Journal of Structural Engineering

An innovative composite column, which consists of a high strength concrete (HSC) core, engineered cementitious composites (ECC) ring, and fiber-reinforced polymer (FRP) tube, has recently been developed and subjected to monotonic axial compression testing by the authors. In this study, the cyclic compressive behavior of this proposed FRP-ECC-HSC composite column was examined. Test parameters, including HSC core strength, FRP tube thickness, and ECC ring thickness, were investigated. Typical failure modes, dilation behavior, and axial load versus axial strain behavior were discussed and analyzed. It was found that the FRP-ECC-HSC composite columns exhibited improved deformability, compared with the counterpart traditional FRP-confined HSC columns, with the ultimate axial compressive strain increased by 0.7%–69.1% for the tested specimens. Meanwhile, the ultimate axial strain for cyclically loaded specimens is larger than that for monotonically loaded specimens in general, indicating a delayed column failure. Cyclic axial load-axial strain models, including the envelope model, unloading and reloading models, plastic strain equation, and stress deterioration equation, were proposed to predict the cyclic compressive behavior of the tested specimens. The proposed model was verified with the test results and exhibited good performance.

A widespread problem in regions of low to moderate seismicity is the failure of buildings with soft-story collapse mechanisms. A reliable approach to improve the design of such buildings is to use concrete-filled steel tube (CFT) columns to form a ‘ductile’ soft story to arrest damage at the first level. This can perform as an isolator to limit the damage and prevent it from spreading to the rest of the building. In this paper, the multiaxis hybrid simulation method is used to evaluate the three-dimensional response of CFT columns while they serve as part of a building developing ductile soft first story mechanism. For this purpose, the multiaxis substructure testing (MAST) system at Swinburne University of Technology was utilized to simulate realistically the time-varying multi-directional boundary forces generated by ground motions on the CFT columns. The circular and square cross-section shapes as the most popular type of CFTs were tested and the damage progression, global hysteretic behavior, and deteriorating mechanisms were studied. The obtained data were then used to conduct a fragility analysis to compute the risk of collapse. The results highlight the excellent performance of CFTs and their potential to construct low-damage collapse resistant buildings.

Despite the growing interest in the concept of topology optimization, its acceptance in civil structures, especially in prestressed concrete structures, is still faced with practical obstacles primarily due to the geometric complexities of optimized structures. Quite often, complex concrete topology yields a complex distribution of tensile zones, which are hard to be effectively prestressed with continuous steel reinforcement. Shape memory alloys (SMAs), with their ability to apply localized prestressing force only at target tensile regions, can offer solutions to the issues facing conventional prestressing steel reinforcement in topology-optimized concrete structures. This paper investigates the topology optimization of prestressed concrete bridge girders using locally prestressed SMAs. A prototype continuous concrete bridge is selected to be optimized under the AASHTO loading conditions. To prove the feasibility of the optimized design, a detailed 3D finite element analysis is performed. The performance of the optimized girder is compared with that of two commonly used conventional designs. The results show that the optimized design can effectively satisfy the AASHTO limit state with less material than the conventional cases.

Concrete-filled thin-walled helical corrugated steel tubes (CFCST) are innovative composite members suitable for rehabilitating or reconstructing piers/columns under earthquake or long-term corrosion damage. The strength and ductility of the concrete can be effectively improved by the lateral confinement of the thin-walled corrugated steel tube (CST). However, for such a member, the previously proposed monotonic model is not applicable to large helical angles, and no existing cyclic model can be directly employed. Hence, some key indicators, including the nominal hoop stress, equivalent confining stress, peak stress, peak strain, plastic strain, and stress deterioration, are examined based on an enlarged experimental database and the working mechanism of CFCST. Subsequently, a systematic constitutive model with an updated monotonic stress–strain relationship and rational unloading/reloading rules was developed for the CST-confined concrete in this study. The accuracy of the proposed model was validated by the experimental results of both the monotonic and cyclic responses of CST-confined concrete specimens.

