This document discusses the structural idealization of aircraft wings for stress analysis purposes. It begins by describing the various structural components of a wing, including spars, ribs, skins, and stringers. It then explains that real wing structures are complex, so they must be simplified for analysis by idealizing them as direct stress-carrying booms and shear stress-carrying panels. The document provides examples of constructing idealized wing box sections and calculating the areas of stress-carrying booms based on equilibrium of bending stresses. It also discusses modeling idealized wing structures in a global finite element model using bar and shell elements.
This document discusses the structural idealization of aircraft wings for stress analysis purposes. It begins by providing an overview of aircraft wing structure components like spars, ribs, skins and stringers. It then discusses simplifying the complex wing structure into an idealized beam model by concentrating the stress carrying portions into "booms". This idealization assumes booms carry direct stresses and skins carry only shear stresses. The document provides an example of calculating boom areas based on equilibrium of bending stresses. It also discusses calculating the second moment of area of the idealized section. The next lecture will cover impacts of this idealization on bending, shear and torsion analysis of the wing.
IRJET- Static and Fracture Analysis for Aircraft Fuselage and Wing Joint with...IRJET Journal
This document discusses static and fracture analysis of aircraft fuselage and wing joints using composite materials. Finite element analysis software ANSYS and a post-processing program called 3MBSIF are used to determine stress intensity factors for cracks in longitudinal and circumferential fuselage joints under internal pressure loading. Residual strength is predicted using strain energy density theory of fracture. Fatigue life is represented using the Goodman curve. The structural component is designed and analyzed in CREO and ANSYS to calculate stresses and determine fatigue life for different loading conditions.
A Study on Damage Tolerance Evaluation of the Vertical Tail with the Z stiffe...IRJET Journal
This document discusses damage tolerance evaluation of the vertical tail with a stiffened panel on a transport aircraft. It begins with an introduction to aircraft structures and importance of vertical tails. Then it describes the stiffened panel that will be analyzed which makes up part of the vertical tail. Finite element analysis is performed to identify stress concentrations on the panel. A crack is initiated at the location of maximum stress and crack growth analysis is performed to evaluate the panel's damage tolerance capabilities. Stress intensity factors at the crack tip are calculated using the modified virtual crack closure integral method and compared to fracture toughness to assess crack growth.
Structural Analysis and Optimization for Spar Beam of an AircraftIRJET Journal
This document summarizes a study analyzing and optimizing the structural design of a tapered spar beam for an aircraft wing. The study involved creating a geometric model of the spar beam, applying loads and boundary conditions representative of flight loading, conducting a finite element analysis to determine stresses and displacements, and performing topological optimization to reduce weight. Key results were stresses of up to 38 MPa at the fixed end of the beam, displacements of up to 3.1 mm at the free end, and a 40% reduction in web weight achieved through topological optimization while maintaining structural integrity. The optimized design demonstrated potential to strengthen the spar beam structure while reducing material usage and weight.
Structural Weight Optimization of Aircraft Wing Component Using FEM Approach.IJERA Editor
One of the main challenges for the civil aviation industry is the reduction of its environmental impact by better fuel efficiency by virtue of Structural optimization. Over the past years, improvements in performance and fuel efficiency have been achieved by simplifying the design of the structural components and usage of composite materials to reduce the overall weight of the structure. This paper deals with the weight optimization of transport aircraft with low wing configuration. The Linear static and Normal Mode analysis were carried out using MSc Nastran & Msc Patran under different pressure conditions and the results were verified with the help of classical approach. The Stress and displacement results were found and verified and hence arrived to the conclusion about the optimization of the wing structure.
Optimizationof fuselage shape for better pressurization and drag reductioneSAT Journals
Abstract
The fuselage of any aircraft is essentially to accommodate the payload. It is normally not as streamlined as the wing. Cabin pressurization has been a major concern in the manufacturing of aircrafts. Generally, a cylindrical shape is preferred from a pressurization point of view as it has a higher strength and weighs less too. On the other hand, a sphere is considered as the best pressure vessel among all the shapes, but, sphere being a bluff body is not suitable for carrying payloads. On this note, a cylinder is considered to be better than a sphere to carry the payload and mainly to achieve a streamlined flow. In this paper, the shape chosen is a combination of the sphere and the cylinder to achieve optimum results for pressurization as well as a better streamlined flow. Our prime aim is to convert this bluff body into something more efficient and useful, rather than only for carrying the payload. We have focused basically on two details viz. 1) Better Pressurization and 2) to assist in minimizing the drag, thereby increasing the overall lift of the aircraft and hence increasing the fuel efficiency. The proposed fuselage structure was designed in CATIA V5 software and structural analyses were done in Auto-Desk Multi-Physics software. As a result, a better structural load capacity was found. A load of 10 N/mm2 was applied on both the bodies under consideration (cylinder and ellipse) having the same material, surface area, volume and weight. For the proposed elliptical design, 78% reduction in the minimum stress value and 10% reduction in the maximum stress value were noticed.
Keywords: Fuselage, Lifting Fuselage, Drag Reduction, Pressurization, Hoop Stress, Multi body design, Toroidal Shells, Multi-cylinder, Channel Propeller Configuration, Carbon Fiber, Graphite Fiber, Stabilization and Carbonization.
The document discusses the major components of aircraft, including the fuselage, wings, empennage, landing gear, and power plant. It describes the construction and design of aircraft fuselages, including open truss, monocoque, and semi-monocoque structures. It also briefly discusses wings, the empennage, landing gear, and factors considered in aircraft component design like fatigue life and material selection.
