Examining the presence of Arching-Action in Edge Stiffened Bridge Deck Cantilever Overhangs Subjected to a Wheel Load

Engineers have proposed the idea that there may be some arching action present in bridge deck cantilever overhangs stiffened along their longitudinal free edge, via a traffic barrier, subjected to a wheel load. This paper includes the details of a full-scale corrosion-free bridge deck with cantilever overhangs stiffened along their longitudinal free edge by a traffic barrier wall that has been constructed and tested under static and fatigue wheel loads at the University of Manitoba. It also reviews experimental test results and postulates various discussions that suggest the presence of arching-action in cantilever slab overhangs. Test results indicated static ultimate load capacities significantly greater than the ultimate capacity if the mode of failure and behavior of the cantilever overhang was completely flexural. These early results confirm and indicate the presence of arching-action resulting in a significant break-through in cantilever behavior when subjected to a wheel load. The theory to account for this arching-action is not yet developed and further research should be conducted.

Comportamiento a fatiga por cortante de elementos lineales de hormigón armado sin cercos

Las estructuras de hormigón son susceptibles de sufrir los efectos asociados a las acciones de fatiga cuando estas se ven sometidas a un elevado número de cargas repetidas. Muchas de estas estructuras no requieren armadura transversal para cumplir los condicionantes de dimensionamiento estático como por ejemplo las losas superiores de tableros de puentes, los muros de contención, las losas de transición de puentes, las torres eólicas o las estructuras marítimas. La mayor parte de los códigos de diseño vigentes no incluyen una comprobación específica del nivel de seguridad a cortante de estas estructuras para acciones de fatiga, y aquellas que lo hacen prefieren utilizar expresiones de tipo empírico basadas en curvas S-N que relacionan el número de ciclos resistentes con el valor de la carga aplicada. A pesar de que el empleo de curvas S-N es de gran utilidad desde un punto de vista práctico, estas curvas no permiten comprender el proceso de rotura por cortante para cargas repetidas. El objetivo principal de esta Tesis es el de estudiar el comportamiento a cortante de elementos de hormigón armado sin cercos sometidos a fatiga. Además, el análisis es ampliado al estudio del comportamiento transversal de los voladizos de las losas superiores de tableros de puentes de hormigón que de forma habitual son diseñados sin armadura de cortante. De forma habitual estos elementos se diseñan atendiendo a criterios de dimensionamiento estáticos sin tener en cuenta la resistencia a cortante cuando se ven sometidos a cargas cíclicas. A pesar de que las cargas de fatiga son inferiores a aquellas que producen el fallo estático, es importante tener en cuenta el comportamiento de estos elementos ante cargas repetidas. Los trabajos experimentales existentes en vigas de hormigón armado sin cercos evidenciaron diferencias significativas entre los modos de fallo ante cargas estáticas y cíclicas. Estos trabajos llegaron a la conclusión de que estos elementos diseñados para tener un fallo dúctil por flexión pueden llegar a desarrollar un tipo de fallo frágil por cortante cuando se ven sometidos a cargas repetidas. El proceso de rotura por cortante en elementos de hormigón armado sin cercos sometidos a fatiga es un proceso complejo que debe ser estudiado en profundidad debido al carácter frágil de este tipo de fallo. Los trabajos experimentales permitieron comprobar que el origen de este fallo tiene lugar tras la formación de una fisura de cortante a partir de una fisura de flexión formada durante los primeros ciclos en el vano de cortante. Tras la formación de esta fisura, esta se va propagando hacia la cabeza de compresión hasta que finalmente se produce el fallo como consecuencia de la destrucción de la cabeza de compresión cuando la altura alcanzada por esta es insuficiente para resistir la fuerza de compresión aplicada en esta zona. Por otra parte, la propagación de esta fisura diagonal puede desarrollarse por completo en el instante en el que esta se forma derivando en un tipo de fallo por cortante más frágil que el anterior. El proceso de fatiga es estudiado en esta Tesis mediante un modelo mecánico. Por una parte, se propone un modelo predictivo para determinar el número de ciclos acumulados hasta que se forma la fisura diagonal en función del estado tensional que se tiene en la punta de una fisura crítica de flexión formada en los primeros ciclos. Por otra parte, la resistencia a fatiga tras la formación de la fisura diagonal se analiza teniendo en cuenta el daño por fatiga acumulado en la cabeza de compresión y las variables que afectan a la propagación de esta fisura de cortante. Para la evaluación de la resistencia a fatiga tras la formación de la fisura crítica de cortante en este tipo de elementos, se plantea un modelo teórico basado en conceptos de Mecánica de la Fractura adaptados al hormigón. Este modelo puede ser aplicado a vigas de hormigón armado sin cercos de canto constante o variable siguiendo diferentes procedimientos. Una campaña experimental ha sido llevada a cabo con el objetivo de estudiar el comportamiento a cortante de vigas de hormigón armado sin cercos de canto variable sometidas a cargas estáticas y de fatiga. Se han