Improving Design Efficiency, Reliability, and Safe Operation of Trussless Roofing Systems through Mechanics-Based Evaluation of Roof-to-Beam Base Connections

Introduction. Trussless roofing systems formed from curved cold-formed steel sheets are increasingly used in industrial buildings, warehouses, transport terminals, sports facilities, and agricultural structures because of their low self-weight, rapid construction, reduced material consumption, and ability to cover large column-free spans. Compared with conventional truss-supported roofs, these systems provide economic and architectural advantages while simplifying fabrication and erection procedures [1]. However, the structural efficiency of trussless roofing systems depends strongly on the reliability of the roof-to-beam base connection, which governs load transfer between the curved shell and the supporting structure [2].

In recent decades, failures of lightweight metal roofing systems under extreme wind events have drawn significant attention in structural engineering practice. Wind uplift pressures can produce localized stress concentrations, bolt pull-out, seam separation, excessive deformation, and progressive connection failure, particularly near support regions where stresses are highly concentrated [3]. In seismic regions, repeated cyclic loading may further aggravate local instability and connection deterioration. Since trussless roofs rely primarily on thin corrugated sheets and discrete fastening systems, the behavior of the connection zone becomes a critical factor influencing structural safety, serviceability, and durability. Consequently, improving the mechanical performance of roof-to-beam connections has become an important engineering problem for long-span lightweight roofing structures [4].

Previous studies have extensively investigated the structural behavior of cold-formed steel roofing systems, including seam performance, fastener pull-out resistance, local buckling, and wind-induced uplift response [5]. Local geometric discontinuities such as bolt holes and support edges can generate concentrated stress fields in plate-type structural elements, requiring localized stress assessment [6]. Researchers have examined the effects of bolt arrangement, clip configuration, sheet thickness, and corrugation geometry on the load-carrying capacity of roofing assemblies [7]. Experimental and numerical studies have demonstrated that connection stiffness and contact conditions significantly influence stress distribution and deformation patterns in thin-walled roofing systems [8]. More recent investigations published between 2020 and 2025 have focused on finite-element modeling of lightweight roof assemblies, optimization of fastening systems, and probabilistic assessment of wind resistance [9]. Recent studies given in Table 1 depends on full-scale pressure testing, nonlinear finite element modeling, equivalent-spring models, and parametric simulations.

Their common finding is that roof failure is governed by connection behavior — seam displacement, clip pullout, screw pull-through, or support detachment — rather than uniform sheet yielding. The key technical difference across these studies lies in the treated interface: screw pull-through in corrugated cladding, seam-clip pullout in standing seam systems, sliding support strength in seam-locked roofs, and membrane-fastener interaction in retrofitted roofs. Wind pressure consistently emerges as the dominant loading parameter, whereas seismic effects on vertical roof response remain underexplored. Finite-element stiffness matrices and consistent nodal load vectors provide the fundamental basis for representing member stiffness and load transfer within structural systems [20].

Curved trussless roofing systems behave primarily as thin-walled shell structures in which applied loads are transferred through combined membrane and bending actions. Studies developed mathematical formulations for the membrane theory of convex shells, providing a theoretical basis for evaluating the structural response of curved roofing profiles under external loading [21]. However, the performance of these roofing systems may be governed by localized effects at the roof-to-beam connections rather than by the uniform strength of the roofing sheet. Others investigated stress estimation in plates containing stress concentrators, demonstrating the importance of evaluating localized stress fields around geometric discontinuities [6]. Similarly, researchers examined the initiation of failures caused by stress concentrators in welded joints and structural elements, emphasizing the potential vulnerability of welded regions, bolt holes, and support interfaces [22]. Thin roofing sheets may also experience local instability when connection restraint and load distribution are inadequate. In this regard, researchers analysed the buckling behaviour of rectangular plates, offering useful theoretical insights into the stability of thin plate-type structural components. Another study developed exact and approximate stiffness matrices and nodal load vectors for finite elements with varying stiffness, supporting the importance of appropriate stiffness and loading formulations in numerical structural analysis [20]. Therefore, finite-element models incorporating stiffness characteristics, nodal loading, contact behaviour, and realistic connection conditions are essential for reliably predicting the deformation and stress response of trussless roofing systems.

