Damage detection in cable structures using vibration characteristics

Cable structures find many applications such as in power transmission, in anchors and especially in bridges. They serve as major load bearing elements in suspension bridges, which are capable of spanning long distances. All bridges, including suspension bridges, are designed to have long service lives. However, during this long life, they become vulnerable to damage due to changes in loadings, deterioration with age and random action such as impacts. The main cables are more vulnerable to corrosion and fatigue, compared to the other bridge components, and consequently reduces the serviceability and ultimate capacity of the bridge. Detecting and locating such damage at the earliest stage is challenging in the current structural health monitoring (SHM) systems of long span suspension bridges. Damage or deterioration of a structure alters its stiffness, mass and damping properties which in turn modify its vibration characteristics. This phenomenon can therefore be used to detect damage in a structure. The modal flexibility, which depends on the vibration characteristics of a structure, has been identified as a successful damage indicator in beam and plate elements, trusses and simple structures in reinforced concrete and steel. Successful application of the modal flexibility phenomenon to detect and locate the damage in suspension bridge main cables has received limited attention in recent research work. This paper, therefore examines the potential of the modal flexibility based Damage Index (DI) for detecting and locating damage in the main cable of a suspension bridge under four different damage scenarios. Towards this end, a numerical model of a suspension bridge cable was developed to extract the modal parameters at both damaged and undamaged states. Damage scenarios considered in this study with varied location and severity were simulated by changing stiffness at particular locations of the cable model. Results confirm that the DI has the potential to successfully detect and locate damage in suspension bridge main cables. This simple method can therefore enable bridge engineers and managers to detect and locate damage in suspension bridges at an early stage, minimize expensive retrofitting and prevent bridge collapse.

Second-order inelastic analysis of composite framed structures based on the refined plastic hinge method

Composite steel-concrete structures experience non-linear effects which arise from both instability-related geometric non-linearity and from material non-linearity in all of their component members. Because of this, conventional design procedures cannot capture the true behaviour of a composite frame throughout its full loading range, and so a procedure to account for those non-linearities is much needed. This paper therefore presents a numerical procedure capable of addressing geometric and material non-linearities at the strength limit state based on the refined plastic hinge method. Different material non-linearity for different composite structural components such as T-beams, concrete-filled tubular (CFT) and steel-encased reinforced concrete (SRC) sections can be treated using a routine numerical procedure for their section properties in this plastic hinge approach. Simple and conservative initial and full yield surfaces for general composite sections are proposed in this paper. The refined plastic hinge approach models springs at the ends of the element which are activated when the surface defining the interaction of bending and axial force at first yield is reached; a transition from the first yield interaction surface to the fully plastic interaction surface is postulated based on a proposed refined spring stiffness, which formulates the load-displacement relation for material non-linearity under the interaction of bending and axial actions. This produces a benign method for a beam-column composite element under general loading cases. Another main feature of this paper is that, for members containing a point of contraflexure, its location is determined with a simple application of the method herein and a node is then located at this position to reproduce the real flexural behaviour and associated material non-linearity of the member. Recourse is made to an updated Lagrangian formulation to consider geometric non-linear behaviour and to develop a non-linear solution strategy. The formulation with the refined plastic hinge approach is efficacious and robust, and so a full frame analysis incorporating geometric and material non-linearity is tractable. By way of contrast, the plastic zone approach possesses the drawback of strain-based procedures which rely on determining plastic zones within a cross-section and which require lengthwise integration. Following development of the theory, its application is illustrated with a number of varied examples.

Nonlinear pre-fire and post-fire analysis of steel frames

A numerical procedure based on the plastic hinge concept for study of the structural behaviour of steel framed structures exposed to fire is described. Most previous research on fire analysis considered the structural performance due to rising temperature. When strain reversal occurs during the cooling phase, the stress–strain curve is different. The plastic deformation is incorporated into the stress–strain curve to model the strain reversal effect in which unloading under elastic behaviour is allowed. This unloading response is traced by the incremental–iterative Newton–Raphson method. The mechanical properties of the steel member in the present fire analysis follows both Eurocode 3 Part 1.2 and BS5950 Part 8, which implicitly allow for thermal creep deformation. This paper presents an efficient fire analysis procedure for predicting thermal and cooling effects on an isolated element and a multi-storey frame. Several numerical and experimental examples related to structural behaviour in cooling phase are studied and compared with results obtained by other researchers. The proposed method is effective in the fire safety design and analysis of a building in a real fire scenario. The scope of investigation is of great significance since a large number of rescuers would normally enter a fire site as soon as the fire is extinguished and during the cooling phase, so a structural collapse can be catastrophic.

Second-order elastic finite element analysis of steel structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies.

