module connection i, h₀ is the reference height, and n_col,i denotes the number of columns resisting the lateral load in each reported test.

A hollow-section column of 150 × 150 × 9 mm of 350 MPa steel, with a height of 3.00 m, is adopted to define the reference section. This size and height were selected as a mid-point representative of the column dimensions reported across the studies. Selecting a mid-range reference section ensures a practical and consistent baseline for normalisation. Since all adjustments are ratio based, this choice does not affect the relative ranking of the inter-module connections; it only scales the values proportionally.

It is worth noting that two inter-module connections (TR01 and PB01) incorporate concrete into the steel columns, which were not included in the material strength adjustment to avoid unnecessary complexity.

By determining the adjustment factors for the various actions (i.e., Equations (1)–(4)), the adjusted capacity for each inter-module connection is obtained as

$$C_{i,adj}=C_i\times F$$

(5)

where

• C_i is the original reported capacity.
• F is the Capacity Adjustment Factor.

5.4.2. Normalised Capacity Index (NCI) Computation

With all capacities adjusted to a reference section size and material strength, the Normalised Capacity Index (NCI) for each structural action is computed by comparing the adjusted capacity of a given inter-module connection to the maximum adjusted capacity reported for that action across all studies. The Normalised Capacity Index for an inter-module connection under a specific capacity type k is defined as

$${NCI}_{i,k}={\displaystyle \frac{C_{i,adj,k}}{max\left(C_{adj,k}\right)}}$$

(6)

where

• NCI_i,k is the Normalised Capacity Index for inter-module connection i under capacity type k.
• C_i,adj,k is the adjusted capacity of connection i for capacity type k.
• C_adj,k is the set of all adjusted capacities reported across all inter-module connections for capacity type k.
• max(C_adj,k) is the maximum adjusted capacity among all inter-module connections for capacity type k.

This normalisation is applied separately for each load type k to capture the unique structural response associated with different capacity measures for each connection. Consequently, a given connection may have up to seven individual NCI values, depending on which capacity types were reported in the original studies. These load capacity types include

• NCI_Tension;
• NCI_Compression;
• NCI_Moment;
• NCI_Shear;
• NCI_Lateral;
• NCI_Slip;
• NCI_{Rotational Stiffness}.

These individual scores enable precise assessment of a connection’s behaviour under distinct loading types. However, since not all connections are tested under all loading types, and to facilitate meaningful comparisons, three aggregate NCI indicators were defined, as presented in

Table 10. Aggregate NCI indicators and their description.

Indicator	Description
${NCI}_{min}$	The lowest NCI score reported for a given connection, highlighting its weakest structural dimension.
${NCI}_{max}$	The highest NCI score reported for a given connection, reflecting its strongest structural dimension.
${NCI}_{avg}$	The mean of all available NCI scores for a given connection representing its overall normalised structural performance across tested capacities.

.

By focusing on relative capacity rather than absolute capacity, the NCI framework avoids the challenge of comparing fundamentally different capacity types, such as tension versus moment, on an equal basis. This normalisation eliminates any possible inconsistencies that arise from varying load types, effectively enabling “apples-to-apples” comparison.

In applying this normalisation approach, it is important to note that many inter-module connections were reported with only one structural capacity type, and several others included only a few capacity parameters. In these cases, aggregate indicators (NCI_min, NCI_max, NCI_avg) were calculated based on the available reported capacity data for that connection, acknowledging that these scores represent limited evidence rather than comprehensive performance.

A brief sensitivity check indicated that varying the reference assumption (using either smaller or larger sections) naturally altered the adjustment factors and consequently the NCI values; however, this did not affect the relative ranking of the connections in terms of their comparative performance.

The NCI framework is intended as an indicative structural rating tool rather than a design guideline. Its primary purpose is to enable a structured, comparative evaluation of inter-module connections across diverse studies, rather than dictate design decisions.

6. Performance Evaluation for Inter-Module Connections

6.1. Structural Performance Evaluation Using Normalised Capacity Index (NCI)

This section presents the NCI results for all evaluated inter-module connections, grouped by inter-module connection type: TR inter-module connection in

Table 11. NCI results for tie-rod (TR) connections, including min, max, and average values, capacity types, and NCI metrics reported.

