Ordinary Bridge Research Articles

Exploring the Use of Orientation-Independent Inelastic Spectral Displacements in the Seismic Assessment of Bridges

ABSTRACT Seismic intensity measures (IMs) provide a link between the seismic hazard and the dynamic response of structures subjected to earthquake shaking. The spectral acceleration at the first and usually dominant vibration mode, Sa(T 1), is a popular choice for building structures. Meanwhile, the IM selection for bridges is non-trivial since they do not typically possess a single dominant mode. Even for ordinary bridges with a dominant mode, the behavior can change significantly in each principal direction through the activation, or yielding, of its different components. This study examines the performance of a novel IM that incorporates ground motion directionality and structure non-linearity in this context: the nn th percentile of all rotation angles of the inelastic spectral displacement, Sd i,RotDnn. This evaluation is carried out within the context of an ordinary bridge structure and is compared with other conventional IMs used in regional risk assessment of bridges. The case study bridge utilized is a highway overcrossing located in California with two spans and a continuous prestressed reinforced concrete box girder deck section. A large ground motion set was selected from the NGA-West2 database, and incremental dynamic analysis was carried out on the structure to assess the IM performance to characterize collapse. The results indicate that Sd i,RotDnn performs very well compared to other IMs for the bridge structure and could be a prudent choice to characterize inelastic response of bridges with several possible mechanisms in different principal directions. Also, using the RotD50 definition, typically used in ground motion models, showed a 17.3% increase in efficiency compared to RotD100 definition typically used in engineering practice.

Seismic evaluation method on shear strength models for round-end hollow piers of high-speed railway bridges

Round-end hollow pier has been widely used in China's high-speed railway (HSR) lines. Experimental studies have shown that the HSR round-end hollow pier may experiece bending shear failure in the transverse direction of bridge, which is a brittle failure. Although it is of great significance to clarify the shear strength model for HSR round-end hollow piers, their seismic shear performance and failure mode criterion are still unclear. Considering the existing seismic design codes of bridges are mostly applicable to ordinary bridge components, this paper proposes a shear strength model for HSR round-end hollow piers based on the truss model limiting equilibrium theory, and quasi-static test results. According to the proposed shear strength model, a bending-shear coupling numerical pier model was established using OpenSees. Then the accuracy of the proposed shear strength model is verified. The study results show that the proposed shear strength model can accurately obtain the shear strength of HSR round-end hollow piers compared with other evaluation methods. Besides, the numerical simulation results illustrate that the HSR round-end hollow pier is not prone to damage under the design seismic excitation. Corresponding to the extreme seismic excitation with the peak ground acceleration of 0.75 g, the HSR round-end hollow pier experiences bending shear failure, which can be accurately determine by the proposed shear strength model.

Fragility and vulnerability analysis of deteriorating ordinary bridges using simulated ground‐motion sequences

