Abstract This paper presents a numerical study of heat transfer through a downstream annulus using water as the working fluid within the laminar flow region. The annulus consisted of an outer twisted square duct and an inner circular pipe. A three-dimensional formulation was used to solve the Navier-Stokes equations numerically for the laminar flow system with a low Reynolds number. Three parameters were used in the numerical simulation: the length of the twisted square (a: 6.6, 8.2 10.2, 12.6 mm) the inner diameter of the inner circular pipe (d: 19, 21, 23 and 25 mm); and the twist angle (θ: 0° (smooth), 45°, 60°, and 90°). Numerical calculations were conducted on sixteen twisted square duct heat exchangers, with water flowing within a Reynolds number range of 220 – 1100. The results were illustrated as a profile of the thermal enhancement factor, the friction factor and the Nusselt number. The results show that the twisted outer duct of the heat exchanger can create a swirl flow along the length of the heat exchanger. It also caused a boundary layer separation-reattachment on the wall of the inner pipe. Moreover, an increase in the twist angle increased the Nusselt number by 20 %, and the friction factor was also increased as the annular gap of the heat exchanger decreased.
{"title":"Numerical Study on Thermal Performance of Water Flow in a Twisted Duct Heat Exchanger","authors":"Musaab K. Rashed, K. Jehhef, F. A. Badawy","doi":"10.2478/ijame-2022-0028","DOIUrl":"https://doi.org/10.2478/ijame-2022-0028","url":null,"abstract":"Abstract This paper presents a numerical study of heat transfer through a downstream annulus using water as the working fluid within the laminar flow region. The annulus consisted of an outer twisted square duct and an inner circular pipe. A three-dimensional formulation was used to solve the Navier-Stokes equations numerically for the laminar flow system with a low Reynolds number. Three parameters were used in the numerical simulation: the length of the twisted square (a: 6.6, 8.2 10.2, 12.6 mm) the inner diameter of the inner circular pipe (d: 19, 21, 23 and 25 mm); and the twist angle (θ: 0° (smooth), 45°, 60°, and 90°). Numerical calculations were conducted on sixteen twisted square duct heat exchangers, with water flowing within a Reynolds number range of 220 – 1100. The results were illustrated as a profile of the thermal enhancement factor, the friction factor and the Nusselt number. The results show that the twisted outer duct of the heat exchanger can create a swirl flow along the length of the heat exchanger. It also caused a boundary layer separation-reattachment on the wall of the inner pipe. Moreover, an increase in the twist angle increased the Nusselt number by 20 %, and the friction factor was also increased as the annular gap of the heat exchanger decreased.","PeriodicalId":37871,"journal":{"name":"International Journal of Applied Mechanics and Engineering","volume":"56 1","pages":"199 - 216"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77174567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
B. Kholboev, D. P. Navruzov, D.S. Asrakulova, N.R. Engalicheva, A.A. Turemuratova
Abstract In this work, a numerical study of a sharply expanding highly swirling flow is carried out using v2-f models based on the Comsol Multiphysics 5.6 software package and a two-fluid turbulence model. The results obtained are compared with known experimental data with different pipe diameters. The purpose of this work is to test the ability of models to describe anisotropic turbulence. It is shown that the two-fluid model is more suitable for studying such flows.