This document discusses the structural idealization of aircraft wings for stress analysis purposes. It begins by providing an overview of aircraft wing structure components like spars, ribs, skins and stringers. It then discusses simplifying the complex wing structure into an idealized beam model by concentrating the stress carrying portions into "booms". This idealization assumes booms carry direct stresses and skins carry only shear stresses. The document provides an example of calculating boom areas based on equilibrium of bending stresses. It also discusses calculating the second moment of area of the idealized section. The next lecture will cover impacts of this idealization on bending, shear and torsion analysis of the wing.
IRJET- Static and Fracture Analysis for Aircraft Fuselage and Wing Joint with...IRJET Journal
This document discusses static and fracture analysis of aircraft fuselage and wing joints using composite materials. Finite element analysis software ANSYS and a post-processing program called 3MBSIF are used to determine stress intensity factors for cracks in longitudinal and circumferential fuselage joints under internal pressure loading. Residual strength is predicted using strain energy density theory of fracture. Fatigue life is represented using the Goodman curve. The structural component is designed and analyzed in CREO and ANSYS to calculate stresses and determine fatigue life for different loading conditions.
A Study on Damage Tolerance Evaluation of the Vertical Tail with the Z stiffe...IRJET Journal
This document discusses damage tolerance evaluation of the vertical tail with a stiffened panel on a transport aircraft. It begins with an introduction to aircraft structures and importance of vertical tails. Then it describes the stiffened panel that will be analyzed which makes up part of the vertical tail. Finite element analysis is performed to identify stress concentrations on the panel. A crack is initiated at the location of maximum stress and crack growth analysis is performed to evaluate the panel's damage tolerance capabilities. Stress intensity factors at the crack tip are calculated using the modified virtual crack closure integral method and compared to fracture toughness to assess crack growth.
Structural Analysis and Optimization for Spar Beam of an AircraftIRJET Journal
This document summarizes a study analyzing and optimizing the structural design of a tapered spar beam for an aircraft wing. The study involved creating a geometric model of the spar beam, applying loads and boundary conditions representative of flight loading, conducting a finite element analysis to determine stresses and displacements, and performing topological optimization to reduce weight. Key results were stresses of up to 38 MPa at the fixed end of the beam, displacements of up to 3.1 mm at the free end, and a 40% reduction in web weight achieved through topological optimization while maintaining structural integrity. The optimized design demonstrated potential to strengthen the spar beam structure while reducing material usage and weight.
Structural Weight Optimization of Aircraft Wing Component Using FEM Approach.IJERA Editor
One of the main challenges for the civil aviation industry is the reduction of its environmental impact by better fuel efficiency by virtue of Structural optimization. Over the past years, improvements in performance and fuel efficiency have been achieved by simplifying the design of the structural components and usage of composite materials to reduce the overall weight of the structure. This paper deals with the weight optimization of transport aircraft with low wing configuration. The Linear static and Normal Mode analysis were carried out using MSc Nastran & Msc Patran under different pressure conditions and the results were verified with the help of classical approach. The Stress and displacement results were found and verified and hence arrived to the conclusion about the optimization of the wing structure.
Optimizationof fuselage shape for better pressurization and drag reductioneSAT Journals
Abstract
The fuselage of any aircraft is essentially to accommodate the payload. It is normally not as streamlined as the wing. Cabin pressurization has been a major concern in the manufacturing of aircrafts. Generally, a cylindrical shape is preferred from a pressurization point of view as it has a higher strength and weighs less too. On the other hand, a sphere is considered as the best pressure vessel among all the shapes, but, sphere being a bluff body is not suitable for carrying payloads. On this note, a cylinder is considered to be better than a sphere to carry the payload and mainly to achieve a streamlined flow. In this paper, the shape chosen is a combination of the sphere and the cylinder to achieve optimum results for pressurization as well as a better streamlined flow. Our prime aim is to convert this bluff body into something more efficient and useful, rather than only for carrying the payload. We have focused basically on two details viz. 1) Better Pressurization and 2) to assist in minimizing the drag, thereby increasing the overall lift of the aircraft and hence increasing the fuel efficiency. The proposed fuselage structure was designed in CATIA V5 software and structural analyses were done in Auto-Desk Multi-Physics software. As a result, a better structural load capacity was found. A load of 10 N/mm2 was applied on both the bodies under consideration (cylinder and ellipse) having the same material, surface area, volume and weight. For the proposed elliptical design, 78% reduction in the minimum stress value and 10% reduction in the maximum stress value were noticed.
Keywords: Fuselage, Lifting Fuselage, Drag Reduction, Pressurization, Hoop Stress, Multi body design, Toroidal Shells, Multi-cylinder, Channel Propeller Configuration, Carbon Fiber, Graphite Fiber, Stabilization and Carbonization.
The document discusses the major components of aircraft, including the fuselage, wings, empennage, landing gear, and power plant. It describes the construction and design of aircraft fuselages, including open truss, monocoque, and semi-monocoque structures. It also briefly discusses wings, the empennage, landing gear, and factors considered in aircraft component design like fatigue life and material selection.
The document provides an overview of aircraft structures and their key components. It discusses the fuselage, wings, empennage, landing gear, and powerplants. For each component, it describes the basic design and functions. It also covers important aircraft structural concepts like stressed skin construction, monocoque vs semi-monocoque design, and choices of lightweight metal materials. Overall the document serves as a high-level introduction to aircraft structures and the major structural components of airplanes.
Bend twist coupling effect on the Performance of the Wing of an Unmanned Aeri...IRJET Journal
This document discusses the design and analysis of a composite wing for an unmanned aerial vehicle (UAV) to minimize weight while maintaining stiffness and strength. Two wing models are created - one with all isotropic materials and one with composite materials. The composite wing is designed with glass-epoxy ribs and carbon-epoxy spars to take advantage of intrinsic bend-twist coupling effects. The wing models are analyzed in ANSYS to compare the performance of composite and isotropic materials. The results show that a composite wing can achieve lower weight without compromising structural performance.