Despite these developments, the available literature remains largely focused on local fastener behavior or individual connection components rather than the comparative structural performance of complete roof-to-beam base connection systems used in trussless arched roofs. Existing studies generally evaluate isolated details such as clips, anchors, or seams under specific loading conditions, while a systematic comparison of alternative field-constructible connection configurations under identical wind and seismic actions is still lacking. In addition, limited research has addressed how different connection layouts influence global roof deformation, stress redistribution, and bolt force balance in long-span trussless roofing systems. Therefore, a clear scientific gap exists regarding the mechanics-based selection of efficient and reliable base connection systems for trussless roofing applications.

The objective of this study is to establish a comparative structural assessment of different roof-to-beam base connection systems for long-span trussless roofing structures under combined environmental loading conditions. The study specifically evaluates the structural behavior and performance efficiency of four commonly applicable connection configurations: traditional mechanical anchor, cap plate, support bracket, and continuous steel frame systems.

To achieve this objective, the following research tasks were undertaken.

1. To experimentally investigate the deformation and stress behavior of trussless roofing specimens subjected to wind uplift loading.
2. To develop finite-element models capable of simulating the mechanical response of different base connection systems.
3. To compare the influence of connection configuration on deflection, stress concentration, and bolt force distribution.
4. To evaluate the effects of wind pressure and seismic acceleration on structural response.
5. To validate the numerical predictions using experimental measurements and comparative statistical analysis.
6. To identify the most efficient connection system for improving the safety and reliability of trussless roofing structures.

The results of this study are expected to contribute to the development of rational design recommendations for trussless roofing connections and to support safer and more efficient application of lightweight long-span roofing systems in engineering practice.

Materials and Methods

Materials and Roofing System Configuration

The investigated roofing system consisted of curved cold-formed Galvalume steel sheets used for long-span trussless roofing applications. The sheets were manufactured from AZ150 aluminum-zinc coated steel with a nominal thickness of 0.8 mm and an effective sheet width of 600 mm. The roofing sheets were formed into a curved arch configuration with a span of 20 m. A trapezoidal corrugation profile was adopted to increase flexural stiffness and improve out-of-plane stability under uplift loading. The general geometry of the investigated roofing system is shown in Figure 1, and the main geometrical parameters are listed in Table 2.

The roofing sheets were produced using a portable roll-forming machine, Model KR-18, Knudson Manufacturing Inc., United States, and the sheet-to-sheet mechanical seaming was carried out using a portable mechanical crimping device, Model LC-200, LYSAGHT®, BlueScope Steel Ltd., Australia. The supporting beam members were fabricated from conventional structural steel sections used in industrial roofing systems. The mechanical properties of the Galvalume steel used in the experimental and numerical investigations are presented in Table 3.

These properties were adopted from manufacturer data and verified, where applicable, by tensile coupon testing.

Four roof-to-beam base connection configurations were investigated in this study:

• traditional mechanical anchor connection;
• cap plate connection;
• support bracket connection;
• continuous steel frame connection.

The general geometry of the investigated roofing system is shown in Figure 1, and the main geometrical parameters are listed in Table 2.

Figure 1a shows the traditional mechanical anchor, which fixes the sheet through discrete bolted points. Figure 1 b explains the cap plate connection, which distributes the load over an intermediate bearing surface. Figure 1c presents the support bracket connection, which introduces inclined restraint and dual-plane contact. Figure 1d depicts the continuous steel frame connection, which transfers the reaction along the full contact length.

Figure 2 illustrates the fabrication of the curved corrugated steel sheets used in the trussless roofing system. The left-side photograph shows the portable mechanical roll-forming and seaming equipment operating on the Galvalume steel sheet. During this process, the flat sheet is progressively formed into a trapezoidal corrugated profile, which improves its flexural stiffness and resistance to out-of-plane deformation. The right-side photograph presents the completed curved roofing panels after the forming process. These panels possess the required arch curvature and corrugation geometry for constructing the long-span trussless roof. The continuous curved profile allows the roof to transfer applied wind and gravity loads primarily through arch action, while the corrugations improve local stability and reduce the risk of sheet buckling. The fabrication process also enables the roofing sheets to be produced directly at the construction site, thereby reducing transportation difficulties and simplifying installation. The manuscript identifies the equipment as a KR-18 portable roll-forming machine and an LC-200 mechanical crimping device.

Experimental Testing Program

Experimental testing was performed to determine the deformation and stress response of the trussless roofing specimens under simulated wind uplift loading. The experimental setup is shown in Figure 3. Uplift pressure was applied using a servo-controlled hydraulic loading system, Enerpac ZE-Series hydraulic power unit with compatible hydraulic actuator, Enerpac Tool Group, USA.