Connection ID	Minimum NCI Value	Capacity Type (Min)	Maximum NCI Value	Capacity Type (Max)	NCI Metrics Reported	Average NCI Value
TR01	0.84	Lateral Load	0.84	Lateral Load	1	0.84
TR02	0.25	Lateral Load	0.25	Lateral Load	1	0.25
TR03	0.24	Slip Resistance	0.24	Slip Resistance	1	0.24
TR04	0.57	Axial Compression	0.57	Axial Compression	1	0.57

, LM inter-module connection in

Table 12. NCI results for locking mechanism (LM) connections, including min, max, and average values, capacity types, and NCI metrics reported.

Connection ID	Minimum NCI Value	Capacity Type (Min)	Maximum NCI Value	Capacity Type (Max)	NCI Metrics Reported	Average NCI Value
LM01	0.23	Axial Tension	0.39	Moment	2	0.31
LM02	0.03	Moment	1.00	Shear	4	0.30
LM03	0.31	Rotational Stiffness	0.40	Moment	3	0.35
LM04	0.24	Axial Tension	0.24	Axial Tension	1	0.24
LM05	0.22	Slip Resistance	0.45	Moment	2	0.34
LM06	0.39	Shear	0.61	Axial Compression	3	0.53
LM07	---		---		0	---

, DB inter-module connection in

Table 13. NCI results for direct bolted (DB) connections, including min, max, and average values, capacity types, and NCI metrics reported.

Connection ID	Minimum NCI Value	Capacity Type (Min)	Maximum NCI Value	Capacity Type (Max)	NCI Metrics Reported	Average NCI Value
DB01	0.13	Axial Tension	0.13	Axial Tension	1	0.13
DB02	---		---		0	---
DB03	0.35	Lateral Load	0.35	Lateral Load	1	0.35
DB04	0.37	Moment	0.37	Moment	1	0.37
DB05	0.74	Moment	0.74	Moment	1	0.74
DB06	---		---		0	---
DB07	1.00	Axial Tension	1.00	Axial Tension	1	1.00
DB08	0.22	Shear	0.22	Shear	1	0.22
DB09	0.51	Moment	0.76	Rotational Stiffness	2	0.64
DB10	0.18	Moment	0.18	Moment	1	0.18
DB11	0.21	Rotational Stiffness	1.00	Lateral Load	2	0.61
DB12	1.00	Rotational Stiffness	1.00	Moment	2	1.00
DB13	---		---		0	---
DB14	0.75	Moment	0.75	Moment	1	0.75
DB15	0.49	Lateral Load	0.49	Lateral Load	1	0.49
DB16	0.54	Axial Compression	0.54	Axial Compression	1	0.54
DB17	0.58	Axial Tension	0.64	Axial Compression	2	0.61
DB18	0.33	Axial Tension	0.77	Axial Compression	2	0.55
DB19	0.55	Axial Tension	1.00	Axial	2	0.78
DB20	0.20	Moment	0.20	Moment	1	0.20
DB21	0.04	Rotational Stiffness	0.08	Moment	3	0.06
DB22	0.27	Moment	0.65	Axial Compression	2	0.46

, and PB inter-module connection in

Table 14. NCI results for plug-assisted (PB) connections, including min, max, and average values, capacity types, and NCI metrics reported.

Connection ID	Minimum NCI Value	Capacity Type (Min)	Maximum NCI Value	Capacity Type (Max)	NCI Metrics Reported	Average NCI Value
PB01	0.72	Lateral Load	0.72	Lateral Load	1	0.72
PB02	0.13	Axial Tension	0.13	Axial Tension	1	0.13
PB03	0.19	Lateral Load	0.19	Lateral Load	1	0.19
PB04	0.28	Moment	0.28	Moment	1	0.28
PB05	0.57	Lateral Load	0.57	Lateral Load	1	0.57
PB06	0.79	Lateral Load	0.79	Lateral Load	1	0.79
PB07	0.18	Axial Compression	0.18	Axial Compression	1	0.18
PB08	0.26	Slip Resistance	0.26	Slip Resistance	1	0.26
PB09	0.07	Shear	1.00	Slip Resistance	3	0.48
PB10	0.52	Lateral Load	0.52	Lateral Load	1	0.52
PB11	0.03	Shear	0.48	Lateral Load	3	0.25
PB12	0.79	Axial Compression	0.79	Axial Compression	1	0.79
PB13	0.85	Rotational Stiffness	0.85	Moment	2	0.85
PB14	---		---		0	---

. Each table includes each connection’s minimum, maximum, and average NCI scores, along with the corresponding structural capacity types and the number of NCI metrics reported. The results enable standardised comparison across diverse inter-module connection types.