{"title":"Comparison of the Results for Calculation of Vortex Currents After Sudden Expansion of the Pipe with Different Diameters","authors":"B. Kholboev, D. P. Navruzov, D.S. Asrakulova, N.R. Engalicheva, A.A. Turemuratova","doi":"10.2478/ijame-2022-0023","DOIUrl":"https://doi.org/10.2478/ijame-2022-0023","url":null,"abstract":"Abstract In this work, a numerical study of a sharply expanding highly swirling flow is carried out using v2-f models based on the Comsol Multiphysics 5.6 software package and a two-fluid turbulence model. The results obtained are compared with known experimental data with different pipe diameters. The purpose of this work is to test the ability of models to describe anisotropic turbulence. It is shown that the two-fluid model is more suitable for studying such flows.","PeriodicalId":37871,"journal":{"name":"International Journal of Applied Mechanics and Engineering","volume":"30 1","pages":"115 - 123"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83863233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
F. Khrouf, H. Tebassi, M. Yallese, K. Chaoui, A. Haddad
Abstract An experimental investigation is carried out to examine the effects of various cutting parameters on the response criteria when turning EN-AW-1350 aluminum alloy under dry cutting conditions. The experiments related to the analysis of the influence of turning parameters on the surface roughness (Ra) and material removal rate (MRR) were carried out according to the Taguchi L27 orthogonal array (313) approach. The analysis of variance (ANOVA) was applied to characterizing the main elements affecting response parameters. Finally, the desirability function (DP) was applied for a bi-objective optimization of the machining parameters with the objective of achieving a better surface finish (Ra) and a higher productivity (MRR). The results showed that the cutting speed is the most dominant factor affecting Ra followed by the feed rate and the depth of cut. Moreover, the Artificial Neural Network (ANN) approach is found to be more reliable and accurate than its Response Surface methodology (RSM) counterpart in terms of predicting and detecting the non-linearity of the surface roughness and material removal rate mathematical models. ANN provided prediction models with a precision benefit of 8.21% more than those determined by RSM. The latter is easier to use, and provides more information than ANN in terms of the impacts and contributions of the model terms.
{"title":"Modeling and Optimization of Cutting Parameters When Turning EN-AW-1350 Aluminum Alloy","authors":"F. Khrouf, H. Tebassi, M. Yallese, K. Chaoui, A. Haddad","doi":"10.2478/ijame-2022-0024","DOIUrl":"https://doi.org/10.2478/ijame-2022-0024","url":null,"abstract":"Abstract An experimental investigation is carried out to examine the effects of various cutting parameters on the response criteria when turning EN-AW-1350 aluminum alloy under dry cutting conditions. The experiments related to the analysis of the influence of turning parameters on the surface roughness (Ra) and material removal rate (MRR) were carried out according to the Taguchi L27 orthogonal array (313) approach. The analysis of variance (ANOVA) was applied to characterizing the main elements affecting response parameters. Finally, the desirability function (DP) was applied for a bi-objective optimization of the machining parameters with the objective of achieving a better surface finish (Ra) and a higher productivity (MRR). The results showed that the cutting speed is the most dominant factor affecting Ra followed by the feed rate and the depth of cut. Moreover, the Artificial Neural Network (ANN) approach is found to be more reliable and accurate than its Response Surface methodology (RSM) counterpart in terms of predicting and detecting the non-linearity of the surface roughness and material removal rate mathematical models. ANN provided prediction models with a precision benefit of 8.21% more than those determined by RSM. The latter is easier to use, and provides more information than ANN in terms of the impacts and contributions of the model terms.","PeriodicalId":37871,"journal":{"name":"International Journal of Applied Mechanics and Engineering","volume":"11 1","pages":"124 - 142"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78803460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we focus on the effect of the inner diameter and Reynolds number on the recirculation zone in an annular jet flow with numerical simulation by resolving the Reynolds-averaged Navier-Stokes equations with the first closed model of turbulence k-epsilon. The annular jet plays an essential role in stabilizing the flame in the burner which is used in many industrial applications. The annular jet is characterized by the inner and outer diameter. In this study, three different inner diameters are adopted with constant width of the annular jet. We adopted also three different values of the Reynolds number show the effect of the Reynolds number on the recirculation zone. The simulation is realized by a CFD code which uses the finite element method. The results obtained from this study are in good agreement with the experimental data. Two recirculation zones are shown; a large recirculation zone at the outlet of the flow and a small recirculation zone just near the injection generated by the annular flow and the inner diameter Di; it is observed that the size of the recirculation zone increases when the inner diameter increases and the length of the recirculation zone depends only on the inner diameter. This recirculation zone is also affected by the Reynolds number with a very low variation of the recirculation length.