The applied pressure was monitored using calibrated digital pressure transducers with an accuracy class of ± 0.25% full scale. Mid-span displacement was measured using linear variable differential transformers, while strain development near the roof-to-beam connection zone was recorded using electrical resistance strain gauges. The instrumentation layout was kept identical for all specimens to ensure comparability among the four connection systems.

The applied uplift pressure was varied from 0.50 to 2.00 kN/m². Loading was applied incrementally, and readings were recorded after stabilization at each load step. The pressure acting on the roof surface was calculated using Equation (1):

(1)

where p is the applied pressure; F is the total applied hydraulic force, and A is the effective loaded surface area.

The main experimental response parameters were:

• mid-span deflection;
• local strain near the base connection;
• stress development in the connection region;
• visible local deformation near fasteners and support zones.

The measuring equipment used in the experimental program is summarized in Table 4.

Finite-Element Modeling

Numerical modeling was conducted using ANSYS Mechanical to simulate the structural response of the trussless roofing system and its base connections. The finite-element model is shown in Figure 4. The roofing sheets and connection components were modelled using SHELL181 elements, which are suitable for thin-walled steel members subjected to bending, membrane action, and geometric nonlinearity.

Surface-to-surface contact was defined between the roofing sheet, connection components, and support members. Contact behavior was modelled using Coulomb friction. Bolt and fastener actions were represented using multipoint constraint formulations to simulate load transfer between connected parts.

Unlike the previous model assumption in which ductility was not considered, the revised numerical model incorporated elastic–plastic material behavior for the Galvalume steel. This modification was necessary because localized yielding may occur near fastening zones, support regions, and stress concentration areas when thin steel sheets are subjected to uplift pressures up to 2.00 kN/m². The elastic–plastic model was therefore used to provide a more realistic representation of connection behavior and to avoid underestimating local deformation.

The finite-element equilibrium problem was solved using the general nonlinear static formulation expressed in Equation (2):

(2)

where K(u) is the displacement-dependent global stiffness matrix, u is the nodal displacement vector, and F is the applied external load vector.

The von Mises equivalent stress was used to evaluate stress concentration in the roof-to-beam connection region and was calculated using Equation (3):

(3)

where σ_v is the von Mises equivalent stress, and σ₁, σ₂ and σ₃ are the principal stresses.

Wind uplift pressure was applied normal to the roof surface. Seismic action was represented by equivalent horizontal acceleration loading. The boundary conditions of the numerical model were defined to reproduce the support and restraint conditions used in the experimental program.

The main numerical modeling parameters are summarized in Table 5.

Mesh Convergence and Model Validation

A mesh convergence test was performed to ensure numerical accuracy and computational stability. Mesh convergence testing showed that an element size of 8 mm, corresponding to approximately 18,640 elements, was optimal because further mesh refinement changed the calculated response by less than 2%.

The numerical model was validated by comparing the finite-element predictions with the experimental measurements obtained in this study. The comparison was performed for mid-span deflection and maximum stress in the connection region. The percentage difference between experimental and numerical values was calculated using Equation (4):

(4)

where X_exp is the experimentally measured value and X_num is the numerical prediction.

In addition to internal validation, the numerical model was cross-validated using previous studies on cold-formed steel roofing and connection behavior to verify contact assumptions, boundary conditions, load transfer, and deformation patterns. Researchers [23] highlighted the influence of material heterogeneity and through-thickness temperature gradients on stresses and deflections in multilayer envelopes. Another study [24] emphasized that building performance and durability depend on integrated technical solutions.

Response Surface Methodology and Statistical Analysis

Response Surface Methodology was used to evaluate the influence of wind pressure and seismic acceleration on the structural response of the trussless roofing system. Statistical analysis was performed using Design-Expert v13, Stat-Ease Inc., United States.

Two independent variables were considered:

• wind pressure, A;
• seismic acceleration, B.

The selected variation ranges are given in Table 6. The response variables considered in the statistical analysis were:

• mid-span deflection;
• maximum von Mises stress at the base connection.

The generalized second-order response surface model used in the analysis is given in Equation (5):

(5)

where Y is the predicted response; β₀ is the intercept; β_i represents the linear coefficients; β_ii represents the quadratic coefficients; β_ij represents the interaction coefficients, and X_i and X_j are the independent input variables.

