Deflection-based Method Research Articles

Exploring the Limits of a Deflection-Based Method for the Estimation of Dynamic Stress in Beams

Estimation of the dynamic stress in structures, such as beams and plates, has previously been made using the relationship between stress and velocity spatial maxima based on farfield assumptions. This paper presents a method for the estimation of dynamic stress in a beam using Euler-Bernoulli beam theory, where deflection data from a grid of measurement points on the surface of the beam is used to estimate the dynamic bending stress in the structure. The limitations of the method are investigated via response data provided by a numerical model of a free-free beam. A non-dimensional wavenumber analysis is used to determine the number of points required for an accurate estimate of stress. Beams with a range of material and geometric parameters are modelled in order to explore the limits of the estimation method, and parameters representative of several real-world materials are used to assess the suitability of the method for practical applications.

Load Transfer Efficiency Assessment of Concrete Pavement Joints Using Distributed Optical Vibration Sensor

This paper presents a method to assess the load transfer efficiency (LTE) of concrete pavement joints using distributed optical vibration sensors. First, a theoretical analysis of concrete pavement vibration was conducted to investigate how to reflect LTE by spectral amplitude. Second, distributed optical vibration sensor (DOVS) was applied to measure vibration around joints distributedly. Third, the corresponding processing method for DOVS data was proposed to calculate the ratio of spectral amplitude from different slabs through power spectral density (PSD) analysis. Then, field tests were conducted on nine concrete pavement slabs with three different types of joints (dummy joint, rabbet joint, and dowel bars). The deflection-based method as well as the proposed vibration-based method were employed to assess the LTE of eleven joints on two different dates. The comparative analysis results indicate the deflection-based LTE (DLTE) and the ratio of PSD (RPSD) have a strong correlation (0.871) and a slight difference (<±0.03) overall. The correlation is robust in different dates and types of joints (0.844~0.88). These findings prove the accuracy and effectiveness of the proposed vibration-based method.

Damage Estimation of a Concrete Pier When Exposed to Extreme Flood and Debris Loading

The structural safety and serviceability during extreme weather, such as floods and storms, is critical. Due to global warming in the last decades, the increase in the intensity of natural disasters, i.e., flood loading and the durability of the road structures and infrastructures, is becoming critical. Bridges and structures lose their capacity because of ageing over time. On the other hand, the load intensity is another reason for the structural damage. Debris loading due to the flooding on bridges is one of the reasons for the increase in flood loading and eventually structural damage. Measuring the level of structural damage under extreme events is vital in determining the vulnerability and resilience of structures during a disaster. A damage index (DI) can be defined as a measurement tool for the levels of structural damage. Oftentimes, damage indices are developed to measure the deterioration of the system under earthquake loading. Little work has been published on damage indices (DIs) under flood loading, where a uniform pressure is applied to a structure. This paper presents a comprehensive review of DIs published in the literature and compares two approaches to assess the system’s damage utilising finite element methodologies. The structure model developed in the ABAQUS software package is used to predict the failure of a concrete component under applied lateral loading. The model is validated using published experimental work. The model is verified, and then it is used to compute the damage indicators using two primary techniques, including a deflection-based method and an energy loss-based approach. Using the two offered DIs, the change in damage levels is displayed underwater flow uniform loading. A comparison of the two methods is conducted. In this paper, differences between the two concepts are analysed and presented.

A deflection-based practicable method for health monitoring of in-service bridges

This paper presents a static deflection-based method for structural health monitoring of in-service bridges. In the past, the use of static as well as dynamic measurements has been investigated for damage detection in bridge elements. However, most of these methods are complex and work only in laboratory settings. Moreover, implementing such methods for in-service bridges is a challenging task. The method presented in this paper is based on a simple structural analysis principle and can be implemented for in-service bridges. Using the principle of virtual work, an analytical expression for deflection change (DC) (i.e. the difference in deflection for healthy and damaged beams) and a consistency function are derived. A plot of the DC curve reveals the damage location, and the consistency function is used to assess the damage severity. Numerical case studies and laboratory experiments are presented to investigate the effectiveness of the proposed method in different cases, such as a simply supported beam subjected to uniform loading and a cantilever beam subjected to uniform loading. Satisfactory damage localization and quantification results were achieved even with a small number of sensors. Both numerical and experimental analysis results show that the proposed model performs reasonably well at detecting and assessing the damage in bridge elements.

