Substructure Model Research Articles

Experimental investigation of progressive collapse resistance of bonded local prestressed concrete frame substructures

Bonded local prestressed concrete (BLPC) frames represent a structural form that combines long spans with prestressing and short spans without prestressing. Progressive collapse has become a focus of research in recent years, given the potential for severe consequences. BLPC frames exhibit distinct progressive collapse resistance compared to symmetrical structures due to their notable asymmetry. Therefore, this paper tested the behavior of two BLPC substructures and one unequal-span reinforced concrete (USRC) substructure against progressive collapse in the middle column removal scenario. The tests were conducted using displacement-controlled static loading, with the loading point situated at the top of the middle column. The test results demonstrate that the BLPC frame employs a two-stage mechanism to resist progressive collapse, comprising the beam-beam stage and the beam-link stage. Additionally, the frame exhibits a tri-fold failure mode. At the location of attachment of the short-span beam to the side column, the top rebars were found to be entirely fractured. At the junction of the reinforced and non-reinforced regions of longitudinal rebar in the long-span beam, a substantial crack developed, extending almost through. This indicates that the plastic hinge of the long-span beam appeared at the location where the longitudinal rebars were changed, rather than at the beam end. This paper also established a refined numerical model of the BLPC substructures based on LS-DYNA, and the modeling method was verified by comparison with the tests.

Experimental study on seismic damage of SRC-RC vertical hybrid structure

In order to analyze the seismic performance of the SRC-RC vertical hybrid structure, three substructure models were designed, and the key data of structural performance, such as hysteresis curve, skeleton curve, bearing capacity, energy dissipation of structure, residual deformation and damage degree were obtained by carrying out low cyclic loading tests. According to the tests, the plastic development at the column base was delayed because of the reinforcement of section steel, and the plastic development at beam end was much more sufficient, which benefited the beam hinge mechanism in the transition area, so that the transition area has better energy dissipation capacity and deformation capacity. Based on the more sufficient lateral displacement of beam hinge, the beams suffered bending deformation obviously, and interaction between the beams and the infilled wall was significant, which led to a more complex interface force transmission, so the bending cracks and the shearing cracks were densely distributed along the full length of the beam. Meanwhile, the reinforcement of section steel not only improved the deformation capacity of the models but also resulted in more significant damage difference in positive and negative loading. To quantitatively evaluate the damage level, a seismic damage index system was proposed, including displacement damage degree, bearing capacity damage degree and residual deformation index, which reflect the increment of deformation caused by structural damage, the deterioration of bearing capacity and the residual deformation, respectively. It is suggested that the structural failure should be defined respectively under different modes: For the strength degradation behavior mode and ductility behavior mode, structural failure should be confirmed if the load reduces to 0.90 and 0.85 times of the peak load, respectively; and for the brittle behavior mode, the frame is considered to fail when the load reaches the peak without considering the structural performance after the peak load.

Dynamic Behaviors of Composite-Laminated Concentrically Stiffened Rectangular Plates by Substructure Modal Synthesis

Existing numerical analysis methods often incur high computational costs when directly solving multi-degree-of-freedom systems due to computer capacity limitations. To address this issue, this paper took the composite laminated concentrically stiffened rectangular plate as the research object. The modal synthesis method was employed to reduce the degrees of freedom of the model, enabling the solution of complex dynamic characteristics. In the research process, the domain decomposition theory was used to divide the research object into plate and rib substructures. Based on the spectral Chebyshev method, the substructure dynamic model of the composite laminated rectangular plate was constructed. Subsequently, the function expressions of the complex load excitation on each substructure were derived, and the fixed modal synthesis method was introduced to construct the spectral Chebyshev reduced model of the substructures. According to the artificial spring theory equivalent, the interface force, and the whole reduction model of the composite laminated concentrically stiffened rectangular plate were obtained by assembling the substructure models. The time–domain and frequency–domain dynamic behaviors of composite laminated concentrically stiffened rectangular plates are yielded by solving the whole reduced model. The novelty of this work lies in combining the spectral Chebyshev method with the modal synthesis method. The established reduced model no longer depended on mesh quality and required fewer matrix dimensions and computation time compared to the whole model, while still achieving sufficiently accurate results. Additionally, based on the reduced model, an effective parametric study scheme was proposed to analyze the impact of dimensions and material properties of rib substructures on the dynamic behaviors of the composite laminated concentrically stiffened rectangular plate. These findings can be used to guide the optimal design of laminated concentrically stiffened rectangular plates in engineering practice.

