Rock thin section description is an essential method for examining lithology,structure,diagenesis,and sedimentary environment,playing a pivotal role in fields such as geology,geophysics,and petroleum exploration.To ov...Rock thin section description is an essential method for examining lithology,structure,diagenesis,and sedimentary environment,playing a pivotal role in fields such as geology,geophysics,and petroleum exploration.To overcome the challenges of subjectivity,low efficiency,and high expertise requirements in describing rock thin sections,we design a multimodal mapping network,ThinGPT,which aligns the feature spaces of the contrastive language-image pre-training(CLIP)and Generative Pre-trained(GPT-2)through network training.Given the high frequency of keywords and the structured sentence patterns in thin-section descriptions,we introduce a tokenization method tailored for rock thin sections.This approach enhances GPT-2's ability to effectively encode text and produce text feature vectors.We conducted comparative experiments using ThinGPT and other models on common sedimentary rocks.The results demonstrate that ThinGPT exhibits excellent potential in generating thin-section feature descriptions of rocks.Based on the geological expert evaluation criteria proposed in this study,ThinGPT achieved a score of 1.62 on the test set.For model complexity,ThinGPT avoids heavy initial training of large language models(LLMs).This training strategy makes the model lighter and improves the efficiency of rock thin section descriptions.As an innovative application of a LLMs within a lightweight architecture for rock thin section description,ThinGPT has significant implications for intelligent geology,geophysics,and petroleum exploration.展开更多
Maria sites are important historical sites, backing to the Byzantine period. The sites suffer from weathering noted as honeycomb, exfoliation and discoloration with white salt efflorescence at some parts. These are di...Maria sites are important historical sites, backing to the Byzantine period. The sites suffer from weathering noted as honeycomb, exfoliation and discoloration with white salt efflorescence at some parts. These are diagnostic features for salt weathering as confirmed by the laboratory investigations using thin section analysis. The salt is found to be from three sources, namely, water spray, chemical alteration of the mortar＇s carbonate content into sulfate salts by acid rain, and wet deposition of air pollutants on the surface of the stones ruins. The cracks noted in the structures of this archeological building are the results of landslides in this area. Knowledge of the archeological sites material examined can be greatly enhanced by understanding the process in their formation of degradation. This paper aims to describe the use of thin sections/micromorphology in the archeological sites. Analysis data of physical sitting, geology, geomorphology, and climate have been done to determine the main nature of hazards in this sites. Dynamic processing problems are existing along Alexandria coast including beach erosion, pollution and manmade. Thin section analysis is used to determine the factor in increasing the hazard level.展开更多
The sambong (Blumea balsamifera (L.) DC.) leaf was investigated by applying frozen section and thin section technology, and observed through optical microscope. The results showed that the sambong leaf was firstly ori...The sambong (Blumea balsamifera (L.) DC.) leaf was investigated by applying frozen section and thin section technology, and observed through optical microscope. The results showed that the sambong leaf was firstly originated nearby the apical bud at the stem tip. The first leaf grows fast, that the mitosis happens frequently and the cytoplasm manufacture rapidly. The cells in the first few leaves have not yet differentiated into the spongy parenchyma and palisade parenchyma. In the mature leaf, the spongy parenchyma and palisade parenchyma were fully developed. The epidermal hairs were firstly developed on the abaxial side of the first leaf.展开更多
Convolutional neural networks have been widely used for analyzing image data in industry,especially in the oil and gas area.Brazil has an extensive hydrocarbon reserve on its coast and has also benefited from these ne...Convolutional neural networks have been widely used for analyzing image data in industry,especially in the oil and gas area.Brazil has an extensive hydrocarbon reserve on its coast and has also benefited from these neural network models.Image data from petrographic thin section can be essential to provide information about reservoir quality,highlighting important features such as carbonate lithology.However,the automatic identification of lithology in reservoir rocks is still a significant challenge,mainly due to the heterogeneity that is part of the lithologies of the Brazilian pre-salt.Within this context,this work presents an approach using one-class or specialist models to identify four classes of lithology present in reservoir rocks in the Brazilian pre-salt.The proposed methodology had the challenge of dealing with a small number of images for training the neural networks,in addition to the complexity involved in the analyzed data.An auto-machine learning tool called AutoKeras was used to define the hyperparameters of the implemented models.The results found were satisfactory and presented an accuracy greater than 70%for image samples belonging to other wells not seen during the model building,which increases the applicability of the implemented model.Finally,a comparison was made between the proposed methodology and multiple-class models,demonstrating the superiority of one-class models.展开更多
