Statistics and Probability Commons^™

Shear Strength Test Of Uhpc-Nc Bonding Surface, Zhang Shichang, Yan Donghuang, Liu Yun, Yuan Sheng, Wang Shuo

Journal of China & Foreign Highway

As a cement-based composite material with excellent mechanical properties,ultra-high performance concrete (UHPC ) demonstrates outstanding performance in tensile and compressive strength,durability,and impermeability.This material is suitable for the reinforcement and repair of normal concrete (NC) bridge structures.To study the shear behavior of the UHPC-NC bonding interface and its reinforcement effect,this paper conducted interface shear tests using Z-shaped specimens and designed a total of six sets of comparative specimens.The influence of parameters such as the planted bar ratio,implantation depth,and bonding surface size on the shear strength was explored.Through experiments,the load –slip curve and the shear strength data were obtained.The results show that:① …

Field Measurement And Analysis Of Wind Characteristics At Xuefenghu Bridge Site, Yu Wenhao, Yi Lu

Journal of China & Foreign Highway

Wind field parameters at bridge sites serve as an important basis for wind-resistant bridge design.The terrain surrounding the Xuefenghu Bridge is unique-mountains flank both sides in the bridge-aligned direction,and the bridge spans the wide surface of the Zhexi Reservoir.In order to investigate the wind field characteristics under such complex topographic conditions,an observation,acquisition,and wireless data transmission system was established at the bridge site.A one-year in-situ wind measurement campaign was conducted,and the characteristics of average wind and fluctuating wind were deeply analyzed.The results show that the average wind speed at the bridge site generally follows a Weibull distribution,and the average wind direction …

Experimental Study On Shear Resistance Of Existing Prestressed Concrete Hollow Slabs, Lu Youfu, Di Jin, Qin Fengjiang, Sun Yifei

Journal of China & Foreign Highway

Prestressed concrete hollow slabs are widely used in small- and medium-sized span highway bridges in China.With the increase in load ratings,many hollow slab bridges built in early periods fail to meet the current specifications for shear bearing capacity.Nevertheless,these hollow slabs continue to function adequately under existing vehicle loads,making it essential to conduct an in-depth investigation into their shear bearing capacity.Shear bearing capacity tests were conducted on five 16 m-span hollow slabs dismantled from a renovation and expansion project,including three top slabs with a 15 cm cast-in-place concrete structural layer.Various parameters,such as load-displacement curves,web concrete strain,cracking loads,crack development patterns,failure modes,and ultimate …

Analysis Of Flexural Bearin G Ca Pacity Of Concrete Box Girders Reinforced With, Cfrp Mesh End Anchorshu Guihua

Journal of China & Foreign Highway

Carb on fiber reinforced polymer (CFRP ) composite s have significant advantages in the reinforcement of concrete structures.It is worth systematically studying the effect and mechanism of applying this material in embedded end-anchored reinforcement of concrete box girders on improving the load-bearing capacity of the component.Based on the Abaqus finite element analysis (FEA ) platform,two numerical analysis models considering slip contact and full bonding contact between CFRP mesh and polymer mortar were established.A full-scale concrete box girder model test was conducted for validation.The results show that the FEA results are in good agreement with the experimental results.The FEA model that …

Wind Tunnel Test On Wind-Resistant Performance Of Suspended Monorail Cable-Stayed Bridge, Chen Yujiang

Journal of China & Foreign Highway

To investigate the wind-induced vibration of a suspended monorail bridge,a full-bridge aeroelastic model at a 1∶40 scale was designed and fabricated according to the geometrical parameters and dynamic characteristics of the real bridge.Wind tunnel tests on the bridge in both the completed state and the maximum cantilever state were conducted under different conditions,including uniform flow and turbulent flow,yaw angles of ± 45°,±30°,±15°,and 0°,and wind attack angles of ‒ 3°,0°,and + 3°.Both vertical and torsional displacements of the structure under different wind speeds were measured.The test results show that the vertical displacements and torsional responses of the cable-stayed bridge increase when …

Research On Autonomous Deviation Correction Of Tunnel Boring Machines And Parameters Based On Machine Learning, Zhang Jun, Li Maopeng

