Finite Element Numerical Model Research Articles

Tidal Current Modeling Using Shallow Water Equations Based on the Finite Element Method: Case Studies in the Qiongzhou Strait and around Naozhou Island

Abstract: Tidal currents are a crucial oceanic process with significant implications for marine engineering and the sustainable use of coastal and marine resources. This paper presents the development of a finite element numerical model to simulate tidal currents. The model was mathematically formulated using the shallow water equations, which are applicable to fluid dynamics where the horizontal scale is significantly larger than the vertical scale. The finite element method was employed to discretize and solve the equations, with the bottom slope source term incorporated into the pressure equation to ensure numerical consistency. Furthermore, characteristic line theory was applied to derive the relationship between boundary tidal levels and current velocities to satisfy boundary compatibility conditions. The model was initially applied to the Qiongzhou Strait, and the results demonstrated good agreement with observed data. Subsequently, the model was implemented at Naozhou Island and its adjacent waters. The results revealed that the tidal currents around Naozhou Island exhibit oscillatory flow patterns, with the flow direction near Donghai Island oriented northeast–southwest (NE-SW) and the flow direction near Leizhou Bay oriented northwest–southeast (NW-SE). This study provides a hydrodynamic basis for marine engineering projects and the sustainable utilization of marine resources in the Naozhou Island area.

Thermal performance of a solar-assisted slinky foundation heat exchanger coupled with a heat pump in a cold climate

Using the excavation of a building’s foundation offers a cost-effective solution to alleviate the high installation costs hindering the widespread adoption of ground-source heat pump systems. However, limited land space in urban areas and higher heating loads in cold climates pose challenges. Issues like ground thermal imbalances and prolonged freezing around the heat exchanger can impair performance. To address these, a novel solar-assisted ground source heat pump with a slinky foundation ground heat exchanger and a solar-heated recovery heat exchanger loop embedded in the building’s foundation is proposed. A 3D transient finite element numerical model is developed to evaluate the performance of the proposed system. Realistic building energy loads obtained from a building energy simulation with time-varying ambient temperature and solar irradiation are coupled to the foundation heat exchanger to predict the long-term transient performance of the system. Results show that implementing a solar-assisted foundation heat exchanger system reduces soil freezing from 58.3 % to 32.4 % of the year, and heat pump shut-off occurrences caused by low entering fluid temperature drop from 38.9 % to 5.8 %. Additionally, incorporating an auxiliary heater eliminates heat pump shut-offs and reduces the soil freezing period to 6.3 %. Moreover, extending the heat exchangers beyond the footprint of the house mitigates the soil freezing problem completely and reduces the demand for auxiliary heating.

Reliability study on crack propagation life of aluminum alloy repair structure

In this paper, the life reliability analysis of AL-AL repair structure is studied. Firstly, the fatigue life of the repair structure is predicted by finite element numerical modeling combined with Forman’s empirical formula, and the influence law of the variation of the repair structure parameters on the fatigue life is investigated. Secondly, the uncertain factors affecting the fatigue life of the structure are considered, the objective function of the structure is linearly fitted, and the fatigue reliability model of the repair structure is established, and the reliability of the structure is obtained by calculating the probability of predicting the fatigue life to be greater than the allowable life. Finally, the parameters of the repair plate that affect the life reliability are analyzed and studied. The results show that under the same fatigue life, the order of parameters affecting the reliability of the repair structure is: repair plate position x > repair plate width w > repair plate length l.

In-plane mechanical properties of a novel hybrid tetra-chiral honeycomb

This study introduces a novel hybrid tetra-chiral honeycomb (NHTCH) structure achieved by combining a tetra-chiral honeycomb and its inverse configuration. The honeycomb prototype was created through 3D printing, and a quasi-static compression experiment was conducted in the opposite direction. Utilizing Abaqus/Explicit, we developed a finite element numerical model and verified its accuracy. The mechanical properties of the proposed structure, denoted as NHTCH, were compared with those of traditional tetra-chiral honeycombs (TCH). Results indicated that NHTCH exhibits superior mechanical properties compared to TCH, and its plastic deformation displays a noticeable negative Poisson’s ratio effect. Furthermore, we analyzed the in-plane mechanical response of NHTCH under varying impact velocities and conducted parametric studies on the angle between chiral elements and the radius of the node circle. Our findings reveal that, under high-speed impacts, NHTCH demonstrates higher energy-absorbing and load-carrying capacities compared to the other two configurations. Simultaneously, optimizing the clamping angle and nodal circle radius of NHTCH efficiently enhances the mechanical properties within a specific range, without causing significant changes to the plastic deformation of the structure.

