Dynamics of Civil Structures, Vol. 2

A growing number of tall timber buildings have been built across Europe and North America. The major challenge in the design of tall timber buildings is wind-induced vibration due to inherently low mass and flexibility, which makes them susceptible to low-level vibrations. Dynamic properties, such as modal parameters (natural frequencies and damping ratios), are important for accurate estimation of wind-induced response. This chapter presents the identification results of an ambient vibration testing campaign on five timber buildings, including the two tallest all-timber buildings in the world, Treet in Bergen and Mjøstårnet in Brumunddal, Norway. The two most common construction types: Cross-laminated timber (or mass timber) buildings and glue-laminated timber buildings were tested. The random decrement technique and frequency-domain decomposition method were used to identify and assess the amplitude dependence of modal properties. The results show that output-only modal analysis can be used for extracting natural frequencies of tall timber buildings. The results of the random decrement method show that modal properties exhibit amplitude-dependent behavior. Additionally, the aspects affecting the dynamic properties such as construction type and height of the building are discussed. The results of this chapter serve as a useful guideline for practicing engineers in designing tall timber buildings.

This chapter aims to characterize footstep-induced floor vibration to detect lower-limb joint motion during walking, including flexion and extension duration of the ankle, knee, and hip. Quantitative analysis of the lower-limb joint motion outside the laboratory setting is essential for early clinical detection and rehabilitation tracking of gait-related disorders (e.g., diabetes, Parkinson’s) and mitigating trip and fall risks for older adults. Existing approaches involve manual observation and monitoring devices, such as cameras, wearables, and pressure mats. However, they have operational constraints such as requiring professionally trained staff, direct line of sight, carrying devices that patients may discard, and dense deployment. In this chapter, we model the footstep-induced floor vibration during walking to infer the lower-limb joint motions through a physics-informed graph neural network. Our floor vibration sensing approach is contact-less, wide-ranged, and perceived as more privacy-friendly, allowing continuous gait health monitoring in daily life. The primary research challenge is the indirect relationship between floor vibrations and joint motions. Especially, floor vibrations only capture the interaction between the foot and the floor, making it difficult to infer the rotational characteristics of the ankle, knee, and hip joints above the floor. Moreover, there are complex dependencies between the joint motions of the ankle, knee, and hip, making it more challenging to model their characteristics through floor vibrations. To overcome these challenges, we leverage the insights that (1) critical joint motions (e.g., maximum extension and flexion) exert unique footstep forces in terms of direction and magnitude to the floor and (2) these joint motions have dependencies based on their physiological relationships, which are encoded by the floor structure as vibration signals. We characterize and model the relationship between the floor vibration and the critical joint motions to decode such a relation through a state-of-the-art heterogeneous graphical transformer, which represents the physical interaction between the lower limbs and the floor through their heterogeneous motion and vibration information. To incorporate the complex dependencies between ankle, knee, and hip joints, we model their relationship by spatial edges in the graphical model, allowing information sharing among various joints. The output metric of this approach is the duration of critical motion segments. In this chapter, we focus on the ankle extension time during terminal stance, and ankle, knee, and hip flexion time during swing to assess the risk of trips and falls. We evaluate our approach with 10 participants through a real-world experiment. Our approach achieved an average of 2.87% (0.016s) mean absolute error in extracting the duration of critical joint motion segments on four test subjects, reducing \(\sim 50\%\) of the error from the baseline using a Long Short-Term Memory (LSTM) model (0.028s MAE), leading to a comparable accuracy to the existing sensing approaches in medical practices, such as cameras and wearables.

The objective of this chapter is to summarize the results of experimental modal testing performed on all-steel modular floor assemblies in a laboratory environment. An assembly is a prototype system that is 10 ft. × 40 ft. on the plan and consists of three W-section beams and an attached top plate. Two assemblies have been tested as isolated floor specimens at West Virginia University. The research team conducted experimental modal testing on bare steel conditions of the specimens to determine the dynamic characteristics of the specimens such as modal frequencies, modal damping ratios, and mode shapes. The tests after the installation of raised access floor (RAF) units are ongoing and will be compared to the bare steel conditions once complete. Based on the findings of the experimental work in conjunction with further analytical work, a larger system of 30 ft. × 40 ft. will be designed, intended for a typical bay of commercial building structures. The proposed system intends to increase the speed of construction by eliminating the placing of a concrete deck and thus reduce the time from conception to occupancy for steel building structures.