The effect of frictions between dies and tube on the cross section quality of thin-walled tube numerical controlled(NC) bending was studied by numerical simulation method, combined with theoretical analysis and experi...The effect of frictions between dies and tube on the cross section quality of thin-walled tube numerical controlled(NC) bending was studied by numerical simulation method, combined with theoretical analysis and experiment. The results show that the frictions between mandrel, wiper, pressure die, bending die and tube have a significant and complicate effect on the section quality of thin-walled tube NC bending. To improve the section quality, frictions between mandrel, wiper and tube should be decreased, but the frictions between the pressure die, bending die and tube increase. The effect on the section distortion is more significant from mandrel, wiper, pressure die to bending die and the effect on the wall thinning more significant from mandrel, pressure die, wiper, to bending die. The effects of frictions between all dies and tube on wall thinning are smaller than their effects on section distortion. Mandrel and wiper should be lubricated well and drawing oil is used to lubricate them in actual production. The frictions between pressure die, bending die and tube should be increased and the dry friction is used between pressure die, bending die and tube in actual production.展开更多
A novel forming method of nickel based super-alloy thin-walled part with variable diameter sections was proposed by using inner and outer pressure with the visco-elasto-plastic pressure-carrying medium at room tempera...A novel forming method of nickel based super-alloy thin-walled part with variable diameter sections was proposed by using inner and outer pressure with the visco-elasto-plastic pressure-carrying medium at room temperature,and the principle of the method was provided.Experiments and FE simulations were carried out to analyze the deformation characteristics for the part with larger variable diameter ratio(35%).The results show that visco-elasto-plastic pressure-carrying medium can meet the requirements of the room-temperature deformation condition for nickel based super-alloy sheet.The inner and outer pressure forming with the visco-elasto-plastic pressure-carrying medium can meet the requirements of dimensional accuracy for the thin-walled part with variable diameter sections.The thinning of wall-thickness is less than 4%.This method provides a new approach for near-net shape forming of nickel based super-alloy thin-walled parts with variable diameter sections.展开更多
This paper is to review the theory of thin-walled beam structures of the open cross-section. There is scant information on the performance of structures made from thin-walled beam elements, particularly those of open ...This paper is to review the theory of thin-walled beam structures of the open cross-section. There is scant information on the performance of structures made from thin-walled beam elements, particularly those of open sections, where the behavior is considerably complicated by the coupling of tensile, bending and torsional loading modes. In the combined loading theory of thin-walled structures, it is useful to mention that for a thin-walled beam, the value of direct stress at a point on the cross-section depends on its position, the geometrical properties of the cross-section and the applied loading. This applies whether the thin-walled section is closed or open but this study will be directed primarily at the latter. Theoretical analyses of structures are fairly well established, considered in multi-various applications by many scientists. However, due to the present interest in lightweight structures, it is necessary to specify where the present theory lies. It does not, for example, deal with compression and the consequent failure modes under global and local buckling. Indeed, with the inclusion of strut buckling failure and any other unforeseen collapse modes, the need was perceived for further research into the subject. Presently, a survey of the published works has shown in the following: 1) The assumptions used in deriving the underlying theory of thin-walled beams are not clearly stated or easily understood;2) The transformations of a load system from arbitrary axis to those at the relevant centre of rotation are incomplete. Thus, an incorrect stress distribution may result in;3) Several methods are found in the recent literature for analyzing the behaviour of thin-walled open section beams under combined loading. These reveal the need appears for further study upon their torsion/flexural behaviour when referred to any arbitrary axis, a common case found in practice. This review covers the following areas: 1) Refinement to existing theory to clarify those observations made in 1 - 3 above;2) Derivation of a general elastic stiffness matrix for combined loading;3) Calculation of the stress distribution on the cross-section of a thin-walled beam. A general transformation matrix that accounts for a load system applied at an arbitrary point on the cross-section will be published in a future paper.展开更多
Free torsion of thin-walled structures of open- and closed-sections is a classical elastic mechanics problem, which, in literature, is often solved by the method of membrane analogy. The method of membrane analogy, ho...Free torsion of thin-walled structures of open- and closed-sections is a classical elastic mechanics problem, which, in literature, is often solved by the method of membrane analogy. The method of membrane analogy, however, can be only applied to structures of a single material. If the structure consists of both open- and closed-sections, the method of membrane analogy is difficult to be applied. In this paper, a new method is presented for solving the free torsion of thin-walled structures of open- and/or closed- sections with multiple materials. By utilizing a simple statically indeterminate concept, torsional equations are derived based on the equilibrium and compatibility conditions. The method presented here not only is very simple and easy to understand but also can be applied to thin-walled structures of combined open- and closed-sections with multiple materials.展开更多