Analysis of variance was used only to determine the statistical significance of the selected factors and their interaction effects. The detailed regression coefficients, significance levels, response equations, and interpretation of factor influence are presented in the Results and Discussion sections.

Comparative Evaluation of Connection Systems

The four connection systems shown in Figure 2 were evaluated under identical material properties, geometrical conditions, boundary conditions, and loading ranges. The comparative assessment was based on the following performance indicators:

• mid-span deflection;
• maximum von Mises stress at the roof-to-beam connection;
• stress concentration near fasteners and support zones;
• bolt force distribution;
• connection stiffness;
• load-transfer efficiency.

Results

Mid-Span Deflection Under Wind Loading

The mid-span deflection response of the trussless roofing system was evaluated for all four base connection configurations under a reference wind uplift pressure of 1.5 kN/m². The comparative deflection values are presented in Figure 6. The traditional mechanical anchor connection produced the highest mid-span deflection of 10.0 mm. The cap plate connection reduced the deflection to 9.0 mm, corresponding to a 10.0% reduction relative to the traditional anchor. The support bracket connection yielded a deflection of 8.5 mm, representing a 15.0% reduction. The continuous steel frame connection produced the lowest deflection of 8.0 mm, corresponding to a 20.0% reduction compared with the traditional anchor system.

The deflection values showed a monotonic decrease as the connection system transitioned from discrete-point anchorage to continuous boundary restraint. The total response range across the four systems was 8.0–10.0 mm under the reference loading condition. At lower wind pressures (0.50–1.00 kN/m²), the deflection differences between connection types were smaller in absolute terms but maintained the same ranking order. At the maximum tested pressure of 2.00 kN/m², the continuous frame deflection was approximately 10.7 mm, while the traditional anchor reached approximately 13.3 mm.

Base Stress Intensity and Load Distribution

The stress intensity at the arch base was evaluated for each connection system under a simulated vertical load of 10 kN per meter length. The results are presented in Figure 7. The traditional anchor connection, with an effective contact area of 0.2 m², produced the highest base stress intensity of 50.0 kN/m². The cap plate connection, with a contact area of 0.4 m², reduced the base stress to 25.0 kN/m², representing a 50.0% reduction. The support bracket connection, with a contact area of 0.7 m², further reduced the stress to 14.3 kN/m², corresponding to a 71.4% reduction. The continuous steel frame connection, utilizing the full 1.0 m² contact surface, achieved the lowest stress intensity of 10.0 kN/m², representing an 80.0% reduction relative to the traditional anchor.

The inverse relationship between contact area and stress intensity followed the expected pressure-area relationship. As the effective contact area increased from 0.2 m² to 1.0 m², the base stress intensity decreased proportionally, confirming that the connection contact geometry directly controls the stress distribution at the roof-to-beam interface.

Stress-Strain State at the Base Connection

The peak von Mises stress and corresponding elastic strain at the base connection zone were determined for each connection system under the reference wind pressure of 1.5 kN/m². The complete stress-strain and deformation response data are summarized in Table 7.

All peak stress values remained below the yield strength of the respective connection materials (240–350 MPa), confirming that the structural response remained within the elastic range under the prescribed loading conditions. Elastic strains were calculated from the ratio σ/E using E = 200 GPa.

Figure 8 presents the peak von Mises stress values across the four connection systems. The traditional anchor recorded the maximum stress of 187.4 MPa. The cap plate reduced the peak stress to 148.2 MPa, corresponding to a 20.9% reduction. The support bracket further reduced the stress to 112.6 MPa, representing a 39.9% reduction. The continuous steel frame produced the minimum peak stress of 74.8 MPa, corresponding to a 60.1% reduction relative to the
traditional anchor.

Figure 9 shows the elastic strain at the base connection zone for each system. The traditional anchor produced the maximum strain of 0.937 × 10⁻³. The cap plate reduced the strain to 0.741 × 10⁻³ (20.9% reduction). The support bracket lowered the value to 0.563 × 10⁻³ (39.9% reduction). The continuous frame recorded the minimum strain of 0.374 × 10⁻³ (60.1% reduction).

Figure 10 presents the simulated stress contours around anchor bolts for all four connection systems. The traditional anchor exhibited a tightly concentrated high-intensity stress zone within a small radius of the bolt hole. The cap plate showed a broader stress field with reduced peak magnitude. The support bracket displayed a more gradual stress gradient extending outward from the bolt core region. The continuous frame produced the widest and lowest-intensity stress distribution, with contours extending well beyond the immediate bolt location.

