Engineering

Abstract: Finite element models play a critical role in evaluating the structural behaviour of concrete arch dams. The challenge in finite element analysis is generating reliable and accurate models that represent the dam's current condition due to unknown or uncertain system properties. In this paper we investigated the sensitivity of the structural response (displacements, natural frequency & mode shapes) to variation in the material properties (dam system stiffness, Poisson’s ratio, concrete density and coefficient of thermal expansion) of various arch dam configurations (under operational conditions in non-seismic regions where the behaviour of arch dams is driven by thermal loads) to identify the best parameters to update to this end. It was observed that both the natural frequency and thermal displacements are sensitive to the system stiffness. In addition, the thermal displacements are sensitive to the coefficient of thermal expansion and the natural frequencies sensitive to the concrete density. We conclude that the system stiffness is best updated using natural frequencies and the coefficient of thermal expansion using the thermal displacements.

Abstract: The monitoring of the dynamic behaviour of concrete dams is an important aspect in their safety evaluation. Dynamic properties (i.e. mode shapes and natural frequencies) provide useful information on the operational behaviour of dams. In this study, the influence of the curvature (single or double), valley characteristics (narrow or wide, U or V) and classification of arch dams (thin, medium-thick and thick) on the dynamic behaviour of these dams was investigated through numerical models. The mode shape sequence was not affected by the curvature, however it was affected by the system stiffness and added mass (water level) for some configurations. The natural frequencies were generally higher for double curvature arch dams, than single curvature arch dams. The first mode shape for all V-shaped valley types was a symmetric mode followed by an antisymmetric mode. Whilst for the U-shaped valley types, the first and second mode varied between symmetric and anti-symmetric modes for different arch classifications. Based on the observations presented in this paper, the site shape, arch type, arch thickness class influence the dynamic behaviour of concrete arch dams together with the stiffness and water level. An accurate representation of these parameters is critical when performing dynamic analysis of these structures.

Abstract: This article presents the findings of an experimental and numerical investigation into 120 mm thick concrete slabs subjected to impact by 7.62 × 51 mm projectiles with both hard (armour-piercing, AP) and soft (lead) cores. The results of laboratory tests, simplified calculations, and numerical simulations performed using ANSYS LS-DYNA software are presented. The material models and the numerical model description are provided. Experimental results demonstrated a substantial increase in both penetration depth and global specimen damage when subjected to the AP projectile. Despite its lower mass, the AP projectile caused significantly greater damage to the specimens than its lead-core counterpart. A comparison of the estimated penetration depths and the test results revealed that the projectile deformation upon impact must be accounted for when evaluating soft-core projectiles. Furthermore, it was observed that the elastic modulus had no influence on the impact resistance of the components.

Abstract: Bond strength between a repair material and a concrete substrate is a principal parameter for assessing repair quality, most commonly evaluated by the semi-destructive pull-off test. Impact-echo (IE), a stress-wave based non-destructive method, is sensitive to interface quality, but the amplitude of characteristic frequency-domain peaks alone is statistically insufficient for reliable bond-strength estimation, motivating more advanced signal processing such as wavelet analysis. This paper presents a discrete wavelet transform (DWT) analysis of IE signals recorded on two groups of concrete repair systems differing in substrate class and surface-preparation technique. Statistical parameters of the detail-coefficient distributions - mean absolute deviation (MAD), standard deviation (SD), range (RG) - and detail energy (EN) were computed at the detail levels corresponding to the interface echo; finite-element simulations confirmed their sensitivity to interfacial voids. Multiple regression showed that detail-coefficient statistics and detail energy correlate with pull-off bond strength markedly better than frequency-peak amplitude, and that adding substrate roughness and near-surface tensile strength further improved the correlation. A multicollinearity and leave-one-out cross-validation analysis showed, however, that the amplitude-distribution statistics - mean absolute deviation, standard deviation and range - are severely collinear and do not validate as predictors at this sample size, whereas detail energy, and particularly the summed energy of details D2 and D3, is comparatively robust and yields the only model in this study that is both statistically significant and positively cross-validated. Regression equations are proposed accordingly, with detail energy identified as the recommended basis for bond-strength estimation. Discrete wavelet analysis - and specifically detail energy at the interface-echo pseudo-frequency - proves a useful and comparatively robust tool for evaluating bond quality and estimating repair-layer bond strength on concrete substrates.