With the increasing demand for vertical isolation in the engineering field, the compressive behavior of low–shape factor (LSF) lead-rubber bearings (LRBs) needs to be further explored. However, the conventional simulation method of lead boundary conditions cannot accurately capture the actual compressive behavior of LSF bearings. Some scientific literature has reported this, but there is a lack of detailed studies to explain it. By comparing the experimental data and numerical simulation results of LSF bearings, the problem of this research is put forward. Thus, a refined numerical simulation method of lead boundary conditions is proposed in this paper based on the manufacturing process of LRBs. Assumed contact types, friction coefficients, and filling ratios of the lead plug are considered as variables of lead boundary conditions. The first shape factor and lead plug diameter are considered bearings variables. The compressive behavior of LRBs, including stiffness, deformation, and stress–strain distribution, are discussed through detailed analysis. The main study results indicate that contact types and filling ratios of lead plugs have a significant influence on the compressive behavior of LSF bearings, and the friction coefficient is negligible. The proposed refined simulation method is capable of capturing LRBs’ mechanical behavior with better accuracy than the conventional model under different stresses, especially LSF bearings. However, the conventional numerical modeling method is recommended for LRBs with high shape factors (e.g., 30–50). Finally, an empirical formula is established based on refined simulation results.

The design of footbridges has begun to receive more attention in recent years due to cases in which undesirable vibrations occurred. The utilization of passive energy dissipation systems to control bridge responses has become popular as a remedy for this matter. This paper proposes the use of inerters to mitigate pedestrian bridge vibrations, and explores their potential. This is done by presenting a topology and sizing optimization methodology for pedestrian bridges equipped with fluid viscous dampers and inerters. Planar truss-like bridges are examined, loaded under dynamic and static loads. All constructive elements’ sizes (including dampers) serve as continuous design variables. The objective is to minimize a cost function of the bridge. The optimization process is constrained by demanding responses of interest not to exceed allowable values, along with global and local buckling. A first-order gradient-based optimization algorithm is adopted to lessen the computational effort. Lastly, a discretization postprocess is offered to lead to discrete designs of relevant design variables, such as steel cross sections. The results shed light on the advantages of combining inerters in pedestrian bridges.

Self-centering piston-based braced frames (SC-PBBFs) are such structural assemblies that can withstand a severe earthquake through passive control. The self-centering motion of the bracing system curtails the seismic permanent damage of a building, thereby considerably mitigating postearthquake repair costs and downtime. This paper proposes a novel hybrid self-centering piston-based bracing (SC-PBB) equipped with friction springs (FS) and superelastic shape-memory alloy (SMA) bars. Analytical formulas are presented for rapid analysis and preliminary seismic design of the SC-PBBFs fitted with SC-PBBs. The general mechanics of the proposed archetypes confirms their symmetric self-centering behavior. To validate the proposed design procedure, a set of SC-PBBFs fitted with tension-only SMA bars and precompressed FS is examined under far-field ground motions. Effects of prestressing of components and earthquake types (crustal, subcrustal, and subduction) are quantified and compared with the responses of buckling-restrained braced frames (BRBFs). The analysis outcomes revealed the effectiveness of the proposed hybrid SC-PBBF subjected to design-level earthquakes.

The Canterbury earthquake royal commission report highlighted that, despite being well-detailed, several reinforced concrete (RC) shear walls did not achieve their anticipated ductility capacities. In order to enhance the performance of such walls during future seismic events, the report recommended the use of concentrated and confined rebars at the wall toes coupled with high reinforcement ratios within the wall to initiate secondary cracks and extend the inelastic wall regions, thus minimizing the corresponding seismic demands. In this respect, the current study evaluates the seismic performance of RC walls with flanged and boundary element configurations compared with their typical rectangular counterparts, when different reinforcement ratios are incorporated. Specifically, the study presents a detailed analysis of six three-story half-scaled RC shear walls tested under quasi-static cyclic loading representing different seismic demands. The six walls were originally tested in two phases, where each phase had three different wall types (i.e., rectangular, flanged, and boundary element configurations). Walls in both phases had the same overall dimension and cross-section area; however, Phase II walls had 2.4 times the vertical reinforcement ratios used in Phase I walls. Following a summary of the experimental program and results, the current study presents the analytical results of the walls in terms of their load-strain relationships, curvature profiles, stiffness degradation trends, energy dissipation capacities, and equivalent viscous damping ratios. A comparison between the theoretical and experimental curvatures is also presented for the test walls at different drift levels. The results show that flanged and boundary element walls had low yield curvatures and high ultimate curvatures which resulted in enhancing their displacement ductility capacities. Flanged and boundary element walls also exhibited higher stiffness degradation rates when compared with their rectangular counterparts, leading to reduced seismic demands. Moreover, flanged and boundary element walls with high vertical reinforcement ratios ($1.58\%–1.63\%$) had higher energy dissipation capacities than their counterparts with low vertical reinforcement ratios ($0.66\%–0.69\%$). However, rectangular walls with low vertical reinforcement ratios (1.17%) showed higher ultimate curvature capacities than rectangular walls with high vertical reinforcement ratios (2.80%). Overall, the results demonstrate that future editions of relevant design standards (e.g., CSA A23.3 and ACI 318-19) should consider assigning different seismic design parameters (e.g., ultimate compressive strains, equivalent viscous damping ratios, and ductility-related modification factors) for RC shear walls based on their end configurations that can significantly alter the performance of such walls under seismic events.

