https://ced.
Damage Detection in Gusset Plates of Steel Truss Bridges using Modal Parameters: Experimental and Numerical Study Kristijanto.
Fitriyah.
2, and Habieb.
1 Department of Civil Engineering.
Sepuluh Nopember Institute of Technology.
Surabaya.
INDONESIA 2 Department of Civil Engineering.
Adhi Tama Surabaya Institute of Technology.
Surabaya.
INDONESIA DOI: https://doi.
org/10.
9744/ced.
Article Info:
Submitted: June 24, 2025 Reviewed: July 17, 2025 Accepted: Sept 28, 2025 Keywords:
damage detection, modal based methods.
SHM, truss bridge.
Corresponding Author:
Kristijanto.
Department of Civil Engineering.
Sepuluh Nopember Institute of Technology.
Surabaya.
INDONESIA Email: heppy.
k@its.
Abstract Corrosion in gusset plate elements has become a critical factor in bridge structural failures, emphasizing the need for more accurate and reliable damage detection methods.
Conventional visual inspections are limited in precision and cannot provide real-time monitoring, underscoring the importance of advanced techniques.
This study proposes a vibrationbased Structural Health Monitoring (SHM) approach employing modal parameter indices, namely Mode Shape (MS).
Mode Shape Curvature (MSC).
Mode Shape Slope (MSS), and Mode Shape Curvature Square (MSCS), to detect damage in bridge components.
Damage scenarios were simulated by introducing gusset plate cuts of 5%, 10%, and 20% to represent different levels of corrosion.
The results indicate that MSC and MSCS are the most reliable methods for identifying damage locations in complex structural systems, as they capture mode shape alterations with high sensitivity.
Furthermore, the accuracy of modal parameter analysis improves with increasing damage severity.
These findings confirm MSC and MSCS as robust tools for early-stage corrosion detection in SHM applications.
This is an open access article under the CC BY license.
INTRODUCTION
Structural failure detection in bridges has become a key research focus, especially after the 2007 collapse of the I35W Bridge in Minneapolis.
Studies identified gusset plate failure as a major contributing factor.
Even minor, undetected damage (Figure .
can shorten a bridgeAos service life and lead to serious structural failure as key components degrade.
The gusset plate, which connects the main truss to the deck, is crucial to structural integrity.
Corrosion in this area can cause cracks that spread under load .
, potentially leading to progressive collapse (Figure .
The bridge was about 40 years old .
, nearing the end of its service life.
Bridges with a service life of 30 to 40 years should be prioritized for evaluation .
Poor maintenance likely accelerated damage to critical components such as the gusset plate.
This incident emphasizes the need for regular monitoring and timely repairs.
However, conventional inspections, mainly visual checks using simple tools .
, often miss early or hidden damage, especially in complex structures like steel truss bridges.
Visual inspections also depend heavily on the inspectorAos skill and experience .
, making them less reliable for detecting subtle damage in real time.
To overcome these limitations, researchers have developed vibration-based damage detection (VBDD) methods as a more objective and accurate alternative .
, .
Note : Discussion is expected before November, 1st 2025, and will be published in the AuCivil Engineering DimensionAy, volume 28, number 1.
March 2026.
ISSN
: 1410-9530 print / 1979-570X online Published by : Petra Christian University Damage Detection in Gusset Plates of Steel Truss Bridges .
Corrosion at Roller Bearing .
Corrosion at Gusset Plate Figure 1.
Corrosion Observed on the I-35W Bridge at .
the Roller Bearing and .
the Gusset Plate .
Figure 2.
Photograph of the I-35W Bridge Collapse .
Vibration-Based Damage Detection (VBDD) identifies structural damage by analyzing changes in physical properties .
ass, damping, and stiffnes.
that influence a structureAos vibration behavior.
Damage typically alters modal properties like natural frequency and mode shape .
, .
VBDD methods are generally divided into traditional and modern approaches.