Protecting critical equipment in seismically excited buildings is essential for maintaining their functionality after an earthquake. One approach for protecting equipment is through isolation, where individual pieces of equipment, or equipment sets, are isolated from the building motion. Because critical equipment often contains acceleration-sensitive components that can be damaged during an earthquake, it is necessary to limit the inertial forces experienced by the equipment during an event. This is particularly challenging on the upper floors of buildings where dynamic amplification of the ground acceleration is significant. Protecting equipment on the upper floors of buildings can be achieved using special isolators with restoring forces that can be shaped according to the isolator displacements. The objective of this research is to investigate an adaptive restoring force (ARF) device that can be used for the horizontal isolation of acceleration-sensitive equipment. The force-displacement relationship of the ARF device is characterized by high stiffness at small and large isolator displacements and low stiffness in between. It utilizes cables to transfer motion and forces between the isolation platform and the device components. The force-displacement characteristics of the ARF device can be controlled through the proper selection of its component geometry to produce a wide range of isolator responses. Numerical analyses were performed to evaluate the effectiveness of the device for horizontal seismic isolation of lightweight equipment installed at various levels of a multistory building. The results suggest that isolation systems using ARF devices are capable of significantly reducing floor accelerations transmitted to floor-mounted equipment. However, this often comes at the cost of large isolator displacements.

Vibration-based damage identification methods are increasingly adopted for the structural condition assessment of heritage buildings and ancient masonry structures. Structural health monitoring relies on the assumption that structural damages cause observable changes in the dynamic properties of the building itself. Damage identification and condition assessment are needed to assure the serviceability and safety of heritage buildings since they can be damaged due to environmental conditions or material deterioration over the years. The subject of this chapter is the medieval fortress known as Doria Castle, located in Vernazza, one of the most important architectural sites along the coast of Liguria, Italy. During the last winter (2022/23) restoration works have been completed, and in spring the tower was reopened to public access. In this chapter a series of operational modal analysis (OMA) tests have been performed to determine the system’s dynamic characteristics such as natural frequencies and mode shapes at four different states of restoration stages. Modal parameters have been estimated using the frequency-domain decomposition (FDD) method applied to the response of the structure to ambient vibration. It is possible to observe that natural frequencies increase constantly with the stiffening of the tower as the restoration work proceeded.

Vibration serviceability has been widely discussed in the last decades since the changes in the features of contemporary structures led to their susceptibility to vibrate excessively, even due to usual human-induced loads, such as walking. Despite that, guidelines and standards still neglect the intrinsic interaction between pedestrians and structures. Therefore, models considering such interaction require a more profound understanding and experimental validation to be a reliable mathematical framework for practical design applications. The present study investigates a biodynamic single degree-of-freedom bipedal model (BM) performance against experimental data obtained from two lively footbridges. The measured filtered accelerations from a single-pedestrian crossing in resonance with the first vertical vibration mode are used as a reference. An interaction formulation is applied for this matter, and the influence of the bipedal nature of walk simulation and ground reaction forces (GRFs) predictions were analysed. There was evidence that BM overestimated the GRF and that is perceivable through the values of the dynamic load factors (DLFs) employed to characterize such forces. For the case where vibration levels were more prominent, the reciprocal effects due to the human-structure interaction resulted in remarkable amplifications for the applied forces and structure’s response, featuring significant differences from the experimental results. The model simplifications likely led to this overestimation. However, only additional investigations against experimental data measured at the pedestrian body in varied vibration levels can confirm this since perceivable vibrations can interfere with the walking pattern.

Structural control devices can help mitigate the response and subsequent damage to structures that result from dynamic loads, such as earthquakes and wind loads. Rotational inertial mechanisms offer a promising avenue for achieving this goal by providing significant mass effects without the need for large physical masses. Among these mechanisms, the variable inertia rotational mechanism (VIRM) is a nonlinear control device with adjustable rotational inertia and thus produces modifiable mass effects, achieved by incorporating slider masses inside the device’s flywheel. While previous research on the VIRM has predominantly focused on active or semi-active control systems, the passive implementation of VIRM and its efficacy in vibration mitigation remains relatively unexplored. As a result, the effects of the device parameters, most prominently slider stiffness, and the impact of these parameters on the device’s ability to reduce response under random excitation are uncertain. This chapter addresses these gaps in knowledge through a numerical study considering a single-degree-of-freedom primary structure. The study aims to investigate the different stiffness characteristics of the VIRM, including modeled properties of the stiffness element attached to the slider masses, on the natural frequency shifts and response mitigation. The natural frequency and response measures are evaluated by estimating the system’s instantaneous frequency and an H₂-based measure. The results of this study highlight the ability of VIRM to shift natural frequencies and reduce response in structures subjected to random excitation and will encourage the further study of these innovative devices.

