Study of deflection of PCI girder bridges using rotation data

A bridge is an infrastructure that experiences dynamic and repetitive load for a long period of time, so it is necessary to monitor the condition of the bridge structure to ensure that the bridge is always in a proper condition. This study aims to develop an equation model using multiple regression analysis to establish the relationship between deflection values and rotation values obtained from a PCI girder bridge as a project case study. The results demonstrate that the proposed regression equation accurately estimates the maximum deflection, with an average accuracy rate of 96.4%. The highest level of accuracy is 99.9497 % when the deflection is 0.0606m. The minimum level of accuracy is 86.3821 when the deflection is 0.0346. This result indicated that low accuracy happened at relatively small deflection values of particular load configurations. Thus, this method presents a reliable approach for estimating the maximum deflection based on tiltmeter readings, offering a practical solution with a commendable level of accuracy.


Introduction
A bridge is an infrastructure that experiences dynamic and repetitive loads over a long period of time, so that conditions deteriorate from time to time.It is necessary to make efforts to monitor the condition of the bridge structure to ensure that the bridge is in a proper condition with a system called the Structural Health Monitoring System (SHMS) which aims to obtain information suitable for civilian buildings in a sustainable manner (either in conditions changing gradually or changing suddenly) in the form of a working load and its mechanical response [1] [2].
To date, more and more structures have been monitored and tested.This has an impact on increasing knowledge about the behavior of structures as well.Deflection, strain and rotation measured during load tests and long-term monitoring of the structure can be used to detect signs of changes that could be detrimental to the structure.The development and successful implementation of long-term structural monitoring systems on bridges have been widely reported by researchers.In recent years, tiltmeters (also called inclinometers) have been widely used for construction monitoring, structural examiners, and long-term performance monitoring of bridges by promoting a simple method at an affordable cost [3][6] [7][8] [9].The method of measuring bridge deflection using rotational data from the tiltmeter (inclinometer) is considered quite promising, practical, inexpensive, and simple to measure static and dynamic deflection of bridge spans under load, even for bridge spans that cross heights.This method does not require a fixed viewing position as the tiltmeter is mounted on the bridge directly which greatly increases the measurement efficiency.The results obtained indicate that the rotation method is a potential method for measuring bridge deflection, so that the tiltmeter has significant technical application value and promising future with the approaching results [3] This study directly supports SDG 9 by enhancing bridge resilience, introducing cost-effective monitoring technology for sustainable infrastructure, and fostering innovation for safer and more accessible infrastructure overall by developing and implementing structural health monitoring systems for bridges, enhancing their ability to withstand dynamic and repetitive loads and ensuring their structural integrity.

Research Methodology
The research methodology for this study involves a structured sequence of steps, designed to comprehensively investigate the deflection of a PCI girder bridge using rotation data.The key phases of this methodology are as follows: a. Selection of Study Location.The research was conducted on a 50-meter single-span PCI girder bridge located in Kalimantan, Indonesia.This particular bridge was chosen as the primary subject of investigation due to its relevance to the study objectives.b.Crafting a Two-dimensional Finite Element Model.A two-dimensional Finite Element Method (FEM) model of the bridge was developed.This model accurately represents the geometrical and mechanical properties of the PCI girder beam, enabling a thorough analysis and simulation of its structural responses.c.Collection of Empirical Data.In order to obtain empirical data regarding maximum deflection and rotations, a range of loading conditions was applied to the two-dimensional FEM model of the bridge.These loading conditions were carefully designed to simulate real-world scenarios that the bridge might encounter during its operational lifespan.Subsequently, the FEM model generated the necessary dataset for further analysis.d.Computation of Maximum Deflection Formulas.To calculate maximum deflection based on rotation data, formulas were derived through Multiple Regression analysis.The primary objective of this phase was to establish a robust relationship between the measured rotations and the corresponding maximum deflection values.e. Validation of Maximum Deflection.To validate the accuracy of the maximum deflection estimates obtained from the regression equations, a comparative analysis was performed against maximum deflection values obtained through two-dimensional structural analysis using FEM structural analysis software.This validation step ensured the credibility and reliability of the proposed estimation technique by assessing its agreement with the comprehensive analysis conducted using the FEM software.By adhering to this systematic approach, the research achieved a precise estimation of the maximum deflection of the PCI girder bridge.This, in turn, enables effective monitoring and evaluation of its structural performance.

Case Study
The case study utilized a prestressed-I girder bridge design as the subject of investigation.The bridge featured a span length of 50 meters and a width of 10 meters, accommodating two lanes in each direction.Situated in Barito Kuala, South Kalimantan, this particular bridge provided an ideal testbed for the research.
Figures 1 and 2 depict the transversal sections of the bridge, providing visual representations of its structural composition.These illustrations offer insights into the cross-sectional geometry and  To quantify the bridge's deflection accurately, precise rotation measurements were focused exclusively at the extremity of the bridge span.This choice was deliberate, as it offers crucial insights into the maximum deflection encountered by the bridge, furnishing invaluable data for the ensuing analytical and estimation procedures.