Traditional methods focus on parameters such as modal strain energy, frequency, and damping, and are commonly applied through techniques like acoustic emission, ultrasonic testing, thermal imaging, and vibration analysis .
, .
Several studies have explored VBDD for identifying damage location .
However, accurately locating damage remains a key challenge in Structural Health Monitoring (SHM), especially for complex structures like steel truss bridges .
Several recent studies have evaluated VBDD algorithms in both experimental and numerical settings.
Moradipour et .
evaluated the Modal Strain Energy (MSE) method experimentally and numerically on a steel truss bridge model with simulated damage up to 5%.
The first five vertical vibration modes were used as analysis parameters.
The results showed that the MSE method is effective in monitoring structural conditions and accurately identifying damage locations.
Manoach et al .
examined several modal parameter methods including Modal Displacement.
MSS.
Modal Curvature.
MSCS, and MSE, for damage detection in a beam specimen.
Using both finite element analysis and experimental testing under intact and damaged conditions, all methods effectively identified the induced Zhou et al.
applied five VBDD algorithms (CMS.
MSC.
CF.
DI, and CUFC) on a dismantled bridge girder.
Despite using only six sensors and the fundamental vibration mode, all methods localized low-level damage Frans et al.
compared MSC and DLV methods on various truss damage types and found both algorithms sensitive and reliable, with DLV pinpointing damaged members well.
Further.
Janeliukstis et al.
introduced Dynamic MSCS to detect cracks in concrete railway sleepers using modal deflection data, while Rucevskis and Wesolowski .
used MSCS to locate damage in aluminum beams without full modal data.
Building on this foundation, the present study compares four VBDD algorithms to detect gusset plate damage in steel truss bridges.
Using both experimental and numerical methods, artificial damage levels of 5%, 10%, and 20% are Kristijanto.
Fitriyah.
, and Habieb.
introduced at different gusset locations.
Analysis focuses on changes in mode shapes and algorithm sensitivity, tested on a 1:12 scale steel truss bridge model.
DAMAGE DETECTION BASED ON PARAMETER MODAL
The four Vibration-Based Damage Detection (VBDD) algorithms employed in this study include the Mode Shape Index (MS.
Mode Shape Slope Index (MSS.
Mode Shape Curvature Index (MSC.
, and Mode Shape Curvature Square Index (MSCS.
These methods are commonly used for identifying damage locations in structures by calculating mode shape curvature .
In this study, the methods will be tested for their sensitivity to artificial A detailed summary of the VBDD formulation techniques is presented through the referenced literature.
Mode Shape (MS) Damage Index This method is relatively simple and utilizes the mode shape damage index to represent the changes in mode shapes between the undamaged structure and the damaged structure .
OIyuayuaycnycn = yuayuaycnycnyccycc Oe yuayuaycnycn Where yuayuaycnycnyccycc is the mode shape of the damaged structure, yuayuaycnycn is the mode shape of the intact structure, and ycnycn represents the measurement point .
This method is based on the idea that the mode shape curvature of a healthy structure is smooth and can be modeled using a polynomial function.
By applying polynomial regression to curvature data from a damaged structure, the curvature of the undamaged state can be estimated.
Laboratory tests may show false peaks due to local disturbances, which can be mistaken for damage.
To minimize such errors, averaging the damage index across all analyzed modes is recommended .
ycAycA ycAycAycAycAycnycn = (OIyuayuaycnycn )ycuycu ycAycA ycuycu=1 Where N is the total number of mode shape measurements.
Mode Shape Slope (MSS) Damage Index This algorithm uses changes in the slope of the mode shape .
Where.
OIyuayuaAycnycn = yuayuaAyccyccycnycn Oe yuayuaAycnycn yuayuaAycnycn = .
uayuaycnycn 1 Oe yuayuaycnycnOe1 ) 2Ea ycAycA ycAycAycAycAycAycAycnycn = (OIyuayuaAycnycn )ycuycu ycAycA ycuycu=1 Where Ea is the distance between two consecutive measurement points.
If there are multiple mode measurements, the index is used.