Machine learning algorithms offer a promising approach for vibration-based Structural Health Monitoring (SHM) to assess damage in real time. However, the scarcity of labelled health-state data, especially considering various environmental conditions and damage cases, remains a significant challenge. Population-based Structural Health Monitoring (PBSHM) addresses this issue by enriching the available data via knowledge transfer across a population of similar structures. This approach is particularly powerful in bridge networks where structures can be classified into a few typologies. Scaling SHM from single assets to the entire network is crucial for modern risk assessment in transportation networks. However, PBSHM faces the challenge of obtaining and validating relevant technologies using datasets from multiple similar structures representing various health states. This chapter presents an experimental dataset from a model bridge, where the positions of supports were varied to represent different structures. The dataset includes a wide range of temperatures, including freezing effects, simulated using an environmental chamber. Multiple damage scenarios are also introduced to enable the investigation of damage detection and classification methods for both conventional SHM and PBSHM. This chapter provides an analysis of the dataset and demonstrates the assessment of damage under changing environmental conditions. The whole dataset contributes to advancing the field of PBSHM by providing valuable insights into the limitations of existing SHM methods towards damage assessment in diverse environmental conditions.

Fatigue failures at fastener holes in operating structures are undesirable as they can lead to catastrophic mechanical failures and casualties. Interference pins create interference fits with joined components to reduce stresses around fastener holes and extend the fatigue life of operating structures. In this chapter, a novel method for finite element (FE) modeling of interference pin connections in a wind turbine lattice tower component is developed. Installation of interference pins is modeled as a multistage process. It causes local changes in stiffness in joined members of the component. The local stiffness changes are accounted for in the FE model of the component through the creation of cylinders to represent interference pins. An experimental setup, including a three-dimensional (3D) scanning laser vibrometer and a mirror, was used to measure out-of-plane and in-plane natural frequencies and mode shapes of the component. Ten out-of-plane modes and one in-plane mode from the FE model are compared with the experimental results to validate the accuracy of the FE modeling approach. The maximum percent difference between the theoretical and experimental natural frequencies of the component is 3.21%, and the modal assurance criterion (MAC) values between the theoretical and experimental mode shapes are 0.92 or greater.

Structural health monitoring (SHM) provides insights into the health of large civil structures, such as bridges, using data obtained by sensors. Population-based structural health monitoring (PBSHM) takes this a step further, allowing engineers to gain additional insights into structural health by incorporating the sensor data obtained from a population of similar structures instead of individual structures.

To enable the transfer of knowledge between structures, population similarity scoring metrics are being used where structures that have a high similarity will get a high similarity score. The similarity scoring is being achieved through the development of irreducible element (IE) models and graph neural networks (GNNs) in addition to other methods of generating similarity scores. Whilst an initial schema has been developed to facilitate the creation of IE models for various structures, further work needs to be undertaken in order to facilitate the rapid modelling of structures of greater complexity to enable real-world utilisation of PBSHM technology.

This chapter presents work that expands upon the current IE model schema to allow the IE models to more readily represent real-world bridges. Two bridges are investigated with the aim of examining their construction, including their geometrical options, e.g. identifying some of the standard section types commonly found in structures. Following these case studies, expansion recommendations are proposed to the schema related to the geometrical options with the aim of evolving the current version of the IE model schema so that a greater variety of structures, such as bridges or high-guided masts, can be modelled effectively by these IE models.

Occupant footfalls are often the most critical sources of floor vibration on elevated floors of buildings. Achieving often stringent vibration criteria on these floors requires sufficiently stiff and massive floor structures to effectively resist the forces exerted by user traffic. The difficulty for engineers in modelling these buildings can be complicated for structures that have a significant number of partitions that span from slab to slab, where conventional literature guidance recommends that these partitions be modelled as increased damping only.

In this chapter, three case studies of structures with significant partitions that span from slab to slab are presented. In all three cases, dynamic testing has been performed on various areas of the floors, and during various stages of fit-out in order to provide insight as to what impact these partitions have on the behaviour of the floors. In all three cases, Finite element modelling was also conducted to calibrate the models with the testing. The testing and subsequent modelling showed that although damping was relatively high, these partitions provided a more significant contribution to increasing the stiffness of the floors. Recommendations for appropriate stiffness coefficients are provided as guidance for future dynamic floor modelling.

Vortex shedding is historically a concern among tall tubular pole structures, whose geometric characteristics present an ideal scenario for the phenomenon to occur. Vortex shedding leads to amplified vibration responses that may lead to structural fatigue damage under constant cyclic loading for the duration of a wind event. This potentially long and frequent duration of cyclic loading can ultimately cause catastrophic failure of the structure well before it reaches the end of its design life. Various mitigation techniques can be used to prevent such failures, so detection of this behavior would be advantageous in preserving the health of the structure. Detection of vortex shedding is defined by two components: wind direction and the primary direction of motion of a structure at a particular modal frequency. Vortex shedding is present if the amplified vibration response can be characterized and is determined to be perpendicular to the wind direction. This chapter presents a study that explored the development and application of an algorithm to efficiently characterize the independent directions of the amplified vibration responses of a pole structure and compares these to the wind direction for a particular time period of interest. The motion of the structure can vary significantly over a period of time, even when wind speed and direction are constant. The algorithm considers this and produces a quantitative confidence value providing insight on the presence of vortex shedding. Further data analysis can utilize this value and correlate it with wind speed data to ultimately predict if vortex shedding is likely to occur in a future wind event. An existing tubular pole structure was equipped with a structural health monitoring system capable of measuring accelerations and lateral displacements at the top of the pole for this study. This pole structure historically had visible amplified vibrations under wind loads which made the dataset promising for the development of the vortex shedding detection algorithm. The pole was not equipped with an anemometer; therefore, data from a nearby weather station was collected to provide the required wind parameters needed for the analysis. This chapter describes the structural health monitoring system, the data collection and analysis, and the development and implementation of the vortex shedding algorithm. The implemented algorithm was able to automatically detect vortex shedding activity with good confidence.

