Analytical investigation of squeeze film dampers

Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Starting from linear Reynolds equation which governs the fluid behavior coupled with structure domain which is modeled by Kirchhoff plate equation, the effects of nondimensional parameters on the damped natural frequencies are presented using boundary characteristic orthogonal functions. For this purpose, the nondimensional coupled partial differential equations are obtained using Rayleigh-Ritz method and the weak formulation, are solved using polynomial and sinusoidal boundary characteristic orthogonal functions for structure and fluid domain respectively. In order to implement present approach to the complex geometries, a two dimensional isoparametric coupled finite element is developed based on Reissner-Mindlin plate theory and linearized Reynolds equation. The coupling between fluid and structure is handled by considering the pressure forces and structural surface velocities on the boundaries. The effects of the driving parameters on the frequency response functions are investigated. As the next logical step, an analytical method for solution of squeeze film damping based upon Green’s function to the nonlinear Reynolds equation considering elastic plate is studied. This allows calculating modal damping and stiffness force rapidly for various boundary conditions. The nonlinear Reynolds equation is divided into multiple linear non-homogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling calculation of damping ratio and frequency shift as well as complex resistant pressure. Moreover, the theoretical results are correlated and compared with experimental results both in the literature and in-house experimental procedures including comparison against viscoelastic dampers.

Construction and first validation of the comprehensive inventory of mindfulness (CHIME)

Introduction: Measuring trait mindfulness and change in mindfulness may be a crucial prerequisite for the evaluation and further development of mindfulness based interventions for the treatment of mental disorders. This endeavour is nontrivial as current measures cover varying aspects and mindfulness and may have problems regarding validity. This presentation describes the development and validation of a questionnaire for the comprehensive assessment of mindfulness: the Comprehensive Inventory of Mindfulness Experiences (CHIME). Method: The factor structure, reliability, and validity of the CHIME were established in a community sample (N = 298) and a sample of MBSR group participants (N = 161). Results: Factor-analytical procedures supported an eight-factor structure. The structure was tested in a further confirmatory sample (N = 202). The questionnaire and its subscales exhibited good reliability (internal consistency and retest-reliability). Analysis of the measurement invariance of the single items over groups differing in age, gender, meditation experience, and symptom load pointed to the absence of systematic differences in the items' semantic understanding. Parameters reflecting construct validity, criterion validity, and incremental validity as well as change sensitivity were all at least satisfactory. Conclusions: The CHIME is a self-report measure with favorable psychometric properties based on all aspects of mindfulness that are included in current mindfulness scales. This scale may be helpful in the evaluation and further development of mindfulness based interventions.

Composition of bottom sediments from Core SO201-2-101, Shirshov Ridge, Bering Sea

Analysis of lithology, grain-size composition, clay minerals, and geochemistry of Upper Pleistocene bottom sediments from the submarine Shirshov Ridge (Bering Sea) showed that the Yukon-Tanana terrane of the Central Alaska was main source area of the sediments. Sedimentary material was transported by the Yukon River through Beringia up to the shelf break, where they were entrained by a strong north-west sea current. Lithological data revealed several pulses of ice-rafted debris deposition roughly synchronous with Heinrich events and periods of weaker bottom current intensity. Based on geochemical results we distinguished intervals of an increase in paleoproductivity and extension of the oxygen minimum zone. Our results suggest that there were three stages of deposition driven by glacioeustatic sea-level fluctuations and glacial cycles in Alaska.

Measurements of seawater and aerosol particles during POLARSTERN cruise ANT-XXVII/4