AbstractHighway bridges are critical components of the lifeline transport infrastructure in urban areas. They are designed with the expectation of not sustaining significant structural/non‐structural damage after major earthquake‐induced ground shaking. However, in the current structural performance‐based assessment practice, the effects of a pre‐damaged state during ground‐motion sequences are often neglected. Additionally, environmentally induced deterioration mechanisms (e.g., steel rebar corrosion) may exacerbate the consequences of such ground‐motion sequences on the seismic structural performance during the bridge design lifetime; yet such effects are commonly overlooked. This study proposes a computational methodology to derive state‐dependent fragility and vulnerability relationships (i.e., explicitly depending on the damage state achieved by the bridge structure during a first shock) for bridge structures subjected to chloride‐induced corrosion deterioration and ground‐motion sequences. The methodology is demonstrated for a case‐study ordinary bridge structure (representing a typical bridge vulnerability class in southern California) under seismic sequences assembled from the CyberShake 15.12 (hybrid) simulated ground‐motion database. In the proposed approach, parameterised (i.e., dependent on the corrosion deterioration level) vector‐valued probabilistic seismic demand models are developed for the bridge components (i.e., columns and shear keys). These models, calibrated through sequential cloud‐based nonlinear time‐history analyses, relate the dissipated hysteretic energy in the ground‐motion sequence to a deformation‐based engineering demand parameter induced by the first shock and a ground‐motion intensity measure of the second shock for a given corrosion deterioration level. Fragility relationships are first derived for a single ground motion at the component‐level; state‐dependent fragility relationships are then derived by considering the additional damage induced by a second ground motion within the simulated sequence (structure‐specific damage states are considered). Furthermore, a component‐based simulation approach accounting for the correlations across the components’ response is utilised to derive fragility relationships at the system level (i.e., for the bridge structure). Finally, appropriate damage‐to‐loss models for ordinary bridges are used to derive state‐dependent vulnerability relationships. The results demonstrate the significant impact of earthquake‐induced ground‐motion sequences and environmentally‐induced corrosion deterioration, emphasising the necessity of accounting for this multi‐hazard threat in the structural performance‐based assessment of bridges. Relative variations up to 120% can be found in the system‐level state‐dependent fragility median values comparing the results for the bridge in pristine and deteriorated conditions.

A New Experimental Investigation for Improving Bridge Management Systems and Road Operation Sustainability

Generally, during maintenance operations on bridges and motorway viaducts, the circulation of vehicles is limited or suspended. This causes significant economic losses due to the increase in the costs of transport: delays, increased fuel consumption, higher emissions of pollutants into the atmosphere, increased risk of accidents, etc. However, few studies have analyzed the influence of bridge vibrations on the final mechanical properties of the cement mortar placing during ordinary bridge service. As such, interest is increasing in repair techniques that could achieve high structural performance without reducing road service levels. This paper provides the results obtained through an innovative laboratory trials campaign that evaluated the influence of vibrations on the mechanical properties of high-performance mortar used for repairing bridge decks. The results of 24 cubic and prismatic specimens showed the relationship between the traffic-induced vibrations and the mechanical characteristics of the studied mortar. The findings can be considered as the first methodologic step that is necessary to address further field studies, drawing a detailed link between the repair techniques and transportation user costs. Based on the obtained results, a synthetic bridge management system framework was developed that merges the road function into the structural issue with the goals of increasing the resilience of road networks and optimizing the maintenance resources budget.

Flexural Performance of a Hybrid Bridge Deck with Pultruded Fibre Reinforced Polymer Composite Sandwich Panels

Hybrid bridge decks with the pultruded fibre reinforced polymer have advantageous properties but easily crack because of their unsatisfactory transverse strength and shear strength. This study proposed a type of bridge deck composed of innovative pultruded fibre reinforced polymer composite sandwich panels. Using four-point bending tests, concentric wheelloading tests and eccentric wheel-loading tests combined with first-order shear deformation theory, this study investigated the failure mode, flexural capacity, deformation and ductility of hybrid bridge decks under different working conditions. Under four-point bending and concentric wheel loading, the primary failure modes for this hybrid bridge deck were shear failures along the fibre direction and buckling failure of the upper panel. Under eccentric wheel loading, the primary failure mode was a torsional failure due to the eccentric load. The bearing capacities of the hybrid bridge deck under the three working conditions were 3.8, 3.5 and 3.2 times the service load of a Class I vehicle load, respectively. Besides, the hybrid bridge deck remained in the linear elastic stress state at 2.6 times the service load, indicating that this hybrid bridge deck withstands relatively large vehicle overload without visible damage. The ductility values of this hybrid bridge deck under the three working conditions were 1.79, 2.09 and 2.00, respectively, which are higher than the values for an ordinary pultruded bridge deck. Therefore, the proposed design has the relatively good energy-dissipating capacity, which improves the emergency capacity of the bridge deck.