Mode Shape Curvature (MSC) Damage Index In this algorithm, the difference in mode shape curvature between the intact and damaged structures serves as an indication of where the damage occurs .
OIyuayuaycnycn = yuayuayccycc ycnycn Oe yuayuaycnycn Damage Detection in Gusset Plates of Steel Truss Bridges Where, yuayua"ycnycn = .
uayuaycnycn 1 Oe 2yuayuaycnycn yuayuaycnycnOe1 ) Ea2 Mode Shape Curvature Square (MSCS) Damage Index The damage index is defined as follows.
METHODS
Ayccycc2 OIyuayua2 Oe yuayua2 ycnycn = yuayuaAycnycn Figure 3 outlines the research workflow, which combines numerical and experimental approaches to assess the effectiveness of four VBDD methods in locating damage in deteriorated bridge elements.
Figure 3.
Research Flow Chart The process begins with dynamic testing of a scaled steel truss bridge model.
Accelerometers were used to record time-domain vibration data.
This data was then converted into frequency-domain information using the Fast Fourier Transform (FFT), enabling analysis of natural frequencies and mode shape changes due to damage.
Displacement values, derived from acceleration data, were key to identifying potential damage locations.
Next, numerical analysis was performed using mode shape-based algorithms with ABAQUS software to identify and localize damage.
In this study, only the first mode shape (Mode .
was used due to its stability and reliability in both simulation and As a low-order mode, it captures the overall structural behavior, is easier to measure accurately, and is more sensitive to damage, especially in gusset plates.
Prior research confirms that lower modes are more effective for damage detection, while higher modes are often affected by noise and harder to interpret .
, .
, .
Section properties of the Truss Bridge Model This section describes the 1:12 scale steel truss bridge model, including accelerometer placement and data acquisition The model, constructed from steel angle profiles, is a scaled-down version of a full-scale prototype for testing purposes.
The original bridge is 60 meters long .
enter to cente.
, 10 meters wide including pedestrian paths, and 7.
2 meters It consists of ten equal spans, each 6 meters long.
Due to laboratory space limits, the model was scaled down to 1:12, resulting in a bridge that is 500 cm long, 84 cm wide, and 60 cm tall (Table .
Superstructure Bridge length Bridge width Bridge height Transverse girder spacing Longitudinal girder spacing Table 1.
Dimensions of the Truss Bridge Model Original Model Dimensions .
Scaled Model Dimensions .
Kristijanto.
Fitriyah.
, and Habieb.
In the finite element model, the bridge ends are supported by pinned and roller supports that only allow translational The entire structure uses structural steel with a YoungAos modulus of 200,000 MPa and a PoissonAos ratio of 0.
Each truss element is built from angle steel profiles (Table .
, connected using 4 mm thick gusset plates (Figure .
All modeling and analysis were done using ABAQUS software.
Dimensions of the 1:12 Scale Laboratory Bridge Model .
Accelerometer Sensor Layout Figure 4.
1:12 Scale Laboratory Bridge Model and .
Accelerometer Sensor Layout Table 2.
Section Properties of the Laboratory-Scale Bridge Model Bridge Member Steel Profile Main truss frame 2L 40x40x4 Diagonal truss member L 30x30x3 Cross girder L 50x50x5 Longitudinal girder Lx40x40x4 Top chord L 30x30x3 End portal L 30x30x3 Gusset plate 4mm steel plate Experimental Set-Up The specifications and cross-sections of the scaled bridge model are listed in Tables 1 and 2.
The model was supported by pinned and roller bearings to simulate real boundary conditions.
Accelerometers were installed (Figure .
to capture the structureAos dynamic response.
Ideally, 18 accelerometers were needed to monitor all gusset plate points.
However, due to equipment limits, only 6 were used.
To address this, a relocation method was applied: two accelerometers stayed fixed at mid-span, while the other four were moved sequentially to cover all points.
This relocation approach was justified based on a comparative analysis, which showed that the experimental results using six accelerometers yielded mode shape patterns comparable to those from the FEM simulation where all nine points were monitored at once.