Abstract: This article presents a qualitative engineering assessment of non-standard structural connections used in streetscape elements, including shelters, canopies, pergolas, recreational facilities, and other small-span structures. The analysed structures are made of steel, aluminium alloys, timber, and hybrid material systems. The need for individually designed connections arises primarily from specific functional and loading conditions, small member cross-sections, the use of hollow sections, restricted installation access, demanding architectural requirements, constraints associated with bending, hot-dip galvanising, and transportation, as well as the risk of galvanic corrosion. The research methodology comprises the identification of key design constraints, the analysis of selected case studies, and a comparative assessment of connection solutions in terms of structural performance, durability, constructability, maintainability, adaptability, demountability, and circularity. The solutions discussed include concealed connections within hollow sections, small-diameter and stainless-steel fasteners, locally reinforced joints, modular field splices, and electrically isolated interfaces between dissimilar metals. The findings indicate that appropriately designed non-standard connections can support durability, selective component replacement, upgrading, relocation, non-destructive disassembly, and the reuse of structural components. However, these benefits do not arise automatically from the customised nature of a connection, as additional material use, fabrication complexity, limited fastener accessibility, and degradation-sensitive interfaces may increase whole-life impacts. Structural connections should therefore be assessed as integral components influencing the performance of a structure throughout its service life rather than solely as local load-transfer details.

Abstract: Monopile-supported offshore wind turbines are increasingly deployed in shallow to medium water depths because of their structural simplicity and economic efficiency. However, in seismic regions with liquefiable sandy deposits, earthquake-induced excess pore water pressure can substantially reduce soil stiffness and strength thereby modifying the dynamic response of the coupled soil-foundation-structure system. This study presents a three-dimensional dynamic finite element analysis of a monopile-supported DTU 10-MW offshore wind turbine using PLAXIS 3D. The liquefiable sand was modeled using UBC3D-PLM effective-stress constitutive model to investigate the influence of liquefiable layer thickness on soil stiffness degradation, apparent natural frequency, and structural response. The findings demonstrate that the response is governed not only by liquefiable-layer thickness but also by the coupled interaction between the liquefiable layer, non-liquefiable layer, and the monopile foundation. Increasing the liquefiable-layer thickness increases the tower and monopile lateral displacements and rotations, while slightly reducing acceleration transmission. The thicker softened liquefied layer reduced soil-foundation dynamic coupling and slightly attenuated the transmission of seismic acceleration to the superstructure. Time-frequency analysis revealed a liquefaction-induced reduction in the apparent first natural frequency (AFNF), as evidenced by the lower post-earthquake AFNF, followed by progressive recovery with soil-stiffness recovery. This recovery was progressively delayed as the liquefiable-layer thickness increased.

Abstract: The growing complexity of urban infrastructure and the demand for sustainability are propelling the development of digitalization in cities. Urban digital twins (UDTs) are an emerging digital transformation solution for smart city management; however, there is limited knowledge about the empirical use of UDTs in developing countries. In this research, the first three stages of descriptive statistical analysis, multi-criteria decision making, and structural equation modeling are used for designing and validating a multi-layered governance structure for the implementation of UDTs in Iranian smart cities. A structured questionnaire, grounded on a horizontal digital twin architecture based on five layers, Technological Infrastructure (TI), Connectivity and Access (CA), Data and Processing (DP), Governance and Operational Management (GOM), and Innovation Enablement (IE), was used to conduct a quantitative expert-based survey. 22 experts in the civil engineering, construction, safety management, and digital technology fields rated the 12 components on the five-point Likert scale. All the components were significantly higher than the neutral value (3.0), with a range of means from 3.59 – 4.36 (Hedges’ g = 0.52 – 2.23), showing a high level of consensus among all components. Phase 2 applied the Best-Worst Method, assigning the highest priority to TI (0.284), followed by DP (0.246), GOM (0.221), CA (0.152), and IE (0.097); all consistency ratios were below 0.10. Structural equation modeling (SEM) was used in phase 3. The sample size (n = 22) was expanded by Monte Carlo data augmentation, resulting in 80 observations, which had the multivariate dependence retained by Cholesky decomposition. The statistical equivalence was checked by comparing with the Frobenius norm (2.070) and the analysis of the eigenvalue spectrum. The model demonstrated excellent fit (χ²/df = 1.87; CFI = 0.96; TLI = 0.95; RMSEA = 0.063; SRMR = 0.071). The direct influence on TI was greatest for Public–Private Partnership (PPP) (β = 0.74, p < 0.001). The results highlight the importance of scalable, federated infrastructure, open data policies, national standards, and IoT governance to support the development of UDT implementation in Iran.