{"title":"Effect of the Inner Diameter and Reynolds Number on the Recirculation Zone in Annular Jet Flow","authors":"M. Habib, Sahnoun Rachid, Drai Ismail","doi":"10.2478/ijame-2022-0021","DOIUrl":"https://doi.org/10.2478/ijame-2022-0021","url":null,"abstract":"Abstract In this paper, we focus on the effect of the inner diameter and Reynolds number on the recirculation zone in an annular jet flow with numerical simulation by resolving the Reynolds-averaged Navier-Stokes equations with the first closed model of turbulence k-epsilon. The annular jet plays an essential role in stabilizing the flame in the burner which is used in many industrial applications. The annular jet is characterized by the inner and outer diameter. In this study, three different inner diameters are adopted with constant width of the annular jet. We adopted also three different values of the Reynolds number show the effect of the Reynolds number on the recirculation zone. The simulation is realized by a CFD code which uses the finite element method. The results obtained from this study are in good agreement with the experimental data. Two recirculation zones are shown; a large recirculation zone at the outlet of the flow and a small recirculation zone just near the injection generated by the annular flow and the inner diameter Di; it is observed that the size of the recirculation zone increases when the inner diameter increases and the length of the recirculation zone depends only on the inner diameter. This recirculation zone is also affected by the Reynolds number with a very low variation of the recirculation length.","PeriodicalId":37871,"journal":{"name":"International Journal of Applied Mechanics and Engineering","volume":"109 1","pages":"87 - 97"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79201098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Nowadays, there is still a need for the development of a high-precision vibration measurement system for aircraft wings. By analyzing the wing vibration characteristics a lot of aviation studies could be conducted, including the wing health monitoring, the fluttering phenomenon and so on. This paper presents preliminary results of the research carried out toward building a promising system designed to measure vibration parameters of aircraft wing. Comparing it with the existing analogue systems, the proposed system features the use of approaches that are traditional for solving orientation and navigation problems for vibration measurements. The paper presents the basic structure of the system, the fundamentals of its operation, the mathematical errors models of its main components, the correction algorithms using optimal Kalman filter. Finally, the initial simulation results of system operation are shown, demonstrating the expected accuracy characteristics of the system, which confirms its effectiveness and the prospects of the chosen direction of research.
{"title":"Promising Wing Vibration Measurement System Using MEMS IMUS and Kalman Filter Correction","authors":"M. S. Maamo, A. Afonin, A. S. Sulakov","doi":"10.2478/ijame-2022-0025","DOIUrl":"https://doi.org/10.2478/ijame-2022-0025","url":null,"abstract":"Abstract Nowadays, there is still a need for the development of a high-precision vibration measurement system for aircraft wings. By analyzing the wing vibration characteristics a lot of aviation studies could be conducted, including the wing health monitoring, the fluttering phenomenon and so on. This paper presents preliminary results of the research carried out toward building a promising system designed to measure vibration parameters of aircraft wing. Comparing it with the existing analogue systems, the proposed system features the use of approaches that are traditional for solving orientation and navigation problems for vibration measurements. The paper presents the basic structure of the system, the fundamentals of its operation, the mathematical errors models of its main components, the correction algorithms using optimal Kalman filter. Finally, the initial simulation results of system operation are shown, demonstrating the expected accuracy characteristics of the system, which confirms its effectiveness and the prospects of the chosen direction of research.","PeriodicalId":37871,"journal":{"name":"International Journal of Applied Mechanics and Engineering","volume":"44 1","pages":"143 - 157"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75318265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This work addresses to joining aluminum alloy AA6061 to carbon steel AISI 1006 sheets using the friction spot joining technique. The steel sheets were pre-holed and threaded with an internal M6 thread. The joining process was carried out by extruding the aluminum through the steel hole and thread using a rotating tool with friction between the tool and aluminum. Three process parameters were used: pre-heating time, rotating speed and plunging depth of the tool, with four levels for each parameter. The results indicated that the two materials joined by a micro-scale mechanical interlock at an interface line of a width ranged between 0.7 to ~ 2.5 mm. The joint’s shear force reached a minimum and maximum value of 2000 and 2500 N, respectively. The plunging depth was the most effective factor affecting the amount of the extruded aluminum and the joint’s shear force.
