Stiffness Of Structural Elements Research Articles

A framework for computer vision-based health monitoring of a truss structure subjected to unknown excitations

Computer vision (CV) methods for measurement of structural vibration are less expensive, and their application is more straightforward than methods based on sensors that measure physical quantities at particular points of a structure. However, CV methods produce significantly more measurement errors. Thus, computer vision-based structural health monitoring (CVSHM) requires appropriate methods of damage assessment that are robust with respect to highly contaminated measurement data. In this paper a complete CVSHM framework is proposed, and three damage assessment methods are tested. The first is the augmented inverse estimate (AIE), proposed by Peng et al. in 2021. This method is designed to work with highly contaminated measurement data, but it fails with a large noise provided by CV measurement. The second method, as proposed in this paper, is based on the AIE, but it introduces a weighting matrix that enhances the conditioning of the problem. The third method, also proposed in this paper, introduces additional constraints in the optimization process; these constraints ensure that the stiff ness of structural elements can only decrease. Both proposed methods perform better than the original AIE. The latter of the two proposed methods gives the best results, and it is robust with respect to the selected coefficients, as required by the algorithm.

A criticism on strengthening glued laminated timber beams with fibre reinforcement polymers, numerical comparisons between different modelling techniques and strengthening configurations

The application of CFRP for strengthening timber structures has proven its efficiency in enhancing load-bearing capacity and, in some cases, the stiffness of structural elements, thus providing cost-effective and competitive alternatives both in new design and retrofitting existing historical buildings. In this study, glued laminated timber beams strengthened with CFRP were examined. A number of test beams with different reinforcement configurations and beam sizes were selected from the literature. These beams were analysed with three different methods as numerical, theoretical and code perspective. For the numerical method, a 3D nonlinear finite element model which includes damage and fracture mechanics was constructed. All test beams were studied with different methods and results were compared with respect to initial flexural stiffness, midspan vertical displacement and failure load. The effectiveness of methods and strengthening configurations were stated and suggestions for practical application of FRP-strengthened timber beams were presented.

Influence of the Order Exchange of the Node Connection in the Force Analysis of Steel Structures

In the mechanical analysis of steel structures, whether it is static analysis or dynamic analysis, it is necessary to establish the structural stiffness matrix first. In the process of building the structural stiffness matrix, the same element usually has different node code connection orders, and it has never been argued whether the different connection orders of the same element will have an effect on the building of the stiffness matrix. In this study, the influence of the difference in the node connection order on the construction of the element stiffness matrix is studied. First, the structural element stiffness matrix in the global coordinate system is established when the node connection order is different. It is found that the element stiffness matrix in the global coordinate system is indeed inconsistent for the same element with different connection orders. In this study, the elements of the established element stiffness matrix are extracted into the global stiffness matrix of the structural system based on the law of energy conservation; it is found that the global stiffness matrix finally established by using two different connection relationships is the same. The research results of the example show that in the stress analysis of steel structures, selecting different node connection sequences to establish the structural stiffness matrix will obtain the element stiffness matrix under different global coordinate systems. However, through the aggregation process of the global stiffness matrix of the structural system, the global stiffness matrix obtained is consistent, so the different connection sequences of nodes will not affect the stress analysis of steel structures. The example further analyzes the static stress and dynamic responses of the steel structure. The conclusions of this study provide a reliable theoretical basis for the situation that the order of node connections need not be consistent in the finite element modeling of steel structures and are of reference value for the finite element modeling of steel structures.

Strengthening Timber Structural Members with CFRP and GFRP: A State-of-the-Art Review.

The application of fibre-reinforced polymers (FRP) for strengthening timber structures has proven its efficiency in enhancing load-bearing capacity and, in some cases, the stiffness of structural elements, thus providing cost-effective and competitive alternatives both in new design and retrofitting existing historical buildings. Over the last few decades, several reinforcing materials and techniques evolved, and considerable progress was made in numerical modelling, especially using the finite element method. As this field of research has become extensive and diversified, as well as numerous contradicting results have emerged, a thorough review is necessary. This manuscript covers the topics of historical preliminaries, reinforcing with carbon and glass fibre composites, bond characteristics, main reinforcing techniques, modelling of knots, and the effects of the fibre waviness on the composite behaviour. A detailed overview is given on the experimental and numerical investigation of mechanics of strengthened beams. A one-of-a-kind table is presented that compares the stiffness improvement observed in several studies with analytical estimates. Attention is drawn to a number of challenges that have arisen, e.g., the moderate stiffness enhancement, composite-to-wood interface, modelling of knots, and strengthening of defected timber members. This paper can be used as a starting point for future research and engineering projects.