Abstract: Over the last two decades, climate change events have significantly affected the stability of geotechnical infrastructure, caused damage and resulting in injuries and loss of life. Climate-change events such as heavy rainfall, high temperatures, and permafrost thaw can affect the stability of slopes and embankments, causing problems with tunnel linings and foundation failures. The effects of climate change-induced extreme weather events on geotechnical infrastructure and people's lives can be minimized by using advanced data analysis techniques for monitoring and design. Recently, Large Language Models (LLMs) have become popular for efficient and accurate infrastructure design and monitoring because they are trained on large volumes of data. This review summarizes the contributions of different researchers on the effects of climate change-induced extreme weather events on geotechnical infrastructure, including slopes, tunnels, embankments, and foundations. Moreover, this research proposes avenues for using LLMs for efficient monitoring and design of geotechnical infrastructure. By summarizing the findings, this paper highlights the impact of extreme weather events on geotechnical infrastructure and helps engineers adopt LLMs for the design and monitoring of geotechnical infrastructure. Overall, integrating LLMs into the design and monitoring of geotechnical infrastructure can improve safety by enhancing early-warning systems for slopes, embankments, and tunnels and by enabling designs that account for the variability of environmental forces during extreme weather events.

Abstract: The symbol θ is used in reinforced-concrete analysis for several physically different quantities. In two-way slabs these include the strut-and-tie-model (STM) strut inclination, a spacing-based geometric load-diffusion angle, reinforcement-family and yield-line orientations, crack-normal misalignment, and the inclination associated with tensile membrane action. Treating these quantities as interchangeable can produce misleading comparisons between reinforcement spacing and code provisions. This paper establishes a unified framework for conventional orthogonal (0°/90°) and triaxial (0°/60°/120°) reinforcement. The triaxial network is described as a planar triangular reinforcement lattice, while a hexagonal cell is used only as a geometric representation. The geometric dispersion angle is defined using nodal pitch rather than the perpendicular bar spacing. For the orthogonal mesh ℓ_o=s_o, whereas for the triaxial mesh ℓ_h=2s_h/√3. Combining this geometry with the reinforcement-density transformation gives tanθ_h=(R_h/√3)tanθ_o. The frequently cited 1.85d value is shown to be a derived geometric expression associated with a 25° reference under the adopted triaxial geometry; it is not presented as an independent reinforcement-spacing requirement of ACI. A new analytical framework is introduced for nodal force transfer, idealized directional response, three-dimensional load-path geometry, and possible confinement effects. The confinement and strain-energy interpretations are explicitly treated as research hypotheses rather than established mechanisms because their quantitative calibration for triaxial slab reinforcement is not available. The S1–S10 ABAQUS matrix from the source finite-element study is used as a numerical illustration. Particular attention is given to S8 and S9: with the density definitions used here, S9 contains 25% of the total steel density of S8, not 50%; S9 is 50% of the orthogonal 120-mm reference used in the same model family. The results show that θ_d does not uniquely control ultimate pressure. Accordingly, θ_d is proposed as a geometric/detailing and load-path screening descriptor, whereas θ_STM should be obtained from actual compression trajectories in mechanically appropriate discontinuity regions.

Abstract: This study develops a research and verification framework for a triaxial reinforcement topology consisting of three continuous reinforcement families oriented at 0°, 60°, and 120° in two-way reinforced-concrete slabs. The manuscript is reorganized around a four-axis framework linking (I) topology, density, and spacing; (II) reinforcement quantity and reduction; (III) structural resistance and serviceability; and (IV) effective depth and load-transfer geometry. Four complementary methods are used: analytical derivation, code-based reference checks, nonlinear finite-element analysis in ABAQUS/Standard, and comparative calibration against the S1–S10 numerical matrix. The analytical model establishes the exact density transformation s_h=[3/(2R_h)]s_o and the equal-steel spacing relation s_h=1.5s_o. It also gives the idealized equal-steel relations E_hex=0.75E_0 and m_n=1.5m_0 within the adopted mesh formulation. These identities are explicitly separated from research hypotheses, including the 50% total-steel reduction target and k=0.60. The FE matrix shows matched resistance ratios ranging from approximately 0.957 to 1.028, with S9 reaching 225 kN/m2 relative to 235 kN/m2 for S8 and a reported peak central deflection of 0.77 mm. A 1.83 × 1.83 m demonstration, matched directly to four of the original ABAQUS specimens under four-edge simply supported conditions, shows that preliminary code-based reinforcement quantities substantially exceed the nominal steel embedded in the reference finite-element models, underscoring that any claimed reduction must be verified case by case rather than assumed. The resulting framework is therefore presented as a testable research methodology rather than a finalized design code.