Model updating method for offshore jacket platforms using improved DNN and OOA considering non-uniform corrosion and structural responses

During the service life of offshore jacket platforms, the harsh marine environment leads to severe structural corrosion and damage, necessitating structural health monitoring. Ensuring the accuracy of numerical finite element models (FEM) requires critical model updating. This study introduces an improved DNN-OOA model updating method by incorporating actual structural responses into the optimization objective function and considering non-uniform corrosion of the structure. We utilized Pyansys to automatically generate large-scale datasets, simplifying the simulation process. An accurate and responsive surrogate model is generated using the improved deep neural network (DNN), and the optimal solution for the parameters to be corrected is sought through the Osprey optimization algorithm (OOA), completing the FEM updating. The main innovation of this study lies in incorporating non-uniform corrosion caused by the real marine physical environment into the model updating process. This phenomenon is employed to determine the updating range for different structural members. Furthermore, the parameters subject to updating include structural damage to the members and changes in the upper mass. Incorporating the structural response under static loading into the optimization objective function allows for a more comprehensive reflection of the structure’s dynamic and static behavior, addressing the regression confusion problem in the optimization process of purely modal frequency updating. Experimental results demonstrate that the proposed improved DNN-OOA model updating method effectively eliminates inaccuracies in simulated structural responses and mitigates the local optimum problem inherent in pure modal frequency updating. In the updated scaled jacket platform FEM, the maximum relative error of the modal frequencies is reduced to 2.624%, and the maximum error in structural response is reduced to 3.510%. This approach provides a more accurate and reliable FEM for the maintenance and safety assessment of offshore jacket platforms.

A study on the effect of crack orientations, crack types and SHPB characteristics on the failure behaviour of pre-cracked sandstone rock specimens

The present study aims to understand the experimental and numerical behavior of intact and pre-cracked fine-grained sandstone specimens under indirect dynamic tensile loading conditions. The dynamic experimental analyses are carried out using the split Hopkinson pressure bar (SHPB) device to determine the tensile strength of sandstone rock. In addition to the dynamic tests, the physical, petrological, and mechanical tests under static loading of the sandstone rock are also studied. Thereafter, a three-dimensional (3D) finite element (FE) numerical model is developed, and a strain rate-dependent modified Drucker Prager constitutive model is used to validate the numerical model with the indirect dynamic tensile experimental test results. The validated parameters are then used to determine the behavior of pre-cracked sandstone specimens through numerical simulations. Two sets of numerical models with diametral cracks and cross-sectional cracks are introduced into the intact rock specimens. The orientation of the crack is changed from 0° to 90° and the numerical analyses are performed for 0°, 30°, 45°, 60°, 75° and 90° crack orientations with respect to the loading axis of the bars in the SHPB setup. Along with crack orientations, the loading rate is changed with varying gas gun pressures for the two sets of numerical models. The stress-strain responses are retrieved from the center and tip of the pre-crack introduced in the sandstone specimen. A comparative analysis is conducted for the responses obtained at the center and tip of the diametral and cross-sectional cracks and the results are stated herein.

Modeling and Analysis of the Electrical Signal Transmission Mechanism of an Electronic Analgesic Apparatus

Objective: This study analyzes the transmission of the current signal of an electronic analgesic apparatus in arm muscles and provides a theoretical foundation for electrical stimulation analgesia. Methods: By combining human anatomy and tissue structure, a numerical simulation-based finite element model of the electronic analgesic apparatus is established using a frustum, cylinder, and ellipsoid as geometric entities in COMSOL Multiphysics 5.5. In the frequency domain environment, the transmission mechanism of the signal in the arm is analyzed by inputting current signals of 100 kHz, 1 MHz, and 10 MHz with an amplitude of ±20 mA. Results: With a continuous increase in carrier frequency, the effect of skin tissue becomes increasingly clear, and the signal becomes increasingly concentrated in the part of the skin that contacts the electrode. Moreover, diffusion inside the volume conductor loses consistency. At 100 kHz, as the communication distance from the electrode center gradually increases, the signal spreads more evenly within the arm. Conclusions: In the process of implementing a muscle soreness treatment using the electronic analgesic apparatus, a higher communication frequency makes it more difficult for the signal to enter the interior of the body and degrade the consistency of the signal. Therefore, the signal electrode should be placed as close as possible to the analgesic target area during the implementation of electric current analgesia.