This document summarizes a seminar presentation on landing gear arrangement analysis. It discusses different landing gear configurations, including tricycle and taildragger arrangements. It also examines factors like landing gear height, steering systems, shock absorbers, and case studies of the Cessna 172, Boeing 757, and F-14 Tomcat. The conclusion compares the shock absorber stroke lengths between these aircraft, finding that the Cessna 172 has the shortest at 0.21 meters while the F-14 Tomcat has the longest at 0.55 meters due to its higher design landing speeds.
This document presents a methodology for performing static structural analysis of fighter aircraft wing spars to identify critical stresses. It involves calculating bending, shear and von mises stresses analytically and numerically under different loading conditions. CAD models of the wing and spars are imported into ANSYS for finite element analysis. Von Mises yield theory is used to identify stresses exceeding the yield limit, which indicate critical stresses and locations. Results from analytical calculations and ANSYS simulations are analyzed to mark stresses exceeding the safety factor of 1.5 as critical. Locations with critical stresses are identified as the attachment points of wing spars.
This is Part 4 (in work) of work for my Advanced Technology Demonstration Aircraft project, to inspire interest in aerospace engineering for the RAeS and AIAA.
Boeing 777X Wingtip Analysis - FEM Final ProjectMatt Hawkins
This document summarizes a mechanical investigation of the folding wingtip mechanism on the Boeing 777X aircraft. The author models a simplified section of the 777X wingtip to calculate the strain energy and rotational stiffness of the hinge mechanism during steady, level flight. Using beam theory and finite element analysis software, the author determines that the hinge latching mechanism must produce an equivalent rotational stiffness of over 10 million newton-meters per radian to prevent failure under flight loads. The analysis presents simplifications and assumptions due to the proprietary nature and complexity of the actual 777X wingtip design.
Blended Wing Body (BWB) - Future Of AviationAsim Ghatak
What is Blended Wing Body, History, Advantages And Disadvantages, Design and Structure, How airplanes Fly, Conventional airplanes vs. BWB, Future Scope And Challenges.
Blended Wing Body (BWB) - Future Of AviationAsim Ghatak
What Is Blended Wing Body, History of BWB, How Airplanes Fly, Aircraft Control Surfaces, Design and Structure of BWB, Advantages and Disadvantages, Conventional aircraft vs. BWB, Future Scope and Challenges
It is a major project report on DIFFERENT TYPES OF WINGLETS AND THEIR CORRESPONDING VORTICES, and it can be helpful for a person looking for specifically about winglet and vortex formation and relation among them. It is a very good source for aerospace engineering student as well coz they will get to knew about vortex and winglet.
The document summarizes five common wing planforms - rectangular, elliptical, tapered, swept, and delta wings. It provides examples of aircraft that use each type of wing and notes their aerodynamic efficiencies and manufacturing complexities. Additional wing variations discussed include trapezoidal, ogive, swept back, swept forward, and variable sweep wings.
IRJET- Analysing the Performance of Solar Powered Wing (UAV)IRJET Journal
This document analyzes the performance of a solar-powered wing for an unmanned aerial vehicle (UAV) consisting of two different airfoil sections. Computational fluid dynamics (CFD) software is used to model and analyze wings with the Eppler 421 and Selig 1223 airfoils individually and as a combined wing. Results show that the combined wing profile has lift and drag characteristics between the individual airfoils. Specifically, the Selig 1223 airfoil produces higher lift but also higher drag. The combined wing design and CFD analysis indicate that a solar-powered wing could provide long endurance flights for UAVs.
This document discusses weight optimization of the vertical tail in-board box structure of an aircraft through stress analysis. The vertical tail structure is modeled in CATIA and imported into MSC Patran for finite element analysis. The structure is meshed and material properties are applied. Boundary conditions representing the fixed root and free top surface are applied. Stress analysis is performed and high stress regions are identified. An iterative approach is used to introduce lightening cutouts in the spar and rib webs to reduce weight. Two iterations are performed, reducing the total weight by 1.66kg while maintaining similar deformation levels and stresses below material yield strength, demonstrating an effective weight optimization approach.
Aerodynamics design of formula sae race car 41372EditorIJAERD
This document describes the aerodynamic design of a Formula SAE race car. It discusses the design of the front and rear wings using computational fluid dynamics to maximize downward force and minimize drag. A three-element wing design is used for the front, and a four-element design for the rear. The nose, diffuser, and underside of the car are also designed to guide airflow and utilize the venturi effect to further increase downward force. Computational analysis and optimization were performed to evaluate different designs. The final aerodynamic package is within Formula SAE rules and aims to improve the car's performance.
Design, Fabrication and Aerodynamic Analysis of RC Powered Aircraft WingIRJET Journal
This document describes the design, fabrication, and aerodynamic analysis of a radio-controlled aircraft wing. The researchers designed a rectangular wing with a Gottingen 526 airfoil profile using computational fluid dynamics software to analyze lift and drag coefficients. The wing structure and control surfaces were fabricated based on the optimal design parameters. Wind tunnel testing was then used to validate the aerodynamic performance and characteristics of the wing.
The document outlines a research project to design and test advanced wing structures for unmanned aerial vehicles that are lighter yet able to withstand greater loads. Various wing design options and materials will be considered and prototypes will be manufactured and tested to evaluate their strength, weight, production cost, and feasibility. The goals are to develop a wing design that meets criteria for the annual AIAA Student Design Build Fly competition and can be modified for future competitive aircraft designs.
