In our exploration of seismic isolation in bridge design, we've covered the importance of seismic forces and detailed the loading and seismic design parameters critical to understanding bridge behavior under seismic activity. This post dives into the seismic analysis of a typical continuous bridge using conventional bearing systems, including fixed and free bearings, to highlight the challenges and solutions inherent in traditional seismic design approaches.
For a background on this study review Post #1 here.
Understanding Bearing Systems in Bridge Design
Bridges are dynamic structures that must accommodate movement while maintaining structural integrity. Bearings play a crucial role in this balance, allowing for controlled movement due to thermal expansion, traffic loads, and seismic forces. In the context of seismic design, bearings determine how seismic forces are transferred from the superstructure to the substructure and, ultimately, to the foundation.
Fixed Bearings: Typically located at one or more piers, fixed bearings restrict movement in all directions (lateral and vertical), transferring both vertical loads and lateral seismic forces to the supporting piers.
Free Bearings: These bearings allow for movement in one (guided) or both directions (multidirectional), accommodating thermal expansion and contraction while limiting the transfer of seismic forces to the substructure.
Seismic Analysis Approach
The case study employs a dual approach to seismic analysis, utilizing both manual calculations and analysis using MIDAS Civil software. This comprehensive analysis aims to understand how different bearing configurations affect the bridge's response to seismic forces.
Manual Calculations: Employing the seismic coefficient method as per IRC:SP:114, manual calculations provide initial insights into the expected seismic forces acting on the bridge. This method simplifies the seismic analysis by applying a coefficient to the static loads, estimating the base shear force that the bridge piers must withstand. Figures 1 and 2 summarize the manual calculations for the seismic horizontal coefficients in the longitudinal and transverse directions, respectively.
Seismic Analysis: The analysis on MIDAS Civil offers a greater accuracy through 3D space frame modeling, allowing for a dynamic response analysis that considers the bridge's natural frequencies and mode shapes. This method provides a deeper understanding of how seismic forces are distributed across the structure. Figures 3 to 6 illustrate the shear and flexural demands in the bridge piers, in the longitudinal and transverse directions respectively.
Results and Observations
The seismic analysis yields valuable data on shear forces, bending moments, and the overall seismic performance of the bridge with conventional bearing systems.
Shear Force and Bending Moment Diagrams: Figures 3 to 6 (Figure 6 to 9 from the original paper) illustrate the distribution of shear forces and bending moments along the bridge for both longitudinal and transverse seismic cases. These diagrams highlight the critical areas where seismic forces concentrate, informing the design and reinforcement strategies.
Comparison of Seismic Analysis vs. Manual Calculations: The study finds a close match between the manual calculations and MIDAS seismic analysis results in the longitudinal direction, validating the assumptions and simplifications made during the analysis. However, discrepancies in the transverse direction underscore the importance of considering the superstructure's stiffness in the seismic response, an aspect that manual calculations may oversimplify.
Figures 7 and 8 respectively display the comparison of base shear in the transverse direction obtained from seismic analysis and manual calculations. Figure 7 corresponds to R=1 (no ductile detailing) and Figure 8 corresponds to R=3 (where ductile detailing is done).
Significance of Findings
The analysis underscores several key points relevant to the seismic design of bridges with conventional bearings:
Force Distribution: The choice of bearing system significantly influences how seismic forces are distributed across the bridge. Fixed bearings, while providing stability, may concentrate forces at specific piers, necessitating robust design and reinforcement.
Seismic Demands: The comparison of analysis methods reveals the complex nature of seismic forces, particularly in the transverse direction, where the interaction between superstructure stiffness and seismic inputs becomes critical.
Design Implications: Understanding the seismic performance of fixed and free bearing systems is crucial for designing bridges that are not only safe but also cost-effective. The analysis highlights the need for a nuanced approach to bearing selection, considering both seismic and non-seismic loads.
Conclusion
This post has illustrated the complexities and considerations of performing seismic analysis on bridges using conventional bearing systems. By comparing different methodologies and analyzing the results, we gain insights into the challenges of designing bridges to withstand seismic forces. As we move forward in our series, we'll explore how seismic isolation techniques, such as friction pendulum bearings, offer innovative solutions to these challenges, potentially enhancing the seismic resilience of bridge designs.
This series is brought to you by Varun Garg, based on a paper he co-authored with Mr. Rajiv Ahuja for the Structural Engineering Digest, Quarterly Journal for the Indian Association of Structural Engineers in March 2021. The paper can be downloaded by clicking the link below.