On Internal Resonance Analysis of a Double-Cable-Stayed Shallow-Arch Model with Elastic Supports at Both Ends

In previous research on the nonlinear dynamics of cable-stayed bridges, boundary conditions were not properly modeled in the modeling. In order to obtain the nonlinear dynamics of cable-stayed bridges more accurately, a double-cable-stayed shallow-arch model with elastic supports at both ends and the initial configuration of bridge deck included in the modeling is developed in this study. The in-plane eigenvalue problems of the model are solved by dividing the shallow arch (SA) into three partitions according to the number of cables and the piecewise functions are taken as trial functions of the SA. Then, the in-plane one-to-one-to-one internal resonance among the global mode and the local modes (two cables\u27 modes) is investigated when external primary resonance occurs. The ordinary differential equations (ODEs) are obtained by Galerkin\u27s method and solved by the method of multiple time scales. The stable equilibrium solutions of modulation equations are obtained by using the Newton-Raphson method. In addition, the frequency-/force-response curves under different vertical stiffness are provided to study the nonlinear dynamic behaviors of the elastically supported model. To validate the theoretical analyses, the Runge-Kutta method is applied to obtain the numerical solutions. Finally, some interesting conclusions are drawn

Revealing Bluff-Body Aerodynamics on Low-Rise Buildings under Tornadic Winds using Numerical Laboratory Tornado Simulator

Tornadoes result in death and property loss in communities around the world. To quantify the actions of tornadoes on civil structures, researchers have built physical laboratory tornado simulators to simulate tornadoes in the lab environment and tested building models in the simulated tornadic wind field, which is similar to wind tunnel testing when quantifying the wind effects induced by straight-line winds. Unfortunately, physical tornado simulators are much less common than straight-line wind tunnels, leading to the lack of research on bluff-body aerodynamics on civil structures under tornadic winds. Considering that it is expensive to conduct experimental testing in physical tornado simulators, numerical models of physical tornado simulator has been developed using computational fluid dynamics (CFD) simulations. However, they have not been validated at the level of pressure distribution on the structural surface of the testing model. In this study, the numerical model developed for the large-scale tornado simulator of the Missouri University of Science and Technology (Missouri S&T), which is based on the numerical simulation of the entire process of the physical testing in tornado simulator, will be validated by the measured data on the building model tested in the physical tornado simulator. Then, through the validated numerical simulation model, the bluff-body aerodynamics of buildings under tornadic winds will be revealed. To be specific, CFD simulation is first applied to model the entire process of experimental testing of a low-rise building model in the physical tornado simulator. Then, the obtained results are compared with laboratory-measured data to evaluate the effects of the building model on the wind field and the surface pressure on the building model. Then, the bluff-body aerodynamics on low-rise buildings under tornadic winds will be revealed based on the data obtained from numerical simulations using the relationship between streamline pattern change and velocity magnitude change (mass continuity theorem) and using the relationship between the velocity magnitude change and the pressure change (Bernoulli\u27s theorem), as well as the flow separation and vortex shedding

Quantifying The Role Of Insurance In Tornado-Impacted Community Recovery: A Survey And Simulation-Based Approach

Insurance against disasters plays a critical role in community recovery by providing policyholders with reliable and timely payments for repairing or reconstructing damaged houses. By allowing homeowners to transfer risk, insurance enables homeowners to address house without experiencing significant financial burdens. Although historical events have highlighted the importance of insurance, its quantitative impact on community recovery, particularly in tornado-impacted communities, is understudied. This study focuses on advancing our understanding of whether sufficiently insured houses can have a positive impact on the recovery of tornado-impacted communities (i.e., the main research question). This paper proposes a two-stage simulation framework to quantitatively evaluate the effects of insurance on community recovery. In the first stage of the framework, we developed statistical models to estimate homeowners\u27 insurance decisions prior to a tornado event. In the second stage, we examined the effects of insurance on various aspects of community recovery. To develop empirical and statistical models regarding insurance decisions and their impacts on housing recovery, we collected data through online surveys targeting residents whose properties were damaged by the tornadoes that occurred in May 2019 in the United States. Finally, the proposed simulation framework was applied to the City of Dayton, Ohio following those May 2019 tornado events to address the main research question. The results of the simulation concluded that sufficiently insured houses can have a positive impact on community recovery and highlighted the need for effective policies and economic incentives to encourage individuals to purchase insurance