Modal, Fatigue and Fracture Analysis of Wing Fuselage Lug Joint Bracket for a...IRJET Journal
This document summarizes a study on the modal, fatigue, and fracture analysis of a wing fuselage lug joint bracket for a transport aircraft. Finite element analysis was conducted in ANSYS to determine the modal frequencies and stress distributions. The first six natural frequencies were identified. Fatigue analysis using the Goodman diagram estimated the fatigue life to be 1 million cycles, qualifying it as a high cycle fatigue case. Fracture mechanics analysis identified maximum stresses near rivet holes and predicted crack initiation. The finite element analysis results for stresses, frequencies, and fatigue life were validated using analytical methods. The study aimed to understand the dynamic behavior and improve the structural integrity of the wing attachment point.
This document discusses various concepts related to aircraft structural design and airworthiness requirements. It describes how aircraft structure is divided into primary, secondary, and tertiary categories based on their importance. Primary structure, if failed, could cause loss of control or structural collapse. Examples provided stress the importance of withstanding forces like tension, compression, shear, bending, and torsion to ensure structural integrity and safety. Station identification systems are also covered to precisely locate structural components through methods like station numbering and zoning.
Static and Dynamic Analysis of Floor Beam (Cross beam) of AircraftIRJET Journal
This document summarizes a study analyzing the static and dynamic behavior of floor beams used in aircraft. Floor beams experience bending stresses and support the weight of the aircraft. The researchers modeled a floor beam in CATIA and analyzed it in ANSYS to study stresses under different loads. They also analyzed a carbon fiber reinforced plastic floor beam. Modal analysis determined the beam's natural frequencies under vibration to ensure it can withstand operating conditions. The study aims to optimize floor beam design and materials to reduce weight while maintaining strength.
1) The document describes the design of a dragonfly-inspired aircraft with two different wing configurations: an elliptical wing and a forward-swept wing.
2) The design process involved taking measurements from existing aircraft like the Sukhoi-47, X-29, and Supermarine Spitfire to inform the conceptual and detailed design of the dragonfly aircraft.
3) CFD analysis of the 2D aircraft model showed that the unique dual-wing configuration is capable of producing lift, indicating that the design could potentially fly. The analysis paves the way for future dual-wing aircraft designs.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.
The document provides an overview of aircraft structures and their key components. It discusses the fuselage, wings, empennage, landing gear, and powerplants. For each component, it describes the basic design and functions. It also covers important aircraft structural concepts like stressed skin construction, monocoque vs semi-monocoque design, and choices of lightweight metal materials. Overall the document serves as a high-level introduction to aircraft structures and the major structural components of airplanes.
Bend twist coupling effect on the Performance of the Wing of an Unmanned Aeri...IRJET Journal
This document discusses the design and analysis of a composite wing for an unmanned aerial vehicle (UAV) to minimize weight while maintaining stiffness and strength. Two wing models are created - one with all isotropic materials and one with composite materials. The composite wing is designed with glass-epoxy ribs and carbon-epoxy spars to take advantage of intrinsic bend-twist coupling effects. The wing models are analyzed in ANSYS to compare the performance of composite and isotropic materials. The results show that a composite wing can achieve lower weight without compromising structural performance.
This document summarizes a seminar presentation on landing gear arrangement analysis. It discusses different landing gear configurations, including tricycle and taildragger arrangements. It also examines factors like landing gear height, steering systems, shock absorbers, and case studies of the Cessna 172, Boeing 757, and F-14 Tomcat. The conclusion compares the shock absorber stroke lengths between these aircraft, finding that the Cessna 172 has the shortest at 0.21 meters while the F-14 Tomcat has the longest at 0.55 meters due to its higher design landing speeds.
This document presents a methodology for performing static structural analysis of fighter aircraft wing spars to identify critical stresses. It involves calculating bending, shear and von mises stresses analytically and numerically under different loading conditions. CAD models of the wing and spars are imported into ANSYS for finite element analysis. Von Mises yield theory is used to identify stresses exceeding the yield limit, which indicate critical stresses and locations. Results from analytical calculations and ANSYS simulations are analyzed to mark stresses exceeding the safety factor of 1.5 as critical. Locations with critical stresses are identified as the attachment points of wing spars.
This is Part 4 (in work) of work for my Advanced Technology Demonstration Aircraft project, to inspire interest in aerospace engineering for the RAeS and AIAA.
Boeing 777X Wingtip Analysis - FEM Final ProjectMatt Hawkins
This document summarizes a mechanical investigation of the folding wingtip mechanism on the Boeing 777X aircraft. The author models a simplified section of the 777X wingtip to calculate the strain energy and rotational stiffness of the hinge mechanism during steady, level flight. Using beam theory and finite element analysis software, the author determines that the hinge latching mechanism must produce an equivalent rotational stiffness of over 10 million newton-meters per radian to prevent failure under flight loads. The analysis presents simplifications and assumptions due to the proprietary nature and complexity of the actual 777X wingtip design.
Blended Wing Body (BWB) - Future Of AviationAsim Ghatak
What is Blended Wing Body, History, Advantages And Disadvantages, Design and Structure, How airplanes Fly, Conventional airplanes vs. BWB, Future Scope And Challenges.
Blended Wing Body (BWB) - Future Of AviationAsim Ghatak
What Is Blended Wing Body, History of BWB, How Airplanes Fly, Aircraft Control Surfaces, Design and Structure of BWB, Advantages and Disadvantages, Conventional aircraft vs. BWB, Future Scope and Challenges
It is a major project report on DIFFERENT TYPES OF WINGLETS AND THEIR CORRESPONDING VORTICES, and it can be helpful for a person looking for specifically about winglet and vortex formation and relation among them. It is a very good source for aerospace engineering student as well coz they will get to knew about vortex and winglet.
