The objective of the present paper is to introduce a theoretical analysis of bending I-sections after pure bending. The springback values are determined to provide a quantitative method for predicting the springback u...The objective of the present paper is to introduce a theoretical analysis of bending I-sections after pure bending. The springback values are determined to provide a quantitative method for predicting the springback using von Mises criteria. The analytical methods for the I-section are given for two cases according to the positions of the yield point along the height of the beam. The controlling parameters on the springback of I-sections are studied. The results obtained are quite successful for the prediction of springback for bending I-sections.展开更多
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
In this paper by means of the exact analytic method [1], the general solution fordynamic response of nonhomogeneous beam with variable cross section is obtained un-der arbitrary resonant load and boundary conditions. ...In this paper by means of the exact analytic method [1], the general solution fordynamic response of nonhomogeneous beam with variable cross section is obtained un-der arbitrary resonant load and boundary conditions. The problem is reduced to solvea non-positive differential equation. Generally, it is not solved by variational method.By the present method, the general solution for this problem may be written as an ana-lytic form. Hence, it is convenient for structure optimizing problem. In this paper, itsconvergence is proved. Numerical examples are given at the end of the paper. which in-dicates satisfactory results can be obtained.展开更多
This paper presents the results of an experimental investigation on explosive breaching of p-section concrete beams. Twenty three p-section concrete beams with a 100 cm length were tested. TNT charges were placed at t...This paper presents the results of an experimental investigation on explosive breaching of p-section concrete beams. Twenty three p-section concrete beams with a 100 cm length were tested. TNT charges were placed at three positions: contact detonation in the center, contact detonation above the web and close-in detonation in the center. The external and internal breach parameters of the panels were evaluated by measuring the diameter of the ejection crater, spalling crater and breach hole created by the charge detonation. The experimental results were compared to predict values obtained by the analytical models proposed by McVay, Morishita and Remennikov. A modified breach with crater limit line and breach without crater limit line were put forward based on the experimental results. The maximum cross-sectional destruction area ratio(MCDAR) values were used to evaluate the damage degree. The maximum value of MCDAR reached 0.331 corresponding to the C5 experimental condition, of which explosion occurred above the web.展开更多
This paper deals with finite deformation problems of cantilever beam with variable sec- tion under the action of arbitrary transverse loads.By the use of a method of variable replacement, the nonlinear differential eq...This paper deals with finite deformation problems of cantilever beam with variable sec- tion under the action of arbitrary transverse loads.By the use of a method of variable replacement, the nonlinear differential equation with varied coefficient for the problem can be transformed into an equation with variable separable.The exact solution can be obtained by the integration method. Some examples are given in the paper,and the results of these examples show that this exact solution includes the existing solutions in references as special cases.展开更多
In this paper, the step reduction method is discussed, which was advanced by Prof. Yeh Kai-yuan for calculating a non-uniform beam with various sections. The following result is proved. The approximate solution by thi...In this paper, the step reduction method is discussed, which was advanced by Prof. Yeh Kai-yuan for calculating a non-uniform beam with various sections. The following result is proved. The approximate solution by this method approaches the true solution if the number of the steps approaches the infinity. However, the measure of the error between the limit solution and the ture solution is not in the pure mathematics sense but in the mechanics sense.展开更多
In most framed structures anticipated deformations in accordance with current codes fall into acceptable limit states, whereas they go through substantial residual deformations in the aftermath of severe ground motion...In most framed structures anticipated deformations in accordance with current codes fall into acceptable limit states, whereas they go through substantial residual deformations in the aftermath of severe ground motions. These structures seem unsafe to occupants since static imminent instability in the immediate post-earthquake may be occurred. Moreover, rehabilitation costs of extensive residual deformations are not usually reasonable. Apparently, there is a lack of detailed knowledge related to reducing residual drift techniques when code-based seismic design is considered. In this paper, reduced beam section connections as a positive approach are taken action to mitigate the huge amount of residual drifts which are greatly amplified by P-Δ effects. To demonstrate the efficacy of RBS, a sixteen-story moment resisting frame is analyzed based on a suite of 8 single-component near field records which have been scaled according to the code provisions. The results are then processed to assess the effects of RBS detailing on drift profile, maximum drift, and residual drift. Besides, a special emphasis is given to estimate overall trend towards drift accumulation in each story in the presence of RBS assembly. A main conclusion is that using this connection predominantly alleviates the adverse effects of P-Δ on amplifying residual drifts.展开更多
A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigate...A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule （GDQR） method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.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
This study covers optimization of I-sectional flange beams. Scope of this study is limited to medium weight flange beams of Table 1 of IS 808:1983 but it can be further extended for the other sections of this code. Be...This study covers optimization of I-sectional flange beams. Scope of this study is limited to medium weight flange beams of Table 1 of IS 808:1983 but it can be further extended for the other sections of this code. Best possible geometric shape of the cross-section is found for maximum performance of the beam with minimum material consumption. All possible loading conditions are considered in the study for which a beam in flexure undergoes in its life. ANSYS software program is used for the analysis and optimizing the sections. It is found that sections MB 125, MB 300 and MB 400 of Table 1 of IS 808 are not the optimum sections but other alternative of these cross-sections is available which within the same material consumption performs better than these sections of IS code.展开更多
文摘The objective of the present paper is to introduce a theoretical analysis of bending I-sections after pure bending. The springback values are determined to provide a quantitative method for predicting the springback using von Mises criteria. The analytical methods for the I-section are given for two cases according to the positions of the yield point along the height of the beam. The controlling parameters on the springback of I-sections are studied. The results obtained are quite successful for the prediction of springback for bending I-sections.