All evaluated TR connections reported only a single NCI metric, reflecting a limited scope of structural capacity testing. This restricts the depth of performance evaluation for this connection type.

LM connections exhibited the most diverse NCI metric coverage among all types, with several reporting multiple structural capacities, enabling a more comprehensive assessment. These connections generally performed best under moment capacity, with axial tension emerging as the weakest dimension in more than one case.

DB connections most frequently reported moment capacity as their highest-performing metric, followed by axial compression. A smaller number demonstrated strength in initial rotational stiffness or lateral load, indicating varied performance profiles within this inter-module connection type.

PB connections generally achieved their highest NCI values under maximum lateral load, indicating strong lateral performance within this connection category. However, it is vital to note that across all types, many connection entries report only a single NCI metric, limiting the ability to fully assess their performance across different loading types.

Scope of Normalised Capacity Index (NCI) Assessment

While the evaluation framework offers a structured comparison for the NCI metric, it is important to note that the depth of assessment varies among connections. Many designs were reported with only one or a few structural capacity parameters, which limits the completeness of their NCI profile. In such cases, the aggregate NCI indicators represent the available evidence rather than a fully multi-dimensional capacity assessment.

For the complete dataset, Appendix A presents the reported structural capacity values for each inter-module connection across the relevant structural performance metrics, while Appendix B.1 provides the corresponding capacity adjustment factors. Appendix B.2 lists the adjusted structural capacity values, and Appendix C presents the corresponding NCI score values derived from those adjusted structural performance metrics.

6.2. Comparative Performance Across Evaluation Metrics

This section presents the performance score results for all evaluated inter-module connections, grouped by inter-module connection type: TR in

Table 15. Performance scores for tie-rod (TR) inter-module connections.

Connection ID	CCS	VES	DRS	NCIavg
TR01	5	4	2	0.84
TR02	1	3	1	0.25
TR03	1	4	1	0.24
TR04	1	4	1	0.57

, LM in

Table 16. Performance scores for locking mechanism (LM) inter-module connections.

Connection ID	CCS	VES	DRS	NCIavg
LM01	2	4	3	0.31
LM02	2	5	3	0.30
LM03	2	3	4	0.35
LM04	2	5	4	0.24
LM05	4	4	3	0.34
LM06	2	5	4	0.53
LM07	4	4	2	-

, DB in

Table 17. Performance scores for direct bolted (DB) inter-module connections.

Connection ID	CCS	VES	DRS	NCIavg
DB01	5	2	4	0.13
DB02	2	4	4	-
DB03	2	2	3	0.35
DB04	4	5	2	0.37
DB05	3	4	3	0.74
DB06	4	4	2	-
DB07	4	2	2	1.00
DB08	4	4	2	0.22
DB09	3	4	4	0.64
DB10	1	3	4	0.18
DB11	2	4	3	0.61
DB12	3	5	3	1.00
DB13	4	5	2	-
DB14	2	3	3	0.75
DB15	4	3	4	0.49
DB16	4	4	2	0.54
DB17	2	4	2	0.61
DB18	2	5	2	0.55
DB19	2	4	2	0.78
DB20	2	4	2	0.20
DB21	2	5	2	0.06
DB22	2	2	2	0.46

, and PB in

Table 18. Performance scores for plug-assisted bolted (PB) inter-module connections.

Connection ID	CCS	VES	DRS	NCIavg
PB01	5	4	4	0.72
PB02	3	3	3	0.13
PB03	4	2	4	0.19
PB04	4	4	3	0.28
PB05	4	4	4	0.57
PB06	4	4	4	0.79
PB07	4	4	3	0.18
PB08	4	4	4	0.26
PB09	2	5	2	0.48
PB10	4	3	4	0.52
PB11	2	5	2	0.25
PB12	4	2	3	0.79
PB13	4	4	4	0.85
PB14	2	4	3	-

. Each table reports the Composite Compatibility Score (CCS), Validation Evidence Score (VES), Demountability and Reusability score (DRS), and average Normalised Capacity Scores (NCI_avg) for individual inter-module connections.

TR connections consistently showed low composite compatibility and limited demountability, with all but one entry receiving the lowest possible score in both CCS and DRS. NCI_avg values varied across the group, though overall performance was modest.