The document summarizes five common wing planforms - rectangular, elliptical, tapered, swept, and delta wings. It provides examples of aircraft that use each type of wing and notes their aerodynamic efficiencies and manufacturing complexities. Additional wing variations discussed include trapezoidal, ogive, swept back, swept forward, and variable sweep wings.
IRJET- Analysing the Performance of Solar Powered Wing (UAV)IRJET Journal
This document analyzes the performance of a solar-powered wing for an unmanned aerial vehicle (UAV) consisting of two different airfoil sections. Computational fluid dynamics (CFD) software is used to model and analyze wings with the Eppler 421 and Selig 1223 airfoils individually and as a combined wing. Results show that the combined wing profile has lift and drag characteristics between the individual airfoils. Specifically, the Selig 1223 airfoil produces higher lift but also higher drag. The combined wing design and CFD analysis indicate that a solar-powered wing could provide long endurance flights for UAVs.
This document discusses weight optimization of the vertical tail in-board box structure of an aircraft through stress analysis. The vertical tail structure is modeled in CATIA and imported into MSC Patran for finite element analysis. The structure is meshed and material properties are applied. Boundary conditions representing the fixed root and free top surface are applied. Stress analysis is performed and high stress regions are identified. An iterative approach is used to introduce lightening cutouts in the spar and rib webs to reduce weight. Two iterations are performed, reducing the total weight by 1.66kg while maintaining similar deformation levels and stresses below material yield strength, demonstrating an effective weight optimization approach.
Aerodynamics design of formula sae race car 41372EditorIJAERD
This document describes the aerodynamic design of a Formula SAE race car. It discusses the design of the front and rear wings using computational fluid dynamics to maximize downward force and minimize drag. A three-element wing design is used for the front, and a four-element design for the rear. The nose, diffuser, and underside of the car are also designed to guide airflow and utilize the venturi effect to further increase downward force. Computational analysis and optimization were performed to evaluate different designs. The final aerodynamic package is within Formula SAE rules and aims to improve the car's performance.
Design, Fabrication and Aerodynamic Analysis of RC Powered Aircraft WingIRJET Journal
This document describes the design, fabrication, and aerodynamic analysis of a radio-controlled aircraft wing. The researchers designed a rectangular wing with a Gottingen 526 airfoil profile using computational fluid dynamics software to analyze lift and drag coefficients. The wing structure and control surfaces were fabricated based on the optimal design parameters. Wind tunnel testing was then used to validate the aerodynamic performance and characteristics of the wing.
The document outlines a research project to design and test advanced wing structures for unmanned aerial vehicles that are lighter yet able to withstand greater loads. Various wing design options and materials will be considered and prototypes will be manufactured and tested to evaluate their strength, weight, production cost, and feasibility. The goals are to develop a wing design that meets criteria for the annual AIAA Student Design Build Fly competition and can be modified for future competitive aircraft designs.
Modal, Fatigue and Fracture Analysis of Wing Fuselage Lug Joint Bracket for a...IRJET Journal
This document summarizes a study on the modal, fatigue, and fracture analysis of a wing fuselage lug joint bracket for a transport aircraft. Finite element analysis was conducted in ANSYS to determine the modal frequencies and stress distributions. The first six natural frequencies were identified. Fatigue analysis using the Goodman diagram estimated the fatigue life to be 1 million cycles, qualifying it as a high cycle fatigue case. Fracture mechanics analysis identified maximum stresses near rivet holes and predicted crack initiation. The finite element analysis results for stresses, frequencies, and fatigue life were validated using analytical methods. The study aimed to understand the dynamic behavior and improve the structural integrity of the wing attachment point.
This document discusses various concepts related to aircraft structural design and airworthiness requirements. It describes how aircraft structure is divided into primary, secondary, and tertiary categories based on their importance. Primary structure, if failed, could cause loss of control or structural collapse. Examples provided stress the importance of withstanding forces like tension, compression, shear, bending, and torsion to ensure structural integrity and safety. Station identification systems are also covered to precisely locate structural components through methods like station numbering and zoning.
Static and Dynamic Analysis of Floor Beam (Cross beam) of AircraftIRJET Journal
This document summarizes a study analyzing the static and dynamic behavior of floor beams used in aircraft. Floor beams experience bending stresses and support the weight of the aircraft. The researchers modeled a floor beam in CATIA and analyzed it in ANSYS to study stresses under different loads. They also analyzed a carbon fiber reinforced plastic floor beam. Modal analysis determined the beam's natural frequencies under vibration to ensure it can withstand operating conditions. The study aims to optimize floor beam design and materials to reduce weight while maintaining strength.
1) The document describes the design of a dragonfly-inspired aircraft with two different wing configurations: an elliptical wing and a forward-swept wing.
2) The design process involved taking measurements from existing aircraft like the Sukhoi-47, X-29, and Supermarine Spitfire to inform the conceptual and detailed design of the dragonfly aircraft.
3) CFD analysis of the 2D aircraft model showed that the unique dual-wing configuration is capable of producing lift, indicating that the design could potentially fly. The analysis paves the way for future dual-wing aircraft designs.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
3. LEARNING OBJECTIVES
This Lecture (Lecture 6):
◾ Familiarisation with the functions of various structural components in an aircraft;
◾ Familiarisation with simplifying complex wing structure into an idealised structure for stress
analysis purposes;
Next lecture (Lecture 7):
◾ Impact of idealisation on bending of beam cross section;
◾ Impact of idealisation on shear flow and its distribution within the beam cross section;
◾ Impact of idealisation on torsion of beam cross section;
3
4. NOTE TO THE STUDENTS
◾ You are required to read the following paper before attending this lecture;
◾ Note that this document is uploaded on blackboard;
Odeh Dababneh, Altan Kayran, (2014) "Design, analysis and optimization of thin walled semi-
monocoque wing structures using different structural idealization in the preliminary design
phase", International Journal of Structural Integrity, Vol. 5 Issue: 3, pp.214-226,
https://doi.org/10.1108/IJSI-12-2013-0050
4
6. LIFT LOADS
◾ Lift is generated by producing a higher pressure below the wing than above it.