desarrollado un total de diez ensayos estáticos y de fatiga para diferentes niveles de carga y esbelteces de cortante, teniendo lugar diferentes modos de fallo. Estos elementos fueron diseñados para reproducir, a escala real y de forma simplificada, los voladizos laterales de las losas superiores de tableros de puentes de carretera de hormigón. Los resultados experimentales demostraron que el tipo de fallo desarrollado depende de varios parámetros como por ejemplo el nivel de carga máxima, el nivel de oscilación de tensiones en la armadura longitudinal, la esbeltez de cortante o la calidad del hormigón utilizado entre otros. Para valores similares de esbeltez de cortante, los ensayos de fatiga realizados permitieron comprobar que la rotura por cortante de estos elementos está asociada a niveles de carga máxima elevados, mientras que el fallo por fatiga de la armadura longitudinal tiene mayor probabilidad de ocurrir en elementos sometidos a elevados niveles de oscilación de tensiones en esta armadura. Además, estos ensayos han sido analizados a través del modelo propuesto para tratar de comprender el comportamiento resistente de estos elementos sometidos a cargas de fatiga. Concrete structures are able to suffer fatigue when they are subjected to high number of cyclic loads. Many of these need not shear reinforcement to satisfy static design requirements, such as bridge deck slabs, retaining walls, bridge approach slabs, wind towers or maritime structures among others. Many codes of practice do not include a verification of the shear fatigue safety. Moreover, those which include it still prefer empirical S-N-based approaches that provide the number of cycles as a function of applied forces. S-N models are practical but they do not provide information to understand the shear fatigue process. The main objective of this Thesis is to study shear behaviour of reinforced concrete elements without stirrups subjected to fatigue loads. In addition, the analysis is extended in order to study the transverse behaviour of cantilever slabs of concrete bridges that traditionally are designed without shear reinforcement. These elements usually are designed on the basis of static strength and it is unusual that codes consider fatigue strength of concrete in shear. Accordingly, it is important to take into account the fatigue behaviour of structural members subjected to cyclic loads although these loads are lower than those which produce the static failure. Existing experimental works show important differences between the static and cyclic failure modes of reinforced concrete beams without stirrups. These works concluded that beams without transverse reinforcement, designed to have a ductile failure mode in flexure, can submit a brittle shear failure mode when they are subjected to repeated loads. Shear fatigue failure of reinforced concrete beams without stirrups is a rather complex process from the mechanical viewpoint. Since it leads to a brittle failure mode it should be better understood. Experimental evidence indicates that a diagonal crack first develops from the inclination of flexural cracks in the shear span. Thereafter, the diagonal crack propagates into the compression zone. Failure normally takes place by the destruction of the compression zone when its depth is too small to resist the applied force. The propagation of the diagonal crack can also be instantaneous, leading to sudden diagonal cracking fatigue failure rather than shear-compression failure. Fatigue process is studied in this Thesis on a mechanical basis. On the one hand, a predictive model is derived to obtain the number of cycles up to diagonal cracking, as a function of the stress state at the tip of a critical flexural crack. On the other hand, the residual fatigue strength after diagonal cracking is analyzed taking into account the fatigue damage accumulated by the compression zone and the variables affecting the propagation of the diagonal crack. In order to assess the residual fatigue strength after diagonal cracking of such elements, a theoretical model is proposed based on concepts from fracture mechanics adapted to concrete. This model can be successfully applied for straight or haunched reinforced concrete beams without stirrups following different procedures. In order to achieve a more advanced knowledge in this subject, an experimental campaign has been carried out with the aim of study the shear behaviour of reinforced concrete haunched beams without stirrups subjected to static and fatigue loads. A total of ten static and fatigue tests have been performed with distinct load levels and shear span-to-depth ratios, presenting different failures modes. These elements were designed to reproduce in a simplified form the cantilever slab of concrete bridges at real scale. Experimental results showed that the type of failure depends on several parameters as for example the maximum load level, the stress oscillation level on the longitudinal reinforcement, the shear span-to-depth ratio or the quality of the concrete used among others. For a similar value of the shear span-to-depth ratio, tests evidenced that shear fatigue failure is related to high maximum load levels, while steel fatigue failure is easier to occur in elements subjected to high stress oscillation level on the reinforcement bars. Besides, these tests have been analyzed through the proposed model in order to clarify the structural behaviour of such elements subjected to fatigue loads.

