Analytical solution for a strained reinforcement layer bonded to lip-shaped crack under remote mode III uniform load and concentrated load

The concept of arch longitudinal beam wharf was brought out in the contemporary shipping industry of China as a result of the conflict between traditional high-piled wharfs and the increasing size of freights. Different alignments of arch axis will lead to different internal force distributions and the most dangerous section. A series of equations for the arch axis are derived through the transformation of the exponential function under a 40-meter-long span. Based on the analysis of equations affected by the combined force of uniform load and concentrated load, it is providing reference for engineers and analysts with the internal force distribution under some commonly used axis and the location of the most dangerous section for the archs.

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An Exact Analytical Solution for Star-Shaped Cracks

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1094.458 ◽

2015 ◽

Vol 1094 ◽

pp. 458-463 ◽

Cited By ~ 1

Author(s):

Zhu Chen

Keyword(s):

Stress Intensity Factor ◽

Stress Intensity ◽

Analytical Solution ◽

Complex Analysis ◽

Exact Analytical Solution ◽

Plane Elasticity ◽

Type I ◽

Griffith Crack ◽

Shaped Crack ◽

Plane Elasticity Problem

Using the method of complex analysis and by constructing conformal mapping, the study investigates the plane elasticity problem of star-shaped cracks and provides an analytical solution for the stress intensity factor (SIF) of crack-tip type I and II. Problems of the classic Griffith crack, the cross-shaped crack, concurrent uniformly distributed three-cracks and symmetrical eight-cracks are also simulated.

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Analytical Solution of the Star-Shaped Crack in One-Dimensional Hexagonal Quasicrystals

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.838-841.2254 ◽

2013 ◽

Vol 838-841 ◽

pp. 2254-2261

Author(s):

Lu Guan ◽

Zhu Chen

Keyword(s):

Stress Intensity Factor ◽

Stress Intensity ◽

Intensity Factor ◽

Analytical Solution ◽

Conformal Mapping ◽

Complex Analysis ◽

Crack Tip ◽

One Dimensional ◽

Shaped Crack ◽

Shear Problem

With the use of complex analysis, and by introducing adequate conformal mapping, the anti-shear problem of the star-shaped crack in One-dimensional Hexagonal Quasicrystals was studied. An analytical solution to the crack tip stress intensity factor is found.

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A stress analytical solution for Mode III crack within modified gradient elasticity

Mechanics Research Communications ◽

10.1016/j.mechrescom.2017.07.003 ◽

2017 ◽

Vol 84 ◽

pp. 142-147 ◽

Cited By ~ 2

Author(s):

Bing Zhao ◽

Tao Liu ◽

Jun Pan ◽

Xulong Peng ◽

Xuesong Tang

Keyword(s):

Analytical Solution ◽

Gradient Elasticity ◽

Mode Iii ◽

Mode Iii Crack

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Solution for the Shear Lag Problem of U-Shaped Beam by Three Bar Stimulation Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.405-408.1161 ◽

2013 ◽

Vol 405-408 ◽

pp. 1161-1165

Author(s):

Ya Wen An ◽

Qi Zhen Zheng ◽

Ya Min Bao

Keyword(s):

Differential Equation ◽

Beam Theory ◽

Shear Lag ◽

Uniform Load ◽

Concentrated Load ◽

Simply Supported ◽

Shaped Beam ◽

Relative Stress ◽

Stimulation Method ◽

Theoretical Results

three bar stimulation method was adopted to build a differential equation about shear stress for U-shaped beam slab. Relative stress formula for simply supported beam which is subject to uniform load and concentrated load was obtained by solving and deducing differential equation.In order to compare with general beam theory simply,this paper introduced a concept of shear lag coefficient. Finally,combined with a actual example,after compared with measured value and other theoretical results,final result was satisfactory.

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Analytical Solution for Lateral-Torsional Buckling of Concrete-Filled Tubular Flange Girders with Torsional Bracing

Advances in Civil Engineering ◽

10.1155/2020/4340381 ◽

2020 ◽

Vol 2020 ◽

pp. 1-14

Author(s):

Yingchun Liu ◽

Zhaoming Hang ◽

Wenfu Zhang ◽

Keshan Chen ◽

Jing Ji

Keyword(s):

Analytical Solution ◽

Lateral Displacement ◽

Data Sets ◽

Torsional Angle ◽

The Finite Element Method ◽

Lateral Torsional Buckling ◽

Torsional Buckling ◽

Concentrated Load ◽

Buckling Strength ◽

Parametric Studies

Concrete-filled tubular flange girders have been used in bridges, and torsional bracings are widely used in them to increase the lateral-torsional buckling strength. This article proposes an analytical solution for the lateral-torsional buckling (LTB) of concrete-filled tubular flange steel girders with torsional bracing under a concentrated load. The modal trial functions of lateral displacement and the torsional angle are expressed by the first six terms of the trigonometric function. By introducing dimensionless parameters, the variational solution of energy for the buckling equation of the LTB of the girders is obtained, and the formula for the dimensionless critical moment of its LTB is derived using 1stOpt based on 32,550 data sets. Compared with the finite element method, the proposed critical formula is highly accurate and can be applied to engineering design. Finally, parametric studies were conducted on the effects of the stiffness of torsional bracing, the span of the girder, and the flange steel ratio.

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