Application of Maclaurin Series in Structural Analysis

In the simple theory of flexure of beams, the slope, bending moment, shearing force, load and other quantities are functions of a derivative of y with respect to x. It is shown that the elastic curve of a transversely loaded beam can be represented by the Maclaurin series. Substitution of the values of the derivatives gives a direct solution of beam problems. In this paper the method is applied to derive the Theorem or three moments and slope deflection equations. The method is extended to the solution of a rigid portal frame. Finally the method is applied to deduce results on which the moment distribution method of analyzing rigid frames is based.

Stress Analysis of Deep Beams

In a beam whose depth is comparable to its span, the distribution of bending and shear stresses differs appreciably from those given by the ordinary flexural theory. In this paper, a general solution for the analysis of a rectangular, single-scan beam, under symmetrical loading is developed. The Multiple Fourier procedure is employed using four series by which it has been possible to satisfy all boundary and the resulting relation among the co-efficient are derives.

Analysis of laminated shells with laminated stiffeners using rectangular shell finite elementsstar

A finite element analysis of laminated shells reinforced with laminated stiffeners is described in this paper. A rectangular laminated anisotropic shallow thin shell finite element of 48 d.o.f. is used in conjunction with a laminated anisotropic curved beam and shell stiffening finite element having 16 d.o.f. Compatibility between the shell and the stiffener is maintained all along their junction line. Some problems of symmetrically stiffened isotropic plates and shells have been solved to evaluate the performance of the present method. Behaviour of an eccentrically stiffened laminated cantilever cylindrical shell has been predicted to show the ability of the present program. General shells amenable to rectangular meshes can also be solved in a similar manner.

Analysis of Daphnane Orthoesters in Poisonous Australian Pimelea Species by Liquid Chromatography-Tandem Mass Spectrometry.

Cattle grazing in arid rangelands of Australia suffer periodic extensive and serious poisoning by the plant species Pimelea trichostachya, P. simplex, and P. elongata. Pimelea poisoning (also known as St. George disease and Marree disease) has been attributed to the presence of the diterpenoid orthoester simplexin in these species. However, literature relating to previous studies is complicated by taxonomic revisions, and the presence of simplexin has not previously been verified in all currently recognized taxa capable of inducing pimelea poisoning syndrome, with no previous chemical studies of P. trichostachya (as currently classified) or P. simplex subsp. continua. We report here the isolation of simplexin from P. trichostachya and the development of a liquid chromatography-mass spectrometry/mass spectrometry (LC-MS/MS) method to measure simplexin concentrations in pimelea plant material. Simplexin was quantified by positive-ion atmospheric pressure chemical ionization (APCI) LC-MS/MS with selected reaction monitoring (SRM) of the m/z 533.3 > 253.3 transition. LC-MS/MS analysis of the four poisonous taxa P. trichostachya, P. elongata, P. simplex subsp. continua, and P. simplex subsp. simplex showed similar profiles with simplexin as the major diterpenoid ester component in all four taxa accompanied by varying amounts of related orthoesters. Similar analyses of P. decora, P. haematostachya, and P. microcephala also demonstrated the presence of simplexin in these species but at far lower concentrations, consistent with the limited reports of stock poisoning associated with these species. The less common, shrubby species P. penicillaris contained simplexin at up to 55 mg/kg dry weight and would be expected to cause poisoning if animals consumed sufficient plant material.

Drug Analysis without Primary Reference Standards : Application of LC-TOFMS and LC-CLND to Biofluids and Seized Material

Drug Analysis without Primary Reference Standards: Application of LC-TOFMS and LC-CLND to Biofluids and Seized Material Primary reference standards for new drugs, metabolites, designer drugs or rare substances may not be obtainable within a reasonable period of time or their availability may also be hindered by extensive administrative requirements. Standards are usually costly and may have a limited shelf life. Finally, many compounds are not available commercially and sometimes not at all. A new approach within forensic and clinical drug analysis involves substance identification based on accurate mass measurement by liquid chromatography coupled with time-of-flight mass spectrometry (LC-TOFMS) and quantification by LC coupled with chemiluminescence nitrogen detection (LC-CLND) possessing equimolar response to nitrogen. Formula-based identification relies on the fact that the accurate mass of an ion from a chemical compound corresponds to the elemental composition of that compound. Single-calibrant nitrogen based quantification is feasible with a nitrogen-specific detector since approximately 90% of drugs contain nitrogen. A method was developed for toxicological drug screening in 1 ml urine samples by LC-TOFMS. A large target database of exact monoisotopic masses was constructed, representing the elemental formulae of reference drugs and their metabolites. Identification was based on matching the sample component s measured parameters with those in the database, including accurate mass and retention time, if available. In addition, an algorithm for isotopic pattern match (SigmaFit) was applied. Differences in ion abundance in urine extracts did not affect the mass accuracy or the SigmaFit values. For routine screening practice, a mass tolerance of 10 ppm and a SigmaFit tolerance of 0.03 were established. Seized street drug samples were analysed instantly by LC-TOFMS and LC-CLND, using a dilute and shoot approach. In the quantitative analysis of amphetamine, heroin and cocaine findings, the mean relative difference between the results of LC-CLND and the reference methods was only 11%. In blood specimens, liquid-liquid extraction recoveries for basic lipophilic drugs were first established and the validity of the generic extraction recovery-corrected single-calibrant LC-CLND was then verified with proficiency test samples. The mean accuracy was 24% and 17% for plasma and whole blood samples, respectively, all results falling within the confidence range of the reference concentrations. Further, metabolic ratios for the opioid drug tramadol were determined in a pharmacogenetic study setting. Extraction recovery estimation, based on model compounds with similar physicochemical characteristics, produced clinically feasible results without reference standards.