Cross-section deformation is one of important factors affecting the quality of tube formation, and the tube＇s capability of transporting liquid and gas will be reduced because of the cross-section ellipse deformation...Cross-section deformation is one of important factors affecting the quality of tube formation, and the tube＇s capability of transporting liquid and gas will be reduced because of the cross-section ellipse deformation due to the effect of shear load in plastic bending process. When the tube is bent, the extrados-wall bears the tension stress and the intrados-wall bears the compression stress, synchronously the cross-section is affected by the circumferential stress. According to the above, the distribution function and curve of tangential stress can be obtained according to force balance differential equations on circumferential direction and Trasca rule. Subsequently the real state and virtual state moment equations were established, a new method was presented adopting the virtual principle of deformation system to calculate the x-axis and y-axis displacement of arbitrary point on cross-section. So the major and minor axes of deformed cross-section can be calculated according to the displacements of each point, and the variety value of major and minor axes will be obtained further. Finally the theoretical calculating result is compared with NC tube rotary-bending experiment results to verify the rationality of theoretical analysis, and the cross-section deformation rule of thin-walled tube can be received.展开更多
The effect of mandrel with the structure of ball and socket on the cross section quality of thin-walled tube numerical controlled(NC) bending was studied by numerical simulation method, combined with theoretical (anal...The effect of mandrel with the structure of ball and socket on the cross section quality of thin-walled tube numerical controlled(NC) bending was studied by numerical simulation method, combined with theoretical (analysis) and experiment. Influencing factors of the mandrel include the count of mandrel heads, the diameter of mandrel and its position. According to the principle of NC tube bending, quality defects possibly produced in thin-walled tube NC bending process were analyzed and two parameters were proposed in order to describe the cross section quality of thin-walled tube NC bending. According to the geometrical dimension of tube and dies, the range of mandrel protrusion was derived. The finite element model of thin-walled tube NC bending was established based on the DYNAFORM platform, and key technological problems were solved. The model was verified by experiment. The effect of the number of mandrel heads, the diameter of mandrel and the protrusion length of mandrel on the cross section quality of thin-walled tube NC bending was revealed and how to choose mandrel parameters was presented.展开更多
For a thin-walled box column with variable cross-section, the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients, so ...For a thin-walled box column with variable cross-section, the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients, so it is very difficult to solve them by means of an analytic method. In this paper, polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differential equations. Based on the energy principle and the Galerkin's method, the approximate formulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively, and numerical examples are used to verify the correctness of the solutions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box columns with variable cross-section. This paper is of practical value.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
基金supported by a grant from the National Natural Science Foundation of China(Grant No.42174156).
文摘Rock thin section description is an essential method for examining lithology,structure,diagenesis,and sedimentary environment,playing a pivotal role in fields such as geology,geophysics,and petroleum exploration.To overcome the challenges of subjectivity,low efficiency,and high expertise requirements in describing rock thin sections,we design a multimodal mapping network,ThinGPT,which aligns the feature spaces of the contrastive language-image pre-training(CLIP)and Generative Pre-trained(GPT-2)through network training.Given the high frequency of keywords and the structured sentence patterns in thin-section descriptions,we introduce a tokenization method tailored for rock thin sections.This approach enhances GPT-2's ability to effectively encode text and produce text feature vectors.We conducted comparative experiments using ThinGPT and other models on common sedimentary rocks.The results demonstrate that ThinGPT exhibits excellent potential in generating thin-section feature descriptions of rocks.Based on the geological expert evaluation criteria proposed in this study,ThinGPT achieved a score of 1.62 on the test set.For model complexity,ThinGPT avoids heavy initial training of large language models(LLMs).This training strategy makes the model lighter and improves the efficiency of rock thin section descriptions.As an innovative application of a LLMs within a lightweight architecture for rock thin section description,ThinGPT has significant implications for intelligent geology,geophysics,and petroleum exploration.