Journal of China & Foreign Highway

In order to solve the problem of realizing the autonomous deviation correction of tunnel boring machines (TBMs ), a TBM deviation correction control method that integrated the random forest (RF) algorithm with the genetic algorithm (GA) was proposed based on actual engineering data.The method combined a prediction model with an optimization model,using target deviation values as input to invert and output the required TBM deviation correction parameter values,thereby further improving the automation level of TBM deviation correction.By comparing it with the actual data,the feasibility of the model was verified.The results show that the RF algorithm-based prediction model achieves an R2 …

Study On Mechanical Effect Of Backfill Construction In Orthogonal Underpass Section Of An Open-Cut Interchange Tunnel, Li Qingda, Li Dexing, Yu Tingshun, Han Xi, Liu Jiansong

Journal of China & Foreign Highway

This study investigated the mechanical effects of backfill construction in the orthogonal underpass section of a full-section complex open-cut interchange tunnel.The research was based on the small-clear-distance interchange tunnel project at the extension section of Jinzhou Avenue and Xingguang Avenue in Chongqing.A combined approach of numerical simulation and on-site in-situ test measurement was adopted to analyze the influence of different backfill materials,tunnel cross-section types,and complex construction procedures on the mechanical behavior of the underpass tunnel.The mechanical effects of backfill construction in the orthogonal underpass section were determined.The following findings are revealed:During the backfill construction process,the displacement and internal force of …

Research On Automatic Review Method Of Highway Bim Based On Knowledge Graph, Wang Wuyu, Shao Kebo, Zhang Feng

Journal of China & Foreign Highway

Building information modeling (BIM ),characterized by multi-dimensional modeling and multi-source data integration,is becoming a key technology to promote the innovation and digital transformation of the highway design industry.Taking BIM as the design deliverable is an inevitable trend in the future development of highway engineering design.However,the current highway BIM review is mainly conducted manually,which brings about problems such as low efficiency,susceptibility to errors,and high subjectivity.This makes it difficult to adapt to the review requirements of the three-dimensional (3D) digital design mode.To this end,this study proposed an automatic review method of highway BIM based on a knowledge graph.By constructing the knowledge graph …

Research On Multi-Classification Prediction Of Traffic Accident Severity On Mountainous Expressways, Wang Hao, Yan Jie, Guo Jianmin, Zhang Yu, Sun Chengji

Journal of China & Foreign Highway

To enhance the safety level of mountainous expressways and establish an accurate and effective prediction model for traffic accident severity,this study analyzed 2 484 traffic accidents on mountainous expressways in Chongqing from 2010 to 2016.A total of 17 influencing factors were selected from four aspects:human,vehicle,road,and environment,to serve as explanatory variables.Partial proportional odds model,random forest algorithm,and XGBoost algorithm were used to construct multi-class prediction models for traffic accident severity.The model performance was evaluated using the confusion matrix,accuracy,and minority class recall rate.The results show that the XGBoost model achieves the highest prediction accuracy in multi-class prediction of traffic accident severity on mountainous …

Application And Analysis Of Energy-Conservation And Carbon-Reduction Technologies In Green Highways, Huang Xuewen, Wang Kai, Huang Shanqian, Xiong Xinzhu, Fu Jinsheng

Journal of China & Foreign Highway

To improve the low-carbon development level of highway engineering,this study relied on a typical green highway in Anhui Province and established a calculation model for energy-conservation and carbon-reduction in highway engineering based on the emission factor method.A combination of quantitative and qualitative approaches was adopted to evaluate the benefits of 33 energy-conservation and carbon-reduction technologies in reducing life cycle energy consumption and carbon emissions,based on life cycle assessment (LCA ) theory.The results show that during the material production stage,through channel resource coordination and the application of low-carbon,energy-saving materials,comprehensive reductions in the embodied carbon can be achieved.During the construction stage,energy consumption …

Reference And Inspi Ration From Low-Carbon Development Experience Of Foreign Highway Infrastructure, Lu Chunying, Gao Shuohan, Du Xueyua N, Jian Li, Wang Xinjun, Kong Yaping

Journal of China & Foreign Highway

In order to provide supp ort for the scie ntific formulation of low-carbon highway infrastructure development policies in China,empirical analysis,comparative analysis,and other methods were utilized,and the construction goals and action strategies of low-carbon highway infrastructure in the United Kingdom,the United States,and Australia were sorted out.Advanced experience in the development of low-carbon highways abroad was summarized.On this basis,combined with the current situation and existing problems of low-carbon development of China ’s highway infrastructure,the following countermeasures and suggestions were proposed:① strengthening top-level design and formulating low-carbon development goals and paths;② implementing the concept of life cycle and strengthening the research and promotion …