Finite element analysis of laminated anisotropic thin-walled open-section beams

A finite element analysis of thin-walled open-section laminated anisotropic beams is presented herein. A two-noded, 8 degrees of freedom per node thin-walled open-section laminated anisotropic beam finite element has been developed and used. The displacements of the element reference axes are expressed in terms of one-dimensional first order Hermite interpolation polynomials and line member assumptions are invoked in the formulation of the stiffness matrix. The problems of: 1. (a) an isotropic material Z section straight cantilever beam, and 2. (b) a single-layer (0°) composite Z section straight cantilever beam, for which continuum solutions (exact/approximate) are possible, have been solved in order to evaluate the performance of the finite element. Its applicability has been shown by solving the following problems: 3. (c) a two-layer (45°/−45°) composite Z section straight cantilever beam, 4. (d) a three-layer (0°/45°/0°) composite Z section straight cantilever beam.

HPLC analysis of plant sterol oxidation products

Increased interest in the cholesterol-lowering effect of plant sterols has led to development of plant sterol-enriched foods. When products are enriched, the safety of the added components must be evaluated. In the case of plant sterols, oxidation is the reaction of main concern. In vitro studies have indicated that cholesterol oxides may have harmful effects. Due their structural similarity, plant sterol oxidation products may have similar health implications. This study concentrated on developing high-performance liquid chromatography (HPLC) methods that enable the investigation of formation of both primary and secondary oxidation products and thus can be used for oxidation mechanism studies of plant sterols. The applicability of the methods for following the oxidation reactions of plant sterols was evaluated by using oxidized stigmasterol and sterol mixture as model samples. An HPLC method with ultraviolet and fluorescence detection (HPLC-UV-FL) was developed. It allowed the specific detection of hydroperoxides with FL detection after post-column reagent addition. The formation of primary and secondary oxidation products and amount of unoxidized sterol could be followed by using UV detection. With the HPLC-UV-FL method, separation between oxides was essential and oxides of only one plant sterol could be quantified in one run. Quantification with UV can lead to inaccuracy of the results since the number of double bonds had effect on the UV absorbance. In the case of liquid chromatography-mass spectrometry (LC-MS), separation of oxides with different functionalities was important because some oxides of the same sterol have similar molecular weight and moreover epimers have similar fragmentation behaviour. On the other hand, coelution of different plant sterol oxides with the same functional group was acceptable since they differ in molecular weights. Results revealed that all studied plant sterols and cholesterol seem to have similar fragmentation behaviour, with only relative ion abundances being slightly different. The major advantage of MS detection coupled with LC separation is the capability to analyse totally or partly coeluting analytes if these have different molecular weights. The HPLC-UV-FL and LC-MS methods were demonstrated to be suitable for studying the photo-oxidation and thermo-oxidation reactions of plant sterols. The HPLC-UV-FL method was able to show different formation rates of hydroperoxides during photo-oxidation. The method also confirmed that plant sterols have similar photo-oxidation behaviour to cholesterol. When thermo-oxidation of plant sterols was investigated by HPLC-UV-FL and LC-MS, the results revealed that the formation and decomposition of individual hydroperoxides and secondary oxidation products could be studied. The methods used revealed that all of the plant sterols had similar thermo-oxidation behaviour when compared with each other, and the predominant reactions and oxidation rates were temperature dependent. Overall, these findings showed that with these LC methods the oxidation mechanisms of plant sterols can be examined in detail, including the formation and degradation of individual hydroperoxides and secondary oxidation products, with less sample pretreatment and without derivatization.

