scholarly journals Analytical calculation of the deflection of the lattice truss

2018 ◽  
Vol 193 ◽  
pp. 03015 ◽  
Author(s):  
Mikhail Kirsanov ◽  
Dmitriy Tinkov
Keyword(s):  
Asymptotic Property ◽  
Analytical Calculation ◽  
Extreme Points ◽  
Horizontal Displacement ◽  
Vertical Force ◽  
Uniform Load

An algorithm is given for deriving the dependence of the deflection of a planar statically determinate beam truss on the number of panels, dimensions and load. Three load cases are considered: uniform load on the lower belt, upper belt and vertical force in the middle of the span. By induction, generalizing a series of solutions for trusses with a consecutively increasing number of panels, the desired formula is obtained for the deflection and horizontal displacement of the mobile support of the truss. All transformations are performed in the system of symbolic mathematics Maple. For a sequence of coefficients of the desired formula, using the special Maple operators, homogeneous recurrent equations are constructed and solved. The coefficients found are in the form of polynomials in the number of panels. The asymptotic property of the solution is found. On the graphs of the dependence of the deflection on the number of panels and on the height, extreme points are found. The solution can be used to test the calculations obtained numerically.

Study on Isolated Layer Mechanics Character of Combined Base Isolated Structure Based on Axial Forces Redistribute

2012 ◽  
Vol 166-169 ◽  
pp. 627-631 ◽  
Author(s):  
Fu You Zhang ◽  
Ming Gu ◽  
Yun Song ◽  
Song Xu
Keyword(s):  
Axial Force ◽  
Horizontal Displacement ◽  
Vertical Force ◽  
Isolation System ◽  
Isolation Layer ◽  
Calculating Method ◽  
Axial Forces ◽  
Rubber Bearings

Abstract：Combined isolation system is combined with rubber bearings which provide resilience forces and sliding isolated bearings which provide damp. According to the rule of axial forces redistributing between two kinds of bearings under earthquake, a calculating method considering the vertical force redistribute of isolation layer was given. With this method, the results of an example show that axial force will transfer from rubber bearings to sliding isolated bearings along with the horizontal displacement of isolation layer. The bigger the displacement is the more axial force transfers. So the axial-forces redistribution is a self-adjustable performance of the system, and also is an advantage for the system.

3D Analytical Solution of Soil Deformation Induced by Shield Tunnelling Construction

2011 ◽  
Vol 261-263 ◽  
pp. 1814-1819
Author(s):  
Gang Wei ◽  
Jie Hong ◽  
Xin Jiang Wei
Keyword(s):  
Analytical Solution ◽  
Ground Deformation ◽  
Three Dimensional ◽  
Analytical Calculation ◽  
Horizontal Displacement ◽  
Ground Movement ◽  
Soil Deformation ◽  
Loss Ratio ◽  
Shield Tunnelling ◽  
Ground Loss

Three-dimensional (3D) analytical solution of soil deformation induced by ground loss in shield tunnelling construction was researched. It is put forward that the ground loss ratio is not a fixed value, but changes in driving direction. The calculation formula of ground loss ratio in driving direction was deduced. Based on two-dimensional (2D) analytical solution of uniform ground movement model of shield tunnelling, the three-dimensional analytical solution of ground deformation induced by ground loss is deduced. The settlement in vertical direction and the displacement in lateral horizontal direction at any point can be calculated; and the method is only applied to the construction phase. In analytical calculation: the predicted soil displacements are in good agreement with the measured values, and the method is easy to use; the closer the soil to tunnel is, the faster the lateral horizontal displacement changes; the extent of change of lateral horizontal displacement in longitudinal direction is smaller than displacement in lateral direction.

Ground Deformation Rule Induced by Shield Tunneling Construction

2011 ◽  
Vol 90-93 ◽  
pp. 670-675
Author(s):  
Xin Jiang Wei ◽  
Yang Zhou ◽  
Gang Wei ◽  
Jie Hong
Keyword(s):  
Ground Deformation ◽  
Three Dimensional ◽  
Analytical Calculation ◽  
Horizontal Displacement ◽  
Tunnel Construction ◽  
Shield Tunneling ◽  
Dimensional Solution ◽  
Ground Loss ◽  
Good Agreement ◽  
Ground Displacements