Abstract: Reliable prediction of tunnelling-induced ground deformation is essential for assessing differential settlement of surface buildings and deformation of subsurface structures in densely built urban areas. This study establishes a multi-source engineering-evidence framework for parameter selection in the modified Peck model. An interval database containing 39 published correction-coefficient records is compiled to investigate the maximum-settlement correction coefficient α and settlement-trough-width correction coefficient β, while an independent dataset comprising 24 international shield-tunnelling cases and 84 surface and subsurface observations is used to evaluate depth-dependent settlement characteristics. Descriptive statistics, the Mann–Whitney U test, Cliff’s δ, bootstrap resampling, interval Monte Carlo simulation, and case-level trend analysis are employed. The median values α are 0.650 for soft soil and 0.550 for composite strata. Although the difference is not statistically significant (p=0.150,δ=0.302), interval Monte Carlo analysis gives a probability of 0.907 that the median α is higher in soft soil, indicating a directional ground-condition dependence. In contrast, β shows substantial between-group overlap and no robust ground-condition dependence. With increasing normalized observation depth z/T, i(z)/i(0) decreases strongly (ρ=-0.898), whereas S_max(z)/S_max(0) generally increases, with consistent within-case trends in 17/17 and 20/22 cases, respectively. The results support treating α as a ground-conditioned prior and β as an updateable project-specific parameter rather than prescribing either as a fixed constant. The proposed framework provides a transparent basis for settlement assessment of the built environment and highlights the need for depth-dependent corrections when subsurface structures are involved.

Abstract: Urban densification and high-rise buildings alter local wind flows, thereby affecting structural aerodynamic loads. To address this issue, the present numerical study investigates the insertion of a standard high-rise building within the Oklahoma City urban dataset. Computational Fluid Dynamics simulations were conducted across eight wind incidence angles (from 0° to 360° at 45° intervals) using two turbulence models, the Reynolds-Averaged Navier-Stokes (RANS) with k-ω Shear Stress Transport closure equations and the hybrid approach Shear Stress Transport Delayed Detached-Eddy Simulations (SSTDDES). A numerical validation was conducted using the Michelstadt experimental dataset, showing that both turbulence models achieved satisfactory statistical agreement with wind tunnel data. Structural forces were quantified using aerodynamic coefficients, and the results demonstrate that while the surrounding neighborhood provides a shielding effect, it simultaneously induces complex wakes that amplify localized peak lateral forces and torsion. Notably, the SSTDDES model captured higher peak structural loads and gusts compared to the RANS approach, concluding that domain-averaged criteria can obscure severe localized hazards, emphasizing that safe high-density developments require adequate turbulence models and site-specific aerodynamic investigations.

Abstract: A clay flow rule governs contraction or dilation during plastic shearing. A fractional replacement must preserve the zero-dilatancy critical state and remain compatible with elasticity and hardening. We examine these requirements for a terminal-directed Caputo operator on a teardrop surface. The operator integrates surface slopes over a logarithmic stress interval, not elapsed loading history. Analytical derivations and incremental tests separate terminal compatibility, operator composition, stress-path identifiability and admissibility. The operator zero matches the non-associated base-model critical state only if Ω = Ψ. For kaolin, the alternative zero raises the normally consolidated undrained terminal mean stress by 18.6%. An exact identity shows why the flow candidates share the same normally consolidated stress locus yet progress differently in a numerical coordinate. Mean-stress preservation permits exact scalar composition with the SMP transformation but supplies no physical strain mapping. Two direct overconsolidated substitutions expose distinct deficiencies: coupling the loading modulus to the fractional dilatancy (F2) reverses its sign above OCR=exp(1/Ψ), whereas retaining the inherited loading modulus (F1) causes hardening inconsistency, low-OCR surface drift or negative assigned work at high OCR. These results define requirements a fractional clay formulation must satisfy before stress and strain data can test its predictions.

