Modal flexibility method for structural damage detection in suspension bridges

Suspension bridges meet the steadily growing demand for lighter and longer bridges in today’s infrastructure systems. These bridges are designed to have long life spans, but with age, their main cables and hangers could suffer from corrosion and fatigue. There is a need for a simple and reliable procedure to detect and locate such damage, so that appropriate retrofitting can be carried out to prevent bridge failure. Damage in a structure causes changes in its properties (mass, damping and stiffness) which in turn will cause changes in its vibration characteristics (natural frequencies, modal damping and mode shapes). Methods based on modal flexibility, which depends on both the natural frequencies and mode shapes, have the potential for damage detection. They have been applied successfully to beam and plate elements, trusses and simple structures in reinforced concrete and steel. However very limited applications for damage detection in suspension bridges have been identified to date. This paper examines the potential of modal flexibility methods for damage detection and localization of a suspension bridge under different damage scenarios in the main cables and hangers using numerical simulation techniques. Validated finite element model (FEM) of a suspension bridge is used to acquire mass normalized mode shape vectors and natural frequencies at intact and damaged states. Damage scenarios will be simulated in the validated FE models by varying stiffness of the damaged structural members. The capability of damage index based on modal flexibility to detect and locate damage is evaluated. Results confirm that modal flexibility based methods have the ability to successfully identify damage in suspension bridge main cables and hangers.

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.

A simulation-based large deflection and inelastic analysis of steel frames under fire

This paper presents an accurate and robust geometric and material nonlinear formulation to predict structural behaviour of unprotected steel members at elevated temperatures. A fire analysis including large displacement effects for frame structures is presented. This finite element formulation of beam-column elements is based on the plastic hinge approach to model the elasto-plastic strain-hardening material behaviour. The Newton-Raphson method allowing for the thermal-time dependent effect was employed for the solution of the non-linear governing equations for large deflection in thermal history. A combined incremental and total formulation for determining member resistance is employed in this nonlinear solution procedure for the efficient modeling of nonlinear effects. Degradation of material strength with increasing temperature is simulated by a set of temperature-stress-strain curves according to both ECCS and BS5950 Part 8, which implicitly allows for creep deformation. The effects of uniform or non-uniform temperature distribution over the section of the structural steel member are also considered. Several numerical and experimental verifications are presented.

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.

Higher-order non-linear analysis of steel structures. Part I : elastic second-order formulation

This paper presents a higher-order beam-column formulation that can capture the geometrically non-linear behaviour of steel framed structures which contain a multiplicity of slender members. Despite advances in computational frame software, analyses of large frames can still be problematic from a numerical standpoint and so the intent of the paper is to fulfil a need for versatile, reliable and efficient non-linear analysis of general steel framed structures with very many members. Following a comprehensive review of numerical frame analysis techniques, a fourth-order element is derived and implemented in an updated Lagrangian formulation, and it is able to predict flexural buckling, snap-through buckling and large displacement post-buckling behaviour of typical structures whose responses have been reported by independent researchers. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. The higher-order element forms a basis for augmenting the geometrically non-linear approach with material non-linearity through the refined plastic hinge methodology described in the companion paper.

Higher-order non-linear analysis of steel structures. Part II : refined plastic hinge formulation

In the companion paper, a fourth-order element formulation in an updated Lagrangian formulation was presented to handle geometric non-linearities. The formulation of the present paper extends this to include material non-linearity by proposing a refined plastic hinge approach to analyse large steel framed structures with many members, for which contemporary algorithms based on the plastic zone approach can be problematic computationally. This concept is an advancement of conventional plastic hinge approaches, as the refined plastic hinge technique allows for gradual yielding, being recognized as distributed plasticity across the element section, a condition of full plasticity, as well as including strain hardening. It is founded on interaction yield surfaces specified analytically in terms of force resultants, and achieves accurate and rapid convergence for large frames for which geometric and material non-linearity are significant. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. In addition to the numerical efficiency, the present versatile approach is able to capture different kinds of material and geometric non-linearities on general applications of steel structures, and thereby it offers an efficacious and accurate means of assessing non-linear behaviour of the structures for engineering practice.

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.

Direct second-order elastic analysis for steel frame design

The traditional structural design procedure, especially for the large-scale and complex structures, is time consuming and inefficient. This is due primarily to the fact that the traditional design takes the second-order effects indirectly by virtue of design specifications for every member instead of system analysis for a whole structure. Consequently, the complicated and tedious design procedures are inevitably necessary to consider the second-order effects for the member level in design specification. They are twofold in general: 1) Flexural buckling due to P-d effect, i.e. effective length. 2) Sway effect due to P-D effect, i.e. magnification factor. In this study, a new system design concept based on the second-order elastic analysis is presented, in which the second-order effects are taken into account directly in the system analysis, and also to avoid the tedious member-by-member stability check. The plastic design on the basis of this integrated method of direct approach is ignored in this paper for simplicity and clarity, as the only emphasis is placed on the difference between the second-order elastic limit-state design and present system design approach. A practical design example, a 57m-span dome steel skylight structure, is used to demonstrate the efficiency and effectiveness of the proposed approach. This skylight structure is also designed by the traditional design approach BS5950-2000 for comparison on which the emphasis of aforementioned P-d and P-D effects is placed.