Analysis And Control Of Impact Of Wide Waterway Excavation On Adjacent Bridge Pile Foundations, Zhang Peisheng, Qiao Lyu, Sheng Jianchao, Sheng Haoxiang, Liu Hanchen, Wang Zhe

Journal of China & Foreign Highway

When excavating a waterway beneath an existing bridge,the pile foundations are subjected to unloading from excavation and the loading from the superstructure,which may lead to excessive displacement and potential safety hazards.Based on the underpass project of the Desheng Expressway Bridge along the Zhejiang section of the Beijing ‒ Hangzhou Canal,this study established a three-dimensional finite element model (FEM ) and combined it with field monitoring to investigate the impact of wide waterway excavation on adjacent bridge pile foundations and corresponding control measures.A novel combined control method involving a retaining wall with supporting piles and fully enclosed isolation piles was proposed.The …

Influence Of Horizontal Curve Radius On Vehicle Fuel Consumption And Pollutant Emissions On Tw O-Lane Highways, Tu Shengwen, Lei Meimei, Guo Wenyu

Journal of China & Foreign Highway

To investigate the influence of horizontal curve radius on vehicle fuel consumption and pollutant emissions on two-lane highways,this study developed a model based on running speed theory,vehicle driving dynamics,and a fuel consumption and emission analysis system.Fuel consumption and emissions of CO2,CO,HC,and NOx were calculated for a passenger car traveling along horizontal curves under three design speeds:40 km/h,60 km/h,and 80 km/h.The results show that the horizontal curve radius has a significant effect on vehicle fuel consumption and pollutant emissions.The trends of fuel consumption,CO2,and NOx emissions vary consistently with curve radius,while CO and HC emissions follow a similar but different trend.At the …

Advancing Real-World Implementation Of The Well Optimized Linear Finder (Wolf) High-Speed Atmospheric Turbulence Compensation Method, Timothy Evan Coon

Theses and Dissertations

This dissertation advances the real-world implementation of the Well Optimized Linear Finder (WOLF) method for high-speed Atmospheric Turbulence Compensation (ATC). Atmospheric turbulence introduces phase aberrations into optical wavefronts and degrades image quality in terrestrial imaging systems. Traditional phase diversity methods are computationally intensive and poorly suited to real-time operation. The WOLF method addresses these limitations through a novel, point-wise formulation of the optical transfer function (OTF) as a structured autocorrelation of the generalized pupil function (GPF). This formulation enables the estimation of phase aberrations at individual spatial coordinates with distributed computational complexity.

The research begins by developing a MATLAB-based simulation …

Predicting Sleep And Sleep Stage In Children Using Actigraphy And Heartrate Via A Long Short-Term Memory Deep Learning Algorithm: A Performance Evaluation, Robert Weaver Med, Phd, James White, Olivia Finnegan, Hongpeng Yang, Zifei Zhong, Keagan Kiely, Catherine Jones, Yan Tong, Srihari Nelakuditi, Rahul Ghosal, David E. Brown, Russell R. Pate Ph.D., Gregory J. Welk, Massimiliano De Zambotti, Yuan Wang, Sarah Burkart, Elizabeth L. Adams Phd, Bridget Armstrong, Michael Beets Med, Mph, Phd

