Analysis of shear lag in cylindrical tubes of arbitrary cross section

1983 ◽  
Vol 389 (1797) ◽  
pp. 259-277
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Bending Moment ◽  
General Purpose ◽  
Simple Eigenvalue ◽  
Arbitrary Cross Section ◽  
Longitudinal Distribution ◽  
Shear Lag ◽  
Cylindrical Tubes ◽  
Polynomial Distribution

A very general analysis is given of the phenomenon of shear lag in thin-walled cylindrical tubes, with single-cell cross sections of arbitrary shape, containing any number of concentrated longitudinal booms that carry direct stress only, and subjected to any longitudinal distribution of bending moment and torque. Two equations relating the distributions of direct and shearing stresses on the cross section are derived for the most general case where the tube is non-uniform because of an arbitrary longitudinal variation of wall thicknesses and boom areas. These equa­tions, which are remarkably simple in view of their generality, incor­porate all the requirements of equilibrium and compatibility and provide corrections to the stresses, curvature and twist calculated from the engineers’ theory of bending and torsion. They also govern the distri­bution of stresses arising from the application of self-equilibrating systems of tractions to the end cross sections. Exact solutions are ob­tained for the case of a uniform, but otherwise arbitrary, cross section under any polynomial distribution of bending moment and torque, and it is shown how conditions at the end cross sections can be satisfied with the aid of solutions of a simple eigenvalue problem. The equations are in a particularly ideal form for incorporating into a general purpose com­puter program for the automatic numerical solution of any problem of this type.

scholarly journals Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

2021 ◽  
Author(s):  
Dang-Bao Tran ◽  
Jaroslav Navrátil
Keyword(s):  
Numerical Method ◽  
Cross Section ◽  
Cross Sections ◽  
Arbitrary Cross Section ◽  
Local Analysis ◽  
3D Analysis ◽  
Shear Lag ◽  
Isoparametric Element ◽  
Cross Sectional ◽  
The Cross

This paper presents the use of a finite element method (FEM) to analyze the shear lag effect due to the flexure of beams with an arbitrary cross-section and homogeneous elastic material. Beams are constrained by the most common types of supports, such as fixed, pinned, and roller. The transverse, concentrated, or distributed loads act on the beams through the shear center of the cross-section. The presented FEM transforms the 3D analysis of the shear lag phenomenon into separated 2D cross-sectional and 1D beam modeling. The characteristics of the cross-section are firstly derived from 2D FEM, which uses a 9-node isoparametric element. Then, a 1D FEM, which uses a linear isoparametric element, is developed to compute the deflection, rotation angle, bending warping parameter, and stress resultants. Finally, the stress field is obtained from the local analysis on the 2D-cross section. A MATLAB program is executed to validate the numerical method. The validation examples have proven the efficiency and reliability of the numerical method for analyzing shear lag flexure, which is a common problem in structural design.

A shear center demonstration model using 3D-printing

2021 ◽  
pp. 030641902110574
Author(s):  
Lawrence N Virgin
Keyword(s):  
3D Printing ◽  
Cross Section ◽  
Cross Sections ◽  
Principal Axis ◽  
Practical Importance ◽  
Bending Moment ◽  
Shear Center ◽  
Cross Sectional ◽  
Thin Walls ◽  
Section Profile

Locating the shear, or flexural, center of non-symmetric cross-sectional beams is a key element in the teaching of structural mechanics. That is, establishing the point on the plane of the cross-section where an applied load, generating a bending moment about a principal axis, results in uni-directional deflection, and no twisting. For example, in aerospace structures it is particularly important to assess the propensity of an airfoil section profile to resist bending and torsion under the action of aerodynamic forces. Cross-sections made of thin-walls, whether of open or closed form are of special practical importance and form the basis of the material in this paper. The advent of 3D-printing allows the development of tactile demonstration models based on non-trivial geometry and direct observation.

Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

2020 ◽  
pp. 2050047
Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li
Keyword(s):  
Finite Volume ◽  
Cross Section ◽  
Cross Sections ◽  
Open Channel ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Cross Sectional ◽  
Shallow Flows ◽  
Natural Streams ◽  
Saint Venant Equations

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

scholarly journals NUMERICAL INVESTIGATION OF THE ELASTIC-PLASTIC LINEAR HARDENING STRESS-STRAIN STATE OF THE FRAME ELEMENT CROSS-SECTION

2016 ◽  
Vol 8 (3) ◽  
pp. 94-100
Author(s):  
Andrius Grigusevičius ◽  
Gediminas Blaževičius
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Software Environment ◽  
Stress Strain ◽  
Hardening Material ◽  
Frame Element ◽  
Nonlinear Stress

The aim of this paper is to present a solution algorithm for determining the frame element crosssection carrying capacity, defined by combined effect of bending moment and axial force. The distributions of stresses and strains inside a cross-section made of linearly hardening material are analysed. General nonlinear stress-strain dependencies are composed. All relations are formed for rectangular cross-section for all possible cases of combinations of axial force and bending moment. To this end, five different stress-strain states are investigated and four limit axial force values are defined in the present research. The nonlinear problem is solved in MATLAB mathematical software environment. Stress-strain states in the cross-sections are investigated in detail and graphically analysed for two numerical experiments.

scholarly journals IV. On the practical solution of the most general problems in continuous beams

1879 ◽  
Vol 29 (196-199) ◽  
pp. 493-505
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
General Problem ◽  
Bending Moment ◽  
Moment Of Inertia ◽  
Shearing Stress ◽  
Practical Solution ◽  
Continuous Beams ◽  
The Moment

1. It is not necessary to enter into the question of the advisability of employing continuous girders in bridges with spans of less than 200 feet, but it is generally conceded that the increased economy due to the employment of continuous girders in longer spans more than counterbalances the well-known practical objections to continuity. Hence the practical solution of the general problem—given the conditions at the ends of a continuous girder, the spans, the moment of inertia of all cross sections, and the loading, to find the bending moment and shearing stress in every cross-section, is not unworthy of our attention.