◾ Higher speed airflow above wing than below (streamlines closer together).
Lift
6
• Streamlines around an aerofoil.
(Above)
• Pressure Distribution around an
aerofoil. (Below)
• Resultant lift force (red arrow) acts through
centre of pressure (cop), normal to stream
• cop varies with α(angle of attack)
• Pitching Moment caused by unequal pressure
distribution around aerofoil.
7. WING STRUCTURE
◾ The Wing
◾ Wingbox
◾ Primary wing structure
◾ Leading edge
◾ Fixed Leading Edge
◾ Slats
◾ Droop Nose
◾ Pylon (Engine) Attachments
◾ Trailing Edge
◾ Fixed Trailing Edge
◾ Spoilers
◾ Ailerons
◾ Flaps
◾ Wing Landing Gear Attachments
◾ Wingtip and Fairings
7
Digital Mock-Up of the A350
Wing
Digital Mock-Up of a Wing-Box
(Upper Cover removed)
9. WING-BOX
◾ Carries the main
structural loads from
the wing;
◾ Aerodynamic, inertial,
movables, fuel;
◾ Closed-cell structure
allowing resistance to
shear, torsion and
tension loads;
◾ Location of fuel tanks;
◾ Supports the landing
gear and engines, if
they are wing mounted.
9
Wing in
Plan View
A380 Wingbox
in Production
A380 Wingbox in
Production
10. WING LOADS
◾ Wing Finite Element Model provides
Shear , Moment and Torsion
10
11. WING COMPLEXITY (SPARS)
◾ Provide mounting for
WLG Fittings and Leading
and Trailing edge fittings.
11
Track Can
Cut-Outs
Rib Post
Spars
Exploded View of a generic Wing
Digital Mock-Up of Wingbox
(Upper Cover removed)
◾ Span-wise members that
carry shear loads;
◾ Fuel Tank Boundary;
12. WING COMPLEXITY (SPARS)
◾ For larger aircraft, the spars are usually made
up from multiple sections;
◾ Sections are normally joined together with joint
plates and straps.
12
Web Joint
Plate
Boom
Straps
Spar
Spar
Digital Mock-Up of Wingbox (Upper Cover removed)
14. WING COMPLEXITY (RIBS)
◾ Castellated edge allows the stringers to pass through rib feet to attached to the skin.
◾ Manholes allow access within the wingbox and movement of fuel.
◾ Stiffeners and crack stoppers are machined or bolted on to increase the strength of the overall
structure.
14
Castellation
Stringer
Manhole
Stiffener
Crack stop
/
per
View inside the Wing Box onto Rib looking
outboard
Computer Rendering of Typical Large Rib
16. WING COMPLEXITY (SKINS AND STRINGERS)
◾ The skin may be
assembled from multiple
panels. Joints between
skin panels are made at
with
stringer locations and
Butt
reinforced
Straps.
◾ Stringers prevent skin
buckling in compression
16
Stringer
Butt
Strap
Digital Mock-Up of Lower Wing Skins with
Stringers
Skin
Panel
Skin
Panel
Stringer being installed on an A340 Wing
and aid with bending
strength in tension.
◾ The Tension (Lower Cover) – Fatigue
& Damage Tolerance
◾ Compression (Top Cover) - Strength
◾ Stringers are riveted onto the skin or integrally
machined/formed onto the panel.
◾ Access holes on the bottom skin allow entry into the
wing-box for inspection of the internal structure and
cleaning of the fuel tanks.
18. ROOT JOINT
◾ Where the wing attaches
to the centre wing box in
the fuselage;
◾ The cruciform and tri-form
fittings are used to attach
the upper and lower
covers respectively to the
centre wing box. Patent
application number:
20110089292;
◾ Upper and lower joint
fittings are used to attach
the spars.
18
19. WING TIP
◾ Rigid structure fixed to end of the wing-box;
◾ The structure is built in a similar way to the wing-box, with spars, ribs, stringers and skin
forming the structure;
◾ Contains the navigation and strobe lights.
19
A320 Wing tip installed on end of Wing
at Broughton
Illustration of Wing Tip Structure
Navigation
Lights
Wing Tip
Fence
Wing
Tip
20. WINGTIP (WINGLET & WING FENCE)
◾ A winglet or wing fence can be added
to the end of the wingtip to reduce the
induced drag effect of the wing;
◾ A winglet generates more load than a
wing fence but design of the wing and
wingtip considers these extra forces;
◾ “Sharklet” is Airbus’s trade name for
the winglets being added to the A320
family.
20
Wing Tip with blended Winglet installed
Illustration of vortices
created at the Wing Tip
Blended
Winglet
21. SLATS
◾ Extend out from the leading edge to increase lift and
allow the wing to be flown at a higher angle of attack
(i.e. slower speeds);
◾ Extended by a rack and pinion arrangement.
Protection exists to avoid inadvertent asymmetric
deployment of slats;
◾ Supported by slat tracks which run along a set of
rollers carrying the vertical and side loads;
◾ Slat Cans house the slat tracks when retracted and
act as a fuel boundary;
21
Cross-Sectional diagram of Slat arrangement
Aircraft Wing with Slats deployed
Slats
22. FLAPS
◾ Extend to increase the
effective wing area and
camber;
◾ This increases wing lift
and also increases drag to
enable a steeper descent
when landing without the
increase in airspeed.