Faculty Publications

Children's ambulatory sleep is commonly measured via actigraphy. However, traditional actigraphy measured sleep (e.g., Sadeh algorithm) struggles to predict wake (i.e., specificity, values typically < 70) and cannot predict sleep stages. Long short-term memory (LSTM) is a machine learning algorithm that may address these deficiencies. This study evaluated the agreement of LSTM sleep estimates from actigraphy and heartrate (HR) data with polysomnography (PSG). Children (N = 238, 5–12 years,52.8% male, 50% Black 31.9% White) participated in an overnight laboratory polysomnography. Participants were referred be-cause of suspected sleep disruptions. Children wore an ActiGraph GT9X accelerometer and two of three consumer wearables(i.e., Apple Watch Series 7, Fitbit Sense, Garmin Vivoactive 4) on their non-dominant wrist during the polysomnogram. LSTM estimated sleep versus wake and sleep stage (wake, not-REM, REM) using raw actigraphy and HR data for each 30-s epoch. Logistic regression and random forest were also estimated as a benchmark for performance with which to compare the LSTM results. A 10-fold cross-validation technique was employed, and confusion matrices were constructed. Sensitivity and specificity were calculated to assess the agreement between research-grade and consumer wearables with the criterion polysomnography. For sleep versus wake classification, LSTM outperformed logistic regression and random forest with accuracy ranging from 94.1to 95.1, sensitivity ranging from 94.9 to 95.9 across different devices, and specificity ranging from 84.5 to 89.6. The addition of HR improved the prediction of sleep stages but not binary sleep versus wake. LSTM is promising for predicting sleep and sleep staging from actigraphy data, and HR may improve sleep stage prediction.

Unified Hybrid Censoring Samples From Power Pratibha Distribution And Its Applications, Mahmoud Mansour, Hebatalla H. Mohammad Dr, Khalaf S. Sultan Prof.

Basic Science Engineering

This paper suggests an extensive inferential method for the Power Pratibha Distribution (PPD) under Unified Hybrid Censoring Schemes (UHCSs), since there is a growing interest in flexible models in both reliability and service operations. This work studies the PPD model using standard Maximum Likelihood Estimation methods and modern Bayesian approaches too. Using a complex architecture, UHCS simulates tests more closely to what is done in practice than by using more basic censoring schemes. Using analysis, the probability and statistical ranges are carefully calculated for the parameters. Tests demonstrate that Bayesian estimation gives better results than many other methods for estimation, …

Dice Math And Probability, Warren Campbell

SEAS Faculty Publications

The manufacture of dice for tabletop games is a billion-dollar industry. In gaming circles and online forums, the concept of “cursed dice” is a popular topic. Dice are inherently unfair due to the difficulty of manufacturing them with perfect geometric tolerances and uniform material densities. A common method for testing dice fairness is the chi-square statistic, which is typically assumed to follow the chi-square distribution. However, this assumption is only asymptotically valid.

Exact distributions of the statistic can be computed for dice with few sides and a limited number of rolls—such as 2-sided (D2) and 4-sided (D4) dice—but the computational …

Syntax-Enhanced Boundary-Aware Named Entity Recognition Model, Chuanming Yu, Bin Deng, Zhengang Zhang

Journal of Scientific Information Research

[Purpose/significance] This study addresses the issue of inadequate perception of entity boundaries in traditional character-level modeling-based named entity recognition models by integrating syntax information containing entity boundary features into the task using a multi-head graph attention network with dense connections. This integration enhances the effectiveness of named entity recognition.

[Method/process] This study proposes a Syntax-enhanced Boundary-aware Named Entity Recognition Model (SynBNER), which utilizes BERT for text semantic representation and integrates syntax information using a dense-connected graph attention network. This integration incorporates implicit entity boundary information from syntax information into word representations, thereby enhancing the model's entity boundary perception capability.

[Result/conclusion] …

Study On Reasonable Parameters Of Natural Smoke Exhaust Shafts In Tunnels With Different Longitudinal Slopes, Yang Tao, Zeng Yuekai, Li Peijun, Ren Rui, Deng Min, Zhang Aoyu

Journal of China & Foreign Highway

To obtain the reasonable parameters of a smoke exhaust shaft in a tunnel under different longitudinal slope conditions,the temperature,flow velocity,and smoke exhaust efficiency of the tunnel were taken as indexes,and the numerical model was established by using fire dynamics simulator (FDS ) software to study the influence of the longitudinal slope of the tunnel,shaft width,and shaft length on the ventilation and smoke exhaust in case of a fire.The results show that under the longitudinal slope conditions,with the increase in the shaft width and length,the maximum temperature in the tunnel decreases,and the smoke exhaust efficiency of the shaft increases.However,the influence of …

Study On Salt Release Mechanism Of Self-Melting Ice Asphalt Mixture And Its Impact On Road Performance, Li Tao, Zhang Xiu ’Ang