A mass timber lateral force resisting system (LFRS) is proposed using a mass timber buckling restrained brace (TBRB) to improve the seismic resilience of mass timber buildings. To develop a resilient braced frame, it is essential to understand and quantify the behavior of the connections, including the possible failure modes and moment-rotation capacities. Cyclic and monotonic tests were conducted on six mass timber beam-column connections to study the response of a mass timber joint connected with slotted-in steel plates and mild steel dowels. The primary goal of the subassembly tests was to measure the maximum rotation, stiffness, ductility, and failure modes of such connections for both monotonic and cyclic loads. The tests showed that the connections with three steel dowel details reached a maximum rotation of 0.11 radians (6.3 degrees) with no loss of strength. In addition, a numerical model was developed to represent the moment-rotation relationship of the mass timber beam-column connections.

Links in eccentrically braced frames (EBFs) are designed with transverse web stiffeners to achieve the desired seismic performance targets established in current design standards. Prior studies have suggested that stiffener spacing requirements in the standards may be conservative. This paper proposes new stiffener spacing design requirements for short EBF links. The proposed limits were established on the basis of a methodology that combines a numerical solution of the classical problem of inelastic plate buckling of a thick plate under shear thrusts along with comparisons with available experimental data. The resultant design equation was verified through complementary continuum finite-element simulations of 18 wide-flange short links under symmetric cyclic loading. The finite-element simulations suggested that the proposed design equation reduce the stiffener requirements by about 35%, on average, relative to the current stiffener spacing requirements for short EBF links. Limitations and suggestions of future work are discussed.

The main objective of this study was to develop an analytical model for predicting the diaphragm deflection and the induced shear force at the panel joints when the applied load is perpendicular to the panel length. An equivalent finite-element model was developed to capture the elastic behavior of the diaphragm made from the panels and the connections in between. The analytical model’s predictions were compared with predictions from finite-element models. The results of an experimental test were used to partially validate the analytical and numerical models in the absence of full-scale diaphragm test data. A sensitivity analysis was carried out with the aim of finding the most influential parameters in the behavior of the cross-laminated timber (CLT) diaphragm. The connection’s stiffness and diaphragm size were varied. The difference in diaphragm deflection was investigated, and it was found that under realistic material properties and geometry, the diaphragm deflection was not strongly related to the connection’s stiffness. However, the floor’s geometry was the key influencing parameter. A parametric study was performed, and the contribution of each deflection component was quantified for each specific case. It was observed that the floor’s flexibility was dominated mainly by the shear deflection of the cross-laminated timber panels as well as the slip in the panel joints as the length of the diaphragm increased. This study proposes a method that designers may use to estimate the in-plane displacement of the cross-laminated timber diaphragm when it is loaded perpendicular to the panel’s length.

In this paper, the seismic design factors for uncoupled composite plate shear walls/concrete filled (C-PSW/CF), a.k.a. SpeedCore, are verified by conducting a study using FEMA methodology. These are the seismic response modification factor, R, the deflection amplification factor, Cd, and the overstrength factor, Ωo; and their values for C-PSW/CF are specified as 6.5, 5.5, and 2.5, respectively. A study was needed, as these factors for uncoupled C-PSW/CFs, included in ASCE 7 since as far back as its 2000 edition, were chosen solely based on the seismic performance of similar structural systems and engineering judgment of the committee members. For this study, four archetypes with planar walls and three archetypes with C-shaped C-PSW/CF walls were chosen. Two different damage measures (DM) were chosen for this study; namely, 3% and 5% maximum interstory drifts. Based on FEMA methodology, all archetypes satisfied the specified performance requirement considering a “good” rating for total system collapse uncertainty (βTOT).