Cause Analysis of Rail Corrugation in Metro Lines Based on System Vibration Characteristics

The mechanism of rail corrugation remains unclear, and the research methods require improvement. The vibration characteristics represent the system’s external manifestations, but a comprehensive analysis is still lacking. Taking the vibration characteristics of the wheel-rail system as a starting point, this study investigates the formation mechanisms of rail corrugation on measured metro lines. The line sections included both steel spring floating slab tracks and long sleeper embedded tracks. First, the wavelength and frequency attributes of rail corrugation were obtained through field measurements. Then, referencing line conditions, three-dimensional finite element numerical models were established, frequency response calculations were performed, and the relationship between the vibration responses of the wheel-rail system and rail corrugation was analyzed. Finally, a parameter sensitivity analysis of the wheel-rail system was conducted to control the further development of rail corrugation. The results show distinct corrugation phenomena on both inner and outer rails in the measured sections. The characteristic wavelengths of inner and outer rail corrugation on the steel spring floating slab track are 34 mm and 59 mm, respectively, and the characteristic wavelengths of inner and outer rail corrugation on the long sleeper embedded track are 46 mm and 47 mm, respectively. The frequency response analysis indicates that the numerical results exhibit eigenfrequencies close to the passing frequencies of the measured corrugations. The formation mechanism of inner rail corrugation on the steel spring floating slab track is attributed to the third-order bending vibration of the wheelset, which leads to the generation of inner rail corrugation. In contrast, the formation mechanism of outer rail corrugation is attributed to the lateral bending vibration of the outer rail. For the long sleeper embedded track, inner rail corrugation is generated by the lateral bending vibration of the inner rail, while outer rail corrugation results from the lateral bending vibration of the outer rail. Appropriate adjustments to the fastener’s vertical and lateral stiffness, as well as the steel spring’s vertical and lateral stiffness, can shift the rail corrugation eigenfrequencies, thereby inhibiting the development of corrugation with the original wavelength. Changes in other parameters have no effect on the rail corrugation eigenfrequencies and only influence the development speed of corrugation with the original wavelength. This research effectively elucidates the cause of rail corrugation from the system vibration perspective and provides a valuable complement to the corrugation analysis method.

Finite Element Simulation and Experimental Analysis of the Thermo-Mechanical Properties of Dissimilar S275 and 316L Austenite Stainless Steels using the RFW Process

This research examines the effect of thermomechanical and microstructural constituents on welding of AISI 316L (austenite stainless steel) and S275 steel. A Finite Element Model (FEM) was constructed using ANSYS 19.1, and an experimental study was conducted using the Rotary Friction Welding (RFW) process. It was determined that there is a genuine correlation between the simulation FEM and the experimental procedure with regard to the thermal profile and ultimate yield strength, particularly when a welding speed of 2,000 rev/min is employed. At that speed, the higher temperature recorded and calculated was 1,450 oC. The discrepancy between the numerical FEM and the experimental temperature profile for the peak temperature calculation was determined to be 2.78%. The mechanical analysis was conducted through tensile force calculations and experiments, the results of which indicated an estimated error of 12%. The calculated error for the ultimate yield strength of the various samples is less than 6% for tensile strength. Upon tensile testing, failure occurred in the S275 sample. The microstructure exhibited increases in Cr and Ni of 1.2% and 1.01%, respectively, in comparison to the base metal of 316L stainless steel.

Seismic Performance Assessment of an Unreinforced Masonry Historical Building Using Nonlinear Static Methods

Historical heritages embody the identity and evolution of a people, making their preservation paramount. Buildings from the 17th and 18th centuries constitute a significant portion of this heritage, and evaluating their behavior under potentially damaging actions is crucial for mitigating and preventing irreparable losses. Despite Brazil's location in a tectonically stable region, seismic events with the potential for considerable damage have occurred and could impact these historical structures. Among the methods for assessing the seismic vulnerability of buildings, nonlinear static methods stand out, aiming to quantify the effect of earthquakes on a structure using an incremental lateral force analysis considering nonlinearity, known as pushover analysis. This study aims to evaluate the seismic performance of an 18th-century masonry historical building using a nonlinear static method, notably the oldest one in the urban complex of the central-south region of the state of Ceará. To this end, a finite element numerical model of the main façade was developed to represent the historical building. The seismic performance of the building was then evaluated, and the expected damage to the historical building under seismic loading was quantified.