LM connections demonstrated strong validation support, with consistently high VES scores and moderate demountability. However, composite compatibility remained low across the group, and the average NCI_avg was among the lowest of all inter-module connection types.

DB connections displayed considerable variation across all evaluation metrics. Composite compatibility and demountability were generally moderate, and validation scores clustered around mid-to-high levels. Among all inter-module connection types, DB connections recorded the highest average NCI_avg, indicating relatively stronger structural capacity overall.

PB connections generally performed well across all evaluation metrics. Composite compatibility and demountability scores were relatively high, and validation support was generally strong. NCI_avg values showed some variability, but the group exhibited balanced performance overall.

To place these findings in a comparative context,

Table 19. Average scores by inter-module connection type across all evaluation metrics. NCI_avg was scaled by 5 for total score calculation.

Connection Type	Avg CCS	Avg VES	Avg DRS	Avg NCIavg	Total Avg (Out of 20)	Comment
Tie-Rod (TR)	2.0	3.8	1.25	0.48	9.45	Poor composite compatibility and very limited demountability
Locking Mechanism (LM)	2.4	4.3	3.3	0.35	11.65	Strong validation and demountability; weaker composite suitability and lower NCIavg
Direct Bolted (DB)	2.9	3.7	2.7	0.51	11.85	Broad range in performance; highest NCIavg averages
Plug-Assisted Bolted (PB)	3.6	3.7	3.3	0.46	12.91	Highest overall average connection type

presents the average scores across the key performance metrics (CCS, VES, DRS, NCI_avg) and an aggregated average total score, along with summary comments highlighting their relative strengths and limitations.

The cross-comparison presented shows clear differences in average performance across inter-module connection types. TR connections scored the lowest overall, particularly due to limited composite compatibility and demountability. LM connections demonstrated strong validation but remained constrained by low CCS values. DB connections exhibited a broad range of performance with moderate-to-high scores across most metrics. PB connections achieved the highest overall total score, reflecting balanced performance across all evaluation criteria. These aggregated results provide a baseline for discussion and further interpretation in the next section.

7. Discussion of Inter-Module Connection Performance

This section provides a detailed analysis of inter-module connection performance across four key evaluation metrics: Composite Compatibility Score (CCS), Validation Evidence Score (VES), Demountability and Reusability Score (DRS), and Normalised Capacity Index (NCI). The following discussion examines trends, trade-offs, and notable distinct performance characteristics within each metric, while also considering how these results inform the suitability of different connection types for modular construction applications.

For visual consistency across charts and scoring tables, NCI_avg values were scaled by a factor of 5 to align with the 5-point scale used for the other metrics.

7.1. Tie-Rod Inter-Module Connection Performance Discussion

The bar chart in Figure 6 illustrates the comparative performance of the TR connections (TR01–TR04) across the different metrics. TR01 stands out as the most well-rounded connection, achieving the highest possible score in CCS and a DRS score of 2, along with a strong average NCI_avg value of 0.84, indicating strong compatibility with composite modules due to its tailored design for composite modules. In contrast, TR02 represents the lowest performing design, with CCS and DRS scores of 1, as well as having the second lowest NCI_avg score of 0.25. TR03 shows only marginal improvement, attaining a VES score of 4 but having the lowest NCI_avg score of 0.24 while also remaining limited in both CCS and DRS. TR04 has a higher NCI_avg score of 0.57; however, it shares the same low CCS and DRS scores of 1 as TR02 and TR03.

Overall, tie-rod inter-module connections tend to score poorly in CCS and DRS, pointing to limitations in composite modular adaptability and ease of assembly and disassembly. TR01 is an exception due to its deliberate design for CFST columns, resulting in better scoring.

7.2. Locking Mechanism Inter-Module Connection Performance Discussion

The bar chart in Figure 7 illustrates the performance of the LM connection group (LM01–LM07). The chart exhibits a notable trend of consistently high VES scores across all LM connections. Six of the seven connections achieved a score of 4 or higher, which indicates that LM connections are among the most rigorously validated inter-module connection types, with extensive experimental and numerical studies. LM06 stands out with one of the strongest overall performances, combining the highest structural capacity as indicated by an NCI_avg score of 0.53 and strong demountability with a DRS score of 4. However, its CCS remains low at 2, consistent with the majority of LM connections.