{"title":"Friction Spot Lap Joining of Aluminum Alloy AA6061 to Pre-Holed and Threaded Carbon Steel AISI 1006","authors":"H. K. Ibrahim, S. K. Hussein, K. J. Jadee","doi":"10.2478/ijame-2022-0005","DOIUrl":"https://doi.org/10.2478/ijame-2022-0005","url":null,"abstract":"Abstract This work addresses to joining aluminum alloy AA6061 to carbon steel AISI 1006 sheets using the friction spot joining technique. The steel sheets were pre-holed and threaded with an internal M6 thread. The joining process was carried out by extruding the aluminum through the steel hole and thread using a rotating tool with friction between the tool and aluminum. Three process parameters were used: pre-heating time, rotating speed and plunging depth of the tool, with four levels for each parameter. The results indicated that the two materials joined by a micro-scale mechanical interlock at an interface line of a width ranged between 0.7 to ~ 2.5 mm. The joint’s shear force reached a minimum and maximum value of 2000 and 2500 N, respectively. The plunging depth was the most effective factor affecting the amount of the extruded aluminum and the joint’s shear force.","PeriodicalId":37871,"journal":{"name":"International Journal of Applied Mechanics and Engineering","volume":"73 1","pages":"67 - 77"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86387003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Experimental regulating parameters of the non-stationary expansion of air inside a bladder-type hydraulic accumulator, working with the simple short pipeline, are presented in the paper. The technique of continuous online monitoring of changes in time of volume and absolute air pressure inside the hydraulic accumulator during the discharge process has been improved. Three series of experimental studies of transient gas processes inside the accumulator at different values of the average volume flow rate are made. Tendencies of change of the integral parameters of the hydraulic accumulator are obtained and analyzed depending on the serial number of the discharge cycle. A general dependence of dimensionless storage volume Kreg on the polytropic index n in series # 1–3, approximated by single power-law dependence, is obtained. The systematic changes of integral parameters in each subsequent discharge cycle can be explained by the non-stationary transient thermodynamic processes in air inside the accumulator until the thermodynamic equilibrium with the ambient air parameters is reached.
{"title":"Experimental Regulating Parameters of Bladder-Type Hydraulic Accumulator","authors":"V. Zhuk, Orest Verbovskyi, Ihor Popadiuk","doi":"10.2478/ijame-2022-0015","DOIUrl":"https://doi.org/10.2478/ijame-2022-0015","url":null,"abstract":"Abstract Experimental regulating parameters of the non-stationary expansion of air inside a bladder-type hydraulic accumulator, working with the simple short pipeline, are presented in the paper. The technique of continuous online monitoring of changes in time of volume and absolute air pressure inside the hydraulic accumulator during the discharge process has been improved. Three series of experimental studies of transient gas processes inside the accumulator at different values of the average volume flow rate are made. Tendencies of change of the integral parameters of the hydraulic accumulator are obtained and analyzed depending on the serial number of the discharge cycle. A general dependence of dimensionless storage volume Kreg on the polytropic index n in series # 1–3, approximated by single power-law dependence, is obtained. The systematic changes of integral parameters in each subsequent discharge cycle can be explained by the non-stationary transient thermodynamic processes in air inside the accumulator until the thermodynamic equilibrium with the ambient air parameters is reached.","PeriodicalId":37871,"journal":{"name":"International Journal of Applied Mechanics and Engineering","volume":"65 1","pages":"232 - 243"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83952245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This work presents the factors determining cast iron, and particularly austenitic high-alloy cast iron as a construction material, which is ranked among the leading casting alloys of iron with carbon, mainly due to its very good service properties, which makes it dedicated as a material for automotive castings, pipe and fitting castings and components resistant to elevated temperatures, corrosion and abrasive wear. Construction materials currently used in industry have increasingly better properties and their potential is depleting quickly. This forces the manufacturers to adjust the requirements and production capabilities of cast iron using the most modern technologies that give the expected beneficial economic and operating effects. The paper quotes the results of research in the field of the offered technologies that give special surface features to machine parts made of cast iron by modernising the parameters of the technological process of obtaining high-alloy austenitic cast iron, i.e., by applying coatings, as well as by appropriate surface treatment, the aim of which is and reinforce the material surface with those properties which are important in a given application.