On the advanced analysis of steel frames allowing for flexural, local and lateral-torsional buckling

Detailed procedure for second-order analysis has been coded in the newest Eurocode 3 and the Hong Kong steel code (2005). The effective length method has been noted to be inapplicable to analysis of shallow domes of imperfect members exhibiting snap-through buckling, to portals with leaning columns and others. On the other hand, the advanced analysis is not limited to buckling design of these structures. This paper demonstrates its application to the design of a simple plane sway portal and a three diminsional non-sway steel building. The results by the advanced analysis and the first-order linear analysis are compared and the technique for practical second-order analysis steel structures is described. It is observed that the use of a straight element by itself cannot model the buckling resistance of columns governed by different buckling curves for hot-rolled and cold-formed sections of various shapes like I, H, hollow etc. Also the curvature of the conventional cubic Hermite element is not varied by the external axial force and thus it cannot simulate the response of a buckling column. Thus its use for second-order analysis is basically unacceptable. A technique for additional checking of beams undergoing lateral-torsional buckling is also suggested making the advanced analysis a complete design tool for conventional steel frames.

Effects of cold weather on durability of CFRP strengthened circular hollow steel members

Tubular members have become progressively more popular due to excellent structural properties, aesthetic appearance, corrosion and fire protection capability. However, a large number of such structures are found structurally deficient due to reduction of strength when they expose to severe environmental conditions such as marine environment, cold and hot weather. Hence strengthening and retrofitting of structural members are in high demands. In recent times Carbon Fibre Reinforced Polymers (CFRP) composites appears to be an excellent solution to enhance the load carrying capacity and serviceability of steel structures because of its superior physical and mechanical properties. However, the durability of such strengthening system under cold environmental condition has not yet been well documented to guide the engineers. This paper presents the findings of a study conducted to enhance the bond durability of CFRP strengthened steel tubular members by treating steel surface using epoxy based adhesion promoter under cold weather subjected to bending. The experimental program consisted of six number of CFRP strengthened specimens and one bare specimen. The sand blasted surface of the three specimens to be strengthened was pre-treated with MBrace primer and other three were remained untreated and then cured under ambient temperature and cold weather (3oC) for three and six months period of time. The beams were then loaded to failure under four point bending. The structural response of each specimen was predicted in terms of failure mode, failure load and mid-span deflection. The research findings show that the cold weather immersion had an adverse effect on durability of CFRP strengthened structures. Moreover, the epoxy based adhesion promoter was found to enhance the bond durability in elastic range.

Blast response of reinforced concrete pile using fully coupled computer simulation techniques

Pile foundations transfer loads from superstructures to stronger sub soil. Their strength and stability can hence affect structural safety. This paper treats the response of reinforced concrete pile in saturated sand to a buried explosion. Fully coupled computer simulation techniques are used together with five different material models. Influence of reinforcement on pile response is investigated and important safety parameters of horizontal deformations and tensile stresses in the pile are evaluated. Results indicate that adequate longitudinal reinforcement and proper detailing of transverse reinforcement can reduce pile damage. Present findings can serve as a benchmark reference for future analysis and design.

Carbon nanotube composite sensor for structural health monitoring of bridge structures

Bridges are important infrastructures of all nations and are required for transportation of goods as well as human. A catastrophic failure can result in loss of lives and enormous financial hardship to the nation. Although various kinds of sensors are now available to monitor the health of the structures due to corrosion, they do not provide permanent and long term measurements. This paper investigates the fabrication of Carbon Nanotube (CNT) based composite sensors for corrosion detection of structures. Multi-wall CNT (MWCNT)/Nafion composite sensors were fabricated to evaluate their electrical properties for corrosion detection. The test specimens were subjected to real life corrosion experimental tests and the results confirm that the electrical resistance of the sensor electrode was dramatically changed due to corrosion.

Effects of joint thickness, adhesion and web shells to the face shell bedded concrete masonry loaded in compression

The Australian masonry standard allows either prism tests or correction factors based on the block height and mortar thickness to evaluate masonry compressive strength. The correction factor helps the taller units with conventional 10 mm mortar being not disadvantaged due to size effect. In recent times, 2-4 mm thick, high-adhesive mortars and H blocks with only the mid-web shell are used in masonry construction. H blocks and thinner and higher adhesive mortars have renewed interest of the compression behaviour of hollow concrete masonry and hence is revisited in this paper. This paper presents an experimental study carried out to examine the effects of the thickness of mortar joints, the type of mortar adhesives and the presence of web shells in the hollow concrete masonry prisms under axial compression. A non-contact digital image correlation technique was used to measure the deformation of the prisms and was found adequate for the determination of strain fi eld of the loaded face shells subjected to axial compression. It is found that the absence of end web shells lowers the compressive strength and stiffness of the prisms and the thinner and higher adhesive mortars increase the compressive strength and stiffness, while lowering the Poisson's ratio. © Institution of Engineers Australia, 2013.

Structural and material characterisation of insulated rail joints

Insulated rail joints are designed in a similar way to butt jointed steel structural systems, the difference being a purpose made gap between the main rail members to maintain electrical insulation for the proper functioning of the track circuitry at all times of train operation. When loaded wheels pass the gap, they induce an impact loading with the corresponding strains in the railhead edges exceeding the plastic limit significantly, which lead to metal flow across the gap thereby increasing the risk of short circuiting and impeding the proper functioning of the signalling and broken rail identification circuitries, of which the joints are a critical part. The performance of insulated rail joints under the passage of the wheel loading is complex due to the presence of a number of interacting components and hence is not well understood. This paper presents a dynamic wheel-rail contact-impact modelling method for the determination of the impact loading; a brief description of a field experiment to capture strain signatures for validating the predicted impact loading is also presented. The process and the results of the characterisation of the materials from virgin, in-service and damaged insulated rail joints using neutron diffraction method are also discussed.