Resonance Analysis between Deck and Cables in Cable-Stayed Bridges with Coupling Effect of Adjacent Cables Considered

The nonlinear dynamic model of a shallow arch with multiple cables is developed to model a long-span cable-stayed bridge. Based on the veering phenomenon of cable-stayed bridges, the in-plane modal internal resonance between the first mode of the shallow arch and the first mode of the cable is investigated under both primary resonance and subharmonic resonance. Modulation equations of the dynamic system are obtained by Galerkin discretization and the multiple scales method, in which the equilibrium solution of modulation equations is obtained by the Newton–Raphson method. Meanwhile, the Runge–Kutta method is applied to directly solve the ordinary differential equations to verify the accuracy of the perturbation analysis. Numerical analysis shows that the internal resonance occurs in adjacent cables; the energy transfer mechanism and the dynamic behavior of system become more complex

Wind Effects on Dome Structures and Evaluation of CFD Simulations through Wind Tunnel Testing

In the Study, a Series of Wind Tunnel Tests Were Conducted to Investigate Wind Effects Acting on Dome Structures (1/60 Scale) Induced by Straight-Line Winds at a Reynolds Number in the Order of 106. Computational Fluid Dynamics (CFD) Simulations Were Performed as Well, Including a Large Eddy Simulation (LES) and Reynolds-Averaged Navier–Stokes (RANS) Simulation, and their Performances Were Validated by a Comparison with the Wind Tunnel Testing Data. It is Concluded that Wind Loads Generally Increase with Upstream Wind Velocities, and They Are Reduced over Suburban Terrain Due to Ground Friction. the Maximum Positive Pressure Normally Occurs Near the Base of the Dome on the Windward Side Caused by the Stagnation Area and Divergence of Streamlines. the Minimum Suction Pressure Occurs at the Apex of the Dome Because of the Blockage of the Dome and Convergence of Streamlines. Suction Force is the Most Significant among All Wind Loads, and Special Attention Should Be Paid to the Roof Design for Proper Wind Resistance. Numerical Simulations Also Indicate that LES Results Match Better with the Wind Tunnel Testing in Terms of the Distribution Pattern of the Mean Pressure Coefficient on the Dome Surface and Total Suction Force. the Mean and Root-Mean-Square Errors of the Meridian Pressure Coefficient Associated with the LES Are About 60% Less Than Those Associated with RANS Results, and the Error of Suction Force is About 40–70% Less. Moreover, the LES is More Accurate in Predicting the Location of Boundary Layer Separation and Reproducing the Complex Flow Field Behind the Dome, and is Superior in Simulating Vortex Structures Around the Dome to Further Understand the Unsteadiness and Dynamics in the Flow Field

Application of Multidisciplinary Community Resilience Modeling to Reduce Disaster Risk: Building Back Better

From december 10 to december 11, 2021, a deadly tornado outbreak struck across several states in the us, including arkansas, illinois, kentucky, and tennessee. This tornado outbreak resulted in at least $3.9 Billion in damage, more than 90 fatalities, and hundreds of injuries. Mayfield, kentucky, a small city in the eastern united states, was hit by a long-track tornado rated as an enhanced fujita 4 (ef4) scale and was one of the communities most heavily damaged during the tornado outbreak. Following the 2021 tornado event, an analysis was performed in the interdependent networked community resilience modeling environment (in-core) for the city of mayfield to investigate a design code change for residential structures and its effect on communitywide metrics related to functionality and dislocation. Specifically, the in-core modeling environment was used to hindcast the community-level building damage and forecast the community-level building recovery in mayfield for residential buildings. This required the development of a mayfield test bed for in-core with a focus on buildings. The generalization of multidisciplinary community resilience modeling from a test bed community to a real community impacted by a recent major tornado event is intended to benchmark that in-core has a strong potential and capability to forecast/hindcast community resilience and provide what-if scenarios for decision makers, city planners, and stakeholders in communities with similar sizes

