SEMI-ANALYTICAL METHOD FOR SHEAR LAG ANALYSIS OF BEAMS WITH ARBITRARY CROSS SECTION

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.

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Hydrodynamic Entrance Lengths for Ducts of Arbitrary Cross Section

Journal of Basic Engineering ◽

10.1115/1.3609713 ◽

1967 ◽

Vol 89 (4) ◽

pp. 847-850 ◽

Cited By ~ 45

Author(s):

S. T. McComas

Keyword(s):

Velocity Profile ◽

Detailed Analysis ◽

Cross Section ◽

Analytical Method ◽

Arbitrary Cross Section ◽

Numerical Results ◽

Entrance Length ◽

Flow Development

A general analytical method is presented for determination of the hydrodynamic entrance length of ducts of arbitrary cross section. Only knowledge of the fully developed velocity profile is required in order to determine this length in comparison to other approaches which require a detailed analysis of the flow development. This method is applied to circular, elliptical, annular, rectangular, and triangular ducts with numerical results presented.

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

Periodica Polytechnica Civil Engineering ◽

10.3311/ppci.19070 ◽

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.

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