Diagnostics of the strength and stiffness of the loader carrier system structural elements in terms of thinning of walls by numerical methods

1. Tanchenko AY. The stress-strain state of spatial thin-walled structures taking into account the thinning of the walls of the bearing elements. Bulletin of SevNTU: Mechanics, energy, ecology. 2011; 120: 35-40. Google Scholar

Health Assessment of Infrastructures Using Limited Uncertain Dynamic Response Information following Earthquakes

ABSTRACT A health assessment technique for infrastructures is presented following earthquakes using uncertainty-filled information. A system identification (SI)-based concept is used to identify the stiffness of structural elements following earthquakes. The excitation information is not required, and responses need not be measured at all dynamic degrees of freedom. To consider uncertainty in representing a structure and dynamic responses, a significantly modified unscented Kalman filter (UKF)-based approach is used. To implement UKF, a two-stage SI approach is proposed. It is verified using three-dimensional truss-frame systems. The procedure is robust and not sensitive to the variances of initial stiffness and measurement noise, the two most uncertainty-prone parameters.

Bending moment distribution estimation of an actual steel building structure by microstrain measurement under small earthquakes

Most structural health monitoring systems estimate the overall behavior by measuring the acceleration response, which cannot directly measure the stress or damage state of individual structural members. An alternative approach is to use strain measurements; however, methods for analyzing and utilizing strain data for actual steel buildings have not been established. In this study, highly precise semiconductor strain gauges were applied to an actual building. The accelerations and strains measured during earthquake loading were used to calculate the ratio of the bending moment at the beam or column sections to the displacement at the top of the building, which was defined as the “local stiffness.” This physical index represents the stiffness of structural elements near the measurement location and can be easily predicted through simple static frame analysis. The measured local stiffness was comparable to the analytical local stiffness values for the beams but was larger than that for the columns. This indicates that nonstructural members may exhibit a certain degree of restoring force and that the measured local stiffness may be strongly affected by nonstructural elements that are not considered during the structural design stage. Conversely, the measured local stiffness can be used to estimate the behavior of nonstructural components. The measured dominant frequency and local stiffness of the beams and columns showed a dependency on amplitude, but opposite trends were observed for the beams and columns. This indicates that the amplitude dependency of the dominant frequency is not due to the behavior of the beams and columns but to other reasons such as nonstructural components or changes in mass.

СРАВНИТЕЛЬНЫЙ АНАЛИЗСПОСОБОВ ПРОЧНОСТНОГО РАСЧЕТА НА ПРИМЕРЕ ИЗМЕЛЬЧИТЕЛЯ ФУРАЖНОГОЗЕРНА

At the development of new machines or modernization of existing ones a special requirement is applied to the operating safety of this equipment. First of all, this requires certain strength calculations. For this, the manufacturers use various methods of calculating the strength of materi-als using a wide range of software applications and online services. In the calculations, special emphasis should be placed on deformation, that is, on the stiffness of structural elements, since stiffness characterizes the ability of a part to withstand a load without significant deformations. Using the example of calculating the deformation of the plate fixing the knife of a rotary grinder, comparative calculations were made in various ways. This is necessary due to the fact that during operation significant forces arise that can change the structure. The following computational methods were used as the investigated methods: online calculators, the method of initial parameters, Kompas-3D and APM WinMachine software applications, bench tests and opera-tion tests. It seems that the solution of one problem in dif-ferent ways should not cause a problem - the initial condi-tions are the same everywhere. However, each of the con-sidered methods has its own peculiarities just in laying the initial conditions. If the conditions are not laid, the result will be significantly different, and this will lead to incorrect de-sign actions. In this case, the use of various methods of calculation and testing, even at the design stage, should lead to a deep analysis of the results. The calculated data may differ from experimental results. This is due to the inconsistency of the materials under study with the claimed requirements, fastening conditions, load application, etc.