文摘Maria sites are important historical sites, backing to the Byzantine period. The sites suffer from weathering noted as honeycomb, exfoliation and discoloration with white salt efflorescence at some parts. These are diagnostic features for salt weathering as confirmed by the laboratory investigations using thin section analysis. The salt is found to be from three sources, namely, water spray, chemical alteration of the mortar＇s carbonate content into sulfate salts by acid rain, and wet deposition of air pollutants on the surface of the stones ruins. The cracks noted in the structures of this archeological building are the results of landslides in this area. Knowledge of the archeological sites material examined can be greatly enhanced by understanding the process in their formation of degradation. This paper aims to describe the use of thin sections/micromorphology in the archeological sites. Analysis data of physical sitting, geology, geomorphology, and climate have been done to determine the main nature of hazards in this sites. Dynamic processing problems are existing along Alexandria coast including beach erosion, pollution and manmade. Thin section analysis is used to determine the factor in increasing the hazard level.
文摘The sambong (Blumea balsamifera (L.) DC.) leaf was investigated by applying frozen section and thin section technology, and observed through optical microscope. The results showed that the sambong leaf was firstly originated nearby the apical bud at the stem tip. The first leaf grows fast, that the mitosis happens frequently and the cytoplasm manufacture rapidly. The cells in the first few leaves have not yet differentiated into the spongy parenchyma and palisade parenchyma. In the mature leaf, the spongy parenchyma and palisade parenchyma were fully developed. The epidermal hairs were firstly developed on the abaxial side of the first leaf.
基金supported by the R&D cooperation agreement be-tween Petrobras and CBPF(Contract No.0050.0121790.22.9)Brazilian Research Council(CNPq)for the scholarships for students.
文摘Convolutional neural networks have been widely used for analyzing image data in industry,especially in the oil and gas area.Brazil has an extensive hydrocarbon reserve on its coast and has also benefited from these neural network models.Image data from petrographic thin section can be essential to provide information about reservoir quality,highlighting important features such as carbonate lithology.However,the automatic identification of lithology in reservoir rocks is still a significant challenge,mainly due to the heterogeneity that is part of the lithologies of the Brazilian pre-salt.Within this context,this work presents an approach using one-class or specialist models to identify four classes of lithology present in reservoir rocks in the Brazilian pre-salt.The proposed methodology had the challenge of dealing with a small number of images for training the neural networks,in addition to the complexity involved in the analyzed data.An auto-machine learning tool called AutoKeras was used to define the hyperparameters of the implemented models.The results found were satisfactory and presented an accuracy greater than 70%for image samples belonging to other wells not seen during the model building,which increases the applicability of the implemented model.Finally,a comparison was made between the proposed methodology and multiple-class models,demonstrating the superiority of one-class models.
基金Project(50225518) supported by the National Science Foundation of China for Distinguished Young Scholars Projects(50175092+4 种基金 59975076) supported by the National Natural Science Foundation of China Project supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, China Project(04H53057) supported by the Aeronautical Science Foundation of China Project(20020699002) supported by the Specialized Research Fund for the Doctoral Program of Higher Education, China Project(Z200518) supported by the Graduate Starting Seed Fund of Northwestern Polytechnical University, China
文摘The effect of frictions between dies and tube on the cross section quality of thin-walled tube numerical controlled(NC) bending was studied by numerical simulation method, combined with theoretical analysis and experiment. The results show that the frictions between mandrel, wiper, pressure die, bending die and tube have a significant and complicate effect on the section quality of thin-walled tube NC bending. To improve the section quality, frictions between mandrel, wiper and tube should be decreased, but the frictions between the pressure die, bending die and tube increase. The effect on the section distortion is more significant from mandrel, wiper, pressure die to bending die and the effect on the wall thinning more significant from mandrel, pressure die, wiper, to bending die. The effects of frictions between all dies and tube on wall thinning are smaller than their effects on section distortion. Mandrel and wiper should be lubricated well and drawing oil is used to lubricate them in actual production. The frictions between pressure die, bending die and tube should be increased and the dry friction is used between pressure die, bending die and tube in actual production.
文摘A novel forming method of nickel based super-alloy thin-walled part with variable diameter sections was proposed by using inner and outer pressure with the visco-elasto-plastic pressure-carrying medium at room temperature,and the principle of the method was provided.Experiments and FE simulations were carried out to analyze the deformation characteristics for the part with larger variable diameter ratio(35%).The results show that visco-elasto-plastic pressure-carrying medium can meet the requirements of the room-temperature deformation condition for nickel based super-alloy sheet.The inner and outer pressure forming with the visco-elasto-plastic pressure-carrying medium can meet the requirements of dimensional accuracy for the thin-walled part with variable diameter sections.The thinning of wall-thickness is less than 4%.This method provides a new approach for near-net shape forming of nickel based super-alloy thin-walled parts with variable diameter sections.