Design of bridges with skewed abutments for a target tolerable seismic loss

A comprehensive risk based bridge design procedure through which the effect of abutment skew angle is considered upfront aiming at uniformity in seismic risk is presented. We demonstrate a method for conceptual design of bridges with skewed abutments aiming at uniform performance (i.e., tolerable loss) objectives. In the proposed technique, few simple design aid graphs are developed by estimating the bridge repair cost ratios (RCRs) at different levels of column drift ratios (CDRs) and abutment skew angles. The suggested graphs parameters are estimated by implementing a full Monte Carlo probabilistic simulation over Pacific Earthquake Engineering Research Center (PEER) Probabilistic Based Seismic Assessment (PBSA). To show the significance of the proposed conceptual design method, a two-span Caltrans ordinary bridge class is selected for case study while various design parameters such as column diameter, column height to depth ratio, longitudinal reinforcement ratio, and span length are included as design variables. The effect of abutment skew angle on the probability of exceeding an RCR as well as probability of bridge collapse is explored by considering various bridge design parameters. Limitations of the proposed approach are discussed.

Methods for Calculating Shear Capacity on Oblique Section of Bending Members Strengthened with Enlarged Section

We infer that several equations currently used to calculate the bearing capacity of an oblique section of a member strengthened with an enlarged section have several mistakes in the specifications for strengthening the design of highway bridges (JTG/T J22-2008). The shear capacity of the oblique section of a bending member strengthened with an enlarged section could be more accurately and safely calculated using contrastive analysis of relevant design specifications and engineering calculation examples. We particularly challenged the calculation method in which the new stirrups bear the second increased shear based on the proportion of the section area of all web reinforcements. We proposed two calculation methods which can be applied to the general case of unilateral thickening of the member section and the reinforcement of three sides. We also tested an engineering example. The second proposed method, which considered the comprehensive shear capacity of concrete and stirrups, is simple and relatively safe. This method is unified with the design specification of an ordinary bridge component. The proposed method will be adopted in the technical specifications for strengthening of urban bridges which will be enacted soon.

Bridge Estimation for Linear Regression Models with Mixing Properties

SummaryPenalized regression methods have for quite some time been a popular choice for addressing challenges in high dimensional data analysis. Despite their popularity, their application to time series data has been limited. This paper concerns bridge penalized methods in a linear regression time series model. We first prove consistency, sparsity and asymptotic normality of bridge estimators under a general mixing model. Next, as a special case of mixing errors, we consider bridge regression with autoregressive and moving average (ARMA) error models and develop a computational algorithm that can simultaneously select important predictors and the orders of ARMA models. Simulated and real data examples demonstrate the effective performance of the proposed algorithm and the improvement over ordinary bridge regression.

Track-Bridge Longitudinal Interaction of Continuous Welded Rails on Arch Bridge

Taking arch bridges, including deck, half-through, and through arch bridges (short for DAB, HTAB, and TAB) as examples, mechanics analysis models of longitudinal interaction between continuously welded rails (short for CWRs) and arch bridges are established. Based on the finite element method (FEM), the longitudinal interaction calculation software of CWR on arch bridges has been developed. Focusing on an HTAB, the tension, compression, and deflection conditions are calculated and analyzed. The results show that the mechanics analysis models of three types of arch bridges can truly reflect the real state of the structure; the calculation software can be used for systematic research of the CWR on arch bridge; as for HTAB, temperature difference of arch rib has a small effect on rail tension/compression, and arch bridge can be simplified as a continuous beam for rail tension/compression additional force calculation; in calculation of deflection conditions of HTAB, it is suggested that train loads are arranged on half span and full span and take the direction of load entering bridge into account. Additionally, the deflection additional force variation of CFST basket handle arch bridge is different from that of ordinary bridge.