Elastic lateral buckling of cantilever LiteSteel beams under transverse loading

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using its patented dual electric resistance welding and automated continuous roll-forming technologies. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. Its flexural strength for intermediate spans is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion. Recent research on LSBs has mainly focussed on their lateral distortional buckling behaviour under uniform moment conditions. However, in practice, LSB flexural members are subjected to non-uniform moment distributions and load height effects as they are often under transverse loads applied above or below their shear centre. These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The non-uniform moment distribution and load height effects of transverse loading on cantilever LSBs, and the suitability of the current design modification factors to include such effects are not known. This paper presents a numerical study based on finite element analyses of the elastic lateral buckling strength of cantilever LSBs subject to transverse loading, and the results. The applicability of the design modification factors from various steel design codes was reviewed, and suitable recommendations are presented for cantilever LSBs subject to transverse loading.

Damage detection in slab-on-girder bridges using vibration characteristics

This paper develops and applies a multi-criteria procedure, incorporating changes in natural frequencies, modal flexibility and the modal strain energy, for damage detection in slab-on-girder bridges. The proposed procedure is first validated through experimental testing of a model bridge. Numerically simulated modal data obtained through finite element analyses are then used to evaluate the vibration parameters before and after damage and used as the indices for assessment of the state of structural health. The procedure is illustrated by its application to full scale slab-on-girder bridges under different damage scenarios involving single and multiple damages on the deck and girders.

Design and experimental testing of air slab caps which convert commercial electron diodes into dual purpose, correction-free diodes for small field dosimetry

Purpose Two diodes which do not require correction factors for small field relative output measurements are designed and validated using experimental methodology. This was achieved by adding an air layer above the active volume of the diode detectors, which canceled out the increase in response of the diodes in small fields relative to standard field sizes. Methods Due to the increased density of silicon and other components within a diode, additional electrons are created. In very small fields, a very small air gap acts as an effective filter of electrons with a high angle of incidence. The aim was to design a diode that balanced these perturbations to give a response similar to a water-only geometry. Three thicknesses of air were placed at the proximal end of a PTW 60017 electron diode (PTWe) using an adjustable “air cap”. A set of output ratios (ORfclin Det ) for square field sizes of side length down to 5 mm was measured using each air thickness and compared to ORfclin Det measured using an IBA stereotactic field diode (SFD). k fclin, f msr Qclin,Qmsr was transferred from the SFD to the PTWe diode and plotted as a function of air gap thickness for each field size. This enabled the optimal air gap thickness to be obtained by observing which thickness of air was required such that k fclin, f msr Qclin,Qmsr was equal to 1.00 at all field sizes. A similar procedure was used to find the optimal air thickness required to make a modified Sun Nuclear EDGE detector (EDGEe) which s “correction-free” in small field relative dosimetry. In addition, the feasibility of experimentally transferring k fclin, f msr Qclin,Qmsr values from the SFD to unknown diodes was tested by comparing the experimentally transferred k fclin, f msr Qclin,Qmsr values for unmodified PTWe and EDGEe diodes to Monte Carlo simulated values. Results 1.0 mm of air was required to make the PTWe diode correction-free. This modified diode (PTWeair) produced output factors equivalent to those in water at all field sizes (5–50 mm). The optimal air thickness required for the EDGEe diode was found to be 0.6 mm. The modified diode (EDGEeair) produced output factors equivalent to those in water, except at field sizes of 8 and 10 mm where it measured approximately 2% greater than the relative dose to water. The experimentally calculated k fclin, f msr Qclin,Qmsr for both the PTWe and the EDGEe diodes (without air) matched Monte Carlo simulated results, thus proving that it is feasible to transfer k fclin, f msr Qclin,Qmsr from one commercially available detector to another using experimental methods and the recommended experimental setup. Conclusions It is possible to create a diode which does not require corrections for small field output factor measurements. This has been performed and verified experimentally. The ability of a detector to be “correction-free” depends strongly on its design and composition. A nonwater-equivalent detector can only be “correction-free” if competing perturbations of the beam cancel out at all field sizes. This should not be confused with true water equivalency of a detector.