Friction-damping devices are robust, low-cost solutions for structural control. Semi-active friction dampers in particular are able to dissipate sizable amounts of energy with comparatively little input power. However, modeling friction is a difficult problem, and the development of control algorithms for a semi-active friction damper proves challenging. Previously introduced by the authors is a novel semi-active friction damper termed the Banded Rotary Friction Device (BRFD). During operation, the BRFD develops friction between an internal steel drum and friction bands; this is achieved by transducing input displacement into rotation of the drum. Given its unique geometry, the BRFD is capable of providing sizable damping force, especially compared to that afforded using a traditional, planar friction surface. In this preliminary work, a semi-active model for the BRFD is introduced whereby damping is controlled via displacements to electric actuators. The model is validated using devised semi-active displacement profiles, and results show that the BRFD is capable of achieving large levels of force amplification, lending itself to applications in structural control and multihazard mitigation.

Vision-based approaches for structural displacement measurement offer the potential to acquire both static deformations and dynamic responses suitable for system identification, while overcoming challenges and limitations associated with conventional displacement sensing techniques. However, many structures of interest, such as bridges, high-rise buildings, and communication, transmission, and wind turbine towers, have geometric dimensions that are considerably larger in a single direction. Consequently, establishing a field of view that encompasses the entire expanse of a structure results in significantly reduced spatial resolution of either natural features of the structure or tracking targets and imposes practical limitations on the ability to resolve motion from the images. These limitations can be addressed by reducing the camera field of view to a small region of the structure, but multiple synchronized cameras would then be required if displacement measurements are sought from many regions across the structure. Optical multiplexing provides an alternative low-cost solution for increasing the effective spatial resolution and facilitating wide field of view by superimposing images from several fields of view into a composite image. This chapter presents the design of a low-cost liquid crystal optical multiplexer assembly with 3D-printed fixture to permit adjustment of the subfields of view. The technique for reconstructing individual subimages from the composite multiplexed images is reviewed and demonstrated using images acquired from a laboratory structure. Independent measurements of structural displacement acquired from displacement transducers and a laser tracker are used to verify the vision-based measurements and characterize the performance of the measurement approach.

Incorporating damping devices into building structures enhances their safety and serviceability when faced with natural hazards such as earthquakes and strong winds. Depending on their working principle, there are three main categories in which damping devices can be classified: passive, semi-active, and active systems. Passive devices employ natural mechanisms to dissipate energy, whereas active devices enhance their dissipation capabilities using external power. In contrast, semi-active devices integrate both principles, enabling them to reliably dissipate energy akin to passive devices and adapt like active systems, all while consuming less power. Recent trends have shown additional popularity for variable-friction dampers as semi-active devices due to their adaptability with only a variable clamping force. Hence, utilizing a cam (i.e., a surface with a variable radius) to exert a variable normal force, a novel friction damper has been created. The cam is attached to both a lever and a slider-crank mechanism, transforming rotational movement into the linear movement of an actuator. The proposed mechanism offers a mechanical advantage to comfortably adjust the position of the levers and vary the normal force. Previous prototypes were used to improve the mechanism’s behavior and guarantee the efficient application of a normal force. The performance of the proposed devices is evaluated by increasing the number of friction plates beyond the original two plates, with the ultimate goal of determining the scalability of force produced by the system. The latest prototype also examines factors such as manufacturing materials and stiffness of components. The experimental evaluation of the proposed device occurs at a small scale, utilizing aluminum and additive manufacturing of components, and an Arduino microcontroller to adjust the positions of the levers. To characterize the device, the test specimen is exposed to simulated harmonic and earthquake motions through a cyber-physical testing setup to evaluate its performance in a realistic structural control scenario. The results indicate the device can have additional normal forces applied to the friction surface to increase the passive capabilities of the device if the actuation system malfunctions. Overall, this research promotes the use of modern technology in structural engineering to improve system efficiency, reduce costs, and enhance safety and reliability in civil infrastructure.