Wave basin investigation of floating wind turbine model using underwater particle image velocimetry: investigating hydrodynamic wake structures

This paper conducts a fundamental study on the hydrodynamic performance of a floating offshore wind turbine (FOWT). This includes investigating the impacts of platform motion, turbine operation, and environmental conditions on hydrodynamic wake development behind the FOWT. Using underwater particle image velocimetry in a wave basin, the fluid flow behaviour behind the floating wind substructure model is compared for different test configurations. The FOWT is examined in three configurations: I. Zero degrees of freedom (fixed), II. Six degrees of freedom (floating), and III. Floating with turbine in operation (full system). The results reveal significant hydrodynamic wake turbulence differences between fixed and floating systems, with 95% and 89% increases in turbulent kinetic energy (TKE) and turbulence intensity (TI), respectively. Turbine loading in configuration III results in additional damping and reduces eddy shedding, resulting in a 26% and 31% decrease in TKE and TI, compared to the floating configuration II. It is found that neglecting turbine operation overestimates substructure drag terms by at least 30%, while fixing the model underestimates drag terms by 54%. This study highlights a trade-off between model accuracy and dynamic complexity when estimating viscous effects on FOWT. It also provides a valuable set of high-fidelity validation data for the development of numerical tools for FOWT analysis.

Seismic performance analysis of wood-steel frame structures

Wood and steel have different physical properties. By combining the two kinds of materials as bonded parallel beams, wood-steel frame structures can be prepared. This work considers the seismic performance of such engineering structures. Based on the Rayleigh damping model of substructures, the non-proportional damping coefficient is used to quantify the structural non-proportional damping characteristic of wood-steel frame structures. A complex mode superposition method is used to calculate seismic responses. Numerical cases showed that compared with the frame structure with upper steel and lower wood, the overall lateral performance is lower and the local lateral performance is higher for the frame structure with upper wood and lower steel. The overall lateral seismic design needs to be improved for the wood-steel frame structure with upper wood and lower steel. The local lateral seismic design needs be improved for the wood-steel frame structure with upper steel and lower wood.

Optimization analysis of vibration reduction for aeroengine multistage blade-disk system

In order to reduce the vibration localization of multistage blade-disk system of aeroengine compressor, the integral model and substructure model of multistage blade-disk system are established by using substructure modal synthesis method, and the dynamic characteristics of two models are analyzed and the accuracy of the substructure model is verified by comparison. Based on the substructure model, two optimization algorithms of the random wear mass and the snake optimization are proposed. The results show that the vibration amplitudes of the two models are in good agreement in the first 200 modes, and the substructure model meets the requirement of analysis accuracy. Both optimization algorithms can effectively reduce the degree of the vibration localization of the mistuned blade-disk system. The random wear mass algorithm can quickly reduce the amplitude of the blade. The snake optimization algorithm can find the global optimal solution with enough iterations. The results show that the maximum vibration amplitude and the vibration localization factor after optimization are reduced by 5.72 % and 12.0 % respectively by using the random wear mass algorithm, and that of 9.13 % and 16.7 % respectively by using the snake optimization algorithm. The analysis method presented in this paper takes into account the analysis efficiency and analysis precision, it can be used for dynamic analysis and vibration reduction optimization of large power machinery such as aeroengine and gas turbine, and provides a basis for further improving the reliability and service life of aircraft.

Subgrain Size Modeling and Substructure Evolution in an AA1050 Aluminum Alloy during High-Temperature Compression.

For materials with high stacking fault energy (SFE), such as aluminum alloys, dynamic recovery (DRV) and dynamic recrystallization (DRX) are essential softening mechanisms during plastic deformation, which lead to the continuous generation and refinement of newborn subgrains (2° ˂ misorientation angle ˂ 15°). The present work investigates the influence of compression parameters on the evolution of the substructures for a 1050 aluminum alloy at elevated temperatures. The alloy microstructure was investigated under deformation temperatures ranging from 300 °C to 500 °C and strain rates from 0.01 to 0.1 s-1, respectively. A well-defined substructure and subsequent subgrain refinement provided indication of the evolution laws of the substructure under high-temperature compression. Corresponding experimental data on the average subgrain size under various compression conditions were obtained. Two different independent average subgrain size evolution models (empirical and substructure-based) were used and applied with several internal state variables. The substructure model employed physical variables to simulate subgrain refinement and thermal coarsening during deformation, incorporating a corresponding dislocation density evolution model. The correlation coefficient (R) and root mean square error (RMSE) of the substructure-based model were calculated to be 0.98 and 5.7%, respectively. These models can provide good estimates of the average subgrain size, with both predictions and experiments reproducing the expected subgrain size evolution using physically meaningful variables during continuous deformation.