An analytical method for the determination of the alpha dicarbonyls glyoxal (GLY) and methylglyoxal (MGLY) from seawater and marine aerosol particles is presented. The method is based on derivatization with o-(2,3,4,5,6-Pentafluorobenzyl)-hydroxylamine (PFBHA) reagent, solvent extraction and GC-MS (SIM) analysis. The method showed good precision (RSD < 10%), sensitivity (detection limits in the low ng/l range), and accuracy (good agreement between external calibration and standard addition). The method was applied to determine GLY and MGLY in oceanic water sampled during the Polarstern cruise ANT XXVII/4 from Capetown to Bremerhaven in spring 2011. GLY and MGLY were determined in the sea surface microlayer (SML) of the ocean and corresponding bulk water (BW) with average concentrations of 228 ng/l (GLY) and 196 ng/l (MGLY). The results show a significant enrichment (factor of 4) of GLY and MGLY in the SML. Furthermore, marine aerosol particles (PM1) were sampled during the cruise and analyzed for GLY (average concentration 0.19 ng/m**3) and MGLY (average concentration 0.15 ng/m**3). On aerosol particles, both carbonyls show a very good correlation with oxalate, supporting the idea of a secondary formation of oxalic acid via GLY and MGLY. Concentrations of GLY and MGLY in seawater and on aerosol particles were correlated to environmental parameters such as global radiation, temperature, distance to the coastline and biological activity. There are slight hints for a photochemical production of GLY and MGLY in the SML (significant enrichment in the SML, higher enrichment at higher temperature). However, a clear connection of GLY and MGLY to global radiation as well as to biological activity cannot be concluded from the data. A slight correlation between GLY and MGLY in the SML and in aerosol particles could be a hint for interactions, in particular of GLY, between seawater and the atmosphere.

A note on three factor model of discounting

In Montiel Olea and Strzalecki (2014), authors have axiomatically developed an algorithm to infer the parameters of beta-delta model of cognitive bias (present and future biases). While this is extremely useful, it allows the implied beta to become very large when the response is impatient in the future choices relative to present choices, i.e., when there is a strong future bias. I modify the model to further exponentiate the functional form to get more reasonable beta values.

La luz natural como generadora del espacio arquitectónico de la catedral gótica

La historia de la construcción de las catedrales góticas es la historia de la búsqueda de la luz. Esta afirmación casi metafísica, recoge una realidad asumida por todos los historiadores tanto de la arquitectura antigua como del resto de las artes. La luz en el gótico ha sido descrita bajo múltiples matices como son su carácter simbólico, cromático e incluso místico, sin embargo no existe, en el estudio del conocimiento de la luz gótica, ninguna referencia a la misma como realidad física cuantificable, cualificable y por tanto, clasificable. La presente tesis doctoral aborda el concepto de la iluminación gótica desde una perspectiva nueva. Demuestra, con un método analítico inédito, que la iluminación gótica es cuantificable y cualificable. Para ello analiza en profundidad la iluminación de una selección de 6 edificios muestra, las catedrales de Gerona, Toledo, Sevilla y León, la basílica de Santa María del Mar y la capilla de la Sainte Chapelle de París, mediante una toma de datos “in situ” de iluminación y su comparación con los datos lumínicos obtenidos por un programa de soleamiento de la simulación en tres dimensiones de los distintos proyectos originales góticos. El análisis exhaustivo de las muestras y su introducción en el método analítico descrito, permite determinar, en primer lugar, unas cualidades inéditas que identifican la luz de los espacios góticos según unos parámetros nuevos como son la intensidad, expresividad, recorrido, distorsión y color. También describe cuales son los factores determinantes, de nuevo inéditos, que modulan cada una de las cualidades y en que proporción lo hacen cada uno de ellos. Una vez establecidas las cualidades y los factores que las definen, la tesis doctoral establece los rangos en los que se mueven las distintas cualidades y que conformarán la definitiva clasificación según “tipos de cualidad lumínica”. Adicionalmente, la tesis propone un procedimiento abreviado de acercamiento a la realidad de la iluminación gótica a través de unas fórmulas matemáticas que relacionan los factores geométricos detectados y descritos en la tesis con el resultado luminoso del espacio en lo que concierne a las dos cualidades más importantes de las reflejadas, la intensidad y la expresividad. Gracias a este método y su procedimiento abreviado, la clasificación se hace extensible al resto de catedrales góticas del panorama español y europeo y abre el camino a nuevas clasificaciones de edificios históricos de distintas épocas, iniciando un apasionante camino por recorrer en la recuperación de “la luz original”. Esta clasificación y sus cualidades podrán a su vez, ser utilizadas como herramientas de conocimiento de un factor determinante a la hora de describir cualquier espacio gótico y su aportación pretende ser un nuevo condicionante a tener en cuenta en el futuro, ayudando a entender y respetar, en las posibles intervenciones a realizar sobre el patrimonio arquitectónico, aquello que fue en su inicio motor principal del proyecto arquitectónico y que hoy día no se valora suficientemente tan solo por falta de conocimiento: su luz. The history of the construction of the Gothic cathedrals is the history of the search for light. This almost etaphysical statement reflects a reality accepted by all historians both of ancient architecture and other arts. Light in the Gothic period has been described under multiple approaches such as its symbolic, chromatic and even mystical character. However, in the study of the Gothic light, no references exist to it as a physical quantifiable and qualifiable reality and therefore, classifiable. This dissertation deals with the concept of Gothic light from a new perspective. With a new analytical method, it shows that Gothic lighting is quantifiable and can be classified regarding quality. To this end, a selection of 6 buildings light samples are analyzed; the cathedrals of Gerona, Toledo, Seville and León, the basilica of Santa María of the Sea and the Sainte Chapelle in Paris. "In situ" lighting data is collected and it is compared with lighting data obtained by a program of sunlight of the 3D simulation of various Gothic original projects. The comprehensive analysis of the samples and the data introduced in the analytical method described, allows determining, first, important qualities that identify the light of Gothic spaces according to new parameters such as intensity, expressiveness, trajectory, distortion and color. It also describes the determinant factors, which modulate each of the qualities and in what proportion they do it. Once the qualities and factors that define them have been established, in this doctoral dissertation the ranges regarding different qualities are set, which will make up the final classification according to "types of light quality". In addition, this work proposes an abbreviated procedure approach to the reality of the Gothic lighting through some mathematical formulae, relating the geometric factors identified and described in the study with the bright result of space regarding the two most important qualities of the light,intensity and expressiveness. Thanks to this method and to the abbreviated procedure, the classification can be applied to other Spanish and European Gothic cathedrals and opens up the way to new classifications of historic buildings from different eras, starting an exciting road ahead in the recovery of the "original light". This classification and its qualities may in turn be used as tools to know a determinant factor when describing any Gothic space. Its contribution is intended to be a new conditioning factor to keep in mind in the future, helping to understand and respect, in possible interventions on the architectural heritage, what was the main engine to start the architectural project and which today is not valued enough due to the lack knowledge: the light.