A water model study of the flow asymmetry inside a continuous slab casting mold

The work studies the extent of asymmetric flow in water models of continuous casting molds of two different configurations. In the molds where fluid is discharged through multiple holes at the bottom, the flow pattern in the lower portion depends on the size of the lower two recirculating domains. If they reach the mold bottom, the flow pattern in the lower portion is symmetrical about the central plane; otherwise, it is asymmetrical. On the other hand, in the molds where the fluid is discharged through the entire mold cross section, the flow pattern is always asymmetrical if the aspect ratio is 1:6.25 or more. The fluid jet swirls while emerging through the nozzle. The interaction of the swirling Jets with the wide sidewalls of the mold gives rise to asymmetrical flow inside the mold. In the molds with lower aspect ratios, where the jets do not touch the wide side walls, the flow pattern is symmetrical about the central plane.

Free vibration of a kinked cantilever with attached masses

In this paper free vibration characteristics of a centrally kinked cantilever beam of unit mass carrying masses at the kink (m(k)) and at the tip (m(t)) are analyzed. Frequency factors are presented for the first two modes for different combinations of m(k),m(t) and the kink angle delta. A relationship of the form f(m(k),m(t), delta) = m(k) + m(t)(4 + 10/3 cos delta+ 2/3 cos(2) delta)=const appears to give the same fundamental frequency for a given delta and different combinations of [m(k), m(t)]. Mode shapes as well as bending moments at the support and at the kink are also discussed. The utility of a discrete beam model in understanding the free vibration characteristics is also highlighted.

Size optimization of a cantilever beam under deformation-dependent loads with application to wheat stalks

In this paper, we consider the optimization of the cross-section profile of a cantilever beam under deformation-dependent loads. Such loads are encountered in plants and trees, cereal crop plants such as wheat and corn in particular. The wind loads acting on the grain-bearing spike of a wheat stalk vary with the orientation of the spike as the stalk bends; this bending and the ensuing change in orientation depend on the deformation of the plant under the same load.The uprooting of the wheat stalks under wind loads is an unresolved problem in genetically modified dwarf wheat stalks. Although it was thought that the dwarf varieties would acquire increased resistance to uprooting, it was found that the dwarf wheat plants selectively decreased the Young's modulus in order to be compliant. The motivation of this study is to investigate why wheat plants prefer compliant stems. We analyze this by seeking an optimal shape of the wheat plant's stem, which is modeled as a cantilever beam, by taking the large deflection of the stem into account with the help of co-rotational finite element beam modeling. The criteria considered here include minimum moment at the fixed ground support, adequate stiffness and strength, and the volume of material. The result reported here is an example of flexibility, rather than stiffness, leading to increased strength.