Moving Substrate in an Ephemeral Stream

A case study concerns a small bridge site in an arid area where ongoing inhibition of the transport of bed load sediment has caused chronic problems and maintenance issues for many years. The crossing of Guadalupe Arroyo by US-62-180 exhibits many unusual and important characteristics that are seldom seen in one place. Guadalupe Arroyo is an ephemeral stream in a very arid area. The stream originates high on the east slopes of the Guadalupe Mountains of Texas, where the watershed is subject to rainfall generated by orographic lift. The stream traverses several miles of arid land and ultimately disappears into a dry lake. It is subject to severe flash flooding because of the slope and orographic effects of the mountains, and it apparently transports large amounts of widely graded material (silt to boulder sized). A bridge across this stream was constructed for US-62-180 in 1959. Since that construction, the stream has exhibited symptoms of instability in the reach around the bridge, manifesting as chronic, severe aggradation accompanied by widening, avulsion, and bank erosion. Evidence exists of large magnitude transport of very large particles on a regular basis, to the extent of requiring protection of the piles from boulder impacts. Maintenance forces have continually removed accumulated bed material from the bridge opening and the reach immediately upstream. A large lens of bed material has accumulated upstream and extends approximately 1,000 ft (305 m) from the bridge. This site presents a rare opportunity to study an extreme case of the inadvertent inhibition of the transport of bed material in an ephemeral desert stream by the construction of an otherwise ordinary and innocuous highway bridge.

Helix Pedestrian Bridge

Amgen Incorporated, one of the world's largest biotechnology firms, recently developed a new research center on the Elliot Bay waterfront of Seattle, Washington. As part of the research center, a pedestrian bridge was built to connect the campus with a major transportation corridor. The owner's goal for the new pedestrian bridge was to create a signature gateway to Amgen's campus. The pedestrian bridge is a three-arch structure that depicts a three-dimensional helix. The overall shape of the bridge both reflects the helical DNA that connects all life and references the vital research under way at Amgen. The arches create the outline of the basic DNA helix, and the deck support and roof trusses complete the remaining components of the helix. The abstract double helix provided many design and construction challenges. The slim profile, large enclosed areas, and suspended deck meant wind and pedestrian vibration would be critical design considerations. The unique shape made it difficult to apply the standard building or bridge design codes. The contractor was faced with erecting this twisting structure over active railroad tracks while meeting tight geometric specifications. The bridge stands today as a testimony to the owner's vision, teamwork, innovation in bridge design, and creative construction techniques. The bridge combines both form and function to show how an ordinary pedestrian bridge can become an extraordinary statement while serving its intended function. The project has won broad community support in the few months that it has been open.

On duality of probabilities for card dealing

We simplify and generalize a result of Sobel and Frankowski concerning the equality in distribution of certain random quantities associated with dealing cards Sobel and Frankowski [1] recently described a notion of for carddealing probabilities. They prove the equality of certain probabilities for different card-dealing schemes, and then discuss applications of their work. Their proof is quite computationally involved. The purpose of this short note is to present a much simpler and more conceptual proof of their result, which also generalizes it substantially. Consider a deck of N cards, called Deck #1, which contains b different (e.g., suits), of sizes mI, ... , Mb . Consider dealing (uniformly at random) j different hands from this deck, of sizes n, ...I , nj . Without loss of generality we assume that mI +.. +mb=n1 + ++nj=N (since if not, we could always include an extra category or an extra hand to make this so). For clarity, the case N = 52, b = j = 4, imI = = m. 4 = n = ...= n4 = 13 corresponds to dealing an ordinary bridge game. For 1 < x < b and 1 < y < j, we let Cxy by the random variable representing the number of cards from category x dealt to hand y. Let C record these numbers as a random b x j matrix. To explain the duality notion, consider a second deck of N cards, Deck #2, which has the sizes of categories and hands reversed. Thus, this second deck has j different categories of sizes nI, ... , nj, and we deal out b different hands of sizes mI, ... , Mbb. We let Dxy be the random variable representing the number of cards from category x in hand y2. Let D record these numbers as a random j x b matrix. Received by the editors December 15, 1992 and, in revised form, March 31, 1993. 1991 Mathematics Subject Classification. Primary 60C05. ? 1994 American Mathematical Society 0002-9939/94 $1.00 + $.25 per page