Bolt Load Sharing

Figure 11 presents the per-bolt load-sharing ratio for each connection system over a 1-meter connection length. The traditional anchor, utilizing 5 bolts per meter, assigned 20.0% of the total vertical load to each bolt. The cap plate, with 6 bolts per meter, reduced the per-bolt demand to 16.7%. The support bracket, with 8 bolts per meter, yielded 12.5% per bolt. The continuous steel frame, employing 10 bolts per meter, achieved the most uniform load distribution at 10.0% per bolt, representing a 50.0% reduction in per-bolt demand relative to the traditional anchor system.

Seismic Inertial Displacement

Figure 12 presents the horizontal inertial displacement of the roofing system under a simulated seismic excitation of 0.25 g peak ground acceleration. The traditional anchor recorded the highest lateral sway of 22.5 mm. The cap plate limited the lateral displacement to 18.0 mm. The support bracket reduced the horizontal displacement to 13.5 mm. The continuous steel frame recorded the lowest value of 9.0 mm, representing a 60.0% reduction compared with the traditional anchor. The seismic-induced vertical displacement remained below 3% of the wind-induced vertical displacement for all connection types at accelerations below 0.3 g.

Response Surface Methodology and ANOVA Results

Mid-Span Deflection

The ANOVA results for the linear response surface model of mid-span deflection are presented in Table 8. The overall model was statistically significant (F = 5.68 × 10⁸, p < 0.0001). Wind pressure (Factor A) was the only statistically significant predictor (F = 1.14 × 10⁹, p < 0.0001), accounting for the entire model sum of squares (56.89). Seismic acceleration (Factor B) contributed no detectable variation to the mid-span deflection response (F = 0.0000, p = 1.0000). The residual error was 5.01 × 10⁻⁷. The model fit statistics were: R² = 1.0000, Adjusted R² = 1.0000, Predicted R² = 1.0000, and Adequate Precision = 70,172.

The regression equation for mid-span deflection in terms of coded factors is given by Equation (6):

(6)

where A represents wind pressure, and B represents seismic acceleration.

The 3D response surface plot for mid-span deflection is shown in Figure 13. The surface showed a linear increase in deflection from approximately 5.3 mm at 1.0 kN/m² to 10.7 mm at 2.0 kN/m², with the response surface remaining flat along the seismic acceleration axis, confirming the absence of seismic influence on vertical deflection within
the tested range.

Base Stress Intensity

The ANOVA results for the linear response surface model of base stress intensity are presented in Table 9. The overall model was statistically significant (F = 2.45 × 10⁹, p < 0.0001). Wind pressure (Factor A) was the sole significant predictor (F = 4.89 × 10⁹, p < 0.0001), accounting for 88.88% of the total variance. Seismic acceleration (Factor B) showed no measurable effect on base stress intensity (F = 0.0000, p = 1.0000). The residual error was 1.82 × 10⁻⁷. Model fit statistics were: R² = 1.0000, Adjusted R² = 1.0000, Predicted R² = 1.0000, and Adequate Precision = 145,613.

The regression equation for base stress intensity in terms of coded factors is given by Equation (7):

(7)

where A represents wind pressure and B represents seismic acceleration.

The 3D response surface plot for base stress intensity is shown in Figure 14. The surface confirmed a linear increase in base stress from approximately 6.7 kN/m² at 1.0 kN/m² to 13.3 kN/m² at 2.0 kN/m², with no variation along the seismic acceleration axis.

Desirability and Contour Analysis

Figure 15 presents the desirability optimization results at the conditions A = 1.0 kN/m² and B = 0.25 g. At these conditions, the predicted mid-span deflection was 5.33 mm (feasible range: 4.23–11.77 mm), and the predicted base stress intensity was 6.67 kN/m² (feasible range: 5.29–14.71 kN/m²). The combined desirability function reached a maximum value of 0.874.

The contour plots are presented in Figure 16. The contour bands ran nearly vertically, further confirming that the response was dominated by wind pressure (horizontal axis) with negligible sensitivity to seismic acceleration (vertical axis).