A new precast concrete (PC) shear wall system with diagonal-shaped or cross-shaped concealed bracing was developed and experimentally validated, owning sufficient energy-dissipation capacity, in a previous study. Given that the seismic performance of such precast braced concrete shear (PBCS) walls is not comprehensively understood, this paper numerically investigates the influences of axial load ratio (ALR) and various reinforcement ratios (RRs) on the mechanical behavior of PBCS walls under cyclic loading. For this purpose, the numerical models based on the layered-shell element are developed to analyze the PBCS walls and validated regarding the deformation capacity of experimental results. A total of 156 PBCS wall models with different ALRs, longitudinal RRs of the boundary columns and bracing, and horizontal and vertical web RRs are established and tested under cyclic loading. It is concluded that the effects of bracing RR and horizontal web RR on the hysteretic responses are negligible and thus can be designed as the minimum suggested by the codes. However, the ALR, boundary column RR, and vertical web RR can significantly affect the lateral bearing capacity and displacement ductility of PBCS walls. In addition, the ALR limits for both types of PBCS walls are presented to satisfy the ductility requirements. Moreover, the simplified formulations regarding the bearing capacity and ductility of PBCS walls are proposed, respectively, which show good agreement with the numerical results. The outcomes of this research not only provide an in-depth understanding on the seismic behavior of the PBCS walls, but also promote the design code expansion and potential engineering application of such new types of PC shear walls.

A framework to assess the fracture fragility of partial joint penetration (PJP) welded column splices in steel moment frames constructed before the 1994 Northridge earthquake is presented. These pre-Northridge splices feature low flange penetration of the PJP welds, and low-toughness weld materials, such that they are considered susceptible to fracture with possible catastrophic consequences. Estimating their fracture risk is especially important, given that retrofitting them is highly disruptive to building operations. The presented framework addresses shortcomings of previous research and performance assessment guidance that does not consider key mechanistic or statistical effects. To accomplish this, three-dimensional fracture mechanics finite-element simulations are conducted to assess fracture toughness demands. These demands are then interpreted through a master curve–based approach that rigorously considers spatial randomness and weakest-link sampling of weld toughness properties, along with the uncertainty in estimation of these properties. The framework is implemented in a tool which automates the entire process, facilitating application in a professional setting. The tool (and the underlying framework) is demonstrated on a range of splice configurations to examine the effects of configuration, loading, and material parameters. Limitations are outlined.

Abstract

A new type of inerter, called a crank train inerter (CTI), is investigated for structural vibration isolation. The CTI consists of a crank, a linking rod, a gear-pinion box, and a flywheel that generates inertance. It has advantages of quick adjustment of inertance and strong adaptability to other disturbances. First, the inertial force provided by the CTI is linearized and expressed in a simple format; the minimum length of linking rod and crank are obtained for a CTI operating linearly under various deformed configurations. Then, the motion equation of the coupled structure-CTI system is formulated, and transmissibility is analyzed. Laboratory experiments are next carried out to verify the CTI’s mechanical property and vibration isolation performance. It is shown that the inertance of the CTI obtained in the tests agrees well with the analytical result. CTIs can significantly decrease the amplitude-frequency responses at the fundamental frequency but cannot achieve vibration isolation in a full frequency range. Finally, the seismic control effect of base-isolated buildings with and without CTI is numerically studied. An optimal design method of the CTI is proposed, and the story drift ratio and deformation of the isolation layer can be reduced simultaneously with the optimal inertance. The installation methods of CTIs for buildings are also presented.

Practical Applications

A crank train inerter is a kind of vibration isolator with simple structure and low cost. Compared with the traditional rack-and-pinion inerters and ball screw inerters, crank train inerters have the advantages of adjustable inertance and strong adaptability to other disturbances. In this paper, the inertance and linear condition (crank train inerters can be treated as linear inerters) of crank train inerters are obtained through theoretical derivation, and a series of experimental studies are carried out. The experimental results verify the easily adjustable inertance of crank train inerters and their strong adaptability to other disturbances, and also verify the reliability and practicality of its application in vibration isolation system. Crank train inerters can be used as a new implementation of inerter for vibration isolation of building structures, bridge structures, ships, machinery, or vehicles. In addition, crank train inerters can also be combined with a spring and dashpot to form tuned inerter dampers or tuned viscous mass dampers as vibration isolators or shock absorbers. The geometric nonlinearity of crank train inerters for large deformation and the vibration control effect of the integrated device with both a crank train inerter and other elements need further research.