{"title":"Key Determinants for High-Alloyed Cast Irons for Mechanical Engineering","authors":"H. Pacha-Gołębiowska, W. Piekarska","doi":"10.2478/ijame-2022-0010","DOIUrl":"https://doi.org/10.2478/ijame-2022-0010","url":null,"abstract":"Abstract This work presents the factors determining cast iron, and particularly austenitic high-alloy cast iron as a construction material, which is ranked among the leading casting alloys of iron with carbon, mainly due to its very good service properties, which makes it dedicated as a material for automotive castings, pipe and fitting castings and components resistant to elevated temperatures, corrosion and abrasive wear. Construction materials currently used in industry have increasingly better properties and their potential is depleting quickly. This forces the manufacturers to adjust the requirements and production capabilities of cast iron using the most modern technologies that give the expected beneficial economic and operating effects. The paper quotes the results of research in the field of the offered technologies that give special surface features to machine parts made of cast iron by modernising the parameters of the technological process of obtaining high-alloy austenitic cast iron, i.e., by applying coatings, as well as by appropriate surface treatment, the aim of which is and reinforce the material surface with those properties which are important in a given application.","PeriodicalId":37871,"journal":{"name":"International Journal of Applied Mechanics and Engineering","volume":"57 1","pages":"146 - 167"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83112613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A transient flow formation of an incompressible fluid through a horizontal porous channel assuming a ramped pressure gradient is considered with the velocity slip boundary conditions. The flow is a laminar flow caused by ramped pressure gradient along the flow direction. The equation governing the flow is modeled, and solved by the Laplace transformation technique to obtain a semi-analytical solution under slip boundary conditions. It was noted that the flow velocity increases as the slip parameter is increased.
{"title":"Transient Flow Through a Porous Channel with Ramped Pressure Gradient and Velocity Slip Boundary Condition","authors":"B. Jha, Zainab Sa’id Yunus","doi":"10.2478/ijame-2022-0006","DOIUrl":"https://doi.org/10.2478/ijame-2022-0006","url":null,"abstract":"Abstract A transient flow formation of an incompressible fluid through a horizontal porous channel assuming a ramped pressure gradient is considered with the velocity slip boundary conditions. The flow is a laminar flow caused by ramped pressure gradient along the flow direction. The equation governing the flow is modeled, and solved by the Laplace transformation technique to obtain a semi-analytical solution under slip boundary conditions. It was noted that the flow velocity increases as the slip parameter is increased.","PeriodicalId":37871,"journal":{"name":"International Journal of Applied Mechanics and Engineering","volume":"39 1","pages":"78 - 90"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89358534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This study presents an improvement of the graphical method for plotting the shear and moment diagrams for the structural members under linearly varying loads (triangular and trapezoidal loads). Based on the parabolic nature of the shear function, when the loading varies linearly, and on the relations among load, shear, and moment, a mathematical equation is developed to locate the zero-shear point, while a geometric technique is presented to calculate the parabolic shear area. Five comprehensive examples of beams loaded with linearly varying loads are selected to illustrate the steps of the solution for the proposed techniques. The results demonstrated the applicability of the presented method, and gave exact diagrams compared with the basic graphical method. It is concluded that the proposed improved method is generally more convenient, less time-consuming, and has less computational efforts because it does not require sectioning, solving equilibrium equations, and quadratic formulas compared with the basic graphical method.
{"title":"Improvement of the Graphical Method for Plotting the Shear and Moment Diagrams for Members Subjected to Linearly Varying Loads","authors":"M. A. Husain, Abdulkhaliq Salim Ali","doi":"10.2478/ijame-2022-0004","DOIUrl":"https://doi.org/10.2478/ijame-2022-0004","url":null,"abstract":"Abstract This study presents an improvement of the graphical method for plotting the shear and moment diagrams for the structural members under linearly varying loads (triangular and trapezoidal loads). Based on the parabolic nature of the shear function, when the loading varies linearly, and on the relations among load, shear, and moment, a mathematical equation is developed to locate the zero-shear point, while a geometric technique is presented to calculate the parabolic shear area. Five comprehensive examples of beams loaded with linearly varying loads are selected to illustrate the steps of the solution for the proposed techniques. The results demonstrated the applicability of the presented method, and gave exact diagrams compared with the basic graphical method. It is concluded that the proposed improved method is generally more convenient, less time-consuming, and has less computational efforts because it does not require sectioning, solving equilibrium equations, and quadratic formulas compared with the basic graphical method.","PeriodicalId":37871,"journal":{"name":"International Journal of Applied Mechanics and Engineering","volume":"49 1","pages":"46 - 66"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85255498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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