Miniaturized mass spectrometric ionization techniques for environmental analysis and bioanalysis

Miniaturized mass spectrometric ionization techniques for environmental analysis and bioanalysis Novel miniaturized mass spectrometric ionization techniques based on atmospheric pressure chemical ionization (APCI) and atmospheric pressure photoionization (APPI) were studied and evaluated in the analysis of environmental samples and biosamples. The three analytical systems investigated here were gas chromatography-microchip atmospheric pressure chemical ionization-mass spectrometry (GC-µAPCI-MS) and gas chromatography-microchip atmospheric pressure photoionization-mass spectrometry (GC-µAPPI-MS), where sample pretreatment and chromatographic separation precede ionization, and desorption atmospheric pressure photoionization-mass spectrometry (DAPPI-MS), where the samples are analyzed either as such or after minimal pretreatment. The gas chromatography-microchip atmospheric pressure ionization-mass spectrometry (GC-µAPI-MS) instrumentations were used in the analysis of polychlorinated biphenyls (PCBs) in negative ion mode and 2-quinolinone-derived selective androgen receptor modulators (SARMs) in positive ion mode. The analytical characteristics (i.e., limits of detection, linear ranges, and repeatabilities) of the methods were evaluated with PCB standards and SARMs in urine. All methods showed good analytical characteristics and potential for quantitative environmental analysis or bioanalysis. Desorption and ionization mechanisms in DAPPI were studied. Desorption was found to be a thermal process, with the efficiency strongly depending on thermal conductivity of the sampling surface. Probably the size and polarity of the analyte also play a role. In positive ion mode, the ionization is dependent on the ionization energy and proton affinity of the analyte and the spray solvent, while in negative ion mode the ionization mechanism is determined by the electron affinity and gas-phase acidity of the analyte and the spray solvent. DAPPI-MS was tested in the fast screening analysis of environmental, food, and forensic samples, and the results demonstrated the feasibility of DAPPI-MS for rapid screening analysis of authentic samples.

High-throughput prediction of eucalypt lignin syringyl/guaiacyl content using multivariate analysis: a comparison between mid-infrared, near-infrared, and Raman spectroscopies for model development

BACKGROUND: In order to rapidly and efficiently screen potential biofuel feedstock candidates for quintessential traits, robust high-throughput analytical techniques must be developed and honed. The traditional methods of measuring lignin syringyl/guaiacyl (S/G) ratio can be laborious, involve hazardous reagents, and/or be destructive. Vibrational spectroscopy can furnish high-throughput instrumentation without the limitations of the traditional techniques. Spectral data from mid-infrared, near-infrared, and Raman spectroscopies was combined with S/G ratios, obtained using pyrolysis molecular beam mass spectrometry, from 245 different eucalypt and Acacia trees across 17 species. Iterations of spectral processing allowed the assembly of robust predictive models using partial least squares (PLS). RESULTS: The PLS models were rigorously evaluated using three different randomly generated calibration and validation sets for each spectral processing approach. Root mean standard errors of prediction for validation sets were lowest for models comprised of Raman (0.13 to 0.16) and mid-infrared (0.13 to 0.15) spectral data, while near-infrared spectroscopy led to more erroneous predictions (0.18 to 0.21). Correlation coefficients (r) for the validation sets followed a similar pattern: Raman (0.89 to 0.91), mid-infrared (0.87 to 0.91), and near-infrared (0.79 to 0.82). These statistics signify that Raman and mid-infrared spectroscopy led to the most accurate predictions of S/G ratio in a diverse consortium of feedstocks. CONCLUSION: Eucalypts present an attractive option for biofuel and biochemical production. Given the assortment of over 900 different species of Eucalyptus and Corymbia, in addition to various species of Acacia, it is necessary to isolate those possessing ideal biofuel traits. This research has demonstrated the validity of vibrational spectroscopy to efficiently partition different potential biofuel feedstocks according to lignin S/G ratio, significantly reducing experiment and analysis time and expense while providing non-destructive, accurate, global, predictive models encompassing a diverse array of feedstocks.

A transcriptomic analysis of the kidney tissue of Tra catfish (pangasianodon hypophthalmus) reared in saline condition: De novo assembly, annotation, SNP discovery

Pangasianodon hypophthalmus is a commercially important freshwater fish used in inland aquaculture in the Mekong Delta, Vietnam. The current study using Ion Torrent technology generated EST resources from the kidney for Tra catfish reared at a salinity level of 9 ppt. We obtained 2,623,929 reads after trimming and processing with an average length of 104 bp. De novo assemblies were generated using CLC Genomic Workbench, Trinity and Velvet/Oases with the best overall contig performance resulting from the CLC assembly. De novo assembly using CLC yielded 29,940 contigs, and allowing identification of 5,710 putative genes when comppared with NCBI non-redundant database. A large number of single nucleotide polymorphisms (SNPs) were also detected. The sequence collection generated in our study represents the most comprehensive transcriptomic resource for P. hypophthalmus available to date.