Effect of constitutive material models on seismic response of two-story reinforced concrete frame

This paper focuses on the finite element (FE) response sensitivity and reliability analyses considering smooth constitutive material models. A reinforced concrete frame is modeled for FE sensitivity analysis followed by direct differentiation method under both static and dynamic load cases. Later, the reliability analysis is performed to predict the seismic behavior of the frame. Displacement sensitivity discontinuities are observed along the pseudo-time axis using non-smooth concrete and reinforcing steel model under quasi-static loading. However, the smooth materials show continuity in response sensitivity at elastic to plastic transition points. The normalized sensitivity results are also used to measure the relative importance of the material parameters on the structural responses. In FE reliability analysis, the influence of smoothness behavior of reinforcing steel is carefully noticed. More efficient and reasonable reliability estimation can be achieved by using smooth material model compare with bilinear material constitutive model.

Nonlinear analysis for the pre- and post-yield behaviour of a hybrid structure by a higher-order element with the refined plastic hinge approach

Efficient and accurate geometric and material nonlinear analysis of the structures under ultimate loads is a backbone to the success of integrated analysis and design, performance-based design approach and progressive collapse analysis. This paper presents the advanced computational technique of a higher-order element formulation with the refined plastic hinge approach which can evaluate the concrete and steel-concrete structure prone to the nonlinear material effects (i.e. gradual yielding, full plasticity, strain-hardening effect when subjected to the interaction between axial and bending actions, and load redistribution) as well as the nonlinear geometric effects (i.e. second-order P-d effect and P-D effect, its associate strength and stiffness degradation). Further, this paper also presents the cross-section analysis useful to formulate the refined plastic hinge approach.

Thin-Walled Timber Structures

Due to their efficiency, lightweight, ease of erection and low cost, steel and aluminium thin-walled structures have become very popular in the construction industry over the past few decades. Applications include roof and wall systems (purlins and girts), storage racks, and composite concrete and steel slabs. The effectiveness of these structures lies in the cross-sectional shape of the profiles which enhances their strength by controlling the three fundamental buckling modes: local, distortional, and global. However, despite the attractiveness of these structures, steel and aluminium are greenhouse gas intensive materials and do not produce sustainable structural products. This paper presents an investigation performed at the Griffith School of Engineering, Griffith University, which shows manufacturing these types of profiles in timber is possible. Short composite thinwalled timber Cee-sections (500 mm long) were fabricated by gluing together thin softwood (Araucaria cunninghamii) veneers (1 mm thick). Two types of Ceesections were considered, one with a web stiffener to increase the local buckling capacity of the profile and one without. The profiles were tested in compression and the test results are presented and discussed in the paper in terms of structural behaviour and performance. Further research directions are proposed in order to provide efficient and lightweight sustainable structural products to the timber industry. © RILEM 2014.

Damage identification of beam-like structures with contiguous and distributed damage

Structural health monitoring of existing infrastructure is currently an active field of research, where elaborate experimental programs and advanced analytical methods are used in identifying the current state of health of critical structures. Change of static deflection as the indicator of damage is the simplest tool in a structural health monitoring scenario of bridges that is least exploited in damage identification strategies. In this paper, some simple and elegant equations based on loss of symmetry due to damage are derived and presented for identification of damage in a bridge girder modeled as a simply supported beam using changes in static deflections and dynamic parameters. A single contiguous and distributed damage, typical of reinforced or prestressed concrete structures, is assumed for the structure. The methodology is extended for a base-line-free as well as base-line-inclusive measurement. Measurement strategy involves application of loads only at two symmetric points one at a time and deflection measurements at those symmetric points as well as at the midspan of the beam. A laboratory-based experiment is used to validate the approach. Copyright (c) 2012 John Wiley & Sons, Ltd.

Earthquake response of steel braces and braced steel frames

This thesis consists of three parts. Chapter 2 deals with the dynamic buckling behavior of steel braces under cyclic axial end displacement. Braces under such a loading condition belong to a class of "acceleration magnifying" structural components, in which a small motion at the loading points can cause large internal acceleration and inertia. This member-level inertia is frequently ignored in current studies of braces and braced structures. This chapter shows that, under certain conditions, the inclusion of the member-level inertia can lead to brace behavior fundamentally different from that predicted by the quasi-static method. This result is to have significance in the correct use of the quasi-static, pseudo-dynamic and static condensation methods in the simulation of braces or braced structures under dynamic loading. The strain magnitude and distribution in the braces are also studied in this chapter.

Chapter 3 examines the effect of column uplift on the earthquake response of braced steel frames and explores the feasibility of flexible column-base anchoring. It is found that fully anchored braced-bay columns can induce extremely large internal forces in the braced-bay members and their connections, thus increasing the risk of failures observed in recent earthquakes. Flexible braced-bay column anchoring can significantly reduce the braced bay member force, but at the same time also introduces large story drift and column uplift. The pounding of an uplifting column with its support can result in very high compressive axial force.

Chapter 4 conducts a comparative study on the effectiveness of a proposed non-buckling bracing system and several conventional bracing systems. The non-buckling bracing system eliminates buckling and thus can be composed of small individual braces distributed widely in a structure to reduce bracing force concentration and increase redundancy. The elimination of buckling results in a significantly more effective bracing system compared with the conventional bracing systems. Among the conventional bracing systems, bracing configurations and end conditions for the bracing members affect the effectiveness.

The studies in Chapter 3 and Chapter 4 also indicate that code-designed conventionally braced steel frames can experience unacceptably severe response under the strong ground motions recorded during the recent Northridge and Kobe earthquakes.