These findings confirm that the relocation method, despite the restricted number of sensors, is capable of providing accurate and representative dynamic data of the structure.
The experimental test used a dropping weight impact method .
, as shown in Figure 5.
A 12 kg concrete cylinder .
cm diamete.
was dropped from a height of 17.
5 cm onto the mid-span cross beam of the scaled bridge model equipped with accelerometers.
This impact generated vibrations, and the accelerometers recorded the structureAos dynamic response.
The data were then processed into displacement values at each point, with maximum displacements used for modal analysis.
Each test was repeated three times for accuracy.
Damage Detection in Gusset Plates of Steel Truss Bridges A: Computer B: USB gateway C: Accelerometer Sensor D: Bridge Specimen E: Dropping Weight .
Experimental Set-up .
Dropping weight .
Figure 5.
Experimental Set-Up dan .
Dynamic Load in the Experimental Test Six artificial damage scenarios on the gusset plates were tested, as shown in Table 3 and Figure 6.
These scenarios represent common real-world damage such as corrosion and tearing .
, .
If undetected, such damage can worsen over time and lead to structural failure .
, .
The scenarios were created to assess how effectively the Vibration-Based Damage Detection (VBDD) methods can identify damage in gusset plates.
Damage Scenario Gusset plate tear 5% Gusset plate tear 10% Gusset plate tear 20% Gusset plate tear 5% Gusset plate tear 10% Gusset plate tear 20% Table 3.
Artificial Damage Scenarios Code
GCC5%
GCC10%
GCC20%
GCE5%
GCE10%
GCE20%
Damage Location Variation 5 L / Mid-span 5 L / Mid-span 5 L / Mid-span 1/5 L / Edge of span 1/5 L / Edge of span 1/5 L / Edge of span .
5% Cut of Gusset Plate .
10% Cut of Gusset Plate .
20% Cut of Gusset Plate Figure 6.
5% Cut of Gusset Plate, .
10% Cut of Gusset Plate, and .
20% Cut of Gusset Plate
RESULTS AND DISCUSSION
The numerical analysis starts with modeling the bridge (Tables 1 and .
, followed by applying a static load equal to the 12 kg dropped mass used in the experiment.
This load is placed at the mid-span, matching the experimental setup.
Displacement at each point is then used to validate the experimental results.
Mode shapes from the finite element model are also used to compute damage indices.
The displacement data are analyzed using four damage detection methods, with results detailed in Sections 4.
1 to 4.
Damage Detection on the GCC 5% Model at Mid-Span The first stage analyzes the 5% cut damage scenario on the gusset plate at mid-span.
Displacement modes at each observation point are evaluated based on the experimental setup (Figures 7 and .
Finite element results are visually presented in Figure 7.
Figure 9 shows the displacement mode pattern for the 5% mid-span damage scenario.
All four modal parameters (MS.
MSS.
MSC.
MSCS) successfully identified the damage in the experimental results.
In the FEM analysis.
MS and MSC demonstrated high accuracy, with a peak at node 0.
5 confirming effective damage localization by MSS and MSC.
Kristijanto.
Fitriyah.
, and Habieb.
Figure 7.
Bridge Modal Analysis with 5% Cutting Damage of the Gusset Plate in the Mid-Span Modal Parameter Index Figure 8.
Experimental Set-up of 5% Cut Damage on Gusset Plate at Mid-span
MSi-exp
MSi-ABQ
MSSi-exp
MSSi-ABQ
NODE
MSCi-exp MSCi-ABQ MSCSi-exp MSCSi-ABQ Figure 9.
Curvature Patterns from Four Modal Parameter Methods Detecting 5% Gusset Plate Damage at Mid-span Table 4.
Error Metrics of Modal Methods in Identifying Mid-Span Damage .
% GCC) Nodes Modal Parameter MSi
MSSi
MSCi
MSCSi
SSE
To evaluate the accuracy of FEM compared to the experiment.