文摘This paper is to review the theory of thin-walled beam structures of the open cross-section. There is scant information on the performance of structures made from thin-walled beam elements, particularly those of open sections, where the behavior is considerably complicated by the coupling of tensile, bending and torsional loading modes. In the combined loading theory of thin-walled structures, it is useful to mention that for a thin-walled beam, the value of direct stress at a point on the cross-section depends on its position, the geometrical properties of the cross-section and the applied loading. This applies whether the thin-walled section is closed or open but this study will be directed primarily at the latter. Theoretical analyses of structures are fairly well established, considered in multi-various applications by many scientists. However, due to the present interest in lightweight structures, it is necessary to specify where the present theory lies. It does not, for example, deal with compression and the consequent failure modes under global and local buckling. Indeed, with the inclusion of strut buckling failure and any other unforeseen collapse modes, the need was perceived for further research into the subject. Presently, a survey of the published works has shown in the following: 1) The assumptions used in deriving the underlying theory of thin-walled beams are not clearly stated or easily understood;2) The transformations of a load system from arbitrary axis to those at the relevant centre of rotation are incomplete. Thus, an incorrect stress distribution may result in;3) Several methods are found in the recent literature for analyzing the behaviour of thin-walled open section beams under combined loading. These reveal the need appears for further study upon their torsion/flexural behaviour when referred to any arbitrary axis, a common case found in practice. This review covers the following areas: 1) Refinement to existing theory to clarify those observations made in 1 - 3 above;2) Derivation of a general elastic stiffness matrix for combined loading;3) Calculation of the stress distribution on the cross-section of a thin-walled beam. A general transformation matrix that accounts for a load system applied at an arbitrary point on the cross-section will be published in a future paper.
文摘Free torsion of thin-walled structures of open- and closed-sections is a classical elastic mechanics problem, which, in literature, is often solved by the method of membrane analogy. The method of membrane analogy, however, can be only applied to structures of a single material. If the structure consists of both open- and closed-sections, the method of membrane analogy is difficult to be applied. In this paper, a new method is presented for solving the free torsion of thin-walled structures of open- and/or closed- sections with multiple materials. By utilizing a simple statically indeterminate concept, torsional equations are derived based on the equilibrium and compatibility conditions. The method presented here not only is very simple and easy to understand but also can be applied to thin-walled structures of combined open- and closed-sections with multiple materials.
基金supported by "Eleven Five Years Plan" Basic Research Item of National Defense of China (Grant No. B2220060048)
文摘Cross-section deformation is one of important factors affecting the quality of tube formation, and the tube＇s capability of transporting liquid and gas will be reduced because of the cross-section ellipse deformation due to the effect of shear load in plastic bending process. When the tube is bent, the extrados-wall bears the tension stress and the intrados-wall bears the compression stress, synchronously the cross-section is affected by the circumferential stress. According to the above, the distribution function and curve of tangential stress can be obtained according to force balance differential equations on circumferential direction and Trasca rule. Subsequently the real state and virtual state moment equations were established, a new method was presented adopting the virtual principle of deformation system to calculate the x-axis and y-axis displacement of arbitrary point on cross-section. So the major and minor axes of deformed cross-section can be calculated according to the displacements of each point, and the variety value of major and minor axes will be obtained further. Finally the theoretical calculating result is compared with NC tube rotary-bending experiment results to verify the rationality of theoretical analysis, and the cross-section deformation rule of thin-walled tube can be received.
文摘The effect of mandrel with the structure of ball and socket on the cross section quality of thin-walled tube numerical controlled(NC) bending was studied by numerical simulation method, combined with theoretical (analysis) and experiment. Influencing factors of the mandrel include the count of mandrel heads, the diameter of mandrel and its position. According to the principle of NC tube bending, quality defects possibly produced in thin-walled tube NC bending process were analyzed and two parameters were proposed in order to describe the cross section quality of thin-walled tube NC bending. According to the geometrical dimension of tube and dies, the range of mandrel protrusion was derived. The finite element model of thin-walled tube NC bending was established based on the DYNAFORM platform, and key technological problems were solved. The model was verified by experiment. The effect of the number of mandrel heads, the diameter of mandrel and the protrusion length of mandrel on the cross section quality of thin-walled tube NC bending was revealed and how to choose mandrel parameters was presented.
文摘For a thin-walled box column with variable cross-section, the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients, so it is very difficult to solve them by means of an analytic method. In this paper, polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differential equations. Based on the energy principle and the Galerkin's method, the approximate formulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively, and numerical examples are used to verify the correctness of the solutions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box columns with variable cross-section. This paper is of practical value.
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.