Investigation of Structural Failure Modes Induced by Tornadoes through Post-Event Surveys

Tornadoes are violent, short-lived wind phenomenon that can result in catastrophic damage to homes and property. Often times, the occurrence of tornadoes is unpredictable and emergency alerts offer short notice. This leads to families and individuals taking shelter in their own homes or nearby buildings that may not have safe rooms available. The failure of buildings may endanger people\u27s lives. As such, it is imperative to investigate the failure modes of civil structures under tornadoes in order to properly design tornado-resistant buildings. In this study, a comprehensive literature review will be conducted on structural damage to investigate the failure modes caused by real-world tornadoes. To be specific, this research includes the identification of common damage conditions (such as the discontinuity of the load path resulting in the failure of structural components and the breaching of building envelopes resulting in the failure of nonstructural components). The overall goal behind this research is to improve the safety and welfare of the families and individuals living in high tornado risk areas by increasing the knowledge base regarding tornadoes, ultimately making recommendations to update existing building codes in an economically accepted manner

Wind Flow Characteristics of Multivortex Tornadoes

A multivortex tornado refers to a tornado that contains two or more small subvortices in the wind field. Due to the presence of multiple vortices, this type of tornado is likely to be more dangerous and destructive than single-vortex tornadoes. To understand the action of the multivortex tornado on civil structures, the wind flow characteristics are investigated and compared with those of single-vortex tornadoes, by using computational fluid dynamics (CFD) simulations. The results show that the inner flow structure of a multivortex tornado is completely different from that of a single-vortex tornado. First, a multivortex tornado possesses more than one subvortex in the domain around the core radius of the main vortex, and each subvortex flows together with the main vortex while rotating around its own center. Second, the wind flow of a multivortex tornado is more turbulent than a single-vortex tornado, which may lead to significant dynamic responses in some types of civil structures. Third, the maximum negative pressure occurs at the center of each subvortex instead of the center of the main vortex, which means that the largest negative pressure and highest wind speed occur at the same location. This unique feature in the multivortex tornado leads to different worst loading scenarios from single-vortex tornadoes and the worst-case scenario might be the combination of high tangential velocity and high negative pressure around the core radius. Fourth, for a multivortex tornado, the difference between instantaneous values and space-Averaged values of parameters is remarkable. Thus, the space-Averaged values should be carefully used for determining design tornadic wind loads for civil structures

Theoretical Analysis of Dynamic Behaviors of Cable-Stayed Bridges Excited by Two Harmonic Forces

To better understand the dynamic behaviors of cable-stayed bridges, this study investigates the dynamic behaviors of a cable-stayed shallow arch subjected to two external harmonic excitations using the analytical approach. First, dimensionless planar vibration equations of the system are obtained by applying the Hamilton principle, and three ordinary differential equations of the arch and the two cables are obtained by using the Galerkin discretization method. Second, modulation equations involving the amplitude and phase of the dynamic response of the system are derived by applying the method of multiple scales. Third, three simultaneous resonance cases are considered. Finally, parametric study results are illustrated through frequency responses, amplitude responses, phase plane and bifurcation diagrams. Chaos phenomenon is also detected and presented. To validate the developed analytical solutions, numerical simulations are conducted by applying the Runge–Kutta method to integrate the original ordinary differential equations. The results demonstrate that acceptable consistency is reached in the results obtained from the analytical solutions and the Runge–Kutta method in the three simulated cases. The obtained results show that the system’s dynamic responses in the three simulated cases exhibit similarities in their frequency and amplitude responses, while some qualitative differences exist in the phase plane portraits (e.g., period-1, period-2, period-3 solutions) and their bifurcation diagrams