SSE values were calculated (Table .
SSE (Sum of Squared Error.
is a statistical method used to quantify the overall deviation between the observed .
values and the predicted values .
Lower SSE values indicate better alignment with experimental results.
MSSi .
and MSCi .
had the lowest SSE, indicating higher accuracy in detecting damage at node 0.
SSE Value SSE-MSi SSE-MSSi SSE-MSCi SSE-MSCSi Figure 10.
Sum of Squared Error Values from All Modal Parameters .
% GCC) Damage Detection in Gusset Plates of Steel Truss Bridges Figure 10 illustrates the absolute error distribution for each parameter.
These results confirm that MSS and MSC are the most effective parameters for identifying mid-span gusset plate damage.
Damage Detection on the GCC 10% Model at Mid-Span This section evaluates the 10% cut damage scenario on the gusset plate at mid-span.
As shown in Figure 11, a 10% artificial cut was introduced in the structural model, with displacement modes analyzed at observation points matching the experimental setup (Figure .
FEM results are also presented in Figure 11.
Figure 11.
Bridge Modal Analysis with 10% Cutting Damage of the Gusset Plate in the Mid-span Modal Parameter Index Figure 12.
Experimental 10% Tearing Damage on Gusset Plate at Mid-Span
MSi-exp
MSi-ABQ
NODE
MSSi-exp MSSi-ABQ MSCi-exp MSCi-ABQ MSCSi-exp MSCSi-ABQ Figure 13.
Curvature Patterns from Four Modal Parameter Methods in Detecting 10% Gusset Plate Damage at Mid-Span Figure 13 illustrates the displacement mode for this damage scenario.
All four modal parameters (MS.
MSS.
MSC.
MSCS) effectively localized the damage in both experimental and FEM results, with a clear peak at the mid-span.
Table 5.
Error Metrics of Modal Methods in Identifying Mid-Span Damage .
% GCC) Nodes Modal Parameter MSi
MSSi
MSCi
MSCSi
SSE
To assess accuracy.
SSE values were calculated (Table .
All parameters showed low SSE, with MSi and MSCSi having the lowest, and MSSi and MSCi slightly higher.
These values indicate all four methods reliably detect damage.
Kristijanto.
Fitriyah.
, and Habieb.
SSE Value Figure 14 supports these findings, showing low absolute error values for each modal parameter method.
These results confirm the effectiveness of all modal methods in identifying mid-span gusset plate damage.
SSE-MSi SSE-MSSi SSE-MSCi SSE-MSCSi Figure 14.
Sum of Squared Error Values from All Modal Parameters .
% GCC) Mid-Span Damage Detection on the GCC 20% Model Figure 15 shows the FEM results for the 20% gusset plate damage scenario at mid-span.
Displacement modes were analyzed at each observation point, and sensor placement was adjusted to align with the experimental setup.
Modal Parameter Index Figure 15.
Bridge Modal Analysis with 20% Cutting Damage of the Gusset Plate in the Mid-Span
Msi-exp
Msi-ABQ
NODE
MSSi-exp MSSi-ABQ MSCi-exp MSCi-ABQ MSCSi-exp MSCSi-ABQ Figure 16.
Curvature Patterns from Four Modal Parameter Methods in 20% Gusset Plate Damage at Mid-span Figure 16 displays the displacement mode for this damage case.
All four modal parameters (MS.
MSS.
MSC, and MSCS) accurately localized the artificial damage in both experimental and FEM results.
Each method produced distinct curvature patterns centered at the damage point, indicating consistent detection performance.
Table 6.
Error Metrics of Modal Methods in Identifying Mid-Span Damage .
% GCC) Nodes Modal Parameter MSi
MSSi
MSCi
MSCSi
SSE
To quantify accuracy.
SSE values are shown in Table 6.
All methods yielded low errors, with MSCSi .
and MSCi .
being the most accurate, followed by MSi .
and MSSi .
These values confirm the strong performance of all four modal methods in identifying mid-span damage.