Understanding the seismic resistance mechanisms and safety limits of cross-laminated timber (CLT) buildings and performing an accurate evaluation of their seismic performance is critical in earthquake-prone areas such as Japan, the US, and Italy to ensure that human lives are protected against major earthquakes. However, the knowledge from shaking table tests of full-scale CLT buildings is limited, and most tests’ maximum interstory drift is less than 4%. As a first step toward collapse analysis, this study replicated a full-scale two-story shake table experiment with a maximum interstory drift of 8.77%. The analysis software was developed by the authors and modified to consider the restoring force and the $P–\delta$ effect to replicate seismic behavior at large deformation. The skeleton curve parameters were employed in the analysis model and then changed. The results that matched the experimental results well were searched comprehensively by performing data assimilation. As a result, both the overall behavior (story shear force–interstory drift relationship) and the detailed behavior (uplift displacement of CLT wall foot of the first story) were consistent with the experimental results, indicating that the proposed analytical method can replicate the seismic behavior of CLT buildings even at large deformation.

Directly welded truss girder joints result in high-stress development on the tube wall, which leads to increased chord thicknesses, requires extra welding, and presents detailing difficulties. Laser cutting technology (LCT) allows us to make precise cuts and pass through the truss members, welding the connection on the two sides. This can reduce geometrical imperfections, and, as a result, it increases joint strength. This paper presents truss girder joints developed with LCT that can develop higher resistance to static gravity loads with respect to conventional connections thanks to the pass-through solution. An extensive experimental campaign (31 specimens) has been carried out involving the monotonic gravity loading of several truss specimens to simulate their in-service conditions. Different truss typologies are tested (Warren and Pratt) using circular and square hollow section profiles, at different scales (full-scale and small-scale). The results showed that Warren-type structures with LCT connection solutions had a 20% higher strength with respect to the equivalent structures with directly welded joints. Furthermore, the correlation between the different failure modes and joint parameters (e.g., angles and distance between brace members) has been discussed.

Most research on circular hollow section (CHS) flange-plate connections deals with axial tension loading, yet bending action is a common load case. Prior researchers have studied both ring and blank-flange-plate connections, using a four-point-bending setup, generating a database of 10 experimental tests and five numerical models on bolted blank-flange-plate connections under pure bending. This limited data is extended herein by two large-scale laboratory tests with blank-flange-plate connections having a large span-to-tube diameter ratio, and 120 numerical models. Flange-plate plastification and bolt fracture are the valid failure modes for this splice, so all data was meticulously assessed to exclude experimental tests or numerical models not governed by connection failure. Existing design models for calculating the connection capacity under pure bending are evaluated and revised. Moreover, based on rectangular flange-plate connections, a novel method is proposed to design its circular counterpart under pure bending. For all methods, the difference in using the ultimate stress for flange-plate moment capacity—instead of the conventional yield stress—is also analyzed. Lastly, a reliability analysis is conducted to support the proposed design method.

The paper presents the results of an experimental investigation of the behavior of RC interfaces subjected to cyclically imposed shear slips. Several parameters are examined, namely, the embedment length of the interface reinforcement (consisting of reinforcing bars), the diameter of bars and the percentage of reinforcement, as well as the loading history imposed on the interfaces. The experimental results have shown that embedment lengths smaller than the development length of bars lead to unfavorable failure modes, as well as to small interface resistance. Independently of the values of the examined parameters, cycling of shear slips led to significant force response degradation during the third cycle, at least equal to 40%, as compared to the response of the first cycle. This is a typical feature that should be adequately taken into account in the design of interfaces expected to be subjected to cyclic deformations.