Cooling of a composite slab

A mixed boundary value problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite parallel-sided composite slab, is solved completely by using the Wiener-Hopf technique. An analytical expression is derived for the sputtering temperature at the quench front being created by a cold fluid moving on the upper surface of the slab at a constant speed v. The dependence of the various configurational parameters of the problem under consideration, on the sputtering temperature, is rather complicated and representative tables of numerical values of this important physical quantity are prepared for certain typical values of these parameters. Asymptotic results in their most simplified forms are also obtained when (i) the ratio of the thicknesses of the two materials comprising the slab is very much smaller than unity, and (ii) the quench-front speed v is very large, keeping the other parameters fixed, in both the cases.

Optimum design of cantilever sheet pile walls in sandy soils using inverse reliability approach

In this paper an approach for obtaining depth and section modulus of the cantilever sheet pile wall using inverse reliability method is described. The proposed procedure employs inverse first order reliability method to obtain the design penetration depth and section modulus of the steel sheet pile wall in order that the reliability of the wall against failure modes must meet a desired level of safety. Sensitivity analysis is conducted to assess the effect of uncertainties in design parameters on the reliability of cantilever sheet pile walls. The analysis is performed by treating back fill soil properties, depth of the water table from the top of the sheet pile wall, yield strength of steel and section modulus of steel pile as random variables. Two limit states, viz., rotational and flexural failure of sheet pile wall are considered. The results using this approach are used to develop a set of reliability based design charts for different coefficients of variation of friction angle of the backfill (5%, 10% and 15%). System reliability considerations in terms of series and parallel systems are also studied.

Target reliability based design optimization of anchored cantilever sheet pile walls

In this study, the stability of anchored cantilever sheet pile wall in sandy soils is investigated using reliability analysis. Targeted stability is formulated as an optimization problem in the framework of an inverse first order reliability method. A sensitivity analysis is conducted to investigate the effect of parameters influencing the stability of sheet pile wall. Backfill soil properties, soil - steel pile interface friction angle, depth of the water table from the top of the sheet pile wall, total depth of embedment below the dredge line, yield strength of steel, section modulus of steel sheet pile, and anchor pull are all treated as random variables. The sheet pile wall system is modeled as a series of failure mode combination. Penetration depth, anchor pull, and section modulus are calculated for various target component and system reliability indices based on three limit states. These are: rotational failure about the position of the anchor rod, expressed in terms of moment ratio; sliding failure mode, expressed in terms of force ratio; and flexural failure of the steel sheet pile wall, expressed in terms of the section modulus ratio. An attempt is made to propose reliability based design charts considering the failure criteria as well as the variability in the parameters. The results of the study are compared with studies in the literature.

The vibration of cantilever bridges.

The natural frequencies of symmetrical double cantilever bridges are studied. Determinantal frequency equations are derived for the symmetric and the antisymmetric modes of vibration. They are solved numerically on a computer by the bisection method for the frequency parameter. The values of the frequency parameter for the first four modes are presented. Typical mode shapes are also presented.

Analysis of Long Cantilever Cylindrical Shell Subjected to Wind Loading

Bending analysis of closed cylindrical shells subjected to asymmetric load and having different support conditions is of interest in the design of chimneys, water towers, oil storage tanks, etc. A simple method of analyzing a long cantilever cylindrical shell, subjected to asymmetric load, is presented in the paper, using Schorer’s shell theory and orthogonal functions. The application of the solution has been illustrated with an example of a cantilever shell subjected to wind loads. The results obtained for this problem have been compared with the previously available results to illustrate the accuracy of the results obtained here. The solution presented can also be extended to a cylindrical shell with other support conditions, as well as to the study of free vibration of a cylindrical shell. The present solution will be very useful for designers who need to obtain numerical results for specific problems with minimum computational effort.

Cooling of a composite slab in a two-fluid medium

A mixed boundary value problem associated with the diffusion equation that involves the physical problem of cooling of an infinite parallel-sided composite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speedv. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming the front layer of the fluid to be of finite width and the back layer of infinite extent. The main problem is solved through a three-part Wiener-Hopf problem of a special type and the numerical results under certain special circumstances are obtained and presented in the form of a table.