Damage Detection in Gusset Plates of Steel Truss Bridges SSE Value SSE-MSi SSE-MSSi SSE-MSCi SSE-MSCSi Figure 17.
Sum of Squared Error Values from All Modal Parameters .
% GCC) Figure 17 shows the total SSE for each modal parameter, confirming that MSCSi and MSCi have the highest accuracy, while MSSi shows the largest error.
This supports the results in Table 6 and highlights the effectiveness of the modal parameters, especially MSCSi, in detecting gusset plate damage.
Damage Detection on the GCE 5% Model at 1/5 Span Figure 18 shows the structural model with 5% gusset plate damage at 1/5 span.
Displacement modes were analyzed at each point, with measurement positions adjusted to match the experimental setup.
Finite element results are visually presented in Figure 18.
Modal Parameter Index Figure 18.
Bridge Modal Analysis with 5% Cutting Damage of the Gusset Plate at 1/5 of the Span
Msi-exp
Msi-ABQ
MSSi-exp
MSSi-ABQ
NODE
MSCi-exp MSCi-ABQ MSCSi-exp MSCSi-ABQ Figure 19.
The Curvature Patterns of the Four Modal Parameter Methods in Detecting 5% Gusset Plate Damage at 1/5 of the Span Figure 19 illustrates the displacement mode for the 5% GCE damage scenario.
Of the four modal parameters, only MSCi consistently identified the damage location in both experimental and FEM results, as indicated by a distinct curvature peak at the 1/5 span position.
Table 7.
Error Metrics of Modal Methods in Identifying 1/5 Span Damage .
% GCE) Nodes Modal Parameter MSi
MSSi
MSCi
MSCSi
SSE
The error metrics are summarized in Table 7.
While MSSi and MSCi recorded low SSE values .
43 and 0.
, only MSCi accurately localized the damage.
MSi and MSCSi produced higher SSE .
05 and 3.
and failed to detect the damage effectively.
Kristijanto.
Fitriyah.
, and Habieb.
SSE Value Figure 20 shows the total SSE for each modal parameter, confirming that MSCSi and MSi have the highest accuracy, while MSSi shows the largest error.
This supports the results in Table 7 and highlights the effectiveness of the modal parameters, especially MSCi, in detecting gusset plate damage.
SSE-MSi SSE-MSSi SSE-MSCi SSE-MSCSi Figure 20.
Sum of Squared Error Values from All Modal Parameters .
% GCE) Damage Detection on the GCE 10% Model at 1/5 Span Figure 21 displays the FEM model of the bridge with 10% gusset plate damage located at 1/5 of the span.
Displacement modes were analyzed based on the experimental configuration, and the FEM results confirm structural deformation concentrated near the damage zone.
Modal Parameter Index Figure 21.
Bridge Modal Analysis with 10% Cutting Damage of the Gusset Plate at 1/5 of the Span
Msi-exp
Msi-ABQ
MSSi-exp
MSSi-ABQ
NODE
MSCi-exp MSCi-ABQ MSCSi-exp MSCSi-ABQ Figure 22.
Curvature Patterns from Four Modal Parameter Methods Detecting 10% Gusset Plate Damage at 1/5 of the Span Figure 22 illustrates the curvature patterns derived from the four modal parameters.
The MS.
MSC, and MSCS indices successfully localized the damage, as shown by clear curvature peaks at 1/5 span in both experimental and FEM data.
Conversely, although MSSi shows a low RMSE, it fails to indicate the damage visually.
Table 8.
Error Metrics of Modal Methods in Identifying 1/5 Span Damage .
% GCE) Nodes Modal Parameter MSi
MSSi
MSCi
MSCSi
SSE
The corresponding error metrics are presented in Table 8.
MSSi and MSi record the lowest SSE values at 0.
39 and 77, respectively.
However, due to its lack of visual indication.
MSSi is deemed unreliable in this damage scenario.
MSCi and MSCSi both yield SSE values of 0.
95 but demonstrate better consistency in detecting damage.