Simultaneous Identification of structures and unknown seismic excitations for chain-like systems with unknown mass using partial absolute responses

It is necessary to identify structures with unknown mass and unknown seismic excitations simultaneously, but very limited methods have been proposed. In this paper, an algorithm is proposed to identify structural element mass, stiffness, and seismic excitations using only partial absolute structural responses of chain-like systems. In the first stage, the identification of structural element stiffness-mass coupled coefficients and unknown seismic excitations is conducted based on the generalized extended Kalman filter with unknown input (GEKF-UI) developed by the authors. In the second stage, these coupled coefficients are decoupled by cluster analysis and the least squares estimation (LSE) to obtain structural element stiffness and mass changes. The effectiveness of the proposed algorithm is numerically investigated using a four-story frame structure under three scenarios of changed conditions. Moreover, experimental validation by the shaking table test of a shear structure under two scenarios is also performed to identify structures and seismic excitations simultaneously.

Basic recommendations for strengthening of RC beams with Ultra High Performance Fiber Reinforced Concrete (UHPFRC) – conclusions from experimental investigation

In modern engineering practice, it is very often necessary to look for alternative solutions for increasing the load-bearing capacity and stiffness of various structural elements of buildings, due to unsatisfactory requirements of the current regulations, increasing the load, occurring damages and defects. The modern approach, which implies that construction contributes to the sustainable development of society, requires the use of high-tech materials with significantly higher strength characteristics than traditional ones. One such material is the Ultra High Performance Fiber Reinforced Concrete (UHPFRC), which differs significantly from conventional concrete because of its specific structure and composition. In this aspect, there are a number of challenges that need to be overcome in order to provide the practical application of UHPFRC in Bulgaria – optimal mixture, technological problems, national regulations, economic indicators, etc. All this necessitates a thorough study of the actual behaviour of structures strengthen by UHPFRC. This paper presents an experimental study of the stress and strain conditions of a reinforced concrete beam with rectangular cross section strengthen with a 5 cm layer of UHPFRC concrete in the compressive zone. The analysis of the results from the experimental tests provides a number of important practical conclusions and general recommendations for the application of UHPFRC for strengthening of reinforced concrete beams in real structures.

Identification of structural element mass and stiffness changes using partial acceleration responses of chain-like systems under ambient excitations

It is important to conduct structural damage detection using only output time histories of structures under ambient excitations. Recently, an approach has been proposed for structural damage detection under ambient excitations using the synthesis of cross-correlation functions of partial structural responses and the extended Kalman filter (EKF). However, structural mass is assumed known in this approach. Although some methodologies have been presented for detecting damage due to relative structural mass and stiffness changes in chain-like systems, measurements of structural responses including acceleration, velocity, and displacement at each degree of freedom are required. This greatly limits the application of these methodologies. In this paper, without structural mass information, an algorithm is proposed to identify structural element mass and stiffness changes using only partial acceleration responses of chain-like systems under ambient excitations. First, based on the equations for cross-correlation functions of structural responses under ambient stationary excitations modeled as independent stationary white noise processes, EKF is utilized for identifying the structural element stiffness-mass coupled coefficients using only partial acceleration responses. Then, these coefficients are decoupled by cluster analysis and the least squares estimation to obtain structural element stiffness and mass changes. Furthermore, the proposed algorithm is extended for identifying chain-like structural element mass and stiffness changes under non-stationary ambient excitations assumed as time modulating white noises. The performances of the proposed algorithm are numerically investigated using the Phase I The American Society of Civil Engineers structural health monitoring benchmark building under stationary or non-stationary ambient excitations, respectively. Moreover, the experimental data with structural element mass and stiffness changes conducted at the Los Alamos National Laboratory are utilized to test the proposed algorithm.

Progressive Sidesway Collapse Analysis of Steel Moment-Resisting Frames Under Earthquake Excitations

This paper deals with the assessment of seismic collapse capacities and the related collapse durations of steel moment-resisting frames (MRFs). For this purpose, three prototypes of five-story steel structures are studied. These structures are special, intermediate and ordinary moment-resisting frames with high, medium and low ductility, respectively (SMRF, IMRF and OMRF). The structures have been designed in accordance with the Iranian codes. Furthermore, the deterioration effects of strength and stiffness for structural elements have been considered based on the results of reference experimental models. Next, using 22 pairs of far-field ground motion records proposed by FEMA P695 instruction, incremental dynamic analysis is conducted up to the dynamic instability of structures. Afterward, the collapse capacities of these structures are evaluated and compared with the fragility curves. Also, progressive sidesway collapse durations of the structures are estimated under the selected ground motion records. The results show that SMRF has larger collapse capacity than those of the other frames, and can diminish collapse probability by 33.4% and 54.6% compared to IMRF and OMRF, respectively. Moreover, the results reveal that sidesway collapse duration of SMRF is greater than IMRF and OMRF.