22
Diagram of Flap in un-deployed and deployed states
Flaps
View of wing with flaps and spoilers fully deployed
23. AILERONS
◾ Controls the roll rate of
the aircraft, but may
also be used for Load
Alleviation Function in
conjunction with the
spoilers;
◾ Larger aircraft may have
more than one aileron
on each wing;
◾ Attached onto trailing
edge ribs aft of the rear
spar;
◾ Mass weights are
usually added forward of
the hinge line to reduce
flutter.
23
Aileron
Static discharger
View on underside of wing, looking up
Exploded view of Aileron composite structure
24. WING STRUCTURE CATEGORISATION
◾ Category A;
Structure identified as Principal Structural Elements (PSE).
These are the elements that contribute significantly to carrying
flight, ground or pressurisation loads and whose failure could
result in catastrophic failure of the aircraft.(Ref. ACJ 25.571(a) 2.2;
AC 25.571-1C 6d.)
These structures must be replaced or repaired on the discovery of
any damage unless specific rational is provided.
24
◾ Category B;
Structures whose failure or detachment could indirectly
compromise continued safe flight or landing by an adverse effect
on a CategoryA structure.
These structures must be replaced or repaired on the discovery of
any damage unless specific rational is provided.
◾ Category C;
Structures whose failure or detachment will not compromise
continued safe flight or landing but where the potentially large size
of released elements needs to be considered.
As these structures are not identified as either category A or B,
any failure or departure from the aircraft must be demonstrated as
not preventing continued safe flight and landing and the probability
of occurrence is acceptably low (Ref. ACJ 25C- 571 (a)2.1.1e.).
No detachment of structure is allowed (Ref. NPA25C-290).
These structures must be replaced or repaired on discovery of
element failure at an appropriate time.
◾ Category D;
Structures whose failure or detachment has no airworthiness
consequence but only has an economic impact.
These structures may have to be replaced or repaired on
discovery of failure if they form part of the aircraft external envelop.
26. WHAT IS THE POINT?
◾ So far, we have been dealing with simple
structural components such as plates and
beams;
◾ Real life structures are complex and in order
to analyse them simplification must be
made;
◾ The behaviour of the simplified/idealised
structure must be as close as that of the real
structure;
◾ Stresses/strains obtained from the idealised
structure are representative of the real
complex structure.
26
Actual cross-section
of a thin-walled beam
Sheet-stringer
idealisation of the
same section
27. IDEALISATION
27
Stringers and spar flanges
have small cross-sectional
dimensions compared to
the complete section
R
R
e
e
p
p
l
l
a
a
c
c
e
e
w
w
i
i
t
t
h
hb
b
o
o
o
o
m
m
s
s
(concentration of area) at
the midline of skin
Carrying direct
stresses only
Carrying direct and
shear stresses
We will further assume all
direct stresses are taken
by stringers and spar
flanges. Skin takes all the
shear
The variation of stress
(due to bending) over the
cross section is small
28. PANEL IDEALISATION
◾ We would like to idealise the
panel into the following;
◾ Direct stress carrying booms
◾ Shear stress carrying skins
◾ All direct stresses are given
to booms;
◾ Note that the distribution of
stress has disappeared in
idealised structure though;
◾ As long as we can get the
extremes of stress, it is fine;
◾ What should be the area of
booms?
28
By putting the thickness as zero, i.e.
𝐴 = 0, the direct stress carrying
ability of skin vanishes (𝜎 = 𝑃/𝐴)
29. ◾ For idealisation;
PANEL IDEALISATION
29
M1 M2
Taking moment about
the orange line
tDb
3
b
2
1
b2
M1
2tD
2
2
1
2
Taking moment about
the orange line
M2 B1
1b
Actual thickness of
skin
Direct stress carrying
thickness of skin
31. WING IDEALISATION AS DONE IN INDUSTRY (GLOBAL FEM)
31
View from the top
◾ Skin is modelled as shell elements
◾ Stringers as bar elements
◾ Spar caps as bar elements
View from the bottom
32. GFEM OF A SECTION THROUGH THE WING
32
Upper skin
Lower skin
Stringer
Spar cap
Rib
33. EXAMPLE
◾ Part of a wing section is in the form of the
two-cell box shown in figure, in which the
vertical spars are connected to the wing
skin through angle sections, all having a
cross-sectional area of 300mm2. Idealise
the section into an arrangement of direct
stress-carrying booms and shear-stress-
only-carrying panels suitable for resisting
bending moments in a vertical plane.
Position the booms at the spar/skin
junctions.
33
34. SOLUTION
34
The idealised structure with booms modelled as
concentration of area located at the mid-plane of skins
What are the cross section areas?
From symmetry we know 𝐵1 = 𝐵6, 𝐵2 = 𝐵5, 𝐵3 = 𝐵4
Note that 𝜎6/𝜎1 = −1. When 1 is in tension 6 will be in
equal compression and vice versa due to bending
35. SOLUTION
35
The idealised structure with booms modelled as
concentration of area located at the mid-plane of skins
What are the cross section areas?
From symmetry we know 𝐵1 = 𝐵6, 𝐵2 = 𝐵5, 𝐵3 = 𝐵4
𝑦1/𝑦2 𝑦3/𝑦2
𝑦5/𝑦2
36. SOLUTION
36
The idealised structure with booms modelled as
concentration of area located at the mid-plane of skins
What are the cross section areas?
From symmetry we know 𝐵1 = 𝐵6, 𝐵2 = 𝐵5, 𝐵3 = 𝐵4
37. FEA OF ORIGINAL SECTION
37
Load applied
at shear centre
7 ribs equally
spaced
Von Mises
stresses
38. SECOND MOMENT OF AREA FOR IDEALISED SECTIONS
◾ We have n booms with areas B1, B2, … Bn the second moment of areas are;
◾ The next two examples demonstrate this.