Capture of field stars by dark substructures

ABSTRACT We use analytical and N-body methods to study the capture of field stars by gravitating substructures moving across a galactic environment. The majority of stars captured by a substructure move on temporarily bound orbits that are lost to galactic tides after a few orbital revolutions. In numerical experiments where a substructure model is immersed into a sea of field particles on a circular orbit, we find a population of particles that remain bound to the substructure potential for indefinitely long times. This population is absent from substructure models, initially placed outside the galaxy on an eccentric orbit. We show that gravitational capture is most efficient in dwarf spheroidal galaxies (dSphs) on account of their low velocity dispersions and high stellar phase-space densities. In these galaxies, ‘dark’ sub-subhaloes, which do not experience in situ star formation, may capture field stars and become visible as stellar overdensities with unusual properties: (i) they would have a large size for their luminosity, (ii) contain stellar populations indistinguishable from the host galaxy, and (iii) exhibit dark matter (DM)-dominated mass-to-light ratios. We discuss the nature of several ‘anomalous’ stellar systems reported as star clusters in the Fornax and Eridanus II dSphs that exhibit some of these characteristics. DM sub-subhaloes with a mass function ${\rm d}N/{\rm d}M_\bullet \sim M_\bullet ^{-\alpha }$ are expected to generate stellar systems with a luminosity function, ${\rm d}N/{\rm d}M_\star \sim M_\star ^{-\beta }$, where $\beta =(2\alpha +1)/3=1.6$ for $\alpha =1.9$. Detecting and characterizing these objects in dSphs would provide unprecedented constraints on the particle mass and cross-section of a large range of DM particle candidates.

Component tests and numerical simulations of 3D steel frame structures for progressive collapse

This paper presents a comprehensive study on three-dimensional steel frame structures subjected to progressive collapse, drawing insights from a full-scale steel frame substructure test. The investigation encompasses connection component tests and numerical simulations, focusing on extended end plate and double-angle cleat connections employed in the substructure test. The mechanical properties of the connection components were tested, forming a basis for defining component properties in subsequent connection models. Finite element (FE) models of the test substructure were developed, utilizing hybrid elements for the steel frame part, which include beam, connector, and spring elements based on the component method. To simulate reinforced concrete slabs, a combination of refined solid elements and simplified shell elements was employed. The former accurately captures detailed failure modes, while the latter efficiently simulates the collapse behavior of large-scale steel frame structures. Validation of the established models against test results encompassed load-displacement responses, internal forces in structural members, and failure modes. The validated FE models were then utilized to analyze and discuss the contributions of various structural components in resisting progressive collapse. Specific focus was placed on the development of load-resisting mechanisms in the floor slab and the influence of beam-column connection types on structural behavior. The paper explores the role of bracing systems in a building in resisting progressive collapse. Additionally, it evaluates the effectiveness of the restraint systems used in the test, shedding light on their ability to accurately reflect real restraint effects from the surrounding structure. The findings presented herein contribute valuable insights to the understanding of progressive collapse behavior in steel frame structures, with implications for robustness design of multi-story steel buildings.