Phylogenetic analyses and toxigenic profiles of Fusarium equiseti and Fusarium acuminatum isolated from cereals from Southern Europe

Fusarium equiseti and Fusarium acuminatum are toxigenic species that contaminate cereal crops from diverse climatic regions. They are common in Spanish cereals. The information available on their phylogenetics and toxigenic profiles is, however, insufficient to assist risk evaluation. In this work, phylogenetic analyses were performed using partial sequences of the translation elongation factor gene (EF-1a) of F. equiseti and F. acuminatum strains isolated from barley and wheat from Spain and other countries. The Northern and Southern European F. equiseti strains largely separated into two phylogenetically distinct clusters. This suggests the existence of two distinct populations within this species, explaining its presence in these regions of markedly different climate. Production of type A and B trichothecenes by the Spanish strains, examined in wheat cultures using a multitoxin analytical method, indicated that F. equiseti could produce deoxynivalenol and nivalenol and other trichothecenes, at concentrations that might represent a significant risk of toxin contamination for Southern European cereals. F. acuminatum showed low intraspecific genetic variability and 58% of the strains could produce deoxynivalenol at low level. Neither species was found to produce T-2 or HT-2 toxins. The present results provide important phylogenetic and toxigenic information essential for the accurate prediction of toxigenic risk.

Analytical evaluation of uncertainty on active antenna arrays

An analytical method for evaluating the uncertainty of the performance of active antenna arrays in the whole spatial spectrum is presented. Since array processing algorithms based on spatial reference are widely used to track moving targets, it is essential to be aware of the impact of the uncertainty sources on the antenna response. Furthermore, the estimation of the direction of arrival (DOA) depends on the array uncertainty. The aim of the uncertainties analysis is to provide an exhaustive characterization of the behavior of the active antenna array associated with its main uncertainty sources. The result of this analysis helps to select the proper calibration technique to be implemented. An illustrative example for a triangular antenna array used for satellite tracking is presented showing the suitability of the proposed method to carry out an efficient characterization of an active antenna array.