Abstract: Road traffic injuries remain a leading cause of preventable death and disability worldwide, with disproportionate impacts on vulnerable and underserved populations. While transportation safety efforts have traditionally focused on engineering countermeasures and behavioral modification, persistent inequities in crash risk and injury outcomes indicate the need for a broader systems-based approach. This discursive paper applies the National Institute on Minority Health and Health Disparities (NIMHD) Research Framework to conceptualize road traffic safety across multiple domains, i.e., biological, behavioral, physical/built environment, sociocultural environment, and health care system, and levels of influence including individual, interpersonal, community, and societal factors. By integrating transportation engineering strategies such as Safe System design, roadway countermeasures, and vehicle technologies with public health perspectives on injury prevention and health equity, the paper illustrates how structural conditions shape crash occurrence, injury severity, and post-crash outcomes. The proposed multilevel and multisectoral framework emphasizes cross-sector collaboration among engineers, public health professionals, policymakers, and community stakeholders to reduce preventable injury and advance equity. This integrated model offers a conceptual foundation for future empirical research, policy development, and implementation strategies aimed at achieving population-level improvements in road safety.

Abstract: Artificial intelligence (AI) increasingly interprets vibration and dynamic-response measurements for bridge nondestructive testing (NDT) and structural health monitoring (SHM), yet predictive performance within a dataset does not establish diagnostic or operational maturity. This investigation searched Scopus, Web of Science Core Collection, and IEEE Xplore through 23 August 2026, screening 3,412 records and retaining 727 peer-reviewed studies as the systematic core. Unlike prior reviews organised by algorithm type, each study was coded at the level of the individual validation case for diagnostic capability (D0-D4), validation realism (R1-R4), damage authenticity (A0-A4), generalisation (G0-G3), temporal maturity (T0-T2), engineering-use maturity (M0-M3), and five independent trustworthiness attributes (E, U, X, P, F). The corpus is dominated by enabling inference and detection (D0-D1, 67.4%), whereas prognosis (D4) appears in only 6 studies (0.8%). Numerical validation predominates (R1, 48.1%), confirmed full-scale physical damage occurs in 61 studies (8.4%), and only 8 (1.1%) combine operational monitoring with confirmed damage. Cross-bridge transfer (2.1%), long-term monitoring (2.2%), decision support (0.4%), and explicit trustworthiness (none of the five attributes in 67.0%) are all rare, and only one study combines operational validation, confirmed damage, and verified transfer. The principal gap is therefore not AI capability but the scarcity of evidence where capability, realistic validation, authentic damage, transferability, durability, trustworthiness, and decision relevance converge.

Abstract: Progressive Design-Build (PDB) has gained increasing attention as an alternative project delivery method that promotes early collaboration between owners and design-builders. However, limited empirical research has systematically identified the factors that are critical to successful PDB project delivery. This study identifies and evaluates critical success indicators (CSIs) and groups them into broader critical success factors (CSFs) affecting the cost and schedule performance of PDB projects during the procurement and implementation phases. A literature review and exploratory expert survey were used to identify and validate the CSIs, followed by a questionnaire survey of industry professionals. Twenty-nine valid responses representing 55 PDB projects across multiple infrastructure sectors were analyzed using statistical analyses. Six procurement-phase and eight implementation-phase CSIs were identified as critical. Principal Component Analysis (PCA) was used to group the procurement indicators into four CSFs related to owner competencies, owner–design-builder working relationships, design-builder competencies, and owner procurement processes. Four implementation CSFs were identified: owner–design-builder working relationships; owner project management processes; owner and design-builder competencies; and owner-, design-, and change-management processes. The findings provide empirical guidance for owners and design-build teams to prioritize organizational, relational, and managerial practices that support successful PDB project delivery.

Abstract: Value for Money (VfM) analysis is the primary mechanism by which U.S. state agencies evaluate whether a project should be delivered through a public-private partnership (P3) or conventional public procurement. While the methodology has been widely applied, relatively little is known about how practitioners conduct these analyses and apply VfM in practice. This study addresses that gap through semi-structured interviews with ten practitioners involved in VfM analyses for U.S. highway projects. Framework analysis was used to examine practitioner perspectives on VfM objectives, assumption development, risk assessment, financing, discounting, and critical success factors. The findings indicate that VfM practice is shaped by funding constraints, reliance on professional judgment, and the quality of stakeholder engagement. Participants described project environments in which fiscal considerations strongly influenced procurement decisions and payment mechanisms. Across all major modeling components, practitioners relied heavily on historical benchmarks, expert judgment, and comparable project experience due to the limited availability of project-specific empirical data during the pre-procurement stage. Communication, stakeholder engagement, and the transparency of assumptions were consistently identified as important contributors to analytical credibility and reliability. The study contributes a practitioner-centered perspective to the VfM literature and highlights the importance of strengthening the institutional foundations of VfM practice through improved data collection, post-completion evaluation, transparency, independent review and public-sector analytical capacity. The findings suggest that enhancing the quality of information and governance surrounding VfM analysis may be as important as methodological refinement in improving future procurement evaluations.