Study on predicting plate deformation under double charges coupled loading based on GBR-RFR stacking model

Abstract In modern information warfare, quickly and accurately destroying enemy key targets is crucial. The single damage mode of traditional ammunition no longer meets the demands of complex combat environments. Therefore, it is necessary to explore the damage modes and plastic deformation of targets under double charges coupling to achieve precision strikes. This paper studies the predictive model of plate deformation under double charges coupling. A double charges synchronous explosion was used as the means of coupling shock wave loading, and double charges experiments on the damage to Q235 metal plates were conducted. Based on the experimental results, a three-dimensional finite element numerical simulation model was established and its accuracy was verified. Further simulation conditions were added, and data on the plastic deformation at the center of the metal plate under double charges synchronous loading were calculated. A predictive model for the plastic deformation at the center of the metal plate was constructed based on the GBR-RFR stacking model, thereby obtaining a predictive model for the plastic deformation at the center of the metal plate under double charges synchronous loading. Through dual-source synchronous explosion experiments and finite element numerical simulations, plastic deformation data at the center of Q235 metal plates under different loading conditions were obtained. Validation results show that the finite element simulation model can accurately predict the deformation of the plate. On this basis, the predictive model constructed based on the GBR-RFR stacking model demonstrates high prediction accuracy, providing an effective method for predicting the deformation of metal plates under double charges synchronous loading.

FEM Parameters for Earthquake Analysis of Retaining Walls

Abstract The paper presents the main characteristics and features of numerical finite element (FE) models for the study of the seismic response of soil-retaining wall. Since walls are linear structures, 2D plane strain models are suitable for conducting of the analysis. The models need to include a finitely sized soil domain, whose boundary conditions are defined according to the way earthquake loading is defined, respectively as pseudo-static impact or dynamic impact as a function of time. The FE mesh must meet the criteria of sufficient density in order to ensure the necessary accuracy of the solution. With the use of multi-nodal finite elements the displacements function in the model is improved. Retaining walls as well as other structural elements and devices are modelled with 2D plate and 1D linear elements defined in terms of a full or limited set of stresses. To simulate the behaviour in the contact of the structural elements and soil, interface elements are introduced modelling the gapping and slipping in the contact. The material parameters are determined depending on the selected constitutive models. In dynamic earthquake analyses, parameters shall be introduced to take into account the reduction of the soil stiffness. Dynamic loading is usually introduced with an accelerogram whose selection is made on the basis of an analysis of the parameters of strong motion records.

Проекционный метод определения аномальных датчиков в задачах виброакустики

A common problem in measurements using a set of vibration sensors in vibroacoustics is the lack of an accurate signal model on the receivers. Such uncertainty can lead to processing algorithms errors and an incorrect solution to the inverse problem. Due to a malfunction, vibration sensors data can also be bad, deteriorating the quality of measurements. In practice, the search for such anomalous sensors is a non-trivial task. In this paper, an original method related to projection algorithms is proposed for this problem. It is shown that the proposed method allows detecting anomalous sensors of various types. The method main feature is using both numerical finite element model of the object and experimental data. The efficiency of the proposed method is demonstrated in the localizing vibration sources problem. The new method can be used in other applications where the inverse problem is solved using a numerical or analytical model.