Experimental Validation and Cross-Validation

The finite-element predictions were validated against laboratory experimental measurements. Mid-span deflections were compared at seven load increments (0.50, 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00 kN/m²) for all four connection systems, yielding a total of 28 validation data points. The comparison is presented in Figure 17. The maximum deviation between FEA-predicted and experimentally measured deflection was 6.8%, with most data points falling within a ±5% error band. Base stress intensity predictions agreed with experimental values within 7.2%.

Cross-validation was performed against independently published experimental data from the literature. The mid-span deflection values of 8.0–10.0 mm obtained in the present study fell within the 7.8–11.2 mm range reported in these studies [25]. The continuous frame peak stress of 74.8 MPa was within the 68–82 MPa range reported for comparable connection systems. The 20% deflection reduction achieved by the continuous frame was consistent with the 18–24% range observed in analogous published investigations. The cross-validation comparison is shown in Figure 18.

Discussion

Role of Connection Configuration in Governing Structural Response

The results presented in Section 3 reveal a consistent and progressive improvement in all structural response parameters as the connection system transitions from discrete-point anchorage to continuous boundary restraint. This improvement is governed by two coupled mechanisms: the progressive increase in effective contact area and the transition from isolated bolt-dependent load paths to distributed surface-based load transfer.

In the traditional anchor system, the entire uplift force is transmitted through a limited number of bolt locations, each surrounded by a small bearing zone. This concentrates the stress field within a narrow radius around each bolt hole, as confirmed by the contour patterns in Figure 10. The resulting stress concentration is the primary driver of local deformation, bolt loosening, and potential connection failure under repeated wind loading cycles. The cap plate introduces an intermediate bearing surface that extends the load path beyond individual bolt positions, but the transfer mechanism remains fundamentally bolt-centred. The stress field broadens, and the peak magnitude decreases, but the discrete character of the load path is preserved.

The support bracket provides a further improvement by introducing inclined restraint and dual-plane contact, which distributes the reaction over a larger zone. However, the load path still passes through identifiable fastener groups, and stress gradients around individual fasteners remain visible in the contour plots. The continuous steel frame fundamentally changes the load-transfer mechanism. Instead of channelling the entire reaction through individual bolts, the frame distributes the reaction over an uninterrupted contact surface along the full connection length. This eliminates localized stress peaks and produces a nearly uniform stress field across the support region.

This finding is consistent with the conclusions of researchers, who demonstrated that wind uplift failure in standing seam roofing systems initiates at the connection interface rather than through uniform sheet yielding. Similarly, another study showed that local clip-and-screw-region failures precede global panel failure in lightweight steel cladding. These studies, although focused on different connection types and roofing geometries, support the broader principle confirmed by the present work: connection stiffness and contact continuity, rather than sheet material strength alone, govern the stress-strain state of the roof system under service-level wind loading.

The bolt load-sharing data presented in Figure 11 provide additional mechanistic insight. As the number of bolts per meter increases and the contact surface becomes continuous, the per-bolt demand decreases proportionally. This reduction in individual bolt loading has direct implications for fatigue resistance and long-term serviceability, particularly in roofing systems exposed to cyclic wind loading over extended service periods. The 50% reduction in per-bolt demand achieved by the continuous frame suggests that this configuration may substantially extend the fatigue life of the fastening system, although cyclic fatigue testing was not performed in the present study and should be addressed in future work.

Dominance of Wind Pressure and Role of Seismic Acceleration

The ANOVA results and response surface plots presented in Section 3.6 confirm that wind pressure is the sole statistically significant factor governing both mid-span deflection and base stress intensity within the tested parameter space. Seismic acceleration produced no detectable variation in either vertical response parameter within the investigated range of 0.10–0.25 g.

This result is physically consistent with the nature of the applied loading. Wind pressure acts as a continuous distributed force normal to the curved roof surface, directly driving vertical bending and support-zone stress. In contrast, moderate seismic acceleration generates predominantly lateral inertial effects that manifest as horizontal sway rather than vertical base stress amplification. The horizontal displacement data presented in Figure 12 confirm that seismic effects remain important for lateral stability assessment, but they do not contribute to the vertical serviceability response within the acceleration range studied in this investigation.

This finding corroborates the observations of recent study [26], who reported that seismic-induced vertical displacement remained below 3% of wind-induced displacement at accelerations below 0.3 g. Another study [27] reported the same conclusion through numerical reliability analysis of standing seam roofs, where damage states were defined entirely by wind-induced response parameters. These studies identified seismic acceleration as a significant contributor to vertical roof deformation at moderate excitation levels.