38
39. EXAMPLE
◾ Construct an idealised cross-section by evaluating the boom areas at points A, B, C, D, E and
F. Use the method based on the equilibrium of bending stresses. Moreover, calculate the
second moment of area of the idealised section.
39
42. EXAMPLE
42
◾ Construct the idealised section for the following airfoil. It can be assumed that stringers are
spaced at 50 mm interval and 45o in the straight and curved section, respectively. It can be
further assumed that the only loading is Mx. Obtain centroidal location and second moment of
areas for the idealised section. Calculate direct stress in the booms under bending moment of
500,000 N.mm.All dimensions are in millimetres.
y
x
43. SOLUTION (BOOM CROSS SECTION AREAS)
43
x
y
7
11 9 8
6
2 4 5
1
12
2
21 66.67mm
B6 B7
6 6
21
1001.6
501.6
3 4 5 8 9 10
6 6
B B B B B B
501.6
2 1
501.6
2 1 80mm2
3
10
44. SOLUTION (BOOM CROSS SECTION AREAS)
◾ The vertical distance between boom 1 and 2
(blue arrow in opposite figure) is as below;
◾ The length of chord from boom 1 to boom 2
is a quarter of circumference of the semi
circle;
b12 0.25
R 12.5
◾ Therefore, we have;
44
x
y
7
11 9 8
6
2 4 5
1
12
3
10
2
2 1
y y 50 50
2
14.65mm
B2 B11
50
50
6
6
501.6
2
2 2 75.44mm2
2 1
12.5 2
45. SOLUTION (BOOM CROSS SECTION AREAS)
◾ The length of chord from boom 1 to boom 12 is
half of the circumference of semi circle as
below;
b112 0.5
R 25
◾ Therefore, we have;
45
B1 B12
50
2
70.87mm2
50
2
6
6
25 2
2
2 1
12.5 2
x
y
7
11 9 8
6
2 4 5
1
12
3
10
46. SOLUTION (SECOND MOMENT OF AREAS)
◾ Centroidal location can be found by taking the
moment of concentrated areas about 6-7 and 11-7:
◾ Second moment of areas can be readily calculated
as below:
46
x
y
7
11 9 8
4 5 6
1
12
2 3
10
x
B6 0 B5 50 B4 100 B3 150 B2 200 B1 235.35
B6 B5 B4 B3 B2 B1
x 123.11mm
y 50mm
I 266.67502
380502
75.44502
70.8735.352
2087671mm4
xx
Iyy 266.67123.11 38073.11 75.4476.89 70.87112.24 7264173mm
2 2 2 2 4
Ixy 0
47. SOLUTION (DIRECT STRESSES)
◾ Normal stress can be calculated as;
◾ At booms 2-6, we have;
◾ At booms 7-11, we have;
◾ At booms 1, we have;
◾ At boom 12, we have;
47
yy xy z
xx
I
M 0, I 0
Mxx y
208767.1
z
500,00050
11.9MPa
500,00050 11.9MPa
208767.1
z
x
y
7
11 9 8
4 5 6
1
12
2 3
10
208767.1
z
500,00035.35
8.46MPa
500,00035.35 8.46MPa
208767.1
z
48. SOLUTION (FEA-DISPLACEMENTS)
◾ In the FEM, an upward 1,000N force is applied at the tip at
the location of the shear centre.
◾ By plotting the displacement
contours in the vertical
direction, i.e. U2, it can be
confirmed that at each section
the vertical displacements are
almost equal suggesting that
the load is applied at the
shear centre with no twist of
the section.
48
49. SOLUTION (FEA-DIRECT STRESSES)
◾ At a section 500mm from the tip, the
direct stresses are plotted in the
opposite figure.
◾ The direct stress on the upper skin is
-12.13MPa whereas for the bottom
skin it reads as +12.13MPa.
◾ This value is 1.2% more than hand
calculation for the idealised section.
49
50. SOLUTION (FEA-SHEAR FLOW)
◾ Let’s look at shear flow distribution, i.e.
SF3, in the section.
◾ The shear flow is as the result of shear
force only as the force was applied at the
shear centre meaning no twist of the
section, hence no shear stresses due to
twist.
◾ Pay attention to the location of zero shear
flow and linear distribution of shear flow
in flanges and quadratic in the webs.
50
Quadratic shear
flow distribution
Linear shear
flow distribution
Point with zero
shear flow
51. TUTORIAL 1
51
◾ Idealise the box section into an arrangement of direct stress-carrying booms positioned at the
four corners and panels which are assumed to carry only shear stresses. Find the centroid
location of the idealised section and then calculate second moment of area for the idealised
section about x and y axis.
52. SOLUTION
52
1 2
3
4
500 mm
300
mm
6 6
2
B 508 328
50010
2 1
3008
2 1 B 3556mm2
B
2 3
6 6
1
B 6010 4010
50010
21
30010
21 B 4000mm2
B
1 4
53. SOLUTION
◾ To obtain the second moment of area, it is
essential to find the neutral axis location;
◾ Taking moment about bottom skin, line 43;
4 4
yBi Bi yi
i1 i1
◾ Taking moment about spar 14;
4 4
xBi Bi xi
i1 i1
53
1 2
3
4
500 mm
300
mm
24000 3556
y
4000300 3556300
150mm
23556500
24000 3556
235.3mm
x
54. SOLUTION
54
1 2
3
4
500 mm
300
mm
x
y
234.75
150
4
2 2
xx
I 24000150 23556150 340,020,000 mm
yy
941,238,752.08 mm4
I 24000235.32
23556500 235.32
0
Ixy 235.31504000 235.31504000
500 235.31503556500 235.31503556 No need to calculate
as it is singly
symmetric