LM07 is unique in achieving the highest CCS of 4 among LM connections, suggesting greater compatibility with composite modules. However, structural performance data for this connection is not reported, preventing a complete performance evaluation. Overall, LM inter-module connections consistently demonstrate good performance in terms of demountability, with most designs achieving DRS scores of 3 or 4, but tend to fall short in CCS, highlighting a common challenge in adapting LM designs for use in composite modular systems.

7.3. Direct Bolt Inter-Module Connection Performance Discussion

The performance evaluation of the DB inter-module connection subtype (DB01–DB22), as illustrated from Figure 8, Figure 9 and Figure 10, shows substantial diversity, with connections showing varying strengths in composite compatibility, experimental validation, demountability, and structural performance. From a validation standpoint, 15 out of the 22 DB connections achieved a VES score of 4 or 5, suggesting that DB connections are generally well-supported by both experimental and numerical analyses. However, the CCS results reveal that only half of the DB connections attained a score of 3 or higher, while the remaining half scored 2 or below, signifying that a significant portion of these DB designs are not easily adaptable for composite modularity. A similar constraint is evident in terms of DRS results, where no DB connection received the highest score of 5, and only five connections achieved a score of 4. The remaining 17 connections scored 3 or below; this likely stems from the reliance on conventional bolting methods used in this type of inter-module connection.

At the individual inter-module connection level, only a select subset of DB designs demonstrates balanced performance across all evaluation metrics. DB12 stands out as the top performer with a near maximum total score, combining a CCS of 3, VES of 5, and the highest NCI_avg value of 1.00. Similarly, DB09, DB05, and DB15 exhibit relatively higher scores across all dimensions, closely aligning with DB12’s well-rounded performance profile. Positioned just below this top tier is DB07. Despite the highest NCI_avg score of 1, it is constrained by low VES and DRS scores, both being 2.

Conversely, at the lower end of the spectrum, connections such as DB22, DB03, and DB10 demonstrate consistently weak performance across most metrics. These designs exhibit low CCS and DRS of 2 or lower, and an NCI_avg value below 0.5. Intermediate performers like DB19 and DB14 display moderate-to-high NCI_avg scores of 0.78 and 0.75, respectively, but are hindered by low CCS and DRS scores. A notable trend is observed in DB17, DB18, and DB20, which also demonstrate strong validation support with VES scores of 4 or higher, but similarly low CCS and DRS scores of 2. Overall, the collective results reinforce that while some DB connections perform well in certain metrics, only one demonstrates consistently high performance across all evaluation criteria.

7.4. Plug-Assisted Bolt Inter-Module Connection Performance Discussion

The plug-assisted bolted (PB) inter-module connection (PB01–PB14) evaluation presented in Figure 11 and Figure 12 show generally favourable performance. In terms of validation, this connection subtype is well supported, with 10 out of 14 connections receiving VES scores of 4 or higher, which indicates that PB connections have extensive experimental and numerical verification. Similarly, with demountability, almost half of the PB connections achieved a DRS score of 4 or higher, suggesting a design emphasis on ease of assembly and disassembly.

In terms of individual performance, PB13 emerges as the top-performing connection in this subtype and across all inter-module connection subtypes, achieving a score of 4 across CCS, VES, and DRS, together with a high NCI_avg score of 0.85. PB06 follows closely, recording the third-highest overall score across all subtypes, with a strong score of 4 in CCS, VES, and DRS and a competitive NCI_avg of 0.79. PB01 also performs strongly, achieving a high CCS and VES scores of 5 and 4, respectively, together with a solid DRS score of 4 and an NCI_avg of 0.72. The high ratings for PB01 reflect their intentional design tailored specifically for composite modular systems. Overall, these results position PB13, PB06, and PB01 not only as the top-performing designs within the PB subtype but also among the leading inter-module connections across all evaluated types.

Several other designs, including PB12, PB04, and PB07, fall within the mid-range performer group, each achieving CCS and DRS scores of 4 and 3, respectively, and corresponding NCI_avg values of 0.79, 0.28, and 0.18, respectively. In contrast, PB11 and PB02 represent the lower end of the spectrum, with CCS and DRS scores of 3 or lower and NCI_avg scores of 0.25 and 0.13, respectively.

Overall, the PB connection subtype demonstrates a relatively high degree of performance consistency compared to other connection types, with several well-rounded connection designs such as PB13, PB06, and PB01 excelling across all evaluation metrics.