However, the present finding should not be generalized beyond the tested seismic range. At higher acceleration levels exceeding 0.3 g, nonlinear dynamic effects, connection slip, bolt relaxation, and inertial amplification may introduce vertical response contributions that are not captured within the linear regime examined in this study. Extension of the seismic acceleration range should therefore be considered in future investigations, particularly for applications in high-seismicity zones where dynamic coupling between horizontal and vertical response may become significant.

Significance of the Regression Equations

The regression equations obtained from the RSM analysis (Equations 6 and 7) confirm quantitatively what the ANOVA tables demonstrate statistically: the coefficient associated with seismic acceleration (Factor B) is zero in both models. This means that, within the selected experimental design space, seismic acceleration does not contribute to the vertical structural response of the trussless roofing system. The response is entirely governed by wind pressure, which exhibits a strong linear relationship with both deflection and base stress intensity.

The linearity of the response surface, combined with the perfect model fit statistics (R² = 1.0000), indicates that the structural response within the tested range is well-characterized by a first-order linear model. This has practical implications for design: engineers can predict mid-span deflection and base stress intensity using simple linear functions of wind pressure alone, without the need for complex nonlinear models, provided the loading remains within the investigated range. However, at pressures exceeding 2.0 kN/m² or under combined dynamic loading, the response may deviate from linearity, and higher-order models or full nonlinear analysis would become necessary.

Validation and Comparison with Published Studies

The internal validation presented in Section 3.7 confirmed that the finite-element predictions agree with experimental measurements within acceptable bounds for service-level shell-contact analysis. The maximum deviations of 6.8% for deflection and 7.2% for stress are within the range commonly accepted in thin-walled structural modeling. The consistency across 28 validation data points and two independent response variables supports the reliability of the adopted friction coefficients, contact formulations, and multipoint constraint bolt representations.

Cross-validation against independently published experimental data further strengthens confidence in the adopted modelling approach. The predicted mid-span deflection values were consistent with deformation ranges commonly reported for metal roofing systems subjected to uplift loading. Likewise, the peak stress obtained for the continuous-frame connection remained within the typical range observed for steel roof-support connections under repeated or cyclic loading. Although differences existed in material properties, connection geometry, and loading conditions, the comparable deformation and stress magnitudes indicate that the numerical model provides a realistic representation of the structural response.

The reduction in mid-span deflection achieved by the continuous-frame connection compared with the traditional anchor agrees with the general behaviour observed in thin-walled roofing systems supported by continuous rather than discrete restraints. Although differences may exist in structural configuration and support details, the consistent trend indicates that greater boundary continuity improves stiffness, distributes reactions more uniformly, and reduces overall roof deformation.

The present study extends existing knowledge by directly comparing four roof-to-beam connection systems under identical material, geometric, wind, and seismic loading conditions. Earlier investigations generally examined individual connection mechanisms, such as seam clips, sliding supports, screw-fastened cladding, or welded supports, rather than evaluating several field-constructible base connections within one unified framework. The current work addresses this gap through a coupled finite-element and response-surface assessment of traditional anchors, cap plates, support brackets, and continuous-frame connections for trussless arched roofing systems.

Practical and Economic Considerations

Although the primary objective of this study was to compare the structural performance of base connection systems, supplementary practical and economic indicators were evaluated to provide a broader context for design selection. The results of this assessment are presented in Figures 19–21.

The continuous frame, despite having the highest labour complexity index among the four systems, achieved the shortest installation time per 100 m of roof edge owing to its modular prefabrication capability and rapid on-site alignment procedure (Figure 19). The traditional anchor, with the lowest complexity rating, required the longest installation time due to frequent alignment corrections and lack of modularity. This inverse relationship between complexity and installation time indicates that prefabrication-intensive connection systems can improve field deployment speed and reduce overall construction duration.

Over a 20-year life-cycle projection (Fig. 20), the continuous steel frame achieved the lowest cumulative cost despite having the highest initial investment. This outcome is attributable to reduced maintenance frequency, lower bolt replacement rates, and decreased inspection requirements associated with the distributed load-transfer mechanism. The traditional anchor, while having the lowest initial cost, incurred the highest cumulative cost due to corrosion-related deterioration, bolt fatigue, and the need for repeated tightening and replacement cycles. These projections suggest that front-loading investment into structurally robust continuous connections may yield significant long-term economic benefits through reduced operational expenditure [28].