Effective thermal conductivity of composites using homogenization

Composite materials are extensively used in engineering applications due to their customizable properties and high performance. Determining the equivalent homogenized properties of composites, such as thermal conductivity, is crucial for their effective use. Various theoretical, analytical, and experimental methods have been developed to assess these properties. This study investigates the effective thermal conductivity of composites using a deterministically based procedure for thermal analysis. This procedure accounts for the combined influences of the inclusions’ volume fractions, shapes, orientations, and locations within the matrix to determine the effective thermal conductivity of composites. The specific composite analyzed consists of a cubical PLA matrix with a single spherical or elliptical void inclusion with perfect interfaces. For that purpose, an analytical approach was developed, and MATLAB® code was created to calculate the effective thermal conductivity tensor. To benchmark the analytical results, comparisons were made against numerical finite element modeling (FEM) results conducted using ANSYS®; in addition, to previously reported analytical models from the literature. Corroboration was also obtained by comparing the results against experimental data from the literature. The accuracy of the proposed homogenization scheme was demonstrated by achieving a low mean absolute percentage error (MAPE) compared to FEM (2.88%) and to the experimental results (2.72% for void inclusion and 6.99% for filled inclusion). Additionally, a high R-squared (R2) value of 0.986 was achieved compared to FEM, and values of 0.97 and 0.998 were achieved compared to the experimental results for void and filled inclusions, respectively.

Machine Learning–Finite Element Mesh Optimization-Based Modeling and Prediction of Excavation-Induced Shield Tunnel Ground Settlement

Ground settlement prediction for shield construction is highly important and challenging. This study introduces a machine learning algorithm combined with finite element numerical simulation, i.e., machine learning–finite element mesh optimization. For surface subsidence prediction, 16 combination models of ANN, KNN, RF and SVR were optimized by PSO, GA, BT and BO, involving raw data preprocessing, principal component analysis, hyperparameter selection and prediction accuracy evaluation. A subway shield tunneling project was analyzed, in which the meshes of finite element numerical models were discretized into different sizes from 1.0[Formula: see text]m to 2.0[Formula: see text]m. In total, 360 sets of data points were extracted from the simulation results, including stress, strain, shield jacking force, internal friction angle, cohesion force, and settlement, of which 252 data points were used as the input parameters of machine learning model. Analysis of average error rate of finite element–machine learning coupling models showed that the finite element model had the highest accuracy of settlement prediction when the mesh size of the finite element model was 1.4[Formula: see text]m, and the GA-SVR model had the highest accuracy and generalization ability in ground settlement prediction. This study highlights the uniqueness of machine learning–finite element mesh optimization model in application.

UHPC girder multi-modal deformation measurements: Photogrammetry, physical sensing, and FEA

Ultra-high performance concrete (UHPC) has become increasingly popular in flexural design of structural members that require high performance. Although numerous experimental studies on passively reinforced UHPC flexural members exist, studies on monolithic members with larger cross sections are limited, and no information exists on full-field deformation measurements of such specimens. An experimental program consisting of 8 large-scale UHPC doubly-reinforced specimens with continuous longitudinal rebars was conducted under 4-point monotonic loading. The experimental objectives were to investigate rebar slip from one side of the specimens (longitudinal rebar with hooks only on one side), track crack propagation, and capture the full-field displacement and strain measurements during the loading. The noncontact measurements from the multi-camera computer vision system using 3D digital image correlation (3D-DIC) and AprilTag-based photogrammetry were compared with the physical (contact) displacement measurement system. Strain fields were obtained using dual-camera 3D-DIC and finite element (FE) analysis. Results showed a close agreement of the point-wise displacements obtained from the physical and computer vision monitoring systems. The asymmetric structural design caused slip that delayed rebar fracture and reduced the peak load below that predicted by sectional analysis. The measured global force-deflection curve was predicted by the FE model when using a calibrated bond-slip model between rebar and UHPC. Comparison between the full-field measurements using 3D-DIC and FE numerical models showed that the evolution of principal strains and cracking were consistent. 3D-DIC proved to be a promising measurement method for monitoring strain/displacement and calibrating/confirming FE model that conventional methods without full-field measurements cannot provide.

Reliability and durability assessment of bridge stay cables

An algorithm for the reliability and durability assessment of stay cables in bridges is presented in this study enabling their probability of failure and a safe working period to be determined under various loading scenarios. The algorithm was originally developed based on data collected from an extensive structural monitoring campaign of the biggest single-pylon concrete cable-stayed bridge in Poland and used to assess the durability of its suspension system. It was then modified to be suitable for the evaluation of stay-cables subjected to wind excitation and structural reliability of the suspension system in a real steel bridge where permanent plastic deformations occurred in the anchor zones of the stay cables. The algorithm takes into account analytical models describing the stay cables and their numerical finite element models (FEM). As such, it is a universal tool having a wide range of applications, also beyond stay cables often encountered in medium- and long-span bridges forming a critical part of the civil engineering infrastructure.