Locating and Quantifying Damage in Beam-like Structures Using Modal Flexibility-based Deflection Changes

This paper presents an enhanced method to locate and quantify damage in beam-like structures using changes in deflections estimated from modal flexibility (MF) matrices. The method is developed from explicit relationship between a series of MF-based deflection change vectors and the damage characteristics. Based on this, three damage locating criteria are defined and used to detect and locate damage. Once the damage is located, its severity is estimated conveniently from a closed-form function. The capability of the proposed method is examined through numerical and experimental verifications on a steel beam model. The result shows that the method accurately locates and quantifies damage under various scenarios using a few modes of vibration, with satisfactory or even better results compared to those obtained from traditional static deflection-based method. The performance of the proposed method is also compared with three well-known vibration-based damage detection methods using changes in MF and modal strain energy. It is found that the proposed method outperformed the other three methods, especially for multiple damage cases. As beams can represent various structural components, the proposed method provides a promising damage identification tool targeting the application to real-life structures.

Novel Assessment Method for Support Conditions of Concrete Pavement under Traffic Loads using Distributed Optical Sensing Technology

Loss of support is a common concrete pavement distress that may affect pavement performance directly. Previous studies have proved that vibration-based methods have the potential for detecting loss of support in a more efficient way but this is limited by loading conditions. This paper presents a further study concerning the effects of moving loads and proposes a novel method for assessing support conditions of concrete pavement under traffic loads using distributed optical vibration sensing technology. First, finite element analysis and laboratory tests were conducted to investigate the impact of loss of support on pavement vibration induced by moving loads with reference to the frequency spectrum. The impact of loading conditions, including loading position and speed, was also studied using the same methods. The results indicate that both loss of support and loading characteristics have a considerable effect on the distribution of the frequency spectrum. It is proved that weighted frequency can be utilized for assessment of support conditions under a specific loading condition. It is suggested the loading position needs to be close to the measurement point (distance < 0.3 m) to obtain stable and reliable data for assessment of support conditions. In addition, the loading speed should be adequately fast and steady (4 to 5 m/s) to ensure the significance of the effect of loss of support. A field test was conducted in an airport, and the novel assessment method was validated by comparing it with a conventional deflection-based method. The novel method proved to be reliable for implementation in practice.

Output-only damage diagnosis for plan-symmetric buildings with asymmetric damage using modal flexibility-based deflections

Effective methods for vibration-based damage diagnosis in building structures are based on the estimation of structural deflections from identified modal flexibility (MF) matrices. However, most of the existing methods and previous studies that use MF-based deflections were developed by considering the case of buildings that can be modeled as planar structures (e.g. plan-symmetric buildings) both in the baseline and possibly damaged states. In an attempt to fill this research gap, a deflection-based method for output-only damage diagnosis in building structures tested under ambient vibrations is proposed in this paper. The method is applicable for simple rectangular plan-symmetric “box type” 3D building structures which may experience asymmetric damage, and it can be used for detecting, localizing and quantifying the damage. One of the main differences between the proposed and the existing methods is related to the inspection loads adopted to estimate the MF-based deflections. The inspection loads of the proposed method are more complex than the uniform translational loads adopted in the existing methods. Such proposed loads in fact can be assembled only after having estimated the position of the center of stiffness for each story of the structure. According to the proposed approach, the locations of the centers of stiffness are extracted from the experimentally-derived modal flexibility matrices, before performing the damage diagnosis process. The effectiveness and validity of the proposed method was demonstrated both through numerical analyses and by executing experimental ambient vibration tests on a frame building. The results of the proposed method were also compared with the existing approach which was developed for planar structures. This comparison (made both through numerical and experimental analyses) demonstrated that only the proposed approach can be used to perform a correct damage diagnosis process in plan-symmetric buildings which may experience asymmetric damage, especially when considering the damage quantification problem.

A Semi-Empirical Deflection-Based Method for Crack Width Prediction in Accelerated Construction of Steel Fibrous High-Performance Composite Small Box Girder.

Accelerated construction in the form of steel–concrete composite beams is among the most efficient methods to construct highway bridges. One of the main problems with this type of composite structures, which has not yet been fully clarified in the case of continuous beam, is the crack zone initiation that gradually expands through the beam width. In the current study, a semi-empirical model was proposed to predict the size of cracks in terms of small box girder deflection and intensity of load applied on the structure. To this end, a set of steel–concrete composite small box girders were constructed by the use of steel fibrous concrete and experimentally tested under different caseloads. The results were then used to create a dataset of the box girder response in terms of beam deflection and crack width. The obtained dataset was then utilized to develop a simplified formula providing the maximum width of cracks. The results showed that the cracks initiated in the hogging moment region when the load exceeded 80 kN. Additionally, it was observed that the maximum cracked zone occurred in the center of the beam due to the maximum negative moment. Moreover, the crack width of the box girder at different loading cases was compared with the test results obtained from the literature. A good agreement has been found between the proposed model and experiment results.