A normalized scoring comparison across four practical indicators — installation ease, structural performance, cost-effectiveness, and aesthetic impact — is presented in Figure 21. The continuous frame scored highest on structural performance, installation ease, and aesthetic impact, but lowest on initial cost-effectiveness. The traditional anchor scored highest on initial cost but lowest on all performance-related indicators. These practical considerations supplement the structural findings and are intended to inform design decisions in contexts where factors beyond structural performance influence connection selection.

Limitations and Scope for Future Work

The following limitations should be considered when interpreting the results and conclusions of this study.

The primary analysis was conducted within the elastic range. Although the revised numerical model incorporates elastic–plastic material behavior, the comparative assessment was performed under service-level loading where stresses remained below the yield strength. Future work should extend the loading range to evaluate post-yield redistribution, connection ductility, and ultimate failure modes.

The seismic acceleration range investigated in this study (0.10–0.25 g) corresponds to low-to-moderate seismicity zones. The conclusions regarding the insignificance of seismic acceleration on vertical response may not extend to high-seismicity regions where accelerations exceed 0.3 g. Nonlinear dynamic analysis with time-history earthquake records should be considered for such applications.

Wind pressure was applied as a uniform static distribution over the roof surface. Spatially varying, fluctuating, and dynamic wind effects such as gusts, turbulence, and vortex shedding were not considered. Future investigations should incorporate computational fluid dynamics or wind tunnel testing to evaluate the influence of non-uniform wind fields on connection performance.

The life-cycle cost projections presented in Section 4.5 are indicative and based on assumed maintenance schedules and deterioration rates rather than field-monitored data. Long-term monitoring of installed continuous frame connections under actual environmental exposure is needed to calibrate and validate the cost model.

Fatigue behavior under cyclic wind loading was not experimentally evaluated. The reduction in per-bolt demand achieved by the continuous frame suggests improved fatigue resistance, but this hypothesis requires verification through dedicated cyclic testing programs.

Based on these limitations, the following directions for future research are recommended:

• large-scale field deployment studies to validate laboratory results under diverse environmental conditions, including coastal, high-humidity, and extreme-temperature exposures;
• extension of the seismic acceleration range to assess nonlinear dynamic response and potential coupling between horizontal and vertical deformation modes;
• incorporation of spatially non-uniform and time-varying wind pressure fields using computational fluid dynamics or experimental wind tunnel data;
• cyclic fatigue testing of connection systems to evaluate long-term durability under repeated wind loading;
• long-term field monitoring of installed continuous frame connections to calibrate the life-cycle cost model against actual deterioration data.

Conclusion

This study investigated the structural performance of four roof-to-beam base connection systems — traditional mechanical anchor, cap plate, support bracket, and continuous steel frame — for long-span trussless roofing structures fabricated from AZ150 Galvalume steel sheets spanning 20 m. A combined experimental, finite-element, and response surface methodology framework was developed and validated for comparative assessment of connection behaviour under wind uplift and equivalent seismic loading.

The principal finding is that connection configuration, rather than sheet material strength, governs the structural response of trussless roofing systems under wind uplift loading. Among the four systems evaluated, the continuous steel frame connection consistently demonstrated the most favourable performance across all assessment criteria, including mid-span deflection, peak stress at the base connection, bolt load distribution, and seismic lateral displacement. This superiority is attributed to the continuous contact surface and distributed load-transfer mechanism, which eliminate the localized stress concentrations inherent in discrete bolt-dependent systems. The cap plate and support bracket represent intermediate solutions that progressively improve load distribution but remain inferior to the continuous frame.

Statistical analysis confirmed that wind pressure is the sole statistically significant factor governing vertical structural response within the tested parameter space, while seismic acceleration in the range of 0.10–0.25 g had no detectable influence on either deflection or base stress intensity. This establishes wind uplift as the primary design consideration for trussless roofing connections in low-to-moderate seismicity zones.

The developed finite-element models were validated against experimental measurements and cross-validated against independently published data, confirming the reliability and applicability of the adopted modeling framework for comparative connection assessment.

Based on these findings, the continuous steel frame is recommended as the preferred connection system for long-span trussless roofing applications where structural safety, serviceability, and long-term durability are prioritized. Future research should extend the investigation to higher seismicity levels, non-uniform and dynamic wind fields, cyclic fatigue behaviour of connections, and long-term field monitoring under actual environmental exposure conditions to further validate and generalize the present conclusions.