A Calculation Method for Interconnected Timber Elements Using Wood-Wood Connections

Wood-wood connections, widely used in the past, have been progressively replaced by steel fasteners in timber constructions. Currently, they can be manufactured and implemented more efficiently thanks to digital fabrication techniques. In addition, with the emergence of new timber plate engineered products, digitally produced wood-wood connections have been developed with a strong focus on complex free-form geometries. The gained knowledge through research and building implementations have pushed the development of more standardized structural elements. As a result, this work presents a new concept of building components using through tenon connections based on the idea of transportable flat-packs directly delivered and assembled on site. The main objective of this research is to develop a convenient calculation model for practice that can capture the semi-rigid behavior of the connections and predict the effective bending stiffness of such structural elements. A case study is used as a reference with three large-scale slabs of a 8.1 m span. Bending and vibration tests are performed to study the mechanical behavior and assess the proposed calculation method. The results show the high influence of the semi-rigid behavior of connections on the bending properties and, therefore, on the serviceability limit state. The model is in good agreement with the test results, and further improvements can be made regarding the local behavior of the connection. This study demonstrates the feasibility of the proposed construction system and the applicability of the developed calculation model to design practice.

Contribution of coupling elements to the seismic demand of walls in reinforced concrete buildings

Abstract Architectural configurations of reinforced concrete (RC) wall buildings force the connection of structural walls with beams, slabs and adjacent walls to distribute habitational spaces, generating interaction between those structural elements that results in a coupled structural system. Studies on resisting planes of RC buildings damaged during 2010 Chile earthquake suggest that the behavior of structural walls was highly influenced by the interaction of the resisting plane with the rest of the structure. Furthermore, researchers have identified 7the high levels of axial load as one of the principal causes of the observed wall damage on these buildings, and that a significant amount of this load comes from the seismic demands. However, there is uncertainty about how different coupling elements contribute to the seismic demands in RC walls. In this work, the seismic demands of axial load, shear and moment of RC walls are estimated from three buildings damaged during the 2010 earthquake using detailed finite element models that consider their three-dimensional layout. the contribution of coupling elements to the seismic demands of the studied RC walls is determined. Additionally, the effects of the assumed stiffness of structural elements over the seismic demands is evaluated. The results show that slabs have the largest contribution to the seismic axial load in walls, contributing with more that 90%, followed by adjacent walls and connecting beams. Furthermore, the obtained moment and shear diagrams of the studied walls are significantly different than those of cantilever walls, and it was found that the assumed stiffness of structural elements exerts an important effect on the prediction of the seismic demands in RC walls.

Comparison of analytical and difference sensitivity methods for structural damage identification

The sensitivity-based damage identification method receives much attention due to its ability to identify structural damages at element level. This paper aims to discuss the influence of two different deduction algorithms of sensitivity matrix, the analytical method and the numerical difference method, on the parameter identification results of structures with the same identification index. In order to compare the difference between the two sensitivity-based damage identification methods, the frequency-domain mode shape and the time-domain acceleration response information are used as the updating objectives, respectively. And then, the sensitivity matrices of the updating objectives to the same identification index, structural element stiffness parameters, are respectively derived based on the analytical method and the numerical difference method. Finally, a simply supported box girder bridge is used to illustrate the difference between the two sensitivity-based methods. Numerical simulations with initial model errors and measurement noise show the two types of methods both can accurately detect local damages and identify unknown initial model errors. The presence of random noise has some bad effect on the identified results of structural parameters, but the identified accuracy is still acceptable for normal noise level.

Stiffness and Strength Estimation of Damaged Unreinforced Masonry Walls Using Crack Pattern

ABSTRACT After an earthquake, the residual stiffness and strength of structural elements are typically estimated based on a qualitative visual inspection of cracks that is prone to error. In this paper a new approach is proposed to automatically estimate the updated stiffness and strength of damaged unreinforced masonry walls by characterization of crack patterns by a mathematical index. It is shown that structural and textural fractal dimensions of a crack pattern reflect the extent of cracking and the type of cracking or crushing, i.e., whether the cracks pass through joints or whether bricks have been damaged and crushed. Using results of six quasi-static cyclic tests on unreinforced brick masonry walls with different failure modes at various drift ratios, it is shown that the structural and textural fractal dimensions of the crack patterns are an accurate predictor of the stiffness and strength degradation. This procedure seems therefore a promising approach for replacing the traditional assessment methods that are based on visual inspection and engineering judgment by an analytical procedure based on image processing that can eventually be completely automated.