Damage Detection in Gusset Plates of Steel Truss Bridges SSE Value SSE-MSi SSE-MSSi SSE-MSCi SSE-MSCSi Figure 23.
Sum of Squared Error Values from All Modal Parameters .
% GCE) Figure 23 shows the total SSE for each modal parameter, confirming that MSi.
MSCSi, and MSCi have higher accuracy, while MSSi records the lowest error.
However, despite its low SSE.
MSSi fails to visually indicate the damage location.
This supports the results in Table 8 and highlights the effectiveness of the modal parameters .
specially MSC.
in detecting gusset plate damage.
Damage Detection on the GCE 20% Model at 1/5 Span Figure 24 presents the structural model with 20% gusset plate damage at 1/5 span.
Displacement modes were analyzed at each point, adjusted to match the experimental sensor positions, and visualized through FEM results.
Modal Parameter Index Figure 24.
Bridge Modal Analysis with 20% Cutting Damage of the Gusset Plate at 1/5 of the Span Msi-exp Msi-ABQ MSSi-exp NODE MSSi-ABQ MSCi-exp MSCi-ABQ MSCSi-exp MSCSi-ABQ Figure 25.
Curvature Patterns from Four Modal Parameter Methods Detecting 20% Gusset Plate Damage at 1/5 of the Span Figure 25 presents the curvature pattern derived from the four modal parameters.
Among these.
MSCi and MSCSi exhibit pronounced peaks at the damage location in both experimental and FEM mode shapes, indicating their effectiveness in accurately detecting and localizing the 20% damage.
Table 9.
Error Metrics of Modal Methods in Identifying 1/5 Span Damage .
% GCE) Nodes Modal Parameter MSi
MSSi
MSCi
MSCSi
SSE
Table 9 displays the associated error metrics.
MSCi records the lowest SSE .
, followed by MSSi .
Although MSCSi shows clear curvature peaks, its higher SSE .
reflects reduced consistency across data points.
SSE Value Kristijanto.
Fitriyah.
, and Habieb.
SSE-MSi SSE-MSSi SSE-MSCi SSE-MSCSi Figure 26.
Sum of Squared Error Values from All Modal Parameters .
% GCE) Figure 26 further validates these findings by demonstrating low absolute errors near the damaged zone .
articularly for MSC.
thereby confirming strong correlation between experimental and numerical results.
Based on these indicators.
MSCi is again confirmed as the most reliable parameter for identifying 20% gusset plate damage at 1/5 CONCLUSIONS This study focuses on identifying the location of gusset plate cut damage through dynamic experimental testing on a steel truss bridge.
Numerical analysis was conducted to validate the damage locations detected during the tests.
The proposed damage detection approach utilizes modal parametersAivibration-based damage detection (VBDD) methodsAiincluding Mode Shape (MS).
Mode Shape Slope (MSS).
Mode Shape Curvature (MSC), and Mode Shape Curvature Square (MSCS).
The effectiveness of MSC and MSCS was assessed through simulated gusset plate damage scenarios involving 5%, 10%, and 20% cuts at various locations.
The results indicate that among the four methods.
MSC and MSCS consistently demonstrated superior performance in identifying damage locations on gusset plates.
Displacement values at each measurement pointAicorresponding to gusset plate positionsAiserved as reference indicators and were validated through both experimental testing and numerical simulation.
Furthermore, the analysis shows that the accuracy of modal parameter methods increases with the severity of the damage, indicating that larger damage volumes lead to more reliable detection results.
From a theoretical standpoint, the dynamic response of a structure cannot, in general, be inferred solely from static analysis or modal .
Only in special cases where the response is strongly dominated by the fundamental .
mode can equivalent static approximations or single-mode approaches provide reasonable Accordingly, this study is primarily applicable to systems with first-mode-dominated behavior.
For more general applications, where higher modes structurally contribute to deformation and response, the proposed approach may not be directly applicable and would require further development that explicitly accounts for multi-modal effects.
REFERENCES