Comprehensive Property Retrieval and Measurement of Concrete Spalling Using Machine Vision for Post-Earthquake Safety Assessments

Active vibration control (AVC) is a relatively new technology for the mitigation of annoying human-induced vibrations in floors. However, recent technological developments have demonstrated its great potential application in this field. Despite this, when a floor is found to have problematic floor vibrations after construction the unfamiliar technology of AVC is usually avoided in favour of more common techniques, such as Tuned Mass Dampers (TMDs) which have a proven track record of successful application, particularly for footbridges and staircases. This study aims to investigate the advantages and disadvantages that AVC has, when compared with TMDs, for the application of mitigation of pedestrian-induced floor vibrations in offices. Simulations are performed using the results from a finite element model of a typical office layout that has a high vibration response level. The vibration problems on this floor are then alleviated through the use of both AVC and TMDs and the results of each mitigation configuration compared. The results of this study will enable a more informed decision to be made by building owners and structural engineers regarding suitable technologies for reducing floor vibrations.

An efficient approach of modelling the flexural cracking behaviour of un-notched plain concrete prisms subject to monotonic and cyclic loading

In the field of vibration-based damage detection of concrete structures efficient damage models are needed to better understand changes in the vibration properties of cracked structures. These models should quantitatively replicate the damage mechanisms in concrete and easily be used as damage detection tools. In this paper, the flexural cracking behaviour of plain concrete prisms subject to monotonic and cyclic loading regimes under displacement control is tested experimentally and modelled numerically. Four-point bending tests on simply supported un-notched prisms are conducted, where the cracking process is monitored using a digital image correlation system. A numerical model, with a single crack at midspan, is presented where the cracked zone is modelled using the fictitious crack approach and parts outside that zone are treated in a linear-elastic manner. The model considers crack initiation, growth and closure by adopting cyclic constitutive laws. A multi-variate Newton-Raphson iterative solver is used to solve the non-linear equations to ensure equilibrium and compatibility at the interface of the cracked zone. The numerical results agree well with the experiments for both loading scenarios. The model shows good predictions of the degradation of stiffness with increasing load. It also approximates the crack-mouth-opening-displacement when compared with the experimental data of the digital image correlation system. The model is found to be computationally efficient as it runs full analysis for cyclic loading in less than 2. min, and it can therefore be used within the damage detection process. © 2013 Elsevier Ltd.

The sensitivity of vibration characteristics of reinforced concrete beams under incremental static and cyclic loading

The use of changes in vibration properties for global damage detection and monitoring of existing concrete structures has received great research attention in the last three decades. To track changes in vibration properties experimentally, structures have been artificially damaged by a variety of scenarios. However, this procedure does not represent realistically the whole design-life degradation of concrete structures. This paper presents experimental work on a set of damaged reinforced concrete beams due to different loading regimes to assess the sensitivity of vibration characteristics. Of the total set, three beams were subject to incremental static loading up to failure to simulate overloading, and two beams subject to 15 million loading cycles with varying amplitudes to produce an accelerated whole-life degradation scenario. To assess the vibration behaviour in both cases, swept sine and harmonic excitations were conducted at every damage level. The results show that resonant frequencies are not sensitive enough to damage due to cyclic loading, whereas cosh spectral and root mean square distances are more sensitive, yet more scattered. In addition, changes in non-linearity follow a softening trend for beams under incremental static loading, whilst they are significantly inconsistent for beams under cyclic loading. Amongst all examined characteristics, changes in modal stiffness are found to be most sensitive to damage and least scattered, but modal stiffness is tedious to compute due mainly to the difficulty of constructing restoring force surfaces from field measurements. © (2013) Trans Tech Publications.

Shear transfer across a diagonal crack in reinforced concrete strengthened with externally bonded FRP fabric

Aging concrete infrastructure in developed economies and more recently constructed concrete infrastructure in the developing world are frequently found to be deficient in structural strength relative to current needs. This can be attributed to a variety of factors including deterioration, construction defects, accidental damage, changes in understanding and failure to design for future loading requirements. Strengthening existing concrete structures can be a cost and carbon effective alternative to replacement. A competitive option for the strengthening of concrete slab-on-beam structures that are deficient in shear capacity is the U-wrapping of the down-stand beam portion of the shear span with externally bonded FRP fabric. While guidance exists for the strengthening of reinforced concrete by U-wrapping, the interaction between internal steel reinforcement, concrete and external FRP in the presence of a dominant diagonal shear crack is not well understood. An approach adopted in previous work has been to explore this interaction through conventional push-off testing. In conventional push-off testing, unlike in a beam, the shear plane is parallel to the direction of loading and perpendicular to the principal fibre orientation. This paper presents a novel push-off test variation in which the shear plane is inclined at 45° to the direction of loading and the principal fibre orientation. A variety of reinforcement ratios, FRP thicknesses and FRP end conditions are modelled. The implications of inclined cracking on debonding of FRP are investigated. The suitability and relevance of inclined push-off tests for further work in this area is also assessed. © 2013, NetComposite Limited.