In this paper, Ground deformation in shield tunneling construction is researched. It is put forward that ground deformation is caused by three reasons, which are ground loss, the positive thrust and the friction. By solving the three-part respectively, the three-dimensional solution formula can be obtained after superposing these. This method is used to calculate the tunnel construction phase at any point in the level of vertical settlement and horizontal displacement. As shown in analytical calculation, the predicted ground displacements of this method are in good agreement with the measured values.

scholarly journals ANALYSIS OF THE DEFLECTION OF A TRUSS WITH A DECORATIVE LATTICE

2019 ◽  
Author(s):  
Mikhail N. Kirsanov
Keyword(s):  
Simple Formula ◽  
Linear Equations ◽  
Horizontal Displacement ◽  
Trigonometric Functions ◽  
System Of Linear Equations ◽  
Uniform Load ◽  
Total Load ◽  
Recurrence Equations ◽  
The Matrix ◽  
Monotonic Character

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.

scholarly journals Calculation of the deflection of an arched truss with suspended elements depending on the number of panels

2020 ◽  
Vol 16 (3) ◽  
pp. 179-184
Author(s):  
Mikhail N. Kirsanov
Keyword(s):  
Asymptotic Properties ◽  
Analytical Calculation ◽  
General System ◽  
Uniform Load ◽  
Equilibrium Equations ◽  
Rounding Errors ◽  
Symbolic Form ◽  
Total Load ◽  
Independent Parameters ◽  
System Of Equilibrium Equations

The aim of the work - to propose a scheme and analytical calculation of a statically definable planar truss with a suspended lower belt. Methods. The formula for the dependence of the deflection of the truss under the action of a uniform load on the lower belt on its size and the number of panels is derived in the computer mathematics system Maple. The forces in the rods are found from the solution of the general system of equilibrium equations of all nodes in symbolic form. The deflection is calculated using the Maxwell - Mohr's formula. Generalization of a number of formulas for deflection obtained by increasing the number of panels sequentially to an arbitrary number is performed by double induction using two independent parameters. In this case, special operators of the Maple system are used, allowing for a sequence of coefficients in the desired formula to create and solve recurrent equations that satisfy the elements of the sequences. Results. The obtained solutions have a polynomial form for the number of panels. Curves of deflection dependence on the number of panels are constructed and analyzed. Asymptotic properties of solutions are found in the case of a fixed span length of the structure and a given total load. The proposed scheme is a statically determinate structure with two independent parameters of regularity allows for the finding of a fairly simple analytical solution. The resulting formula is most effective in calculating systems with a large number of elements, where numerical methods tend to accumulate rounding errors.

Analytical Procedures for Calculation of Horizontal Displacement of Timber Shear Walls

2017 ◽  
Vol 21 ◽  
pp. 135-140
Author(s):  
Ion Florenţa ◽  
Nicolae Ţăranu ◽  
Alexandru Secu ◽  
Ana Raluca Roşu ◽  
Dragoş Ungureanu
Keyword(s):  
Seismic Design ◽  
Lateral Displacement ◽  
Analytical Calculation ◽  
Shear Walls ◽  
Horizontal Displacement ◽  
Shear Wall ◽  
Calculation Model ◽  
Analytical Models ◽  
European Norm ◽  
Displacement Based

The shear wall horizontal displacement is one of the most important parameters involved in the seismic design of the timber framed structures. This paper presents the fundamentals of displacement-based seismic design, along with a description of the requirements for its application: checking of the maximum allowable displacement, checking of the buildings’ separation and determining the stiffness of the walls. The horizontal displacement of a shear wall is determined through the analytical calculation of the wall elements’ displacements. For timber framed structure, the International Building Code (IBC), recommends analytical models for the determination of the horizontal displacement. However, the European norm, Eurocode 5 does not provide any calculation model for the lateral displacement. A comparative study of the available analytical models and the corresponding results are presented in this paper.

Advantages of Complementary Stereo Images as Viewed with the Low-Temperature Field-Emission SEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1314-1315
Author(s):  
William P. Wergin ◽  
Eric F. Erbe
Keyword(s):  
Fold Increase ◽  
Horizontal Displacement ◽  
Three Dimensions ◽  
Stereo Image ◽  
Stereo Pair ◽  
Sem Micrograph ◽  
Left And Right ◽  
The Common ◽  
The Brain ◽  
Pair Analysis

The eye-brain complex allows those of us with normal vision to perceive and evaluate our surroundings in three-dimensions (3-D). The principle factor that makes this possible is parallax - the horizontal displacement of objects that results from the independent views that the left and right eyes detect and simultaneously transmit to the brain for superimposition. The common SEM micrograph is a 2-D representation of a 3-D specimen. Depriving the brain of the 3-D view can lead to erroneous conclusions about the relative sizes, positions and convergence of structures within a specimen. In addition, Walter has suggested that the stereo image contains information equivalent to a two-fold increase in magnification over that found in a 2-D image. Because of these factors, stereo pair analysis should be routinely employed when studying specimens.Imaging complementary faces of a fractured specimen is a second method by which the topography of a specimen can be more accurately evaluated.