Diseño basado en técnicas de fiabilidad del tratamiento de mejora del terreno mediante columnas de grava

El proyecto geotécnico de columnas de grava tiene todas las incertidumbres asociadas a un proyecto geotécnico y además hay que considerar las incertidumbres inherentes a la compleja interacción entre el terreno y la columna, la puesta en obra de los materiales y el producto final conseguido. Este hecho es común a otros tratamientos del terreno cuyo objetivo sea, en general, la mejora “profunda”. Como los métodos de fiabilidad (v.gr., FORM, SORM, Monte Carlo, Simulación Direccional) dan respuesta a la incertidumbre de forma mucho más consistente y racional que el coeficiente de seguridad tradicional, ha surgido un interés reciente en la aplicación de técnicas de fiabilidad a la ingeniería geotécnica. Si bien la aplicación concreta al proyecto de técnicas de mejora del terreno no es tan extensa. En esta Tesis se han aplicado las técnicas de fiabilidad a algunos aspectos del proyecto de columnas de grava (estimación de asientos, tiempos de consolidación y aumento de la capacidad portante) con el objetivo de efectuar un análisis racional del proceso de diseño, considerando los efectos que tienen la incertidumbre y la variabilidad en la seguridad del proyecto, es decir, en la probabilidad de fallo. Para alcanzar este objetivo se ha utilizado un método analítico avanzado debido a Castro y Sagaseta (2009), que mejora notablemente la predicción de las variables involucradas en el diseño del tratamiento y su evolución temporal (consolidación). Se ha estudiado el problema del asiento (valor y tiempo de consolidación) en el contexto de la incertidumbre, analizando dos modos de fallo: i) el primer modo representa la situación en la que es posible finalizar la consolidación primaria, parcial o totalmente, del terreno mejorado antes de la ejecución de la estructura final, bien sea por un precarga o porque la carga se pueda aplicar gradualmente sin afectar a la estructura o instalación; y ii) por otra parte, el segundo modo de fallo implica que el terreno mejorado se carga desde el instante inicial con la estructura definitiva o instalación y se comprueba que el asiento final (transcurrida la consolidación primaria) sea lo suficientemente pequeño para que pueda considerarse admisible. Para trabajar con valores realistas de los parámetros geotécnicos, los datos se han obtenido de un terreno real mejorado con columnas de grava, consiguiendo, de esta forma, un análisis de fiabilidad más riguroso. La conclusión más importante, obtenida del análisis de este caso particular, es la necesidad de precargar el terreno mejorado con columnas de grava para conseguir que el asiento ocurra de forma anticipada antes de la aplicación de la carga correspondiente a la estructura definitiva. De otra forma la probabilidad de fallo es muy alta, incluso cuando el margen de seguridad determinista pudiera ser suficiente. En lo que respecta a la capacidad portante de las columnas, existen un buen número de métodos de cálculo y de ensayos de carga (tanto de campo como de laboratorio) que dan predicciones dispares del valor de la capacidad última de las columnas de grava. En las mallas indefinidas de columnas, los resultados del análisis de fiabilidad han confirmado las consideraciones teóricas y experimentales existentes relativas a que no se produce fallo por estabilidad, obteniéndose una probabilidad de fallo prácticamente nula para este modo de fallo. Sin embargo, cuando se analiza, en el contexto de la incertidumbre, la capacidad portante de pequeños grupos de columnas bajo zapatas se ha obtenido, para un caso con unos parámetros geotécnicos típicos, que la probabilidad de fallo es bastante alta, por encima de los umbrales normalmente admitidos para Estados Límite Últimos. Por último, el trabajo de recopilación sobre los métodos de cálculo y de ensayos de carga sobre la columna aislada ha permitido generar una base de datos suficientemente amplia como para abordar una actualización bayesiana de los métodos de cálculo de la columna de grava aislada. El marco bayesiano de actualización ha resultado de utilidad en la mejora de las predicciones de la capacidad última de carga de la columna, permitiendo “actualizar” los parámetros del modelo de cálculo a medida que se dispongan de ensayos de carga adicionales para un proyecto específico. Constituye una herramienta valiosa para la toma de decisiones en condiciones de incertidumbre ya que permite comparar el coste de los ensayos adicionales con el coste de una posible rotura y , en consecuencia, decidir si es procedente efectuar dichos ensayos. The geotechnical design of stone columns has all the uncertainties associated with a geotechnical project and those inherent to the complex interaction between the soil and the column, the installation of the materials and the characteristics of the final (as built) column must be considered. This is common to other soil treatments aimed, in general, to “deep” soil improvement. Since reliability methods (eg, FORM, SORM, Monte Carlo, Directional Simulation) deals with uncertainty in a much more consistent and rational way than the traditional safety factor, recent interest has arisen in the application of reliability techniques to geotechnical engineering. But the specific application of these techniques to soil improvement projects is not as extensive. In this thesis reliability techniques have been applied to some aspects of stone columns design (estimated settlements, consolidation times and increased bearing capacity) to make a rational analysis of the design process, considering the effects of uncertainty and variability on the safety of the project, i.e., on the probability of failure. To achieve this goal an advanced analytical method due to Castro and Sagaseta (2009), that significantly improves the prediction of the variables involved in the design of treatment and its temporal evolution (consolidation), has been employed. This thesis studies the problem of stone column settlement (amount and speed) in the context of uncertainty, analyzing two failure modes: i) the first mode represents the situation in which it is possible to cause primary consolidation, partial or total, of the improved ground prior to implementation of the final structure, either by a pre-load or because the load can be applied gradually or programmed without affecting the structure or installation; and ii) on the other hand, the second mode implies that the improved ground is loaded from the initial instant with the final structure or installation, expecting that the final settlement (elapsed primary consolidation) is small enough to be allowable. To work with realistic values of geotechnical parameters, data were obtained from a real soil improved with stone columns, hence producing a more rigorous reliability analysis. The most important conclusion obtained from the analysis of this particular case is the need to preload the stone columns-improved soil to make the settlement to occur before the application of the load corresponding to the final structure. Otherwise the probability of failure is very high, even when the deterministic safety margin would be sufficient. With respect to the bearing capacity of the columns, there are numerous methods of calculation and load tests (both for the field and the laboratory) giving different predictions of the ultimate capacity of stone columns. For indefinite columns grids, the results of reliability analysis confirmed the existing theoretical and experimental considerations that no failure occurs due to the stability failure mode, therefore resulting in a negligible probability of failure. However, when analyzed in the context of uncertainty (for a case with typical geotechnical parameters), results show that the probability of failure due to the bearing capacity failure mode of a group of columns is quite high, above thresholds usually admitted for Ultimate Limit States. Finally, the review of calculation methods and load tests results for isolated columns, has generated a large enough database, that allowed a subsequent Bayesian updating of the methods for calculating the bearing capacity of isolated stone columns. The Bayesian updating framework has been useful to improve the predictions of the ultimate load capacity of the column, allowing to "update" the parameters of the calculation model as additional load tests become available for a specific project. Moreover, it is a valuable tool for decision making under uncertainty since it is possible to compare the cost of further testing to the cost of a possible failure and therefore to decide whether it is appropriate to perform such tests.