Differentially DC biased type magnetic field sensor of high sensitivity

The detection principle of a novel magnetic field sensor called the differentially-DC-biased magnetic field sensor which uses a magnetic core is described. The detectable lower limit is extended up to the order of 10/sup -13// square root Hz by virtue of the detection principle used, which is analogous to the equilibrium condition of ordinary bridge circuits. By using two cores, a kind of bridge circuit is constituted. The field to be detected breaks the equilibrium condition, which leads to the variation of incremental permeability. The means adapted to detect the variation with high sensitivity are described.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dielectric studies on synthetic and natural polyelectrolytes

Abstract Several characteristics of the dielectric properties of aqueous polyelectrolyte solutions are reviewed on the basis of our theoretical and experimental studies on these materials. Samples used were ionic homopolymers, copolymers of maleic acid, and natural polysaccharides, all of which were flexible linear polymers having a number of ionizable groups. Measurements were made by using an ordinary bridge method or a pseudo-random noise spectrometer in a frequency region between 10 Hz and 1 to 5 MHz. These polyelectrolyte solutions exhibit quite a large dielectric constant, e.g., several times larger than the value of water below 100 Hz. The dispersion profile consists of two regions, one in the low frequency region below 10 kHz (LFD), and the other in the high frequency region near 1 MHz(HFD). The results are consistent with the counterion fluctuation theory proposed previously. Namely, according to the theory, the dielectric polarization is related to the fluctuation of the bound ions and its dispe...

A note on the correct evaluation of junction capacitance of a solar cell

Abstract In the fabrication of low-cost solar cells one has often to contend with finite series and shunt resistances. These tend to give misleading values of the junction capacitance as measured with an ordinary bridge. The problem is discussed analytically and graphical plots are given for determination of the true values from the measured ones. Practical use of these plots is discussed and illustrated with the help of experiments on thin-film Cu2S-CdS solar cells.

Measuring the mass burning rate of solid explosives

are attached to the fixed end. The strain gages are connected to an ordinary bridge circuit with thermal compensation. For purposes of additional temperature stabilization the measuring bridge and the bracket are located in a massive metal housing 1, filled with silicone oil 4. The oil bath simultaneously serves to damp the natural vibrations of the bracket. The natural frequency of the bracket in the oil was about 70 Hz for wire resistance strain gages and 120 Hz for semiconductor devices. The signal was amplified by means of an amplifier 7 capable of operating in the static-dynamic regime. The amplifier output signal was registered with an N-70O loop oscillograph 8. The frequency response and sensitivity of the measuring apparatus are determined by both the dimensions and material of the bracket and the selected transducer circuit. The natural frequency of the bracket is expressed in terms of its parameters by the relation

Elastic Equilibrium in the Theory of Structures

The standard specifications and formulas used in structural design, were devised to meet the problems encountered in ordinary bridge and building construction. They are well adapted to this purpose and have been found convenient and practical. When, however, an attempt is made to treat certain special problems, the limitations of these standard formulas become apparent. For instance, in the reinforcement of existing structures, an investigation of their strength depends on a rational analysis of their loads, stresses, and strains, and the design of their reinforcement must be based on such analysis, rather than on any empirical formulas. Another class of structure which demands special treatment is that used in railroad electrification work for the support of transmission wires, trolley catenary wiring, outdoor sub-station wiring, and switching. For some years, the writer has been actively engaged in the design of such structures, and has found it entirely practical to use bents which, while thoroughly braced, neither follow the usual design nor stay within the limits set up in some of the conventional rules.