Compressive Column Load Identification in Steel Space Frames Using Second-Order Deflection-Based Methods

This paper presents a comparison of two static nondestructive methods used to assess compressive loads in columns of steel space frames. The first method requires knowledge of the flexural rigidity of the column under investigation, whereas the second method requires knowledge of the column’s buckling load. In each method, short-term displacements are measured at given cross-sections along the member under examination, which is subjected to an additional transverse load. The two methods were verified in this study through experimental and numerical tests on a column of a small-scale space frame prototype with generic connections and end conditions. Estimations of compressive forces were generally reliable when second-order effects were accurately considered. In conclusion, the two methods can be successfully used to test steel space frames in a laboratory or under real conditions.

Validation of method for analysing mechanics of unloader brace for medial knee osteoarthritis

Unloader braces are one non-invasive treatment of knee osteoarthritis, which primarily function by applying an external abduction moment to the joint to reduce loads in the medial compartment of the knee. We developed a novel method using brace deflection to estimate the mechanical effect of valgus braces and validated this model using strain gauge instrumentation.Three subjects performed static and walking trials, in which the moment applied by an instrumented brace was calculated using the deflection and strain methods. The deflection method predicted average brace moments of 8.7 Nm across static trials; mean error between the deflection model predictions and the gold-standard strain gauge measurements was 0.32 Nm. Mean brace moment predictions throughout gait ranged from 7.1 to 8.7 Nm using the deflection model. Maximum differences (MAE) over the gait cycle in mean and peak brace moments between methods were 1.50 Nm (0.96) and 0.60 Nm (0.42).Our proposed method enables quantification of brace abduction moments without the use of custom instrumentation. While the deflection-based method is similar to that implemented by Schmalz et al. (2010), the proposed method isolates abduction deflection from the 3 DOF angular changes that occur within the brace. Though the model should be viewed with more caution during swing (MAE = 1.16 Nm), it was shown that the accuracy is influenced by the uncertainty in angle measurement due to cluster spacing. In conclusion, the results demonstrate that the deflection-based method developed can predict comparable brace moments to those of the previously established strain method.

Serviceability limit state of vibrations in under-deck cable-stayed bridges accounting for vehicle-structure interaction

Verification of the serviceability limit state of vibrations due to traffic live loads can be neglected in conventional types of concrete road bridges but becomes critical in the design of slender structures like under-deck cable-stayed bridges. The novelty of the work presented in this article is that an innovative vehicle-bridge interaction model is employed, in which realistic wheel dimensions of heavy trucks, road roughness profiles and the cross slope of the road are considered in nonlinear dynamic analyses of detailed three-dimensional finite element models. An extensive parametric study is conducted to explore the influence of the bridge parameters such as the longitudinal and transverse cable arrangement and the support conditions, in addition to the load modelling, road quality, the wheel size, the transverse road slope and the vehicle position and speed on the response of under-deck cable-stayed bridges. It has been observed that the vibrations perceived by pedestrians can be effectively reduced by concentrating the cable-system below the deck at the bridge centreline. The Fourier amplitude spectrum of the acceleration at critical positions along the deck proved that the response of under-deck cable-stayed bridges is not dominated only by contributions at the fundamental mode and, consequently, the conventional deflection-based methods are not valid to assess the users comfort. Instead, Vehicle-Bridge Interaction analyses are recommended for detailed design, considering the wheel dimensions if the pavement quality is bad and/or if the wheel radius is large. Finally, we verify through multiple approaches that the comfort of pedestrian users is more critical than that of vehicle users. However, the comfort of vehicle users is shown to be significantly affected when the road quality is poor.

