1,778 research outputs found

    An inductive method of calculation of the deflection of the truss regular type

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    In this paper, the author proposes a regular option of statically determinate flat truss with a lattice of Shukhov's type working under beam scheme. By induction, using Maple computer algebra system, the exact formula for the mid-span deflection under the action of the uniform load is obtained. The deflection of the elastic structure is defined by the formula of Maxwell – Mohr. Forces in the rods are found using cut nodes method with the composition of the management of the matrix of equations in vector form. The analysis of the coefficients in the truss evaluation with a different number of panels revealed the recurrence equation satisfied by these coefficients, and then the determined operators of a specialized package genfunc give a solution of the resulting equation that determines the required general formula. The case of a uniform load on the top horizontal zone is considered. The author obtained a simple asymptotic evaluation of this solution, proving the cubic nature of the growth of deflection for a fixed span length and a given nodal load. The solution found for an even number of panels and rods of the same cross-section, has a polynomial form; the dependence is non-monotonic and detects extremum, which allows optimizing the design

    ANALYSIS OF THE DEFLECTION OF A TRUSS WITH A DECORATIVE LATTICE

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    Introduction. A scheme is proposed for a planar symmetric statically determinate beam truss with a rectilinear lower belt, struts, multidirectional braces and a polygonal outline of the upper belt. The belts of the truss are rectilinear, the hinges are ideal. The truss belongs to the class of regular trusses having periodic cells. The supporting rods are not deformable. The truss is evenly loaded around the nodes of the lower belt. Materials and methods. The task is to deduce the dependence of the deflection of the truss on the number of panels in the span. The deflection is obtained from the Maxwell-Mora formula under the assumption that all the rods have the same rigidity. Forces in the structural rods from the effective uniform load and from the unit vertical in the middle of the span are determined by the method of cutting the nodes. The matrix of the system of linear equations of node equilibrium is made up of the cosines of the forces with the coordinate axes. To compile a system of equations and solve it, the program of symbolic mathematics Maple is used. To obtain the general formula, a number of problems of trusses with a number of panels from 2 to 29 are solved. Sequences of the coefficients of the deflection formula have common terms for which homogeneous recurrence equations are also compiled using the methods of the Maple system using specialized operators. Results. The solutions of recurrence equations have the form of polynomials with coefficients that depend on the parity of the number of panels and contain trigonometric functions. The graphs of the solutions obtained are constructed and analysed. Sharp changes of deflection characteristic for such truss and their non-monotonic character are noted. It is shown that for a fixed, independent on the number of panels, length of the span and the total load, the relative deflection with increasing number of panels first decreases, then varies little. Conclusions. The asymptotic property of the solution is obtained by the methods of the Maple system: an inclined asymptote is found. The slope is calculated using the analytical capabilities of Maple. A simple formula is derived for the horizontal displacement of the mobile support from the action of the load. The dependence is monotonic. The height of the truss is included in the denominator of the formula

    ONE FEATURE OF THE CONSTRUCTIVE SOLUTIONS OF THE LATTICE GIRDER

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    The problem of the deflection of a planar symmetric statically determinable truss with a double lattice depending on the number of panels was solved in an analytical form. The angle of inclination of the ascending and descending rods of the truss is different. A load is applied to the truss, evenly distributed over the nodes of the lower chord. Special operators of the Maple computer math system and the induction method were used to generalize individual particular solutions to an arbitrary case. Formulas are obtained for the forces the most compressed and stretched truss rods. Cases of kinematic variability of the structure are revealed. A picture of the possible speeds of truss nodes in these cases is constructed. The asymptotic behavior of the deflection is found with a large number of panels and a fixed span length. The deflection was determined by the formula of Maxwell – Mohr

    Detection of Heavy Majorana Neutrinos and Right-Handed Bosons

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    The SU_C(3) otimes SU_L(2) otimes SU_R(2) otimes U(1) left-right (LR) symmetric model explains the origin of the parity violation in weak interactions and predicts the existence of additional W_R and Z' gauge bosons. In addition, heavy right-handed Majorana neutrino states N arise naturally within LR symmetric model. The N s could be partners of light neutrino states, related to their non-zero masses through the see-saw mechanism. This makes the searches of W_R, Z' and N interesting and important. This note describes the study of the potential of the CMS experiment to observe signals from the N and W_R production at the LHC. It is shown that their decay signals can be identified with a small background. For the integral LHC luminosity of L_t = 30 fb^ -1, the 5 sigma discovery of W_R - boson and heavy Majorana neutrinos N_e with masses up to 3.5 TeV and 2.3 TeV, respectively is found possible

    Analytical evaluation of the fundamental frequency of natural vibrations of the spatial coverage

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    The scheme of statically definable truss of spatial coverage is proposed. The formula for the dependence of the vibration frequency on the number of panels is derived. The Dunkerley lower bound and the induction method are used to generalize particular solutions to the case of an arbitrary number of panels. The calculation of the forces in the rods by cutting out the nodes and the analytical transformations to obtain the desired dependence are performed in the Maple computer mathematics system. The solution is compared with the numerical one obtained by solving the problem on the eigenvalues of the characteristic matrix for a system with many degrees of freedom. It is shown that the estimation accuracy depends on the number of panels

    Analytical calculation of the deflection of an externally statically indeterminate lattice truss

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    A scheme of a statically definable truss with additional supports is proposed. Derive formulas for the dependence of the deflection of the truss against the number of panels for three types of symmetrical loads. It is shown that for definite numbers of panels the determinant of the system of equations for the equilibrium of nodes degenerates. This indicates an instant changeability of the structure. To generalize particular solutions to an arbitrary number of panels, the induction method is applied. For this purpose, in the computer mathematics system Maple linear recurrence equations are constructed for the terms of a sequence of coefficients from individual solutions. The graphs of the dependences obtained indicate a nonmonotonic character of the solutions found and the possibility of optimizing the design by choosing the number of panels

    Juxtaposing BTE and ATE – on the role of the European insurance industry in funding civil litigation

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    One of the ways in which legal services are financed, and indeed shaped, is through private insurance arrangement. Two contrasting types of legal expenses insurance contracts (LEI) seem to dominate in Europe: before the event (BTE) and after the event (ATE) legal expenses insurance. Notwithstanding institutional differences between different legal systems, BTE and ATE insurance arrangements may be instrumental if government policy is geared towards strengthening a market-oriented system of financing access to justice for individuals and business. At the same time, emphasizing the role of a private industry as a keeper of the gates to justice raises issues of accountability and transparency, not readily reconcilable with demands of competition. Moreover, multiple actors (clients, lawyers, courts, insurers) are involved, causing behavioural dynamics which are not easily predicted or influenced. Against this background, this paper looks into BTE and ATE arrangements by analysing the particularities of BTE and ATE arrangements currently available in some European jurisdictions and by painting a picture of their respective markets and legal contexts. This allows for some reflection on the performance of BTE and ATE providers as both financiers and keepers. Two issues emerge from the analysis that are worthy of some further reflection. Firstly, there is the problematic long-term sustainability of some ATE products. Secondly, the challenges faced by policymakers that would like to nudge consumers into voluntarily taking out BTE LEI

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