Finite element analysis of laminated anisotropic beams of bimodulus materials

This paper presents finite element analysis of laminated anisotropic beams of bimodulus materials. The finite element has 16 d.o.f. and uses the displacement field in terms of first order Hermite interpolation polynomials. As the neutral axis position may change from point to point along the length of the beam, an iterative procedure is employed to determine the location of zero strain points along the length. Using this element some problems of laminated beams of bimodulus materials are solved for concentrated loads/moments perpendicular and parallel to the layering planes as well as combined loads.

Fracture Behavior of Multidirectional DCB Specimen: Higher-Order Beam Theories

Mathematical models, for the stress analysis of symmetric multidirectional double cantilever beam (DCB) specimen using classical beam theory, first and higher-order shear deformation beam theories, have been developed to determine the Mode I strain energy release rate (SERR) for symmetric multidirectional composites. The SERR has been calculated using the compliance approach. In the present study, both variationally and nonvariationally derived matching conditions have been applied at the crack tip of DCB specimen. For the unidirectional and cross-ply composite DCB specimens, beam models under both plane stress and plane strain conditions in the width direction are applicable with good performance where as for the multidirectional composite DCB specimen, only the beam model under plane strain condition in the width direction appears to be applicable with moderate performance. Among the shear deformation beam theories considered, the performance of higher-order shear deformation beam theory, having quadratic variation for transverse displacement over the thickness, is superior in determining the SERR for multidirectional DCB specimen.

Factors influencing kinetic and equilibrium behaviour of sodium ion exchange with strong acid cation resin

This study reports an investigation of the ion exchange treatment of sodium chloride solutions in relation to use of resin technology for applications such as desalination of brackish water. In particular, a strong acid cation (SAC) resin (DOW Marathon C) was studied to determine its capacity for sodium uptake and to evaluate the fundamentals of the ion exchange process involved. Key questions to answer included: impact of resin identity; best models to simulate the kinetics and equilibrium exchange behaviour of sodium ions; difference between using linear least squares (LLS) and non-linear least squares (NLLS) methods for data interpretation; and, effect of changing the type of anion in solution which accompanied the sodium species. Kinetic studies suggested that the exchange process was best described by a pseudo first order rate expression based upon non-linear least squares analysis of the test data. Application of the Langmuir Vageler isotherm model was recommended as it allowed confirmation that experimental conditions were sufficient for maximum loading of sodium ions to occur. The Freundlich expression best fitted the equilibrium data when analysing the information by a NLLS approach. In contrast, LLS methods suggested that the Langmuir model was optimal for describing the equilibrium process. The Competitive Langmuir model which considered the stoichiometric nature of ion exchange process, estimated the maximum loading of sodium ions to be 64.7 g Na/kg resin. This latter value was comparable to sodium ion capacities for SAC resin published previously. Inherent discrepancies involved when using linearized versions of kinetic and isotherm equations were illustrated, and despite their widespread use, the value of this latter approach was questionable. The equilibrium behaviour of sodium ions form sodium fluoride solution revealed that the sodium ions were now more preferred by the resin compared to the situation with sodium chloride. The solution chemistry of hydrofluoric acid was suggested as promoting the affinity of the sodium ions to the resin.

Orbit perturbation theory of beam-plasma instability

The nonlinear theory of the instability caused by an electron beam-plasma interaction is studied. A nonlinear analysis has been carried out using many-body methods. A general formula for a neutral collisionless plasma, without external fields, is derived. This could be used for calculating the saturation levels of other instabilities. The effect of orbit perturbation theory on the beam-plasma instability is briefly reviewed.

Analysis of vibration of clamped square plates by the Rayleigh-Ritz method with asymptotic solutions from a modified Bolotin method

Estimates of flexural frequencies of clamped square plates are initially obtained by the modified Bolotin's method. The mode shapes in “each direction” are then determined and the product functions of these mode shapes are used as admissible functions in the Rayleigh-Ritz method. The data for the first twenty eigenvalues in each of the three (four) symmetric groups obtained by the (i) Bolotin, (ii) Rayleigh and (iii) Rayleigh-Ritz methods are reported here. The Rayleigh estimates are found to be much closer to the true eigenvalues than the Bolotin estimates. The present product functions are found to be much superior to the conventional beam eigenmodes as admissible functions in the Rayleigh-Ritz method of analysis.