Investigation into Top-Down Cracking of Asphalt Pavements in North Carolina

Top-down cracking has become a commonly reported cracking mechanism in asphalt pavements worldwide. In top-down cracking, a crack initiates at the surface of an asphalt concrete pavement and propagates to the bottom of the asphalt pavement layer. Because the location and governing state of stress for top-down cracking are different from those for bottom-up cracking, analysis of pavement cracking performance must be robust enough to account for the complex mechanisms that are involved in top-down cracking. This study applies the viscoelastic continuum damage finite element model to the evaluation of two pavement sections in North Carolina where top-down cracking has been identified. Small specimen geometries are used to perform simplified viscoelastic continuum damage testing on individual asphalt layers obtained from field cores. This testing model and the Fourier finite element program are used together for pavement cracking performance simulations, and the joint model uses the structure and layer material properties obtained from the two study pavements. The simulation results clearly support the propensity of these pavements to exhibit top-down cracking. In addition to laboratory testing and analysis, the deflection-based method suggested by Uhlmeyer et al. is applied to the data obtained from pavement sections with known crack initiation locations, and that method's validity is investigated. The Uhlmeyer method uses the AREA parameter, which is determined from falling weight deflectometer deflections, and pavement thicknesses. The analysis results show a clear difference in the AREA versus pavement thickness relationship between the pavement sections with top-down cracking and those with full-depth cracking.

Deflection-based method for seismic response analysis of concrete walls: Benchmarking of CAMUS experiment

A number of shake table tests had been conducted on the scaled down model of a concrete wall as part of CAMUS experiment. The experiments were conducted between 1996 and 1998 in the CEA facilities in Saclay, France. Benchmarking of CAMUS experiments was undertaken as a part of the coordinated research program on ‘Safety Significance of Near-Field Earthquakes’ organised by International Atomic Energy Agency (IAEA). Technique of deflection-based method was adopted for benchmarking exercise. Non-linear static procedure of deflection-based method has two basic steps: pushover analysis, and determination of target displacement or performance point. Pushover analysis is an analytical procedure to assess the capacity to withstand seismic loading effect that a structural system can offer considering the redundancies and inelastic deformation. Outcome of a pushover analysis is the plot of force–displacement (base shear–top/roof displacement) curve of the structure. This is obtained by step-by-step non-linear static analysis of the structure with increasing value of load. The second step is to determine target displacement, which is also known as performance point. The target displacement is the likely maximum displacement of the structure due to a specified seismic input motion. Established procedures, FEMA-273 and ATC-40, are available to determine this maximum deflection. The responses of CAMUS test specimen are determined by deflection-based method and analytically calculated values compare well with the test results.

Environmental Deterioration Model for Flexible Pavement Design: An Ontario Example

Traffic loading, environmental conditions, subgrade soil, and construction and maintenance quality are among the factors that influence pavement performance. Environmental conditions can have a particularly significant impact on the performance of low-volume road pavements. It is intended that the Strategic Highway Research Program performancegraded asphalts ensure that an asphalt binder is selected based on in-service pavement conditions. This new system will enable designers in Ontario to account for differences in climatic conditions and traffic loading, which vary between the southern and northern areas of the province and have always posed a challenge to pavement designers. A deflection-based method was originally developed in the 1970s based on the AASHO road test and the Brampton road test. The design system incorporates elastic layer analysis to determine pavement response. It uses cumulative equivalent single-axle loads, subgrade type, and layer thickness to determine the most effective design. The design system has been recently updated and recalibrated to separate the environment and traffic effects on performance. In effect, the total pavement performance is the cumulative effect of the damage due to the environment and the damage due to traffic. Hence, the differences between roads in southern and northern Ontario can be quantified. The system calculates roughness either in terms of the international roughness index or the riding comfort index, or in terms of performance as a pavement condition index. The mechanistic-empirical performance model can be recalibrated to apply to conditions outside of Ontario. Examples show the relative deterioration and performance curves for various design situations.

Beam-Column Method for Tieback Walls

The beam-column method for the design of tieback walls is of intermediate complexity between the pressure diagram methods and the finite-element method. A set of recommended P-y, F-w, and Q-w curves are presented for the soil model, and the P-y method is described to simulate properly the construction sequence of excavation and tieback stressing. The recommended beam-column method is evaluated by comparing predictions with the measured behavior of four full-scale tieback walls in sand and in clay. The most influencing factors are identified through a parametric analysis and a comparison with four pressure diagram methods is presented. The beam-column method is a deflection-based method that satisfies the vertical, horizontal, and moment equilibrium of the wall. These significant and fundamental advantages over the pressure diagram methods make it a superior method, which should be used anytime the added complexity is warranted. The most severe limitation of the beam-column method is its inability to properly account for mass phenomena, namely, mass movement and downdrag. The most useful aspect of the beam-column method is its ability to give better bending moment profiles than the pressure diagram methods.