A Framework for Structural Analysis of Icebreakers during Ramming of First-Year Ice Ridges

This paper presents a framework for structural analysis of icebreakers during ramming of first-year ice ridges. The framework links the ice-ridge load and the structural analysis based on the physical characteristics of ship–ice-ridge interactions. A ship–ice-ridge interaction study was conducted to demonstrate the feasibility of the proposed framework. A PC-2 icebreaker was chosen for the ship–ice interaction study, and the geometrical and physical properties of the ice ridge were determined based on empirical data. The ice ridge was modeled by solid elements equipped with the continuous surface cap model (CSCM). To validate the approach, the simulated ice resistance was computed using the Lindqvist solution and in situ tests of R/V Xuelong 2. First, the local ice-induced pressure on the hull shell was determined based on numerical simulations. Subsequently, the local ice pressure was applied to local deformable sub-structural models of the PC-2 icebreaker hull by means of triangular impulse loads. Finally, the structural response of sub-structural models with refined meshes was computed. This case study demonstrates that the proposed framework is suitable for structural analysis of ice-induced stresses in local hull components. The results show that the ice load and the structural response obtained based on the four first-year ice-ridge models show obvious differences. Furthermore, the ice load and corresponding structural response increases with the width of the ridge and with increasing ship speed.

Development and verification of real‐time hybrid simulation with deep learning‐based nonlinear numerical substructure

AbstractReal‐time hybrid simulation (RTHS) provides an effective approach for assessing structural responses under dynamic excitation. However, performing RTHS with a complex nonlinear numerical substructure is challenging, as computations must be completed within predefined time steps. In this study, a RTHS framework which contains a rate‐dependent experimental substructure and a nonlinear numerical substructure has been proposed and verified. An OpenSees model was constructed to simulate a three‐story, one‐bay steel building with viscous dampers at each floor and was used to generate the training dataset through a large number of nonlinear time‐history analyses. A Recursive Long Short–Term Memory (LSTM) neural network model was trained to predict the nonlinear structural responses using ground acceleration and time‐delayed damper force located at the first story. Hence, the Recursive‐LSTM model served as a surrogate model for the numerical substructure, implicitly incorporating delay compensation for the experimental substructure. After the training was completed, offline testing was performed to realize the stability of the RTHS framework. Then, online RTHS with a virtual damper taken as the experimental substructure was conducted to further confirm the feasibility and accuracy. Afterwards, a nonlinear rotary fluid viscous damper (RFVD) was fabricated as the actual experimental substructure, whose dynamic response was not considered in training the Recursive‐LSTM model. Finally, RTHS with the RFVD was completed successfully and stably, demonstrating the capability of a well‐trained Recursive‐LSTM model to serve as a nonlinear numerical substructure incorporating constant delay compensation for RTHS. The potential of the proposed RTHS framework is worth further studies in the future.

Modal and response characteristics of rotor with angle misalignment fault based on cross-coordinate system substructure modeling method

Finite element models are widely used in dynamic analysis of misalignment rotor, but present finite element rotor models cannot simulate the axis characteristics of angle misalignment rotor, which consistent with the one with no misalignment. For achieving the precisely modeling of angle misalignment rotor, a novel modeling method called cross-coordinate substructure modeling method is introduced to establish the model of misalignment rotor, in which different parts of rotor rotate around different axis. Based on this modeling method, the 3D solid models of angle misalignment rotor are established with the help of ANSYS, and the modal characteristics and critical speeds of the misalignment rotor are achieved through modal analysis and harmonic response analysis. The numerical simulation based on Newmark method and experiment tests is carried out to obtain the response characteristics of the rotor model under the combined action of unbalanced force and misalignment load. The results show that the modal “rotation of rotor” appears, and the more amounts of response peaks can be aroused in harmonic response analysis when the rotor occurs angle misalignment. The typical fault characteristics of angle misalignment rotor in the spectrums and orbit diagrams are generally consistent both in the numerical simulation and experiment test. The research results can provide a theoretical basis for simulation and identification of the misalignment fault in rotating machinery system.

Search for decaying dark matter in the Virgo cluster of galaxies with HAWC

The decay or annihilation of dark matter particles may produce a steady flux of very-high-energy gamma rays detectable above the diffuse background. Nearby clusters of galaxies provide excellent targets to search for the signatures of particle dark matter interactions. In particular, the Virgo cluster spans several degrees across the sky and can be efficiently probed with a wide field-of-view instrument. The High Altitude Water Cherenkov (HAWC) observatory, due to its wide field of view and sensitivity to gamma rays at an energy scale of 300 GeV–100 TeV is well-suited for this search. Using 2141 days of data, we search for γ-ray emission from the Virgo cluster, assuming well-motivated dark matter substructure models. Our results provide some of the strongest constraints on the decay lifetime of dark matter for masses above 10 TeV. Published by the American Physical Society 2024