Journal of China & Foreign Highway

To study the long-term salt release characteri stics of self-melting ice asphalt mixture and the impact of the complete salt release on pavement durability,an accelerated salt release method was developed using a Los Angeles abrasion tester.The salt release mechanism under varying asphalt types,deicing agent contents,and gradation types was revealed.The impact of the complete salt release on road performance was analyzed.Results show that the Los Angeles abrasion tester-based salt release method achieves 91 times and 114 times higher salt release efficiency than the magnetic stirrer and natural immersion methods,respectively.SBS-modified asphalt mixture exhibits a longer salt release duration.The salt release duration is …

Research On Size Effect On Cubic Compressive Strength Of Ground Granulated Blast Furnace Slag-Fly Ash Stabilized Large-Size Macadam, Liu Qunyan, Liu Liping, He Miao, Yuan Lingqing, Zhang Liang

Journal of China & Foreign Highway

To analyze the effect of specimen size on the compressive strength of ground granulated blast furnace slag-fly ash (GGBFS-FA ) stabilized large-size macadam,the 200 mm × 200 mm × 200 mm cubic specimen and 3 d compressive strength were designated as a reference specimen and strength in this study,and numerical simulations of compressive strength were performed by using a discrete element method for GGBFS-FA stabilized large-size macadam specimens with a maximum particle size (dmax) of 73 mm and five side lengths of 2.0dmax,2.5dmax,3.0dmax,3.5dmax,and 4.0dmax.The size effect mechanism on the mixture ’s compressive strength was revealed from the perspective of energy.By …

Effect Of Mineral Admixtures On Properties Of Shotcrete, Ma Kaikai, Zhao Feng, Sun Rongxiao, Han Song, Hu Peng, Wang Kun

Journal of China & Foreign Highway

To study the influence of different mineral admixtures on the properties of shotcrete,the effects of four kinds of mineral admixtures including fly ash,silica fume,metakaolin,and carbon black on the rebound rate,one-shot thickness,and compressive strength of shotcrete were analyzed through tests on concrete rebound rate,one-shot thickness,and compressive strength.The results show that:① as the content of carbon black,silica fume,and metakaolin increases from 5% to 10%,the rebound rate of shotcrete decreases by 25.76%,16.46%,and 16.70%,respectively;② carbon black and silica fume have a good effect on increasing the one-shot thickness of concrete.When the content of carbon black and silica fume is 10%,the one-shot thickness exceeds 35 …

Study On Rheological Properties Of Basalt Fiber Asphalt Mastic Modified With Silane Coupling Agent, Liu Yuande, Zheng Nanxiang, Zhang Xiang, Gao Haiwei, Zhang Bowen

Journal of China & Foreign Highway

To investigate the rheological properties of basalt fiber asphalt mastic,a silane coupling agent was used as a modifier for basalt fibers,and the effects of varying fiber contents were analyzed. Cone penetration tests,bending beam rheological tests,and dynamic shear rheometer tests were conducted to evaluate the rheological properties of asphalt mastic consistency, high-temperature stability,and low-temperature cracking resistance under different temperatures and fiber contents.The findings show that the silane-coupled basalt fibers enhance the shear strength and consistency of asphalt mastic.After modification,the phase angle decreases;elastic response increases,and complex modulus improves.Adsorption capacity between fibers and asphalt increases significantly,enhancing high-temperature deformation resistance and low-temperature cracking resistance …

Analysis Of Mechanical Properti Es Of Integral Jacking Basket Arch Bridge During C Onstruction, Chen Tao, Qiu Jingkui, Wang Ji

Journal of China & Foreign Highway

Taking the Xindian Bridge in Ni ngbo as the background,this paper analyzed the mechanical properties of the integral jacking basket arch bridge during construction.Midas finite element software was used to establish the spatial model of the main bridge,and the deviation of the suspender force and support reaction force of the completed bridge from the design was 1.84% and 1.8%,respectively.The maximum deviation of the displacement calculation of the tie beam at the bridge completion stage was 22 mm,and the maximum deviation of the displacement of the arch rib at the same stage was ‒ 12 mm,which showed that the finite element …

Internal Force Optimization In Com Pleted Stage And Construction Alignment Control Of Super Long-Span Extradosed Cable-Stayed Bridge, Ba Wenpeng