The paper reports on the computation of the hydrodynamic loads on a full-scale caisson at high Reynolds number in the presence of vortex shedding. The objective was to obtain reliable predictions of the resulting mean and fluctuating forces to guide the design of an actual caisson in the absence of relevant experimental data. A further objective was to investigate the effectiveness of alternative methods for the control of vortex shedding that can be implemented in practice. Two such methods were evaluated: (1) by rounding the corners of the rectangular-sectioned caisson, and (2) by the placement of a splitter plate in the separated wake region. The computations, which were performed using the OpenFOAM open-source software, were for a fixed caisson and hence did not account for motions due to vortex-induced vibrations. The effects of turbulence were accounted for by performing large-eddy simulations, and by using two-equation eddy-viscosity closures, one of which was specifically adapted to account for the interactions between the periodic vortex shedding and the random turbulence. The numerical accuracy was checked using the grid convergence index method, and the computations were extensively validated against data from relevant benchmark flows. The recommendations of this research were implemented in the design of a full-scale caisson that has since been deployed in a bridge construction project.

Connection details are critical for both seismic performance and constructability of underground precast concrete (PC) shear wall systems. Current traditional wall-to-wall shear connection details present considerable constructability issues. To address this issue, application of cast-in-place (CIP) connecting beams (i.e., cap and waling beams) at the top and midheight of a precast shear wall system was studied. Under the capacity design concept specified in current standards, three test specimens were designed and tested under the reversed cyclic loadings. Of the three, two employed CIP connecting beams. The third, which served as the reference specimen, adopted the traditional ductile connection detail of embedded wire loops. In addition, numerical simulations and corresponding reverse analyses were conducted to identify the effect of wall-to-wall shear connection details on seismic performance of the precast shear wall systems. Although excellent seismic performance can be achieved by using traditional shear connection, satisfactory seismic performance may also be achieved with proper integration of only CIP beams.

The Bayesian model updating approach has attracted much attention by providing the most probable values (MPVs) of physical parameters and their uncertainties. However, the Bayesian approach has challenges in high-dimensional problems and requires high computational costs in large-scale engineering structures dealing with structural dynamics. This study proposes a new Bayesian updating framework using the Differential Evolution Adaptive Metropolis (DREAM) algorithm to enhance the Bayesian approach’s performance and computational efficiency. In addition, two time-saving strategies are proposed. Firstly, variance-based global sensitivity analysis is used to eliminate insignificant parameters to model responses and reduce model dimensionality. Secondly, a fast-running kriging model is employed as a surrogate of the time-consuming finite-element (FE) model to alleviate the computational burden. DREAM essentially is a multichain sampling method that runs different paths to seek all possible solutions and accurately approximate the posterior probability distribution function in the Bayesian approach. The proposed updating framework was demonstrated using one numerical example and a real-world cable-stayed pedestrian bridge. The results showed that the proposed method enables rationally identifying structural parameters and recovering dynamic responses. Compared with the traditional Bayesian approach without a surrogate model, the computational cost is orders of magnitude lower.

Seismic behavior and performance of the new Self- Anchored Suspension (SAS) Bridge of the San Francisco Bay Bridge System is studied using response data recorded during the October 14, 2019, $M_{w}4.6$ Pleasant Hill earthquake. The new bridge went into service within the last decade as a replacement for the older truss bridge that spanned between Yerba Buena Island and East Bay. During the October 19, 1989, M6.9 Loma Prieta earthquake, which occurred $\sim 100\mathrm{km}$ away from the Bay Bridge, a section of the upper deck of the old truss bridge fell onto the lower deck—thus closing this important lifeline between San Francisco and East Bay. The new SAS Bridge (as well as the rest of the Bay Bridge) is instrumented by the California Strong Motion Instrumentation Program (CSMIP). The unique SAS Bridge is suspended by a single tower that is pivotal in trafficking the cable and hanger system to support the eastbound (E) and westbound (W) decks. At both the west and east ends of the SAS, there is a hinge system that connects the W and E decks to the skyways leading to highways. For the west side, the SAS is led to a tunnel at Yerba Buena Island. The response data analyses highlight the complex and yet identifiable coupled response of the deck, tower, and cable system. Using system identification methods including spectral analyses of both acceleration and displacement time history data, the fundamental frequencies (periods) and critical damping percentages are extracted for the main components (tower, deck, and cables) of the bridge where the sensors are deployed. Frequencies (periods) are then compared with the values computed during the design and analysis process of the bridge. The analyses in this paper showed that there is strong evidence of a beating effect attributed to low critical damping percentages and coupled modes. A possible correlation of fundamental periods of such suspension bridges with their span lengths is discussed. The beating effect and period versus span length can be significant topics for further research.