On the analytical approach for modeling photovoltaic systems behavior

The 1-diode/2-resistors electric circuit equivalent to a photovoltaic system is analyzed. The equations at particular points of the I–V curve are studied considering the maximum number of terms. The maximum power point as a boundary condition is given special attention. A new analytical method is developed based on a reduced amount of information, consisting in the normal manufacturer data. Results indicate that this new method is faster than numerical methods and has similar (or better) accuracy than other existing methods, numerical or analytical.

Tungsten coil atomic emission spectrometry combined with dispersive liquid–liquid microextraction: A synergistic association for chromium determination in water samples

A novel and environment friendly analytical method is reported for total chromium determination and chromium speciation in water samples, whereby tungsten coil atomic emission spectrometry (WCAES) is combined with in situ ionic liquid formation dispersive liquid–liquid microextraction (in situ IL-DLLME). A two stage multivariate optimization approach has been developed employing a Plackett–Burman design for screening and selection of the significant factor involved in the in situ IL-DLLME procedure, which was later optimized by means of a circumscribed central composite design. The optimum conditions were complexant concentration: 0.5% (or 0.1%); complexant type: DDTC; IL anion: View the MathML sourcePF6−; [Hmim][Cl] IL amount: 60 mg; ionic strength: 0% NaCl; pH: 5 (or 2); centrifugation time: 10 min; and centrifugation speed: 1000 rpm. Under the optimized experimental conditions the method was evaluated and proper linearity was obtained with a correlation coefficient of 0.991 (5 calibration standards). Limits of detection and quantification for both chromium species were 3 and 10 µg L−1, respectively. This is a 233-fold improvement when compared with chromium determination by WCAES without using preconcentration. The repeatability of the proposed method was evaluated at two different spiking levels (10 and 50 µg L−1) obtaining coefficients of variation of 11.4% and 3.6% (n=3), respectively. A certified reference material (SRM-1643e NIST) was analyzed in order to determine the accuracy of the method for total chromium determination and 112.3% and 2.5 µg L−1 were the recovery (trueness) and standard deviation values, respectively. Tap, bottled mineral and natural mineral water samples were analyzed at 60 µg L−1 spiking level of total Cr content at two Cr(VI)/Cr(III) ratios, and relative recovery values ranged between 88% and 112% showing that the matrix has a negligible effect. To our knowledge, this is the first time that combines in situ IL-DLLME and WCAES.