Comparative performance evaluation of RC frame structures using direct displacement-based design method and force-based design method

Force-based design (FBD) method has been practiced for a long time which focuses on the seismic force over the structure. Problems associated with FBD are assumed stiffness of structural elements, inappropriate R factors and others. Thus, a new alternative method is required to overcome these differences. Direct displacement-based design method (DDBD) provides an efficient alternative. It is more straightforward which aims to achieve a specified acceptable level of damage under the design earthquake. The main aim of DDBD is to define the target displacement profile for the structures. In this study, the performance of low- and medium-rise building is evaluated using FBD and DDBD method and results have been compared. Both structures are designed according to Indian standard loading in compliance with IS 1893 (part 1) 2016. Non-linear analyses have been carried out for evaluating structural performance like base shear, maximum displacement and inter-storey drift ratio (IDR%). From the study, it can be concluded that DDBD method is more effective than FBD method.

Upgrading seat suspension of tractor Belarus 1221

Ways to reduce vibrations at the tractor operator’s workplace in the unit with a trailer by improving the design of the suspension cushioning system are considered. Analysis of existing types of suspension systems shows that the most effective, in terms of reducing vibration loading, are active and semi-active systems. To reduce the vibration level at the tractor operator’s workplace in an aggregate with a trailer, an active seat suspension design has been developed. It includes a system of sensors and actuators that allow the current stiffness and damping of structural elements to be highly efficient in controlling the tractor operator’s workplace. To assess the effective use of the developed design, and compare it with the efficiency of the serial seat suspension, road tests were carried out. The tractor-transport unit in the tractor Belarus-1221 and the trailer 2PTS-4.5 with the serial and experienced suspension design were chosen as the object of research. During the field tests, the acceleration values were determined for the operator’s seat, the cab floor, the front and rear axles of the tractor. The test results showed that the developed technical solution allows reducing the vibration acceleration levels by 12-18% in comparison with the serial design.

Synthesis of Cross-Correlation Functions of Partial Responses and the Extended Kalman Filter Approach for Structural Damage Detection Under Ambient Excitations

It is still necessary to investigate the detection of structural damage under ambient excitations since the excitations are random and unmeasured while measurement noises are inevitable. In this paper, a method based on the synthesis of cross-correlation functions of partial structural responses and the extended Kalman filter (EKF) approach is proposed for the identification and damage detection of structures under ambient excitations, in which both independent stationary and non-stationary white noise excitations in the product models are discussed. First, the equations of cross-correlation functions of structural responses are established when the ambient excitations are independent stationary white noise processes. Then, the EKF approach is utilized to identify structural parameters and cross-correlation functions using partial measurements of structural acceleration responses. Structural damage is detected based on the degradations of the identified structural element stiffness parameters. Finally, the proposed method is extended to deal with independent non-stationary white noise excitations in the product models. The numerical simulation examples of the ASCE structural health monitoring benchmark building subject to ambient excitation, a moment resisting frame model under white noise excitation, and a cantilever beam model under multiple independent non-stationary excitations are used to validate the feasibility of the proposed method. It is shown that the method is not sensitive to measurement noises. Also, a lab experimental study of the identification of a multi-story shear structure is investigated to further illustrate the applicability of the proposed method.

Stiffness Effects of Structural Elements on the Seismic Response of RC High-Rise Buildings

Abstract The stiffness of structural elements (columns, beams, and slabs) significantly contributes to the overall stiffness of reinforced concrete (RC) high-rise buildings (H.R.B.s) subjected to earthquake. In order to investigate what percentage each type of element contributes to the overall performance of an H.R.B. under seismic load, the stiffness of each type of element is reduced by 10% to 90%. A time history analysis by SAP2000 was performed on thirteen 3D models of 12-story RC buildings in order to illustrate the contribution of column stiffness and column cross sections (rectangular or square), building floor plans (square or rectangular), beam stiffness and slab stiffness, on building resistance to an earthquake. The stiffness of the columns contributed more than the beams and slabs to the earthquake resistance of H.R.B.s. Rectangular cross-section columns must be properly oriented in order for H.R.B.s and slender buildings to attain the maximum resistance against earthquakes.