A Galvanometer for Alternate Current Circuits

Tests of effects due to change of current, such as induction phenomena, are often hard to carry out because the ballistic galvanometer available is not sensitive enough. Alternate current tests are still less satisfactory owing to special difficulties. The vibration galvanometer overcomes only a few of these difficulties. It must be adjusted to resonance for the best effects, and its indications vary with current frequency. The sensitiveness of ballistic galvanometer tests can be greatly increased by the use of some form of mechanical commutator by means of which a crude form of alternate current is produced. A better method would be to generate the current in the usual way if a suitable instrument existed. The galvanometer here described is the result of an attempt to construct a measuring instrument by means of which inductances and capacities can be compared by bridge methods as accurately as it is possible to compare resistances. The instrument is like a moving coil galvanometer in almost every respect, except that its field is due to a specially constructed electromagnet excited by an alternating voltage. This voltage V is applied to a winding of m turns of the electromagnet, and the core flux N is such that V = rA + mN, where r is the resistance of the winding and A the current traversing it. The coil and electromagnet are so designed that for currents of the frequencies used the value of rA is negligible in comparison with V. The rate of change of N will therefore be at each instant a measure of V, whatever the permeability or hysteresis of the core. The instrument has a laminated electromagnet formed of stampings of two kinds - a rectangular portion with two straight limbs forming the core of the electromagnet, and a specially shaped stamping between the poles. The moving coil of 50 turns swings in a narrow gap separating the stampings, in much the same way as in a permanent magnet instrument. On the limbs of the magnet are windings of 200, 2000, and 4000 turns. The iron will not be too strongly magnetised if the winding used contains 20 turns per volt on 50 similar circuits, but the instrument is so sensitive that such excitation will only be needed for exceptional tests. If a voltage V be applied to one of the field coils of m turns, and if the same, or another, field winding of n turns be joined up, through a condenser of K microfarads, to the moving coil, the torque acting on this moving coil will be a measure of Kn(V/m)2; i.e. the deflexion is proportional to the square of the voltage. By suitably choosing K, m and n, the voltmeter may be used over a large number of ranges. Thus with the instrument shown a deflexion of 200 mm. on a scale at 1 metre distance, can be obtained either for 200 volts or for 20 millivolts. The deflexion is independent of frequenev and wave-form if the field-winding to which the voltage is applied has a resistance negligible in comparison with its impedance. Thus with m=4000 and n=200 it was found that the value of V2 required to give a certain deflexion was independent of frequency between 50 similar and 100 similar, but at 25 similar it was 6½ per cent. less than at 50 similar. At any fixed frequency the deflexion will always measure KV2. The instrument may be used with great advantage to compare inductances and capacities by the ordinary bridge methods, the working conditions being (i.) the alternating voltage V applied to the field coil of the instrument must also cause the current in the bridge conductors, (ii.) the alternate current in the bridge must be made in phase with the voltage V by the use of suitable non-inductive resistances, (iii.) the moving coil must be placed directly across the bridge. The balance can be adjusted with ease to 1 part in 10,000 when the voltages set up on the coils or condensers are of the order of 1 volt. When a balance of great precision is needed, the minute electromotive force e induced in the moving coil by the alternating field of the magnet, tends to cause a small deflexion disturbing the balance. When the moving coil circuit is non-inductive, the current due to e will be in phase with e and in quadrature with the flux so that the corresponding deflexion will be negligible. But in all cases any effect due to e can be accurately eliminated by working to a false zero. As illustrations of the behaviour of the instrument, the results of tests are given on the measurement of the mutual induction of coils, the comparison of capacities, and the measurement of Specific Inductive capacity.

2. On the Measurement of Resistance to Electrolytes

The difficulties attending the measurement of the electrical resistance of electrolytes are well known, the rapid growth of the polarisation of the electrodes especially preventing the application of the ordinary Wheatstone Bridge method. The polarisation may be kept down by using alternating currents, as was done by Kohlrausch; and this method is no doubt the most general and most accurate which has yet been applied.