Delamination Arrestment in Bonded-Bolted Composite Structures by Fasteners

Thesis (Ph.D.)--University of Washington, 2016-06

Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process, is used to obtain the vibration frequencies for plates with various boundary conditions. Material properties are assumed to be temperature-dependent. Special attention is given to the effects of sine type imperfection, localized imperfection, and global imperfection on linear and nonlinear vibration behavior. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with graded silicon nitride/stainless steel layers. It is shown that the vibration frequencies are very much dependent on the vibration amplitude and the imperfection mode and its magnitude. While most of the imperfect laminated plates show the well-known hard-spring vibration, those with free edges can display soft-spring vibration behavior at certain imperfection levels. The influences of material composition, temperature-dependence of material properties and side-to-thickness ratio are also discussed. (C) 2004 Elsevier Ltd. All rights reserved.

Shortcomings of protein removal prior to high performance liquid chromatographic analysis - A case study using method development for BAY 11-7082

During the analytical method development for BAY 11-7082 ((E)-3-[4-methylphenylsulfonyl]-2-propenenitrile), using HPLC-MS-MS and HPLC-UV, we observed that the protein removal process (both ultrafiltration and precipitation method using organic solvents) prior to HPLC brought about a significant reduction in the concentration of this compound. The use of a structurally similar internal standard, BAY 11-7085 ((E)-3-[4-t-butylphenylsulfonyl]-2-propenenitrile), was not effective in compensating for the loss of analyte as the extent of reduction was different to that of the analyte. We present here a systematic investigation of this problem and a new validated method for the determination of BAY 11-7082. (c) 2006 Elsevier B.V. All rights reserved.

The strength of column-to-foundation joints in reinforced concrete

This thesis is concerned with the experimental and theoretical investigation into the compression bond of column longitudinal reinforcement in the transference of axial load from a reinforced concrete column to a base. Experimental work includes twelve tests with square twisted bars and twenty four tests with ribbed bars. The effects of bar size, anchorage length in the base, plan area of the base, provision of bae tensile reinforcement, links around the column bars in the base, plan area of column and concrete compressive strength were investigated in the tests. The tests indicated that the strength of the compression anchorage of deformed reinforcing steel in the concrete was primarily dependent on the concrete strength and the resistance to bursting, which may be available within the anchorage . It was shown in the tests without concreted columns that due to a large containment over the bars in the foundation, failure occurred due to the breakdown of bond followed by the slip of the column bars along the anchorage length. The experimental work showed that the bar size , the stress in the bar, the anchorage length, provision of the transverse steel and the concrete compressive strength significantly affect the bond stress at failure. The ultimate bond stress decreases as the anchorage length is increased, while the ultimate bond stress increases with increasing each of the remainder parameters. Tests with concreted columns also indicated that a section of the column contributed to the bond length in the foundation by acting as an extra anchorage length. The theoretical work is based on the Mindlin equation( 3), an analytical method used in conjunction with finite difference calculus. The theory is used to plot the distribution of bond stress in the elastic and the elastic-plastic stage of behaviour. The theory is also used to plot the load-vertical displacement relationship of the column bars in the anchorage length, and also to determine the theoretical failure load of foundation. The theoretical solutions are in good agreement with the experimental results and the distribution of bond stress is shown to be significantly influenced by the bar stiffness factor K. A comparison of the experimental results with the current codes shows that the bond stresses currently used are low and in particular, CPIlO(56) specifies very conservative design bond stresses .