7.5. Overall Inter-Module Connection Assessment

The overall ranked performance chart, illustrated in Figure 13, presents the comparative outcomes for all evaluated inter-module connections based on the combined scores across the four assessment metrics. The results reveal clear trends and directional differences among connection types. The top-performing designs include PB13, DB12, PB06, and PB01, each achieving a total score above 15.6. Notably, three of these four top-performing connections are plug-assisted bolted inter-module connections.

PB connections lead in the upper ranks, with five entries in the top ten. DB connections, while more varied in performance, also provide strong candidates such as DB12 and DB09, though their scores are often tempered by lower CCS and DRS scores. LM connections are skewed more towards the mid-range, typically achieving high DRS and VES scores but struggle in CCS and NCI_avg scores. TR connections exhibit the greatest variation in performance, while TR01 ranks among the top overall, and TR02 and TR03 occupy the lowest positions. This suggests that TR connections generally underperform unless designed for composite module applicability.

Across the four evaluation metrics, distinct trends emerge when comparing connection types. LM connections generally exhibit the highest VES scores, with the majority scoring 4 or 5, reflecting their prevalence in experimental and numerical studies. They also perform well in DRS, as their inherent design typically emphasises mechanisms that facilitate straightforward assembly and disassembly. PB connections outperform others in CCS and DRS scores, with several designs scoring 4 or 5 in both dimensions. DB connections lead in normalised capacity, having many of the highest NCI_avg scores. TR connections generally show low performance in CCS and DRS, reflecting limited suitability for composite modules and demountability, unless composite modularity is addressed in the design, as seen in TR01.

Viewed holistically, the dataset underscores the importance of a multi-criteria evaluation framework when assessing inter-module connections. While some connection designs achieve exceptional composite module compatibility and a high Normalised Capacity Index, their demountability may be limited. Taken collectively, the results indicate that plug-assisted bolted connections offer the most consistently balanced performance for composite module structures, although high-performing designs can still be found within each connection category.

8. Conclusions and Recommendations

This paper presented a comprehensive review and classification of inter-module connection types for modular structures, with a specific emphasis on steel–concrete composite modules. A key contribution of this study is the development of a structured evaluation framework comprising Composite Compatibility Score (CCS), Validation Evidence Score (VES), Demountability and Reusability Score (DRS), and Normalised Capacity Index (NCI), enabling multidimensional performance comparisons across 47 inter-module connections. In addition, this study introduces a novel sub-classification of bolted inter-module connections into direct bolted (DB) and plug-assisted bolted (PB) sub-categories, based on their assembly method.

Unlike prior reviews that focused solely on steel module connections, this study applies an evaluation framework to assess the adaptability of existing inter-module connection types specifically for steel–concrete composite modular systems. The results indicate that plug-assisted bolted (PB) connections exhibit the most balanced performance across all evaluation criteria, particularly excelling in composite compatibility and demountability. Direct bolted (DB) connections also demonstrate strong structural capacity but are less adaptable to composite systems. While locking mechanism (LM) connections show the highest validation depth, they often require redesign for effective use in composite modular systems. Tie-rod (TR) connections, though structurally capable, generally show poor composite compatibility and limited demountability unless specifically developed for composite modules.

Although the proposed evaluation metrics enable structured comparison, incomplete experimental datasets limit the ability to perform direct comparisons across equivalent structural capacities, thereby affecting the completeness of the NCI metric profile. Many inter-module connections were reported with only one or a few structural capacity types, meaning aggregate indicators represent the available evidence rather than a full multi-metric profile. This highlights the need for future research to expand testing coverage and provide more comprehensive performance data. Beyond this, the evaluation framework proposed in this study can be further expanded by incorporating environmental impacts and cost-related considerations, enabling a more holistic approach to inter-module connection assessment.

The findings underscore the importance of designing inter-module connections with direct consideration for composite module applications, rather than adapting steel-only solutions. Moreover, the framework provides engineers and researchers with a conceptual benchmark for assessing the suitability of different inter-module connection types for steel–concrete composite modular structures. In practice, this framework can serve as a decision support tool, enabling designers and engineers to prioritise inter-module connection options based on project specific requirements. For example, in high-rise modular buildings where steel–concrete composite compatibility is essential, connections with higher CCS scores should be considered, whereas projects emphasising demountability and future adaptability should focus on DRS. This flexible approach allows practitioners to tailor decisions to their overall design objectives.