Journal of China & Foreign Highway

This paper is based on a super long-span extradosed cable-stayed bridge with a main span of 400 m.In view of the technical challenges of high negative bending moment at the quarter point of the bridge and large deformation during the cantilever assembly process in the non-cable area,a systematic solution was proposed in combination with the entire construction process.This paper proposed three schemes:permanent cable over-tensioning,temporary cable setting,and large segment closure.The bending moment ratio (λM) and structural deformation were used as quantitative indicators,and a finite element model was established to compare the three schemes.The results show that all three schemes can improve …

Comparative Study On Differences In Asphalt Pavement Design Between China And Southern Africa, Wang Qing, Lin Yangyang, Yan Hongxiang, Zhao Bin, Xia Moxuan, Li Ning, Si Wei

Journal of China & Foreign Highway

To facilitate the successful implementation of projects in the Southern Africa region and promote the application and internationalization of China ’s standards,this study compared the asphalt pavement design systems,construction materials,design parameters,and structural design methods of both regions based on the main asphalt pavement design specifications currently in use in China and Southern Africa.The results show that among Southern African countries,South Africa has a comprehensive and widely applied standard system,while other Southern African countries adopt more varied and less theoretical standards.In contrast,China ’s standard system is complete and highly practical.Due to differences in regional climates,the selection principles and mechanical requirements for …

Discontinuous Deforma Tion Analysis Of Progressive Toppling Of Rock Slopes With Fractured Slab Structure, Yuan Sifan, Li Tonglu, Haider Mumtaz, Zhang Changliang, Li Ping

Journal of China & Foreign Highway

Progressive toppling of rock sl opes with fractured slab structures is quite common in the slopes of hydropower and highway engineering,posing a potential safety risk during both construction and operational phases.The field investigation found that progressive toppling mostly occurs on slopes with concentrated tectonic stress,intense river incision,and high steepness.Typically,these slopes are composed of hard,thinly-layered,and overthrusted rock mass with a fractured slab structure.From a macroscopic point of view,progressive toppling failure is neither a collapse nor a slide but a form of discontinuous deformation.The traditional limit equilibrium method for slope stability analysis is not suitable for evaluating such slopes.In this paper,by taking …

Prediction For Humidity Adjustment Factor And Dry-Wet Cycle Reduction Factor Of Resilient Modulus Of Subgrade Soil Based On Ann, Wang Xufeng, Fu Wei, Peng Junhui, Hu Jiankun, Zhang Junhui, Li Zhiguang

Journal of China & Foreign Highway

Existing methods for determining the humidity adjustment factor and dry-wet cycle reduction factor of the resilient modulus of subgrade soil are mostly based on laboratory tests that consume a large amount of manpower and time,and the prediction accuracy is limited due to the constraints of specification value ranges.In order to achieve fast and accurate prediction of these two factors,the effects of stress state,moisture content,and the number of dry-wet cycles on the resilient modulus of subgrade soil were investigated through laboratory dynamic triaxial tests.Based on existing literature,physical parameters,state parameters,and stress parameters of subgrade soil were selected,and an artificial neural network prediction …

Semi-Flexible Pavement Structure Analysis Based On Double Modulus Theory, Pan Qinxue, Zhou Shurui, Hu Jia, Zhang Long, Song Xiaojin, Liu Hongfu

Journal of China & Foreign Highway

Semi-flexible pavement materials have significant differences in tension and compression.If the mechanical response analysis of pavement structures is conducted by using the traditional linear elastic theory with a single modulus,there will be a considerable deviation from actual situations.To analyze and optimize semi-flexible pavement structures,this paper compared the changes in key mechanical responses of pavement structures under six different semi-flexible layer positions and thickness combinations based on the double modulus theory.The results show that there is a significant difference in the calculation results of key mechanical responses of the pavement based on the double modulus theory and the single modulus theory,with …

Structural System Reliability Analysis Method For Cable-Supported Bridges Based On Deep Belief Networks, Chen Zhenyu, Xie Bo, Lu Naiwei

Journal of China & Foreign Highway

Aiming at the high-precision reconstruction of structural function functions caused by the strong nonlinearity of cable load-bearing bridge structures,this study presented a structural system reliability analysis method based on a deep belief network (DBN ).A long-span suspension bridge was used as the engineering background to identify the dominant fault path of the structural system and analyze the law of structural fault path transfer caused by the deterioration of the suspender strength.Numerical analysis results show that DBN can capture the nonlinear mechanical behavior of the finite element model of the suspension bridge,thereby making the implicit statically indeterminate functional function explicit and …