Design and Fabrication of a General Purpose 3D Digitizer Based on Grinding Technique

2008 ◽  
Vol 594 ◽  
pp. 7-14 ◽  
Author(s):  
Wei Chen Lee ◽  
Liang Wei Chen
Keyword(s):  
Thin Layer ◽  
Cross Section ◽  
Cross Sections ◽  
Ccd Camera ◽  
General Purpose ◽  
Cad Model ◽  
3D Cad ◽  
The Cross ◽  
Grinding Technique

The objective of this research is to design and fabricate a general purpose 3D digitizer based on grinding technique to completely acquire the geometry of an object, including its inner structure, and accurately create its CAD model. How the 3D digitizer works is as follows. First a thin layer of an object that is fixed in epoxy is removed by a grinder and the image of the cross section is taken by a CCD camera. The process is repeated until the images of all the cross sections of the object are captured. Then the images are stacked up by using software 3D-DOCTOR to obtain the 3D CAD model. The accuracy of the 3D digitizer developed in the research was within 0.03 mm when measuring a length of 5.50 mm and the gauge R&R percentage was 25.99%. The performance shows that the 3D digitizer is promising for use in industry.

REGULATION OF GUYED MAST STRESSES

2009 ◽  
Vol 1 (2) ◽  
pp. 65-72 ◽  
Author(s):  
Donatas Jatulis ◽  
Algirdas Juozapaitis
Keyword(s):  
Numerical Experiment ◽  
Cross Section ◽  
Cross Sections ◽  
Mobile Communications ◽  
Bending Moment ◽  
Physical Parameters ◽  
Bending Moments ◽  
Rational Distribution ◽  
Guyed Mast ◽  
Prestressed Structures

Development of mobile communications and their networks in Lithuania produced an essential influence on high telecommunications structures design activities. In its turn it has stimulates their research and innovations of such structural systems. One of the most efficient systems of telecommunication structures is guyed mast. It should be indicated that the behaviour of prestressed structures systems has been thoroughly examined in many investigations. But recently the increase of economical efficiency of guyed masts becomes undoubtedly actual. The development of such structures in many cases is directed to the selection in the mast elements scheme and their cross-sections. It should be underlined that geometric and physical parameters have a decisive moment on prestressed structures. An exact parameters choice allows to obtain in the mast rational distribution of bending moments, predetermining a project solution closely connected with the mass criteria. The diagram of bending moment’s distribution in guyed mast is considered rational when negative and positive moment values are absolutely equal. In the present research, analytical expressions for rational bending moments determining are presented. Above mentioned non-linear expressions estimate an influence of axial force for the bending moments. When solving the task of rational bending moments in a guyed mast, it is necessary to select suitable (i.e. rational) guyed mast bending spans. In the article is described the calculations of the guys fastening altitudes when guy level number is known. It should be noted that it is necessary to use the way of gradual approximation. The sequence of calculations is interrupted, when the sum of guyed mast spans corresponds to the exactness selected. The decisive part in mast behaviour is played by guys. The main parameters of them are pretension and cross-section area. In the article the equations are presented for determining the above-mentioned parameters. It should be stressed that after making uniform stresses of the guys on the different level of each of them it is possible to minimise some steel quantities. In the article a numerical experiment is presented for determining the technical-economical effectiveness of stress regulation. For the analysis, a standard three edged lattice guyed mast with cross-section parameters was selected in a usual way. By the suggested beam composition methods the design of the shaft was performed, and the results obtained were compared to a standard guyed mast shaft. For determining the stresses of beam elements Robot Millennium software was used; its reliability was demonstrated by earlier investigations. The results of numerical experiment that the maximal bending moment of composed guyed mast is three times less than that of a standard maximal one. An applied regulation of stresses has allowed to lessen much of the cross-section of guy rope. By applying the suggested methods it was possible to diminish the steel expenditure of shaft by more than 30%.

scholarly journals Transfer relations: useful basis for computer-aided engineering of circular arch structures

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jiao-Long Zhang ◽  
Xian Liu ◽  
Yong Yuan ◽  
Herbert A. Mang ◽  
Bernhard L.A. Pichler
Keyword(s):  
Cross Section ◽  
Bending Moment ◽  
Arbitrary Cross Section ◽  
Computer Aided Engineering ◽  
Arch Bridge ◽  
Content Type ◽  
Circular Arch ◽  
Computer Aided ◽  
Arch Structures

Purpose Transfer relations represent analytical solutions of the linear theory of circular arches, relating each one of the kinematic and static variables at an arbitrary cross-section to the kinematic and static variables at the initial cross-section. The purpose of this paper is to demonstrate the significance of the transfer relations for structural analysis by means of three examples taken from civil engineering. Design/methodology/approach The first example refers to an arch bridge, the second one to the vault of a metro station and the third one to a real-scale test of a segmental tunnel ring. Findings The main conclusions drawn from these three examples are as follows: increasing the number of hangers/columns of the investigated arch bridge entails a reduction of the maximum bending moment of the arch, allowing it to approach, as much as possible, the desired thrust-line behavior; compared to the conventional in situ cast method, a combined precast and in situ cast method results in a decrease of the maximum bending moment of an element of the vault of the studied underground station by 46%; and the local behavior of the joints governs both the structural convergences and the bearing capacity of the tested segmental tunnel ring. Originality/value The three examples underline that the transfer relations significantly facilitate computer-aided engineering of circular arch structures, including arch bridges, vaults of metro stations and segmental tunnel rings.

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