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In this paper by means of the exact analytic method [1], the general solution fordynamic response of nonhomogeneous beam with variable cross section is obtained un-der arbitrary resonant load and boundary conditions. The problem is reduced to solvea non-positive differential equation. Generally, it is not solved by variational method.By the present method, the general solution for this problem may be written as an ana-lytic form. Hence, it is convenient for structure optimizing problem. In this paper, itsconvergence is proved. Numerical examples are given at the end of the paper. which in-dicates satisfactory results can be obtained.
基金supported by The National Natural Science Foundation of China under Grant No.11390362 and No. 11221202
文摘This paper presents the results of an experimental investigation on explosive breaching of p-section concrete beams. Twenty three p-section concrete beams with a 100 cm length were tested. TNT charges were placed at three positions: contact detonation in the center, contact detonation above the web and close-in detonation in the center. The external and internal breach parameters of the panels were evaluated by measuring the diameter of the ejection crater, spalling crater and breach hole created by the charge detonation. The experimental results were compared to predict values obtained by the analytical models proposed by McVay, Morishita and Remennikov. A modified breach with crater limit line and breach without crater limit line were put forward based on the experimental results. The maximum cross-sectional destruction area ratio(MCDAR) values were used to evaluate the damage degree. The maximum value of MCDAR reached 0.331 corresponding to the C5 experimental condition, of which explosion occurred above the web.
基金Projects Supported by the Science Foundation of the Chinese Academy of Sciences.
文摘This paper deals with finite deformation problems of cantilever beam with variable sec- tion under the action of arbitrary transverse loads.By the use of a method of variable replacement, the nonlinear differential equation with varied coefficient for the problem can be transformed into an equation with variable separable.The exact solution can be obtained by the integration method. Some examples are given in the paper,and the results of these examples show that this exact solution includes the existing solutions in references as special cases.
文摘In this paper, the step reduction method is discussed, which was advanced by Prof. Yeh Kai-yuan for calculating a non-uniform beam with various sections. The following result is proved. The approximate solution by this method approaches the true solution if the number of the steps approaches the infinity. However, the measure of the error between the limit solution and the ture solution is not in the pure mathematics sense but in the mechanics sense.
文摘In most framed structures anticipated deformations in accordance with current codes fall into acceptable limit states, whereas they go through substantial residual deformations in the aftermath of severe ground motions. These structures seem unsafe to occupants since static imminent instability in the immediate post-earthquake may be occurred. Moreover, rehabilitation costs of extensive residual deformations are not usually reasonable. Apparently, there is a lack of detailed knowledge related to reducing residual drift techniques when code-based seismic design is considered. In this paper, reduced beam section connections as a positive approach are taken action to mitigate the huge amount of residual drifts which are greatly amplified by P-Δ effects. To demonstrate the efficacy of RBS, a sixteen-story moment resisting frame is analyzed based on a suite of 8 single-component near field records which have been scaled according to the code provisions. The results are then processed to assess the effects of RBS detailing on drift profile, maximum drift, and residual drift. Besides, a special emphasis is given to estimate overall trend towards drift accumulation in each story in the presence of RBS assembly. A main conclusion is that using this connection predominantly alleviates the adverse effects of P-Δ on amplifying residual drifts.
文摘A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule （GDQR） method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.
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.
文摘This study covers optimization of I-sectional flange beams. Scope of this study is limited to medium weight flange beams of Table 1 of IS 808:1983 but it can be further extended for the other sections of this code. Best possible geometric shape of the cross-section is found for maximum performance of the beam with minimum material consumption. All possible loading conditions are considered in the study for which a beam in flexure undergoes in its life. ANSYS software program is used for the analysis and optimizing the sections. It is found that sections MB 125, MB 300 and MB 400 of Table 1 of IS 808 are not the optimum sections but other alternative of these cross-sections is available which within the same material consumption performs better than these sections of IS code.