Abstract: The global growth of concrete is a strong indication of the urgent need for sustainable construction materials to reduce carbon footprints and reuse industrial waste. In this work, we study the combined effect of mixing two industrial by-products, silica fume and mill scale. The concrete mixes were prepared with combined substitution levels of 0, 20, 25, and 30%. Fresh properties were evaluated by slump, flow table, and compaction factor tests. Hardened performance was studied by compressive, flexural, splitting tensile, and non-destructive ultrasonic pulse velocity (UPV) tests. The long-term chemical durability of the combinations was studied by exposure for 91 days to magnesium sulfate (MgSO₄), sulfuric acid (H₂SO₄), and NaCl conditions. The performance of the trial indicated that a moderate replacement level of 20% is optimum for the fresh properties, resulting in the highest slump and flow values due to paste modification and improved particle packing. The result of non-destructive testing showed that the mix with 25% replacement achieved the highest UPV, which means the microstructure was highly dense and the interfacial transition zone was improved. The modified mixes exhibited better resistance against the mass loss of sulfuric acid when exposed to aggressive chemical environments than the control mix. The maximum acid resistance was found to be highest in the 30% substitution due to the decreased reserves of Ca(OH)₂. The 25% mix showed the best microstructural density and steady long-term development of compressive strength under sulfate and marine conditions. However, the high replacement (30%) resulted in a high dilution of cement clinker and a major decrease in mechanical performance and workability. The study shows that, in general, a replacement rate of 20% to 25% provides a good compromise between environmental sustainability and waste management, on one hand, and good mechanical performance and chemical durability, on the other, concerning modern concrete architecture.

Abstract: Currently, rapid digital revolution in the building industry due to the necessity to solve chronic challenges such as low productivity, inconsistent execution quality, and difficulty in controlling costs and schedules. Construction supervision is one area where digital transformation can have a significant impact, given the repetitive nature of its tasks, which rely heavily on human expertise and manual labor. The aim of this study is to develop a comprehensive framework to evaluate the effectiveness of the digital transformation on supervision in construction projects using modeling of structural equations (PLS-SEM). The data obtained was examined. and evaluated utilizing technique PLS-SEM software to build the proposed model. The results show a positive correlation between the supervisor's productivity and the utilization of digital technology, depending on the context of the task and the nature of the work. The study also proposes a methodology for the use of SEM in this area, comprising model construction steps and evaluation indicators, and it provides suggestions for researchers and practitioners to improve the effectiveness of using digital transformation in construction supervision.

Abstract: Thin-walled cold-formed C- and Z-sections are widely used in lightweight structural systems, where web openings are frequently introduced for service integration, weight reduction, or manufacturing requirements. However, local perforations alter not only the classical bending and shear stiffness but also torsional response, warping, and the coupling between generalized deformation modes. This study develops a reduced stiffness framework for perforated thin-walled members based on static condensation of detailed shell finite element models. Each perforated segment is first condensed to its boundary degrees of freedom (DOF) and subsequently projected onto an enriched beam-type kinematic basis comprising six classical rigid-section modes and an additional sectorial warping mode. The resulting reduced element is described by a compact stiffness matrix that preserves the energetic influence of local deformation around the opening while enabling efficient one-dimensional assembly of long perforated members. The effect of perforation is expressed through an opening-induced stiffness correction relative to the corresponding unperforated segment. A low-dimensional representation of this correction is further investigated using proper orthogonal decomposition (POD), allowing the dependence of the reduced stiffness matrix on opening geometry to be represented by a limited number of dominant stiffness modes. Only three POD modes were required to represent more than 99.9% of the snapshot energy of the combined C- and Z-section stiffness-correction database, while the surrogate reconstruction error of the complete correction matrix remained approximately 1.5% on average. At member level, the proposed seven-DOF formulation reduced the number of structural degrees of freedom by approximately 400–455 times while keeping displacement and twist profile errors below 3.2%.