Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under trans...Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.展开更多
The mechanical properties of rocks under cyclic and dynamic loading are important research topics for solving the structural stability of large engineering rocks. As underground mining in coal mines goes deeper, groun...The mechanical properties of rocks under cyclic and dynamic loading are important research topics for solving the structural stability of large engineering rocks. As underground mining in coal mines goes deeper, ground stresses are increasing and instability damage of coal rocks by shear loading is frequent. Therefore, in order to investigate the shear mechanical properties and section morphological characteristics of intact coal samples in the direct shear test, the RDS-200 rock direct shear instrument was used to carry out direct shear tests on intact coal samples under different normal stresses, and the shear section was scanned for three-dimensional morphology. The results show that: 1) from the strength characteristics, the peak shear strength of the coal samples increased linearly with increasing normal stress, and the residual shear strength increased logarithmically. 2) In terms of deformation characteristics, the peak shear displacement of the coal sample increases linearly with increasing normal stress, the pre-peak shear stiffness increases logarithmically, and the residual normal displacement decreases linearly. 3) From the morphological characteristics of the shear surface, with the increase of normal stress, the section transitions from high-order undulating to flattening type. The maximum height of the fracture surface profile and kurtosis coefficient of the shear section decreased linearly, and the profile area ratio and root mean square of slope decreased as a power function, i.e. the higher the normal stress, the smaller the undulation of the section, the sharpness of the roughness shape and the roughness coefficient JRC, and the flatter and smoother the section. The findings of this study can help to provide some reference for the evaluation of shear instability occurring in coal bodies under different normal stresses.展开更多
In this paper, a finite element method is developed to numericallyevaluate the shear coefficient of Timoshenko's beam with multiplyconnected cross section. With focus on analyzing shear stressesdistributed at the ...In this paper, a finite element method is developed to numericallyevaluate the shear coefficient of Timoshenko's beam with multiplyconnected cross section. With focus on analyzing shear stressesdistributed at the neutral axis of the beam, an improved definitionof the shear coeffi- cient is presented. Based on this definition, aGalerkin-type finite element formulation is proposed to analyze theshear stresses and shear deflections. Numerical solutions of theexamples for some typical cross-sections are compared with thetheoretical results. The shear coefficient of tower sections of theTsing Ma Bridge is calculated by use of the proposed approach, sothat the finite element modeling of The bridge can be developed withthe accurate values of the sectional properties.展开更多
For the instability problem of density stratified shear flows in sea straits with variable cross sections, a new semielliptical instability region is found. Rurthermore, the instability of the bounded shear layer is s...For the instability problem of density stratified shear flows in sea straits with variable cross sections, a new semielliptical instability region is found. Rurthermore, the instability of the bounded shear layer is studied in two cases： （i） the density which takes two different constant values in two layers and （ii） the density which takes three different constant values in three layers. In both cases, the dispersion relation is found to be a quartic equation in the complex phase velocity. It is found that there are two unstable modes in a range of the wave numbers in the first case, whereas there is only one unstable mode in the second case.展开更多
文摘Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.
文摘The mechanical properties of rocks under cyclic and dynamic loading are important research topics for solving the structural stability of large engineering rocks. As underground mining in coal mines goes deeper, ground stresses are increasing and instability damage of coal rocks by shear loading is frequent. Therefore, in order to investigate the shear mechanical properties and section morphological characteristics of intact coal samples in the direct shear test, the RDS-200 rock direct shear instrument was used to carry out direct shear tests on intact coal samples under different normal stresses, and the shear section was scanned for three-dimensional morphology. The results show that: 1) from the strength characteristics, the peak shear strength of the coal samples increased linearly with increasing normal stress, and the residual shear strength increased logarithmically. 2) In terms of deformation characteristics, the peak shear displacement of the coal sample increases linearly with increasing normal stress, the pre-peak shear stiffness increases logarithmically, and the residual normal displacement decreases linearly. 3) From the morphological characteristics of the shear surface, with the increase of normal stress, the section transitions from high-order undulating to flattening type. The maximum height of the fracture surface profile and kurtosis coefficient of the shear section decreased linearly, and the profile area ratio and root mean square of slope decreased as a power function, i.e. the higher the normal stress, the smaller the undulation of the section, the sharpness of the roughness shape and the roughness coefficient JRC, and the flatter and smoother the section. The findings of this study can help to provide some reference for the evaluation of shear instability occurring in coal bodies under different normal stresses.
文摘In this paper, a finite element method is developed to numericallyevaluate the shear coefficient of Timoshenko's beam with multiplyconnected cross section. With focus on analyzing shear stressesdistributed at the neutral axis of the beam, an improved definitionof the shear coeffi- cient is presented. Based on this definition, aGalerkin-type finite element formulation is proposed to analyze theshear stresses and shear deflections. Numerical solutions of theexamples for some typical cross-sections are compared with thetheoretical results. The shear coefficient of tower sections of theTsing Ma Bridge is calculated by use of the proposed approach, sothat the finite element modeling of The bridge can be developed withthe accurate values of the sectional properties.
基金supported by University Grants Commission-Junior Research Fellowship, Government of India
文摘For the instability problem of density stratified shear flows in sea straits with variable cross sections, a new semielliptical instability region is found. Rurthermore, the instability of the bounded shear layer is studied in two cases： （i） the density which takes two different constant values in two layers and （ii） the density which takes three different constant values in three layers. In both cases, the dispersion relation is found to be a quartic equation in the complex phase velocity. It is found that there are two unstable modes in a range of the wave numbers in the first case, whereas there is only one unstable mode in the second case.