A Damage Identification Method for Transmission Towers Based on Substructure Model Reduction and Data Driving

A Damage Identification Method for Transmission Towers Based on Substructure Model Reduction and Data Driving

Finite element analysis of progressive collapse resistance of precast concrete frame beam-column substructures with UHPC connections

Compared with reinforced concrete structure, precast concrete structure is prone to progressive collapse due to its poor continuity. The use of ultra-high performance concrete (UHPC) provides a feasible solution. To this end, investigate the influence of UHPC on the progressive collapse resistance of precast beam-column substructures, the finite element model of precast beam-column substructures with UHPC connections was established. The model was validated using available experimental data. Specifically, the cohesive-Coulomb friction model was used to simulate the interface behavior between precast concrete and cast-in-place concrete, and the metal ductile damage model was used to simulate rebar failure. The finite element simulation results show good agreement with experimental results, with an average error of less than 5 %. Additionally, five sets of full-scale analysis models were designed to analyze the effect of cast-in-place UHPC on the progressive collapse resistance of precast beam-column substructures. The results indicated that UHPC enhances the compressive arch action (CAA) capacity and catenary action (CA) capacity of precast beam-column substructures. Parametric analysis was conducted based on these models. The results indicated that the increase of UHPC strength grade can improve the CAA capacity of the structure, but reduce the CA capacity. Interface roughness has a certain effect on CAA capacity, but has no obvious effect on CA capacity. Finally, the accuracy of existing analytical models in predicting the CAA and CA capacity of UHPC-connected precast beam-column substructures is evaluated. The research results can provide reference for the design and application of precast concrete structures connected by UHPC.

Collapse-resistant mechanisms induced by various perimeter column damage scenarios in RC flat plate structures

This paper aims at assessing the impact of removing various numbers of perimeter columns on the integrity of RC flat plate substructures. Compared to interior columns, those at the corner and edge positions on the building perimeter are more likely to damage by accidental and abnormal loads, which in turn may cause progressive collapse of the entire structure. Given the uncertainty of the loading events, the likelihood of multiple perimeter columns being simultaneously destroyed is also high. However, existing research has primarily focused on the single column removal cases. To address this research limitation, a 3D high-fidelity finite element model of a flat plate substructure with a missing corner column (named Model C) was developed. The accuracy of the model was validated based on our previous experiment of the same substructure. The validated model was subsequently modified to cover two and multiple perimeter column removal scenarios. The two new models are namely, Model C_1e in which a corner column and an adjacent edge column were damaged and Model C_2e, with a corner column and two adjacent edge columns being removed. The simulation results reveal that flexural action was the primary load resisting mechanism in all three models. The load carrying capacity with three column removals was reduced by 75.6% compared to the removal of a single corner column. Full-depth cracks were found at the cut-off position of the top slab rebars for the columns adjacent to the removed one(s). In Model C and Model C_2e, cracks exhibited a diagonal axisymmetric failure pattern of the corner of the slab, with equal load transfer to two adjacent columns. In contrast, Model C_1e exhibited a diagonal non-axisymmetric failure pattern of the slab corner, with more loads being transferred to the adjacent column along the shorter bay. The energy-based dynamic response analyses were also performed to obtain the Dynamic Increase Factor (DIF) for the substructure models under different column removal scenarios. Based on the nonlinear regression analysis, the DIFs for the substructures with one and two column removals were found to be ranged between 1.22 and 1.51, and 1.28–1.68, respectively.

Deep learning–based automatic segmentation of cardiac substructures for lung cancers

PurposeAccurate and comprehensive segmentation of cardiac substructures is crucial for minimizing the risk of radiation-induced heart disease in lung cancer radiotherapy. We sought to develop and validate deep learning–based auto-segmentation models for cardiac substructures. Materials and MethodsNineteen cardiac substructures (whole heart, 4 heart chambers, 6 great vessels, 4 valves, and 4 coronary arteries) in 100 patients treated for non-small cell lung cancer were manually delineated by two radiation oncologists. The valves and coronary arteries were delineated as planning risk volumes. An nnU-Net auto-segmentation model was trained, validated, and tested on this dataset with a split ratio of 75:5:20. The auto-segmented contours were evaluated by comparing them with manually drawn contours in terms of Dice similarity coefficient (DSC) and dose metrics extracted from clinical plans. An independent dataset of 42 patients was used for subjective evaluation of the auto-segmentation model by 4 physicians. ResultsThe average DSCs were 0.95 (+/– 0.01) for the whole heart, 0.91 (+/– 0.02) for 4 chambers, 0.86 (+/– 0.09) for 6 great vessels, 0.81 (+/– 0.09) for 4 valves, and 0.60 (+/– 0.14) for 4 coronary arteries. The average absolute errors in mean/max doses to all substructures were 1.04 (+/– 1.99) Gy and 2.20 (+/– 4.37) Gy. The subjective evaluation revealed that 94% of the auto-segmented contours were clinically acceptable. ConclusionWe demonstrated the effectiveness of our nnU-Net model for delineating cardiac substructures, including coronary arteries. Our results indicate that this model has promise for studies regarding radiation dose to cardiac substructures.

