Author: Muhammad Hafidh Dhiaulhaqi – Innovation Engineer PT Optimaxx Prima Teknik (2025)
BRIDGE DESCRIPTION
ABSTRACT AND INTRODUCTION TO THE SIMULATION
Why is it important for the engineering industry?
In this blog post, a study case of vibration analysis of a suspension bridge is conducted using ANSYS Mechanical. The structural, modal analysis and response spectrum were utilized to simulate pre-stressed analysis, modal analysis and response spectrum analysis respectively. The subsystems used in the workbench can be coupled as follows.
The configuration of the suspension bridge that is created for this simulation is shown as follows:
Figure 4. Suspension bridge configuration
Take note that the bridge configuration (shape-wise) is the same but the total span of the bridge that was done in this simulation is scaled down with a span of 15m in total as shown in Figure 5.
Figure 5. Suspension bridge CAD created in SpaceClaim.
Properties of the beam profiles Cross-Sectional Area (CSA)
Figure 6. Bream area of cross-section profiles applied in the bridge structural properties, A – I Profile, B – Rectangle Profile – C- Circular Profile
Table 1. Beam area of cross-section profile properties
MESH
Show a brief description of the mesh.
Figure 7. Suspension bridge mesh
As shown in Figure 7, the mesh was done using global element sizing control. But for further analysis, concentration using biasing of elements in certain areas and localising mesh can be utilised.
SETUP
Pre-Stressed Analysis
The pre-stressed analysis is used to introduce initial loading that exists within the bridge environment to ensure that a high-fidelity simulation can be obtained. This is crucial to create accurate modal shapes in the modal analysis subsystem. In this case, the dead load of the bridge is applied in the centre of gravity (COG) of the geometry. Other loading such as Live load (from traffic) & Environmental load (from wind, earthquake, water) is not taken into account. Since both loads are not considered to be constant. Fixed support and displacement BC are placed on A and B respectively as shown in Figure 6.
Figure 8. Boundary conditions applied on the bridge
Modal Analysis
In the Modal Analysis, it is imperative to understand that different frequencies will create different shapes that the structure will vibrate on. We call this “Mode Shapes”. Evaluating these shapes can help engineers create design modifications to ensure that the mode shapes that are dominant and can lead to failure can be prevented.
In the mode shapes analysis, the following parameters need to be taken care of:
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- Participation Factor
- Ratio of Effective Mass to Total Mass
The participation factor indicates how much a mode shape would be affected if an excitation factor is applied to the system in a specific DOF. The higher its value, the more that mode shape would participate in the overall shape during the vibration motion of that structure.
As for effective mass, it shows how much mass has been simulated and accumulated from all the mode shapes that have been created. If this value does not meet a certain requirement when compared to the total mass of the structure (I.e. 90%) (RISA, 2020), insufficient mode shapes would be created for the response spectrum analysis (RSA), underestimating the structure performance in RSA. In this simulation, the ratio of the effective mass to the total mass is around 70%. Yes, it is still under the requirements of ASCE 7 (ideCAD, 2024) but due to the limitations of computer power and RS input, 70% was considered sufficient for this particular study of vibration analysis.
Response Spectrum Analysis (RSA)
Response spectrum analysis is used in dynamic analysis of a structure with the application of response spectrum, most used in earthquake structural analysis to ensure that deformations of a structure does not extend to a certain benchmark, ensuring structural integrity.
The response spectrum that is applied to the system is built upon maximum responses (in displacement, velocity or acceleration) in each respective natural frequency. Creating the maximum vibration geometry motion. However, due to the fact that the application of RS is only in 1 degree of free in each analysis, limitations of multiple DOF applications simultaneously are what limits the RSA in vibration analysis.
For RSA, a RS is required to be inputted into the system in the form of either RS acceleration, RS velocity or RS displacement. In this simulation, values of RS acceleration that represent the earthquake that happened back in 2004 in Banda Aceh was used as provided in Table 2.
Table 2. Response spectra at soil level at SMK- Dirmutala Stadium, Banda Aceh (Setiawan, 2013)
Figure 9. Log Spectral Acceleration plotted against the Frequency of the RS acceleration for seismic analysis.
POST-PROCESSING
RESULTS
Pre-stressed static structural results
Figure 10. Axial force experienced on the beams
Figure 11. Total bending moment experienced on the beams.
Figure 12. Total deformation of the suspension bridge
Modal analysis results
Figure 13. Dominant modes in the Y-direction excitation
Figure 14. Dominant Modes in the X-axis Rotation
Response spectrum results
Figure 15. Total deformation using Square Root of the Sum of the Squares (SRSS) in RSA
Figure 16. Total deformation using Complete Quadratic Combination (CQC) in RSA
Figure 17. Total deformation using ROSE in RSA
INTERPRETATION OF RESULTS
For the modal analysis, mode shapes with respect to their frequencies were obtained. It was determined that only the mode shapes in the Y-direction and X-axis excitation were extracted in this simulation due to the fact that the ratio of the effective mass to the total mass in these excitation DOFs meets the minimum 70% requirement. Which can be observed in the Appendix Table 3.
As for the response spectrum results, the total deformation indicates the possible maximum displacement of the bridge during seismic dynamic application. Formulations are used that is integrated within the ANSYS Mechanical software to combine the possible mode shapes during these dynamic loads’ applications. It can be observed that from all formulations utilised in the mode shape combinations, mode 4 and mode 5 are the dominant mode shapes during the Banda Aceh seismic earthquake application with a maximum displacement of 3.22 e-5, 1.6 1e-5 & 3.264 e -5 [mm] using SRSS, CQC & ROSE formulation respectively. As extracted, the values from SRSS and ROSE show some similarity in total deformation while the CQC is the only anomaly among the three. This is because the SRSS and ROSE formulation treat the peak responses from the modal analysis to be independent from each other while the CQC tries to find some correlations/cancellations between the mode shapes. For future reference, CQC can be more accurate with the application of more mode shapes to increase the ratio of the effective mass to the total mass and with the right damping application since the coefficient in the CQC can be greatly affected by these variables.
Thus, this type of simulation can be applied to real-life applications of bridges, allowing behaviour analysis during seismic dynamic load application. With more computer expense, more mode shapes can be obtained with more accurate results than can be extracted from the simulation itself. But if the computer expense is enough to do a full transient structural simulation, it is recommended to do so as it does not require any dependency on any formulations for the seismic response application because the RSA simulation gives a shortcut by only applying the peak responses of each mode based on the spectrum while in transient simulation, you are actually applying earthquake motion to capture how the structure behaves during these conditions.
REFERENCES
[1] Brown, B. 2025. What Is A Suspension Bridge? B2: Bill Brown’s Bridges. [Online]. [Accessed 21 February 2025]. Available from: https://b2.co.uk/what-is-a-suspension-bridge/.
[2] Engineering Infinity 2024. 7 Main Types Of Bridges. [Accessed 12 March 2025]. Available from: https://engineeringinfinity.com/7-main-types-of-bridges/.
[3] ideCAD 2024. Modal Response Spectrum Analysis per ASCE 7-16 §12.9.1. [Accessed 5 March 2025]. Available from: https://help.idecad.com/ideCAD/12-9-1-modal-response-spectrum-analysis.
[4] RISA, R. 2020. RISA | Improving Mass Participation in RISA-3D. [Accessed 4 March 2025]. Available from: https://blog.risa.com/post/improving-mass-participation-in-risa-3d.
[5] Setiawan, B. 2013. Banda Aceh-Indonesia Ground Response Analysis During the 2004 Indian Ocean Mega Earthquake. International Conference on Case Histories in Geotechnical Engineering.