Maximum Deflection and Rotation Data
To capture maximum deflection and rotation data, a meticulous consideration of 45 distinct load configurations was undertaken.These configurations were meticulously chosen to simulate a diverse array of practical scenarios reflective of the bridge's operational experiences.Refer to Table 1 for a representative subset of these load configurations, illustrating a spectrum of load magnitudes and distributions scrutinized during the study.
The Two-dimensional Finite Element Method (FEM) analysis was employed to derive the maximum deflection values and associated rotations at the bridge's endpoint.The findings of this analysis, presenting the computed maximum deflection values and corresponding rotations for each load configuration, are detailed in Table 2.

Regression Equation to Estimate Maximum Deflection from Rotation Data
The maximum deflection and rotation values, as depicted in Table 2, underwent a rigorous multiple regression analysis to derive a robust equation that encapsulates the relationship between maximum deflection and rotation.This regression analysis aimed to construct a mathematical model that precisely predicts maximum deflection based on the associated rotation measurements.
The resulting regression equations, stemming from this in-depth analysis, are presented herein as Equation 1.
These equations intricately capture the connection between rotation values and their corresponding maximum deflection, serving as invaluable tools for estimating the bridge's maximum deflection using measured rotation data.This, in turn, facilitates the effective monitoring and evaluation of the bridge's structural performance

Level of Accuracy of the Estimated Maximum Deflection
The Level of accuracy of the proposed approach was thoroughly evaluated by comparing the maximum deflection values obtained from the Two-dimensional FEM model with those calculated using the regression equation.This accuracy assessment aimed to validate the reliability and precision of the developed regression equation in estimating the maximum deflection of the bridge.
The results of this level of accuracy check are summarized in Table 3, which presents a comprehensive comparison of the maximum deflection values obtained from both the FEM model and the regression equation.The table provides insights into the level of agreement between the two methods, offering quantitative measures of accuracy by means of level of accuracy value.
Table 3 reveals that the average level of accuracy of the maximum deflection values obtained from the Two-dimensional FEM model and the regression equation is only 96.2092%.This high vale of level of accuracy signifies a high level of agreement between the two methods in estimating the maximum deflection of the bridge.

Figure 4. Level of Accuracy vs Deflection
However, it is noteworthy that the highest level of accuracy, reaching an impressive 99.9497%, corresponds to a deflection of 0.0606 meters.Conversely, the minimum level of accuracy, recorded at 86.3821%, is associated with a deflection of 0.0346 meters.These findings, in conjunction with Figure 4, reveal that lower accuracy tends to occur when estimating deflections at relatively modest values for specific load configurations.The inherent limitations of the regression equation and the unique characteristics of certain load scenarios can pose challenges when accurately predicting extremely small deflection values.
Nevertheless, the overall conclusions affirm that the regression equation demonstrates exceptional accuracy in estimating the bridge's maximum deflection.The minimal average disparity observed between the FEM model and the regression equation underscores the effectiveness and reliability of the proposed approach in precisely assessing the bridge's maximum deflection.

Conclusion
Based on the comprehensive analysis conducted in this research, the following key conclusions can be drawn: a.The application of the regression formula to estimate maximum deflection in a simple span PCI girder bridge yields a commendable level of accuracy.The developed equation model provides a robust and efficient method for estimating maximum deflection based on rotation measurements.b.Consequently, employing tilt meter sensors for measuring rotations at bridge ends and estimating maximum deflection proves to be a cost-effective and effective solution for implementing a structural monitoring system.This approach offers a practical and accessible means of monitoring the structural behavior of bridges.c.It's important to note that the accuracy of the estimation improves as deflection values increase.
Higher deflection values allow for more precise and reliable estimations using the regression equation.This relationship between deflection values and estimation accuracy should be considered in practical applications.d.To validate and enhance the practicality of the proposed system, it is highly recommended to conduct field tests on real bridges.Implementing the system in real-world scenarios will provide valuable insights into its performance, reliability, and potential for broader application.In summary, this research underscores the effectiveness of the regression-based estimation approach for assessing maximum deflection in a simple span PCI girder bridge.By leveraging tilt meter sensors and recognizing the correlation between deflection values and estimation accuracy, this method offers a viable and cost-effective option for structural monitoring.Further field tests and real-world applications are essential for validating and refining the system to facilitate broader adoption.

Figure 3 .
Figure 3. Two-dimensional finite element modelling of the bridge

Table 1 .
Load Configuration

Table 3 .
Maximum Deflection from FEM Analysis vs Deflection from Regression Equation