A proposed approach for failure analysis of lattice transmission towers considering geometric imperfection effects

Different types of geometric imperfections can be observed in power transmission lattice towers. These imperfections include eccentricity resulting from the utilization of steel angles, joint slippage, initial crookedness, and dimensional tolerances in the cross-section of lattice tower members. These imperfections contribute to intricate structural behavior, particularly in members experiencing compressive forces. A comprehensive examination of geometric imperfections in lattice tower is crucial, yet research in this vital area is limited. Therefore, for proper modeling of these imperfections and better prediction of lattice tower failure capacity, it is necessary to provide a suitable approach in the modeling of the tower. In the present paper, a modeling method has been developed to analyze the failure of lattice towers, considering geometric imperfections effects (such as eccentricity, joint slippage, initial crookedness, and cross-section dimensional tolerances in the members). The results of the proposed modeling method have been compared with the results of a full-scale failure test conducted on a 400 kV tower. The results of the study show that the proposed modeling method, considering the effect of geometric imperfections, provides a suitable prediction of the tower’s load-carrying capacity. Also, to investigate the effects of each geometric imperfection, various finite element numerical models were established, and their force–displacement responses were evaluated. The results show that to make an acceptable estimation of the tower failure behavior, it is not enough to introduce geometric imperfections individually into the analysis. Rather, considering the collective effect of imperfections altogether can give an acceptable estimate of the tower’s load-bearing capacity.

Numerical modeling of high-velocity groundwater flow influence on the thermal-hydraulic characteristics and energy extraction from energy piles

This study investigates the potential for energy extraction from energy piles under high-velocity groundwater flow, considering different soil thermodynamic properties, pile characteristics, heat-exchange pipe shapes, and thermo-hydraulic parameters. Accordingly, finite element numerical modeling was employed along with Brinkman's equation, which was then verified using three sets of previously published data. The utilization of Brinkman's equation has revealed notable differences from the traditional Darcy's law approach, particularly regarding soil thermodynamic properties. The key findings indicate that groundwater flow has minimal impact on energy output per pile length (Q/Lep) until 10−7 m/s, after which Q/Lep increases significantly up to 10−3 m/s with no further effect. The influence of soil thermodynamic characteristics on Q/Lep decreases with increasing groundwater velocity, and Brinkman's equation is recommended for analyzing flows above 10−7 m/s, especially in soils with low thermodynamic properties. Low-velocity flows with high soil permeability can disrupt horizontal groundwater flow and impact energy extraction, while mixed convection minimizes the difference in energy received between the 2nd and 180th days and increases the slope of the Q/Lep diagrams. This research offers valuable insights into the complexities of energy extraction from energy piles, emphasizing the importance of considering groundwater flow and various design factors for accurate evaluations.

Experimental and numerical investigations of double bracket to CHS column joints

The primary objective of this study is to precisely characterize the behavior of double bracket-to-circular Hollow Section (CHS) column joints due to combined internal forces resulting from double tensile loading in opposite directions. In order to accomplish this goal, an experimental program consisting of eight test specimens has been carried out and numerical finite element modeling has been employed for the same specimens to analyze the stresses and deformations that occur within the vicinity of bracket-to-CHS joints. A total of 15 finite element models were constructed to simulate the initial study, addressing boundary conditions and facilitating verification and results comparison. The study included an investigation of various parameters, including the spacing between brackets in the longitudinal direction, as well as the depth-to-thickness ratio of the CHS columns and adding a T-stiffener to the bracket configuration. The study determined that an increase in the diameter-to-thickness ratio of the CHS columns significantly reduced the overall strength of the joint. Furthermore, findings suggested that increasing the longitudinal spacing between brackets resulted in an increase in single-bracket joint strength and a minor reduction regarding joint strength considering the effect of line loading. Moreover, adding a T-stiffener shape for the brackets enhanced the joint strength and prevented bracket tip fracture. In addition, a distinct behavior arises when considering joints with positive eccentricity, where the forces’ line of action extends beyond the circular cross-section of the CHS. In such cases, a reduction in joint strength is observed. Finally, a modification factor “A” is applied to the X-type branch plate-to-CHS strength equation presented by the AISC360-22 to account for the longitudinal spacing between brackets.