Extended component mode synthesis method for dynamic analysis of mechanical systems with local nonlinearities

Engineering structures are generally designed based on linear elasticity assumptions. However, it is difficult to describe the connected structures using a simple linear system, due to factors such as sliding and friction at interfaces, and variations in contact areas during vibration processes. Therefore, it is necessary to develop an approach to tackle such systems with interface nonlinearities. In this paper, we proposed an extended free-interface component mode synthesis method. According to the proposed method, the substructures are separated at the nonlinear interfaces. Then the component mode synthesis procedure is carried out. By reasonably neglecting the contributions of higher order modes to the damping and inertia terms, it is demonstrated that the nonlinear interface forces and their time derivatives can be expressed as functions of themselves, as well as modal displacements and velocities. This characteristic facilitates the synthesis of the reduced order models for substructures in the state space. Also owing to this operation, the original properties of nonlinear interface forces can be preserved as much as possible, without any linearization. This method is suitable for non-proportionally damped structures with local nonlinearities such as mechanical structures with nonlinear spring and dashpot connections, rotor-bearing systems and so on. It also may be an alternative for the dynamic analysis of jointed structures with contact nonlinearities. Two numerical examples are presented to demonstrate the capability of the proposed method: (1) an eighteen degrees of freedom spring-dashpot-mass system with cubic spring and cubic dashpot interface connections is studied and (2) a more complex mechanical structure: a dual-rotor system with deep-groove ball bearing inter-shaft support. The numerical simulation results indicate that the dynamic responses of the reduced order model match very well with that of the full model, revealing the high accuracy of the proposed method with low computational costs.

Simplified methods to predict the robustness of steel parking-structure joints

An innovative simplified method for incorporating the behaviour of structural joints in structural analyses of steel parking-structure is proposed in this study. The method is based on the conventional mechanical modelling of joints through special springs that accommodate the arching effect and moment-axial force (M-N) interaction. The characterization of these springs in terms of stiffness and resistance is performed using analytical formulae. The accuracy of the proposed method is validated through comparisons to results from advanced numerical methods conducted on a multi-scale approach. Its implementation in sub-structure models is then demonstrated, with the main advantage of extremely reducing the modelling and computational time. Validated sub-structure models are finally employed to investigate the influence of the joint properties on the response of parking structures under vehicle collision scenarios. The results show that considering the rigid and semi-rigid joints in the research are characterised by the welded and bolted connections in the research, for a structure built in a courtyard, bolted connections (semi-rigid joints) are recommended, while for the same structure built near an urban road, welded connections (rigid joints) should be considered to enhance the overall robustness.

Hierarchical verification and validation in a forward model-driven structural health monitoring strategy

This paper presents a demonstrative application of a forward model-driven approach to structural health monitoring (SHM), incorporating hierarchical validation methods. A key tenet of the approach is that an SHM system can be constructed that is capable of diagnosing damage at the full system level, without full system damage-state data having been used in its development; achieving this would be highly impactful as the system-level damage state data is generally not feasible to acquire (previous SHM methods such as data-driven SHM have been hindered by their dependence on these data). This is achieved by carrying out validation activities on the damage model at the subassembly level of the structure. The particular focus of the present paper is on damage detection and assessment, although the approach offers a natural basis for extension to other damage identification activities such as damage location and prognosis. The present study focuses on two of the key elements of the model-driven approach: validation of the predictive substructure models and their application in the assembled model. The ideas discussed are demonstrated in a case study based on a laboratory-scale truss bridge structure.