Monte Carlo Modelling of Secondary Electron Yield from Rough Surfaces

1990 ◽  
Vol 48 (1) ◽  
pp. 422-423
Author(s):  
John C. Russ
Keyword(s):  
Monte Carlo ◽  
Energy Loss ◽  
Secondary Electron ◽  
Secondary Electron Emission ◽  
Analytical Calculation ◽  
Mean Free Path ◽  
Single Scattering ◽  
High Energy ◽  
Secondary Electron Yield ◽  
Electron Yield

Monte-Carlo programs are well recognized for their ability to model electron beam interactions with samples, and to incorporate boundary conditions such as compositional or surface variations which are difficult to handle analytically. This success has been especially powerful for modelling X-ray emission and the backscattering of high energy electrons. Secondary electron emission has proven to be somewhat more difficult, since the diffusion of the generated secondaries to the surface is strongly geometry dependent, and requires analytical calculations as well as material parameters. Modelling of secondary electron yield within a Monte-Carlo framework has been done using multiple scattering programs, but is not readily adapted to the moderately complex geometries associated with samples such as microelectronic devices, etc.This paper reports results using a different approach in which simplifying assumptions are made to permit direct and easy estimation of the secondary electron signal from samples of arbitrary complexity. The single-scattering program which performs the basic Monte-Carlo simulation (and is also used for backscattered electron and EBIC simulation) allows multiple regions to be defined within the sample, each with boundaries formed by a polygon of any number of sides. Each region may be given any elemental composition in atomic percent. In addition to the regions comprising the primary structure of the sample, a series of thin regions are defined along the surface(s) in which the total energy loss of the primary electrons is summed. This energy loss is assumed to be proportional to the generated secondary electron signal which would be emitted from the sample. The only adjustable variable is the thickness of the region, which plays the same role as the mean free path of the secondary electrons in an analytical calculation. This is treated as an empirical factor, similar in many respects to the λ and ε parameters in the Joy model.

Force Plate Analysis of Dogs with Bilateral Hip Dysplasia Treated with a Unilateral Triple Pelvic Osteotomy: A Long-term Review of Cases

1998 ◽  
Vol 11 (02) ◽  
pp. 85-93 ◽  
Author(s):  
Joanne R. Cockshutt ◽  
H. Dobson ◽  
C. W. Miller ◽  
D. L. Holmberg ◽  
Connie L. Taves ◽  
...  
Keyword(s):  
Gait Analysis ◽  
Hip Dysplasia ◽  
Weight Bearing ◽  
Force Plate ◽  
Case Series ◽  
Pelvic Osteotomy ◽  
Vertical Force ◽  
Long Term Outcome ◽  
Case Series Study

SummaryA retrospective case series study was done to determine the long-term outcome of operations upon dogs treated for canine hip dysplasia by means of a triple pelvic osteotomy (TPO). Twentyfour dogs with bilateral hip dysplasia, that received a unilateral TPO between January 1988 and June 1995, were re-examined at the Ontario Veterinary College. The assessment included physical, orthopedic and lameness examinations, standard blood work, pelvic radiographs and force plate gait analysis. They were compared to bilaterally dysplastic dogs that had not been treated, and also to normal dogs. Force plate data analysis demonstrated a significant increase in peak vertical force (PVF) and mean vertical force over stance (MVF) in the limb that underwent surgical correction by means of a TPO, when compared to the unoperated hip. It was determined that performing a unilateral TPO on a young dysplastic dog resulted in greater forces and weight bearing being projected through the TPO corrected limb when compared to the unoperated limb.Dogs with bilateral hip dysplasia treated with a unilateral triple pelvic osteotomy (TPO) were assessed by force plate gait analysis, radiographs and orthopedic examination. There was a significant increase in hip Norberg angles over time, although degenerative changes did progress. Limbs that had been operated upon had significantly greater peak and mean ground reaction forces than limbs that had not received an operation.

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